Rod Bundle Heat

Transfer Test Facility 

Test Plan and Design 

Office of Nuclear Regulatory Research 

NUREG/CR-6975
Rod Bundle Heat

Transfer Test Facility

Test Plan and Design

Manuscript Completed: October 2008 

Date Published: July 2010

Prepared by

L.E. Hochreiter, F-B Cheung, T.F. Lin, C. Frepoli, A. Sridharan,

D.R. Todd, E.R. Rosal 

The Pennsylvania State University

University Park, PA 16802

K. Tien, NRC Project Manager 

NRC Job Code W6855

Office of Nuclear Regulatory Research

NUREG/CR-6975
iii

ABSTRACT 

This report describes the program objectives of the Rod Bundle Heat Transfer (RBHT) Program 

as well as the proposed test design, scaling efforts and the integration of the program into the 

analysis efforts for improving the best-estimate thermal-hydraulic computer codes. The primary 

area of investigation is the dispersed flow film boiling processes associated with the reflood 

portion of a large-break Loss of Coolant Accident. A detailed Phenomena Identification Ranking 

Table was developed for the reflood process in which the phenomena were subdivided into the 

individual component phenomena, which a best-estimate computer code models or represents. 

The individual component models are added in the computer code to provide a prediction of the 

overall wall heat flux as a function of time during the transient. Since the best-estimate 

computer codes are modeling individual phenomena on a component level, the experiments 

and the test instrumentation were developed to provide the detailed information such that the 

modeling could be confirmed. In this manner, the effects of compensating errors in the 

modeling will be minimized. 

A comprehensive review of other experimental programs has been performed as well as the 

open literature such that the facility design benefits from the previous experimental work. In 

addition, a detailed scaling analysis was performed of the facility to determine what, if any, 

distortion effects could be present which could influence the quality of the experimental data. 

Both a top down and bottom up scaling analysis was performed using the Zuber-Wulff scaling 

approach which is state-of-the-art for thermal-hydraulic scaling. The Pi groups were calculated 

for the facility and for a pressurized water reactor (PWR) and a boiling water reactor (BWR) 

plant reflood transient and compared. It was found that there is some distortion in the test 

facility due to material differences of the heater rods relative to nuclear fuel rods, and the 

radiation heat sink effects of the housing which surround the heater rod bundle. The result was 

to increase the bundle size, and to investigate the different material types in a separate effects 

test. 

The instrumentation requirements for the facility were driven by the phenomena modeling needs 

identified in the PIRT. There will be ample instrumentation, as compared to previous tests, to 

obtain data on void fraction, vapor superheat temperatures in addition to heater rod wall 

temperatures. In addition, a laser illuminated digital system will be used to measure the 

entrained droplet size and velocity distributions within the rod bundle. Also, a gamma 

densitometer may be used to measure the void fraction at fixed locations to compare with the 

void fraction data from the differential pressure cells. A conceptual design for the test facility has 

been developed along with a detailed instrumentation plan which addresses the phenomena 

which was identified in the PIRT. There are over 400 channels of instrumentation for the facility. 

The RBHT facility is a unique facility which will provide new data for the fundamental 

development of best-estimate computer code models. This effort will reduce the uncertainty in 

the NRC’s thermal-hydraulic computer codes which will enhance the understanding of the 

complex two-phase phenomena which is modeled for the reflood transient. 
iv
 v

FOREWORD 

Reflood thermal-hydraulics represents an important set of phenomena during a hypothetical 

loss-of-coolant-accident (LOCA) that results in core uncovery. These phenomena must be 

accurately simulated by systems codes in determining plant response to a LOCA. In spite of 

significant research into reflood thermal-hydraulics, there still exists a large uncertainty in these 

calculations. As a result, the Nuclear Regulatory Commission (NRC) conducts experimental 

investigations of reflood thermal-hydraulics in order to provide data for model development and 

to more thoroughly assess its systems codes. 

The NRC is currently assessing and improving the TRAC/RELAP Computational Engine 

(TRACE) code for best estimate analysis of light water reactors. While calculation of reflood by 

TRACE appears to be reasonable, higher accuracy is beneficial as the code is applied to power 

uprates and new plant designs to ensure acceptable margin between expected plant 

performance and the regulatory limits. Accurate prediction of the consequences of a LOCA is 

important because it is one of the postulated accident scenarios that determine the licensed 

core power and several other operational parameters. As the NRC places greater emphasis on 

risk-informed regulation, a more accurate and reliable systems code will be useful to obtain 

realistic rather than conservative predictions. 

To acquire detailed, fundamental data for use in developing models for a LOCA, the NRC 

sponsored the design and construction of a Rod Bundle Heat Transfer (RBHT) Test Facility. 

Some of these detailed data have only recently become possible because of recent advances in 

instrumentation technology for two-phase flow measurements. 

This report describes the program objectives of the RBHT Program as well as the proposed test 

design, scaling efforts and the integration of the program into the analysis efforts for improving 

the best-estimate thermal-hydraulic computer codes. A detailed Phenomena Identification 

Ranking Table was developed for the reflood process in which the phenomena were subdivided 

into the individual component phenomena, which a best-estimate computer code models or 

represents. As such, this report will prove useful in understanding the detailed scaling analysis 

which was performed for the RBHT Test Facility to determine what, if any, distortion effects 

could be present which could influence the quality of the experimental data. 

With improved data and code models for simulating LOCAs, we can more accurately predict 

the consequences of these scenarios and provide better technical bases for regulations 

associated with such accidents. As a result, this study will help to ensure the agency’s 

regulations are effective and efficient. 

 

 

 
 vi
 vii

CONTENTS 

Page

ABSTRACT ................................................................................................................................. iii 

FOREWORD ............................................................................................................................... v 

 

EXECUTIVE SUMMARY .......................................................................................................... xxi 

 

NOMENCLATURE .................................................................................................................. xliii 

 

ACKNOWLEDGEMENTS ........................................................................................................ xlvii

1. INTRODUCTION .................................................................................................................... 1

 1.1 Background ................................................................................................................ 1

 1.2 Program Objectives ................................................................................................... 6

 1.3 Products from the Rod Bundle Heat Transfer Program ........................................... 10

 1.4 Technical Approach ................................................................................................. 10

 1.5 References ............................................................................................................... 11 

2. ROD BUNDLE HEAT TRANSFER PROGRAM PHENOMENA IDENTIFICATION 

 AND RANKING TABLE (PIRT) ............................................................................................ 13 

 2.1 Introduction/Background .......................................................................................... 13

 2.2 Preliminary PIRT for the Rod Bundle Heat Transfer Tests - PWR Phenomena ...... 15 

 2.2.1 Introduction ............................................................................................ 15 

 2.2.2 Development of the Classifications for the Different Regions for the 

 Rod Bundle Heat Transfer Program Preliminary PIRT........................... 16

 2.3 PIRT for Rod Bundle Heat Transfer Tests - BWR Phenomena ............................... 34 

 2.3.1 Introduction ............................................................................................ 34 

 2.3.2 BWR Reflood Phenomena of Interest .................................................... 34

 2.4 Conclusions ............................................................................................................. 37

 2.5 References ............................................................................................................... 37 

3. LITERATURE REVIEW ........................................................................................................ 39

 3.1 Introduction .............................................................................................................. 39

 3.2 Rod Bundle Tests .................................................................................................... 39

 3.3 Single-Tube Tests and Related Studies .................................................................. 42 

 3.3.1 Liquid Entrainment and Breakup ............................................................ 42 

 3.3.2 Drop Size Distribution and Number Density ........................................... 46 

 3.3.3 Droplet Velocity, Interfacial Shear, and Interactions .............................. 47 

 3.3.4 Droplet-Enhanced Heat Transfer ........................................................... 48 

 3.3.5 Droplet Evaporative Heat Transfer ......................................................... 49 

 3.3.6 Direct Contact Heat Transfer ................................................................. 50 

 3.3.7 Total Wall Heat Transfer ........................................................................ 51 

 3.3.8 Effects of Spacer Grids .......................................................................... 51 

 3.3.9 Effects of Inlet Flow Oscillation and Thermal Non-equilibrium ............... 52 

 3.3.10 Other Factors ......................................................................................... 52 

 
 viii

3.4 Master Table: Previous Studies Relevant to the High-Ranking Phenomena 

 Identified in the PIRT for the RBHT Program ........................................................... 53 

 3.5 References ............................................................................................................... 59 

 3.5.1 Rod Bundle Tests ................................................................................... 59 

 3.5.2 Single Tube Tests and Related Studies ................................................. 61 

4. DEFINE INFORMATION NEEDED FOR NEW CODE MODELING CAPABILITIES, 

 VALIDATION, AND ASSESSMENT .................................................................................... 83

 4.1 Introduction .............................................................................................................. 83

 4.2 Brief Review of Heat Transfer Models Used in Best-Estimate Codes for Reflood ... 84 

 4.2.1 RELAP5/MOD3 ...................................................................................... 84 

 4.2.1.1 Introduction ....................................................................................... 84 

 4.2.1.2 RELAP5/MOD3 Heat Transfer Package .......................................... 85 

 4.2.1.3 Single Phase Liquid .......................................................................... 86 

 4.2.1.4 Single Phase Vapor .......................................................................... 86 

 4.2.1.5 Nucleate Boiling ............................................................................... 86 

 4.2.1.6 Critical Heat Flux .............................................................................. 86 

 4.2.1.7 Minimum Stable Film Boiling Point ................................................... 86 

 4.2.1.8 Transition Boiling .............................................................................. 87 

 4.2.1.9 Film Boiling ....................................................................................... 89 

 4.2.1.10 Interfacial Heat Transfer ................................................................... 89 

 4.2.1.11 Quench Front Model ......................................................................... 89 

 4.2.1.12 Liquid Entrainment ........................................................................... 89 

 4.2.1.13 Conclusions ...................................................................................... 89 

 4.2.2 TRAC-BF1 Reflood Model ..................................................................... 91 

 4.2.2.1 Introduction ....................................................................................... 91 

 4.2.2.2 Quench Front Model ......................................................................... 91 

 4.2.2.3 Fine-Mesh Algorithm ........................................................................ 92 

 4.2.3 TRAC-PF1 Reflood Model ..................................................................... 92 

 4.2.3.1 Introduction ....................................................................................... 92 

 4.2.3.2 Quench Front Model ......................................................................... 92 

 4.2.3.3 Fine-Mesh Algorithm ........................................................................ 92 

 4.2.3.4 Heat Transfer Model during Reflood ................................................ 93 

 4.2.3.5 Bubbly-Flow Models ....................................................................... 103 

 4.2.3.6 Dispersed and Post-Agitated Inverted Annular Flows .................... 104 

 4.2.3.7 Inverted Annular Flow .................................................................... 105 

 4.2.3.8 Spacer Grid Model ......................................................................... 105 

 4.2.3.9 Noncondensables............................................................................ 105 

 4.2.4 COBRA-TF Code ................................................................................. 105 

 4.2.4.1 Introduction ..................................................................................... 105 

 4.2.4.2 COBRA-TF Heat Transfer Package ............................................... 106 

 4.2.4.3 Single Phase Vapor ........................................................................ 112 

 4.2.4.4 Single Phase Liquid ........................................................................ 112 

 4.2.4.5 Nucleate Boiling ............................................................................. 113 

 4.2.4.6 Subcooled Nucleate Boiling ........................................................... 113 

 4.2.4.7 Critical Heat Flux .............................................................................113 

 4.2.4.8 Minimum Stable Film Boiling Point ................................................. 114 

 4.2.4.9 Transition Boiling ............................................................................ 114 

 4.2.4.10 Inverted Annular Film Boiling ......................................................... 114 
 ix

 4.2.4.11 Dispersed Flow Film Boiling ........................................................... 114 

 4.2.4.12 Quench Front Model ....................................................................... 116 

 4.2.4.13 Spacer Grid Heat Transfer Models ..................................................116 

 4.3 Road Map from the PIRT, to the Code Models, to the Test Instrumentation 

 and Data Analysis .................................................................................................. 119 

 4.3.1 Single Phase Liquid Convection Below the Quench Front ................... 119 

 4.3.2 Subcooled and Saturated Boiling Below the Quench Front ................. 123 

 4.3.3 Quench Front Behavior ........................................................................ 127 

 4.3.4 Two-Phase Froth Region for the Core Component .............................. 134 

 4.3.5 Dispersed Flow Film Boiling Region .................................................... 140 

 4.3.6 Top Down Quench in Core Components ............................................. 145 

 4.3.7 Other Effects: Spacer Grids, Housing .................................................. 145

 4.4 Conclusions ........................................................................................................... 147

 4.5 References ............................................................................................................. 147 

 

5. ROD BUNDLE HEAT TRANSFER PROGRAM OBJECTIVES AND FACILITY 

 MISSION ............................................................................................................................ 151

 5.1 Introduction ............................................................................................................ 151

 5.2 Rod Bundle Heat Transfer Program Objectives ..................................................... 151 

 5.3 Conclusions ........................................................................................................... 154 

 

6. FIRST TIER SCALING FOR THE ROD BUNDLE HEAT TRANSFER TEST FACILITY .... 155 

 6.1 Introduction ............................................................................................................ 155

 6.2 Two Tier Scaling Approach .................................................................................... 156 

 6.3 Application of the Top-down Scaling Approach ..................................................... 156 

 6.3.1 Fluid Energy Equation .......................................................................... 156 

 6.3.2 Heater Rod (Fuel Rod) Energy Equation Scaling ................................ 171 

 6.3.3 Momentum Equation Scaling for the Rod Bundle Heat Transfer 

 Test Facility .......................................................................................... 175

 6.4 Calculation of Pi Groups for Flow Energy Equation ............................................... 187 

 6.4.1 Introduction .......................................................................................... 187 

 6.4.2 Calculation of Convective Heat Transfer Pi Groups ............................. 187 

 6.4.2.1 Methodology Used for Calculations ................................................ 187 

 6.4.2.2 Numerical Input Quantities ............................................................. 189 

 6.4.2.3 Numerical Values of the Convection Pi Groups ............................. 189 

 6.4.3 Quench Energy Groups ....................................................................... 191 

 6.4.4 Thermal Radiation Heat Transfer Pi Group Calculations ..................... 194 

 6.4.5 Summary .............................................................................................. 200

 6.5 Calculations of Pi Groups for the Rod Energy Equation ........................................ 200 

 6.5.1 Introduction .......................................................................................... 200 

 6.5.2 Convection and Stored Energy Pi Groups ........................................... 204 

 6.5.3 Thermal Radiation Heat Transfer Pi Groups ........................................ 207 

 6.5.4 Summary .............................................................................................. 212 

 6.6 Calculation of Pi Groups for Flow Momentum Equation ........................................ 212

 6.7 Calculation of PWR and BWR Pi Groups .............................................................. 214 

 6.7.1 Introduction .......................................................................................... 214 

 6.7.2 Calculation of Pi Groups for PWR ........................................................ 214 

 6.7.3 Calculation of Pi Groups for BWR ........................................................ 216
 x

 6.8 Conclusions ........................................................................................................... 217

 6.9 References ............................................................................................................. 218 

7. SECOND TIER SCALING FOR THE ROD BUNDLE HEAT TRANSFER TEST 

 FACILITY ........................................................................................................................... 221

 7.1 Introduction ............................................................................................................ 221

 7.2 Housing Effects and Studies .................................................................................. 222 

 7.2.1 Introduction .......................................................................................... 222 

 7.2.2 Results ................................................................................................. 223 

 7.2.2.1 Bundle Size .................................................................................... 226 

 7.2.2.2 Housing Thickness ......................................................................... 228 

 7.2.2.3 Housing Preheating ........................................................................ 228 

 7.2.2.4 Surface Emissivity .......................................................................... 228 

 7.2.2.5 Axial Power Distribution ................................................................. 228 

 7.2.2.6 Effect of the Corner Dummy Rods ................................................. 231

 7.3 Material Differences ............................................................................................... 231 

 7.3.1 Introduction .......................................................................................... 231 

 7.3.2 Rod Comparison .................................................................................. 231

 7.4 Surface Properties Differences .............................................................................. 235

 7.5 Scaling Conclusions ............................................................................................... 235 

 7.6 References ............................................................................................................. 236 

8. INSTRUMENTATION REQUIREMENTS FOR THE ROD BUNDLE HEAT TRANSFER 

 TEST FACILITY ................................................................................................................. 239 

 8.1 Introduction ............................................................................................................ 239

 8.2 Instrumentation Requirements ............................................................................... 239 

 8.3 Proposed New Instrumentation .............................................................................. 241 

 8.4 Instrumentation Plan Comparison to the PIRT ...................................................... 242

 8.5 Conclusions ........................................................................................................... 257

 8.6 References ............................................................................................................. 257 

9. DEVELOPING A FACILITY INPUT MODEL ...................................................................... 259

 9.1 Introduction ............................................................................................................ 259

 9.2 Two-Channel Model ............................................................................................... 259 

 9.2.1 Input Deck Description ......................................................................... 259 

 9.2.2 Results of Two-Channel Model ............................................................ 263

 9.3 Individual Sub-Channel Model ............................................................................... 271 

 9.3.1 Input Deck Description ......................................................................... 271 

 9.3.2 Results of Sub-Channel Model ............................................................ 272

 9.4 Conclusions ........................................................................................................... 274

 9.5 References ............................................................................................................. 274 

10. ROD BUNDLE HEAT TRANSFER TEST MATRIX .......................................................... 275

 10.1 Introduction ............................................................................................................ 275

 10.2 Types of Tests Which are Proposed ...................................................................... 275 

 10.3 Range of Conditions Considered for the Experiments ........................................... 277 

 10.4 Proposed Preliminary Test Matrix .......................................................................... 279 

 10.5 Conclusions ........................................................................................................... 281

 10.6 References ............................................................................................................. 281 
 xi

11. TEST FACILITY DESIGN ................................................................................................. 283

 11.1 Introduction ............................................................................................................ 283

 11.2 General Design Description ................................................................................... 283

 11.3 Detailed Component Design Description ............................................................... 284 

 11.3.1 Test Section ......................................................................................... 284 

 11.3.2 Lower Plenum ...................................................................................... 290 

 11.3.3 Upper Plenum ...................................................................................... 290 

 11.3.4 Carryover Tanks ................................................................................... 292 

 11.3.5 Steam Separator and Collection Tanks .............................................. 292 

 11.3.6 Pressure Oscillation Damping Tank ..................................................... 292 

 11.3.7 Exhaust Piping ..................................................................................... 294 

 11.3.8 Injection Water Supply Tank ................................................................ 296 

 11.3.9 Water Injection Line ............................................................................. 296 

 11.3.10 Steam Supply ....................................................................................... 296 

 11.3.11 Droplet Injection System ...................................................................... 296

 11.4 Test Facility Instrumentation .................................................................................. 296 

 11.4.1 Loop Instrumentation and Controls ...................................................... 297 

 11.4.2 Test Section Instrumentation ............................................................... 299 

 11.4.3 Data Acquisition System ...................................................................... 314

 11.5 RBHT Test Facility Improvement ........................................................................... 314

 11.6 Conclusions ........................................................................................................... 315

 11.7 References ............................................................................................................. 315 

12. CONCLUSIONS ............................................................................................................... 317 

 

APPENDIX A. LITERATURE REVIEW 

 A1 FLECHT Low Flooding Rate Cosine Test Series ................................................... A-1

 A2 FLECHT Low Flooding Rate Skewed Test Series ................................................. A-6

 A3 Westinghouse FLECHT-SEASET 21-Rod Bundle Test Facility ........................... A-13

 A4 FLECHT-SEASET 161-Rod Unblocked Bundle Tests ......................................... A-22

 A5 FEBA - Flooding Experiments With Blocked Arrays ............................................. A-35

 A6 Oak Ridge National Laboratory Thermal-Hydraulic Test Facility (THTF) ............. A-54

 A7 FRIGG-2 36-Rod Loop (Sweden) ......................................................................... A-63

 A8 GE 9-Rod Bundle Facility ..................................................................................... A-72

 A9 PNL LOCA Simulation Program at NRU Reactor, Chalk River, Canada ............. A-78

 A10 ACHILLES Reflood Heat Transfer Tests .............................................................. A-90

 A11 Lehigh 9-Rod Bundle Tests ................................................................................ A-102 

 

APPENDIX B. 

 B1 Radiation Heat Transfer Network and Calculation of Pi Groups ............................ B-1

 B2 Rod Grid Radiation Network for RBHT .................................................................. B-5

 B3 Rod Grid Radiation Network for PWR .....................................................................B-6 

 B4 Rod Grid Radiation Network for BWR .................................................................... B-7

 B5 Fortran Program RADNET ..................................................................................... B-8 

 

APPENDIX C. 

 C1 Bundle Model Description ...................................................................................... C-1

 C2 Fortran Program BUNDLE ..................................................................................... C-4 

 
 xii

APPENDIX D. 

 D1 COBRA-TF Listings ............................................................................................... D-1 

 D2 Two-Channel Model Listing ................................................................................... D-2 

 D3 Sub-Channel Model Input Deck ........................................................................... D-38 

 
 xiii

FIGURES 

 Page

1.1 Reflood Flow Regimes for High and Low Reflood Rates ................................................. 3 

1.2 Detailed Low Flooding Rate Reflood Flow Regimes ....................................................... 4 

1.3 Transition and Quench Fronts for FLECHT-SEASET Test 31504 ................................... 5 

1.4 Entrainment Behavior for Rod Bundle Reflooding ........................................................... 6 

1.5 Heat and Mass Transfer Mechanism in Dispersed Flow Film Boiling .............................. 7 

1.6 Comparison of Current Best Estimate Calculated PCTs with CSAU Study ................... 10 

2.1 Code Scaling, Applicability and Uncertainty (CSAU) Evaluation Methodology ..............14 

2.2 Froth Region and Quench Front Locations for Reflood ................................................. 17 

2.3 Froth Front and Quench Front Curves for FLECHT-SEASET Run 31203, 

 1.5 in/s, 40 psia Test ..................................................................................................... 18 

2.4 Froth Front and Quench Front Curves for FLECHT-SEASET Run 31504, 

 1.0 in/s, 40 psia Test ..................................................................................................... 19 

2.5 Typical Conditions in Rod Bundle During Reflood ......................................................... 20 

4.1 RELAP5/MOD 3 Vertical Flow Regime Map .................................................................. 85 

4.2 RELAP5 Wall Heat Transfer Flow Chart ........................................................................ 88 

4.3 Void Fraction Superheat Plane ...................................................................................... 94 

4.4 Flow Regime Map During Reflood ................................................................................. 95 

4.5 HTC Correlation Selection Logic ................................................................................... 96 

4.6 HTC Correlation Selection Logic ................................................................................... 97 

4.7 HTC Correlation Selection Logic ................................................................................... 98 

4.8 HTC Correlation Selection Logic ................................................................................... 99 

4.9 HTC Correlation Selection Logic for Reflood Model .................................................... 100 

4.10 HTC Correlation Selection Logic for Reflood Model .................................................... 101 

4.11 HTC Correlation Selection Logic for Reflood Model .................................................... 102 

4.12 Hot Wall Flow Regimes ............................................................................................... 107 

4.13 Hot Wall Flow Regime Selection Logic ........................................................................ 108 

4.14 Schematic Representation of Boiling Curve ................................................................ 109 

4.15 Heat Transfer Regime Selection Logic ........................................................................ 109 

4.16 WCOBRA/TRAC Heat Transfer Regime Map ............................................................. 115 

4.17 Two-Phase Enhancement: Comparison of Models and Reflood Data ........................ 117 

4.18 Radiation Heat Flux Network ....................................................................................... 118 

4.19 Droplet Breakup ........................................................................................................... 119 

4.20 Shattered Droplet Size from Heated Grid Straps ......................................................... 120 

6.1 Mass Balance FLECHT-SEASET Run 31504 ............................................................. 177 

6.2 RBHT Layout ............................................................................................................... 195 

6.3 Six Node Radiation Network ........................................................................................ 195 

6.4 Four Node Radiation Network ..................................................................................... 199 

6.5 PWR Bundle Lumping Approach ................................................................................. 215 

6.6 BWR Bundle Lumping Approach ................................................................................. 217 

7.1 Convective Heat Transfer Coefficient (FLECHT-SEASET Run 31504) ....................... 222 

7.2 Wall Surface Temperature in the 7x7 Bundle (Base Case) ......................................... 224 

7.3 Heat Rate To and From the Housing in the 7x7 Bundle (Base Case) 

 (Bundle Linear Power = 103000 W/m) ........................................................................ 224 

7.4 Clad Temperature Drop in the Inner 3x3 Array Because of Radiative Heat 

 Transfer in a Finite Size Bundle Array ......................................................................... 225 

 
 xiv

7.5 Heat Rate To and From the Housing in the 7x7 Bundle (Base Case) 

 (Bundle Linear Power = 103000 W/m) ........................................................................ 227 

7.6 Inner 3x3 Rod Array Clad Temperature Bias in the RBHT Bundle Housing 

 Thickness Sensitivity ................................................................................................... 227

7.7 Inner 3x3 Rod Array Clad Temperature Bias in RBHT Bundle Housing Initial 

 (Pre-Heating) Temperature Sensitivity ........................................................................ 229 

7.8 Inner 3x3 Rod Array Clad Temperature Bias in RBHT Bundle Wall 

 Emissivity Sensitivity .................................................................................................... 229 

7.9 Inner 3x3 Rod Array Clad Temperature Bias in the RBHT Bundle Radial 

 Power Distribution Sensitivity ...................................................................................... 230 

7.10 Inner 3x3 Rod Array Clad Temperature Bias in the RBHT Bundle Dummy 

 Rods Effect .................................................................................................................. 230 

7.11 Steady-State Temperature Profile ............................................................................... 232 

7.12 Electrical Rod Steady-State Temperature Profile Gap Resistance Sensitivity ............ 233 

7.13 Rod Quenching ............................................................................................................ 234 

7.14 Rod Quench Energy Release ...................................................................................... 234 

7.15 Distribution of Measured Rewet Temperature During Westinghouse G-1 and 

 G-2 Blowdown Rod Bundle Experiments ..................................................................... 235 

9.1 RBHT - Partitioning of Sections, Channels & Gaps ..................................................... 260 

9.2 RBHT - Test Section 7x7 Rod Bundle Array Cross Section ........................................ 260 

9.3 RBHT Heater Rod - Radial Dimensions, Materials & Nodding Scheme ...................... 261 

9.4 RBHT - Radial Dimensions, Materials & Noding Scheme ........................................... 261 

9.5 RBHT - Axial Dimensions & Nodal Scheme ................................................................ 262 

9.6 Axial Power Shape ...................................................................................................... 263 

9.7 Power Decay ............................................................................................................... 264 

9.8 Quench Front - 1.0 in/s Reflooding Rate ..................................................................... 264 

9.9 Hot Rod Clad Temperature - 2.54 cm/s (1.0 in/s) Reflooding Rate ............................. 265 

9.10 Housing Temperature - 2.54 cm/s (1.0 in/s) Reflooding Rate ..................................... 265 

9.11 Hot Rod Clad Temperature - 2.54 cm/s (1.0 in/s) Reflooding Rate ............................. 266 

9.12 Vapor Temperature - 2.54 cm/s (1.0 in/s) Reflooding Rate ......................................... 266 

9.13 Vapor Flow Rate at Outlet of Rod Bundle - 2.54 cm/s (1.0 in/s) Reflooding Rate ....... 267 

9.14 Entrainment Flow Rate at Outlet of Rod Bundle - 2.54 cm/s (1.0 in/s) 

 Reflooding Rate ........................................................................................................... 267 

9.15 Pressure at Inlet of Rod Bundle 1.0 in/s Reflooding Rate ........................................... 268 

9.16 Vapor Reynolds Number - 2.032 cm/s (0.8 in/s) Reflooding Rate ............................... 269 

9.17 Vapor Reynolds Number - 2.54 cm/s (1.0 in/s) Reflooding Rate ................................. 270 

9.18 Vapor Reynolds Number - 3.81 in/s (1.5 in/s) Reflooding Rate ................................... 270 

9.19 Nodal Diagram for a Subchannel Model ...................................................................... 271 

9.20 Axial Nodal Diagram for Subchannel Model ................................................................ 272 

9.21 Temperature Distributions After 50 s Heatup (in degrees C) ....................................... 273 

11.1 RBHT Test Facility Schematic ..................................................................................... 283 

11.2 Test Section Isometric View ........................................................................................ 284 

11.3 Rod Bundle Cross Sectional View ............................................................................... 285 

11.4 Heater Rod .................................................................................................................. 286 

11.5 Heater Rod Axial Power Profile ................................................................................... 286 

11.6 Low-Melt Reservoir ...................................................................................................... 287 

11.7 Low Mass Flow Housing Assembly ............................................................................. 288 

11.8 Housing Window .......................................................................................................... 289 

11.9 Lower Plenum .............................................................................................................. 290 

11.10 Lower Plenum Flow Baffle ........................................................................................... 290 
 xv

11.11 Upper Plenum .............................................................................................................. 291 

11.12 Exhaust Line Baffle ...................................................................................................... 291 

11.13 Large Carryover Tank .................................................................................................. 291 

11.14 Small Carryover Tank .................................................................................................. 291 

11.15 Steam Separator .......................................................................................................... 293 

11.16 Steam Separator Collection Tank ................................................................................ 293 

11.17 Pressure Oscillation Damping Tank ............................................................................ 294 

11.18 Injection Water Supply Tank ........................................................................................ 295 

11.19 Droplet Injection Schematic ......................................................................................... 297

11.20 Loop Instrumentation Schematic ................................................................................. 298 

11.21 Rod Bundle and Housing Instrumentation Axial Locations .......................................... 300 

11.22 Instrumentation Heater Rod Radial Locations ............................................................. 309 

11.23 Traversing Steam Probe Rake .................................................................................... 310 

11.24 Densitometer Schematic .............................................................................................. 311

11.25 Laser Illuminated Digital Camera System Setup ......................................................... 312 

A1.1 FLECHT Low Flooding Rate Test Configuration ......................................................... A-4 

A1.2 Rod Bundle Instrumentation for FLECHT Low Flooding Rate Tests ........................... A-5 

A2.1 FLECHT Low Flooding Rate Test Facility Schematic ................................................ A-10 

A2.2 FLECHT Low Flooding Rate Test Power Shape ........................................................ A-11 

A2.3 FLECHT Low Flooding Rate Test Rod Bundle Cross Section ................................... A-12 

A3.1 Schematic of the Test Bundle .................................................................................... A-14 

A3.2 21-Rod Bundle Flow Blockage Task Instrumentation Schematic Diagram ................ A-15 

A4.1 FLECHT-SEASET Rod Bundle Cross Section ........................................................... A-27 

A4.2 FLECHT-SEASET Facility Flow Diagram .................................................................. A-28 

A5.1 FEBA Test Facility ..................................................................................................... A-37 

A5.2 Axial Power Profile ..................................................................................................... A-38 

A5.3 Upper Bundle End and Upper Plenum ....................................................................... A-38 

A5.4 5x5 Rod Bundle, Test Matrix for Series I Through VIII ............................................... A-39 

A5.5 Rod Geometry and Location of Thermocouple .......................................................... A-40 

A5.6 Radial and Axial Location of Cladding, Fluid and Housing T/C’s for Test Series I ..... A-41 

A5.7 Axial Locations of Various Thermocouples in 5x5 Rod Bundle .................................. A-42 

A5.8 5-Rod Row: Comparison of Different Fluid Temperature Measuring Devices .......... A-43 

A6.1 THTF System With Instrumented Spool Pieces Labeled ........................................... A-55 

A6.2 Identification of THTF Heater Rods, Subchannel Location, and Inactive Rods 

 in THTF Heater Bundle .............................................................................................. A-56 

A6.3 Cross-Section of a Typical Fuel Rod Simulator ......................................................... A-56 

A6.4 Axial Locations of Spacer Grid and Thermocouples .................................................. A-57 

A7.1 36-Rod Bundle of the FRIGG-2 .................................................................................. A-65 

A7.2 Flow Diagram of the FRIGG-2 Loop .......................................................................... A-66 

A8.1 Positions of Pressure Taps for Setting Isokinetic Conditions ..................................... A-74 

A8.2 Schematic of Loop Showing Sampling Circuit ........................................................... A-74 

A9.1 Schematic of NRU Loss-of-Coolant Accident Test Train ........................................... A-79 

A9.2 NRU Reactor Core Configuration ............................................................................... A-80 

A9.3 Instrumentation Levels in the TH-2 Test Assembly .................................................... A-81 

A9.4 Instrumentation Levels in the TH-3 Test Assembly .................................................... A-82 

A10.1 Cross Section of ACHILLES 69-Rod Bundle ............................................................. A-92 

A10.2 Schematic of ACHILLES Flow Loop .......................................................................... A-93 

A10.3 Axial Locations in Test Section .................................................................................. A-94 

A11.1 Cross-sectional View of Test Bundle ....................................................................... A-103 
 xvi

A11.2 Schematic of Test Section Support System ............................................................. A-103 

 

A11.3 Sample Plot of Temperature and Steam Quality Data for the Stabilized 

 Quench Front Experiments ...................................................................................... A-104 

A11.4 Sample Plot of Heat Flux and Steam Quality Data for the Advancing 

 Quench Front Experiments ...................................................................................... A-105 

A11.5 Sample Plot of Rod and Steam Temperature Data for the Advancing 

 Quench Front Experiments ...................................................................................... A-105 

A11.6 Typical Transverse Vapor Temperature Profile for Various Vapor Qualities ........... A-106 

A11.7 Typical Transverse Vapor Temperature Profiles Downstream of the Grid 

 Spacer ...................................................................................................................... A-106 
 xvii

TABLES 

 Page

2.1 Single Phase Liquid Convective Heat Transfer ............................................................. 21 

2.2 Subcooled and Saturated Boiling - The Core Component Below the Quench 

 Front .............................................................................................................................. 22 

2.3 Quench Front Behavior in the Core Component ........................................................... 24 

2.4 Two-Phase Froth (Transition) Region for Core Component .......................................... 26 

2.5 A Dispersed Flow Region for Core Component ............................................................. 28 

2.6 Top Down Quench in Core Component ......................................................................... 31 

2.7 Preliminary PIRT for Gravity Reflood Systems Effects Tests ........................................ 32 

2.8 High Ranked BWR Core Phenomena ........................................................................... 35 

3.1 Comparison of the Data From Various Rod Bundle Tests ............................................. 43 

3.2 Previous Studies Relevant to the High-Ranking Phenomena During the 

 Reflood Stage of a Large Break LOCA .......................................................................... 55 

4.1 RELAP5/MOD3 Heat Transfer Modes .......................................................................... 87 

4.2 Summary of Interfacial Areas and Heat Transfer Coefficients ....................................... 90 

4.3 TRAC-PF1/MOD2 Heat Transfer Regimes .................................................................... 93 

4.4 Weighting Factors of Reflood Interfacial Heat-Transfer Models .................................. 103 

4.5 Interfacial Heat transfer Area Per Unit Volume ............................................................ 110 

4.6 Single Phase Liquid Convective Heat Transfer in the Core Component During 

 Reflood Below the Quench Front ................................................................................ 122

4.7 Subcooled and Saturated Boiling -The Core Component Below the Quench Front .... 125 

4.8 Quench Front Behavior in the Core Component ......................................................... 129 

4.9 Two-Phase Froth (Transition) Region for Core Component ........................................ 136 

4.10 Dispersed Flow Region for Core Component .............................................................. 142 

4.11 Top Down Quench in Core Components ..................................................................... 146 

6.1 Normalizing Factors for Fluid Energy Equation ........................................................... 162 

6.2 List of Initial Conditions and Assumptions ................................................................... 162 

6.3 PWR Comparisons ...................................................................................................... 168

6.4 BWR Comparisons ...................................................................................................... 169

6.5 Normalization Parameters for Rod Energy Equation ................................................... 172 

6.6 Normalizing Parameters for Fluid Momentum Equation .............................................. 180 

6.7 Pi Groups for Fluid Energy Equation ........................................................................... 182 

6.8 RBHT Program Conditions .......................................................................................... 187 

6.9 Reference Conditions for the Fluid Energy Equation Pi Groups .................................. 188 

6.10 Material Properties ....................................................................................................... 192 

6.11 Electrical Rod Geometry .............................................................................................. 192

6.12 Nuclear Rod Geometry for PWR ................................................................................. 192 

6.13 Nuclear Rod Geometry for BWR ................................................................................. 193 

6.14 Numerical Values of Pi Groups - Fluid Energy Equation ............................................. 201 

6.15 Reference Conditions for Rod Energy Equation Pi Groups ......................................... 204 

6.16 Comparison of Calculated Time Constants ................................................................. 205 

6.17 Convection and Stored Energy Pi Groups for Electrical/Nuclear Rod ......................... 206 

6.18 Numerical Values of Pi Groups - Rod Energy Equation .............................................. 210 

6.19 Fluid Momentum Pi Groups ......................................................................................... 212 

6.20 Numerical Values of Pi Groups - Fluid Momentum Equation ...................................... 213 

7.1 Input Data .................................................................................................................... 223 
 xviii

7.2 Input data ..................................................................................................................... 232 

8.1 Single Phase Liquid Convective Heat Transfer in the Core Component During 

 Reflood Below the Quench Front ................................................................................. 243 

8.2 Subcooled and Saturated Boiling - Core Component Below the Quench Front .......... 244 

8.3 Quench Front Behavior in the Core Component ......................................................... 246 

8.4 Two-Phase Froth (Transition) Region for Core Component ........................................ 248 

8.5 Dispersed Flow Region for Core Component .............................................................. 250 

8.6 Top Down Quench in Core Components ..................................................................... 252 

8.7 Preliminary PIRT for Variable Reflood Systems Effects Tests .................................... 253 

8.8 High Ranked BWR Core Phenomena ......................................................................... 255 

9.1 Weber Number Parameter at 425 s ............................................................................. 269 

10.1 Range of PWR Reflood Conditions ............................................................................. 278 

11.1 General Specifications ................................................................................................. 285 

11.2 Thermocouple Specifications ....................................................................................... 287 

11.3 Instrumentation and Data Acquisition Channel List ..................................................... 301 

A3.1 Assessment of FLECHT-SEASET Unblocked 21-Rod Bundle Test to RBHT PIRT: 

 Dispersed Flow Region for Core Component ............................................................ A-16 

A3.2 Assessment of FLECHT-SEASET Unblocked 21-Rod Bundle Test to RBHT PIRT: 

 Top Down Quench in Core Components ................................................................... A-17 

A3.3 Assessment of FLECHT-SEASET Unblocked 21-Rod Bundle Test to RBHT PIRT: 

 Preliminary PIRT for Gravity Reflood Systems Effects Tests .................................... A-18 

A3.4 Assessment of FLECHT-SEASET Unblocked 21-Rod Bundle Test to RBHT PIRT: 

 High Ranked BWR Core Phenomena ........................................................................ A-20 

A4.1 FLECHT-SEASET Unblocked Bundle Reflood Test Data Summary ......................... A-29 

A5.1 Assessment of FEBA Test to RBHT PIRT: Single Phase Liquid Convective Heat 

 Transfer in the Core Component During Reflood Below the Quench Front ............... A-44 

A5.2 Assessment of FEBA Test to RBHT PIRT: Subcooled and Saturated Boiling in 

 the Core Component Below the Quench Front .......................................................... A-45 

A5.3 Assessment of FEBA Tests to RBHT PIRT: Quench Front Behavior in the Core 

 Component ................................................................................................................. A-46 

A5.4 Assessment of FEBA Tests to RBHT PIRT: Froth Region for the Core 

 Component ................................................................................................................. A-48 

A5.5 Assessment of FEBA Tests to RBHT PIRT: Dispersed Flow Region for Core 

 Component ................................................................................................................. A-49 

A5.6 Assessment of FEBA Tests to RBHT PIRT: Top Down Quench in Core 

 Component ................................................................................................................. A-50 

A5.7 Assessment of FEBA Tests to RBHT: Preliminary PIRT for Gravity Reflood 

 Systems Effects Tests ................................................................................................ A-51 

A5.8 Assessment of FEBA Tests to RBHT PIRT for High Ranked BWR Core 

 Phenomena ................................................................................................................ A-52 

A6.1 Assessment of ORNL/THTF Data to RBHT PIRT: Dispersed Flow Region for 

 Core Component ........................................................................................................ A-61 

A7.1 Assessment of FRIGG-2 36-Rod Bundle Test to RBHT PIRT: Single Phase 

 Liquid Convective Heat Transfer in the Core Component During Reflood Below 

 the Quench Front ....................................................................................................... A-69

A7.2 Assessment of FRIGG-2 36-Rod Bundle Tests to RBHT PIRT: Subcooled and 

 Saturated Boiling in the Core Component Below the Quench Front .......................... A-70 

A7.3 Assessment of FRIGG-2 36-Rod Bundle Tests to RBHT PIRT for High Ranked 

 BWR Core Phenomena .............................................................................................. A-71 

 
 xix

A8.1 Assessment of General Electric 9-Rod Bundle Tests to RBHT PIRT: Subcooled 

 and Saturated Boiling in the Core Component Below the Quench Front ................... A-76 

A8.2 Assessment of General Electric 9-Rod Bundle Tests to RBHT PIRT for High 

 Ranked BWR Core Phenomena ................................................................................ A-77 

A9.1 Measured Conditions for the TH-2 Experiment .......................................................... A-83 

A9.2 Measured Conditions for the TH-3 Experiment .......................................................... A-85 

A9.3 Assessment of NRU Inpile Reflood Data to RBHT PIRT: Dispersed Flow Region 

 for Core Component ................................................................................................... A-86 

A9.4 Assessment of NRU Inpile Reflood Data to RBHT PIRT: High Ranked BWR 

 Core Phenomena ....................................................................................................... A-88 

A10.1 Summary of Low Flooding Rate Reflood Experiments ..............................................A-98 

A10.2 Droplet Distribution Experiments ................................................................................ A-99 

A10.3 Airflow and Voidage Distribution Experiments ......................................................... A-100 

A10.4 Summary of Best Estimate Reflood Experiments .................................................... A-101 

A11.1 Sample Tabulation of a Stabilized Quench Front Data Point ................................... A-107 

A11.2 Definition of Parameters Used in Table A11.1 ......................................................... A-108 

A11.3 Sample Tabulation of an Advancing Quench Front Data Point ................................ A-109 

A11.4 Definition of Parameters Used in Table A11.3 ......................................................... A-110 

 

 
 xx
xxi

EXECUTIVE SUMMARY 

A research program entitled “Rod Bundle Heat Transfer (RBHT),” funded by the U.S. Nuclear 

Regulatory Commission, was initiated at The Pennsylvania State University (PSU) on 

November 3, 1997, to develop a RBHT Test Facility and to conduct experiments to aid in the 

development of reflood heat transfer models which could be used in the NRC’s thermalhydraulics computer codes. The RBHT program consists of the following 16 major tasks: 

• Task 1 - Development of a Preliminary Phenomena Identification and Ranking Table 

• Task 2 - Critical Review of Existing Experimental Data Base 

• Task 3 - Defining Information Needed for New Code Modeling Capabilities, 

 Validation, and Assessment 

• Task 4 - Defining the Program Objectives and Facility Mission 

• Task 5 - First Tier Scaling for the Experimental Facility 

• Task 6 - Second Tier Scaling Analysis for the Local Phenomena 

• Task 7 - Defining the Instrumentation Requirements 

• Task 8 - Developing Facility Input Model 

• Task 9 - Drafting a Test Matrix 

• Task 10 - Test Facility Design 

• Task 11 - Construction and Characterization of the RBHT Facility 

• Task 12 - Definition of Test Initial and Boundary Conditions 

• Task 13 - Performing Tests and Qualifying the Test Data 

• Task 14 - Analyzing the Test Data 

• Task 15 - Assessing New or Modified Models 

• Task 16 - Final Model Description, Implementation, and Scaling Report 

This report describes the results obtained in the initial phase of the program; i.e., Tasks 1 

through 10. It is written for NRC review purpose to insure that the course of the program is 

properly directed and that the RBHT Facility is adequately designed, consistent with the NRC 

model development and improvement efforts which are underway. 

This report (i.e., the program objectives, test design, and the test and analysis approach) was 

also peer reviewed by individuals who are very knowledgeable and have significant expertise in 

the heat transfer and two-phase flow area. The individuals were selected by the Nuclear 

Regulatory Commission. The comments made by the different individuals were incorporated 

into the report as well as into the planning, design, and analysis plans for the RBHT program. In 

addition, there was also a specific Instrumentation Peer Review Meeting in which the facility 

instrumentation plan was reviewed with specialists in two-phase flow testing and 

instrumentation to provide guidance, comments, and critique of the proposed instrumentation for 

the RBHT program. Again, the comments and ideas provided by the Peer Review Panel were 

factored into the instrumentation design, testing methods and the resulting data analysis. 

An introduction, providing the pertinent background information to justify the needs for and the 

significance of conducting the RBHT program, is given in Section 1 of the report. 

Section 2 presents a preliminary reflood-heat-transfer specific Phenomena Identification and 

Ranking Table (PIRT) developed under Task 1 using the same ranking methodology as that 

employed by Los Alamos, Brookhaven and Idaho National Laboratories, and the NRC. 
xxii

Separate preliminary PIRTs are provided for each of the important reflood regions such that the 

particular reflood phenomena for a given region could be subdivided into specific component 

models and phenomena for which a computer code would be used to perform the calculation. 

The relative rankings listed in these PIRTs clearly indicate the most important reflood 

phenomena which a best-estimate computer code should simulate with high accuracy. They 

also serve as a guide in the execution of the subsequent Tasks set forth in the program. 

Section 3 describes the results of a comprehensive review of the literature on reflood heat 

transfer performed under Task 2. Unique information from the available rod bundle data and 

selective tube data useful to address the phenomena identified in the PIRTs is gathered and 

then subdivided into several different classifications to indicate which information can be used 

for each specific type of phenomena. A master cross-reference table is constructed identifying 

the data source for the highly ranked PIRT phenomena and indicating the applicability and 

major deficiencies (if any) of the data to determine and quantify the particular phenomena of 

interest. Based on the results of Task 2, new or improved data that will contribute to reducing 

the large uncertainties associated with some of the highly ranked phenomena, have been 

identified. 

Using the PIRTs developed in Task 1 and the master reference tables in Task 2, the modeling 

capabilities of the current best-estimate computer codes including RELAP5/MOD3, TRAC-B, 

TRAC-P, and COBRA-TF have been examined under Task 3 to determine how well the current 

models in these codes can represent the highly ranked phenomena in the PIRTs. The past 

code validation has also been reviewed to determine the state of the validation of the codes. 

These are discussed in Section 4 of the report. Based on the results of Tasks 1, 2, and 3, the 

data needed to either help develop specific models or validate specific models for the highly 

ranked reflood phenomena calculated in a best-estimate code have been identified. These data 

needs were used to define the mission for the RBHT facility and then translated into the 

program objectives which have been established under Task 4, as described in Section 5. 

Separate-effect component experiments will be performed to meet the program objectives by 

isolating each highly ranked PIRT phenomenon as best as possible so as to permit specific 

model development for that particular phenomenon and to minimize the risk of introducing 

compensating errors into the advanced reflood model package. The proposed experiments will 

provide new data as well as supplement existing reflood heat transfer data. 

Section 6 presents a first tier “top-down” systems scaling on the RBHT test facility performed 

under Task 5 using the combined Zuber-Wulff scaling approach which is the current state-ofthe-art methodology for scaling thermal-hydraulic systems. The fluid energy equation, the rod 

energy equation and the bundle fluid momentum equations have been developed and made 

dimensionless such that the various dimensionless Pi groups are derived to examine the 

similitude between the proposed RBHT test facility and prototypical pressurized water reactor 

(PWR) and boiling water reactor (BWR) fuel assemblies. Comparisons of the derived Pi groups 

indicate that if prototypical fluid conditions are used in the tests, and the bundle geometry is 

retained, including using the prototypical spacer grids, there is a very strong similarity between 

the RBHT test bundle and the PWR and BWR fuel assemblies, and the data should be 

applicable to either reactor fuel assembly type. However, the presence of a test housing in the 

proposed RBHT facility does lead to extra Pi groups for this structure relative to modeling of a 

PWR fuel assembly, indicating that distortion in the test is possible. The RBHT facility is 

actually a closer representation to a BWR fuel assembly which also has a Zircaloy can or 
xxiii

channel surrounding the fuel rod bundle. For code modeling and validation purposes, the 

effects of the test housing need to be accounted for. In addition to the first tier scaling, a 

“bottom-up” second tier scaling has also been performed under Task 6 as described in 

Section 7. 

The second tier scaling, which focuses on the Pi groups in the system of equations governing 

the particular phenomena of interest, is used to characterize the transport terms and to establish 

relationships for calculating them when comparing the terms of the scaled facility to those of 

the full size prototype. As mentioned above, the main distortion of the RBHT facility when 

compared to a PWR situation is the presence of the housing. Thus the housing effects have 

been studied using the MOXY computer program. The housing represents a heat sink for the 

radiative heat transfer from the rods and, subsequently, a heat source because of the stored 

energy during the quench period. Another possible distortion is that due to rod material 

differences which may alter the heat capacity, thermal time constants, surface emissivity, and 

surface rewetting characteristics. A detailed analysis is made to account for the fact that 

Inconel-600 is used in the electrical rods instead of Zircaloy for the clad, while Boron Nitride is 

used instead of Uranium Dioxide. The gap conductance is 96.875 kW/m2

-K (5000 Btu/hr-ft2-F) 

for the electrical rods as compared to approximately 19.375 kW/m2

-K (1000 Btu/hr-ft2-F) for 

nuclear fuel rods. The effects of gap conductance and material differences are found to be 

moderately small with the possible exception of the minimum film boiling temperature. 

Section 8 describes the instrumentation requirements for the proposed RBHT facility, developed 

under Task 7, using the PIRTs as a guide for the important phenomena for the different types of 

tests which the experiments must capture for model development and code validation. There 

will be ample instrumentation, proven to perform in previous rod bundle experiments, which will 

be used in the proposed RBHT experiments. There will also be state-of-the-art instrumentation 

which will be used to measure the details of the two-phase flow field to determine, for example, 

void fraction, droplet size, droplet velocity, and droplet number density at and above the quench 

front. The instrumentation requirements described in Section 8 represent a robust 

instrumentation plan that allow most of the highly ranked phenomena to be either directly 

measured or directly calculated from the experimental data. 

Two facility input models were developed under Task 8 using COBRA-TF as the source code as 

presented in Section 9. A two-channel model was used to estimate the fluid conditions for a 

given reflood transient and to help set test conditions. A more detailed model considered a 1/8 

sector of the 7x7 bundle comprised of 45 heater rods, four unheated corner rods, and the 

surrounding housing. A fine nodal structure is adopted so as to resolve, in more detail, the 

housing and rod temperature distribution at and just above the quench front where the droplet 

entrainment occurs, as well as the flow behavior downstream of spacer grids where local heat 

transfer enhancement occurs in both single and two-phase flows. 

A test matrix for the planned tests has been developed under Task 9 as presented in Section 

10. A “building block” approach has been used in developing the test types and the test matrix 

such that simpler experiments will first be performed to quantify a particular reflood heat transfer 

mechanism alone and then add the additional complications of the two-phase dispersed flow 

film boiling behavior of the test facility. 

The planned test types include single phase pressure drop, heat loss, subcooled and saturated 

boiling, radiation only tests with an evacuated rod bundle, single-phase steam convective heat 

transfer, two-phase droplet-injection convective heat transfer, forced reflood, and variable 
xxiv

reflood experiments. The range of conditions has been chosen for each type of experiments so 

as to overlap those conditions currently calculated with best estimate and Appendix K safety 

analysis codes, to compliment the existing data base, and to provide new data for model 

development and code validation. The ranges to be examined will cover the expected ranges 

that best-estimate codes are expected to calculate with accuracy. 

Based upon the results of Tasks 1 through 9, the RBHT test facility was successfully designed 

under Task 10 as a flexible rod bundle separate-effects test facility which can be used to 

perform single and two-phase experiments under well-controlled laboratory conditions to 

generate fundamental reflood heat transfer data. The facility is capable of operating in both 

forced and gravity reflood modes covering wide ranges of flow and heat transfer conditions at 

pressures up to 0.402 MPa (60 psia). It has five major components: (i) a test section consisting 

of a 7x7 electrically heated rod bundle contained in a low mass flow housing with windows, a 

lower plenum, and an upper plenum, (ii) a coolant injection and steam injection system, (iii) a 

phase separation and liquid collection system, (iv) a downcomer and crossover leg system, and 

(v) a system pressure oscillation damping tank and steam exhaust piping. A detailed 

description of the component design is given in Section 11. The test facility has instrumentation 

that meets all the instrumentation requirements developed under Task 7 (see Section 8). The 

heater rods have been designed using prototypical spacer grids such that they can be used in 

two bundle builds to conduct all types of the planned experiments according to the test matrix 

developed under Task 9 (see Section 10). 

The RBHT facility, with its robust instrumentation, is a unique facility that can be used to provide 

new data for the fundamental assessment of the physical relationships upon which the code 

constitutive models are based. It will aid in reflood model development and uncertainty 

reduction for the NRC’s thermal-hydraulics computer code. Preliminary conclusions drawn 

from the results obtained in Tasks 1 through 10 are given in Section 12. An executive summary 

of the work performed and the major findings obtained in each of the first ten tasks of the RBHT 

program is given below. 

Task 1 - Development of a Preliminary Phenomena Identification and Ranking Table 

To aid in the development for the experimental requirements of the RBHT facility, a Preliminary 

PIRT was developed, focusing on the low pressure reflood portion of the PWR and BWR LOCA 

transients. The objective was to sub-divide the phenomena down to the lowest level by which a 

best-estimate computer code would calculate these phenomena. With the phenomena broken 

down, the capabilities of the proposed test facility were assessed to determine which could be 

measured with confidence, which could only be qualitatively measured, and what 

instrumentation would be needed. 

The phenomenon in the core region is of most interest since the core thermal-hydraulic 

response determines the resulting peak cladding temperature (PCT). In PWR reflood 

calculations, the core is reflooded by the gravity head of water in the downcomer. This gravity 

head refloods and quenches the core, at a rate determined by the venting of steam and water 

which exits the top of the core. The core heat transfer response is a dependent parameter 

since it depends on the gravity flow into the core and, the ability of the reactor system to vent 

the two-phase mixture. 
xxv

The approach for developing the Preliminary PIRT for the core region is based on examining the 

FLECHT-SEASET test data and analysis. Six regions of interest within the core during 

reflooding have been identified. These include: 

1) the single-phase heat transfer region below the quench front, 

2) the subcooled and saturated nucleate boiling region below the quench front, 

3) the quench front region, 

4) the froth region above the quench front, 

5) the dispersed flow film boiling region above the froth region, 

6) the topdown quench front. 

At the bottom of the fuel rod (or heater rods in the experiment), the heat transfer is by single 

phase forced or natural convection. As the coolant temperature approaches the saturation 

temperature, subcooled nucleate boiling occurs and eventually saturated boiling. The quench 

front region is the next region of interest. At this point, the stored energy from the fuel/heater 

rods is released into the coolant which results in significant steam generation. The result of the 

steam generation at the quench front produces a two-phase froth mixture which entrains liquid 

flow. The froth region above the quench front is the location where the steam generated from 

the quench front acts to shear the liquid flow into liquid ligaments and eventually into a spectrum 

of droplets which are then entrained upward. 

Above the froth region, the flow field consists of entrained droplets in a superheated steam flow. 

This is the heat transfer regime where the calculated PCT typically occurs. It is a region of low 

heat transfer since the vapor sink temperature is superheated and can approach the rod surface 

temperature. Since cladding temperatures are high, radiation heat transfer to surfaces, droplets 

and vapor must be accounted for. 

At the very top of the rod bundle, there can be a top quench front which moves down the 

fuel/heater rod. The movement of the top quench front depends on the amount of liquid 

entrainment in the flow and the power profile of the fuel/heater rod as well as the previous 

blowdown heat transfer history. The top quench occurs at elevations which are significantly 

above the location of the PCT so its behavior does not influence the PCT value. However, the 

top quench front is related to the amount of liquid which leaves the core and may affect the 

overall reflood system behavior. 

Separate preliminary PIRTs were developed for each of these six regions such that the 

particular phenomena for a particular region could be subdivided into specific component 

models which a computer code would be used to perform the calculation. The same ranking 

method as that employed by Los Alamos National Laboratory is used to denote the relative 

importance of the "High", "Medium", and "Low" phenomena. The highly ranked phenomena that 

were identified for the PWR transient are listed in six separate PIRT tables, one for each of the 

six regions of interest. To be complete, the tables also contain medium and low-ranked 

phenomena. These PIRT tables were used to develop and guide the design of the RBHT 

facility and to structure the instrumentation plan for the single phase convection tests, radiationonly tests, dispersed flow heat transfer tests (i.e., droplet injection tests), and the forced reflood 

tests. A separate PIRT table is also presented for the gravity or variable flow reflood transients. 

Nearly all the phenomena identified with rod bundle heat transfer for PWRs are applicable to the 

hot assembly in a BWR since it refloods in a similar manner. However, one difference between 

the reflooding behavior of the high power BWR assemblies and a PWR assembly is the 
xxvi

presence of the fuel assembly shroud in the BWR design. The shroud is calculated to quench 

from the liquid in the bypass region such that there is additional surface-to-surface radiation 

heat transfer occurring in the BWR fuel assembly as compared to a PWR fuel assembly. The 

additional surface-to-surface radiation can be simulated in the RBHT experiments since the test 

facility will have a shroud around the test bundle. There is also surface-to-surface radiation 

within a PWR fuel bundle, due to colder guide tube thimbles. The RBHT bundle simulates a 

Westinghouse or Framatome fuel assembly with smaller thimbles. A Combustion Engineering 

fuel assembly design would have larger guide tube thimbles. The difference in the radiation 

heat transfer can be calculated. Since the high power BWR fuel assemblies are in co-current 

upflow, similar to PWR fuel assemblies, the key thermal-hydraulic phenomena identified as 

being highly ranked for PWR are also highly ranked for the BWR design. (The one factor which 

would change is the surface-to-surface radiation heat transfer in the dispersed flow film boiling 

regime is a higher ranked phenomenon for the BWR application as compared to the PWR 

application.) 

The ability of the proposed RBHT facility to simulate the highly ranked PWR and BWR PIRT 

items has also been assessed and it has been found that the test facility can represent nearly all 

the phenomena of interest. The areas where the simulation is the weakest is in the materials 

used for the cladding, heater rods and the housing, as compared to nuclear fuel rods and a 

BWR Zircaloy channel box. Scaling studies have been performed as part of the program to 

select the materials such that the deviation from the true plant design is minimized. 

Task 2 - Critical Review of Existing Experimental Data Base 

A number of important rod bundle experiments have been reviewed to determine the availability 

of data, test facility design, types of tests, instrumentation, and data from tests. These rod 

bundle experiments include FLECHT Cosine Tests (NRC/Westinghouse), FLECHT Skewed 

Axial Power Shape Tests (NRC/Westinghouse), FLECHT-SEASET 21 Rod Bundle Tests 

(NRC/Westinghouse), FLECHT-SEASET 161 Unblocked Bundle Tests (NRC/Westinghouse), 

FEBA Reflood Tests (Germany), THTF Rod Bundle Tests (NRC/Oak Ridge National Lab), 

FRIGG Rod Loop Tests (Sweden), GE 9-Rod Bundle Tests (General Electric), NRC/NRU Rod 

Bundle Tests (Canada), ACHILLES Reflood Tests (Great Britain), NRC/Lehigh 9-Rod Bundle 

Tests (Lehigh University), and PERICLES Reflood Tests (France). In addition to the above rod 

bundle tests that are included in the first portion of the review, more than three hundred articles 

on single tube tests and related studies have been included in the second portion of the review. 

The relevant information is sub-divided into 10 different classifications. These include: 

1) liquid entrainment and breakup, 

2) drop size distribution and droplet number density, 

3) interfacial shear and droplet acceleration, 

4) droplet-enhanced convective heat transfer, 

5) droplet evaporative heat transfer, 

6) direct contact heat transfer, 

7) total wall heat transfer, 

8) effects of spacer grids, 

9) effects of variable inlet flow, and 

10) thermal non-equilibrium, and other factors. 

From the literature survey, it was found that there are large differences between the data 

obtained from the rod bundle tests and those from the single tube tests. The RBHT test facility 
xxvii

is designed specifically to address this data deficiency. The RBHT program will aim at obtaining 

not only wall-to-fluid heat transfer correlations but also models for interfacial heat transfer. To 

develop and assess models for interfacial phenomena with the goal of significantly improved 

accuracy and to minimize the potential for compensating errors will require a new or improved 

database that includes more detailed information than is currently available. The specific needs 

for new or improved data are described below: 

1. In dispersed flow film boiling, the primary heat transfer mechanism is convective heat 

transfer to superheated steam. It is now recognized that the steam convective heat transfer 

coefficient can be enhanced by up to 100 percent due to the presence of entrained droplets. 

No suitable models currently exist for this phenomenon. The combination of single-phase 

convection experiments and two-phase convection experiments with droplet injections (with 

known drop sizes and flow rates) to be performed in the RBHT test facility will provide 

important new data and result in the development of the needed model. 

2. Once the uncertainty involving droplet-enhanced heat transfer is resolved, there still 

remains the difficulty in predicting the heat transfer rate for the dispersed flow film boiling 

(DFFB) regime due to the difficulty in calculating the steam superheat. The amount of 

steam superheat is governed by the interfacial heat transfer between the steam and the 

evaporating droplets. To correctly calculate the interfacial heat transfer requires the 

knowledge of both the entrained drop size and the droplet flow rate. There is very little data 

of this type currently available for quenching rod bundles. The RBHT program will generate 

the needed database through advanced instrumentation involving the use of a laser 

illuminated digital camera system to determine the entrained drop size and measure the 

droplet flow rate. 

3. Although data showing the effects of spacer grids are available, the phenomenon is still 

not completely understood. In particular, the separate-effects of spacer grids for interfacial 

shear in rod bundles at low pressures, in dispersed flow film boiling, and in transition boiling 

heat transfer during reflood, are not known. It is necessary to determine the grid geometry 

effects. The RBHT program, which will explore two or more types of space grids and will 

perform heat transfer measurements in various flow regions at locations just before and 

after the spacer grids, will greatly augment the database needed for modeling the spacer 

grid effects. 

4. There is insufficient data on transition boiling heat transfer during quenching in rod 

bundles. This is especially true regarding the minimum film boiling temperature. For reflood 

conditions where precursory cooling is important, the transition regime is responsible for the 

final quench which influences the quench front propagation. The emphasis of the RBHT 

program to measure the local values of the void fraction in the quench front region will 

provide the much needed database. 

5. When the flow at the quench front is subcooled, an inverted annular film boiling (IAFB) 

regime would develop immediately downstream of the quench front. The liquid-rich region 

provides the precursory cooling that controls the quench front velocity and provides the 

source of vapor and entrained liquid for the DFFB region. It has been demonstrated that 

many of the apparent functional dependencies for the IAFB regime are primarily due to the 

axial profile of the void fraction in this region. Currently available data for this regime in rod 

bundles is insufficient for model development due to the coarse spacing used for the void 

fraction measurements. The RBHT program will address this data need through the use of 
xxviii

finely spaced differential pressure cells and by a local void fraction measurement provided 

by a low energy gamma-densitometer. 

6. The heat transfer rate in the IAFB region increases rapidly with liquid subcooling. Higher 

subcooling promotes heat transfer to the liquid core and reduces vapor generation and the 

thickness of the vapor film, thus enhancing heat transfer. It is traditional to formulate reflood 

test matrices by fixing the inlet subcooling and then vary the inlet flow rate. This procedure 

does not provide a true single parameter variation needed for model development at the 

subcomponent levels. In the RBHT program, non-traditional procedures involving fixing 

either the local subcooling or the mass flux at constant values at the quench front will be 

done by choosing appropriate combinations of the inlet flow rate and subcooling in the 

planned experiments. This will provide important new data not available heretofore. 

7. The database in the nucleate boiling regime for void fraction (i.e., interfacial shear) in rod 

bundles at low pressure conditions has been identified as a code deficiency during the 

AP600 code applicability program. Some data exist or can be calculated from other reflood 

test data after the bundle has quenched. The RBHT will be conveniently used to generate a 

database with systematic variation of parameters that would greatly aid model development 

and assessment. 

The various technical issues discussed above provide clear justifications for the need for 

developing the RBHT facility. Separate-effects tests will be performed in this facility to obtained 

new or improved data for model development and code validation at the most fundamental 

subcomponent levels practicable. 

Task 3 - Defining Information Needed for New Code Modeling Capabilities, Validation, and 

Assessment. 

The modeling capabilities of the best-estimate codes including RELAP5/MOD3, TRAC-B, 

TRAC-P and COBRA-TF systems computer codes have been examined. All of these codes 

attempt to predict a transient boiling curve for a heated surface with internal heat generation for 

a given surface temperature and the fluid conditions adjacent to the surface such as the 

pressure, void fraction, vapor temperature and mass flow rate. The calculated boiling curve is 

generated by combining different individual heat transfer correlations which model one specific 

phenomenon such that a continuous calculation can be performed, as the fluid conditions 

change, the boiling curve predicted by the computer code also changes as some phenomena 

become larger and others become smaller such that the calculated surface heat transfer 

coefficient between the coolant and the heated surface may result in the surface heating-up to 

higher temperature, or the surface cooling down to a lower temperature. 

Individual empirical or semi-empirical heat transfer correlations are used to calculate the local 

heat transfer behavior from the heated surface to the fluid. The difference between the 

empirical and semi-empirical correlations is meant to indicate the degree to which the true 

physical condition is modeled by the correlation. Most correlations are usually empirical, that is, 

derived from a specific set of data, and predict a single phenomenon, or several phenomena in 

parallel. These correlations are often applied to conditions and geometries which were not 

included in the original basis for the correlation when performing reactor safety analysis. The 

heat transfer correlations may also require some modifications to make the correlation 

consistent with the numerical solution scheme of the code such that rapid calculations can be 

performed in a reliable fashion. Such modifications can result in essentially a different 
xxix

correlation than was originally developed. The process of combining different individual specific 

correlations can lead to compensating errors, in which one calculates the “right” answer for the 

wrong reason because there are multiple errors in the calculational scheme. The heat transfer 

correlations, which comprise the calculated boiling curve, are also usually based on test data 

which is scaled relative to the reactor system. The resulting reactor systems code is also 

validated against scaled systems experiments. Therefore, one must address the effects and 

uncertainties of applying the correlations which are developed from scaled data to the analysis 

of a full scale reactor system. 

While each code had the basic models for a boiling curve, and thermal and mechanical nonequilibrium, as well as the use of particular sets of heat transfer correlations, the COBRA-TF 

thermal-hydraulic formulation and additional detailed component models makes this code an 

attractive choice to refine reflood development. COBRA-TF can be used on a sub-channel 

basis to model the limiting hot fuel pin in a rod bundle. COBRA-TF is also a three field 

formulation with an explicit entrained liquid field and a corresponding interfacial area transport 

equation which permits more accurate modeling of the entrained liquid phase, which is most 

important for calculating dispersed flow film boiling. Using the unique representation of the third 

field or entrained droplet field results in more accurate predictions of flow regimes, their 

transition, and the resulting heat transfer in the different regimes. There is also believed to be 

less of a chance of compensating error since one is not adjusting a two field model to represent 

the effects of three fields. Specific attention has been spent in the COBRA-TF dispersed flow 

heat transfer model to account for the different component models which represent "reflood" 

heat transfer. Fine mesh renodalization for the heated conductors is used to better represent 

the quench front, the two-phase convective enhancement is accounted for in the calculations 

and a subchannel radiation model is used to more accurately represent radiation within a rod 

bundle. COBRA-TF also models the effects of spacer grids in the dispersed two-phase flow in a 

mechanistic manner accounting for the convective effects of spacer grids, the spacer grid 

quenching behavior and the droplet breakup caused by spacer grids. In particular, a small 

droplet field has been added to COBRA-TF to model the heat transfer effects of the much 

smaller drops as they evaporate and provide additional cooling downstream of the grids. 

Compensating errors, however, remain an important issue in using COBRA-TF to predict the 

large-break LOCA transient. In view of this, complete sets of valid test data and the associated 

data analysis are needed to improve the specific models in the computer code to insure that 

compensating errors are minimized, the heat transfer models are applicable at full scale with 

acceptable uncertainty, and the implementation of the correlations into the code do not change 

the nature or predictability of the original correlation. 

The formulation of the COBRA-TF code, as developed as part of the FLECHT-SEASET 161 

Blocked Bundle Program, has the desired basic structure to develop the improved component 

models needed for dispersed flow film boiling in reflood. The RBHT program will utilize 

COBRA-TF for modeling purposes, and predictions and model validation purposes in the 

development of improved reflood models. 

Task 4 - Defining the Program Objectives and Facility Mission. 

The results of Task 1, 2, and 3 have identified the phenomena of interest and the existing data 

base for reflood component model development and validation over the range of conditions of 

interest. Improved analysis models are the objective of the RBHT program. The needs define 
xxx

the specific mission of the test program as well as the analysis efforts which will compliment the 

experiments. 

The objectives of the RBHT program are to: 

1. Develop a Phenomena Identification Ranking Table for reflood heat transfer on a 

component model level and estimate the relative importance of each phenomenon for 

predicting reflood heat transfer, 

2. Develop a test facility design which has a minimum of distortion to represent reflood heat 

transfer in PWR and BWR cores, 

3. Assess the needs of best-estimate computer codes on their modeling approaches for 

reflood heat transfer and the component models used in the computer codes, 

4. Perform component experiments which isolate individual phenomena that influence 

reflood heat transfer, 

5. Determine the effects of the fuel assembly spacer grids on the dispersed flow film boiling 

heat transfer of the grid, 

6. Develop specific component models from these experiments, 

7. Add the component models into a best-estimate computer code and compare to the 

forced reflood heat transfer data from this series of experiments as well as other sets of 

reflood heat transfer data, 

8. Validate the new proposed component reflood heat transfer models over their range of 

application, 

9. Document the results of the experiments and analysis in a form that it can be used by 

others. 

The first three objectives have already been met by performing the tasks described in this report 

whereas the last six objectives will be achieved by the conduct of specifically directed 

experiments, development of physically based heat transfer models and implementation of 

these models into a best-estimate code. 

The proposed experiments will be performed in a building block approach such that the more 

complex experiments occur after the more fundamental experiments. In this fashion, additional 

information and desired test conditions can be modified as needed to optimize the test matrix of 

the forced reflooding tests which are the most difficult tests to perform. The proposed 

experiments will provide new data as well as supplement existing reflood heat transfer data but 

they will focus on the improvements of specific best-estimate thermal-hydraulic models rather 

than identifying licensing margin. 

To achieve the objectives of the experiments and to capture the important thermal-hydraulic 

phenomena which have been identified for reflood heat transfer, several new or novel 

approaches are proposed for the bundle instrumentation. 
xxxi

Experiments will be performed using new instrumentation to isolate a specific phenomenon as 

best as possible so as to permit specific model development for that phenomenon. In this 

fashion, the risk of introducing compensating error into the advanced reflood model package 

can be minimized. 

Task 5 - First Tier Scaling Analysis for the Local Phenomena 

The combined Zuber-Wulff scaling approach which is the current state-of-the-art methodology 

for scaling thermal-hydraulic systems, has been used to assess the ability of the RBHT facility to 

capture the phenomena of interest for the reflood phase of a LOCA transient such that the data 

can be used with confidence to verify and develop heat transfer and two-phase flow models for 

best-estimate thermal-hydraulic computer codes. In addition to verifying that the test facility can 

produce the desired data, the two-tiers scaling process also identifies possible distortions in the 

test facility relative to the nuclear reactor core and will provide a numerical assessment of the 

importance of the possible distortion. 

There are three equations which are examined in the first-tier "top-down" systems scaling for 

the RBHT facility: these are the fluid energy equation, the solid energy (heater rod, fuel rod) 

equation and the fluid momentum equation. Each conservation equation is derived in the 

fashion as recommended by Zuber and Wulff, the equations are normalized and the terms are 

divided by the "driver term" such that the resulting Pi groups are dimensionless. This approach 

is applied to both the RBHT facility as well as to a PWR and a BWR fuel assembly to indicate 

the non-typical effects and distortions in the test facility relative to the actual plant component. 

The fluid energy equation, which represents the energy balance for the fluid in the entire bundle 

at a given time, includes 23 Pi groups. These Pi groups can be categorized into quench energy 

terms, convective heat transfer terms, and radiative heat transfer terms. In general, the stored 

energy, the rod quench energy, the convection from rod to vapor, the interfacial heat transfer 

and the flow energy terms are of significance. On the other hand, the values of the radiation Pi 

groups are negligibly small, thereby indicating the predominance of convection over radiation 

heat transfer. Though the rod quench energy term is significant, the housing, grid and the guide 

tube thimble rod quench energy terms are small. 

The rod energy equation includes 13 Pi groups, among which the significant terms are the 

convective heat transfer to the surrounding fluid, the radiation from hot rod to the cold rods and 

radiation to entrained drops. Property differences exist between the electrical rod and the 

nuclear rod exist and hence the Pi groups involving the properties of the rods are different. 

The flow momentum equation Pi groups, which involved eight terms, are calculated using the 

given inlet conditions of 0.27 MPa (40 psia), 60 degrees C (140 degrees F) subcooling, and 

flooding rate of 0.0254 m/s (1 in/s) with the known value of flow area. The inlet is assumed to 

be single phase and the exit is dispersed two-phase mixture. The quench front is assumed to 

be at 1.22 m (4 ft) elevation and there are two grids that are covered with water, therefore there 

are six grids in the two phase region. Hydraulic diameter is calculated based on the wetted 

perimeter and flow area. Based on this hydraulic diameter, the Reynolds number and the single 

phase friction factor are calculated. Results indicate that the only important Pi group is the term 

representing the liquid gravity head. 

In summary, it is found that the presence of a test housing leads to extra Pi groups for this 

structure relative to modeling of a PWR fuel assembly, thereby indicating that distortion in the 
xxxii

test is possible. The test facility is actually a closer representation to a BWR fuel assembly 

which also has a Zircaloy shroud surrounding the fuel rods. Therefore, for code modeling and 

validation purposes, the effect of the test housing will have to be modeled including the rod-torod and rod-to-housing radiation heat transfer. The housing effects will also have to be 

considered in the analysis of the test data such that the radiation effects can be determined. 

The housing had a less important effect on the fluid momentum equation since it only affected 

the hydraulic diameter and resulting fluid Reynolds number and friction factor such that the 

frictional component of the fluid pressure drop would be somewhat larger than a PWR fuel 

assembly. Since the majority of the pressure drop in the bundle is due to the spacer grid form 

losses and the elevation head, and since prototypical grids are used in the test bundle, the 

hydraulic distortion is negligible. 

There also can be some difference in the PWR/BWR Pi groups relative to the test due to the 

material differences. These effects are believed to be relatively small and can be accounted for 

in the analysis of the data. Comparisons of the derived Pi groups for the test and a PWR and a 

BWR fuel assembly indicate that if prototypical fluid conditions are used in the tests, and the 

bundle geometry is retained, there is a very strong similarity between the bundle and the PWR 

and BWR fuel assemblies and the data should be applicable to either reactor fuel assembly 

type. 

Task 6 - Second Tier Scaling Analysis for the Local Phenomena. 

In the second-tier "bottom-up" scaling approach, analysis was performed to determine the 

radiation heat transfer effects of the test section housing relative to an infinite size rod bundle. 

These calculations would tend to over-emphasize the distortion of the test relative to a PWR fuel 

assembly. For a BWR fuel assembly, the BWR fuel assembly channel is very similar to that of 

the RBHT facility such that the distortion would be less. 

Calculations were also performed modeling a fuel rod, with its properties and the fuel-pellet gap 

as well as the electrical heater rod, to determine the heat released at quench as well as the 

stored energy effects and maximum temperatures and radial temperature distributions. A stepchange transient in the fluid temperature was combined with the rod power being kept constant 

during the transient. 

The effect of difference in the cladding material on the value of Tmin was assessed by 

comparing Inconel and Zircaloy cladding quench data from different tests. These comparisons 

indicate that there is a bias in which the Zircaloy cladding would be expected to quench at a 

higher temperature relative to stainless steel or Inconel cladding. 

One of the main distortions of the RBHT facility, when compared to a PWR fuel assembly, is the 

presence of the housing which represents a heat sink for the radiative heat transfer from the 

rods. The housing can also be a heat source for the fluid later into the transient because of the 

release of its stored energy during the quenching period at a given elevation. In order to 

address housing behavior in more detail, a rod-to-rod, rod-to-housing radiation heat transfer 

model based on the MOXY computer program was developed. 

Another issue which arose from the scaling analysis is the rod material differences. The 

electrical heater rods use Inconel-600 instead of Zircaloy for the clad, and Boron Nitride is used 

instead of Uranium Dioxide. The electric power is generated only in an annulus area inside the 
xxxiii

rod made of Monel K-500 coil. Another difference is the gap conductance which is assumed to 

be 5.678 kW/m2

-K (1000 Btu/hr-ft2-F) for a nuclear rod and 28.39 kW/m2-K (5000 Btu/hr-ft2-F) 

for the electrical rod. A detailed analysis was performed to quantify the transient temperature 

response distortion of an electrical rod when compared with a nuclear rod. 

Results of the second-tier scaling indicate that the housing acts as a radiation and convection 

heat sink for the fluid and heater rods, as well as a heat source to the fluid as the housing 

quenches. The presence of the housing induces a radial temperature distribution across the 

bundle, which in turn causes energy to flow from the inner portion of the bundle to the housing. 

As a result, during the transient the temperature in the inner region of the RBHT bundle is lower 

than the temperature in an ideal case where the housing is not present such as in a PWR 

bundle. The effect of the housing is less important for a large bundle since the inner region is 

shielded by the outer region of the bundle. Sensitivity analyses have been carried out to 

quantify the housing distortion for different bundle sizes starting from a 5x5 bundle up to a 

11x11 bundle. The distortion decreases significantly when the bundle size is increased from 

5x5 to 7x7 while for further increases the distortion reduction becomes less and less significant. 

A 7x7 bundle size appears to be a good compromise in the attempt to reduce costs and scaling 

distortions at the same time. In this case the maximum temperature distortion in the inner 3x3 

rods array respect to an infinite (no-housing) bundle is about 121 degrees C (250 degrees F). 

The second-tier scaling analysis shows the sensitivity of other parameters such as housing 

thickness, housing initial temperature, surfaces emissivity, radial power distribution and dummy 

rods contribution. These are generally second order effects and the temperature in the center 

region of the bundle changes by 10 degrees C (50 degrees F) at most. The material differences 

between the electrical heater rods and the nuclear rods, which also include a gap between the 

fuel pellet and the cladding, is the second major facility distortion. The analysis shows that the 

quench time can be affected by these parameters especially by the material difference. Starting 

from the same temperature, the nuclear rod is expected to quench almost in the same time 

interval since the average thermal inertia of the electrical heater rod is very close to the 

corresponding value for the nuclear rod. The separate effect of the gap heat transfer coefficient 

is small. In addition, differences of the cladding material on the value of Tmin were assessed by 

comparing Inconel and Zircaloy cladding quench data from different tests. These comparisons 

indicate that there is a bias in which the Zircaloy cladding would be expected to quench at a 

higher temperature relative to stainless steel or Inconel cladding. 

Task 7 - Defining the Instrumentation Requirements. 

The objective of the RBHT program is to provide data on the key thermal-hydraulic phenomena 

of interest for dispersed flow film boiling and reflood heat transfer. To accomplish this objective, 

specific instrumentation requirements have been developed such that the experiments will 

provide the data needed. One major requirement is the detailed measurements of the void 

fraction, droplet size, droplet velocity, as well as the local heat transfer from the heater rods. 

The liquid entrainment at the quench front and the resulting droplet field downstream are 

responsible for the improved cooling at the upper elevations in the rod bundle where the peak 

cladding temperature occurs. Most computer codes have difficulty predicting the correct 

amount of liquid entrainment as well as the timing of the entrainment. The instrumentation used 

in the RBHT program should help resolve this modeling issue for best-estimate computer codes. 

The guideline for the RBHT tests is that the instrumentation should allow transient mass and 

energy balances be performed on the test facility. The inlet flow, pressures, and coolant 
xxxiv

temperatures will be measured for each type of experiment. The outlet vapor flow, pressure, 

and liquid flows will also be measured. Since the reflood tests are transients, there will be mass 

accumulation within the bundle. The mass accumulation will be measured using sensitive 

differential pressure cells with fine axial spacing. 

Using the inlet and exit measurements as well as the measured axial heat flux distribution into 

the coolant, the actual quality distribution along the bundle, can be obtained above the quench 

front and the amount of liquid evaporation can be calculated from the data. In a similar fashion, 

the void distribution along the heated bundle can also be determined to indicate the flow and 

heat transfer regimes in the bundle and will be used to correlate the measured heat transfer 

data. The differential pressure drop measurements will have to be corrected for the frictional 

pressure drop as well as any acceleration pressure drop to infer the local void fraction. Since 

the actual quality is non-equilibrium, measurements of the true vapor temperature are needed 

as well as the wall heat flux into the fluid. There will also be ample miniature thermocouples 

placed into the different subchannels along the axial length of the bundle. In addition, since the 

spacer grids can promote improved cooling downstream of the spacer, fluid thermocouples will 

also be placed in these locations. A local quality can be calculated wherever a local vapor 

temperature is measured in the bundle. 

The fuel rods will be simulated using electrical heater rods which will have the power capability 

of simulating the reactor decay power at 20 seconds following reactor scram. These rods will 

have an internal heating coil with a prescribed axial power shape which is representative of 

those shapes calculated in Best-Estimate LOCA analyzes. There will be eight thermocouples 

placed in the rod such that all the rods will fully cover the complete axial length of the bundle. 

There will be thermocouples at specific elevations to obtain the radial temperature profile in the 

bundle. The total measured heat flux will be calculated from an inverse conduction calculation 

using the measured thermocouple data. In addition, these experiments are designed for 

computer code validation purposes. Therefore, there will be a specific arrangement of the 

thermocouples and the differential pressure cells within the bundle, such that the heat transfer 

data can be correlated with the local void fraction. 

In addition to the heat transfer behavior and the vapor and structure temperatures, direct data is 

needed on the flow behavior in the test bundle. In the froth or transition region, data on the local 

void fraction distribution, interfacial area, droplet/liquid ligament size are lacking. Also in the 

dispersed flow regime, data are needed on the droplet size, velocity, and number density is also 

needed for the wall-to-drop radiation heat transfer, and the vapor-to-drop radiation and 

convective heat transfer. The facility will characterize the flow regime in the froth region where 

the liquid changes from a continuous liquid flow into a dispersed droplet flow. Therefore, the 

test section has windows which will permit viewing and photographing the flow at important time 

periods in the transient. 

In addition to the fine axial mesh of the differential pressure cells along the length of the bundle 

and across the spacer grids for void fraction measurements, a soft gamma ray measuring 

devise will also be used at selected fixed elevations along the lower portion of the bundle. The 

gamma densitometer will give chordal average densities of the two-phase flow mixture as the 

flow regime changes from a dispersed droplet flow to the froth region and finally to solid water. 

In the RBHT program, a pulsed laser technique will be used in conjunction with a fine grid digital 

camera to obtain drop sizes and droplet velocities. The pulsed laser will provide the 

backlighting as well as the focus volume for pictures in the center subchannels of the rod 

bundle. This measurement technique has software which will allow the determination of the 
xxxv

droplet spectrum, Sauter mean drop size, droplet velocities, and an estimate of the droplet 

number density. These data can be used to calculate the interfacial area of the entrained 

droplet phase. The pulsed laser and digital camera technique has not been applied to reflood 

experiments before. Therefore, to verify the performance of the system and confirm the 

accuracy of the measurements, a series of "bench-top" experiments have been performed with 

the new instrumentation and to develop the data reduction and analysis programs to analyze 

the droplet data. 

With the proposed instrumentation plan, nearly all the highly ranked phenomena will be directly 

measured or directly calculated from the experimental data. When a parameter is directly 

calculated from the experimental data, the calculation uses the transient mass and energy 

balance on the test section to calculate the fluid properties, there is no use of a best-estimate 

computer code at this stage of the analysis such that the data analysis is independent of any 

computer code which may be validated by the experiments. The use of the various techniques 

described above provides a robust instrumentation plan for the RBHT program. 

Task 8 - Developing Facility Input Model. 

The COBRA-TF computer code was used to model the RBHT facility. The purpose of this 

analysis is to perform pre-test calculations to obtain information about the range of the 

parameters to expect during reflood transient. This analysis will also provide basis to develop 

the test matrix and will indicate the maximum temperature conditions reached in the bundle for a 

given set of conditions. 

The COBRA-TF code was developed at the Pacific Northwest Laboratory under the sponsorship 

of NRC to provide the best-estimate thermal-hydraulic analyses of LWR vessel during LOCA 

accidents. The two-phase flow is described with a two-fluid, three-field model. Thermal 

radiation and grid spacer effects are also included in the code as well as a more detailed 

dispersed flow film boiling model as given in Section 4 of this report. The code was developed 

for use with either rectangular Cartesian or sub-channel coordinates. Herein the sub-channel 

scheme is adopted since it is more suitable for complex and irregular geometries. 

Two COBRA-TF models of the RBHT test facility were developed including a two-channel 

model and a more detailed individual sub-channel model. The two-channel model is being used 

to examine the local fluid conditions within the test facility so as to compare them to those 

conditions which are typically predicted in safety analysis calculations for a plant. This model 

does not account for the rod-to-rod or the rod-to-housing radiation heat transfer from the inner 

channel which exists in the test bundle. The model does account for the test section housing 

and calculates the convection heat transfer to the housing as well as the energy released from 

the housing as it quenches. 

The two-channel analysis considered a 7x7 rod array comprised of 45 heater rods, four 

unheated rods, and the surrounding housing. The facility modeling approach was to divide the 

test facility into four sections and five fluid regions, representing the lower and upper plenums, 

the initial unheated length of the rod bundle, the actual heated length of the rod bundle, which 

contains two fluid channels. The inner channel encompasses a total of sixteen ‘hot’ rods; this 

includes the nine center rods and summation of the fractional parts of the rods that lie on the 

channel’s boundary. The second channel is comprised of the remaining twenty-nine heater 

rods, the four unheated rods and the housing. 
xxxvi

Three flooding transients have been considered in the analysis with different flooding rates: 

0.0203, 0.0254 and 0.0381 m/s (0.8, 1.0 and 1.5 in/s). A constant pressure, 0.27 MPa (40 

psia), is set in the upper plenum and the water inlet subcooling is 49 degrees C (120 degrees 

F). Results of the analysis show that the vapor Reynolds number can be in the laminar, 

transition and turbulent flow regimes. In addition, the Weber number could vary from 7.4 just 

above the quench front to 3.9 at the top of the bundle. 

A more detailed, 1/8th sector of the test facility has been modeled on a sub-channel basis with 

each sub-channel uniquely modeled along with each individual surface on the heater rod and 

the gap between rods. The subchannel capability of the COBRA-TF code allows more accurate 

representation of smaller rod bundle arrays since each individual rod can be modeled, each with 

different surfaces for radiation heat transfer, such that the rod-to-rod and rod-to-housing 

radiation heat transfer can be more accurately modeled. In this fashion, the radial temperature 

gradient which develops due to the radiation heat losses to the test section housing can be 

simulated. There are specific experiments planned in the RBHT program which will examine 

the radiation only heat transfer within the rod bundle and to the test section housing. 

The sub-channel model uses the same power profile and linear power densities as the twochannel model, the peak linear power being at 2.743m (108 in) and 2.3 kW/m (0.7 kW/ft). The 

axial noding of the test section is identical to the two-channel model. A plenum is modeled at 

the top and bottom of the test section to provide the inlet and exit boundary conditions. An 

intermediate section with three channels is used to link the test section to the plena because 

COBRA-TF does not allow more then six channels to be directly linked to one channel. 

To determine the effect of the housing on the bundle temperature distribution, the sub-channel 

model was run with and without the ten radiation channels. The inlet conditions were set to zero 

such that the bundle was heated in an adiabatic manner in a stagnant steam environment. 

However, as the bundle was heated, steam convective current developed and steam was 

released from the top pressure boundary to maintain the system pressure at 40 psia. Also, the 

bundle underwent convective heat transfer from the hot rods to the unheated surfaces because 

natural circulation paths were set in motion between grid spans. Results show that the 

outermost row of the rod bundle is quite effective in shielding the remainder of the rods. The 

temperature of the central 5x5 array of rods is practically uniform with the maximum 

temperature difference less than 200 degrees C. 

Task 9 - Drafting a Test Matrix. 

A test matrix for the planned RBHT tests has been developed for each type of planned tests. 

The range of conditions is given and the objectives for the proposed tests are described in 

detail. Some of the proposed tests have been compared to the conditions and types of previous 

rod bundle tests to show how the proposed tests overlap and complement the existing data 

base. The strategy in developing the test types and test matrix will be to use a "building block" 

approach in which simpler experiments are performed first to quantify a particular heat transfer 

mechanism alone and then the additional complications of the two-phase flow film boiling 

behavior of the test facility are added in later experiments. The proposed test conditions and 

fluid conditions also bracket those conditions which would be calculated for a postulated LOCA. 

The types of tests which are proposed for this program include: 

1. Steady-state liquid flow characterization tests to determine the rod bundle frictional 

pressure drop and the spacer grid loss coefficients. 
xxxvii

2. Heat loss experiments which characterize the facility heat loss to the environment. 

3. Radiation only tests with an evacuated rod bundle. These tests will be performed over a 

range of rod bundle powers to achieve a wide range of heater rod surface temperatures, 

characteristic of those expected for dispersed flow film boiling. The objective of these 

experiments will be to confirm the proper emissivities to be used to characterize the rod 

bundle and housing surfaces as well as to verify that the outer row of heater rods effectively 

shields the inner 5x5 rows of rods. 

4. Subcooled and saturated boiling experiments at low flows and low pressure to validate 

existing boiling correlations for these conditions for rod bundles. The experiments will be 

conducted in a steady-state manner and the heat transfer and void distributions will be 

measured along the rod bundle. 

5. Convective steam cooling tests over a wide range of Reynolds numbers to determine the 

single phase convective heat transfer in superheated steam. These tests will be to 

characterize the single phase convective heat transfer cooling separately without the 

complications of a dispersed droplet field. 

6. Steam cooling tests with injected droplets of known initial sizes and velocities at the 

entrance of the test bundle. The objective of these experiments will be to examine the heat 

transfer effects of a highly dispersed phase of entrained liquid droplets, on the convective 

heat transfer within the rod bundle. These tests will be performed under quasi-steady 

conditions such that the Laser-Illuminated Digital Camera Systems (LIDCS) can be used at 

carefully selected elevations to track the droplets and measure their size and velocity 

distributions, such that the change of the droplet interfacial area can be measured and 

compared to predictions. These tests represent a unique contribution to the rod bundle 

dispersed flow film boiling literature. 

7. Forced reflooding experiments will be performed which will overlap and compliment with 

the existing data base. The forced reflooding tests will also overlap the steam cooling and 

the droplet injection two-phase experiments. The forced reflooding experiments will contain 

all the elements of the experiments performed earlier with the additional complications of the 

heater rod quench front movement, quench heat release, and the generation of the 

entrainment heat transfer effects expected for reactor conditions for a prescribed set of initial 

and boundary conditions. The focus of these experiments is to examine the generation of 

the entrainment at the quench front and within the transition region. 

8. Simple gravity reflood experiments or variable inlet injection experiments will also be 

performed. These experiments will examine the system response on the inlet flooding rate 

into the test bundle and the resulting heat transfer within the bundle. 

The ranges of conditions for the experiments will cover the current ranges of conditions which 

best-estimate and Appendix K reflood models are required to calculate. The precise test 

conditions are not given since there is a need to perform pre-test predictions so as to select the 

range of rod powers and initial temperatures to provide the data needed while at the same time, 

to minimize the duty on the heater rods. However, the facility design envelope is sufficiently 

broad such that the tests can be performed over a wide range of initial and boundary conditions. 
xxxviii

Rather than the usual approach of marching blindly through a pre-determined matrix to meet the 

program's milestones, the test matrix for the RBHT program will remain flexible so that it can be 

responsive to model development needs. Although the proposed test matrix is somewhat nonspecific, the various types of tests have been carefully structured. These include a well-defined 

progression from bundle characterization (pressure drop and heat loss experiments) to 

radiation-only tests, single-phase heat transfer tests, quasi-steady dispersed flow heat transfer 

tests (i.e., droplet injection tests), to forced reflood and gravity reflood tests. It is decided that 

flexibility in the test matrix be maintained so that as the model development progresses and 

needs are better identified, the matrix can be adjusted accordingly to make the program most 

cost effective. 

Task 10 - Test Facility Design. 

The RBHT facility is designed to conduct systematic separate-effects tests under well-controlled 

laboratory conditions in order to generate fundamental rod bundle heat transfer data including 

single phase steam cooling tests, low flow boiling tests, steam flow tests with injected droplets 

and inverted annular film boiling and dispersed flow film boiling heat transfer in rod bundles. 

The facility is capable of operating in both forced and variable reflood modes covering wide 

ranges of flow and heat transfer conditions at pressures from 0.233 to 0.501 MPa (20 to 60 

psig). 

The test facility consists of five major components. These are: 

1) test section consisting of a lower plenum, a low-mass flow housing containing the heater 

rod bundle, and an upper plenum, 

2) coolant injection and steam injection systems, 

3) phase separation and liquid collection systems, 

4) downcomer and crossover leg system, and 

5) system pressure oscillation damping tank and steam exhaust piping. 

All components are well insulated to minimize heat losses to the environment, and to minimize 

errors in the overall heat balances calculations around the system. 

The heater rod bundle simulates a portion of a 17x17 reactor fuel assembly. The electrically 

powered heater rods have a diameter of 9.5 mm (0.374 in) arranged in a 7x7 array with a 

prototypical 12.6 mm (0.496 in) pitch. The bundle has 45 heater rods and four unheated corner 

rods. The corner rods are used to support the bundle grids and the grid and fluid thermocouple 

leads. The support rods are made out of Inconel 600 tubing having a diameter of 9.5 mm 

(0.374 in), a wall thickness of 2.11 mm (0.083 in), and are 3.96 m (156 in) long. 

The heater rods are single ended and consist of a Monel 500 electrical resistance element filled 

and surrounded by hot pressed boron nitride (BN) insulation, and enclosed in an Inconel 600 

cladding. This material was chosen for its high strength and low thermal expansion coefficient 

at high temperatures, which minimizes rod bowing and failure at high temperature operating 

conditions since it was desired to reuse the heater rods for a second bundle build. 

The heater rods have a 3.66 m (12 ft) heated length with a skewed axial power profile, with the 

peak power located at the 2.74 m (9 ft) elevation. The maximum-to-average power ratio 

(Pmax/Pavg) is 1.5 and the minimum-to-average power ratio (Pmin/Pavg) is 0.5 at both ends of the 

heated length. The bundle has a uniform radial power distribution. 
xxxix

Power to each rod is provided by a 60 volt, 12,600 amp, 750 kW DC power supply. Each rod is 

rated for 10 kW, and designed to operate at 1.44 MPa (200 psig) at a maximum temperature of 

1200 degrees C (2200 degrees F), but because of its solid construction can be operated at up 

to 10.16 MPa (1500 psig). Each rod is instrumented with eight 20 mil diameter ungrounded 

thermocouples attached to the inside surface of the Inconel sheath at various locations. All of 

the thermocouple leads exit at the bottom end of the heater rod. The rod bundle has eight grids 

located about 0.522 m (20.55 in) apart except for the spacing between the first and second 

grids, which are 0.588 m (23.16 in) apart. 

The flow housing provides the pressure and flow boundary for the heater rod bundle. It has a 

square geometry with rounded corners, with nominal inside dimensions of 0.09x0.09 m 

(3.55x3.55 in) and a wall thickness of 6.35 mm (0.25 in). The low mass housing is made out of 

Inconel 600 material, which is the same material used for the heater rod cladding and 

thermocouple sheath. As pointed out previously, the high strength of Inconel 600 at elevated 

temperatures will minimize housing distortion during testing. The 6.35 mm (0.25 in) wall 

thickness is the minimum allowable wall thickness needed for operating this vessel at 0.501 

MPa (60 psig) and 538 degrees C (1000 degrees F), taking into consideration the cutouts to 

accommodate the large windows and the numerous pressure and temperature penetrations 

through the walls. 

The test facility instrumentation is designed to measure temperatures, power, flows, liquid 

levels, pressures, void fractions, and droplet sizes, distribution, and velocities. Using these 

measurements initial test boundaries can be established. Overall and transient mass and 

energy balances, mass inventories, carryover liquid and steam flows as a function of time can 

be calculated. Heater rod power , temperature, and fluid temperature are used to calculate heat 

fluxes and heat transfer coefficients, quench times, rod bundle energy losses, convective and 

radiation heat transfer to steam, droplets, grids, support rods, and housing. Effects of grids, 

support rods and housing behavior during reflood can be determined. Void fraction 

measurements below the quench front and in the froth level above the quench front, in 

conjunction with the laser illuminated digital camera measurements are used to determine 

droplet entrainment behavior droplet effects on heat transfer, and steam desuperheating. The 

laser illuminated digital camera system measurements provide droplet size distribution and 

velocities during reflood. 

Loop instrumentation has 61 instrumentation channels which are assigned to the measurement 

of electrical power, fluid and wall temperatures, levels, flows, differential pressures, and static 

pressure. The injection water supply tank has three fluid and three wall thermocouples to 

monitor water and wall temperatures during heat-up prior to testing. It has a differential 

pressure transmitter used as a level meter to determine water mass in the tank and mass 

depletion during reflood testing. It also has a static pressure transmitter which monitors the 

nitrogen overpressure and controls the nitrogen flow needed to maintain a constant pressure 

during forced injection reflood tests. 

The Data Acquisition System consists of a digital computer and several analog conversion 

subsystems. It uses a Ziatech ZT-8910 digital processor capable of collecting, storing, and 

retrieving data from power, pressure, temperature, level and flow instrumentation. It can also 

provide control functions, and display critical operating parameters during testing. It is to be 

designed to process up to 412 instrumentation channels at a maximum sampling rate of 10 Hz. 
xl

This system, in conjunction with panel mounted strip chart recorders, gauges, and controllers, is 

used to establish test boundary conditions prior to starting a test. 

In summary, the RBHT facility is designed as a flexible rod bundle separate-effects test facility 

which can be used to perform single-phase and two-phase experiments under well-controlled 

laboratory conditions to generate fundamental reflood heat transfer data. The facility is capable 

of operating in both forced and variable reflood modes covering wide ranges of flow and heat 

transfer conditions at pressures up to 0.402 MPa (60 psia). It has extensive instrumentation 

that meets all the instrumentation requirements developed under Task 7. It can be used to 

conduct all types of the planned experiments according to the test matrix developed under Task 

9. The present design also allows future upgrading of the facility for the performance of highpressure transient film boiling tests. It is felt that the RBHT facility with its robust 

instrumentation represents a unique NRC facility for the in-depth studies of the highly ranked 

reflood phenomena identified in the PIRT table developed under Task 1. 

Concluding Remarks 

The RBHT program will be of considerable benefit to the NRC effort to improve the TRACE 

reflood model. The effort will of necessity include not only wall-to-fluid heat transfer correlations 

but also models for interfacial shear and interfacial heat transfer. To develop and assess 

models for these phenomena with the goal of significantly improved accuracy (to provide a 

better estimate of margin) and to minimize the potential for compensating errors will require a 

database that includes more detailed information than is currently available. In addition, this 

detailed data base needs to be for prototypic rod bundle geometry as large differences exist 

between the data obtained from heated tubes and rod bundles. It is exactly this data deficiency 

for which the Rod Bundle Heat Transfer program is designed. The successful completion of this 

experimental program will make a fundamental contribution to the database for reflood model 

development and is a key component of the NRC's code improvement program. 

Specifically, the RBHT program will generate detailed data for model development that are 

either unique or of higher quality than currently available data in the following areas: 

• Two-Phase Convective Enhancement. In dispersed flow film boiling, the primary heat 

transfer mechanism is convective heat transfer to superheated steam. It is known that 

the steam heat transfer coefficient can be enhanced by up to 100 percent due to the 

presence of entrained droplets. No suitable models currently exist for this phenomenon. 

The combination of single-phase vapor heat transfer tests with the forced droplet 

injection tests (where drop size and flow rate are known) will result in the development of 

the much needed model. 

• "Inverted Annular" Film Boiling. The liquid rich region just downstream of the quench 

front (void fraction of 20 to 60 percent) provides the precursory cooling that controls the 

quench front velocity and provides the source of vapor and entrained liquid for the 

dispersed flow film boiling region. It has been demonstrated that many of the apparent 

functional dependencies (i.e., mass flux, subcooling, and distance from the quench front) 

for this heat transfer regime are primarily due to the axial profile of the void fraction in 

this region. Currently available data for this regime in rod bundles is insufficient for 

model development due to the coarse spacing (from one to two feet) used for the delta-P 

cells to measure the void fraction. The RBHT program will redress this data deficiency 

through the use of finely spaced differential pressure cells (three inches apart over a 
xli

distance of two feet) and by a local void fraction measurement provided by a low energy 

gamma-densitometer. 

• Dispersed Flow Film Boiling. Once the uncertainty involving convective enhancement is 

resolved, there still remains the difficulty in calculating the heat transfer rate for this 

regime due to the difficulty in calculating the steam superheat. The amount of steam 

superheat is governed by the interfacial heat transfer between the steam and the 

evaporating drops. To correctly calculate the interfacial heat transfer requires the 

knowledge of both the entrained droplet flow rate and diameter. There is very little data 

of this type currently available for quenching rod bundles. The RBHT program will 

generate the needed database through the use of advanced instrumentation, specifically 

through the use of the Laser Illuminated Digital Camera System (LIDCS). 

 

This program will also augment the database needed for model development in the areas of grid 

spacer effects in dispersed flow film boiling, transition boiling heat transfer during reflood, and 

for interfacial heat transfer and shear in rod bundles at low pressure. The RBHT program will 

complement NRC's efforts in improving the TRACE reflood models. 
xlii
xliii

NOMENCLATURE 

A area (m2

) 

Bi Biot number (dimensionless) 

c specific heat (J/kg-K) 

D diameter (m) 

e specific internal energy (J/kg) 

f friction factor (dimensionless) 

Fo Fourier number (dimensionless) 

g acceleration due to gravity (m/s2

) 

gc gravitational constant (32.17 lbm-ft/lbf-s2

) 

h enthalpy (J/kg) 

h heat transfer coefficient (W/m2

-K) 

J radiosity (W/m2

) 

k thermal conductivity (W/m-K) 

K loss coefficient (dimensionless) 

L length (m) 

m number of grids in two phase region (Equation 6-78) 

n number of grids in single phase region (Equation 6-78) 

Nu Nusselt number (dimensionless) 

p rod pitch (m) 

P pressure (N/m2

) 

Q heat energy (W) 

R radius (m) 

R resistance (used in radiation network) (Equation 6-102) 

Re Reynolds number (dimensionless) 

t time (s) 

T temperature (degrees K) 

u velocity (m/s) 

V volume (m3

) 

W mass flow rate (kg/s) 

z elevation (m) 

Greek 

α void fraction 

α thermal diffusivity 

μ kinematic viscosity 

π non dimensional ‘Pi’ group 

ρ density 

τ time constant 

Δ increment 

Subscripts 

B bundle 

c cladding 

ci cladding inside surface 
xliv

co cladding outside surface 

cr cold rod 

c convection (usually with heat transfer coefficient) 

CL centerline 

d drops 

dcht direct contact heat transfer 

DP decay power 

DR dead rods 

DR/d dead rods to drops 

DR/v dead rods to vapor 

e exit 

f fluid 

f saturated liquid 

f fuel 

FB film boiling 

g grid 

g saturated vapor 

gap gap in the nuclear fuel rod 

g/d grid to drops 

g/v grid to vapor 

hr hot rod 

H housing 

H/d housing to drops 

H/v housing to vapor 

i reference case 

i inlet 

I Interfacial liquid 

lw liquid-wall contact 

m mixture 

min minimum 

max maximum 

o outlet 

p constant pressure 

q quench 

r rod 

r/d rod to drops 

r/v rod to vapor 

s surface 

s superheated 

sat saturated 

t test 

T total 

v superheated vapor 

v/d vapor to drops 

1φ single phase 

2φ two phase 
Superscripts 

'

 per unit length 

'''

 per unit volume 

* non dimensional variable 

⎯⎯ average 

2 φ fo two phase flow multiplier 

De equivalent diameter 

Rf total frictional and form resistance 

Eb black body emissive power 

xlv
xlvi
xlvii

ACKNOWLEDGEMENTS 

There were several individuals who made significant contributions to this report which the 

authors would like to acknowledge. The technical efforts of Ernest Miklavic, Andrew Ireland, 

Christina D’Arrigo and James Apple are gratefully acknowledged. The editing, correcting, and 

typing efforts of Mrs. Christine Wilson, Kristie Kalvin, Donna Gensimore, and Michelle Alterio 

are also gratefully acknowledged and without their effort this report would not have been 

completed as scheduled. The technical comments and insights by the two independent Nuclear 

Regulatory Commission sponsored peer review panels for the program objectives and 

approach, and for the instrumentation design are also gratefully acknowledged. The authors 

also acknowledge the guidance, review, and active participation that William Macon, Dr. Steve 

Bajorek, Joseph Kelly, Gene Rhee and David Bessette and of the Nuclear Regulatory 

Commission have played in the Rod Bundle Heat Transfer Program. The comments which 

were received were integrated into the test design and analysis and will improve the quality of 

the work performed in the program. 

We also acknowledge the continuing support of Drs. R. C. Benson and K. Thole, former and 

current Head of the Mechanical and Nuclear Engineering Department, respectively. The Rod 

Bundle Heat Transfer Program is a cost shared program between The Pennsylvania State 

University and the Nuclear Regulatory Commission. The authors acknowledge the financial 

support provided by the University for the equipment match and the new building annex for the 

test facility. In particular, the authors acknowledge the support of Drs. D. N. Wormley, L. C. 

Burton, L. R. Hettche, and R. A. Erickson. The experiments will be performed at the Thermal 

Propulsion Research Facility (Test Site) of Applied Research Laboratory, Pennsylvania State 

University. The authors acknowledge the continuing support and help of Dr. D. H. Kiely, R. A. 

Grove, I. S. McClellan, R. A. Peters, C. P. Jones, D. M. Adams, and J. R. Bischof from the 

Applied Research Laboratory.
xlviii
1

1. INTRODUCTION 

1.1 Background

Safety analysis is performed on Nuclear Reactor power plants to ensure the health and safety of 

the public, for accidents which are postulated to occur. Accidents are analyzed which are 

anticipated to occur over the life time of the plant as well as hypothetical accidents which are not 

expected to occur but are postulated to determine the mitigating features of the particular 

reactor design. Each reactor design has Engineered Safeguard Systems which are safety 

systems designed to mitigate accident scenarios. 

 

Within the reactor design basis, the most challenging accident which is examined is a largebreak Loss of Coolant Accident (LOCA). Analysis of this particular accident can result in limits 

in the reactor total core power as well as the allowable peak linear fuel rod power in the hottest 

rods. For this type of accident, the initial coolant in the reactor core is expelled out the broken 

piping and the core cooling is dependent on the Engineered Safeguards Systems. Analysis of 

the particular accident verifies that the design of the Engineered Safeguards Systems will 

mitigate the accident. In a large-break LOCA, the fuel rod cladding is calculated to rupture at 

high temperatures, and the primary piping is assumed to have failed so as to generate the 

LOCA. Without adequate core cooling the reactor core will continue to overheat and can lead 

to failure thereby releasing fission products from the fuel. 

The Nuclear Regulatory Commission developed the requirements of Title 10 of the Code of 

Federal Regulations, Part 50, Appendix K (Appendix K), in 1973 for acceptable analytical 

methods used to predict the safety performance of the Engineered Safeguards System for 

reactor designs. The requirements were acknowledged to be conservative to account for the 

uncertainties in the calculation and the database at that time. A significant research effort was 

performed by the NRC, Electrical Power Research Institute (EPRI), and the reactor vendors 

from 1973 to 1988 to determine the degree of conservatism in the Appendix K requirements. 

During the same time period, the American Physical Society urged the NRC to develop 

improved, more realistic “Best-Estimate” analytical computer models for the reactor systems 

such that realistic calculations could be performed. In 1988, the Appendix K rule was revised 

and Best-Estimate thermal-hydraulic methods were allowed to be used to evaluate the reactor 

system and the Engineering Safeguards System response to a postulated LOCA. 

With the approval of the Appendix K rule revisions, vendors are starting to utilize “BestEstimate” safety analysis thermal-hydraulic methods to perform large-break LOCA analysis to 

evaluate the allowable core thermal limits. Even with the application of best-estimate methods, 

the large-break LOCA still is generally the most limiting transient and results in establishing the 

maximum allowable fuel rod linear power level (kW/ft). Typically what has occurred is that as 

Best-Estimate analysis methods have identified peak linear heat rate margin; this margin has 

been used by the utility or the vendor for power up-ratings, longer fuel cycles, low leakage core 

loadings and advanced fuel designs to improve the economics of the nuclear power plant. All of 

these economic improvements result in the need for higher operating linear heat generation 

rates. This is true for both BWR and PWR designs. When the best-estimate methods are 

applied with the higher linear heat rates, the resulting calculated peak cladding temperatures 

are nearly the same as those previously calculated using the original Appendix K requirements. 

However, the difference is that the allowable linear heat rate (kW/ft) is now higher. 
2

The best-estimate calculations indicate that for nearly all PWR designs the peak cladding 

temperatures are reached during the reflood portion of the transient at low pressures, typically 

0.1 to 0.3 MPa. A similar situation also occurs in the hot channel for the more modern BWR 

designs (BWR5 and 6), as well. The flow pattern in the BWR hot channel is co-current up flow 

during reflood similar to a PWR. 

There are two basic flow regimes for reflooding in a rod bundle. For high flooding rates, 

typically 0.15 m/s (6 in/s), the dominant flow regime for the post-CHF regions in the bundle is an 

inverted annular regime in which a thin layer of vapor separates the heated wall from the sub 

cooled liquid flow which nearly fills the channel. Since the inlet flow is larger than the quench 

rate of the fuel rods, a long region of inverted film boiling can exist above the quench front. As 

one proceeds upward along the bundle, the liquid becomes saturated and begins to break into 

chunks or liquid slugs. The length of the inverted annular and the liquid chunk regimes depends 

on the flooding rate into the heated bundle, the initial sub cooling of the liquid, the system 

pressure, and the rod bundle initial temperature and power level. The heat transfer in this 

regime is very high and results in immediate clad temperature turnover such that lower peak 

cladding temperatures are calculated for this reflood regime. Figure 1.1 shows an example of 

the high flooding rate reflood heat transfer and flow regime. 

For low flooding rates, there is no sub cooled inverted annular film boiling region. Because of 

the low injection flow rate, the liquid quickly reaches saturation and there is bulk boiling of the 

fluid below the quench front. In the quench front region, and above the quench front, there is a 

froth region which has a void fraction which transitions between a low void fraction, below the 

quench front, to the much higher void fraction in the dispersed flow regions above the quench 

front. This behavior is shown in Figure 1.2. The dominant flow regime for the low flooding rates 

is a highly dispersed flow film-boiling region in which the heat transfer rates are very low. The 

heat transfer in this region occurs between the heated wall and the superheated steam. The 

liquid droplets in the superheated steam evaporate reducing the steam temperature as well as 

increasing the flow rate of the steam. As a result, the calculated peak cladding temperature 

usually occurs in this region. In most reactor reflood calculations, after the initial surge into the 

core, the flooding rates are very low, typically 0.0254 m/s (1 in/s) or less, such that the 

dispersed flow film boiling region is the dominant flow regime of interest and is the heat transfer 

regime in which the peak cladding temperature occurs. 

In either case and for all designs, the thermal-hydraulic heat transfer phenomenon which 

dominates the reflood portion of the transient is dispersed flow film boiling. The heat transfer 

rates during this period are very low and several different mechanisms are responsible for the 

total wall heat flux. No single mechanism dominates the heat transfer process such that several 

different mechanisms must be predicted by the best-estimate calculational tool with roughly 

equal precession. Those mechanisms include: 

• Convection to superheated vapor, 

• Surface radiation to vapor and droplets, 

• Interfacial heat transfer between droplets and superheated vapor, 

• Direct contact heat transfer between the wall and entrained liquid, 

• Convective enhancement of the vapor by the entrained droplets 

• Impact of structures (grids) in the rod bundle causing flow acceleration and droplet 

break-up,

• Quench fronts at the top and bottoms of the rods. 
Figure 1.1 Reflood Flow Regimes for High and Low Reflood Rates. 

Also, since the different mechanisms are of comparable magnitude, improving one particular 

model is difficult since very little data is available to isolate its particular contribution to the total 

wall heat flux. Therefore, compensating errors can result as the code's predictive capabilities 

are improved.

Dispersed flow film boiling also dominates the down flow period of the PWR blow down transient 

as well as the reflood transient. Similar heat transfer mechanisms are present for the blow 

down flow period as well as the reflood period. The primary difference is that the vapor

3
convection term is more dominate for the blow down situation as compared to the reflood

phase, and the vapor has less superheat. 

Figure 1.2 Detailed Low Flooding Rate Reflood Flow Regimes. 

The single largest uncertainty in predicting the dispersed flow film boiling heat transfer in 

reflooding rod bundles is the liquid entrainment at the top of the froth region just above the 

quench front. The froth region is a region at and above the quench front in which the void 

fraction changes from low values typical of the boiling below the quench front, to the very high 

values in the dispersed flow film-boiling regime. The froth regime is a liquid rich regime while 

the dispersed flow regime is very liquid deficient. Figure 1.3 shows the quench front data from a 

low flooding rate FLECHT-SEASET test (Ref. 1) with the froth region location indicated. Figure

4
1.4 indicates a schematic of the flow regime just above the quench front within the froth region

of the flow. In this region, the steam generation from the quenching of the fuel rods results in

Figure 1.3 Transition and Quench Fronts for FLECHT-SEASET Test 31504. 

very large vapor velocities which entrain and shear liquid filaments into droplets which are then

swept into the upper regions of the rod bundle. The entrained droplets provide cooling by 

several different mechanisms in the upper regions of the rod bundle where the resulting peak 

clad temperatures are calculated. 

Figure 1.5 shows the different heat transfer mechanisms which are present in the high 

temperature portions of the rod bundle where the peak cladding temperatures are calculated 

(Refs. 1 and 2). The heat transfer process is a combination of a “two-step” and “three-step” 

dispersed flow film boiling process. A “two-step” dispersed flow film boiling process consists of 

heat transfer from the wall to the vapor flow by convection as well as by radiation. There is also 

wall-to-wall radiation heat transfer and wall-to-entrained droplet heat transfer. The vapor is the 

heat sink and quickly reaches superheated conditions as it receives energy from the wall. The 

second step of the “two-step” process is the heat transfer between the superheated vapor and

the entrained droplets. The interfacial heat transfer between the drops and the vapor lowers the 

vapor temperature which is the fluid heat sink for the wall heat transfer. The “two-step” film 

boiling process becomes a “three-step” process as the wall temperature decreases such that 

there can be intermittent direct (or near direct) droplet-wall contact heat transfer. It is believed 

that the direct wall contact heat transfer component occurs within and just above the froth region 

5
which results in improved heat transfer. The improved heat transfer in this region can be seen 

from the FLECHT-SEASET test data. 

Figure 1.4 Entrainment Behavior for Rod Bundle Reflooding. 

The ability of a best-estimate computer code to accurately predict the integrated effects of the 

individual phenomena for the dispersed flow film-boiling region is a challenge. The uncertainty 

in the individual models is large and the integrated effects of the uncertainties will accumulate 

as the calculation progresses upward along the heated channel. The error or uncertainty 

accumulation is one reason that the code predictions of temperatures above the mid-plane of 

the FLECHT-SEASET rod bundle or the Japanese Cylindrical Core Test Facility have always 

been worse than predictions lower in the bundle, closer to the froth region. Also, code 

calculations for lower flooding rates which are reflected in a slower quench front velocity and a 

longer transient time show poorer predictions relative to the test data. 

1.2 Program Objectives

Reflood Heat Transfer experiments have been performed since the original Full Length 

Emergency Core Heat Transfer (FLECHT) program began in 1967. These experiments were 

designed to examine the total heat transfer for a heated rod bundle subjected to reflood bottom 

or top spray effects. At this time no data existed for rod bundles in the literature, therefore, the 

6
initial tests were more scoping and were designed to provide data on the overall heat transfer 

rather than the phenomena which were responsible for the heat transfer. The initial FLECHT 

tests were more sparsely instrumented and one could not perform a mass balance on the tests. 

Figure 1.5 Heat and Mass Transfer Mechanism in Dispersed Flow Film Boiling. 

The test conditions in the original FLECHT series did not reflect the effects of steam binding and 

hence the flooding rates are much larger than current plants. The rod peak powers were also 

higher. Other FLECHT test series were also performed in which the flooding rates were 

reduced to better cover the plant calculated conditions. However, the objective remained the 

same, to determine the total heat transfer over a wider range of conditions. A very highly 

empirical heat transfer correlation was developed, which was a function of the reactor system 

parameters (not local thermal-hydraulic conditions) and was used in the Appendix K models by 

the vendors and the NRC. Because the heat transfer correlation was empirical and not based 

on any physical model, the application for different rod bundle arrays, conditions, axial power 

shapes, and geometries was suspect. 

7
8

Improved reflood experiments were performed in the FLECHT-SEASET program which was 

initiated in the mid 1970's. The FLECHT-SEASET tests represent the first attempt to 

understand the reflood phenomena. Additional instrumentation was added to examine the 

thermal-hydraulic conditions within the test bundle. However, the tests were conducted in the 

same manner as the previous FLECHT tests and the primary result of these tests was the 

overall reflood heat transfer for a different rod bundle array which was correlated in a similar 

manner as the previous FLECHT experiments. There was additional analysis performed on the 

FLECHT-SEASET tests to attempt to divide the measured total heat transfer into the individual 

heat transfer components, however, the uncertainties were very large such that the phenomena 

could be identified but not quantified with sufficient confidence. The ACHILLES and PERICLES 

experiments were similar to the FLECHT-SEASET tests in size and types of test performed. 

Both of these test series used prototypical spacer grids, which were found to enhance heat 

transfer. However, no local data was obtained to explain the reflood heat transfer phenomena. 

There were also systems reflood tests such as the FLECHT-SET tests, the 2D/3D program 

Cylindrical Core Test Facility (CCTF), the Slab Core Test Facility (SCTF); and the KWU 340 rod 

systems tests. These experiments primarily examined the effects of the reactor system effects 

on the core reflooding rate and the resulting heat transfer within the core. No attempts were 

made to instrument these experiments to determine the local heat transfer phenomena within 

the rod bundle, rather, the determination of the system response during reflood was the test 

objective. The overall heat transfer in the rod bundle was measured as well as the heater rod 

temperatures. 

All of these experiments made important contributions to the total understanding of the reflood 

process for a PWR or a BWR and the data is useful, in varying degrees, for safety analysis 

computer code validation. However, none of these experiments were designed with the 

objective of model development and validation based on the local thermal-hydraulic conditions. 

The experiments which have been conducted were primarily to provide data over a wide range 

of system conditions for an Appendix K reactor safety analysis and not to examine the details of 

the local two-phase flow and heat transfer effects which could occur in a rod bundle during 

reflooding. Therefore, when this data is used for computer code validation and the predictions 

do not agree with the data, the analyst does not have sufficient experimental information to 

determine which of the many models is causing the mis-prediction. As a result, as models are 

“improved”, compensating errors can enter into the calculations which tend to make the 

computer code suspect when extrapolating the results to the full scale PWR or BWR. 

One important feature of the RBHT program is that the experiments and the instrumentation are 

designed from a model development and validation point of view, rather than an Appendix K 

margin approach. Much of the instrumentation will be unique and will be used to determine 

local conditions. The data can be used to validate specific models in a manner such that the 

effects of compensating error can be identified and corrected. The program will also break the 

dispersed flow film boiling phenomena into its individual contributions such as: 

• Single phase pressure drop experiments to characterize the spacer grids and the rod 

bundle, 

• Surface-to-surface, surface to liquid, and surface to vapor radiation heat transfer, 

• Convection of superheated steam over a wide range of Reynolds numbers. 
9

• The effects of entrained droplets within a superheated steam flow, and the effects of the 

droplets on convection enhancement, as well as evaporation, 

• Forced reflood tests which will cover a wide range of reflood flow regimes and heat 

transfer state, 

• Variable reflood tests in which the interaction of the injected flow and the quench front 

can be assessed. 

The instrumentation is designed to provide data on the local void fraction within the froth 

regions, the steam superheating that occurs along the bundle, the liquid entrainment within the 

bundle, entrained drop sizes, distributions, velocities and droplet velocity distributions. 

The RBHT program is needed to provide detailed data which can be used to improve the NRC’s 

safety analysis prediction capabilities for the large break LOCA transient. The NRC needs a 

large break LOCA analysis tool that can be applied with a high degree of confidence to assure 

the public safety without unduly penalizing the utilities. Initial validation of the TRAC-PF1/MOD1 

code was performed and the code and model uncertainty was determined as part of the Code 

Scaling Applicability and Uncertainty (CSAU) (Ref. 3) effort which also provided an initial 

estimate the 95th percentile peak cladding temperature. However, these calculations were 

performed at approximately 30.68 kW/m (9.35 kW/ft) while today, plants are being licensed at 

49-59 kW/m (15-18 kW/ft). Figure 1.6 shows the peak cladding temperatures for the original 

CSAU study and a more recent safety analysis calculation performed at 49.54 kW/m (15.1 peak 

kW/ft). 

A complex reflood heat transfer package has been rewritten as part of TRAC-PF1/MOD2 (Ref. 

4) using primarily single tube and Winfrith “Hot Patch” tests as a basis for the models. Initial 

calculations for separate effects tests indicate the new models significantly under-predict the 

cooling at low flooding rates and can exhibit large oscillations which make the interpretation of 

the results difficult at best. Before the code and model uncertainty can be determined for 

TRAC-PF1/MOD2, there is the need for significant reflood heat transfer model improvement. 

The approach which has been used in the past has been to try different correlations, tune 

coefficients of the correlations, try smoothing relationships for the correlations, and developing 

an “ad hoc” model or correlation which has no physical basis but allows to the code to continue 

to perform calculations. These approaches can lead to codes with large biases and uncertainty 

when compared to a comprehensive data set. Also, adjusting coefficients on correlations to 

match data can result in compensating errors which may not scale properly from the test 

configuration to the full size reactor. 

The RBHT program is designed to provide detailed data on local conditions which can be used 

for model development. Models will be developed and selected based on fundamental 

assessments such that the correct heat transfer is predicted for the given local fluid conditions. 

The tests in the RBHT program are structured so as to decompose the complex nature of 

dispersed flow film boiling into the component models that a computer code would calculate. In 

this fashion, compensating errors in the models will be reduced. The result will be a more 

accurate analysis tool for the NRC for best-estimate audit calculations. 
Figure 1.6 Comparison of Current Best Estimate Calculated PCTs with CSAU Study. 

1.3 Products from the Rod Bundle Heat Transfer Program

The detailed experimental data and the associated model development will provide the NRC 

with an improved analytical capability to be applied for Risk Informed Regulation for the large 

break LOCA. Improved models will reduce the code uncertainty which must be assessed as 

part of the best-estimate methodology using CSAU. The resulting analysis method will be more 

accurate, credible, and robust. 

The RBHT program will significantly expand the existing database which can be used to 

develop and validate reflood heat transfer models. It should be noted that the RBHT program is 

specifically developed to support best-estimate Safety Analysis model development methods, 

not as a demonstration of the Appendix K margin. The database will be expanded with detailed 

measurements of local conditions which are targeted to address existing code modeling issues. 

The data will be provided in a format which will be user friendly such that it can be used for code 

validation purposes. 

The RBHT facility is being designed as a flexible rod bundle separate effects test facility which 

can be used to perform single and two-phase experiments. Development of the RBHT facility 

will help maintain the NRC’s leadership in the reactor thermal-hydraulics safety analysis area in 

the world. Placing the test facility in a university setting also provides educational opportunities 

for students who will become the next generation of reactor engineers in the United States. 

1.4 Technical Approach

A reflood heat transfer specific Phenomena Identification and Ranking Table (PIRT) has been 

developed which indicates the individual component models which constitute “reflood heat 

10
11

transfer.” The PIRT and its relative rankings indicate the important phenomena which a bestestimate computer code should simulate with a high degree of accuracy. The PIRT will also be 

used as a guide when reviewing the reflood heat transfer logic for the different best-estimate 

computer codes. This will indicate the state-of-the-art in reflood modeling. 

Using the PIRT, the available rod bundle data and selective tube data will be examined to see 

whether they can address the important PIRT phenomena. The PIRT also serves as a guide in 

developing the RBHT facility since it will indicate what type of data is needed and which 

measurements should be made, if possible. The PIRT provides guidance on the types and 

number of instrumentation, types of tests to be run and the test conditions to be simulated. The 

result will be data developed specifically for two-fluid, best-estimate computer code 

development and validation. 

The RBHT program will use a full-length, smaller, but well instrumented rod bundle which will 

provide data for the fundamental assessment of the physical relationships upon which the code 

constitutive models are based. This effort will provide new, needed data which is specifically 

targeted at the best-estimate two-fluid code modeling needs. 

1.5 References

1. Lee, N., Wong, S., Yeh, H.C., and Hochreiter, L.E., “PWR FLECHT-SEASET Unblocked 

Bundle, Forced and Gravity Reflood Task Data Evaluation & Analysis Report,” 

NRC/EPRI/Westinghouse Report No. 10, WCAP-9891, NUREG/CR-2256, EPRI NP-2013, 

November, 1981. 

2. Andreani, M., and Yadigaroglu, G., “Prediction Methods for Dispersed Flow Film Boiling,” 

Int. J. Multiphase Flow, Vol. 20, Suppl., 1-51, 1994. 

3. U.S. Nuclear Regulatory Commission, “Quantifying Reactor Safety Margins”, NUREG/CR5249, 1989. 

4. Nelson, R.A., Pimental, D.A., Jolly-Woodruff, S., and J. Spore, “A Phenomenological 

Thermal-Hydraulic Model of Hot Rod Bundles Experiencing Simultaneous Bottom and Top 

Quenching and an Optimization Methodology for Closure Development,” Los Alamos, Draft 

Report, 1998. 

5. Kelly, J.M., Presentation to Advisory Committee on Reactor Safety (ACRS), Rockville, MD, 

February 18, 1998.
12
13

2. ROD BUNDLE HEAT TRANSFER PROGRAM PHENOMENA 

IDENTIFICATION AND RANKING TABLE (PIRT) 

2.1 Introduction/Background

The concept of a Phenomena Identification Ranking Table (PIRT) was first developed as part of 

the Nuclear Regulatory Commission program for assessing safety margins in operating reactors 

as given in the quantifying Reactor Safety Margins report, called; Code Scaling, Applicability 

and Uncertainty or CSAU (Ref. 1). The idea behind the CSAU effort was to provide a rational 

and documented method of determining the applicability and accuracy of a specific safety 

analysis computer code for analysis of a specific Nuclear Power Plant Design for a given 

accident scenario. The accident scenario which was examined in the CSAU effort was the largebreak Loss Of Coolant Accident (LOCA) which is the limiting accident for most light water 

reactor designs. There are three elements to the CSAU methodology: 

a) Requirements and Code Capabilities 

b) Assessment and Ranging of Parameters 

c) Sensitivity and Uncertainty Analysis 

The accident scenario was first specified then the specific nuclear power plant was selected. 

Plants could be grouped if they had sufficient common features. Given the accident and the 

plant design, a Phenomena Identification and Ranking Table was then developed as a basis for 

judging the capabilities of the safety analysis computer code which would be used for the 

transient. The full CSAU flow chart for the code scaling, applicability and uncertainty from 

Reference 1 is shown in Figure 2.1. 

A PIRT is developed by an independent group of experts to rank the most important 

phenomena that need to be simulated for a particular accident scenario. This table and the 

individual ranking can be reviewed by a second set of independent experts (i.e., peer reviewed) 

for completeness and proper ranking of the most important phenomena. Such a procedure was 

followed for the CSAU PIRT, and the Los Alamos PIRT which was developed for the AP600 

(Ref. 2). A similar approach was used for the PIRTs developed at Westinghouse for LOCA 

analysis of three and four loop plants as well as for the AP600 different transient types such as 

Small Break LOCA, Large Break LOCA, Long Term Cooling, Transient Analysis and 

Containment Analysis. Similar PIRT tables have been generated for BWR Transient Analysis 

and LOCA Analysis (Ref. 3). 

The scenarios of interest for the RBHT program are the transients or postulated accidents which 

can lead to core uncovery and recovery at low pressure. In most cases this is a result of a large 

break loss of coolant accident (LOCA) in which nearly the entire initial coolant inventory is lost 

and the core experiences a heat-up. The calculated Peak Cladding Temperature (PCT) occurs 

for a calculated large-break LOCA such that the core limits, reactor power capability, and fuel 

loading patterns are affected by the calculated performance of the plant for a postulated LOCA. 

The component of interest is the response of the core and fuel rods for these transients. 

The objective of the RBHT program is to define the source and nature of the limitations and 

uncertainty in the current thermal-hydraulic models used in best-estimate thermal hydraulic 

codes for reflood heat transfer. The Program will generate fundamental data and information to 
Figure 2.1 Code Scaling, Applicability and Uncertainty (CSAU) Evaluation Methodology. 

14
15

support development of improved multi-field models that will allow more physical and accurate 

modeling of low pressure post Critical Heat Flux (CHF) heat transfer, axial void distribution, 

interfacial area and interfacial drag for reflooding of rod bundles. 

To aid in the development for the experimental requirements of the RBHT facility, a Preliminary 

PIRT was developed which focused on the low pressure reflood portion of the PWR and BWR 

transients. The objective was to sub-divide processes down to the lowest level by which a bestestimate computer code would calculate these phenomena. With the phenomena broken down, 

the capabilities of the proposed test facility were assessed to determine which phenomena 

could be measured with confidence, which phenomena could only be qualitatively measured, 

and what instrumentation would be needed. 

2.2 Preliminary PIRT for the Rod Bundle Heat Transfer Tests - PWR Phenomena

2.2.1 Introduction 

Phenomena occurring in the core region are of most interest for the RBHT program since the 

core thermal-hydraulic response determines the resulting PCT. In PWRs, the core is reflooded 

by the gravity head of water in the downcomer. The core heat transfer response is a dependent 

parameter since it depends on the gravity flow into the core and the ability of the reactor system 

to vent the two-phase mixture generated in the core. The Emergency Core Cooling (ECC) 

System design, break size and location, and the containment pressure influences the flooding 

rate into the core and hence the core cooling. Calculations indicate that there can be an initial 

surge of water into the reactor core which is then reversed due to the steam generation and 

resulting increase in pressure drop downstream of the core. The flooding rate will quickly 

stabilize at a near constant value which slowly decreases over time as the effective driving head 

of the downcomer is decreased. The RBHT program will investigate the reflood heat transfer 

processes by performing separate effects tests to examine the different components of the heat 

transfer phenomena for reflood. 

The experiments and the instrumentation will be designed to complement existing rod bundle 

data and to provide unique data and insights into the thermal-hydraulic phenomena such that 

the existing data and the new data to be gathered in the program can be more effectively 

utilized for computer code validation. In this fashion, the existing rod bundle database will 

become more valuable and can be integrated with the new data. The experiments will be 

structured so as to separate out the individual phenomena which have been identified in the 

preliminary Phenomena Identification and Ranking Table. The experiments will include: 

• Heat loss experiments to characterize the facility for mass and energy balances; 

• Single phase pressure drop experiments to characterize rod bundle and spacer grid 

pressure losses; 

• Radiation heat transfer tests in an evacuated bundle to characterize the rod-to-rod 

radiation heat transfer, surface emissivity, and the rod-to-housing heat transfer; 

• Convection to superheated steam to examine the rod bundle convective heat transfer 

over a wide range of Reynolds numbers and single phase heat transfer for enhancement 

by spacer grids; 
16

• Convection to superheated steam with droplet injection to examine the effects of the 

entrained drops on vapor temperatures due to evaporation, the development and 

change of the interfacial area for heat and mass transfer along the length of the bundle, 

effects of the drops on the convective heat transfer, radiation heat transfer to the drops 

on vapor, spacer grid effects on droplet breakup, vapor de-superheating and grid 

quenching; 

• Forced reflooding experiments over a wide range of conditions of flow, pressure, inlet 

subcooling, initial rod temperature, and rod powers to overlap with existing forced reflood 

data, with the emphasis on the entrainment mechanisms at the quench front; 

• Variable reflooding experiments over a range of conditions of flow, pressure, inlet 

subcooling, initial rod temperatures, rod powers, and outlet liquid and vapor flows to 

overlap with existing reflood data. 

2.2.2 Development of the Classifications for the Different Regions for the Rod Bundle 

Heat Transfer Program Preliminary PIRT 

The Preliminary PIRT for the RBHT program was developed by examining the different 

components in the reactor system for a PWR to identify the key phenomena. The core region is 

the focus of this program to obtain data to improve heat transfer models. The remainder of the 

reactor system components will also be discussed and the phenomena will be identified. 

The approach for developing the Preliminary PIRT for the core region is based on examining the 

FLECHT-SEASET (Ref. 4) test data and analysis. Figures 2.2 to 2.4 show the quench front 

curve and the two-phase froth region, which is above the quench front, for different flooding 

rates at the same pressure and bundle power. A schematic of the flow regimes at and above 

the quench front is shown in Figure 2.5. This figure gives a clearer indication of the flow 

behavior for the region above the quench front and below the dispersed flow film-boiling region. 

Using Figures 2.2 to 2.5 as guides, six regions of interest are identified within the core during 

reflooding. At the bottom of the fuel rod (or heater rods in the experiment), the heat transfer is 

by single phase forced or natural convection. As the coolant temperature approaches the 

saturation temperature, subcooled nucleate boiling begins, and eventually saturated boiling. 

The quench front is the next region of interest. At this point, the stored energy in the fuel or 

heater rods is released into the coolant resulting in significant steam generation. The local rod 

temperature decreases from the minimum film boiling point to the critical heat flux temperature 

and into nucleate boiling. Local temperature decreases in this region are several hundred 

degrees over a short distance such that a substantial volume of steam is generated. The steam 

generated near the quench front entrains liquid. 

The froth region above the quench front is the location where the steam generated near the 

quench front shears the liquid flow into liquid ligaments and eventually into a spectrum of 

droplets which are entrained upwards. Above the froth region, the flow field consists of the 

entrained droplets in a superheated steam flow. This is the heat transfer regime where the 

calculated PCT typically occurs. It is a region of low heat transfer since the vapor sink 

temperature becomes superheated and approaches the rod surface temperature. Since 
temperatures are high, radiation heat transfer to surfaces, droplets, and vapor must be 

accounted for, as indicated by the FLECHT-SEASET experiments. 

Figure 2.2 Froth Region and Quench Front Locations for Reflood. 

At the very top of the rod bundle, there can be a second quench front which moves down the 

fuel/heater rod. The movement of the top quench front depends on the amount of liquid 

entrainment in the flow and the power profile of the fuel/heater rod as well as the previous 

blowdown heat transfer history. Assuming that there is sufficient entrained liquid in the flow 

which can be deposited, the top quench front is an axial conduction progression down the 

fuel/heater rod. The excess liquid flow from the downward liquid film flow is sputtered-off into 

the up flowing steam and is re-entrained with droplets from below. The top quench occurs at 

elevations significantly above the location of the PCT so its behavior does not influence the PCT 

value directly. However, the top quench front will affect the amount of liquid which leaves the 

core and affects the system reflood behavior. 

17
Figure 2.3 Froth Front and Quench Front Curves for FLECHT-SEASET Run 31203, 

1.5 in/s, 40 psia Test. 

The exact nature of the six regions are a function of the flooding rate into the core, system 

pressure, core power level, inlet subcooling and the rod bundle initial temperature. As the 

flooding rate increases, the single-phase convection region increases; there is reduced 

subcooled nucleate boiling and no saturated boiling. The height of the froth region above the 

quench front increases with increased flooding rates into the bundle as shown in Figures 2.2 to 

2.5. As the froth region increases in size, the dispersed flow film-boiling region decreases and 

the resulting vapor superheat in this region is reduced and higher heat transfer rates result. 

Also, the top down quench front is enhanced because of the additional liquid in the entrained 

flow. 

18
Figure 2.4 Froth Front and Quench Front Curves for FLECHT-SEASET Run 31504, 

1.0 in/s, 40 psia Test. 

Since there are different regions in the core during reflooding, with perhaps different 

phenomena which are important, the core was subdivided into six regions for the preliminary 

PIRT and phenomena identified for each. There may be overlap in the phenomena; however, 

different phenomena can have a different weighting for the different regions. The six regions 

identified are: 

a) single phase heat transfer region below the quench front; 

b) subcooled nucleate boiling and saturated boiling region below the quench front; 

c) quench front region where the heat is released from the quenching fuel rods; 

d) froth region where the entrained liquid is sheared into droplets; 

e) dispersed flow film boiling region above the froth region where the PCT occurs; and 

f) top down quench front. 

19
Figure 2.5 Typical Conditions in Rod Bundle During Reflood. 

Separate preliminary PIRTs were developed for each of these core regions such that the 

particular phenomena for a particular region could be subdivided into specific component 

models which a computer code uses to perform the reflood calculation. The same ranking 

method as that employed by Los Alamos will be used to denote the relative importance of the 

“High”, “Medium” and “Low” phenomena. The preliminary PIRTs for the core for each region 

are given in Tables 2.1 to 2.6. These PIRTs will be used to develop and guide the design of the 

RBHT facility for the single phase convection, radiation heat transfer, single phase steam with 

droplet injection, and the forced reflooding tests. 

20
21

Table 2.1 Single Phase Liquid Convective Heat Transfer 

Process/Phenomena Ranking Basis RBHT Progra

Effects of geometry L Limited data exists which can be used 

as a guide, should have little uncertainty on PCT 

There is little data for natural rod bundles, usually Gr/Re2<<

Convective heat transfer M 1Φ convective heat transfer data has 

been correlated for rod bundles, uncertainty will not affect PCT, can affect point of boiling. 

Will Measure Ts, Tf and powe

front so forced convective heanatural convection heat transfcalculated. 

Effects of geometry L De has been shown to be acceptable 

for P/D of 1.3 (Ref. 5). Limited data exists which can be used as a guide, should have little uncertainty on PCT 

There is little data for natural rod bundles, usually Gr/Re2<<

Effects of spacers L Effects of spacers in 1Φ convective heat 

transfer is known, see Reference 7. No impact on PCT uncertainty. Effect unknown for natural convection, but enhances heat transfer. No impact on PCT uncertainty. 

Effects will be measured, with placement of heater rod T/C’s 

Effects of properties L Property effects are accounted for in 

analysis for 1Φ heat transfer, little 

uncertainty. 

Property effects can be calcu

and Tb. 

Liquid velocity (Reynolds number) 

M Determine convective heat transfer, 

onset of boiling 

Will measure total flow Tw, Tf, 

heat transfer from data and c

Liquid subcooling M Liquid is heat sink, determine point of 

boiling 

Fluid temperatures will be meminiature steam probes, seletraverse. 

Decay power H Source of energy for rods, boundary 

condition for test. 

Will be simulated. 
22

Table 2.2 Subcooled and Saturated Boiling - The Core Component Below the Quench F

Process/Phenomena Ranking Basis RBHT Pro

Subcooled boiling heat transfer (BHT) and heat flux, split of energy between liquid and vapor production 

M A significant variation in the subcooled boiling 

heat transfer coefficient will not affect the PCT uncertainty since rod is quenched. Will effect energy partition to sensible heat and vapor generation. 

Will measure rod tem(surface) local fluid te(selectively) and powewall heat flux can be cBundle average qualicalculated from an enCodes that use the C8) which has a superpconvection and boilingbe used to test this tysince both Ts and q” a

However, it will be diffimpossible, to directly heat flux split between boiling without using t

Effects of geometry, P/D, De heater and properties 

L Boiling effects in rod bundles have been 

correlated for our P/D, De range with acceptable uncertainty (Refs. 5 and 6). 

The void fraction will balong the test section and at fixed locations gamma ray detector. 

Effects of spacers M Locally enhances heat transfer; 

correlations/models are available, acceptable uncertainty (Ref. 7). 

Effects of spacer gridmeasured with the proplacement. 

Effects of fluid properties L Data exists for our range of conditions, little 

uncertainty. 

Local void fraction M Data does exist for tubes and rod bundles The void fraction will b

along the test section and at fixed location wgamma ray detector. 

Liquid subcooling M Determines the near wall condensation of 

vapor, energy split between sensible, and net vapor production. 

Subcooling will be meminiatures T/C’s and T/C’s. 
23

Table 2.2 Subcooled and Saturated Boiling - The Core Component Below the Quench Front (C

Process/Phenomena Ranking Basis RBHT Pro

Interfacial heat transfer area M Determines net vapor generation, near wall 

condensation 

Movies can be taken positions but very diffinterfacial area. May bubbles with laser. 

Decay power H Energy source for heat transfer Will be simulated ove

conditions. 

Saturated boiling heat transfer and heat flux 

M Similar to subcooled boiling, data is available for 

our P/D, De range. The uncertainty of Saturated boiling heat transfer coefficient will not significantly impact the PCT since rod is quenched. Can determine and TCHF. 

Rod wall temperature will be measured as wtemperature (saturatio

Effects of geometry, P/D, De L Data exists in the range of P/D, De with 

acceptable uncertainties (Refs. 5 and 6). 

Effects of spacers L Locally enhances heat transfer, 

correlations/models are available (Ref. 7), with acceptable uncertainty. 

Effects of properties L Data exists for our range of conditions, little 

uncertainty. 

Local void fraction H Provide the fluid conditions as the flow enters 

the quench front region and total steam flow which effects the liquid entrainment which directly impacts PCT. 

The void fraction will balong the test section 
24

Table 2.3 Quench Front Behavior in the Core Component 

Process/Phenomena Ranking Basis RBHT Pr

Fuel/heater rod materials, and thickness l, Cp, k, rod diameter 

H These properties effect the stored energy in the 

fuel/heater rod and its quench rate, uncertainty directly impacts PCT. 

Inconel Heater Rods Scaling and sensitivperformed to help derods to be as similar possible. Inconel wiBHT program which close to both ZircaloSteel. Separate effeto address propertie

Gap heat transfer coefficient M Second largest resistance in fuel rod. Can limit 

heat release rate from fuel pellet. Gap heat transfer coefficient has large uncertainty, but its impact on PCT is smaller since all stored energy will be released, timing may change however. 

Heater rods will not fuel rods since they Very high gap resistaheater rods (5000 Btrods are swagged. Gbe directly simulated heaters. 

Cladding surface effects 

• Oxides • Roughness • Materials • Tmin

• TCHF

M Since Zircaloy can oxidize, the oxide layer will 

quench sooner due to its low conductivity, versus Inconel or unoxidized Zircaloy. Also roughness from oxide promotes easier quenching. The surface condition affects Tmin

(Refs. 9 and 10). Quenching is a quasi-steady two dimensional process; values of Tmin and TCHF

can be estimated. Large uncertainty and impact on PCT. 

Inconel will be used since repeated tests Other data on Zircalosought and comparespecific Tmin models, 

simple model can tre(Refs. 9 and 10). Setests planned to add
25

Table 2.3 Quench Front Behavior in the Core Component (Continued) 

Process/Phenomena Ranking Basis RBHT P

Transition boiling heat transfer (surface-intermittent liquid contact heat transfer) 

H Determines the rate of heat release at quench 

front directly impacts PCT, large uncertainty. 

Depends on wall suheats give high valuheats give low valuetwo-dimensional procan be made using theater rod T/C’s to oconduction effects adimensional analysis 

Decay power M Stored energy is the primary source of energy 

for rods. 

Will be simulated in 

Void fraction/flow regime H Determines the wall heat transfer since large α

results in dispersed flow, low α is film boiling. Directly impacts PCT. 

Void fraction will be (estimated) using DP gamma densitomete

Interfacial area H Determines the initial configuration of the liquid 

as it enters the froth region directly impacts liquid/vapor heat transfer and resulting PCT downstream. 

Interfacial area can high-speed photograremain dry) and the measurements. 

Fluid temperature H Influences the quench rate and net vapor 

generation. Note: this is important for high flooding rates, with high subcooling. 

Local miniature fluid measure fluid tempeaxial positions. Void be measured with Dgamma densitomete
26

Table 2.4 Two-Phase Froth (Transition) Region for Core Component 

Process/Phenomena Ranking Basis RBHT Pr

Void fraction/flow regime H Void fraction/flow regime helps determine the 

amount of vapor-liquid heat transfer which affects the downstream vapor temperature at PCT, large uncertainty. 

The average void frameasured with DP cesuperheat will be estminiature fluid T/C’s 

Liquid entrainment H Significant generation of steam in the froth and 

quench regions helps to create the liquid entrainment. 

Can be calculated froenergy balance, howmust be made on vaMass stored in froth measured by DP celmeasurements. 

Liquid ligaments, drop sizes, interfacial area, droplet number density 

H Liquid surface characteristics determine the 

interfacial heat transfer in the transition region as well as the dispersed flow region, large uncertainty 

The flow regime, intedroplet size and veloestimated by high spand laser measurem

Film boiling heat transfer at low void fraction: classical film boiling (Bromley) 

H Film boiling heat transfer is the sum of the 

effects listed below in the adjacent column. Each effect is calculated separately and is added together in a code calculation, large uncertainty. 

The test will measure transfer and the vapowill be estimated from energy balance. The film boiling and directransfer. 

Droplet contact heat transfer H Wall temperature is low enough that some direct 

wall-to-liquid heat transfer is possible with a high heat transfer rate; large uncertainty. 

Some data exists (Rwe cannot separate tfrom total heat flux. 

Convective vapor heat transfer M Vapor convective heat transfer is not quite as 

important since the liquid content in the flow is large and the vapor velocities are low; but large uncertainty. 

Calculate from bundlusing measured vapopossible. 
27

Table 2.4 Two-Phase Froth (Transition) Region for Core Component (Continued) 

Process/Phenomena Ranking Basis RBHT Pr

Interfacial heat transfer M Interfacial heat transfer effects are expected to 

be small since the steam temperature is low, large uncertainty exists. 

The effects of the inttransfer will be inferrtemperature measuras calculated from bbalance and high spvoid fraction data. 

Radiation heat transfer to liquid/vapor 

M The radiation heat transfer effects are also small 

since the rod temperatures are low. 

Radiation tests will hdifferent componentsfrom data. 

Effects of spacers M The velocities and Reynolds numbers are low in 

this region such that droplet breakup and mixing are not as important. Drop deposition could occur. 

Heater rod T/C’s will effects of spacers, sindicate if spacers w

Decay power H Source of power for rods. Will be simulated. 
28

Table 2.5 Dispersed Flow Region for Core Component 

Process/Phenomena Ranking Basis RBHT Pro

Decay power H Energy source which determines the 

temperature of the heater rods, and energy to be removed by the coolant. 

Power is a controllablthe experiment. 

Fuel rod/heater properties ρ, Cp, 

k 

L The exact properties can be modeled and 

stored energy released is not as important. 

Dispersed flow film boiling (components are given below) H Dispersed flow film boiling modeling has a high uncertainty which directly effects the PCT. Current plan for tests 

bundle energy balancquality. The convectiwill be calculated usintests such that a 1Φ c

correlation for BHT faavailable. Specific terun to determine the aenhancement and radtransfer such that the transfer effects should from the total heat train a reflood test. 

Convection to superheated vapor 

H Principle mode of heat transfer as indicated in 

FLECHT-SEASET experiments (Ref. 4). 

Similar behavior is exBHT tests, will have smeasure, can estimatbalance. 

Dispersed phase enhancement of convective flow 

H Preliminary models indicate that the 

enhancement can be over 50 percent in source cases (Ref. 13). 

A series of separate tperformed to examine transfer effect. 

Direct wall contact heat transfer L Wall temperatures are significantly above Tmin

such that no contact is expected. 

Will verify no contact literature. This compdirectly measured in tcan estimate its effecsmall scale tests are 
29

Table 2.5 Dispersed Flow Region for Core Component (Continued) 

Process/Phenomena Ranking Basis RBHT Pr

Dry wall contact M Iloeje (Ref. 12) indicated this heat transfer 

mechanism is less important than vapor convection. 

This component canout of the total heat fBHT tests. Separate tests are needed. 

Vapor interfacial to droplet heat transfer. 

H The interfacial heat transfer reduces the vapor 

temperature which is the heat sink for the wall heat flux. 

The axial vapor tempdistribution will be mbundle average qualcalculated to obtain tAlso, drop sizes, velomeasured. 

Radiation heat transfer to: 

• surfaces • vapor • droplets 

H/M H/M H/M 

This is important at higher bundle elevations (h) where the convective heat transfer is small since the vapor is so highly superheated. Very important for BWR reflood with sprays, and colder surrounding can. Large uncertainty. 

Separate tests will bcharacterize the radithe BHT test facility. transfer will be calcuforced flooding tests

Gap heat transfer L Controlling thermal resistance is the dispersed 

flow film boiling heat transfer resistance. The large gap heat transfer uncertainties can be accepted, but fuel center line temperature will be impacted. 

Heater rods will not sheat transfer, but not regime. 

Cladding material L Cladding material in the tests is Inconel which 

has the same conductivity as Zircaloy nearly the same temperature drop will occur. 

Test will use Inconel

Reaction rate M Inconel will not react while Zircaloy will react and 

create a secondary heat source at very high PCTs, Zirc reaction can be significant. 

Reaction rate not simsince cladding is proInconel. 
30

Table 2.5 Dispersed Flow Region for Core Component (Continued) 

Process/Phenomena Ranking Basis RBHT Pr

Fuel clad swelling/ballooning L Ballooning can divert flow from the PCT location 

above the ballooning region. The ballooned cladding usually is not the PCT location. 

Flow blockage is not was modeled in FLEtest (Ref. 13), heat trimproved at PCT loc
31

Table 2.6 Top Down Quench in Core Component 

Process/Phenomena Ranking Basis RBHT Pro

De-entrainment of film flow L1 The film flow is the heat sink needed to quench 

the heater rod. This has high uncertainty. 

The top quench front but the de-entrainmenfilm will not be measu

Sputtering droplet size and velocity 

L The droplets are sputtered off at the quench 

front and are then re-entrained upward. Since the sputtering front is above PCT location, no direct impact. The entrained sputtered drops do effect the total liquid entrainment into the reactor system, as well as the steam production in the steam generators. 

If the top quench frondownward such that iviewing location then velocity can be estimaspeed movies and lasmeasurements. 

Fuel rod/heater rod properties for stored energy ρ, Cp, k. 

L1 These properties are important since they 

determine the heat release into the coolant. However, since this occurs above PCT level, no impact. 

Heater rod properties the same as fuel rods obtain the correct storelease. 

Gap heat transfer L1 Affects the rate of energy release from 

fuel/heater rod. 

No gap heat transfer 

1Some of these individual items can be ranked as high (H) within the top-down quenching process; however, the 

as low for a PWR/BWR since it occurs downstream of the PCT location. 
32

Table 2.7 Preliminary PIRT for Gravity Reflood Systems Effects Tests 

Process/Phenomena Ranking Basis RBHT P

Upper plenum - entrainment/deentrainment M The plenum will fill to a given void fraction after which the remaining flow will be entrained unto 

the hot leg, large uncertainty. 

A non-scaled plenuin the tests, it shouentrain relative to a 

Hot leg - entrainment/deentrainment L The hot legs have a small volume and any liquid swept with the hot leg will be entrained into the 

steam generator plenums, medium uncertainty. 

Hot leg entrainmenup to the separator the liquid flow. 

Pressurizer L Pressurizer is filled with steam and is not an 

active component- small uncertainty. 

Pressurizer will not 

Steam generators H The generators evaporate entrained droplets and 

superheat the steam such that the volume flow releases (particularly at low pressure). The result is a higher steam flow downstream of the generators-high uncertainty since a good model is needed. FLECHT-SEASET data exists for reflood. 

The steam generatsimulated, but the asteam flow will be aspecifying the inlet 

Reactor coolant pumps H Largest resistance in the reactor coolant system; 

directly affects the core flooding rate; low uncertainty. 

The resistance in thconsidered to give flooding rate responsystem calculations

Cold leg accumulator injection H Initial ECC flow into the bundle. Accumulator flow ra

and simulated. 

Cold leg pumped injection H Pumped injection maintains core cooling for the 

majority of the reflood transient. 

Pumped injection w
33

Table 2.7 Preliminary PIRT for Gravity Reflood Systems Effects Tests (Continued) 

Process/Phenomena Ranking Basis RBHT Pr

Pressure H Low pressure (~35 psia) significantly impacts 

the increased vapor volume flow rate, which decreases the bundle flooding rate 

Pressure range will b

Injection subcooling M/H Lower subcooling will result in more boiling 

below the quench front such that there is additional vapor to vent. 

Subcooling range wi

Downcomer wall heat transfer H The heat transfer from the downcomer walls can 

raise the ECC fluid temperature as it enters the core, resulting in less subcooling and more steam generation. 

Simulate effect by vatemperature. 

Lower plenum wall heat transfer M Same effect as downcomer but less severe. Simulate the metal h

varying the inlet tem

Break L Excess ECC injection spills from system; break 

ΔP helps pressurize reactor system. 

Simulate break ΔP. 
34

In addition to the forced reflood, experiments will be performed to simulate the effects of the 

gravity reflood. Previous large-break LOCA PIRTs were reviewed to determine the most 

important system components which can affect the core thermal response during reflood. Table 

2.7 lists those components designated as having a HIGH ranking by the Los Alamos and the 

Westinghouse PIRTs, along with the ranking as developed in this program. Many of the 

components listed in Table 2.7 will not be simulated in the RBHT facility since the primary focus 

is for separate-effects tests. However, variable reflood tests can be performed in which the 

effects of the most important system parameters can be assessed as discussed in Table 2.7. 

The injection flows, system pressure and the effects of the different core inlet ECC temperatures 

can be simulated. Steam binding due to additional evaporation of liquid carried to the 

generators, which are not modeled in the test facility, can be simulated with the selected 

variable inlet flooding rate. In this table, it is already assumed that the core component is a 

highly ranked parameter and the focus will be on the reactor system components.

2.3 PIRT for Rod Bundle Heat Transfer Tests - BWR Phenomena

2.3.1 Introduction 

Best estimate calculations for a BWR-6 plant were reviewed (Ref. 14). The calculations 

indicated that once the vessel was depressurized, a three-dimensional flow pattern would be 

established in which there was downflow at the core edge through the low powered assemblies 

since the counter current flow was less limiting at these locations, and upflow in the hotter high 

power fuel assemblies. The bypass region also helped direct the spray flow down from the 

upper plenum to the lower plenum. The highest powered assemblies were calculated to be in 

co-current upflow for the majority of the transient such that they reflooded in a very similar 

manner as a PWR hot assembly. The high power assemblies generated sufficient steam flow 

such that they remained above the flooding limit at the top of the fuel assembly and very little, if 

any, water penetrated into the assembly from the upper plenum. 

2.3.2 BWR Reflood Phenomena of Interest 

Nearly all the phenomena identified with rod bundle heat transfer for PWRs are applicable to the 

hot assembly in a BWR since it refloods in a similar manner. However, one difference between 

the reflooding behavior of the high power BWR assemblies and a PWR assembly is the 

presence of the fuel assembly shroud or channel in the BWR design. The shroud is calculated 

to quench from the liquid in the bypass region so there is more surface-to-surface radiation heat 

transfer occurring in the BWR fuel assembly compared to a PWR fuel assembly. The additional 

surface-to-surface radiation can be simulated in the RBHT experiments since the test facility will 

have a shroud around the test bundle. 

Since the high power BWR fuel assemblies are in co-current upflow, similar to PWR fuel 

assemblies, the key thermal-hydraulic phenomena identified as being highly ranked in Tables 

2.1 to 2.6 are also highly ranked for the BWR. The one factor which changes is the surface-tosurface radiation heat transfer in the dispersed flow film boiling regime. It is a higher ranked 

phenomenon for BWRs than PWRs. 
35

Table 2.8 High Ranked BWR Core Phenomena 

Process/Phenomena Basis RBHT Progra

Core 

• Film boiling 

PCT is determined in film boiling period. Film boiling components will be me

• Upper tie plate CCFL Hot assembly is in co-current up flow above 

CCFL 

Similar behavior to PWR reflooding

• Channel-bypass flow Flow bypass will help cool the BWR fuel 

assembly core. 

The housing in the RBHT test will a BWR channel. 

• Steam cooling A portion of the dispersed flow film boiling heat Simulated in RBHT tests. • Dryout Transition from nucleate boiling and film boiling Simulated in RBHT tests, but hot a

to be in upflow. 

• Natural circulation flow Flow into the core and system pressure drops. Flow range can be simulated in RB• Fluid mixing Determines the liquid temperature in the upper 

plenum for CCFL break down. 

Not simulated in RBHT, but hot asbe in upflow. 

• Fuel rod quench front Heat release from quench front will determine 

entrainment to the upper region of the bundle. 

Scaling analysis will be performed release rate relative to nuclear fue

• Decay heat Energy source for heat transfer Simulated in RBHT. • Interfacial shear Affects the void fraction and resulting droplet 

and liquid velocity in the entrained flow. 

Since pressure, temperature, geomsimulated in RBHT, interfacial shesimulated. 

• Rewet: bottom Reflood BWR hot assembly refloods like PWR. Simulated in RBHT. • Rewet temperature Determines the quench front point on the fuel 

rod. 

RBHT will use different materials tdata will be used to support the RB
36

Table 2.8 High Ranked BWR Core Phenomena (Continued) 

Process/Phenomena Basis RBHT Progra

• Top down rewet Top of the hot assembly fuel will rewet in a 

similar manner to PWR. 

Will be simulated in RBHT. 

• Void distribution Liquid distribution in the bundle. Should be same/similar for PWR in • Two-phase level Similar to quench front location, indicates 

location of nucleate and film boiling. 

Two-phase level should be simulattemperature, and pressure are sim
37

The highest ranked phenomena for the reflood period are summarized in Table 2.8. Comparing 

those ranked as HIGH in Tables 2.1 to 2.6 shows that the BWR hot assembly phenomena are 

captured. 

2.4 Conclusions

Preliminary PIRTs were developed in which the components of the heat transfer models were 

identified on a sub-component level in the same fashion as a best-estimate computer code 

would calculate the phenomena for both a PWR and a BWR hot assembly. For either design, 

the hot assembly thermal-hydraulic behavior is very similar so there is substantial over-lap in the 

PIRTs for the large-break LOCA. 

The ability of the RBHT facility to simulate the highly ranked PWR and BWR PIRT items was 

assessed and the test facility can represent nearly all the phenomena of interest. The area 

where the simulation is the weakest is in the materials used for the cladding, heater rods and 

the housing, as compared to nuclear fuel rods and a BWR Zircaloy channel box. Scaling 

studies will be performed as part of the program to select the materials to minimize the deviation 

from the true plant design. Another area where the exact separation of different phenomena is 

difficult is the direct measurement and separation of certain boiling heat transfer mechanisms 

such as the effects of forced convection in convective boiling, direct droplet contact heat transfer 

from film boiling, and dry contact heat transfer from film boiling. The total heat flux will be 

measured, and estimates of these effects will be made. 

Another area of limited simulation is the modeling of system effects behavior using an oscillatory 

injection flow to simulate the effects of gravity refloods. Several of the primary system 

components are not simulated in the proposed facility; however, these effects will be reflected in 

the range of flows simulated in the oscillatory mode. 

2.5 References

1. US Nuclear Regulatory Commission, “Quantifying Reactor Safety Margins”, NUREG/CR5249, 1989. 

2. Boyack, B., “AP600 Large-Break Loss-of-Coolant Accident Phenomena Identification and 

Ranking Tabulation,” LA-UR-95-2718, 1995. 

3. Letter from L. W. Ward to Dr. D. Ebert, “Draft of BWR PIRT Tables and Preliminary 

Assessment Matrix,” September 30, 1997. 

4. Lee, N., Wong, S., Yeh, H. C. and Hochreiter, L. E., “PWR FLECHT-SEASET Unblocked 

Bundle Forced and Gravity Reflood Task Data Evaluation and Analysis Report,” 

NUREG/CR-2256, 1981. 

5. Todreas, N. E. and Kazimi, M. S., Nuclear Systems I, Thermal Hydraulic Fundamentals, 

Hemisphere Pub., 1990. 

6. Tong, L. S. and Tang, Y. S., Boiling Heat Transfer and Two-Phase Flow, Second Edition, 

Taylor & Francis Pub., 1997. 
38

7. Yao, S-C., Hochreiter, L. E. and Leech, W. J., “Heat Transfer Augmentation in Rod 

Bundles Near Spacer Grids,” J. of Heat Transfer, Trans. ASME, Vol 104, No. 1, pg 76-81, 

1982. 

8. Chen, J. C. “A Correlation for Boiling Heat Transfer to Saturated Fluids in Convective 

Flows,” Ind. & Eng. Chem., Process Design and Dev., Vol 5, pg 322, 1963. 

9. Henry, R.E., “A Correlation for the Minimum Film Boiling Temperature,” AIChE 

Symposium, 138, Vol 70, pg 81, 1974. 

10. Shumway, R.W., “Return to Nucleate Boiling,” Presented at the National Heat Transfer 

Conference, Denver, ANS Proc., CONF-850810 (EGG-M-03985), 1985. 

11. Petersen, C. O. “The Dynamics and Heat Transfer Characteristics of Water Droplets 

Impinging on a Heated Surface,” PhD Thesis, Carnegie-Mellon University, 1967. 

12. Iloeje, O. C., Rohsenow, W. M. and Griffith, P., “Three-Step Model of Dispersed Flow Heat 

Transfer (Post CHF Vertical Flow),” ASME Publication, 75-WA-HT-1, Presentation at 

Winter Annual Meeting, Houston, 1975. 

13. Paik, C. Y., Hochreiter, L.E., Kelly, J.M. and Kohrt, R.J., “Analysis of FLECHT-SEASET 

163-Rod Blocked Bundle Data using COBRA-TF,” NUREG/CR-4166, 1985. 

14. Wheatly, P. D., “Analysis of a BWR/6-218 During a Large Break Loss of Coolant Accident 

Using Evaluation Type Boundary Conditions,” EGG-SAAM-6519, 1984.
39

3. LITERATURE REVIEW 

3.1 Introduction

A number of important rod bundle experiments were reviewed to determine the availability of 

data, test facility design, types of tests, instrumentation, and data from tests. These rod bundle 

experiments include: 

• FLECHT Cosine Tests (NRC/Westinghouse) 

• FLECHT Skewed Axial Power Shape Tests (NRC/Westinghouse) 

• FLECHT-SEASET 21 Rod Bundle Tests (NRC/Westinghouse) 

• FLECHT-SEASET 161 Unblocked Bundle Tests (NRC/Westinghouse) 

• FEBA Reflood Tests (Germany) 

• THTF Rod Bundle Tests (NRC/Oak Ridge National Lab) 

• FRIGG Rod Loop Tests (Sweden) 

• GE 9-Rod Bundle Tests (NRC/General Electric) 

• NRU Rod Bundle Tests (Canada) 

• ACHILLES Reflood Tests (United Kingdom) 

• Lehigh 9-Rod Bundle Tests (NRC/Lehigh University) 

• PERICLES Reflood Tests (France) 

In addition to the above rod bundle tests comprising the first portion of the review, more than 

three hundred articles on single tube tests and related studies were included in the second 

portion. The relevant information is sub-divided into 10 different classifications, including liquid 

entrainment and breakup; drop size distribution and droplet number density; interfacial shear 

and droplet velocity; droplet-enhanced heat transfer; droplet evaporative heat transfer; direct 

contact heat transfer; total wall heat transfer; effects of spacer grids; effects of inlet flow 

oscillation and thermal non-equilibrium; and other factors. 

A comprehensive review of the literature on reflood heat transfer was performed; it included two 

major portions. The first portion focused on the rod bundle tests whereas the second portion 

focused on single tube tests and related studies. Unique information useful to address the 

phenomena identified in the PIRT is gathered from both. This information is then sub-divided 

into several different classifications indicating which information can be used for which 

phenomena. A master cross-reference table is constructed identifying the data source for the 

highly ranked phenomena. The applicability of the data to determine and quantify the particular 

phenomena of interest is discussed along with their major deficiencies, if any. 

3.2 Rod Bundle Tests

The dispersed flow film boiling reflood period is the most limiting heat transfer period for the 

large break LOCA. Several experimental programs were performed over the years to provide 

the data needed to develop models for this portion of the LOCA transient. For PWRs, the most 

significant program was sponsored by the Nuclear Regulatory Commission and Westinghouse, 

the Full Length Emergency Core Heat Transfer (FLECHT) Program which was completed in 

1973 (Refs. R1-R4). This initial program, including FLECHT Cosine tests and FLECHT Skewed 

Power Shape tests, provided experimental data used to develop empirical correlations to 
40

calculate heat transfer and entrainment using simple thermal-hydraulic models which would 

conform to the Appendix K rules, as given in 1974. 

The FLECHT Cosine tests produced some data which is of interest for improved reflood 

modeling. In particular, the vapor temperature data at the 2.1, 3.05, 3.81m (7, 10, and 12.5 ft) 

elevations could be useful since these data indicate the degree of non-equilibrium within the 

flow. The pressure drop measurements, however, were too coarse to be used as an indicator of 

the void fraction within the bundle. A more detailed review of the FLECHT Cosine tests is given 

in Appendix A-1. 

The FLECHT Skewed Power Shape tests also produced data of interest. In particular, the 

different axial power shape used in these tests is quite useful for assessing computer codes for 

a cosine power shape. The pressure drop measurements were improved in the skewed bundle 

tests to provide better measurement of local void fraction. In addition, the low flooding rate tests 

provided information on the overall heat transfer process and some of the individual models and 

phenomena which comprise the reflood heat transfer process. However, there was insufficient 

information on the vapor temperature distribution in the test bundle to accurately determine the 

local non-equilibrium. A more detailed review of the FLECHT Skewed Power Shape tests is 

given in Appendix A-2. 

More recently, the Nuclear Regulatory Commission, Westinghouse and Electrical Power 

Research Institute sponsored the FLECHT-Separate Effects and Systems Effects Tests 

FLECHT-SEASET program, which was completed in 1985 (Refs. R5-R8). A total of 16 reports 

were produced. The objectives of this program were to quantify the conservatism in the 

Appendix K rule for the reflood portion of the transient and to provide experimental data which 

could be used to validate a PWR best-estimate thermal-hydraulic computer code. The 

FLECHT-SEASET program provided a portion of the database used by the NRC to revise 

10CFR50.46. 

A detailed review of the FLECHT-SEASET 21-Rod Bundle tests is given in Appendix A-3 while 

a review of the FLECHT-SEASET 161 Unblocked Bundle tests is given in Appendix A-4. The 

21-Rod Bundle tests provided information on single-phase friction factors and grid pressure loss 

coefficients. However, no attempt was made to determine the void fraction, droplet size, and 

droplet velocity since there were no windows in the test bundle. The 161 Unblocked Bundle 

tests did provide data on void fraction, drop size, and droplet velocity as well as local quality, 

vapor temperature, rod surface temperature, and heat flux split between radiation heat transfer 

and convective Dispersed Flow Film Boiling heat transfer. The analysis of the test data was the 

most complete of all the FLECHT series. It is recommended that the 161 Unblocked Bundle 

Tests data be screened and used to validate the NRC consolidated code. 

One of the more interesting rod bundle reflood experiments was the FEBA (Refs. R9-R11) 

program performed at the Karlsruhe Research Center. FEBA examined the effects of spacer 

grids on dispersed flow film boiling by performing tests with and without a spacer grid located at 

the center of the bundle. The data clearly shows the beneficial effects of spacer grids in 

promoting improved heat transfer downstream of the spacer by shattering entrained droplets, 

enhancing convective heat transfer, and quenching of the grid. Current vendor fuel assembly 

designs use mixing vane spacer grids. These types of grids have a higher rod bundle 

subchannel flow area reduction and provide greater heat transfer improvement downstream of 

the spacer grid. The FEBA data, however, provided very little information on the individual 
41

thermal-hydraulic processes during the reflood stage. A more detailed review of the FEBA tests 

is given in Appendix A-5.

The Nuclear Regulatory Commission has sponsored higher pressure rod bundle film boiling, 

steam cooling, and level swell experiments at the Oak Ridge National Laboratory on a full length 

8x8 rod bundle (Refs. R12 and R13) in the Thermal Hydraulics Test Facility (THTF). The THTF 

tests also examined dispersed flow film boiling conditions. However, the pressure was much 

higher, more characteristic of a PWR or BWR blowdown situation. These experiments also 

confirmed the beneficial heat transfer effects of spacer grids for higher-pressure blowdown 

situations as well as for reflood heat transfer. However, the effect of non-equilibrium was not 

accounted for because the fluid conditions were determined from mass and energy 

conservation by assuming thermodynamic equilibrium. A more detailed review of the THTF 

tests is given in Appendix A-6. 

Earlier bundle data include the FRIGG facility performed in Sweden (Refs. R14-R16) and the 

GE 9-Rod Bundle tests performed by General Electric (Refs. R17 and R18). FRIGG employed 

a uniform power shape, improved our understanding of the burnout limits and the natural 

circulation flow inside a simulated Marviken core. The GE 9-Rod Bundle tests improved our 

understanding of the subchannel flow and energy diversions under typical BWR conditions. 

Neither tests, however, addressed the heat transfer phenomena associated with post-LOCA 

reflood conditions. More detailed reviews of FRIGG and the GE 9-Rod Bundle tests are given in 

Appendices A-7 and A-8, respectively. 

NRU rod bundle tests were performed in Chalk River, Canada (Refs. R19 and R20). These 

nuclear fuel rod reflood experiments provide data on cladding temperature, coolant temperature, 

and shroud temperature during the preconditioning, pre-transient, and transient phases. 

However, only the total wall heat transfer was measured so their usefulness in validating models 

is limited. A more detailed review of the NRU Rod Bundle tests is given in Appendix A-9. 

Most recently, the ACHILLES reflood tests (Refs. R21-R26) sponsored by the Central Electricity 

Generating Board (CEGB), were performed by the United Kingdom Atomic Energy Agency 

(UKAEA) at the Winfrith Laboratories as part of the safety case for PWRs in the United 

Kingdom. These tests covered a wide range of conditions and included inlet flow oscillations, 

stepped forced flooding rates, and gravity reflood. They provide some of the best reflood data 

available for computer code validation. Unique data include subchannel droplet distribution, 

spacer grid loss coefficients, instrumented spacer grid and local fluid temperatures, and finely 

spaced heater rod thermocouple data which shows the heat transfer effects of the spacer grids 

and the quench front. The differential pressure data was taken using small spans both between 

grids and across spacer grids. This data must be corrected for frictional and acceleration 

pressure drop to infer the local void fraction. Once this is performed, local heat transfer can 

then be correlated with void fraction. The ACHILLES data should be screened and used to 

validate the NRC consolidated code. A more detailed review of the ACHILLES Reflood tests is 

given in Appendix A-10. 

Finally, there were smaller rod bundle tests performed at Lehigh University (Refs. R27 and 

R28). These tests employed a 9-rod bundle having a four foot test section with one spacer grid 

located at 30 inches from the bottom. The rods had a linear power profile to provide a constant 

heat flux over the length of the test section. Traversing stream probes were used to measure 

the thermodynamic non-equilibrium near the quench front. A more detailed review of these 

tests is given in Appendix A-11. 
42

Only the FLECHT-SEASET experiments attempted to measure the details of the heat transfer 

and non-equilibrium flow such that a best-estimate computer code could be assessed against 

the data. In these experiments, vapor superheat was measured at several axial locations. Wall 

temperatures were measured for the housing, and guide tube thimbles and the heater rods. 

Limited data of droplet diameters and velocities were obtained for a few selected tests using 

high-speed photography. The heater rod total heat flux was calculated from an inverse 

conduction technique using the heater rod thermocouples and measured power. With these 

measurements, the heat transfer due to radiation could be calculated and separated from the 

total wall heat transfer, as shown in Reference 7. Convective heat transfer, droplet evaporation, 

and droplet enhancement of the convection heat transfer were also calculated. Mass and 

energy balances could be calculated for the test bundle such that the axial behavior of the flow 

quality could be calculated. Void fraction was measured along the bundle, with the most 

accurate measurements at or near the quench front. The calculated radiation heat transfer was 

subtracted from the total measured heat flux to obtain the convective portion. The FLECHTSEASET data are useful for code validation. 

Table 3.1 compares the data from the various rod bundle tests indicating the specific data 

source applicable to particular phenomena of interest and the major deficiencies of the data 

source. 

3.3 Single-Tube Tests and Related Studies

3.3.1 Liquid Entrainment and Breakup 

The physical mechanisms that lend to liquid entrainment and breakup are of paramount 

importance in that they affect the drop size distribution and the number density. These two 

quantities together with the droplet velocity determine the interfacial surface area and interfacial 

heat transport. In addition to the interfacial surface area, the presence of droplets in the vapor 

flow directly influences the convective heat transfer by modifying the turbulence structure in the 

flow field, by evaporation of the droplets, and by direct contact heat transfer at the wall. In fact, 

liquid entrainment from the froth region just above the quench front is the single largest 

uncertainty in predicting the DFFB behavior in reflooding the rod bundle. 

This section focuses on the topic of liquid entrainment and breakup. The topics of drop size 

distribution and number density will be discussed in 3.3.2, droplet velocity, drag, and 

interactions in 3.3.3, droplet-enhanced heat transfer in 3.3.4, droplet evaporative heat transfer in 

3.3.5, and direct contact heat transfer in 3.3.6. In addition, total wall heat transfer will be 

discussed in 3.3.7, effects of spacer grids in 3.3.8, the effects of inlet flow oscillation and nonequilibrium in 3.3.9, and other factors in 3.3.10. 

The subject of liquid entrainment and breakup has been studied by Adams and Clare [1, 2], 

Almenas and Lee [6], Binder and Hanratty [22], Clare and Fairbain [46-48], Cousins and Hewitt 

[52], Dallman et al. [55, 56], El Kassaby and Ganic [72], Faeth [79], Ganic et al. [83, 85], 

Hanratty and Engen [98], Hay et al. [106], Hewitt [108], Hughmark [116], Hutchinson [117], Ishii 

[130], Ishii and Grolmes [131], Ishii and Mishima [125, 126], Jensen [132], Kataoka et al. [139], 

Kline et al. [154], Kocamustafaogullari [155], Krzeczkowski [157], Kuo and Cheung [158], 

Kutateladze [159], Lee and Ryley [163], Levy [175, 176], Lindsted et al. [177], Lopes and Dukler 

[180-182], Lopez de Bertodano and Jan [183], Mastanajak [187], Minh and Huyghe [190], Newitt 

et al. [203], Nigmatulin [206], Paras and Karabelas [219], Petrovichev et al. [223],
43

Table 3.1 Comparison of the Data from Various Rod Bundle Tests 

Rod Bundle Tests Specific Data Source Applicable to 

Particular Phenomena of Interest 

Major Deficiencies of the Data Source 

FLECHT Cosine Tests Vapor temperature data at the 7, 10, and 

12.5 foot elevations could be useful since these data indicate the degree of nonequilibrium within the flow. 

Pressure drop measurements too coarse to be used as an indicator of void fraction within the bundle. 

Ma

FLECHT Skewed Power Shape Tests 

The different axial power shape used in these tests and the low flooding rate data could be useful in determining some of the individual models and phenomena. 

Lack of detailed information on the vapor temperature distribution in the test bundle to determine the local non-equilibrium. 

Ma

FLECHT-SEASET 21-Rod Bundle Tests 

Useful information on single-phase friction factors and grid pressure loss coefficients. 

No attempt made to determine the void fraction, droplet velocity, and drop size, no windows in the test bundle. 

Ma

FLECHT-SEASET 161 Unblocked Bundle Tests 

Measured details of non-equilibrium DFFB heat transfer, provided useful data on void fraction, drop size, droplet velocity, local quality, vapor temperature, rod surface temperature, and heat flux split between radiation and convective DFFB. 

Some of the steam probes used in these tests did not function as desired. Also, the bundle was rebuilt due to heater rod problems, so that channel designation may have changed. 

Sh

FEBA Reflood Tests Data show effects of spacer grids in 

promoting mixing downstream of the spacer by shattering entrained droplets, enhanced convective heat transfer, and the quenching effect of the grid. 

Very little information on individual processes such as the droplet behavior was reported. 

Daspacon

THTF Rod Bundle Tests DFFB behavior under high-pressure 

conditions, more characteristic of a blowdown situation. Useful data were obtained on the effect of spacer grid. 

Applicable to high-pressure blowdown situations rather than the reflood stage. Fluid conditions were determined by assuming thermodynamic equilibrium. 

To futupre
44

Table 3.1 Comparison of the Data from Various Rod Bundle Tests (Continued) 

Rod Bundle Tests Specific Data Source Applicable to 

Particular Phenomena of Interest 

Major Deficiencies of the Data Source 

FRIGG Loop Tests Data on burnout limits and the natural 

circulation flow inside the test core may be useful. 

Uniform power shape. Reflood heat transfer phenomena were not addressed. 

Macon

GE 9-Rod Bundle Tests Provide some data on the subchannel flow 

and the energy diversions under typical BWR conditions. 

Very little information was reported for the phenomena associated with post-LOCA reflood conditions. 

Macon

NRU Rod Bundle Tests Nuclear fuel rod reflood experiments. 

Provide some data on the cladding temperature, coolant temperature and shroud temperature during the pre-transient and transient phases. 

Only the total wall heat transfer was measured. No fluid conditions were determined in the experiments. May involve compensating errors. 

Sh

ACHILLES Reflood Tests 

Included inlet flow oscillations, stepped forced flooding, and gravity reflood. Provide some unique data on subchannel droplet distribution, spacer grid loss coefficient, instrumented spacer grid and local fluid temperature, and finely spaced heater rod thermocouple data showing the heat transfer effects of the spacer grids and the quench front. 

The differential pressure data was taken using small spans both between grids and across spacer grids. This data needs to be corrected for frictional pressure drop and acceleration pressure drop in order to be used for inferring the local void fraction. 

Shcon

Lehigh 9-Rod Bundle Tests 

Employed a traversing steam probe in a 4-foot test section with a spacer grid located at the 30-inch elevation to measure the nonequilibrium reflood heat transfer. 

The test section was only 4 feet in length with only one spacer grid. 

Macon
45

Podvysotsky and Shrayber [226], Ramirez [228], Richter [233], Sarjeant [235], Schadel et al. 

[238], Sekoguchi and Takeishi [242], Smith [247], Soliman and Sims [249], Sugawara [256], Van 

der Molen [278], Wicks and Dukler [288], Wilkes et al. [290], Williams et al. [294], Woodmansee 

and Hanratty [297], Yadigaroglu [301], Yao [304, 305, 308], Yoshioka and Hasegawa [315] and 

Zuber [321]. 

Depending on the flow situation, entrainment may take place in a number of different ways. 

Physically, when two fluids flow over each other, the interface of the two fluids is inherently 

unstable. As the relative velocity between the two fluids exceeds a certain critical value, 

instabilities set in and grow in the interfacial region, resulting in the formation of wavy interface 

and large amplitude roll waves (Hanratty and Hershmen [97] and Ishii and Grohmes [131]). 

This so-called Kelvin-Helmholtz instability is responsible for the entrainment of liquid droplets 

from a wavy film into a gas flow. Hydrodynamic and surface tension forces govern the motion 

and deformation of the wave crests. Under certain conditions, these forces lead to extreme 

deformation of the interface resulting in the breakup of a portion of the wave into several fluid 

droplets. 

The forces acting on the wave crests depend on the flow pattern around them as well as the 

shape of the interface. In the reflood phase of LOCA, liquid droplets are likely to be generated 

by shearing off of roll waves. The drag force acting on the wave tops deforms the interface 

against the retaining force of the liquid surface tension. At vapor velocities beyond the inception 

of entrainment, the tops of large amplitude roll waves are sheared off from the wave crests by 

the vapor flow and then broken into small droplets. 

A clear physical understanding of the droplet generation mechanisms is crucial in modeling 

reflood. The initial sizes and velocities of the droplets depend on how they were generated 

above the quench front in the froth region. The onset of entrainment is believed to occur when 

the deforming forces (i.e., the interfacial shear forces or the hydrodynamic drag forces) become 

greater than the retaining forces (i.e., the surface tension forces) [131, 139]. Under some 

special circumstances, however, large liquid globules can be generated above the quench front 

by disintegration of waves formed in the wetted position of a flow channel [2]. 

Inception criteria for the onset of entrainment in annular two-phase flow have been based 

largely on experimental data, as reported by Ardron and Hall [11], Ishii and Grolmes [131], 

Jensen [132], Kataoka et al. [139], Kocamustafaogullari et al. [155], Kutateladze [159], Newitt et 

al. [203], Nigmatulin [206], Richter [233], Sekoguchi and Takeishi [242], Wallis [280], and Zuber 

[321]. Thus far, no dynamic models have been implemented in existing transient analysis codes 

to describe the functional dependence of the initial drop sizes and velocities on the droplet 

generation mechanisms. The key controlling parameters that need to be considered include the 

film Reynolds number, the viscosity numbers of the fluids, the critical Weber number, the critical 

mass flux and the Kutateladze number. 

The rate of entrainment has been correlated by a number of investigators based upon 

measured data. Entrainment measurements in annular gas-liquid flow have been interpreted by 

Dallman et al. [56]. There are two widely used techniques for measuring the fraction of liquid 

flux that is entrained into the gas phase as droplets. The first is based on local measurements 

using a sampling probe to determine the liquid mass flux at the axial location of the probe. 

Usually, measurement is made only along the centerline with the assumption that the mass flux 

is uniform radially. This technique has been used with limited success [52, 289, 299]. The 

second technique is based on the measurement of the liquid film flow by removing it from the 
46

test section. In so doing, it eliminates those uncertainties associated with the local probe 

measurement technique. This liquid film removal method is thought to be more accurate [52, 

126, 218, 223]. 

In general, the entrainment rate, which governs the rate of droplet formation, is measured in 

terms of the so-called entrained fraction. This quantity is defined as the fraction of the liquid flux 

flowing as droplets in the two-phase flow system. Correlations of the entrainment data have 

been made by a number of investigators with limited success. The most widely used 

entrainment correlations include those reported by Dallman et al. [55, 56], Hutchinson and 

Whalley [117], Ishii and Mishima [125], Ishii [130], Minh and Hugghe [190], Nigmatulin [206], 

Paleev and Filipovich [218], Paras and Karabelas [219], Wicks and Dukler [289], and Williams et 

al. [294]. 

An important quantity that needs to be considered along with the rate of liquid entrainment is the 

rate of deposition of droplets carried by the vapor core to the liquid film. Whereas the 

entrainment of liquid from the film will cause an increase in the fraction of liquid entrained in the 

vapor core, the deposition of droplet onto the liquid film will cause a decrease in the fraction of 

liquid in the vapor core. Although the initial drop sizes and velocities are dictated by the 

mechanisms of liquid entrainment, the droplet number density and the drop sizes downstream 

of the point of droplets generation depend on both the rates of entrainment and deposition. 

Specifically, the rate of deposition has direct influence on the evolution of the liquid droplets in 

the downstream locations of the vapor core. 

The process of droplet deposition has been studied by Almenas and Lee [6], Binder and 

Hanratty [22], Cousins and Hewitt [52], Dallman and Kirchner [55], El Kassaby and Ganic [72], 

Ganic et al. [83, 85], Hanratty [99], Hay et al. [106], Langevin [161], Lee and Almenas [164], 

Lopes and Dukler [182], Mastanajah [187], Nishio and Hirata [208], Paras and Karabelas [219], 

Pedersen [221], Schadel et al. [238], Sugawara [256], Wilkes et al. [290] and Williams et al. 

[294]. In general, the rate of deposition of droplets from the vapor core onto the liquid film is a 

function of the fluid properties, the droplet concentration in the vapor core, and the radial 

velocities of the droplets. Experimental observations have indicated that the rate of deposition 

is dependent linearly on the droplet concentration in the vapor core. Useful correlations have 

been obtained by Binder and Hewitt [22], Nigmatulin [206], Schadel et al. [238], and Williams et 

al. [294]. 

3.3.2 Drop Size Distribution and Number Density 

The interfacial area and thus the interfacial heat and mass transfer depend not only on the drop 

size distribution but also on the volumetric concentration of the droplets, i.e., the number 

density. As mentioned in 3.3.1, these two quantities (drop size distribution and number density) 

are functions of the droplet generation mechanisms and their previous history (i.e., time 

evolution of the droplets) in the flow field. The latter requires the consideration of droplet 

entrainment, droplet evaporation, droplet breakup induced by spacer grids, drop coalescence, 

and droplet deposition upon impingement on the wall. The topics of drop size distribution and 

number density have been studied extensively by many investigators in the past, notably among 

which are Adams and Clare [2], Ardron and Hall [11], Claire and Fairbain [46], Coulaloglou and 

Tavlarides [51], Cousins and Hewitt [52], Cumo et al. [54], De Jarlias [58], Hagiwara et al. [96], 

Hay et al. [106], Jepson et al. [133], Juhel [135], Kataoka et al. [139], Kocamustafaogullari et al. 

[155], Kuo and Cheung [158], Lee et al. [165], Mugele and Evans [199], Nukiyama and 
47

Tanazawa [212], Podvysotsky and Shrayber [226], Sarjeant [235], Seban et al. [239, 241], Wick 

and Dukler [289], Wilkes et al. [290], Wong and Hochreiter [295] and Zuber et al. [319, 320]. 

Owing to the difficulty in defining the drop size distribution, many investigators have 

characterized the droplets by an average diameter. This simplification, however, can be 

justified only if the axial velocity of the droplets and the droplet concentration are independent of 

the drop size and do not vary in the radial direction. Whereas the droplet velocities can be 

assumed independent of the drop size in some cases [11, 290], the droplet concentration 

cannot be assumed uniform in the radial direction (Zuber et al. [319, 320]). The data of 

Hagiwara et al. [96] showed that the droplet concentration decreases from the turbulent core to 

zero near the wall. Thus, the use of an average diameter in the expression for the interfacial 

area is questionable. 

Most of the proposed drop size distribution functions are derived from experiments [54, 58, 139, 

155, 165, 212, 295]. The maximum drop size is usually calculated using a critical Weber 

number. However, the standard droplet disintegration mechanism overestimates the observed 

droplet sizes. Most droplets are produced by entrainment at the gas-liquid interface rather than 

generated during their evolution downstream of the points of entrainment above the quench 

front. Experimental data indicate that the droplets downstream of the quench front are too small 

to have been generated by fragmentation (i.e., by the secondary breakup mechanism during 

their flight as droplets in the gas or vapor flow). In other words, the critical Weber number 

based upon the relative velocity between the droplets and the gas flow gives rise to much larger 

droplet sizes than experimentally observed. Sarjeant [235] found that the breakup time and 

number of fragments depend on the Weber number. However, the critical Weber number is 

essentially independent of the droplet Reynolds number. Note that coalescence of droplets may 

take place immediately downstream of the quench front, owing to the chaotic motion of the 

droplets. Whereas the secondary breakup due to fragmentation or disintegration would 

increase the droplet number density (Juhel [135]), coalescence due to collisions of droplets 

could increase the Sauter mean diameter (Clare and Fairbaim [46]). 

3.3.3 Droplet Velocity, Interfacial Shear, and Interactions 

Owing to mechanical non-equilibrium [11, 166], the liquid droplets, once entrained, are 

accelerated by the aerodynamic drag forces exerted by the vapor flow. Thus, the relative 

velocity between the liquid and vapor phases may vary continuously in the flow field. Since all 

the transfer mechanisms at the liquid/vapor interface are affected by the relative velocity, the 

droplet velocity and interfacial drag as well as droplet-droplet interactions need to be taken into 

account in modeling the reflood heat transfer. The concentration of the droplets, i.e., the 

number density, at different elevations above the quench front, depends largely on the velocities 

of the droplets. The topics of droplet velocity, drag and interaction have been studied by a 

number of investigators, including Ardron and Hall [11], Brauner and Maron [26], Chuchottaworn 

and Asano [41], Harmathy [101], Hassan [104, 105], Ishii et al. [127, 128, 129], Kataoka et al. 

[139], Lee et al. [166-174], Lindsted et al. [177], Nigmatulin and Kukharenko [205], Temkin and 

Mehta [263], Tsuji et al. [269], Wilkes et al. [290] and Williams and Crane [292]. 

If the motion of the droplets can be described by a single momentum equation applied to the 

center of mass of the dispersed phase, i.e., the liquid droplets, the drag force per unit volume 

can be expressed in terms of the interfacial area concentration, the droplet velocity, and the 

ratio between the Sauter mean diameter and the mean drag diameter [127]. For spherical 

particles, the ratio of the Sauter mean diameter and the mean drag diameter is essentially equal 
48

to unity regardless of the drop size distribution [139]. For non-spherical particles or distorted 

droplets, the drag force should be better calculated using the drag coefficient. According to Ishii 

and Zuber [128], the distorted droplet regime is characterized by the viscosity number. 

It should be noted that the drag coefficient calculated by the standard laws does not account for 

the effect of mass flux and the droplet-droplet interactions. Chuchottaworn and Assano [41] 

calculated the drag coefficient on an evaporating or condensing droplet and found that the effect 

of mass flux due to phase change can influence the resulting drag coefficient. The experimental 

data of Lee and Durst [166] and Tsuji et al. [269] as well as the analysis of Lee [168], on the 

other hand, indicated a significant effect of droplet-droplet interactions on the drag coefficient. 

The dependency of the drag coefficient on the Reynolds number is modified appreciably in the 

highly dispersed gas-particle viscous regime. For small particles and low concentrations, the 

drag coefficient becomes smaller whereas for large particles and high concentrations, the 

reverse is found to be the case. 

As mentioned above, the droplet motion is usually described by a single momentum equation 

for the center of mass of the droplets. This approach requires that the droplet velocities to be 

independent of the drop sizes. Since the droplets are accelerated by the vapor flow as soon as 

they are generated, one may expect that there are considerable differences in the velocities 

among droplets of different sizes. Small droplets, being entrained readily by the vapor flow, 

should move faster than large droplets. This expectation, however, may not be the case. 

Experimental data for dispersed flow above the quench front [11] and for annular mist flow in 

tubes [290] have shown that droplets of various sizes move axially at nearly the same velocity, 

close to the terminal velocity of the droplets of average size. This behavior may due in part to 

the droplet-droplet interactions and in part to the different radial migration of small and large 

droplets. In the former case, momentum exchange during droplet-droplet interactions tends to 

render the velocities of the droplets uniform. In the latter case, the small droplets are being slow 

down as they are carried by the turbulent eddies toward the wall. On the other hand, the large 

droplets, being less affected by turbulent eddies, continue to be accelerated by the vapor flow. 

As a result, the droplet velocities may not vary considerably with the droplet sizes. 

3.3.4 Droplet-Enhanced Heat Transfer 

The presence of liquid droplets in the dispersed flow region has significant effects on the total 

heat transfer in the reflood phase. First, the droplets are not at thermal equilibrium with the 

vapor flow and there is convective heat transfer between the droplets and the vapor. Second, 

the droplet temperatures are different than those of the wall and there is wall to droplet radiation 

heat transfer. Third, vaporization of the droplets may take place during their flight and the 

phase change process may result in de-superheating of the vapor flow. The rates of convective 

heat transfer between the droplets and the vapor, wall to droplet radiation heat transfer and 

droplet evaporation depend on the total interfacial area which is a function of the drop size 

distribution and number density. Fourth, the liquid droplets may impinge upon the wall which 

results in direct contact heat transfer. Fifth, the droplets are hydrodynamically coupled to the 

vapor flow. Whereas the droplet motion depends strongly on the flow characteristics of the 

continuous vapor phase, the turbulence intensity and transport properties of the vapor flow can 

be substantially modified by the presence of the liquid droplets. In most cases, the liquid 

droplets may induce higher turbulence in the vapor phase, which would enhance convective 

heat transfer of the vapor flow at the wall. 
49

The topic of droplet-enhanced heat transfer (i.e., the fifth item mentioned above) has been 

studied by many investigators, including Aihara [4], Boothroyd and Hague [23], Boothroyd [24], 

Briller and Peskir [27], Chu [40], Danziger [57], Depew and Kramer [61], Drucker et al. [67], 

Evans et al. [77], Farbar and Depew [80], Farbar and Morley [81], Hasegawa et al. [103], 

Holman et al. [114], Kianjah et al. [150], Kiger and Lasheras [151, 152], Koizumi et al. [156], 

Shrayber [245, 246], Spokoynyy [251], Sukomel et al. [261], Theofanous and Sullivan [264], 

Tien and Quan [265], Tsuji et al. [269], and Wilkinson and Norman [291]. In most of these 

studies, solid particles are used to simulate the liquid droplets, excluding the effect of 

evaporation. The modification of the convective heat transfer coefficient is determined by 

comparing the case of an upward gas-particle flow to the case of a pure gas flow. 

In general, a dispersed phase may alter the convective heat transfer to and from the continuous 

gas phase in several ways. First, the presence of particles may strongly modify the turbulence 

structure of the gas phase. Second, the slip between phases may enhance the mixing of the 

carrier gas. Third, the radial motion of the particles may promote energy exchange between the 

laminar sublayer and the turbulent core. Fourth, owing to the penetration of the particles in the 

viscous sublayer, the thickness of the sublayer may be reduced. All these factors tend to flatten 

the gas velocity profile in the core and reduce the viscous sublayer thickness, resulting in a 

steeper temperature gradient at the wall and thus a higher rate of convection. 

Under certain conditions (large particles at small loading ratios), however, the presence of 

particles could dampen the eddy motion in the turbulent flow field and may reduce the 

convective heat transfer due to the transition from turbulent to laminar flow [103, 246]. The key 

parameters that need to be considered include the loading ratio (i.e., the quality), the particle 

size, Reynolds number of the flow, the hydraulic diameter and the wall temperature. Thus far, 

no correlation is available that properly accounts for the effects of all these parameters. 

3.3.5 Droplet Evaporative Heat Transfer 

One characteristic feature of dispersed flow is the presence of very high temperature gradients 

in the continuous vapor phase. Thus, the distribution of the evaporating liquid droplets plays an 

important role in the heat transfer process. The topic of droplet evaporative heat transfer has 

been studied by Bellan and Harstad [18], Duncan and Leonard [70], Faeth [79], Gaugler [86], 

Ghazanfari [87], Harpole [102] Hoffman and Ross [113, 114], Iloeje et al. [123], Kiger and 

Lasheras [151], Labowsky [160], Lee and Ryley [163], Mostinshiy and Lamden [198], O’Rourke 

[216], Rane and Yao [231], Sawan and Carbon [237], Toknoka et al. [266], Unal et al. [274, 

277], Yamanuchi [302], Yao et al. [308], and Yuen and Chen [317]. Perhaps the most important 

effects of droplet evaporation are vapor de-superheating near the wall. Droplets can be 

transported towards the wall by turbulent diffusion. The migration of droplets towards the wall 

and subsequent evaporation of the droplets greatly reduces the vapor temperature near the 

wall. This vapor de-superheating effect increases the driving temperature difference between 

the wall and the vapor and thus enhances the convective heat transfer at the wall. The rate of 

droplet migration, however, depends on the radial droplet concentration distribution and the 

ability of the droplets to penetrate the viscous sublayer at the wall. 

The evaporation of droplets also affects the convective heat transfer from the vapor to the 

droplets. In the range of high Reynolds numbers and high evaporation rates, a shielding effect 

is observed as a result of droplet evaporation [113, 317]. This shielding effect, caused by the 

mass efflux associated with droplet evaporation, reduces convective heat transfer from the 
50

superheated vapor to the liquid droplets. The total evaporation rate for a cloud of droplets can 

be quite different than that predicted by the single-drop model [160]. 

At high droplet concentrations, i.e., for a dense cluster of droplets, there could be an 

appreciable reduction of the droplet evaporation rate. This is probably due to the difficulty of the 

outer flow to penetrate through the dense cluster. Owing to overlapping boundary layers around 

the droplets, the outer flow tends to by pass the cluster of drops. Thus, only those droplets at 

the periphery of the cluster are affected by the outer flow. The droplets inside the cluster 

evaporate at the rate typical of that for droplet evaporation in a quiescent fluid. This cluster 

effect of droplets, however, is somewhat controversial. Bellan and Harstad [18] found that the 

evaporation time for a dense cluster of drops is only weakly dependent on the relative velocity 

between the cloud of droplets and the vapor flow. On the other hand, Faeth [79] found that for 

evaporating sprays, there is very little effect of adjacent droplets on the vaporization rate. 

3.3.6 Direct Contact Heat Transfer 

The topic of direct contact heat transfer has been investigated by Carbajo and Siegal [30]. 

Cokmez-Tuzla et al. [50], Dua and Tien [68], Duffey and Porthouse [69], Elias and Yadigaroglu 

[74], Groeneveld and Stewart [92], Henry [107], Iloeje et al, [123], Kendall [146], Lin and Yao 

[178], Nishio and Hirata [208], Pedersen [221, 222], Piggot et al. [224], Styrikovich et al. [253], 

Yao and Cai [303] and Yao and Henry [307]. A comprehensive review of the subject was 

recently made by Ayyaswamy [13]. In general, droplet impingement onto the wall is capable of 

removing a significant amount of heat from the wall either by direct contact with the hot wall or 

by evaporation in the superheated thermal boundary layer at the wall. The latter case results in 

de-superheating of the vapor phase and thus increasing the driving temperature difference 

between the wall and the vapor, as discussed previously in item V. The former case (i.e., direct 

contact heat transfer) is a very effective cooling mechanism and may lead to a significant 

enhancement of the heat transfer rate above the quench front. However, direct contact heat 

transfer is possible only if the wall is lower than a limiting temperature, i.e., the Leidenfrost 

temperature. It is possible, though, to achieve direct liquid-wall contact momentarily on a very 

small time scale at higher temperatures [92, 107, 303, 307]. Above the limiting temperature, the 

wall is not wettable continuously. 

The wettability of a hot wall is an important issue that has been studied by Duffey and 

Porthouse [69], Groeneveld and Stewart [92], Iloeje et al. [121-123], Kervinen et al. [147], Nishio 

and Hirata [208], Piggot et al. [224] and Yao and Cai [303]. The wettability is a rather 

complicated issue and there is no reliable criterion for the wettability of a hot wall. The limiting 

temperature is not well known, the highest value being the one reported by Nishio and Hirata 

[208]. Yao and Cai [303] found that the wettability of a hot surface depends not only on the 

radial velocity normal to the wall but also on the axial velocity in the tangential direction. 

Iloeje et al. [123] identified the direct contact heat transfer as “wet” contacts so as to distinguish 

it from that of “dry” contacts for which the droplets do not have enough transverse momentum to 

penetrate through the thermal boundary layer. In general, the importance of wet contacts 

diminishes, relative to that of dry contact, with increasing wall temperature. Evidently, the 

relative importance of the wet and dry contacts depends on the probability that a droplet 

reaches the hot surface. One widely used approach is to divide the contact area between the 

wall and the two phases based on the average void fraction. Unfortunately, this approach is not 

physically realistic, though it is convenient to use. A general, reliable criterion for the wettability 

of a hot wall by impacting droplets of various sizes and velocities is needed. 
51

3.3.7 Total Wall Heat Transfer 

In modeling the dispersed flow film-boiling (DFFB) regime, the most complete models are the 

so-called three-step models which consider wall-to-liquid, wall-to-vapor and vapor-to-liquid heat 

transfer. These are mechanistic models as the phenomenon is fully taken into account. The 

only element of empiricism is due to the use of correlations for describing the various 

mechanisms of momentum, heat and mass transfer. As discussed in items IV and V above, the 

turbulence structure of the continuous vapor phase may be significantly modified by the 

dispersed phase whereas droplet evaporation may result in enhanced convective heat transfer 

due to vapor de-superheating near the wall. Thus the vapor-to-liquid heat transfer needs to be 

considered in modeling the DFFB phenomenon. The Dougal-Rohsenow correlation [64], for 

example, fails to predict the wall-to-vapor heat transfer, as it does not account for the effect of 

dispersed droplets. 

The wall-to-liquid heat transfer includes the convective heat transfer from the wall to the droplets 

(i.e., direct contact heat transfer discussed in section 3.3.6 above) and the radiation heat 

transfer from the wall to the droplets. The later has been studied by Chung and Olafsson [44], 

Deruaz and Petitpain [62], and Sun et al. [262]. The liquid droplets are treated as distributed 

heat sinks and the heat transfer from the wall to the fluid is determined by calculating the 

combined radiation and convection from the wall to the two-phase mixture. The total heat 

transfer and the prediction methods for DFFB have been discussed by Afifi [3], Akimoto and 

Murao [5], Andreani and Yadigaroglu [7-10], Arrieta and Yadigaroglu [12], Axford [13], Chen 

[34], Chiou and Hochreiter [37], Choi et al. [39], Chung and Ohafsson [44], De Salve et al. [59], 

Ghiaasiaan [89], Hassan [105], Kaminaga et al. [136, 137], Kawaji and Banerjee [142, 143], 

Kirillov et al. [153], Mastanajah and Ganic [186], Majinger and Langner [188], Moose and Ganic 

[192], Murata et al. [201], Naitoh et al. [202], Ottesen [217], Paras and Karabelas [219], 

Plummer et al. [225], Spencer et al. [250], Sudo [255], Toman et al. [268], Varone and 

Rohsenow [279], Wong and Hochreiter [295, 296], Yadigaroglu [300, 301], Yao and Sun [306], 

Yoder and Rohsenow [310], and Zemlianoukhin et al. [318]. 

3.3.8 Effects of Spacer Grids 

During the reflood phase of LOCA, the enhanced DFFB cooling downstream of spacer grids is 

an important heat transfer mechanism. According to Yao et al. [308, 309], the spacer grids can 

enhance cooling of the fuel rod by four mechanisms. These are the breakup of droplets into 

smaller fragments, flow restructuring associated with thermal boundary layer separation and 

reattachment, spacer grid early rewetting to allow direct contact heat transfer to take place and 

direct radiation from the fuel rods. Usually, overlooking the presence of spacer grids would 

result in under prediction of the cooling rate and over prediction of the cladding temperatures 

downstream of the grids. The effects of spacer grids has been investigated by Adams and 

Claire [2], Becker and Hernborg [17], Cha and Jun [32], Chiou et al. [38], Chung et al. [42, 43], 

Clement et al [49], Crecy [53], Groeneveld and Yousef [93], Hochreiter et al. [112], Ihle and Rust 

[119], Ihle et al. [120], Kanazawa et al. [138], Lee et al. [169-174], Rehme [232], Stosic [252], 

Sugimoto and Murao [257-259], Westinghouse Work [286], Yao et al. [308, 309], and Yoder et 

al. [312-314]. 

The spacer grid is a device that maintains uniform gap between fuel rods and minimizes rod 

vibration. In many cases, mixing vanes are attached to the spacer to enhance turbulent mixing 

and induce swirl flow. Recent experiments by Chung et al. [42, 43] clearly showed that the 

space grids or mixing vanes generally increase the critical heat flux. The presence of spacer 
52

grids tend to breakup large bubbles, direct the entrained liquid droplets to the heated wall, 

improve subchannel mixing, and strip the liquid film off the unheated surface. 

3.3.9 Effects of Inlet Flow Oscillation and Thermal Non-equilibrium 

The effects of flow oscillations and transients on DFFB have been investigated by Cha et al. 

[33], Cheung and Griffith [36], Clement et al. [49], Ghazanfari et al. [88], Kawaji et al. [145], Ng 

and Banerjee [204], Oh [213], Oh et al. [214], and White and Duffey [287]. Cheung and Griffith 

[36] studied the phenomenon of gravity reflood oscillations, Ghazanfari et al. [88] studied the 

unsteady DFFB behavior, Kawaji et al. [145] investigated the flow and heat transfer with 

oscillatory coolant injection, Ng and Banerjee [204] investigated the two-phase flow 

characteristics during controlled oscillating reflooding, Oh et al. [214] determined the quench 

front and liquid carryover behavior during reflooding with oscillating injection, and White and 

Duffey [287] investigated unsteady flow and heat transfer in the reflooding of rod bundles. In 

general, large oscillations have been observed in void fractions and wall temperature for 

reflooding with oscillatory coolant injection. This observed phenomenon implies that there could 

be periodic changes in the flow regime near the quench front. 

The effect of thermal non-equilibrium on reflood heat transfer has been reported by Chen et al. 

[35], Evans et al. [76, 78], Gottula [90, 91], Jones and Zuber [134], Kawaji [144], Loftus et al. 

[179], Morris et al. [193-197], Nijhawan et al. [207], Tuzla et al. [270, 271], Unal et al. [273-275], 

Webb and Chen [281-283], and Williams [293]. Experimental evidence has indicated that 

significant thermal non-equilibrium can be present in DFFB with vapor superheats of several 

hundred degrees. 

3.3.10 Other Factors 

The phenomena of quench front propagation and quench time have been studied by Afifi [3], 

Barnea and Elias [15], Chung et al. [45], De Salve et al. [59], Dhir and Catton [63], Era et al. 

[75], Juhel [135], Seban et al. [241], Ueda et al. [272], Webb and Chen [283], and Yu and 

Yadigaroglu [316]. The regime of film boiling during reflood has been described by Berenson 

[21], Hsu [115], Styrikovich et al. [254], Sudo [255], and Weisman [285], whereas the regime of 

subcooled boiling has been reported by Dowlati et al. [65], Maitra and Subba-Raju [184], Murao 

and Sugimoto [200], Savage et al. [236], and Shoukri et al. [244]. 

The subject of void distribution measurement and prediction has been discussed by Banerjee et 

al. [14], De Young et al. [60], Dowlati et al. [65], Maitra and Subba-Raju [184], Savage et al. 

[236], and Zuber and Findlay [319]. The subject of post-dryout heat transfer has been studied 

by Barnea [16], Chen et al. [34, 35], Evans et al. [76, 78], Gottula et al. [91], Hochreiter et al. 

[109-111], Ishii and De Jarlais [124], Ishii and Mishima [125], Jones and Zuber [134], Kendall 

[146], Mayinger and Langner [188], Obot and Ishii [215], Plummer et al. [225], Stosic [252], and 

Unal et al. [274, 276]. 

The issue of simulating a nuclear fuel pin by an electrically heated rod has been addressed by 

Broughton et al. [28], Carajilescov [29], Casal et al. [31], Malang and Rust [185], McPherson 

and Tolman [189], Raepple et al. [227], Soda [248], Sugimoto et al. [260], and Tolman and 

Gottula [267]. Evaluation of heater rod properties, clad swelling, and rupture behavior has been 

performed by Hanson [100], Larson [162], Mohr and Hesson [191], Nithianandan et al. [209-

211], and Sugimoto et al. [260]. 
53

The heat transfer rate for single phase and two phase flows in tubes or around bundles have 

been discussed by Bennett et al. [19], Benodekar and Date [20], Drucker and Dhir [66], Dwyer 

and Berry [71], El-Genk et al. [73], Forslund and Rohsenow [82], and Groeneveld [94, 95], 

Hynek at al. [118], Kianjah [148-150], Ramm and Johannsen [229] and Rane and Yao [230]. 

Finally, phenomena identification and ranking table (PIRT) has been developed for thermalhydraulic phenomena during large break LOCA by a number of researchers such as Boyack 

[25], Rohatgi et al. [234], Shaw et al. [243], and Wulff [298]. The RBHT PIRT presented in 

section 2 of this report was developed specifically for thermal-hydraulic phenomena during the 

reflood stage of a large break LOCA. The table is most up to date and is most appropriate for 

reflood heat transfer studies. 

3.4 Master Table: Previous Studies Relevant to the High-Ranking Phenomena Identified 

 in the PIRT for the RBHT Program 

Based on the PIRT for the RBHT program described in section 2.0 and the results of the 

literature review presented in sections 3.2 and 3.3, Table 3.2 is developed which summarizes all 

the previous studies relevant to the highly ranked phenomena during the reflood stage of a large 

break LOCA. This master table identifies the data sources listed in section 3.5 that may be 

useful for addressing each type of phenomena taking place in various regions of the rod bundle 

during the reflood stage. 

From the literature survey as highlighted in the master table, it was found that there are large 

differences between the data obtained from the rod bundle tests and those from the single tube 

tests. The RBHT test facility is designed specifically to address this data deficiency. The RBHT 

program will aim at obtaining not only wall-to-fluid heat transfer correlations but also models for 

interfacial heat transfer. To develop and assess models for interfacial phenomena with the goal 

of significantly improved accuracy and to minimize the potential for compensating errors will 

require a new or improved database that includes more detailed information than is currently 

available. The specific needs for new or improved data are described below: 

1. In dispersed flow film boiling, the primary heat transfer mechanism is convective heat 

transfer to superheated steam. It is now recognized that the steam heat transfer 

coefficient can be enhanced by up to 100 percent due to the presence of entrained 

droplets. No suitable models currently exist for this phenomenon. The combination of 

single-phase convection experiments and two-phase convection experiments with droplet 

injections (with known drop sizes and flow rates) to be performed in the RBHT test facility 

will provide important new data and result in the development of the needed model. 

2. Once the uncertainty involving droplet-enhanced heat transfer is resolved, there still 

remains the difficulty in predicting the heat transfer rate for the dispersed flow film-boiling 

(DFFB) regime due to the difficulty in calculating the steam superheat. The amount of 

steam superheat is governed by the interfacial heat transfer between the steam and the 

evaporating droplets. To correctly calculate the interfacial heat transfer requires the 

knowledge of both the entrained drop size and the droplet flow rate. There is very little 

data of this type currently available for quenching rod bundles. The RBHT program will 

generate the needed database through advanced instrumentation involving the use of a 

laser illuminated digital camera system to determine the entrained drop size and measure 

the droplet flow rate. 
54

3. Although data showing the effects of spacer grids is available, the phenomenon is still not 

completely understood. In particular, the separate-effects of spacer grids for interfacial 

shear in rod bundles at low pressures, in dispersed flow film boiling, and in transition 

boiling heat transfer during reflood, are not known. It is necessary to determine the grid 

geometry effects. The RBHT program, which will explore two or more types of space grids 

and will perform heat transfer measurements in various flow regions at locations just 

before and after the spacer grids, will greatly augment the database needed for modeling 

the spacer grid effects. 

4. There is insufficient data on transition boiling heat transfer during quenching in rod 

bundles. This is especially true regarding the minimum film boiling temperature. For 

reflood conditions where precursory cooling is important, the transition regime is 

responsible for the final quench and most likely controls the quench front propagation. The 

emphasis of the RBHT program to measure the local values of the void fraction in the 

quench front region will provide the much-needed database. 

5. When the flow at the quench front is subcooled, an inverted annular film boiling (IAFB) 

regime would develop immediately downstream of the quench front. The liquid-rich region 

provides the precursory cooling that controls the quench front velocity and provides the 

source of vapor and entrained liquid for the DFFB region. It has been demonstrated that 

many of the apparent functional dependencies for the IAFB regime are primarily due to the 

axial profile of the void fraction in this region. Currently available data for this regime in rod 

bundles is insufficient for model development due to the coarse spacing used for the void 

fraction measurements. The RBHT program will address this data need through the use of 

finely spaced DP cells and by a local void fraction measurement provided by a low energy 

gamma-densitometer. 

6. The heat transfer rate in the IAFB region increases rapidly with liquid subcooling. Higher 

subcooling promotes heat transfer to the liquid core and reduces vapor generation and the 

thickness of the vapor film, thus enhancing heat transfer. It is traditional to formulate 

reflood test matrices by fixing the inlet subcooling and then varying the inlet flow rate. This 

procedure does not provide a true single parameter variation needed for model 

development at the subcomponent levels. In the RBHT program, non-traditional 

procedures involving fixing either the local subcooling or the mass flux at constant values 

at the quench front will be done by choosing appropriate combinations of the inlet flow rate 

and subcooling in the planned experiments. This will provide important new data not 

available heretofore. 

7. The database in the nucleate boiling regime for void fraction (i.e., interfacial shear) in rod 

bundles at low-pressure conditions has been identified as a code deficiency during the 

AP600 code applicability program. Some data exists or can be backed out of other reflood 

test data after the bundle has quenched. The RBHT can be conveniently used to 

generate, for negligible additional costs, a comprehensive database with systematic 

variation of parameters that would greatly aid model development and assessment. 

The various technical issues discussed above provide clear justifications for the need for 

developing the RBHT facility. Separate-effects tests will be performed in this facility to obtain 

new or improved data for model development and code validation at the most fundamental 

subcomponent levels. 
55

Table 3.2 Previous Studies Relevant to the High-Ranking Phenomena During the Reflood Stage of a L

Region of Interest High-Ranking Phenomena Basis: Uncertainty and Impact on PCT Citati

Single-Phase Liquid HT Region 

Decay Power Source of Energy for Rods, Boundary 

Condition for Tests. Minimum Uncertainty. 

N/A. KnowCondition. 

Subcooled and Saturated Boiling Region 

Decay Power Source of Energy for Rods, Boundary 

Condition for Tests. Minimum Uncertainty. 

N/A. KnowCondition. 

Quench Front Fuel Rod Material Properties 

Effects on Rod Quench 

Material Properties (r, cp, k) Affect the 

Stored Energy in the Fuel/Heater Rod and Its Quench Rate, Uncertainty Directly Impacts PCT. 

[28], [29], [[189], [227R1, R2, R4

Quench Front Cladding Surface Effects on Rod 

Quench 

The Cladding Surface Effects (Oxides, Roughness, Material, Tmin and TCHF) have 

Large Uncertainty and Impact on PCT. Oxide Layer Quenches Sooner Due to Low k. In addition, Roughness from Oxide Promotes Easier Quenching. Needs to Estimate Tmin and TCHF. Large 

Uncertainty. 

[28], [29], [[107], [121[189], [209[267], [272

Quench Front Transition Boiling Heat Transfer The Rate of Heat Release at the Quench 

Front Directly Impacts PCT. Large Uncertainty. 

[33], [59], [[197], [224R1-R3, R2

Quench Front Steam Generation at Quench 

Front 

The Rapid Generation of Steam at the Quench Front Leads to the Onset of Liquid Entrainment, Important Impact on PCT with Large Uncertainty. 

[19], [89], [[155], [205[254], [277

Quench Front Decay Power Source of Energy for Rods, Boundary 

Conditions for Tests. Minimum Uncertainty. 

N/A. KnowCondition. 

Quench Front Liquid Entrainment at Quench 

Front Which Includes the Initial Drop Size and Droplet Number Density 

Liquid Entrainment Cools the PCT Location Downstream and Directly Impacts PCT. High Uncertainty. 

[6], [15], [5[117], [125[155], [165[219], [223[297], [301R28. 
56

Table 3.2 Previous Studies Relevant to the High-Ranking Phenomena During the Reflood Stage of a L

(Continued) 

Region of Interest High-Ranking Phenomena Basis: Uncertainty and Impact on PCT Citati

Quench Front Rewet Temperature Determine the Quench Front Point on the 

Fuel Rod. Large Uncertainty. 

[69], [92], [[224], [301

Quench Front Void Fraction / Flow Regime Determines the Wall Heat Transfer Since 

Large Void Results in Dispersed Flow, Whereas Small Void Results in Film Boiling. Directly Impacts PCT. Large Uncertainty. 

[14], [15], [[184], [236R18, R21-

Quench Front Interfacial Area Determines the Initial Configuration of the 

Liquid as It Enters the Transition Region. Directly Impacts Liquid/Vapor Heat Transfer and Resulting PCT Downstream. Large Uncertainty. 

[7], [8-10], [135], [141[293], R6, 

Froth Region Decay Power Source of Energy for Rods, Boundary 

Conditions for Tests. Minimum Uncertainty. 

N/A. KnowCondition. 

Froth Region Void Fraction / Flow Regime Helps Determine the Amount of VaporLiquid Heat Transfer Which Affects the 

Downstream Vapor Temperature at PCT. Large Uncertainty. 

[14], [15], [[184], [236R14-R18. 

Froth Region Liquid Ligaments, Drop Sizes, 

Droplet Number Density, Interfacial Area 

Determines the Interfacial Heat Transfer in the Transition Region. Large Uncertainty. 

[2], [6], [11[52], [304], [319-321], 

Froth Region Film Boiling Heat Transfer at Low 

Void Fractions 

This Includes Convective Vapor Heat Transfer, Direct Contact Heat Transfer, Radiation Heat Transfer, etc. Large Uncertainty. 

[21], [58], [[195], [196[307], R1-R

Froth Region Direct Contact Heat Transfer Wall Temperature Is Low Enough to Allow 

Direct Droplet Contact Heat Transfer to the Wall with a Very High Heat Transfer Rate. Large Uncertainty. 

[13], [30], [[107], [123[221], [222[307]. 
57

Table 3.2 Previous Studies Relevant to the High-Ranking Phenomena During the Reflood Stage of a L

(Continued) 

Region of Interest High-Ranking Phenomena Basis: Uncertainty and Impact on PCT Citati

DFFB Region Decay Power Source of Energy for Rods, Boundary 

Conditions for Tests. Minimum Uncertainty. 

N/A. KnowCondition. 

DFFB Region Dispersed Flow Film Boiling Directly Impacts PCT, High Uncertainty in 

Modeling 

[3], [5], [7-

[44], [59], [[136], [137[186], [188[217], [219[268], [279

[301], [306R13, R19-

DFFB region Convection to Superheated Vapor Principal Mode of Heat Transfer, Directly 

Impacts PCT. Large Uncertainty. 

[8-10], [19][94], [105], [143-145], [186], [192[250], [268[306], [310

DFFB Region Drop Sizes, Droplet Number 

Density, Interfacial Area 

Determines the Interfacial Heat Transfer in the DFFB Region. Large Uncertainty. 

[54-56], [58[96], [98], [[125], [130[139], [154[163], [165[187], [190[212], [219[233], [235[242], [247[288-290], 
58

Table 3.2 Previous Studies Relevant to the High-Ranking Phenomena During the Reflood Stage of a L

(Continued) 

Region of Interest High-Ranking Phenomena Basis: Uncertainty and Impact on PCT Citati

DFFB Region Dispersed Phase Enhancement 

of Convective Heat Transfer 

Important Impact on PCT as the Enhancement Can Be Over 50 Percent in Some Cases. Large Uncertainty. 

[4], [23], [2[67], [77], [[150-152], [251], [261[291], R1, 

DFFB Region Droplet to Vapor Interfacial Heat 

Transfer 

The Interfacial Heat Transfer Reduces the Vapor Temperature (i.e., De-superheat) Which Is the Heat Sink for the Wall Heat Flux. Large Uncertainty. 

[18], [70], [[113], [114[163], [198[266], [274[317], R1, R26. 

DFFB Region Radiation Heat Transfer Between 

Surfaces, Vapor, and Droplets 

Very Important at High Bundle Elevations Where the Convective Heat Transfer Is Small Due to Large Vapor Superheat. Very Important for BWR Reflood with Sprays and Cold Surrounding Surfaces. Large Uncertainty. 

[37], [44], [111], [137][261], [262R20, R25. 

DFFB Region Interfacial Shear and Droplet 

Velocity 

Effects the Void Fraction Distribution and Resulting Droplet Velocity in the Entrained Flow. Large Uncertainty. 

[11], [26], [[127-129], [205], [263R6-R8. 

Spacer Grids Effects of Spacer Grids on 

Droplet Deposition, Breakup, and Heat Transfer 

Important Enhanced Cooling Mechanism Especially in the Froth and DFFB Regions Due to Their Effects in Droplet Evolution and Flow Restructuring. Large Uncertainty. 

[2], [17], [3[53], [93], [[166-174], [286], [308R8, R9-R1

Inlet Region Inlet Flow Oscillation Directly Impacts the Flooding Behavior, 

Inducing Large Oscillations in Void Fraction and Wall Temperature, Increasing Entrainment and Initial Liquid Carryover, Altering the Speed of Quench Front Propagation. Large Uncertainty. 

[33], [36], [[213], [214
59

3.5 References

3.5.1 Rod Bundle Tests 

1. Rosal, E. R., et al., “FLECHT Low Flooding Rate Cosine Test Series Data Report,” WCAP8651, Dec. 1975. 

2. Lilly, G. P., H. C. Yeh, L. E. Hochreiter, and N. Yamaguchi, “PWR FLECHT Cosine Low 

Flooding Rate Test Series Evaluation Report,” WCAP-8838, Mar. 1977. 

3. Rosal, E. R., et al., “FLECHT Low Flooding Rate Skewed Test Series Data Report,” 

WCAP-9108, May 1977. 

4. Lilly, G. P., H. C. Yeh, C. E. Dodge, and S. Wong, “PWR FLECHT Skewed Profile Low 

Flooding Rate Test Series Evaluation Report,” WCAP-9183, Nov. 1977. 

5. Loftus, M. J., et al., “PWR FLECHT SEASET 21-Rod Bundle Flow Blockage Task Data 

and Analysis Report,” NUREG/CR-2444, EPRI NP-2014, WCAP-992, Vol. 1, Vol. 2, Sept. 

1982. 

6. Loftus, M. J., et al., “PWR FLECHT-SEASET Unblocked Bundle Forced and Gravity 

Reflood Task Data Report,” NUREG/CR- 1532, June 1980. 

7. Lee, N., S. Wong, H. C. Yeh, and L. E. Hochreiter, “PWR FLECHT-SEASET Unblocked 

Bundle Forced and Gravity Reflood Task, Data Evaluation and Analysis Report,” Feb. 

1982. 

8. Wong, S. and L. E. Hochreiter, “PWR FLECHT-SEASET Analysis of Unblocked Bundle 

Steam-Cooling and Boil-off Tests,” NUREG/CR-1533, January 1981. 

9. Ihle, P. and K. Rust, “FEBA – Flooding Experiments with Blocked Arrays Evaluation 

Report,” KFK 3657, Mar. 1984. 

10. Ihle, P. and K. Rust, “FEBA – Flooding Experiments with Blocked Arrays Data Report 1, 

Test Series I through IV,” KFK 3658, Mar. 1984. 

11. Ihle, P. and K. Rust, “FEBA – Flooding Experiments with Blocked Arrays Data Report 2, 

Test Series V through VIII,” KFK 3659, Mar. 1984. 

12. Mullins, C. B., et al., “ORNL Rod Bundle Heat Transfer Test Data,” NUREG/CR-2525, Vol. 

1 to Vol. 5, 1982. 

13. Yoder, G. L., et al., “Dispersed Flow Film Boiling in Rod Bundle Geometry – Steady State 

Heat Transfer Data and Correlations Comparisons,” NUREG/CR-24351, 1982. 

14. Becker, K. M., J. Flinta, and O. Nylund, “Dynamic and Static Burnout Studies for the Full 

Scale 36-Rod Marviken Fuel Element in the 8 MW Loop FRIGG,” Paper presented at the 

Symposium on Two-Phase Flow Dynamics, Eindhoven, Sept. 1967. 
60

15. Nylund, O., et al., “Measurements of Hydrodynamic Characteristics, Instability Thresholds, 

and Burnout Limits for 6-Rod Clusters in Natural and Forced Circulation,” ASEA and AB 

Atomenergi Report FRIGG-1, 1967. 

16. Nylund, O., K. M. Becker, R. Eklund, O. Gelium, I. Haga, G. Herngorg, Z. Rouhani, and F. 

Åkerhielm, “Hydrodynamic and Heat Transfer Measurements on a Full Scale Simulated 

36-Rod Marviken Fuel Element with Uniform Heat Flux Distribution,” ASEA and AB 

Atomenergi Report FRIGG-2, 1968. 

17. Lahey, R. T. and F. A. Schraub, “Mixing, Flow Regimes, and Void Fraction for Two-Phase 

Flow in Rod Bundles,” Two-Phase Flow and Heat Transfer in Rod Bundles, ASME, Nov. 

1969. 

18. Lahey, R. T., B. S. Shiralkar, and D. W. Radcliff, “Two-Phase Flow and Heat Transfer in 

Multirod Geometries: Subchannel and Pressure Drop Measurements in a Nine-rod Bundle 

for Diabatic and Adiabatic Conditions,” GEAP-13049, AEC. 

19. Mohr, C. L., et al., “Data Report for Thermal-Hydraulic Experiment 2 (TH-2),” NUREG/CR2526, PNL-4164, Nov. 1982. 

20. Mohr, C. L., et al., “Data Report for Thermal-Hydraulic Experiment 3 (TH-3),” NUREG/CR2527, PNL-4165, Mar. 1983. 

21. Denham, M. K., D. Jowitt, and K. G. Pearson, “ACHILLES Unballooned Cluster 

Experiments, Part 1: Description of the ACHILLES Rig, Test Section, and Experimental 

Procedures,” AEEW-R2336, Winfrith Technology Centre (Commercial in Confidence), Nov. 

1989. 

22. Denham, M. K. and K. G. Pearson, “ACHILLES Unballooned Cluster Experiments, Part 2: 

Single Phase Flow Experiments,” AEEW-R2337, Winfrith Technology Centre (Commercial 

in Confidence), May 1989. 

23. Pearson, K. G. and M. K. Denham, “ACHILLES Unballooned Cluster Experiments, Part 3: 

Low Flooding Rate Reflood Experiments,” AEEW-R2339, Winfrith Technology Centre 

(Commercial in Confidence), June 1989. 

24. Pearson, K. G. and M. K. Denham, “ACHILLES Unballooned Cluster Experiments, Part 4: 

Low Pressure Level Swell Experiments,” AEEW-R2339, Winfrith Technology Centre 

(Commercial in Confidence), July 1989. 

25. Dore, P. and M. K. Denham, “ACHILLES Unballooned Cluster Experiments, Part 5: Best 

Estimate Experiments,” AEEW-R2412, Winfrith Technology Centre (Commercial in 

Confidence), July 1990. 

26. Dore, P. and D. S. Dhuga, “ACHILLES Unballooned Cluster Experiments, Part 6: Flow 

Distribution Experiments,” AEA-RS-1064, Winfrith Technology Centre (Commercial in 

Confidence), Dec. 1991. 
61

27. Tuzla, K., C. Unal, O. Badr, S. Neti, and J. C. Chen, “Thermodynamic Non-equilibrium in 

Post-Critical-Heat-Flux Boiling in a Rod Bundle,” NUREG/CR-5095, Vol. 1-4, June 1988. 

28. Unal, C., K. Tuzla, O. Badr, S. Neti, and J. C. Chen, “Convective Boiling in a Rod Bundle: 

Traverse Variation of Vapor Superheat Temperature Under Stabilized post-CHF 

Conditions,” Int. J. Heat and Mass Transfer, Vol. 34, No. 7, pp. 1695-1706, 1991. 

3.5.2 Single Tube Tests and Related Studies 

1. Adams, J. E. and A. J. Clare, “A Preliminary Study of Droplet Breakup at PWR Spacer 

Grids,” PWR/HTWG/P 130, 1983. 

2. Adams, J. E. and A. J. Clare, “Droplet Break-up and Entrainment at PWR. Spacer Grids,” 

First Int. Workshop on Fundamental Aspects of Post-Dryout Heat Transfer, Salt Lake City, 

Utah, NUREG/CP-0060, April 2-4, 1984. 

3. Afifi, J., “Evaluation of Some Large “Best Estimate” Computer Codes for the Prediction of 

Loss of Coolant Accidents in Light Water Reactors,” Ph.D. Thesis, University of London, 

1985. 

4. Aihara, T., “Augmentation of Convective Heat Transfer by Gas-Liquid Mist,” CONF900803, pp. 445-462, 1990. 

5. Akimoto, H. and Y. Murao, “Current Experiment Status and Future Plan for Reflood Tests 

at Japan Atomic Energy Research Institute,” paper presented at ICAP Post-CHF Meeting, 

Winfrith, England, June 22-25, 1987. 

6. Almenas, K. and R. Lee, “Droplet Deposition Above a Quench Front During Reflood,” 

Trans. American Nuclear Society, Vol. 43, pp. 787-788, 1982. 

7. Andreani, M. and G. Yadigaroglu, “A Mechanistic Eulerian-Lagrangian Model for Dispersed 

Flow Film Boiling,” CONF-9005311, pp. 423-432, 1991. 

8. Andreani, M. and G. Yadigaroglu, “Difficulties in Modeling Dispersed-Flow Film Boiling,” 

Waeme- und Stoffuebertragung (Germany), Vol. 27:1, pp. 37-49, Oct. 1991. 

9. Andreani, M. and G. Yadigaroglu, “Dispersed Flow Film Boiling: An Investigation of the 

Possibility to Improve the Models Implemented in the NRC Computer Codes for the 

Reflood Phase for the LOCA,” NUREG/IA-0042, Aug. 1992. 

10. Andreani, M. and G. Yadigaroglu, “Prediction Methods for Dispersed Flow Film Boiling,” 

Int. Journal Multiphase Flow, Vol. 20, pp. 1-51, 1994. 

11. Ardron, K. A. and P. C. Hall, “Droplet Hydrodynamics and Heat Transfer in the Dispersed 

Flow Regime in Bottom Flooding,” CEGB, RD/B/5007N81, University of California at 

Berkeley, 1981. 

12. Arrieta, L. and G. Yadigaroglu, “An Analytical Model for Bottom Reflooding Heat Transfer 

in Light Water Reactors (UNFLOOD Code),” EPRI-NP-756, 1978. 
62

13. Ayyaswamy, P. S., “Direct-Contact Transfer Precesses with Moving Liquid Droplets,” 

Advances in Heat Transfer, Vol. 26, pp. 1-105, 1995. 

14. Banerjee, S., P. Yeun, and M. A. Vanderbroek, “Calibration of Fast Neutron Scattering 

Technique for Measurement of Void Fraction in Rod Bundles,” J. Heat Transfer, Vol. 101, 

May 1979. 

15. Barnea, Y. and E. Elias, “Flow and Heat Transfer Regimes During Quenching of Hot 

Surfaces,” Int. Journal Heat Mass Transfer, Vol. 37, pp. 1441-1453, 1994. 

16. Barzoni, G., “A Study on Postdryout Heat Transfer for Conditions of Interest in Loss of 

Coolant Accident Ananysis,” CISE-1616, P. 31, 1980. 

17. Becker, K. H., and C. M. Hernborg, “Measurements of the Effects of Spacers on the 

Burnout Conditions for Flow Boiling Water in a Vertical Annulus and a Vertical 7-Rod 

Cluster,” AE-165, 1964. 

18. Bellan, J. and K. Harstad, “Analysis of the Convective Evaporation of Nondilute Clusters of 

Drops,” Int. Journal Heat Mass Transfer, Vol. 30, No. 1, pp. 125-136, 1987. 

19. Bennett, A. W., G. F. Hewitt, H. A. Kearsey and R. F. K. Keeys, “Heat Transfer to SteamWater Mixtures Flowing in Uniformly Heated Tubes in Which the Critical Heat Flux Has 

Been Exceeded,” AERE-R-5373, 1967. 

20. Benodekar, R. W., and A. W. Date, “Numerical Prediction of Heat-Transfer Characteristics 

of Fully Developed Laminar Flow Through a Circular Channel Containing Rod Clusters,” 

Int. Journal Heat Mass Transfer, Vol. 21, pp. 935-945, 1978. 

21. Berenson, P. J., “Film Boiling Heat Transfer from a Horizontal Surface,” Journal Heat 

Transfer, Vol. 83, pp. 351-358, 1961. 

22. Binder, J. L. and T. J. Hanratty, “A Diffusion Model for Droplet Deposition in Gas-Liquid 

Annular Flow,” Int. Journal multiphase Flow, Vol. 17, pp. 1-9, 1991. 

23. Boothroyd, R. G. and H. Hague, “Fully Developed Heat Transfer to a Gaseous Suspension 

of Particles Flowing Turbulently in Ducts of Different Size,” Journal Mechanical 

Engineering Science, Vol. 12, No. 3, pp. 191-200, 1970. 

24. Boothroyd, R. G., “Similarity in Gas-Born Flowing Particulate Suspensions,” ASME Paper 

No. 68-MH-11, 1968. 

25. Boyack, B., “AP600 Large Break Loss-of-Coolant Accident Phenomena Identification and 

Ranking Tabulation,” LA-UR-95-2718, 1995. 

26. Brauner, N. and D. M. Maron, “Dynamic Model for the Interfacial Shear as a Closure Law 

in Two-Fluid Models,” Nuclear Engineering and Design, Vol. 149, pp. 67-79, 1994. 

27. Briller, R., and R. L. Peskin, “A Mechanistic Approach to Gas Solid Suspension Heat 

Transfer and Friction Factors,” Augmentations of Convective Heat & Mass Transfer, 

ASME, New York, pp. 124-133, 1970. 
63

28. Broughton, J. M., D. W. Golden, and P. E. MacDonald, “Assessment of Nuclear Fuel Rod 

and Solid Electric Heater Thermal Behavior During the Heatup and Reflood Phases of a 

Large Break LOCA,” CONF-810802-23, P. 12, 1981. 

29. Carajilescov, P., “Limits of the Simulation of a Nuclear Fuel Pin by an Electrically Heated 

Rod,” CONF-921234, P. 3, 1992. 

30. Carbajo, J. J., and A. D. Siegel, “A Review and Comparison Among the Different Models 

for Rewetting in LWR’s,” Nucl. Engr. Design, Vol. 58, pp. 33-44, 1980. 

31. Casal, V., S. Malang, and K. Rust, “Comparison of Thermal Behavior of Different PWR 

Fuel Rod Simulators for LOCA Experiments,” KFK-3416-B, P. 2, Oct. 1982. 

32. Cha, J. H. and H. G. Jun, “Air-Water Flooding in Multirod Channels: Effects of Spacer 

Grids and Blockage,” Journal Korean Nucl. Soc., Vol. 30, pp. 381-393, 1993. 

33. Cha, Y. S., R. E. Henry, and P. A. Lottes, “An Experimental Investigation of Quench Front 

Movement During Bottom Reflood of a Vertical Tube Under Forced-Oscillation Conditions,” 

ANL/RAS/LWR-80-1, Jan. 1980. 

34. Chen, J. C., “A Short Review of Dispersed Flow Heat Transfer in Post-Dryout Boiling,” 

Nucl. Engr. Design, Vol. 95, pp. 375-383, 1984. 

35. Chen, J. C., F. T. Ozkaynak and R. K. Sundaram, “Vapor Heat Transfer in Post-CHF 

Region Including the Effect of Thermodynamic Non-equilibrium,” Nucl. Engineering and 

Design, Vol. 59, pp. 143-155, 1979. 

36. Cheung, Y. L. and P. Griffith, “Gravity Reflood Oscillations in a Pressurized Water 

Reactor,” NUREG/CR-1314, 1980. 

37. Chiou, J. S. and L. E. Hochreiter, “Combined Radiation and Dispersed Flow Film Boiling in 

BWR Rod Bundles with Top Spray,” Proceedings of the 26th Natl. Heat Transfer 

Conference, Philadelphia, PA, Aug. 1989. 

38. Chiou, J. S., L. E. Hochreiter, M. J. Lottus, M. Y. Young, J. Chao, C. Chui, “Effects of 

Spacer Grids on Thermal Hydraulic Performance During a Postulated Reflood Transient,” 

CONF-841075, 1984. 

39. Choi, J. H., S. Y. Lee, and S. K. Kim, “Incorporation of Droplet Breakup Model at Spacer 

Grid into RELAP/MOD2,” J. Korean Nuclear Society, Vol. 22:4, pp. 326-336, Dec. 1990. 

40. Chu, N. C., “Turbulent Heat Transfer of Gas-Solid Two-Phase Flow in Circular Tubes,” 

Ph.D. Thesis, Department of Mechanical Engineering, University of Washington, 1971. 

41. Chuchottaworn, P. and K. Asano, “Calculation of Drag Coefficients on an Evaporating or 

Condensing Droplet,” Journal of Chem. Engineering of Japan, Vol. 18, pp. 91-94, 1985. 

42. Chung, J. B., “An Experimental Study of the Effects of the Mixing Vane of the CHF in the 

Low-Pressure, Low-Flow Conditions,” M.S. Thesis, KAIST, Korea, 1995. 
64

43. Chung, J. B., W. P. Baek and S. H Cheng, “Effects of Spacer and Mixing Vanes on Critical 

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Heated Strips,” Journal Heat Transfer, Vol. 110, pp. 214-220, 1988. 

309. Yao, S. C., L. E. Hochreiter and W. J. Leech, “Heat Transfer Augmentation in Rod Bundles 

Near Grid Spacers,” Journal Heat Transfer, Trans. ASME, Vol. 104, No. 1, pp. 76-81, 

1982. 

310. Yoder, G. L. and W. M. Rohsenow, “A Solution for Dispersed Flow Heat Transfer Using 

Equilibrium Fluid Conditions,” Journal Heat Transfer, Vol. 105, pp. 10-17, 1983. 

311. Yoder, G. L., “Dispersed Flow Film Boiling in Rod Bundle Geometry – Steady State Heat 

Transfer Data and Correlation Comparisons,” NUREG/CR-2435, Mar. 1982. 

312. Yoder, G. L., “Heat Transfer Near Spacer Grids in Rod Bundles,” 1985 Natl. Heat Transfer 

Conference, Denver, Colorado, Aug. 1985. 

313. Yoder, G. L., “Rod Bundle Spacer Grid Heat Transfer Data Base,” NUREG/CR-4421, Sep. 

1985. 

314. Yoder, G. L., D. G. Morris, C. B. Mullins, and L. J. Ott, “Dispersed Flow Film Boiling Heat 

Transfer Data Near Spacer Grids in a Rod Bundle,” Nuclear Technology, Vol. 60:2, pp. 

304-313, Feb. 1983. 

315. Yoshioka, K. and S. Hasegawa, “A Correlation in Displacement Velocity of Liquid Film 

Boundary Formed on a Heated Vertical Surface in Emergency Cooling,” Journal Nuc. Sci. 

Tech, Vol. 12, pp. 735-741, 1975. 

316. Yu, K. P. and G. Yadigaroglu, “Heat Transfer Immediately Downstream of the Quench 

Front During Reflooding,” ASME Paper 79-HT-48, 1979. 

317. Yuen, M. C. and L. W. Chen, “Heat Transfer Measurements of Evaporating Liquid 

Droplets,” Int. Journal Heat Mass Transfer, Vol. 21, pp. 537-542, 1978. 

318. Zemlianoukhin, V. V., L. P. Kabanov, P. L. Makarovski, V. M. Mordashev, and Yu. V. 

Rybakov, “Reflooding Heat Transfer in Zirconium Alloy Rod Bundle of VVER Reactor,” 

CONF-891004, pp. 584-590, 1989. 

319. Zuber, N and J. A. Findlay, “Average Volumetric Concentration in Two-Phase Flow 

System,” Journal Heat Trans., Vol. 87, pp. 453-368, 1965. 

320. Zuber, N. and F. W. Staub, “An Analytical Investigation of the Transient Response of the 

Volumetric Concentration in a Boiling Forced Flow System,” Journal Nuc. Sci. Eng., Vol. 

30, pp. 268-278, 1967. 

321. Zuber, N., “On the Atomization and Entrainment of Liquid Films in Shear Flow,” 62GL513, 

General Electric, 1962. 
 83

4. DEFINE INFORMATION NEEDED FOR NEW CODE MODELING 

CAPABILITIES, VALIDATION, AND ASSESSMENT 

4.1 Introduction

The large reactor safety analysis systems computer codes, such as the TRAC and RELAP, all 

attempt to predict a transient boiling curve for a heated surface with internal heat generation for 

a given surface temperature and fluid conditions adjacent to the surface such as the pressure, 

void fraction, vapor temperature and mass flow rate. The calculated boiling curve is generated 

by combining different individual heat transfer correlations such that a continuous calculation 

can be performed. As the fluid conditions change, the boiling curve predicted by the computer 

code also changes as some phenomena become larger and others become smaller such that 

the calculated surface heat transfer coefficient may result in the surface heating-up to higher 

temperature, or the surface cooling down to a lower temperature. 

The computer codes use individual empirical or semi-empirical heat transfer correlations to 

calculate the local heat transfer behavior from the heated surface to the fluid. The difference 

between the empirical and semi-empirical correlations is meant to indicate the degree in which 

the true physical condition is modeled by the correlation. Most correlations are usually 

empirical, that is, derived from a specific set of data, and predict single phenomena, or several 

phenomena in parallel. These correlations are often applied to conditions and geometries which 

were not included in the original basis for the correlation when performing reactor safety 

analysis. 

The heat transfer correlations may also require some modifications to make the correlation 

consistent with the numerical solution scheme of the code such that rapid calculations can be 

performed in a reliable fashion. Such modifications can result in essentially a different 

correlation than was originally developed by the author. The process of combining different 

individual specific correlations can lead to compensating errors, in which one calculates the right 

answer for the wrong reason because there are multiple errors in the calculational scheme. 

The heat transfer correlations, which compromise the calculated boiling curve, are also usually 

based on test data which is scaled relative to the reactor system. Therefore, one must address 

the effects and uncertainties of applying the correlations which are developed from scaled data 

to the analysis of a full scale reactor system. The computer code must be validated against 

several sets of independent, complete, data at different scales, over the range of conditions that 

the code would calculate, for geometries which would be modeled by the computer code. The 

emphasis is on the data independence, that is, data not used in the original correlation 

development, and a complete set of data such that the effects of compensating error can be 

determined. 

Therefore, complete sets of valid test data and the associated data analysis are one of the most 

needed items to validate the specific models in the computer codes to insure that compensating 

error is minimized, the heat transfer models are applicable at full scale with acceptable 

uncertainty and that the implementation of the correlations into the code do not change the 

nature or predictability of the original correlation. 
 84

The RBHT program is designed to specifically address the need for providing complete sets of 

valid data and data analysis for the low pressure film boiling regime which occurs during the 

reflood process. 

The process which has been used in the RBHT program is to develop the modeling 

requirements by developing a specific reflood PIRT as given in Section 2 which identifies the 

phenomena and the interaction of the different phenomena which the code should be able to 

calculate, then designing the experiments to isolate, as best as possible, those phenomena 

which are most important for the code predictions such that individual component code models 

can be assessed. In this fashion, compensating errors are less likely since the component 

models will be validated over the ranges of interest before they are integrated into the final heat 

transfer correlation package which would be used to predict the boiling curve. 

This Section of the report will provide a road map for the highly ranked phenomena developed 

from the PIRT given in Section 2 of this report, to the code models and finally to the 

instrumentation and methods of the data analysis. The objective is to indicate which code 

models interact to predict the important phenomena, and how the RBHT program will provide 

data and analysis to assess these models. 

4.2 Brief Review of Heat Transfer Models Used in Best-Estimate Codes for 

Reflood

4.2.1 RELAP5/MOD3 

4.2.1.1 Introduction 

The RELAP5 code (Ref. 1) was developed for best-estimate transient simulation of light water 

reactor coolant systems during postulated accidents. The code was developed at Idaho 

National Engineering Laboratory (INEL) for the U.S. Nuclear Regulatory Commission (NRC). 

Code applications include analysis to support rulemaking, licensing audit calculations, 

evaluation of accident mitigation strategies, evaluation of operator guidelines, and experiment 

planning analysis. The MOD3 version has been developed jointly by the NRC and a consortium 

consisting of several countries and domestic organizations that were member of the 

International Code Assessment and Applications Program (ICAP) and its successor 

organization, Code Applications and Maintenance Program (CAMP). 

The RELAP5/MOD3 code is based on a non-homogeneous and non-equilibrium model for the 

two-phase system that is solved by a fast partially implicit numerical scheme. The objective of 

RELAP5 development effort was to produce a code that included important first-order effects 

necessary for accurate prediction of system transients but that was sufficiently simple and cost 

effective so that parametric or sensitivity studies are possible. The code is one-dimensional and 

solves six basic field equations for six dependent variables (pressure, specific internal energies 

for liquid and vapor, void fraction, liquid and vapor velocities). 

The constitutive relations include models for defining flow regimes and flow-regime-related 

models for interface drag and shear, the coefficient of virtual mass, wall friction, wall heat 

transfer, and interface heat and mass transfer. Volumes flow regimes are used for calculations 

of interfacial heat and mass transfer while junction flow regimes are used for interface drag. 

The junction properties are consistent with the state of the fluid being transported through the 
junction. The same approach has been used successfully in the TRAC-B code. The wall heat 

transfer depends on volume flow regime maps in a less direct way. Generally, void fraction and 

mass flux are used to incorporate the effects of the flow-regime and because the wall heat 

transfer is calculated before the hydrodynamics, the flow information is taken from the previous 

time step. 

The vertical volume flow regime map is shown in Figure 4.1. The schematic is threedimensional to illustrate flow regime transitions as function of void fraction, average mixture 

velocity and boiling regime (pre-CHF, transition and post dryout). Heat and mass transfer and 

drag relations for the transition boiling region between pre-CHF and dryout are found by 

interpolating the correlations on either side. This means that for certain void fractions in the 

transition boiling region, two and sometimes three adjacent correlations are combined to obtain 

the necessary relations for heat/mass transfer and drag. 

Figure 4.1 RELAP5/MOD3 Vertical Flow Regime Map. 

4.2.1.2 RELAP5/MOD3 Heat Transfer Package

The heat transfer is viewed as a two-step mechanism: (1) a wall to fluid bulk heat transfer; and, 

(2) a bulk interfacial heat and mass transfer. In addition a separate, near-wall interfacial heat 

transfer is considered to account for the special case when the wall is communicating with a 

two-phase mixture, for then boiling or condensation can occur as direct result of the wall heat 

transfer. 

A boiling curve is used in RELAP5/MOD3 to govern the selection of the wall to fluid heat 

transfer correlations. The RELAP5 boiling curve logic is based on the value of the heat slab 

 85
 86

surface temperature. These correlations are based on fully developed steady-state flow while 

entrance effects are considered only for the calculation of Critical Heat Flux (CHF). Table 4.1 

shows the heat transfer modes and corresponding correlations used while Figure 4.2 shows the 

wall heat transfer mode selection flow chart. 

4.2.1.3 Single Phase Liquid

 

When the wall is subcooled and the void fraction is below 0.1, single-phase convection to liquid 

is assumed. For the vertical flow, depending on the value of the Re number, the heat transfer 

coefficient is calculated with either the Dittus-Boelter correlation (forced turbulent convection) 

(Ref. 2) or Churchill-Chu correlation (natural convection) (Ref. 3). A constant Nu number equal 

to 4.6 is assumed for the forced laminar convection case. 

4.2.1.4 Single Phase Vapor 

In a similar fashion, when the wall is superheated and the quality is greater than 0.99, 

depending on the Re number, the Dittus-Boelter (Ref. 2) and Churchill-Chu (Ref. 3) correlations 

are used for the single phase vapor convection. 

4.2.1.5 Nucleate Boiling 

When the wall is superheated the Chen correlation (Ref. 4) is used for both subcooled nucleate 

boiling and saturated nucleate boiling. Although the correlation was based on saturated liquid 

conditions, it is used for subcooled liquid conditions by using the bulk liquid temperature as the 

reference temperature for the convective part of the correlation. The wall is viewed as fully 

wetted by water except for vertically stratified conditions or, as the void fraction goes above 

0.99, the heat transfer coefficient to liquid is ramped to zero at void fraction equal to 0.999 and 

the heat transfer to vapor is ramped up to the value obtained from the Dittus-Boelter correlation 

(Ref. 2). The standard deviation for all the data considered in the Chen correlation development 

is stated as 11.6 percent for the saturated nucleate boiling conditions. The correlation was 

tested by Moles and Shaw (Ref. 5) for the subcooled nucleate boiling regime where the data 

scatter is large (+180 to -60 percent). The data are generally underpredicted by the correlation. 

4.2.1.6 Critical Heat Flux 

RELAP5/MOD2 has been criticized for using the Biasi correlation (Refs. 6 and 7) for predicting 

the CHF in rod bundles because the correlation is based on tube data. MOD3 uses the 1986 

AECL-UO Critical Heat Flux Lookup Table (Ref. 8) method by Groeneveld and co-workers. The 

table is made from tube data normalized to a tube inside diameter of 0.008 m but has factors 

that are applied to allow its use in other sized tubes or in rod bundles. In addition, it considers 

both forward and reverse flow, axial power shape, and the effect of boundary layer changes at 

both the bundle inlet and downstream of grid spacers. The root-mean-squared error at low 

pressure is generally below 20 percent. Its accuracy for rod bundles is uncertain. 

4.2.1.7 Minimum Stable Film Boiling Point

The other point which is fixed on the boiling curve is the minimum film boiling point, Tmin. In 

RELAP5 a constant Tmin equal to 600 degrees K (620 degrees F) is used. 
Table 4.1 RELAP5/MOD3 Heat Transfer Modes 

4.2.1.8 Transition Boiling 

The Chen transition boiling model (Ref. 9) considers the total transition boiling heat transfer to 

be the sum of two individual components, one describing wall heat transfer to the liquid and a 

second describing the wall heat transfer to the vapor. Radiative heat transfer from the wall to 

the fluid is neglected. The model was compared to data (4167 points) with a standard deviation 

of 16 percent. The calculated heat flux value for transition boiling is applied to post-CHF heat 

transfer if it is larger than the value for film boiling. 

 87
Figure 4.2 RELAP5 Wall Heat Transfer Flow Chart. 

 88
 89

4.2.1.9 Film Boiling

Film boiling heat transfer is calculated with the Bromley correlation (Ref. 10). The data were 

correlated within +18 percent. In this case a radiation heat transfer model is included to 

calculate the radiation heat transfer from the wall to the fluid. This model is attributed to Sun 

(Ref. 11). 

4.2.1.10 Interfacial Heat Transfer 

The flow regime determines the bulk interfacial heat transfer correlation to be used. For each 

vertical flow regime (bubbly, slug, annular-mist, inverted annular, inverted slug and dispersed) a 

correlation is used to calculate the interfacial volumetric heat transfer coefficient for either 

superheated liquid, subcooled liquid, superheated gas or subcooled gas. These are generally 

semi-empirical and/or mechanistic models which have been modified from the original model in 

the literature (Refs. 12-17) to account for numerical stability concerns. The interfacial heat 

transfer is the product of the interfacial area based on the flow regime and the interfacial heat 

transfer coefficient. 

For each flow regime the interfacial heat transfer coefficient is split into superheated-liquid 

(SHL), subcooled-liquid (SCL), superheated-gas (SHG) and subcooled-gas (SCG). In the code 

metastable states are generally driven rapidly to equilibrium by large empirical exponential 

functions. A summary of the interfacial areas and heat transfer coefficients is reported in Table 

4.2 while the original interfacial heat transfer models are reported in References 12 to 17. 

4.2.1.11 Quench Front Model 

Besides the heat transfer to the fluid another important process during reflood transients is the 

rod axial conduction at the quench front. The rod axial conduction is considered in 

RELAP5/MOD3 by a specific reflood heat conduction model which is based on a mesh-rezoning 

scheme very similar to the one used in COBRA-TF. 

4.2.1.12 Liquid Entrainment 

The liquid droplet entrainment process is considered to occur only in the annular-mist flow 

regime where the Ishii and Mishima (Refs. 18 and 19) correlation is used to determine the 

fraction of liquid flux flowing as droplets. The model gives very accurate results at location 

where annular mist flow regime exists. 

4.2.1.13 Conclusions

The heat transfer correlations are used to provide closure for the energy equations and are 

based on data which reflects only a subset of thermal-hydraulic conditions. Such correlations 

are very often applied outside their database. Moreover some of the correlations are based on 

engineering judgment, due partly to incompleteness of the science and partly to numerical 

stability requirements. From this perspective, by treating each correlation individually, the 

critical reviewer will conclude that the models are inadequate. In this case it is recognized that 

only an integral assessment is realistic where the global response of the code rather than the 

local response, becomes more meaningful. 
Table 4.2 Summary of Interfacial Areas and Heat Transfer Coefficients 

 90
 91

For example, the correlation used to calculate the volumetric interfacial heat transfer coefficient 

in the annular mist flow between the liquid annular film and the gas core is based on the work of 

Brumfield et al. (Ref. 12). This is based on a falling liquid film surrounded by quiescent air, 

whereas annular-mist involves a turbulent, flowing vapor core. The correlation is also based on 

the liquid velocity. 

The liquid velocity in the code is a single bulk value representing an average of both liquid 

annular film and the liquid droplets in the vapor core. As such, it is possible for the liquid 

velocity to be zero when the mass flow of droplets in one direction is balanced by the annularfilm flow in the opposite direction. In such case, the code would incorrectly predicted zero for 

the interfacial heat transfer coefficient. 

Another example of application of engineering judgment is the calculation of the droplet size in 

the inverted slug flow and dispersed flow regimes. The characteristic droplet size is calculated 

by assuming a critical Weber number equal to 6.0 and bounded by a minimum value for droplet 

diameter of 2.5 mm at low pressure, to allow more steam superheat during reflood. This is 

inconsistent with what observed during FLECHT-SEASET experiments where the Sauter mean 

diameter was estimated to be close to 1.0 mm. 

A deficiency in RELAP5/MOD3 when compared to COBRA-TF is that there are not specific 

models to calculate the entrainment and/or deentrainment at spacer grids. In addition, 

entrainment and deentrainment are only calculated for annular flow or horizontal stratified flows. 

Concerning the RELAP5/MOD3 capabilities to simulate accurately the phenomena involved in 

reflood transient, a big disadvantage is certainly the two field scheme where a single bulk value 

represents both the liquid in the continuous phase and droplets. 

4.2.2 TRAC-BF1 Reflood Model 

4.2.2.1 Introduction

The TRAC-BF1 model was developed specifically for BWRs and its development followed the 

development of the TRAC-PD2 PWR model. The heat transfer models are somewhat more 

simplified as compared to TRAC-PF1. However, a specific CHAN (channel) component was 

added to allow more accurate modeling of the BWR fuel channel during a LOCA. Surface-tosurface radiation heat transfer models were added with the CHAN component to calculate the 

radiation heat transfer expected in the canned assembly for LOCA conditions. 

4.2.2.2 Quench Front Model

TRAC-BF1 uses a fine mesh renodalization model for modeling quench fronts. The fine mesh 

model inserts additional nodes into the heated wall if significant temperature gradients exist 

along the wall. In the case of reflood modeling, the use of the fine mesh option allows one to 

capture the rapid changes in temperature along a fuel rod due to the presence of the quench 

front. It increases both the accuracy and the robustness of the code. No special heat transfer 

model is employed in TRAC-BF1 to model the quench front. Instead, both the heat transfer and 

flow regime map used in all other wall heat transfer calculations is employed. 
 92

4.2.2.3 Fine-Mesh Algorithm 

To model the advancing quench front, a numerical technique is employed which allows 

additional mesh points to be introduced within the structures (rods) around the quench front. 

The method allows the resolution of the high thermal gradients encountered near a quench 

front. The use of the fine mesh allows a more accurate representation of the heat transfer and 

energy content of the wall. The fine mesh heat transfer nodalization is superimposed on the 

coarse mesh usually used for the heat transfer analysis. Rows of transitory nodes are inserted 

whenever the temperature difference, DTmax, between adjacent nodes exceeds a user specified 

value. The number of nodes inserted is also user specified and remains during the entire 

reflood phase and move with the front. Multiple quench fronts may be modeled. 

 

The model uses two values of DTmax , one for the quenching region that is in nucleate or 

transition boiling and the other to all other heat transfer regimes. The largest wall heat transfer 

occurs in the former regions. 

4.2.3 TRAC-PF1 Reflood Model 

4.2.3.1 Introduction 

The TRAC-PF1 code series is the oldest best-estimate thermal-hydraulic codes developed for 

safety analysis purposes. The code formulation and interfacial heat, mass and momentum 

models have had several improvements over the years as the code has been used in a number 

of applications. TRAC-PF1 models the two-phase flow with two fields, liquid and vapor with 

three-dimensional capability within the vessel component. The coordinate systems used for the 

code are cylindrical such that the core region is modeled as a series of connected pie wedges. 

Specific models used in the code will be discussed below for this version of the code. A more 

recent version of the code, TRAC-PF1/MOD2 has a new reflood model. A brief review of this 

code will be added to this section at a later date. 

4.2.3.2 Quench Front Model

TRAC-PF1 uses both fine mesh renodalization and a special heat transfer model for modeling 

quench fronts. The fine mesh model inserts additional nodes into the heated wall if significant 

axial temperature gradients exist along the wall. In the case of reflood modeling, the use of the 

fine mesh option allows one to capture the rapid changes in temperature along a fuel rod due to 

the presence of the quench front. It increases both the accuracy and the robustness of the 

code. The heat transfer model in MOD2 is based on Ishii and uses a special flow regime map 

which inserts additional regimes near the CHF point. 

4.2.3.3 Fine-Mesh Algorithm

To model the advancing quench front, a numerical technique is employed which allows 

additional mesh points to be introduced within a region around the quench front. The method 

allows the resolution of the high thermal gradients encountered near a quench front. The use of 

the fine mesh allows a more accurate representation of the heat transfer and energy content of 

the wall. The fine mesh heat transfer nodalization is superimposed on the coarse mesh usually 

used for the heat transfer analysis. Rows of transitory nodes are inserted whenever the 

temperature difference, DTmax, between adjacent nodes exceeds a user specified value. The 
 93

number of nodes inserted is also user specified and remains during the entire reflood phase and 

move with the front. Multiple quench fronts may be modeled. 

The model uses two values of DTmax, one for the quenching region that is in nucleate or 

transition boiling and the other to all other heat transfer regimes. The largest wall heat transfer 

occurs in the former regions. 

4.2.3.4 Heat Transfer Model During Reflood

The model for calculating the heat transfer in TRAC-PF1 is based on the void-fraction wallsuperheat plane shown in Figure 4.3, and consists of eight different heat transfer regimes, 

which are listed in Table 4.3. The primary basis for correlation selection in TRAC-PF1 is the 

void fraction and wall superheat. While some pressure dependence enters the correlations 

through the properties of the parameters used in the calculations, the choice of correlation for 

any one particular regime is not based primarily on pressure criteria. The same is true for 

phasic temperatures and phasic velocities, which are introduced into the correlations through 

the heat flux equations and the flow correlations, respectively. To avoid any discontinuities in 

the heat flux, the current version of TRAC-PF1/MOD 2 (Ref. 20) evaluates the heat transfer 

coefficient for both laminar and turbulent natural convection, as well as forced convection, and 

then chooses the maximum value of the heat transfer coefficient to use in calculations. 

Table 4.3 TRAC-PF1/MOD2 Heat Transfer Regimes 

Mode Wall-to-Fluid Heat Transfer Regime 

1 Forced Convection to Single-Phase Liquid 

2 Nucleate Boiling 

3 Transition Boiling 

4 Film Boiling 

6 Convection to Single-Phase Vapor 

7 Convection to Two-Phase Mixture 

11 Condensation 

12 Liquid Natural Convection 

In each of the heat transfer regimes, the heat transfer coefficients are calculated in the 

subroutines HTCOR and HTVSSL. HTVSSL is used during reflood. The correlations used in 

HTVSSL are summarized here in detail. With the exception of the film boiling regime and the 

transition boiling regime, many of the correlations used in HTVSSL are the same as HTCOR. 

The post-CHF flow-regimes in HTVSSL are based on the more recent work done by Ishii, which 

showed that there are four inverted annular flow regimes downstream of the transition boiling 

regime, as shown in Figure 4.4. The selection logic for HTVSSL is shown in detail in Figures 

4.5 through 4.11. 

 
Figure 4.3 Void Fraction Superheat Plane. 

During reflood, TRAC-PF1 employs a special flow-regime map based on the flow-regimes 

depicted in Figure 4.4. According to Ishii, along the flow channel various flow regimes occur 

beyond the point of CHF. These different flow regimes are characterized by different heat 

transfer conditions requiring different closure relations. The different closure relations are 

 94
Figure 4.4 Flow Regime Map During Reflood. 

 95
Figure 4.5 HTC Correlation Selection Logic. 

 96
Figure 4.6 HTC Correlation Selection Logic. 

 97
Figure 4.7 HTC Correlation Selection Logic. 

 98
Figure 4.8 HTC Correlation Selection Logic. 

 99
Figure 4.9 HTC Correlation Selection Logic for Reflood Model. 

 100
Figure 4.10 HTC Correlation Selection Logic for Reflood Model. 

 101
Figure 4.11 HTC Correlation Selection Logic for Reflood Model. 

 102
applied depending upon the location of the flow regime within the cell. A weighting factor is 

applied based on the cell length and the elevation within the cell at which the regime occurs. 

Table 4.4 shows how the weighting factors are calculated (Ref. 20). 

Table 4.4 Weighting Factors of Reflood Interfacial Heat Transfer Models 

z Wsb Wsm Wrw Wds Winv

zt ≤ ZTR 1 0 0 0 0 

ZTR < zt < ZSM Eq. (4 – 102)* Eq. (4 – 103) 0 0 Eq. (4 – 103) 

ZSM ≤ zt < ZAG Eq. (4 – 102) Eq. (4 – 103) Eq. (4 – 104) 0 Eq. (4 – 105) 

ZAG ≤ zt Eq. (4 – 102) Eq. (4 – 103) Eq. (4 – 104) Eq. (4 – 106) Eq. (4 – 105) 

zb ≤ ZAG 0 0 0 1 0 

*See Reference 20 for specific equations

Winv = Wrs + Wsm (4-1) 

Wds = 1 – Wsb – Wrs - Wsm (4-2) 

The closure relationship is then calculated according to 

Xreflood = Wsb . Xbubbly + Wds . Xdispersed + Winv . Xinverted (4-3)

where X represents either Ai , HALVE , HCHTI , or HCHTA. For flashing, the maximum value of HALVE 

or a special model described in the next section is used. For the case of noncondensables, the 

value of HALVE is modified. The exact process is discussed in the references. 

4.2.3.5 Bubbly-Flow Models

In bubbly CHF upstream of the quench front, the void fraction is restricted to be between 0.05 

and 0.30. Slugs are not allowed to be formed. The interfacial area and heat transfer coefficient 

are identical to those used in HTCOR under similar conditions. If Tl is greater than Tsat then the 

heat transfer coefficient is not calculated using this method. Instead, the reflood model uses a 

simple model based on the kinetic theory of evaporation from liquid surfaces. The theoretical 

maximum evaporation rate predicted by this theory was converted by the code authors to a 

Heat Transfer Coefficient (HTC). The coefficient of evaporation of 0.4 is modified to predict 

evaporation rate for each of the flow regimes in nucleate and film boiling. The HTC for flashing 

is given by: 

H Ch C q h

T fls eva fls teo eva

v fg

sat

= =×

⎛

⎝

⎜

⎜

⎞

⎠

⎟ , ⎟ 01857 .

2

1 5. (4-4) 

The coefficient Ceva is defined for bubbly- and mist-annular-flow and is assumed to be void 

fraction dependent in the bubbly flow when the cell void fraction is between 0.3 and 0.5, 

otherwise it is a constant. The interfacial areas in bubbly flow are identical to those in HTCOR. 

 103
The liquid side heat transfer factor during flashing is then given by 

 (4-5) 

H hA ALV = fls I ,bubble

For the mist annular regime, Ceva is equal to 0.0002. 

If the flow regime is determined as the transition between the bubbly and mist annular flows, an 

interpolation is used according to 

 

H WH W H ALV , , trans =⋅ +− ⋅ ALV mist ( ) ALV bubbly 1 , (4-6) 

4.2.3.6 Dispersed and Post-Agitated Inverted Annular Flows

The flow regimes farthest from the quench front according to Ishii are the dispersed and postagitated inverted annular flows. In the reflood model, the void fraction is restricted to be 

between 0.3 and 0.9995. If there is a cold wall in the hydro cell, a thin liquid film can form and is 

allowed by the model. To evaluate the interfacial area it is necessary to divide the liquid into a 

film and droplet phase. The liquid is divided by determining a liquid film thickness and 

equivalent liquid fraction for the film. Once this is determined, a liquid drop fraction may be 

obtained and the corresponding interfacial areas calculated. 

The vapor to interface heat transfer is calculated in the dispersed flow regime by first calculating 

the mass fraction of liquid. The mass fraction is then used to determine a homogeneous void 

fraction. If the homogeneous void fraction is greater than 0.75 and the difference between 1-αdd

is less than or equal to 0.95, then HCHTI,dispersed is set equal to 10-6 W/K. Otherwise a correlation 

is used according to Unal et al (Ref. 21). The correlation was modified to allow its use as a heat 

transfer coefficient instead of a vapor generation rate. Changes were also made to the 

constants which appear in the correlation. 

If the cell void fraction is less than 0.98, then the flow regime is assumed to be post-agitated 

inverted annular flow. In that case, the value of HCHTI is calculated using the value for dispersed 

inverted annular flow with a void fraction weighting according to 

H H CHTI post ag CHTI DP

SM

DP SM

, ,

.

− = −

−

⎡

⎣

⎢ ⎤

⎦

⎥

−

α α

α α

0 01

 (4-7) 

The liquid heat transfer in the reflood model is not calculated using subroutine HTIF when Tl is 

less then Tsat. Rather, the sensible heat that goes to the sub-cooled liquid is calculated in 

HTVSSL in the wall-to-liquid HTC. If the liquid is superheated, then the coefficient in the 

flashing model is set equal to 0.002. The value of HALV for the dispersed or post-agitated 

inverted annular flow is calculated as 

 (4-8) H h A ALV ,( ) , dispersed or post agitated − fls I dispersed (or post agitated = − )

 104

where hfls is calculated according to the flashing model discussed earlier. 
 105

4.2.3.7 Inverted Annular Flow 

In inverted annular flow, the void fraction is limited to between 0.05 and 0.95. In this region, the 

interfacial area and the heat transfer coefficients are calculated according to the following: 

The hydraulic area of the liquid core is calculated by adjusting the hydraulic diameter of the 

channel by multiplying by 1-α. The interfacial area is computed as the product of the core 

hydraulic diameter and the length πD·x. If flashing is occurring, then the interfacial area is 

recalculated using an expression for the film thickness developed by Ishii (Ref. 22). This is then 

used to calculate the wall void fraction and the interfacial surface area near the walls. The void 

fraction for bubbles may then be determined using the interfacial area near the walls and the 

void fraction. The total interfacial area is then the sum of the wall and bubble interfacial area. 

The vapor heat transfer model is a simple product of constant times the interfacial area for 

inverted flow calculated using the method in the previous paragraph. The liquid side heat 

transfer coefficient is not calculated in subroutine HTIF for the inverted annular flow regime 

when Tl is less than Tsat. The sensible heat is calculated in HTVSSL in the wall-to-liquid heat 

transfer coefficient. As is the case for post-agitated flow, the coefficient for evaporation is set 

equal to 0.002. The HALV, uses the same formula as used in dispersed and post-agitated flow. 

4.2.3.8 Spacer Grid Model 

If grid spacers are present, an attempt is made to correct for the cooling effect of the grid 

spacers. The vapor-to-liquid heat transfer coefficient is modified to account for the temperature 

of the grid spacer. 

4.2.3.9 Noncondensables 

An attempt to account for the presence of noncondensables is also made. 

4.2.4 COBRA-TF Code 

4.2.4.1 Introduction 

The COBRA-TF code was developed by Pacific Northwest Laboratory under the sponsorship of 

the Nuclear Regulatory Commission to provide a best-estimate calculational capability for 

transient and accident analysis. The version of the COBRA-TF code (Ref. 24) which is being 

used in the RBHT program was refined from the original version of the COBRA-TRAC code Ref. 

25) as part of the FLECHT-SEASET 163-Rod Blocked Bundle Test and analysis program. 

COBRA-TF has several differences as compared to the TRAC and RELAP codes which make it 

more suitable for analyzing rod bundle reflood tests. COBRA-TF uses a separated flow model 

for the two-phase region conservation equations which model three distinct fields. The three 

fields which are modeled include: the continuous liquid field for low void fraction flow and falling 

or climbing films; vapor field for the steam flow, and the entrained droplet field. Using two liquid

fields is a more accurate and convenient method of representing the liquid phase over a wide 

range of two-phase situations which would occur during reflood of a hot bundle. Flow regimes 

such as inverted annular, churn-turbulent, and droplet flow can be modeled more accurately. 

One can also model the flow regime transitions more accurately as well as countercurrent flow 

in which a liquid film falls and the entrained droplets are carried upward. In addition in the 
 106

FLECHT-SEASET version of the COBRA-TF code, a fourth field exists which models the effects 

of a non-condensable gas. 

Mass conservation equations are written for each field, continuous liquid, vapor, entrained 

liquid, and non-condensable gas. The energy equations are more simplified in that the 

continuous liquid and the entrained liquid are assumed to have the same liquid temperature 

within the same computational cell. Also, a combined energy equation is used for the vapor and 

non-condensable gas. There are three momentum equations solved for the vapor, continuous 

liquid, and the entrained liquid. The momentum equations are three dimensional such that they 

can represent a rod bundle array with the smallest computational cell being a single 

subchannel. When the code is used in the subchannel formulation, some of the higher order 

momentum flux terms which represent the cross products of the lateral velocities are ignored. 

In the FLECHT-SEASET flow blockage program (Ref. 24), the capabilities of COBRA-TF were 

expanded to include a small droplet field which is used to model the smaller micro-droplets 

which are generated as larger drops shatter when they impact structures in the rod bundles 

such as spacer grids and flow blockages. There were some simplifications used for the small 

droplet field model. The small droplet field was not directly coupled to the hydrodynamic 

solution matrix, the interface of the small droplet field occurred as source and sink terms in the 

equation such that the mass of the entrained liquid was preserved. It was also assumed that 

there was no lateral flow of the small droplets, and the model was not valid for negative top 

down flow. 

COBRA-TF is also unique in that in addition to the conservation equations, the code uses a 

interfacial area transport equation which calculates the total droplet interfacial area in a 

computational cell considering the sources and sinks of interfacial area such as entrainment and 

deposition of the drops on to a liquid film. 

One of the differences of COBRA-TF from the other systems codes is that it has both "hot" wall 

and "cold" wall flow regimes. The hot wall regime is used when the wall temperature exceeds 

Tsat + 42 degrees C (75 degrees F). The hot wall regimes include subcooled inverted annular 

flow, saturated liquid churn or slug flow, dispersed droplet-vapor flow, falling film flow, and topdown liquid deluge flow. The hot wall flow regimes and logic selection are shown in Figures 

4.12 and 4.13. For bottom reflood when the reflood flow is subcooled, an inverted annular flow 

regime is assumed. If the liquid is saturated, the liquid churn or slug flow regime is assumed 

and the liquid is treated as very large droplets surrounded by vapor. 

4.2.4.2 COBRA-TF Heat Transfer Package

The heat transfer package in COBRA-TF consists of a library of correlations and a selection 

logic which allows the code to predict a boiling curve as a function of the computational cell void 

fraction, pressure, mass flow and the heated surface temperature. Figure 4.14 shows the 

boiling curve and regions of interest and Figure 4.15 shows the heat transfer regime selection 

logic in a simplified fashion. The heat transfer package which is used by the code calculates 

both the wall-to-fluid heat transfer as well as the interfacial heat transfer between the phases 

(Table 4.5). Since separate energy equations are used for the phases, a non-equilibrium flow 

will be calculated in some cases. Therefore, the interfacial heat transfer and the interfacial heat 

transfer area are calculated to determine the temperature of each phase. Both will be 

discussed below with the emphasis on reflood heat transfer. 
Figure 4.12 Hot Wall Flow Regimes. 

 107
Figure 4.13 Hot Wall Flow Regime Selection Logic. 

 108
Figure 4.14 Schematic Representation of Boiling Curve. 

Figure 4.15 Heat Transfer Regime Selection Logic. 

 109
Table 4.5 Interfacial Heat Transfer Area Per Unit Volume 

 110
Table 4.5 Interfacial Heat Transfer Area Per Unit Volume (Continued) 

 111
Table 4.5 Interfacial Heat Transfer Area Per Unit Volume (Continued) 

4.2.4.3 Single Phase Vapor 

COBRA-TF calculates the local Reynolds number within the computational cell and determines 

if the flow is laminar or turbulent. If the flow is turbulent, it uses the maximum of the DittusBoelter correlation (Ref. 2) or the correlation developed from the FLECHT-SEASET 161-rod 

bundle tests (Ref. 26). If the flow is calculated to be laminar, the code uses a Nusselt number of 

10, which is based on the FLECHT-SEASET data. 

 

4.2.4.4 Single Phase Liquid

In a similar fashion, the code calculates the Reynolds number of the cell and if the flow is 

turbulent, the code uses the Dittus-Boelter correlation for the convective heat transfer. If the 

 112
 113

flow is calculated to be laminar, the heat transfer correlation by Sparrow et al (Ref. 27) is used 

which has a maximum Nusselt number equal to 7.86. 

4.2.4.5 Nucleate Boiling 

When the wall temperature exceeds the saturation temperature but is less than the wall 

temperature at the critical heat flux point, the Chen correlation (Ref. 4) is used to calculate the 

wall heat transfer. The Chen correlation applies to both saturated nucleate boiling and forced 

convection evaporation and will automatically transition into single phase convection at low wall 

superheats and into pool boiling at low mass flow rates. The Chen correlation regards the wall 

heat transfer as consisting of a combination of forced convection heat transfer as well as pool 

boiling heat transfer. In this fashion both extreme limits of forced convection and pool boiling 

are preserved. 

4.2.4.6 Subcooled Nucleate Boiling

The Chen correlation can also be extended into the non-equilibrium regime of subcooled 

nucleate boiling. Again, the Chen correlation combines a forced convective heat transfer 

contribution and a boiling contribution to calculate the total wall heat transfer. For the subcooled 

case, the "F" factor used in the Chen correlation is set to unity but the remainder of the 

correlation is applied as in the nucleate boiling case. 

In subcooled nucleate boiling, there exists thermodynamic non-equilibrium between the voids 

which are formed and the bulk liquid temperature which is subcooled. Therefore, there is heat 

transfer between the vapor and the liquid such that the vapor condenses and the liquid 

temperature increases along the channel. The heat transfer processes of interest include: 

• Forced convection to the liquid, 

• Vapor generation at the wall, 

• Condensation near the wall, and 

• Bulk condensation in the liquid core. 

The partition of the vapor generation and the forced convection portions of the wall heat flux are 

calculated by the Chen correlation for the given set of conditions. The interfacial heat transfer 

processes are directly calculated in the fluid energy equations as part of the fluid conditions for 

the cell. The near wall condensation was calculated using the Hancox-Nicoll correlation (Ref. 

28) which was then subtracted from the nucleate boiling heat transfer to obtain the net vapor 

generation. There were further refinements which accounted for the fraction of the subcooled 

liquid which would penetrate the saturated liquid layer on the wall using the Rouhani and 

Axelsson correlation (Ref. 29). Using this approach, the net amount of vapor generation at the 

wall can be calculated and the remainder of the vapor will then be mixed in to the bulk flow 

through the liquid energy equation and will condense. 

4.2.4.7 Critical Heat Flux 

COBRA-TF calculates the critical heat flux and the wall temperature superheat at the CHF point 

to fix this location on the boiling curve as shown in Figure 4.14. For reflood heat transfer, the 

Zuber (Ref. 30) pool boiling correlation is chosen for the critical heat flux since the liquid flow 

velocities are small. 
4.2.4.8 Minimum Stable Film Boiling Point

The other point which is fixed on the boiling curve is the minimum film boiling point, Tmin. This 

location denotes the boundary between stable film boiling and transition boiling. COBRA-TF 

uses the larger of a modified version of the homogeneous nucleation temperature which is 

curve-fit as a function of the difference between the critical pressure and the local pressure, and 

which has also been modified to account for wall properties and the Henry modification (Ref. 31) 

of the Berenson correlation. In addition, for reflood, COBRA-TF limits the value of Tmin to be 

426 degrees C (800 degrees F) < Tmin < 650 degrees C (1200 degrees F). 

4.2.4.9 Transition Boiling 

The transition region is viewed as a mixture of film boiling with a vapor layer contacting the wall 

and nucleate boiling or wetted wall in which liquid contact with the wall is possible. The wetted 

wall portion of the wall heat flux is calculated using Ganic and Rohsenow (Ref. 32) which uses 

the McCoy and Hanratty model (Ref. 33) for determining the droplet migration to the wall. Once 

the droplet contacts the wall a droplet efficiency is calculated which is a function of the wall 

temperature and the liquid temperature. At high wall temperatures, the efficiency becomes very 

small as the drops will not contact the hot wall. The wetted wall portion of the heat flux is added 

to the dry wall film boiling heat flux calculation to give the total transition boiling wall heat flux. 

There are separate models for top down quench in which the heat transfer is enhanced below 

the top down quench front location which is used as a multiplier on the critical heat flux. 

4.2.4.10 Inverted Annular Film Boiling

COBRA-TF assumes the wall heat transfer is in inverted annular film boiling if the wall 

temperature is greater than Tmin, and the void fraction is less than 0.4. The modified Bromley 

correlation (Ref. 10) is used for the film-boiling portion of the wall heat flux. The radiation heat 

transfer from the wall to the liquid is also accounted for as well as the droplet contact heat 

transfer using the Ganic and Rohsenow correlation as described earlier. Therefore: 

q q qq (4-9) IAFB Brom R W D

" " "" = ++ −

When the cell void fraction is greater than 0.4 and less than 0.9, the wall heat flux is linearly 

interpolated between the value for inverted annular film boiling and dispersed flow film boiling. 

There are also interfacial heat and mass transfer models in the inverted annular film-boiling 

regime which include estimates of the interfacial area between the vapor and the liquid such 

that the proper liquid and vapor temperatures can be calculated. The heat flux behavior as a 

function of void fraction is shown in Figure 4.16. 

4.2.4.11 Dispersed Flow Film Boiling

The dispersed flow film boiling is assumed to occur when the wall temperature exceeds Tmin and 

the void fraction is greater than 0.9. The dispersed flow film boiling heat transfer mode received 

the greatest amount of attention and refinement as part of the FLECHT-SEASET program. The 

wall heat flux in dispersed flow film boiling is comprised of three different heat transfer 

mechanisms which are summed to give the total wall heat flux: 

 114
Figure 4.16 WCOBRA/TRAC Heat Transfer Regime Map. 

 (4-10) q q qq DFFB FC R W D

" " "" = ++ −

where 

qFC

"

 vapor convective heat flux (either laminar of turbulent) 

qR

"

 radiation heat flux 

qW D−

"

 droplet impinging heat flux or droplet contact heat flux 

The vapor convective heat flux is enhanced by a factor Ψ which experimentally accounts for the 

effect of the entrained droplets increasing the convective heat transfer. Data for the 

 115
 116

enhancement factor was obtained from the FLECHT and FLECHT-SEASET programs and has 

been compared to data obtained by Drucker and Dhir (Ref. 34). The two-phase enhancement 

factor can be shown to be an extension of the basic analogy theory between heat transfer and 

momentum transfer as given in Kays (Ref. 35). Figure 4.17 shows the scatter of the data for the 

enhancement value Ψ. Note the scale on the plot. It is relatively easy for value for the singlephase convective heat transfer to be enhanced by 100 percent in a two-phase dispersed flow. 

The radiation heat transfer q"R , consists of two separate models. The surface-to-surface 

radiation is solved on a subchannel basis (Ref. 1) such that small test facilities with colder 

housing can be modeled more accurately. In a separate calculation, the radiation heat transfer 

to the droplets and vapor are calculated using the Sun et al model (Ref. 11) for the fluid 

radiation component. 

The droplet impingement heat flux term is the same as that described earlier. However, this 

term is very small or negligible in the dispersed flow film boiling since the wall temperatures are 

much higher and the heat transfer efficiency of droplets hitting the wall is nearly zero. 

Above a void fraction of 0.999, the heat transfer becomes single-phase vapor. 

4.2.4.12 Quench Front Model 

COBRA-TF uses fine variable mesh (Ref. 36) which will insert additional nodes into the heated 

structure if significant axial temperature gradients exist. This allows a more accurate 

representation of the true localized energy release from a localized portion of a heater or 

nuclear rod rather than the energy release from all the structures within the fluid node. Fine 

mesh heat transfer cells for axial and radial conduction in the structure are superimposed on the 

coarser hydraulic computational cells. The heat transfer package described above is applied to 

each of these smaller structural nodes to obtain the local heat transfer. In this fashion, the 

energy release at the quench front is smoother, and the effects of axial conduction in the 

quench front region are simulated. 

4.2.4.13 Spacer Grid Heat Transfer Models

One of the major additions to the COBRA-TF code was the inclusion of heat transfer models for 

the dispersed flow film-boiling regime (void fraction greater than 0.9) which represented the 

experimental observations on the effects of rod bundle spacer grids. Spacer grids result in 

three additional heat transfer mechanisms in the rod bundle flow, namely: 

• Convective heat transfer enhancement downstream of the grid, 

• Rewetting of the grid structure, and 

• Entrained droplet breakup caused by the grid structure. 

Convective enhancement downstream of the spacer grids was observed in several single phase 

experiments and is due to the thinning of the thermal and velocity boundary layers on the rods 

as well as the additional turbulence introduced by the grid in the flow. Data from these 

experiments were correlated in terms of the grid blockage area in the rod bundle and an 

exponential multiplier, which diminishes downstream of the grid, according to Yao, Hochreiter, 

and Leech (Ref. 37). This correlation is used in COBRA-TF as a multiplier on the vapor 

convective heat transfer calculation described above for the dispersed flow heat transfer regime. 
Figure 4.17 Two-Phase Enhancement: Comparison of Models and Reflood Data. 

 117
Spacer grids can be either dry, that is, with grid temperature which exceed Tmin, or wetted with 

temperatures which are close to the saturation temperature. If a fraction of the grid is at the 

saturation temperature, it is assumed that a liquid film is present on that surface area. Since the 

grids are stationary, they have significant surface area; if the grid wets, a significant amount of 

interfacial heat transfer area is added to the interfacial area transport equation as an area 

source term. The result of this is more rapid de-superheating of the vapor flow in the rod 

bundle. As the vapor de-superheats, the driving temperature for the rod heat flux increases 

(TROD- Tv), and the rod wall heat flux increases and the rod cools. 

There is a two zone detailed spacer grid model in COBRA-TF which calculates the location of 

the quench front on the grid, and the dry and wet grid temperatures considering the radiation 

heat transfer from the heater rods, convective heat transfer from the superheated vapor as well 

as the quenching of the spacer grid. The radiative heat transfer model for the spacer grid is 

shown in Figure 4.18. In this fashion, the fraction of the grid which is either dry or wet can be 

calculated as a function of the thermal-hydraulic conditions within the channel to determine the 

amount of grid area which should be added to the interfacial area transport equation. The 

additional steam generation due to the evaporation of the liquid film on the grid is also added 

into the hydrodynamic solution. 

Figure 4.18 Radiation Heat Flux Network. 

The third spacer grid model indicates that when high velocity entrained liquid droplets impact 

the grid structure, the drops can shatter producing a range of smaller "micro droplets" which are 

more easily evaporated. As the micro droplets are evaporated, the vapor de-superheats due to 

the heat taken up by evaporation as well as the addition of saturated vapor due to the droplet 

evaporation. Both heat transfer effects reduce the vapor temperature and result in a larger 

temperature difference between the vapor and the rod surface which increase the rod heat flux 

promoting improved cooling. 

Figure 4.19 indicates the droplet breakup behavior. The parameter which was found to 

correlate the ratio of the shattered drop size to the initial drop size was the droplet Weber 

 118
number for flow normal to the spacer grids as seen in Figure 4.20. For low Weber numbers, the 

change in the drop size is not significant, at most a factor of two. For these drops, the interfacial 

area of the larger shattered drops was added to the interfacial area transport equation as an 

additional source term. For the very small drops which were generated at higher drop Weber 

numbers, these drops are put into the separate small-drop field described earlier. In addition, if 

there are small drops upstream of a spacer grid, they are also broken-up by the downstream 

spacer and the resulting small drop populations are then merged preserving the droplet mass, 

interfacial area and momentum. 

Figure 4.19 Droplet Breakup. 

COBRA-TF heat transfer models, which are similar to the spacer grid models, have also been 

developed for flow blockage in rod bundle arrays and are described in Reference 24. 

4.3 Road Map from the PIRT, to the Code Models, to the Test Instrumentation 

and Data Analysis

4.3.1 Single Phase Liquid Convection Below the Quench Front (Table 4.6) 

The contribution of the single-phase liquid convection during a reflood transient ranks low in the 

PIRT. To calculate the heat transfer with the liquid single-phase (and vapor single-phase), the 

codes use different correlations depending on the Reynolds number. In general, the DittusBoelter correlation is used for turbulent flow while other correlations are used to calculate heat 

transfer in the laminar flow regime. These correlations are based on pipe geometry data and in 

general to geometries quite different than the bundle geometries. RELAP5/MOD3 uses the P/D

 119
Figure 4.20 Shattered Droplet Size from Heated Grid Straps. 

 120
 121

correction relation to account of this effect but its uncertainty is very high. The two TRAC codes 

do not account of this effect at all. In COBRA-TF a specific correlation was developed during 

FLECHT-SEASET experiments but was tuned on the 163 rod bundle geometry. 

Beside the geometry effect, the flow regime during reflood is often in the transition between 

laminar and turbulent flow and therefore a bundle specific correlation needs to be developed to 

predict accurate convective heat transfer. The RBHT facility can transverse several 

temperature probes across the bundle at different elevations. This allows a better estimate of 

the bulk average temperature which is needed to assess these models. 

The important phenomena were identified in the PIRT in Section 2 for the different periods or 

phases of the reflood transient. Examining the PIRT for single phase convective heat transfer, 

the items which are highly ranked are: 

• The decay power which is the energy source into the fluid, 

• The liquid velocity or Reynolds number, 

• The liquid temperature or subcooling, and 

• The convective heat transfer coefficient, which is ranked as medium. 

The difference in the ranking of the liquid velocity and subcooling and the convective coefficient 

is that the convective fluid conditions will determine the behavior of the flow in different locations 

downstream, whereas the effects of uncertainty on the heat transfer coefficient for single phase 

heat transfer has a very small effect on the calculated peak cladding temperature. 

The decay power is a test boundary condition which is controlled in the experiment and is 

directly measured such that this parameter is known accurately for a given test. 

Although it is not given a ranking of high, convective heat transfer for the single phase 

convective experiments is of interest since most of the current codes use a pipe correlation as 

compared to a rod bundle correlation, as seen in Table 4.6. The computer codes calculate the 

local convective heat transfer from the local node velocity, the fluid properties, and the given 

hydraulic diameter of the node. The correlations for forced convection require the code to 

calculate a local Reynolds and Prandtl number which depends on the flow and temperature 

conditions within the computational node. In the RBHT experiment, the local power is 

calculated from the total power of the rods and the axial power distribution, such that the local 

value of the heat flux is known along the bundle. The heater rods are instrumented with eight 

thermocouples which calculate the local heater rod surface temperature from an inverse 

conduction calculation. 

There are several subchannel fluid temperature measurements along the length of the bundle. 

Most of the temperature measurements have the ability to traverse across the subchannel such 

that the temperature distribution can be obtained within the subchannel. Therefore, the local 

fluid temperature or subcooling will be measured directly in the experiments. The temperature 

traverses will have to be velocity weighted and integrated across the subchannel area to obtain 

the local bulk subchannel fluid temperature. 

The local subchannel flow is not directly measured in the experiment. However, the total liquid 

flow into the bundle is measured. The pressure drop of the bundle will already have been 

characterized by single phase pressure drop experiments which will confirm the losses of the 

spacer grids as well as the frictional loss of the total bundle. The hydraulic data can be used to 
Table 4.6 Single Phase Liquid Convective Heat Transfer in the Core Component During Reflood Below 

 122
 123

benchmark a subchannel computer code such as COBRA-IV or VIPRE-II which will then be 

used to predict the local subchannel velocity and the subchannel Reynolds number. These 

code calculations can be checked, for fully developed flow, with hand calculations to confirm the 

flow split between types of subchannels. Given the measurements of the rod heat flux, the 

heater rod surface temperature, and using the fluid temperature traverses and velocities 

predicted by COBRA-IV, the local convective heat transfer coefficient can be calculated from the 

data. The COBRA-IV local subchannel velocities can also be used with the fluid properties to 

calculate the local fluid Reynolds and Prandtl numbers such that comparisons can be made 

between the correlations used in the computer codes and the RBHT data to determine if the 

current models are adequate. This data analysis approach has been used on the FLECHTSEASET single phase steam tests (Ref. 26). The RBHT tests are designed to be performed 

over a wide range of fluid Reynolds numbers such that either a new convective correlation can 

be developed or an existing correlation can be confirmed. 

 

In the case of single phase natural convection, or mixed convection, the highly ranked PIRT 

items include: 

• Natural convection heat transfer coefficient, 

• Effects of forced or free convection heat transfer, 

• Liquid velocity, 

• Liquid subcooling, and 

• Decay power. 

The local Reynolds and Grashoff numbers can also be calculated from the data using the same 

analysis approaches as given above to determine if forced convective heat transfer of natural 

circulation heat transfer exists within the subchannel. The ratio of the Grashoff to the square of 

the Reynolds will be calculated to determine if the flow is forced, free or mixed convection. For 

most reflood rates of interest, the convective heat transfer will be forced. If the heat transfer is 

free convection, a similar approach to that used for the forced convection heat transfer analysis 

can be used to determine the local heat transfer coefficient excepting that the local subchannel 

velocity will not be needed. If the convection is mixed, the data will be compared to 

conventional methods for mixed convection in which the forced and natural convection heat 

transfer coefficients are raised to a power (typically 3), summed (for aiding flow), and then 

raised to the inverse of the power (typically 1/3). The natural or mixed convective heat transfer 

coefficient is ranked higher as compared to the forced convection coefficient since there is very 

little data available for natural convection heat transfer in bundles. 

4.3.2 Subcooled and Saturated Boiling Below the Quench Front (Table 4.7) 

The heat transfer in this region ranks low in the PIRT but it determines the degree of subcooling 

at the quench front location, which in turn affects the ranking processes in that region. The 

Chen correlation (Ref. 4) is used in the codes to determine the heat transfer in the subcooled 

and saturated boiling regimes. In experiments the total heat transfer to the fluid in the twophase region is measured while the codes need to calculate the heat transfer to each phase 

separately. Once the heat input in each phase is calculated the interfacial heat and mass 

transfer terms provide the closure to the equations. The subcooled boiling is modeled as 

follows: 

1) convection to the liquid, 
 124

2) vapor generation at the wall, 

3) vapor condensation near the wall, 

4) subcooled liquid ‘pumped’ into the thermal boundary layer, and 

5) bulk condensation (subcooled liquid core). 

The fraction of vapor not condensing near the wall represents the net vapor generation term 

which is added explicitly into the mass-energy conservation equations. The condensation of the 

vapor because of the presence of vapor in the liquid core is calculated implicitly during the 

solution of the energy equation and it does not affect the determination of phasic heat inputs. 

The convection to the liquid is calculated starting from the liquid phase Reynolds number. The 

code needs the local liquid bulk temperature, the local flow quality and flow velocity. The 

nucleate boiling component of the Chen correlation defines the amount of heat available to 

cause vapor generation at the wall. A fraction of this vapor condenses near the wall, whereas 

the rest will condense in the liquid core. The near-wall condensation is determined by the 

conditions (flow and thermal) of the fluid near the wall while the bulk condensation is determined 

by the interfacial heat transfer. Detailed void fraction measurements, void distribution, and 

liquid temperature during separate steady-state subcooled boiling tests should provide the 

information needed to assess these models. 

For example, during subcooled boiling experiments, the contribution of the near wall 

condensation combined with the effect of subcooled liquid “pumped” into the thermal boundary 

layer can be calculated from an energy balance if the transverse temperature distribution of the 

liquid in the subchannel is measured or estimated. 

Information about void fraction distribution (bubble size distribution and bubble location) are 

needed to estimated the interfacial heat transfer area. Measurements or estimates of bubble 

velocity can be used to estimate the interfacial drag. Note that the interfacial heat transfer and 

interfacial drag, which determines the condensation of steam in the liquid core and the slip 

between the two phases, rank high in the PIRT. 

During saturated boiling, condensation does not take place. The code divides the total heat 

transfer rate in two contributions. The first is the heat removed by liquid convection, the second 

is the heat removed by boiling. Both components are from wall-to-liquid. Since metastable 

states are essentially not permitted in the code, energy absorbed by the liquid at the wall is 

transformed into vapor generated at the vapor-liquid interphase with an artificially large heat 

transfer coefficient. 

This is modeled in the Chen correlation with the Reynolds number factor which is a function of 

the local quality. The effect of the Reynolds number is also to prevent/suppress boiling and this 

is accounted by the suppression factor in the nucleate boiling heat transfer component of the 

Chen correlation. 

Similarly for the subcooled boiling regime, the code evaluates the flow rate, the quality, the 

temperature of the liquid and the temperature of the wall to calculate the heat transfer. The 

temperature of the liquid is at saturation. The interfacial heat transfer is not important in this 

case because the liquid superheat is prevented numerically in the code and all the energy going 

to the liquid is converted in vapor generation. 
Table 4.7 Subcooled and Saturated Boiling in the Core Component Below the Quench F

 125
 126

Separate steady-state boiling experiments with a detailed measurement of void fraction can be 

used to assess the model in this region. The separate effect of the Reynolds number factor and 

the boiling suppression factor can be quantified in these experiments. Finally bubble velocity 

measurements and transverse void distribution, can be used to estimate the interfacial drag. 

The PIRT table for the subcooled and saturated boiling regions are given in Table 2.2 in Section 

2. The important phenomena identified in this table includes: 

• Decay power, 

• Local void fraction, 

• Interfacial area and heat transfer, and 

• Liquid subcooling. 

As discussed above, decay power is a test boundary condition and is known. Local void 

fraction is measured using finely spaced differential pressure cells as well as using an X-ray 

attenuation technique. The liquid subcooling is measured using traversing temperature rakes at 

several different elevations in the bundle. These miniature thermocouples will traverse across 

the bundle between the heater rods and will measure temperature in the rod-to-rod gap, as well 

as at the center of the subchannel. 

Several different computer code models interact to develop the local void fraction within a 

computational node in the case of subcooled boiling. Models for vapor generation, interfacial 

heat transfer such as condensation of the generated bubbles (if the liquid flow is subcooled), 

single phase convective heat transfer at the wall, criteria for wall voidage, bubble size at 

departure and interfacial drag all influence the resulting void distribution in the rod bundle for 

subcooled and saturated boiling below the quench front. 

In the RBHT program, the total wall heat flux will be determined from the power applied in the 

test and the axial power shape as well as from the inverse conduction calculations using the 

measured heater rod temperature and the power. The local fluid temperature will be measured 

at many elevations using the traversing miniature thermocouples in the bundle which will 

indicate if the bulk liquid flow is subcooled or saturated. The axial behavior of the liquid 

temperature in the bundle can be measured such that the location of where the bulk flow 

becomes saturated can be determined. 

The wall heat flux consists of two components; a direct convective component and a boiling 

component in similar manner as the model by Chen (Ref. 4). The axial fluid temperature 

distribution reflects both the wall convection heat transfer as well as the condensation of the 

voidage generated at the wall. If one assumes that the convective and boiling processes are 

separate and are additive (similar to Chen’s model), the wall convective heat transfer can be 

estimated from the bulk flow conditions as well as the portion of the heat flux which is due to 

convection. Since the total wall heat flux is measured, the difference between the total and the 

convective heat fluxes is the boiling component. This is an estimate since the local liquid phase 

velocity distribution will be different at the wall because of the bubble formation. 

Low void fractions, characteristic of nucleate boiling, will be very difficult to measure even with 

sensitive differential pressure cells. The laser illuminated digital camera system can detect the 

voidage but it may be difficult to quantify wall voidage since the bubbles will adhere to the 

heated surface. As subcooling of the bulk flow is reduced, the fraction will grow and the bubbles 
 127

will depart from the wall and will be condensed in the bulk flow. This can occur for voids of 

approximately 20 percent. In this situation, the finely spaced differential pressure cells data can 

be analyzed to obtain an average void over the cell span with more confidence. Also, the laser 

illuminated camera system can also be used to obtain data on the bubble diameter and velocity 

distributions, for low voidage flows in which there is minimum bubble interaction. 

A measurement of the local void will also be obtained using an X-ray densitometer, and the 

finely spaced pressure drop cells, as well as visual observations. Given the void distribution, 

estimates of the bubble diameters and velocities, rough estimates of the product of the 

interfacial heat transfer and the interfacial area can be made. Therefore, the computer code 

models and correlations for the product of the interfacial hAI can be compared to the rough 

estimates of the hAI estimates from the data. It is expected that the uncertainties will be large. 

Both the axial liquid temperature gradient as well as the void fraction (which represents a net 

situation, that is the void generation minus the condensation) can also be used to develop and 

refine models for the interfacial heat transfer and area. 

When the liquid reaches saturation, all the energy from the heater rods generates vapor since 

there is no longer any liquid subcooling. In this case saturated boiling is occurring on the heater 

rod surfaces and the void fraction increases. The important items from the PIRT Table 2.2 for 

this case are: 

• Void fraction, and 

• Decay power. 

The void fraction in this region is ranked high since it will influence the steam velocity at the 

quench front and the generation of liquid entrainment. The decay power is ranked high since it 

represents the energy input into the fluid which will generate steam. The saturated boiling heat 

transfer coefficient is not ranked as a high since a large uncertainty in its value will not effect the 

peak cladding temperature. Note that there is an overlap between the decay power and the 

boiling heat transfer coefficient since all the energy generated in the rod is transferred to the 

fluid. If the decay power is ranked as a ”high,” in reality, the surface heat transfer coefficient is 

also a high. 

The void distribution will be determined using the finely spaced differential pressure cells which 

will result in a node average void along the axial length of the bundle. In addition, an X-ray 

technique will be used to obtain the void distribution at specific axial locations to confirm the 

values obtained from the differential pressure cells. 

4.3.3 Quench Front Behavior (Table 4.8) 

This is the most complex region in the bundle. There are several process taking place across 

the quench front which rank high in the PIRT table. This is also the most difficult region to 

simulate with the codes because a big transition in the thermal-hydraulic conditions is 

experienced in a small portion of the computational domain. Moreover the hydraulic process is 

strongly coupled with the thermal behavior in this region. The froth region behavior significantly 

affects the heat transfer downstream in the film boiling region. This is where compensating 

errors are most likely to occur. The code has to be able to handle each separate process 

accurately to limit, to a minimum, extent the effect of compensating errors. Unfortunately the 

lack of data in this region causes the models to simulate this region poorly in most of the codes. 

Essentially, the codes need to calculate heat transfer from the rod to the fluid, vapor generation 
 128

and entrainment. The amount of droplets entrained in that region will determine the heat 

transfer downstream, in the dispersed flow region. 

The codes at first calculate TCHF and TMIN and if the clad temperature falls between those two 

values then transition boiling regime is assumed. The heat transfer selection logic of COBRATF is shown in Figure 4.15. The present version of COBRA-TF does not have a specific 

transition boiling model and the heat transfer is calculated by extrapolating the dispersed flow 

film boiling heat transfer or the inverted annular film boiling heat transfer in that region. The 

models used by other codes are described in Section 4.2. A more accurate transition boiling 

model and a more consistent entrainment model need to be developed during the RBHT 

program. 

Critical Heat Flux and TMIN are calculated by different codes using different correlations as 

described in Section 4.2. In the transition boiling regime the codes calculate the total heat 

transfer as the sum of convective heat transfer from the wall to the vapor, radiation heat transfer 

to the liquid and wall-liquid direct contact heat transfer. The radiation heat transfer is a small 

contribution in the froth region where the wall temperature is not very high and the void fraction 

is low. 

The code needs to predict accurately the void fraction and the slip in this region. Therefore, 

detailed information is needed about the void fraction distribution. An estimate of the slip is also 

needed and can be obtained through a mass and energy balance in the froth region when 

sufficient data about void fraction are available. The vapor in this region can be assumed at 

saturation while the liquid can be subcooled. The degree of subcooling is needed to calculate 

the interfacial heat transfer and net vapor generation on condensation. The void fraction 

distribution is also needed to calculate the radiation heat transfer component as well as to 

define the mechanisms of entrainment. The entrainment is a function of the vapor generation 

rate. Information about the size and velocity of the entrained droplets and ligaments just above 

the froth region are also needed to develop a mechanicistic entrainment model. 

Compared to the other codes, COBRA-TF has the unique feature of a three-field approach. 

This is a big advantage in the froth region because continuous liquid, droplets and vapor 

coexist. This feature combined with proper entrainment and de-entrainment model provide a 

more realistic representation of the phenomena at the quench front. Data from RBHT 

experiments can be use to assess these separate models. 

All the codes attempt to calculate the rod axial conduction at the quench front by using a fine 

mesh rezoning in that region. The axial conduction is a very important phenomena during 

reflood because it represents a flow path for the energy from the region above the quench front 

where the heat transfer to the liquid is low to the region below the quench front characterized 

by a much higher heat transfer coefficient. This component needs to be extracted during the 

test data analysis by solving a two-dimensional inverse conduction problem. 

Other effects, such as fuel/heater rod material properties, dimensions and cladding thickness, 

gap heat transfer coefficient, cladding surface effects, need to be correctly simulated and 

measured. 
Table 4.8 Quench Front Behavior in the Core Component 

 129
Table 4.8 Quench Front Behavior in the Core Component (Continued) 

 130
 131

The highly ranked items from the PIRT in Table 2.3 for the quench region are: 

• Fuel/heater rod material properties, dimensions and cladding thickness, 

• Gap heat transfer coefficient, 

• Cladding surface effects, 

• Transition boiling heat transfer(surface-liquid contact heat transfer), 

• Steam generation at the quench front, 

• TCHF the temperature where CHF occurs (maximum limit of nucleate boiling), 

• TMIN the temperature at the minimum film boiling point, and 

• Surface temperature. 

The heater rod physical properties such as the clad conductivity, density and specific heat are 

known as a function of temperature from property tables. The boron nitride filler material 

properties such as the conductivity, specific heat and theoretical density will be determined by 

Purdue University Thermal Physical Property Center such that the heater rods will be well 

characterized. The property and geometric information is used to calculate the surface heat flux 

by an inverse conduction technique using an internal thermocouple. The surface temperature is 

also calculated using the same method. The same information is available for nuclear fuel rods 

such that the differences are known. The scaling analysis given in Sections 6 and 7 addresses 

the differences between the nuclear and the electrically heated rods. 

The gap heat transfer coefficient is very high for the heater rods since they are swagged to 

close the gap between the boron nitride and the inside of the cladding. A typical valued of 

96.875 kW/m2

-K (5000 Btu/hr-ft2-F) is used to characterize this gap resistance. The gap heat 

transfer coefficient in a nuclear fuel rod is a dynamic quantity since it changes over the fuel 

lifetime as well as during the accident. While the fuel rod gap heat transfer coefficient has a 

large uncertainty, this uncertainty will not effect the total stored energy, since it will be released 

during quenching. However, the gap heat transfer can affect the rate at which this energy is 

released. Sensitivity calculations as well as nuclear rod data can be used to quantify these 

effects. 

Cladding surface effects such as crud, oxide layers, roughness, material types, have been 

shown to effect the minimum film boiling temperature, TMIN and the CHF temperature TCHF . 

Both of these temperatures define the region of transition boiling. 

The heater rod surface conditions will be well characterized by the Purdue University Thermal 

Physical Property Center as well as at Penn State. A nuclear fuel rod cladding, however, can 

have a range of surface conditions which affect TMIN and TCHF. Therefore, it has been proposed 

that as part of the Rod Bundle Heat Transfer Program, that a series of “bench top” experiments 

be performed to characterize the surface effects on both TMIN and TCHF using small samples of 

different cladding materials which have known surface conditions. The end result of this effort 

will be to develop specific criteria for a TMIN correlation and to confirm the relationship for TCHF. 

The literature will be reviewed and relevant data for different surfaces will be found and 

assessed. 

Transition boiling heat transfer occurs as the fraction of the heated surface which has liquid 

contact increases until the entire surface is wetted and quenched. The RBHT electrical heater 

rods are well instrumented with internal thermocouples to measure the total wall heat flux using 

a radial inverse conduction calculations given the power and the internal temperature. The local 
 132

fluid thermocouples will measure the local subchannel fluid temperature which should be near 

or at the saturation temperature. As the rod quenches, the measured temperature can be 

influence by the axial conduction down the rod to the quench front since there is a very large 

axial temperature gradient near the quench front. Therefore, the calculation of the radial heat 

flux and the resulting heat transfer coefficient from the inverse conduction scheme must be 

corrected for the axial conduction when the quench front passes a thermocouple location. 

Two-dimensional, transient calculations will be performed on the heater rods to predict the axial 

heat flow such that the data can take account of axial heat flux as the quench front approaches. 

The transition boiling heat transfer will then be calculated as the corrected heat flux divided by 

the difference of the heater rod surface temperature minus the local saturation temperature. 

The data sampling during this time period will be sufficiently rapid such that a number of data 

samples will be obtained as a particular location quenches. Similar calculations will be 

performed on the bench top experiments. 

The values of TMIN and TCHF will be obtained directly from the data as the heater rod quenches. 

The local void fraction will also be available which can be used to determine if the liquid content 

in the flow has an effect on TMIN and TCHF. These values will be supplemented with similar data 

from the bench top experiments such that a material and surface condition specific transition 

boiling correlation could be developed. The RBHT heat transfer data can then be compared to 

different TMIN and transition boiling correlations in the literature as well as those currently used in 

safety analysis computer codes. 

Steam generation near the quench front is responsible for the downstream development of 

drops, liquid ligaments and or chunks which are entrained upward by the steam flow. The 

entrained liquid provides an additional heat sink for the heated surface since the drops 

evaporate in the superheated steam flow, generating additional steam at the saturation 

temperature, which cools the steam. The droplets are also a radiation heat sink for the heated 

surfaces. Local steam flows within the bundle are not measured. The exit steam and liquid 

flows are measured as well as the vapor temperature distribution along the bundle as well as 

the rod bundle total heat flux along the heater rod surfaces. The bundle heat flux represents the 

total energy leaving the heater rods. The rod bundle energy has several different paths, directly 

to the fluid by convection and radiation to steam and droplets, to the colder housing, to colder 

rods, and to the colder support tubes. The temperatures of all the structures in the rod bundle 

are measured at several elevations (heater rods, thimbles, housing, spacer grids). 

The radiation network used to determine the radiation heat transfer in Sections 6 and 7 can be 

used to determine the expected radiation heat fluxes during a two-phase experiment. The 

radiation-only tests will be used to calibrate this method such that the radiation can be 

subtracted from the total measured heat flux to obtain the heat flow into the fluid. 

Constructing a one-dimensional transient heat balance from the exit of the test section, using 

the measured vapor temperatures, the measured vapor flows and liquid flows, and the portion of 

the wall heat which is transferred to the fluid, the axial fluid quality can be calculated in the 

bundle above the quench front. This calculation can be carried to the top of the froth region, 

where the majority of the entrainment occurs. 

The vapor temperature at the top of the froth region is superheated, however, it is expected that 

the miniature thermocouples will have wetted such that they will not yield an accurate reading of 

the true vapor temperature. The vapor superheat will be assumed to be the average of TSAT and 
 133

the heater rod wall temperature TWALL. This approach was successfully used in the analysis of 

the FLECHT-SEASET data. This calculations will yield the bundle average vapor and liquid 

flowrates at the top of the froth region. The local subchannel vapor velocities can be estimated 

using COBRA-IV or VIPRE-II above the froth region assuming that the droplets do not influence 

the vapor flow since the void fraction is very large (i.e., 0.999). 

A similar transient one-dimensional energy balance calculation scheme can written from the 

bundle inlet to the top of the quench front. The local fluid temperatures as well as the heater rod 

temperatures can be used to determine if the flow is saturated or subcooled at the quench front 

such that the quality or subcooling can be calculated from the inlet flow conditions and the 

energy input into the fluid from the rod decay power, housing, and structures, as well as the 

heat release at the quench front. If the fluid conditions are subcooled at the quench front, the 

steam generation can be calculated using the difference between the energy released and the 

energy needed to raise the fluid temperature to the saturation temperature. This approach is 

reasonable for low flooding rate cases in which the flow entering the quench front is at or near 

saturation. 

For higher flooding rate cases, additional assumptions and approximations are required since 

the subchannel fluid thermocouples will wet and read the saturation temperature. For high 

flooding rate cases (flooding rates of 6 in/s or larger), the subchannel thermocouples could read 

the liquid subcooling such that an estimate of the steam flow can be made. Also, for high 

flooding rate cases, the two-phase mixture temperature above the quench front is at or near the 

saturation temperature since steam superheats are small. Therefore, an equilibrium energy 

balance can be used to estimate the flow quality using the bundle exit flows and the rod energy 

which is calculated to go into the mixture. Highly ranked PIRT phenomena of steam generation 

at the quench front can be calculated from the data with reasonable uncertainty and compared 

to the computer code predictions. 

Values of TMIN and TCHF can be obtained directly from the heater rod thermocouple data. TCHF 

can be obtained from plots of the calculated wall heat flux against TWALL - TSAT for the different 

heater rods. TMIN can be obtained from the data by using a criteria that if the temperature 

change is greater than 27.8°C/s (50°F/s), the heater rod is wetting. The 27.8°C/s (50°F/s) is a 

historical value used in the FLECHT and FLECHT-SEASET programs to estimate TMIN. This 

value will have to be verified for the RBHT facility. However, data for both TCHF and TMIN can be 

obtained to address these PIRT phenomena. 

The heater rod surface temperature is also a highly ranked PIRT phenomenon as given in Table 

2.3. The heater rod thermocouple directly measures temperature close to the inside cladding 

temperature. The outside cladding temperature is calculated from the one-dimensional inverse 

conduction calculation at the thermocouple location. For most of the time when the rod is in film 

boiling, the measured inside temperature and the calculated outside temperature are nearly 

identical since the heat flux is very low. Immediately near the quench front, the data have to be 

corrected for two-dimensional effects due to the axial conduction. In either case, the RBHT 

facility will provide data on the surface temperature which is a highly ranked PIRT phenomena 

for the quench period. 

The decay power, which is ranked as high in the PIRT, will be directly simulated in the 

experiments over a range of powers. 
 134

Liquid entrainment at the quench front is also ranked high in the PIRT. Liquid entrainment 

begins at the quench front by the formation of liquid chunks, ligaments, and drops. The liquid 

chunks and ligaments are sheared by the high steam velocity into small particles which are then 

entrained as droplets at the top of the froth region. Large liquid chunks or pieces will fallback 

and will be sheared until they are small enough to be entrained. The bundle energy balance 

calculations described earlier will give the flow quality at the top of the froth region such that the 

bundle average liquid and vapor flowrates can be calculated from the test data. FLECHTSEASET reflood tests indicate that the froth region thickness is approximately constant over 

most of the rod bundle as it refloods. Therefore, the liquid mass stored in the froth region is a 

constant such that the liquid flow at the top of the froth region is approximately the same as the 

liquid flow at the quench front. This is particularly true for lower flooding rate conditions. Using 

the analysis of the test data, the liquid entrainment at the quench front can be determined in the 

RBHT tests. 

The void fraction and flow regime are also ranked high in the reflood PIRT for the quench 

region. The void fraction will be directly measured in the quench region using sensitive 

differential pressure cells with a three-inch span such that more detailed void measurements 

can be made as the quench front advances upward through the bundle. An X-ray attenuation 

technique will be used to obtain the transient chordal-average void fraction along the center 

plane of the bundle to obtain a time dependent void fraction. The local flow regime can also be 

photographed using high speed cameras or videotaped to infer the flow regime in the quench 

region, provided the test section windows have a minimum of wetting. Therefore, these highly 

ranked phenomena can be measured in the RBHT facility. 

Interfacial area is also ranked high for the quench region since it effects the interfacial drag and 

interfacial heat transfer. There is no direct measurement of the interfacial area in the 

experiments. The void fraction will be measured and the liquid and vapor flowrates will be 

calculated from the data such that the phase velocities can be determined from the data. High 

speed photography can be used to infer the flow regime and hence the interfacial area. 

Therefore, this highly ranked PIRT phenomena can not be measured in the RBHT tests, but can 

be inferred from photography. 

The local fluid temperature is also a highly ranked PIRT phenomenon in the quench region. 

The miniature fluid thermocouples which are located at different axial positions in the rod bundle 

will measure the liquid temperature. Liquid subcooling, if present, may be difficult to measure 

since most of the liquid will be at the saturation temperature for most cases. When the liquid 

flowrate is large combined with large liquid subcooling, the subcooled liquid temperature will be 

more accurately measured. Therefore, for the cases when subcooling is important, the RBHT 

facility can measure this highly ranked PIRT phenomenon. 

4.3.4 Two-Phase Froth Region for the Core Component (Table 4.9) 

The PIRT given in Table 2.4 from Section 2 indicates that several of the phenomena are highly 

ranked in this region. The froth region can be described as the region in which a transition is 

occurring between the continuous liquid or low void fraction mixture at and below the quench 

front; to a continuous vapor region with entrained liquid approximately one foot above the 

quench front. The void fraction changes very sharply from typical values of zero to 20 percent 

near the quench front to 0.99 or higher at the top of the froth region. The sudden change in the 

void fraction is the result of the large steam generation at the quench front as discussed earlier. 

It is this steam generation and the resulting film boiling heat transfer in the froth region which 
 135

provides the large steam velocity needed to shear and entrain the liquid upward in the rod 

bundle. The wall temperatures in the froth region is above the wetting temperature such that 

the heated surfaces are in film boiling. The film boiling heat transfer in this region has been 

shown to correlate well with the local void fraction. The phenomena which are highly ranked 

include: 

• Void fraction/flow regime, 

• Liquid entrainment, 

• Liquid ligaments, drops sizes, number density, interfacial area, 

• Film boiling heat transfer, and 

• Decay power. 

The components of film boiling heat trainer include the classical film boiling such as Bromley as 

well as drop contact heat transfer, vapor convection heat transfer as well as interfacial heat 

transfer and radiation heat transfer. 

Void fraction and flow regime are ranked high in the PIRT for this region. Void fraction will be 

measured using the finely spaced differential pressure which should be accurate since the void 

is lower in this region. The local void can also be measured at a fixed point as the froth region 

passes through the location where the X-ray attentuation system is located. If there is 

significant vapor superheat, it maybe detected by the miniature thermocouples; however, since 

the void fraction is lower in the froth region as compared to the dispersed flow region, it is 

expected that the thermocouples will wet and will indicate the saturation temperature. The flow 

regime in this region is difficult to quantify; however, high speed photography can be used to 

indicate the features of the flow regime. Also, examples of the froth flow region exist in the 

FLECHT and FLECHT-SEASET high speed movies. Therefore, the RBHT program can obtain 

the data needed for these PIRT phenomena. 

Liquid entrainment is one of the most highly ranked phenomena in the reflood PIRT since it 

directly determines the peak cladding temperature downstream of the froth region. The mass 

flowrate of the entrained liquid can be calculated, on an bundle average basis, using the energy 

and mass balances described earlier from the exit mass flow measurements, vapor 

temperatures, and the heat flux into the fluid. In the RBHT facility, additional effort has been 

made to design a closely coupled liquid collection tank such that the delay time from the 

beginning of entrainment to the detectible liquid measurement out of the bundle is minimized. 

Estimates of the liquid velocity can also be made using a mass and energy balance from the 

bundle inlet, accounting for the quench energy and the measured void fraction. 

The characteristics of the entrained liquid in the froth region is also a highly ranked PIRT 

phenomenon. Parameters such as liquid ligaments, drop size, interfacial area, droplet number 

density and droplet velocities, are all highly ranked phenomena which directly effect the 

resulting peak clad temperature. The drops sizes and velocities will be measured by the Laser 

Illuminated Digital Camera System (LIDCS) near the top of the froth region. As the froth region 

approaches the measurement point there may be too much liquid for the laser system to 

properly determine the sizes and velocities. However, if there is a significant amount of liquid 

present, the finely spaced differential pressure cells will provide an accurate measurement of 

the void fraction as the froth region passes within the span of the cell. The behavior of the froth 

region was also measured in the FLECHT-SEASET experiments. 
Table 4.9 Two-Phase Froth (Transition) Region for Core Component 

 136
Table 4.9 Two-Phase Froth (Transition) Region for Core Component (Continued) 

 137
 138

Film boiling heat transfer will be measured at many locations along the length of the electrical 

heater rods in the bundle. The heater rod thermocouples have been placed such that they are 

located at or very near the center of a differential pressure span such that the average void 

fraction determined from the differential pressure span can be used to correlate the resulting 

film boiling heat transfer. The data can be corrected for radiation heat transfer assuming that 

the radiation is to a liquid rich two-phase mixture within the froth region. 

Radiation heat transfer can be void fraction weighted and subtracted from the total measured 

heater rod heat transfer. Estimates can also be made of the convective heat transfer to the 

vapor using the single phase heat transfer correlation which was developed earlier in the 

program as well as the wall and vapor temperature. Use of such a correlation assumes that the 

presence of the liquid has a small effect on the local velocity and temperature profiles in the 

steam near the wall. As the void fraction decreases, this assumption becomes invalid and the 

correlation will be suspect. However, for very low void fractions in the froth region, the vapor will 

be concentrated at the wall in a traditional inverted flow film boiling situation. The local vapor 

temperature measurements may also be very uncertain since the miniature thermocouples can 

easily wet in the froth region and will indicate only the saturation temperature, not superheat 

temperature such that the true vapor temperature is underestimated resulting in an overestimate of the convective heat flux. Care will have to be used in the interpretation of these 

results. 

Another component of the heat transfer in the froth region is direct drop-wall contact heat 

transfer. This individual heat transfer component is zero when the surface temperature is above 

the minimum film boiling temperature, TMIN, and increases as the surface temperature 

decreases. Drop contact correlations are usually expressed as a exponential of the surface 

temperature which calculates a multiplier which is then applied to a nucleate boiling flux. The 

drop contact heat transfer cannot be measured directly in the Rod Bundle Heat Transfer facility 

because of the highly turbulent nature of the flow and the advancing quench front along the 

heater rods. The contribution of the drop contact heat transfer is accounted for in the film 

boiling and transition boiling heat transfer which is calculated from the measured heater rod 

surface temperatures and power using the inverse conduction technique, however, the precise 

portion of the total heat transfer attributed to drop contact cannot be separated from the total 

with confidence. If additional detail is needed on this phenomenon, a bench top experiment 

would be useful such that only the effect of the drop contact heat transfer is present. The 

resulting data could then be correlated into a model. 

Vapor convection heat transfer is also an important PIRT phenomenon for the froth region. In 

this situation, the vapor is generated as a very rapidly growing film along the walls of the heater 

rods and then mixes with the large chunks, drops, and ligaments of liquid which are being 

accelerated in the froth region. The bundle average vapor flow rate can be calculated from the 

bundle mass and energy balance and the bundle average vapor velocity can be calculated from 

the measured void fraction. Measurement of the vapor superheat is uncertain. 

The measurement scheme is to use miniature bare thermocouples which point into the flow. In 

the liquid rich froth region, there is a high probability that the thermocouples will be wetted by 

the liquid which is being entrained in the flow. Therefore, the miniature thermocouple probes 

will read the saturation or liquid temperature most of the time. For very low void fraction 

mixtures within the froth region, one could expect that the vapor superheat would be at or near 

the saturation temperature because of the large interfacial heat transfer and the lower mass flow 

of the vapor. As the void fraction increases within the froth region, one could expect that the 
 139

vapor temperature is between the heater rod surface temperature and the local saturation 

temperature such that some vapor superheat exists. 

The vapor superheat data for a given test will be plotted as a function of axial position to 

investigate how to extrapolate the data into the froth region. This has been done in the previous 

FLECHT-SEASET experiments with some success. Knowing the vapor temperature, and 

velocity (from the energy balance and the vapor temperature), the vapor Reynolds number and 

a single phase convective heat flux can be calculated. Since this situation is single phase 

convection in a two-phase mixture, correlation is developed from droplet injection experiments. 

This type of a calculation will give a reasonable estimate of the portion of the total wall heat flux 

which is due to convection. 

Heat transfer by radiation is also an important phenomenon in the froth region because of the 

large liquid content of the flow and the increasing heater rod surface temperatures. However, 

the percentage of the total heat flux due to radiation should be relatively small since the majority 

of the heat is transferred directly by film boiling to the low void fraction mixture. The radiation 

heat transfer to the liquid can be estimated for the test conditions using the void fraction and 

high speed movies which indicate the behavior of the liquid using the measured surface 

temperature and the saturation temperature. Similar calculations can be performed for radiation 

to the vapor using the estimated vapor temperature and the heater rod surface temperature. 

Again, it is expected that the total effect of radiation heat transfer is small for the froth region 

since the absolute value of the film boiling heat transfer is much larger in this region. The 

radiation modeling approach has been used in the FLECHT-SEASET program and would be 

modified for the RBHT facility. 

As liquid is entrained and accelerated in the froth region, both interfacial shear and heat transfer 

occur. Models for both of these important processes are crude, at best. The interfacial area 

and interfacial shear are not measured directly; however, estimates of the interfacial drag 

(shear) times the interfacial area can be made from the data. The local quality can be 

calculated from a detailed mass and energy balance on the bundle, particularly in the froth 

region. The principal uncertainly in this calculation is the vapor temperature. 

Void fraction is also measured such that the average liquid velocity in the rod bundle can be 

calculated. Also, by the same calculation, the average vapor velocity in the bundle can be 

determined at different axial locations, within and above the froth region. At this point, one 

would have to make assumptions which can significantly affect the calculated results. If a twophase frictional pressure drop model is assumed, and set equal to the portion of the measured 

pressure drop which is believed to be caused by friction, a measure of the product of the 

interfacial drag and area can be calculated. Another approach is to review the high speed 

movies in the froth region and postulate a liquid surface area and then calculate the resulting 

drag. 

In the case of interfacial heat transfer, the change in the local quality within the froth region will 

indicate the product of the interfacial heat transfer coefficient times the interfacial area. The 

uncertainly in this calculation is the accuracy of the measured vapor temperature. Heat transfer 

should be a two-step process with the wall energy being transferred to the vapor, and the 

resulting vapor energy causing evaporation of the entrained liquid. The axial dependence of the 

measured vapor temperature will have to be extrapolated into the froth region from the 

dispersed flow film boiling region, using the miniature thermocouples, to obtain an estimate. 
 140

To separate the heat transfer coefficient from the interfacial area, further assumptions must be 

made such as characterizing the liquid surface in the froth region from high speed movies, or 

applying an appropriate convective coefficient to the entrained liquid. Both methods are 

approximate and have large uncertainties but will be examined. The different models in a 

computer code can be compared to the data for void fraction in the froth region, and mass 

balance on the froth region to obtain the entrained liquid flow. The energy balance will give the 

bundle average liquid and vapor velocities. A computer code should match these measured 

and calculated quantities from the data with their particular interfacial models. 

4.3.5 Dispersed Flow Film Boiling Region (Table 4.10) 

In the dispersed flow film boiling region the total wall-to-fluid heat transfer is calculated by the 

codes as the sum of the following contributions: 

1) Forced convection to the vapor, 

2) Radiation heat transfer to both drops and steam, and 

3) Drop direct and dry wall contact heat transfer. 

The forced convection heat transfer is calculated with the Dittus-Boelter correlation by knowing 

the vapor Reynolds number. The vapor Reynolds number is a function of the vapor velocity, the 

void fraction and the vapor temperature. Some dispersed flow experiments have shown that the 

interfacial shear between dispersed particles and a continuous phase increases the turbulence 

level and enhances the convective heat transfer. 

In the COBRA-TF code, this two-phase enhancement factor is approximated by an extension of 

the analogy between wall shear stress and heat transfer. From the momentum-heat transfer 

analogy, the turbulent convection heat transfer coefficient is proportional to the square root of 

the shear stress. The total shear stress for the two-phase is the sum of the vapor-wall shear 

stress and the interfacial stress due to the droplets. The ratio between the interfacial shear 

stress due to the droplets and the vapor-wall shear stress is a function of the vapor velocity, 

interfacial area the droplet velocity and the entrainment phase void fraction. These quantities 

can be estimated from the test data such that this effect can be quantified. 

 

The temperature of the vapor is determined by the interfacial heat transfer and the convection 

from the wall. Information about the drop velocity and size distribution and the vapor 

temperature are also needed to estimate the interfacial heat transfer. Using steady-state 

droplet injection experiments, by measuring the shift in the drop size distribution as the droplets 

move along the channel, it may be possible to estimate the droplet evaporation rate and 

therefore the interfacial heat transfer. 

Radiation heat transfer from wall-to-wall, wall-to-vapor, and to drops need to be analytically 

estimated and separated from the total heat transfer during test data analysis. 

The third component is the most difficult to estimate from the test data. Fortunately this 

component is ranked low-medium in the PIRT. In COBRA-TF, direct wall heat transfer is a 

function of the deentrainment rate and the drop evaporation efficiency. The deentrainment rate 

is a function of the droplets concentration gradient (the concentration is zero at the wall) which 

is a function of the average entrainment fraction. The drop evaporation efficiency is a function 

of the wall superheating. The code needs information about the entrainment volume fraction, 

drop concentration gradient and wall temperature to estimate this component. 
 141

When the direct contact heat transfer becomes important (mostly in transition boiling), the 

intermittent wetting of the surface should produce localized oscillations in the temperature at the 

surface. These oscillations could be capture if the thermocouples response time is fast enough. 

The analysis of the oscillation can be an indirect way to estimate this component. 

The dispersed flow film boiling region is a region of very low heat transfer located above the 

froth front in which the mixture consists of highly superheated steam in which small liquid 

droplets are entrained. The peak cladding temperature is calculated in this region and the 

temperature remains elevated until the froth region approaches the peak temperature axial 

position within the rod bundle. The important PIRT phenomena for this region are given in 

Table 2.5 as: 

• Decay power, and 

• Dispersed flow film boiling, which consists of: 

 * Convective heat transfer to superheated vapor flow, 

 * Dispersed phase enhancement of convective flow and heat transfer, 

 * Radiation heat transfer to drops, vapor and surfaces, 

 * Interfacial heat transfer between drops and superheated vapor, 

 * Interfacial drag between drops and superheated vapor, and 

 * Dry wall drop-contact heat transfer. 

The decay power will be simulated and measured as a test condition and will be ranged over 

typical power values expected in a nuclear power plant. 

The measurement methods used in the RBHT have been developed specifically for the 

dispersed flow film boiling regime since it is the most limiting region of the reflood process. The 

LIDCS will be used to measure the drop size and velocity at different location along the bundle. 

The actual flow quality will be calculated from the bundle mass and energy balance such that 

the bundle average flow rates for the vapor and the liquid can be obtained. Since the vapor 

velocity can be calculated (accounting for the vapor superheat), and the droplet velocity and 

quality are known, the local void fraction can be calculated. The local void fraction can also be 

estimated from the droplets measurements taken with the LIDCS. However, the LIDCS 

measurements can over-estimate the void fraction since the measurement does not record 

droplets which are behind the heater rods since the measuring volume is the gap between the 

rods. 

A separate series of convective heat transfer experiments over a wide range of Reynolds 

numbers is planned as one of the first test series, before the actual reflood experiments. These 

tests will be analyzed on a subchannel basis using COBRA-IV, VIPRE-II, as well as hand 

calculations, to obtain the local subchannel flow for a given measured bundle inlet flowrate. The 

subchannel data will be correlated both on a bundle basis as well as a subchannel basis using 

the bundle or subchannel Reynolds number and the Nusselt number calculated from the 

measured wall heat flux obtained from the heater rod thermocouples. The subchannel vapor 

thermocouples will be used to determine the axial vapor superheat distribution. The correlation 

from these experiments will be compared to existing convective correlations. 

Another series of separate effects experiments will examine the effects of the dispersed 

entrained droplets on the convective heat transfer within the rod bundle. There are different 

postulated phenomena which could be occurring within the dispersed flow regime. One school 
Table 4.10 Dispersed Flow Region for Core Component 

 142
Table 4.10 Dispersed Flow Region for Core Component (Continued) 

 143
 144

of thought is that the droplets increase the total shear which increases the turbulence level in 

the flow such that the single phase convective heat transfer increases. Since the Reynolds 

numbers are very low in superheated steam (typically 1000 to 4000), any increase in turbulence 

could have a significant effect. 

Another thought is that the drop addition acts as a distributed heat sink within the continuous 

steam flow and directly affects the vapor temperature resulting in a larger temperature gradient 

to the wall. These and other heat transfer enhancement mechanisms will be investigated in 

these experiments. The local wall temperature will be measured on the heater rods to obtain 

the wall heat flux, the vapor temperature will be measured on a subchannel basis using the 

traversing miniature thermocouple probes, and the entrained droplet size, distribution, velocity 

and velocity distribution will be measured using the Laser Illuminated Digital Camera System. 

The droplet injection system will be previously characterized in a bench test, such that the initial 

drop size and distribution will be known. The analysis of the test data will provide a basis for the 

development of an improved model for these phenomena. 

Separate experiments are planned to examine the surface-to-surface radiation in an evacuated 

bundle. The purpose to verify the data analysis program which will be used to separate the 

radiation heat transfer components to the surfaces, drops, and vapor, from the measured total 

wall heat flux such that the convective portion of the dispersed flow film boiling can be 

determined. 

Ample heater rod, structure, grid, and housing thermocouples are placed at or very near the 

same elevations such that a radial temperature distribution across the bundle can be obtained. 

These tests will also indicate the influence of the housing and the radiation to the other surfaces 

within the bundle. The emissivity of the surfaces will have already been determined from 

previous tests to characterize the surfaces such that the surface condition uncertainty is 

removed from the analysis. 

Radiation heat transfer components from the wall to the surfaces, drops, and vapor will be 

calculated from the data using the measured temperatures of the heater rods, support tubes, 

and housing, as well as the measured vapor temperature and the droplet temperature, which is 

assumed to be saturation. The uncertainty in this calculation will be reduced because the 

method will have been verified using radiation-only tests as well as the surface emissivity 

properties which were independently measured for the heater rods and surfaces. The droplet 

data obtained from the LIDCS will be used to determine the droplet size and area to determine 

the radiation from the heater rods to the drops. 

Using a bundle energy balance, the local quality can be calculated along the test section. The 

change in the calculated quality due to the interfacial heat transfer can be obtained from the 

energy balance once the heat flux from the wall has been corrected for the radiation effects. The

convective portion of the wall heat flux is determined from the measured value minus the 

radiation component. Using the energy balance data and the LIDCS data, the size and velocity 

of the drops are known and the number of the drops can be estimated such that the interfacial 

area and a droplet heat transfer coefficient can be calculated and compared to correlations used 

in the literature and those used in the computer codes. A similar approach can be used for the 

interfacial drag using the droplet information from the LIDCS and the mass and energy balance 

for the bundle. The above calculations from the data will be estimates since there is a droplet 

spectrum, not single sized droplets. The spacer grids are also postulated to shatter the 

entrained drops resulting in the generation of “micro” droplets which can evaporate faster. 
 145

Therefore, a Sauter mean drop size will be calculated from the distribution measure and will be 

used in the energy calculations. This approach has been used in the FLECHT-SEASET tests 

with some success, although some of the uncertainties were very large. 

Dry wall contact can not be directly measured in the RBHT program as a separate heat transfer 

contribution to the total wall heat flux. The examination of the wall convective heat flux (once 

radiation effects have been subtracted from the measured total heat flux) as a function of void 

fraction will give some guidance on the relative importance of this component. There may be 

double accounting of the single phase convective enhancement of the convective flow and the 

dry wall contact phenomena such that they are really the same since the convective 

enhancement should include the effects of the dry wall phenomena. 

4.3.6 Top Down Quench in Core Components (Table 4.11) 

None of the phenomena identified in Table 2.6 for the top down quench were identified as a 

highly ranked PIRT phenomena. The most important phenomena for this period is the value of 

TMIN which will allow the quench front to propagate down the bundle. TMIN appears elsewhere as 

a highly ranked phenomena and is discussed there. 

 

4.3.7 Other Effects: Spacer Grids, Housing 

The spacer grids affect the total heat transfer during the reflood by: 

1) enhancement of convection heat transfer to the vapor, 

2) large drops are shattered by the grids, and 

3) grid rewetting and deentrainment. 

Specific models to account of these effects are in COBRA-TF. The information needed by the 

code to assess these models are: 

1) temperature of the grid, 

2) vapor temperature axial distribution (downstream of the grid), 

3) the rod temperature axial distribution (downstream of the grid), and 

4) drop velocity and size distribution. 

In COBRA-TF an additional small drop field is added explicitly in the code. The model solves 

the small drop acceleration and interfacial heat transfer downstream the grid once the vapor 

flow solution is known. Information about the small drop velocity and size distribution at 

different position downstream the grid can be used to validate these models. 

The presence of the housing which represents a distortion of the facility if compared with the 

real plant, must be simulated by the code. Therefore the radiation heat transfer from the rods to 

the housing, the heat transfer to the fluid and the quench of the housing (stored heat) need to 

be characterized during the experiments. 

The RBHT test facility instrumentation has been designed specifically to determine the heat 

transfer effects of the spacer grids. The heater rod thermocouples are spaced along the rods to 

determine the convective enhancement of the grids, droplet breakup effects and local 

subchannel vapor temperature. The grids are located within the viewing regions of the windows 

such that the effects of the grids can be observed and measured.
Table 4.11 Top Down Quench in Core Component 

 146
 147

4.4 Conclusions

The different large thermal-hydraulic computer codes have been briefly reviewed and compared 

against the reflood PIRT tables. While each code had the basic models for a boiling curve, and 

thermal and mechanical non-equilibrium, the COBRA-TF thermal-hydraulic formulation and 

additional detailed component models make this code an attractive choice for refined reflood 

development. COBRA-TF can be used on a subchannel basis to model the limiting hot fuel pin 

in a rod bundle. COBRA-TF is also a three-field formulation with an explicit entrained liquid field 

and a corresponding interfacial area transport equation which permits more accurate modeling 

of the entrained liquid phase, which is most important for calculating dispersed flow film boiling. 

Using the unique representation of the third field or entrained droplet field results in more 

accurate predictions of flow regimes, their transition, and the resulting heat transfer in the 

different regimes. There is also believed to be less chance of compensating errors, since one is 

not adjusting a two field model to represent the effects of three fields. Specific attention was 

given in COBRA-TF to the dispersed flow heat transfer model to account for the different 

component models which represent reflood heat transfer. Fine mesh renodalization for the 

heated conductors is used to better represent the quench front. Two-phase convective 

enhancement is accounted for in the calculations and a subchannel radiation model is used to 

more accurately represent radiation within a rod bundle. 

COBRA-TF also models the effects of spacer grids in dispersed two-phase flow in a mechanistic 

manner accounting for convective effects of spacer grids, spacer grid quenching behavior and 

the droplet breakup caused by spacer grids. In particular, a small-droplet field has been added 

to COBRA-TF to model the heat transfer effects of the much smaller drops as they evaporate 

and provide additional cooling downstream of the grids. 

As shown in the PIRT table comparisons, the formulation of the COBRA-TF code, as developed 

as part of the FLECHT-SEASET 163-Rod Blocked Bundle Program, has the desired basic 

formulation to develop the improved component models needed for dispersed flow film boiling in 

reflood. The Rod Bundle Heat Transfer program will utilize COBRA-TF for modeling purposes, 

and predictions and model validation purposes in the development of improved reflood models. 

4.5 References

1. The RELAP5 Code Development Team, “RELAP5/MOD3 Code Manual Volume V: Models 

and Correlation”, NUREG/CR-5535, June 1995. 

2. F. W. Dittus and L. M. K. Boelter, “Heat Transfer for Automobile Radiators of the Tubular 

Type,” University of California, Berkeley Publ. Eng, Vol. 2, No. 13, pp. 442-462, 1930. 

3. S. W. Churchill and H. H. S. Chu, “Correlation Equations for Laminar and Turbulent Free 

Convection From a Vertical Plate,” Int. J. Heat and Mass Transfer,18, pp. 1323-1329, 

1975. 

4. C. Chen, “A Correlation for Boiling Heat Transfer to Saturated Fluids in Convective Flow,” 

Process Design and Development, 5, pp. 322-327, 1966. 
 148

5. F. D. Moles and J. R. G. Shah, “Boiling Heat Transfer to Subcooled Liquids Under 

Conditions of Forced Convection,” Transaction, Institution Chemical Engineers, 45, p. 39, 

1949. 

6. Biasi, et al., “Studies on Burnout Part 3 -- A New Correlation for Round Ducts and Uniform 

Heating and Its Comparison with World Data,” Energia Nucleare, 14, pp. 535-536, 1967. 

7. Sjoberg and D. Caraher, “Assessment of RELAP5/MOD2 Against 25 Dryout Experiments 

Conducted at the Royal Institute of Technology,” NUREG/IA-0009, October 1986. 

8. D. C. Groneneveld, S. C. Cheng, and T. Doan, “1986 AECL-UO Critical Heat Flux Lookup 

Table,” Heat Transfer Engineering, 7, 1-2, pp. 46-62, 1986. 

9. C. Chen, R. K. Sundaram and F. T. Ozkaynak, “A Phenomenological Correlation for PostCHF Heat Transfer,” NUREG-0237, June 1977. 

10. Bromley, L. A., “Heat Transfer in Stable Film Boiling,” Chemical Engineering Progress, Vol. 

46, No. 5, pp. 221-226, 1950. 

11. H. Sun, J. M. Gonzales-Santalo and C. L. Tien, “Calculations of Combined Radiation and 

Convection Heat Transfer in Rod Bundles Under Emergency Cooling Conditions,” J. of 

Heat Transfer, pp. 414.2-420, 1976. 

12. Brumfield, R. N. Houze and T. G. Theofanous, “Turbulent Mass Transfer at Free, GasLiquid Interphases, with Applications to Film Flows,” Int. J. of Heat and Mass Transfer, 18, 

pp. 1077-1081, 1975. 

13. Lee and D. J. Ryley, “The Evaporation of Water Droplets in Superheated Steam,” J. of 

Heat Transfer, ASME, pp. 445-451, November 1968. 

14. S. Plesset and S. A. Zwick, “The Growth of Vapor Bubbles in Superheated Liquids,” 

Journal of Applied Physics, 25, 4, pp. 493-500, 1954. 

15. H. C. Unal, “Maximum Bubble Diameter, Maximum Bubble-Growth Time and Bubble 

Growth Rate During the Subcooled Nucleate Flow Boiling of Water up to 17.7 MN/m2

,” Int. 

J. Heat and Mass Transfer, 19, pp. 643-649, 1976. 

16. G. Brown, “Heat Transmission of Condensation of Steam on a Spray of Water Drops,” 

Proceedings of the General Discussion on Heat Transfer, published by the Institution of 

Mechanical Engineers, pp. 49-52, September 11-13, 1951. 

17. T. G. Theofanous, “Modeling of Basic Condensation Processes,” The Water Reactor 

Safety Research Workshop on Condensation, Silver Springs, MD, May 24-25, 1979. 

18. Ishii and K. Mishima, “Correlations for Liquid Entrainment in Annular Two-Phase Flow of 

Low Viscous Fluid,” ANL/RAS/LWR 81-2, 1981. 

19. Kataoka and M. Ishii, “Entrainment and Deposition Rates of Droplets in Annular TwoPhase Flow,” CONF-830301-11, ASME-JSME Thermal Engineering Joint Conference, 

Honolulu, HI, March 20, 1985. 
 149

20. Jay W. Spore, et. al., Los Alamos National Labratory. TRAC-PF1/MOD2, Vol. I, Theory 

Manual. 

21. C. Unal, K. Tuzla, C. A. Tuzla, and J. C. Chen, “Vapor Generation Model for Dispersed 

Drop Flow,” in ANS Proc. 1989 National Heat Transfer Conf. (August 1989), HTC-Vol. 4, 

1989. 

22. Kataoka and M. Ishii, “Mechanism and Correlation of Droplet Entrainment and Deposition 

in Annular Two-Phase Flow,” Argonne National Laboratory Report ANL-82-44 

(NUREG/CR-2885), 1982. 

23. Borkowski, N. L. Wade, et.al., Idaho National Engineering Laboratory. TRAC-BF1/MOD1 

Models and Correlations, July 1992. 

24. C. Y. Paik, L. E. Hochreiter, J. M. Kelly, and R.J. Kohrt, “Analysis of FLECHT-SEASET163-

Rod Blocked Bundle Data Using COBRA-TF,” NUREG/CR-4166, WCAP- 10375, EPRINP-4111, October 1985. 

25. Thurgood, et al, “COBRA/TRAC: A Thermal-Hydraulic Code for Transient Analysis of 

Nuclear Reactor Vessels and Primary Coolant Systems,” NUREG/CR-3046, Volumes 1-5, 

March 1982. 

26. S. Wong and L.E. Hochreiter, “Analysis of the FLECHT-SEASET Unblocked Bundle Steam 

Cooling and Boil-off Tests,” NRC/EPRI Westinghouse Report 8, January 1981. 

27. E. M. Sparrow, et al, “Heat Transfer to Longitudinal Laminar Flow Between Cylinders,” J. 

Heat Transfer, Vol 83, p. 415, 1961. 

28. W. T. Hancox and W. B. Nicoll, “A General Technique for the Prediction of Void 

Distributions in Nonsteady Two-Phased Forced Convection,” Int. J. Heat and Mass 

Transfer, Vol 14, 1971. 

29. S. Z. Rouhani and F. Axelsson, “Calculation of Void Volume Fraction in Subcooled and 

Quality Boiling Regions,” Int. J. Heat and Mass Transfer, Vol. 13, 1970. 

30. Zuber, et al, “The Hydrodynamic Crisis in Pool Boiling of Saturated and Subcooled 

Liquids,” Part II, No. 27 in International Heat Transfer Conference, Boulder, CO, 1961. 

31. R. E. Henry, “A Correlation for Minimum Film Boiling Temperature,” AlChE Symposium 

Series 70, (138), pp. 81-90, 1974. 

32. E. N. Ganic and W. M. Rohsenow, “Dispersed Flow Heat Transfer,” Int. J. Heat and Mass 

Transfer, Vol 20, pp. 855-866, 1977. 

33. D. McCoy and T. J. Hanratty, “Rate of Deposition of Droplets in Annular Two-Phase Flow,” 

Int. J. Multi Phase Flow, Vol 3, pp. 319-331, 1977. 

34. Drucker and V. K. Dhir, “Studies of Single and Two-Phase Heat Transfer in a Blocked 

Four-Rod Bundle,” EPRI-NP-3481, June 1984. 
 150

35. W. Kays, Convective Heat and Mass Transfer, McGraw-Hill, New York, 1966. 

36. Kelly, “Quench Front Modeling and Reflood Heat Transfer in COBRA-TF,” Paper 79-

WA/HT-63, ASME Winter Annual Meeting, New York, 1979. 

37. S. C. Yao, L. E. Hochreiter, and W. Leech, “Heat-Transfer Augmentation in Rod Bundles 

Near Grid Spacers,” J. Heat Transfer, Vol 104, 1982. 
151

5. ROD BUNDLE HEAT TRANSFER PROGRAM OBJECTIVES AND 

FACILITY MISSION 

5.1 Introduction

Sections 2 and 3 identified the phenomena of interest and the existing database for reflood 

model development and validation over the range of conditions of interest. Section 2 also 

identified the individual component models and phenomena which a computer code uses to 

perform calculations for the complete heat transfer. Section 3 identified those existing data 

useful for addressing particular types of phenomena of importance to reflood heat transfer. 

Section 3 also provided information on the range of parameters to be selected for the various 

types of experiments to be performed in the RBHT program. Section 4 reviewed the different 

reflood heat transfer models in current computer codes and identified the current state-of-the-art 

needs for a best-estimate safety analysis computer code. The need for the improved analysis 

models becomes the objectives of the RBHT program. The needs define the specific mission of 

the test program as well as the analysis efforts which will compliment the experiments. The 

combination of specifically directed experiments and the corresponding data analysis, 

development of physically based heat transfer and two-phase flow models as well as 

implementation of these models into a best-estimate computer code will achieve the program 

objectives. 

5.2 Rod Bundle Heat Transfer Program Objectives

The objective of the RBHT program is to provide needed, unique, separate-effects rod bundle 

data on specific component models which comprise the “reflood” heat transfer phenomena 

observed in PWR and BWR rod bundle situations for a large-break loss of coolant accident. The 

emphasis of the program is to provide specific experimental data and associated analysis which 

will enhance the understanding of the dispersed flow film boiling region which is the limiting heat 

transfer situation for the LOCA transient. The reflood heat transfer processes are very complex. 

The full range of the phenomena identified in a boiling curve occurs in the reflood heat transfer 

calculation as well as the multi-dimensional conduction heat transfer in the fuel rod at the 

quench location. The rod heat transfer is coupled to the two-phase flow behavior of the coolant 

such that as the stored energy from the rods is released into the fluid, the local flow regime can 

change and continuous liquid flow, at the quench front, can be dispersed first into slugs and 

ligaments then sheared into dispersed droplets. The coupling of the rod heat release drives the 

liquid entrainment which then provides additional cooling above the quench front. 

There are several different thermal-hydraulic phenomena which interact to provide the “reflood 

heat transfer” which best-estimate safety analysis computer codes must predict. In the 

dispersed flow film boiling regime, no single phenomenon dominates. The total heat transfer is 

comprised of several different mechanisms as identified in Section 1 of this report. The relative 

importance of a particular mechanism will vary as the rod surface temperature increases or 

decreases, as the pressure varies, and as the flooding rate into the bundle changes. In 

dispersed flow film boiling, the primary heat transfer mechanism is convective heat transfer to 

superheated steam. It is known that the steam heat transfer coefficient can be enhanced by up 

to 100 percent due to the presence of entrained droplets. No suitable models currently exist for 

this phenomenon. 
152

The combination of single-phase vapor heat transfer tests with the forced droplet injection tests 

(where drop size and flow rate are known) will result in the development of the needed model. 

What is needed is a series of experiments which help isolate a particular heat transfer 

mechanism such that its individual effects can be identified, modeled and used to predict the 

total heat transfer in the bundle. 

Therefore, the objectives of the RBHT program are to: 

1. Develop a Phenomena Identification Ranking Table (PIRT) for reflood heat transfer on a 

component model level and estimate the relative importance of each phenomenon for 

predicting reflood heat transfer, 

2. Develop a test facility design which has a minimum of distortion to represent reflood heat 

transfer in PWR and BWR cores, 

3. Assess the needs of best-estimate computer codes on their modeling approaches for 

reflood heat transfer and the component models used in the computer codes, 

4. Perform component experiments which isolate individual phenomena which compromise 

reflood heat transfer, 

5. Determine the effects of the fuel assembly spacer grids on the dispersed flow film boiling 

heat transfer downstream of the grid, 

6. Develop specific component models from these experiments, 

7. Add the component models into a best-estimate computer code and compare to the forced 

reflood heat transfer data from this series of expedients as well as other sets of reflood heat 

transfer data, 

8. Validate the new proposed component reflood heat transfer models over their range of 

application, and 

9. Document the results of the experiments and analysis in a form that it can be used by 

others. 

The majority of the experiments will be separate effects tests which will isolate individual 

models. The separate effects tests which are proposed include: 

1. Single phase flow pressure drop experiments to characterize the hydraulic behavior of the 

facility, 

2. Heat loss experiments which characterize the heat losses to the atmosphere which are 

needed for modeling the facility and analyzing the test data, 

3. Radiation heat transfer experiments in a evacuated bundle to assess the rod-to-surface, and 

rod-to rod radiation heat transfer which is needed to subtract out the radiation contribution 

from the total measured heat transfer, 
153

4. Single phase steam flow convective heat transfer experiments which cover the Reynolds 

number range expected in a rod bundle during reflooding, 

5. Single phase steam flow experiments with injected droplets over a range of conditions to 

simulate the dispersed two-phase flow region above the quench front, 

6. Forced reflooding experiments over a wide range of conditions typical of a PWR and BWR 

rod bundle during reflooding, 

7. Forced oscillating flow experiments which characterize the inlet flow into a reactor system 

during reflooding. 

The proposed experiments will be performed in a building block approach such that the more 

complex experiments occur after the more fundamental experiments. In this fashion, additional 

information and desired test conditions can be modified as needed to optimize the test matrix of 

the forced reflooding tests which are the most difficult tests to perform. The proposed 

experiments will provide new unique data as well as supplement existing reflood heat transfer 

data but they will focus on the improvements of specific best-estimate thermal-hydraulic models 

rather than identifying licensing margin. 

To achieve the objectives of the experiments and to capture the important thermal-hydraulic 

phenomena which have been identified for reflood heat transfer, several new or novel 

approaches are proposed for the bundle instrumentation. The characteristics of the froth region 

are relatively unknown. In this region, the flow changes from a liquid continuous flow to a vapor 

continuous flow as the rods quench and generate a significant amount of steam. The liquid flow 

is sheared by the steam and generates a droplet distribution which is entrained into the upper 

regions of the bundle where the peak cladding temperature occurs. The void fraction in the froth 

region varies from nearly zero to almost one in the span of approximately one-foot. There are 

three different measurement systems which will be used in the RBHT program: 

1. A soft gamma detector with beryllium windows on the test section will measure the chordal 

average void fraction within the rod bundle as the dispersed flow; froth front and quench 

pass at selected elevations. 

2. Finely spaced, very sensitive differential pressure cells will measure the local pressure along 

the test section and will be corrected for frictional and acceleration effects to calculate a 

span average void fraction. It has been demonstrated that many of the apparent functional 

dependencies (i.e., mass flux, subcooling, and distance from the quench front) for this heat 

transfer regime are primarily due to the axial profile of the void fraction in this region. 

Currently available data for this regime in rod bundles is insufficient for model development 

due to the coarse spacing (from 1 - 2 feet) used for the delta-P cells used to measure the 

void fraction. The RBHT program will redress this data deficiency through the use of finely 

spaced delta-P cells (three inch span) and by a local void fraction measurement provided by 

a low energy gamma-densitometer. 

3. A Laser Illuminated Digital Camera System (LIDCS) will be used to measure the drop size, 

distribution, and velocities at the dispersed flow/froth flow boundary such that the droplet 

entrainment distribution can be obtained. To correctly calculate the interfacial heat transfer 

requires the knowledge of both the entrained droplet flow rate and droplet diameter. There 

is very little data of this type available for quenching rod bundles. The RBHT program will 
154

generate the needed database through the use of advanced instrumentation, specifically 

through the use of the LIDCS. 

At several axial locations in the rod bundle, there will also be steam probes to measure the 

vapor temperature in the dispersed two-phase mixture or the local fluid temperature for singlephase tests. The laser illuminated digital camera will also be used in this region to obtain the 

drop distribution, size, and velocity. There will also be ample heater rod temperature 

measurements along the bundle as well as exit and inlet flow measurements such that the 

bundle energy and mass balance can be performed and the total heat flux can be separated 

into radiation heat transfer and flow film boiling heat transfer. 

Spacer grids which support the rods in the rod bundle will be instrumented as well as the rod 

temperatures downstream of the grids and the coolant subchannels downstream of the spacer 

grids. There will be laser illuminated digital camera system data taken above and below the 

spacer grids to observe and quantify the change in the droplet diameter and velocity 

distributions due to the droplet breakup caused by the spacer grids. The heater rod 

thermocouples and the vapor temperature measurements will also measure the local heat 

transfer enhancement caused by the spacer grids. 

Specific bench-top experiments have been designed to aid in the instrumentation development 

for the RBHT program. These bench top experiments test the LIDCS for droplet measurements 

in an unheated 3x7 bundle and in a 3x3 heated one-third length bundle. The 3x7 experiments 

verify the performance of the droplet injector component which will be used in the RBHT 

program. These tests also confirm the ability of the laser illuminated digital camera system to 

measure the droplet distribution accurately. The 3x3 heated bundle experiments will specifically 

examine the effects of spacer grids on the entrained droplet distribution within subchannels. 

This heated bundle will also provide comparison data on the thermal-hydraulic effects of 

different spacer grid designs. The 3x3 bench test will also be used to determine the flow 

disturbance effects of miniature thermocouples which will be used to traverse the rod bundle. A 

reliable measurement of the non-equilibrium vapor temperature is desired, but since the method 

used is intrusive, the measurement method must be assessed to ensure that the rod bundle 

flow is not changed by the measurement technique. 

5.3 Conclusions

The objectives of the RBHT program have been established to provide the needed data on the 

highly ranked PIRT phenomenon for reflood heat transfer. Experiments will be performed to 

isolate a specific phenomenon as best as possible so as to permit specific model development 

for that phenomenon. The test facility instrumentation has been designed to obtain, as best as 

possible, the local fluid conditions within the bundle using new and unique techniques. In this 

manner, the local heat transfer can be related to the local fluid conditions such that the risk of 

introducing compensating errors into the advanced reflood model package is minimized.
155

6. First Tier Scaling for the Rod Bundle Heat Transfer Test Facility 

6.1 Introduction

In order to simulate actual systems (prototype), many experiments are performed at a reduced 

size, with different materials and different working fluids. The object of the experiment is to 

capture the phenomena which have been determined to be important for understanding the full 

size system. Scaling analyses are normally performed for the smaller size models to verify the 

performance of the full size system. 

Scaled experiments have been used for many years in the areas of fluid mechanics for airfoil 

design, hydraulics for ship design as well as water tables for harbor designs and heated effluent 

discharges. Scaling fluids have been used in heat transfer studies to simulate high pressure 

fluids and other dangerous working fluids to examine critical heat flux behavior and core melt 

conditions. More recently, scaling has been used to simulate the thermal-hydraulic conditions 

expected in a nuclear reactor for postulated accident conditions. There have been several 

different thermal-hydraulic scaling approaches proposed by Larson (Ref. 1) and Ishii (Ref. 2) for 

single and two-phase systems. 

A generalized scaling approach has been developed by Zuber (Ref. 3) for thermal-hydraulic 

systems in which a two tier scaling approach is given. An important aspect of Zuber’s approach 

is that the scaling process can be used to help identify the most important phenomena as well 

as the less important phenomena such that when compromises are made, the important 

phenomena are correctly simulated. This approach has been refined by Wulff (Ref. 4) who 

recommended that the full equation be divided by a “driver term” such that the relative 

importance of the different terms could be assessed. Zuber (Ref. 5) also extended the 

methodology by using the maximum ranges to normalize variables such that correct limits would 

be represented. The result has been to translate the scaling analysis into a workable 

methodology which can be used on any general thermal-hydraulic system. 

The Zuber approach was used for the scaling efforts for the Oregon State University AP-600 

small break Loss of Coolant Accident (LOCA) and long term cooling experiments (Ref. 6). The 

combination of the Zuber and Wulff scaling methodologies were used for the other AP-600 

experiments to assess possible test distortions relative to the full size reactor (Ref. 7). The 

combined Zuber-Wulff scaling approach is the current state-of-the-art methodology for scaling 

thermal-hydraulic systems. 

The Zuber-Wulff scaling methodology has been used to assess the ability of the RBHT Test 

Facility to capture the phenomena of interest for the reflood phase of a LOCA transient such 

that the data can be used, with confidence, to verify and develop heat transfer and two-phase 

flow models for best-estimate thermal-hydraulic computer codes. In addition to verifying that the 

test facility can produce the desired data, the two tier scaling process also identifies possible 

distortions in the test facility relative to the nuclear reactor core and provides a numerical 

assessment of the importance of the possible distortion.
156

6.2 Two Tier Scaling Approach

The two tier scaling approach, as developed by Zuber, consists of “top-down” scaling approach 

which gives a scaling group for each transfer process as derived from the dimensionless control 

volume equations for the conservation of mass, momentum, and energy as written for the 

thermal-hydraulic system. The scaling groups which result from the normalization of the control 

volume equations are time ratios for the different processes which occur in the system. These 

groups are called “Pi” parameters. Therefore, top-down scaling or systems approach provides a 

method for identifying the important phenomena, derive similarity groups, weighting of the 

different groups to establish priorities, and providing a basis for decoupling fast and slow acting 

processes which have different time scales. The top-down scaling approach, which is used for 

both the experiment and the prototype, or full scale system, can identify the lack of similarity 

between the test and the prototype which indicates scaling distortions. Top-down scaling also 

identifies those thermal-hydraulic processes which require additional detailed analysis using a 

“bottom-up” scaling approach. 

The bottom-up scaling approach (or process approach) addresses only those thermal-hydraulic 

processes which are identified as being important or can have distortions which could impact 

the experiment. Bottom-up scaling will focus on specific Pi terms in the system equations which 

govern the particular phenomena of interest. The bottom-up scaling can be used to 

characterize the transport terms in the control volume equations (transport of mass, momentum 

or energy), to establish the relationships for calculating these terms and to compare the scaled 

experiment to the full size prototype. 

This section of the report will discuss the application of the first tier or top-down scaling for the 

RBHT Test Facility; the bottom-up scaling will be discussed in Section 7. 

6.3 Application of the Top-down Scaling Approach

There are three equations which are examined for the RBHT Test Facility: the fluid energy 

equation; the solid energy (heater rod, fuel rod) equation; and, the fluid momentum equation. 

Each conservation equation is derived in the fashion as recommended by Zuber and Wulff. The 

equations are normalized and the terms are divided by the “driver term” such that the resulting 

Pi groups are dimensionless. This approach is applied to both the RBHT Test Facility as well as 

to a PWR and a BWR fuel assembly to indicate the possible non-typical effects and distortions 

in the test facility relative to the actual plant component. 

Since the tests proposed for the RBHT Test Facility are separate effects tests, the flow at the 

inlet is forced, or is a prescribed boundary condition. In these situations, the fluid momentum 

equation has less importance as compared to the fluid energy and solid energy equations. 

However, since one of the primary goals of the analysis is to identify test distortions, the 

momentum equation will be used to examine the hydraulic behavior of the test facility relative to 

PWR and BWR fuel assemblies. 

6.3.1 Fluid Energy Equation 

A simplified fluid energy equation is written for the test bundle with the following assumptions: 

• Constant forced flooding rate into the bundle, 
• Zero-dimensional analysis. No radial gradients in the fluid. Single and two-phase 

regions are treated separately, 

• No radial temperature gradient in the structures that interact with the fluid; averaged 

solid temperatures are used, 

• The analysis represents a snapshot in time with a single phase region, a two phase 

region and a quench front on the rods, housing, grids, and dummy (unheated) rods, 

• Once a structure is quenched, there is no longer any energy transfer to or from the fluid, 

flow is assumed to be single phase liquid below the quench front. 

The “fluid” in the fluid energy equation is assumed to be single phase liquid below the quench 

front and superheated vapor in the two-phase mixture, above the quench front. The real flow 

above the quench front is a two-phase dispersed flow mixture. However, the vapor represents 

the continuous phase and is the heat sink for the heat transfer above the quench front. The 

interfacial heat transfer is also modeled such that the correct vapor temperature would be 

calculated. Modeling the superheated vapor above the quench front allows the interfacial heat 

transfer to be directly modeled. 

The single phase liquid (below the quench front) and the superheated vapor (above the quench 

front) thermally connects the electrical heater rods (or fuel rods), the test section housing (no 

housing for a PWR, fuel can for a BWR), the spacer grids used to support the rod bundle and 

the dummy rods in the test bundle (control rod guide tube thimbles in a PWR and water rods in 

a BWR). With these assumptions, the fluid energy equation becomes: 

 (1) (2) (3) (4) (5) (6) (7) 

( ) ( ) p DRqgqHqrqvv QQQQQe DP dt

d VTc

dt

d V +Δ ,,,, ++++=

1

2 1

1

1 ρ φ ρ φ φ

 (6-1) 

,Hloss , , −−−− + − oiiiDRlossgloss hWhWQQQQ 0

 (8) (9) (10) (11) (12) (13) 

where 

term 1 rate of energy change in the single phase region 

term 2 rate of energy change of the vapor in the two-phase region 

term 3 energy release to the fluid from the rod quenching 

term 4 energy release to the fluid from the housing quenching 

term 5 energy release to the fluid from the grids quenching 

term 6 energy release to the fluid from the dummy rods (thimbles) quenching 

term 7 energy release to the fluid from the rods above and below the quench front 

term 8 energy loss to the housing 

term 9 energy loss from the fluid to the spacer grids 

term 10 energy loss from the fluid to the dummy rods or control rod thimbles 

term 11 interfacial heat transfer between vapor and droplets 

term 12 energy flow into the bundle at the inlet 

term 13 energy flow out of the bundle at the exit 

A listing of the nomenclature used for the equation development is given at the end of this 

section. 

157
The quench front represents the dividing line between efficient cooling (nucleate boiling or 

forced convection) and poor cooling (film boiling, either in a froth region or dispersed flow film 

boiling). An alternate expression for term 6 for the energy transport into the fluid on either side 

of the quench front can be used. Below the quench front, the flow will be assumed to be single 

phase such that the energy into the fluid is equal to the decay power which is specified for the 

test. Above the quench front, the energy into the fluid is transported by film boiling heat transfer 

as well as by radiation heat transfer from the heated surfaces to the fluid. Therefore, a more 

general expression for the energy transfer above the quench front is given as 

( ) ( ) = φφ ,22 +− /, −TTAhTTAhQ vrrvrRvrrc (6-2) 

Where h2φ,c is the convective/film boiling heat transfer coefficient, and hR,r/v is the radiation heat 

transfer coefficient from the heated rod surfaces to the fluid. The reference temperatures for 

both transfer processes are the rod wall temperatures (Tr) as well as the local fluid vapor (nonequilibrium) temperature (TV). Therefore, term 7 becomes: 

 Q Q h AT T h AT T h AT T DP DP [ ] c r r v ( ) R r rr v ( ) R d r sat ( ) v r

d = + −+ −+ − 1 2 2 φ φ φ , , , (6-3) 

The heat transfer in the two-phase region can also be written as energy flows (Btu/hr) instead of 

a heat transfer coefficient, area and temperature difference as 

 QQ Q Q DP DP C FB R =+ + (6-4) 1φ /

where Q represents the convective/film boiling portion of the heat transfer while Q R

represents the radiation portion of the total heat transfer from the rods to the fluid above the 

quench front. 

/ FBC

The quench energy release from the heater rods (or the fuel rods), term 3 (Q ), can be 

calculated as 

, rq

 Q cV

dT

dt qr r pr r

r q

, ,

, = ρ

2

 (6-5) 

where T is the property weighted average temperature for the heater rod (or the fuel rod ) with 

ρr, cp,r and Vr being the rod weighted density, specific heat and volume, respectively. The 

temperature-time curve can be estimated from data for heater rod (Ref. 8) and/or nuclear rod 

quenching (Ref. 9), as well as from more accurate calculations for a heater and nuclear rods 

using finite difference methods. Rod quench is assumed to occur when the rod temperature 

reaches the minimum film boiling temperature. The effects of property differences between the 

electrical heater rod and the nuclear rod cladding will be considered when determining the 

minimum film boiling temperatures used to calculate the rod energy release for electrical heater 

rods and Zirconium clad fuel rods. 

r

The test section housing heat release is given in term 4 as 

158
Q cV

dT

dt qH H pH H

H q

, ,

, = ρ

3

 (6-6)

and represents the heat transferred to the coolant when the housing, which is an elevated 

temperature, quenches. TH represents the average housing temperature and ρH, cp,H and Vr 

represent the density, specific heat and volume of the housing which is quenching. The test 

section housing represents an atypicality or distortion of the test rod bundle relative to a PWR 

fuel assembly since there is no housing for the PWR assembly. However, when comparing the 

test facility to a BWR fuel assembly, the similarity is improved since these assemblies have a 

channel similar to a housing. The BWR channel is Zircaloy and not Inconel as used in the 

experiment; therefore, there can be differences in the minimum film boiling temperature and the 

resulting quench energy released to the coolant. 

Term 5 represents the energy release to the coolant from the quenching of the spacer grids, 

which are used to position the heater rods or fuel rods, and is given as 

 Q cV

dT

dt qg g pg g

g q

, ,

, = ρ

4

 (6-7) 

The spacers are constructed from thin metal shim stock, typically 0.010 in thick and 1-2 in high. 

It is assumed that the grid will quench at once such that its entire stored energy is released to 

the coolant. There can be material differences between the test grids, which will be made of 

Inconel or stainless steel and the current generation PWR spacers which use Zircaloy. The 

difference in materials can lead to different minimum film boiling temperatures which in turn 

affect the energy release. For the experiment, the spacers, cladding surface, housing, and the 

dead rods are all made of Inconel, therefore, they all have the same value of Tmin. For a PWR 

or BWR fuel assembly, the cladding and the spacer grids are made of Zircaloy and a Tmin value 

for this material is used. 

Term 6 represents the quenching of the unheated support or dummy rods in the bundle. There 

are four such rods used to represent the presence of guide tube thimbles in the test rod bundle 

and to allow bundle instrumentation to be brought out with minimum flow interference. The 

dummy rod quench energy is given as 

Q cV

dT

dt q DR DR p DR DR

DR q

, ,

, = ρ

5

 (6-8) 

Term 7 represents the energy added to the fluid below and above the quench front, as given 

earlier in Equation 6-3. 

Term 8 represents the heat loss from the fluid to the environment through the housing. This 

term will be most important above the quench front where the fluid, rod and housing 

temperatures are higher. The heat loss from the fluid to the housing is given as 

Q h A T T h A T T h AT T loss H H H v H ( ) ( ) ( ) R v

H

Hv H R H

d , , d H sat , , = −+ −− − 2φ (6-9) 

159
where the first term is the convective/film boiling term, the second term represents the radiation 

from the superheated vapor to the housing structure, and the third term represents the radiation 

heat transfer from the hot housing to the entrained liquid drops. Both the convective and the 

radiation terms will operate on the same housing heat transfer area. The expressions for the 

heat transfer to the housing from the fluid can also be expressed in terms of heat flows (Btu/hr) 

as 

160

, QQQ (6-10) loss H c H R H , ,, = + 2φ

where QR, H is the sum of the two radiation components. 

In a similar fashion, term 9 models the fluid energy losses to the spacer grids and is given as 

Q h AT T h AT T h AT T loss g g g v g ( ) R gv g ( ) ( ) R d g sat v

g g

d , , , , = −+ −− − 2φ (6-11) 

where the fluid will transfer heat by convection/film boiling and radiation heat transfer. This 

equation can also be written as heat flows as 

QQQ loss g c g R g , ,, = + 2φ , (6-12) 

where QR, g is the sum of the two radiation heat transfer terms. 

It should be noted that Equation 6-11 is only relevant above the quench front where the vapor is 

significantly superheated relative to the spacer grids. The differences between the reactor and 

the test facility will be the geometry and materials used for the spacers. Once the spacers are 

quenched, there is no longer any significant heat transfer to or from the spacers and the fluid. 

In a similar manner, term 10 models the fluid energy loss to the dummy rods or the control rod 

guide tubes for the reactor case and is given as 

Q h A T T h A T T h AT T loss DR DR DR v DR ( ) ( ) ( ) R v

DR

DR v DR R v

DR , , d DR sat , , = − 2φ + − − − (6-13) 

The heat transfer from the fluid to these structures is by convection/film boiling and radiation. 

This only occurs above the quench front where the vapor is superheated and saturated 

entrained droplets exist. Once the dead rods or thimbles are quenched, there is no longer any 

energy transfer between these structures and the fluid. 

Since the fluid energy equation is written for superheated vapor, and there are entrained 

droplets present, the two-phase flow above the quench front is not in thermal equilibrium. 

There is heat transfer between the superheated vapor and the entrained droplets, which are at 

the saturation temperature. The heat transfer occurs by two paths. The first is convection heat 

transfer in which the droplet Reynolds and Nusselt numbers depend upon the drop size and the 

relative velocities of the drops and vapor. The second is radiation heat transfer from vapor to 

droplets as they are swept along in the test section. Both terms contribute to the total interfacial 

heat transfer between the continuous vapor phase and the discontinuous entrained droplet 
phase. The interfacial heat transfer will result in generation of additional saturated steam which 

mixes with the superheated steam and results in increased steam flow at a lower temperature. 

The droplet evaporation improves the steam as a heat sink for the heater or fuel rods. 

The expression for the interfacial heat transfer becomes 

Q hA T T h A T T I Id ( ) v sat ( ) R v

d

= −+ d v sat − , (6-14) 

Substituting Equations 6-3 to 6-14 into Equation 6-1 gives the fluid energy equation which 

considers all sources of heat gain and heat loss for the fluid in the test section. 

Q hA T T h A T T I Id ( ) v sat ( ) R v

d

= −+ d v sat − ,

+ + ρ ρ g pg g

g

DR p DR DR

DR c V

dT

dt

c V

dT

dt , ,

4 5

+

( ) ( ) ( )

( ) ( ) ( )

Q h AT T h AT T h AT T

h A T T h A T T h AT T

DP r r r v R r

v rr v R rd

d r sat

HH v H R v

H

Hv H R H

d

d H sat

1 2

2

φ φ

φ

+ −+ −− − ⎡

⎣

⎢ ⎤

⎦

⎥

⎧

⎨

⎩

⎫

⎬

⎭

− −+ −− − ⎡

⎣

⎢ ⎤

⎦

⎥

, , ,

, , ,

 (6-15)

( ) ( ) ( )

( ) ( ) ( )

( ) ( )

− −+ −− −

⎡

⎣

⎢ ⎤

⎦

⎥

− −+ −− ⎡

⎣

⎢ ⎤

⎦

⎥

+ −+ −+−

h AT T h AT T h AT T

h A T T h A T T h AT T

h A T T h A T T Wh W h

gg v g R v

g

gv g R g

d

d g sat

DR DR v DR R v

DR

DR v DR R DR

d

d DR sat

I d v sat R v

d

d v sat i i o o

2

2

φ

φ

, , ,

, , ,

,

−

The same generalized equation can be used to represent the fluid energy in a PWR or BWR 

fuel assembly. The differences will be due to the geometry, materials and possible temperature 

limits. The boundary conditions of flow, pressure and power are the same and can be modeled 

in the experiments. There are also different components in the fluid energy equation as noted 

above. There is no housing for a PWR assembly; therefore, these terms represent a distortion 

of the fluid energy equation relative to a PWR assembly. There is more similarity between a 

BWR fuel assembly and the test facility since both have a channel surrounding the heater rods. 

The next step in the Zuber-Wulff scaling process is to nondimensionalize the equation to 

determine the different Pi groups which represent the different transfer processes in either the 

test facility or in a PWR or BWR fuel assembly. A listing of the parameters used to normalize 

each term in Equation 6-15 is given in Table 6.1. The initial conditions and boundary conditions 

are used for the normalization. Ranges are selected such that they address the variability of the 

different parameters. The initial conditions and their definitions are given in Table 6-2. 

161
Table 6.1 Normalizing Factors for Fluid Energy Equation 

A

A

A

A

A

A

A

A

A

A

A

A

c

c

c

W W

W

W

W

W

W

W

W

DR

DR

DR i

g

g

g i

H

H

H i

r

r

r i

p

p

p i

i

o

i

i

i

i

DP

DP

DP i

i

o

*

,

*

,

*

,

*

,

*

,

*

*

*

*

,

*

=

=

=

=

=

=

=

=

=

=

φ φ

φ

ρ ρ

ρ

 

T T

T T

T T

T

T

T T

T

T

T T

T

T

T T

T

T

T T

h

h

h

h

h

h

h

h

h

h

h

h

h

h

h

r v r v

,r sat

DR q

DR q

DR sat

g q

g q

g sat

H q

H q

H sat

r q

r q

r sat

I

I

I i

DR

DR

s

g

g

s

H

H

s

r

r

s

* *

max

, * ,

min,

,

* ,

min,

,

* ,

min,

,

* ,

min,

*

,

,

* ,

,

* ,

,

* ,

, * ,

− = −

−

= −

= −

= −

= −

=

=

=

=

=

2

2

2

2

2

2

2

2

φ

φ

φ

φ

φ

φ

φ

φ 

h

h

h

h

h

h

h

h

h

h

h

h

h

h

h

h

h

h

h

h

h

h

h

h

h

R r

v

R r

v

R r

v i

R r

d

R r

d

R r

d i

R v

H

R v

H

R v

H i

R H

d

R H

d

R H

d i

R v

g

R v

g

R v

g

i

R g

d

R g

d

R g

d i

R v

DR

R v

DR

R v

DR i

R DR

d

R DR

d

R DR

d i

,

* ,

, ,

,

* ,

, ,

,

* ,

, ,

,

* ,

, ,

,

* ,

, ,

,

* ,

, ,

,

* ,

, ,

,

* ,

, ,

=

=

=

=

=

=

=

=

R v

d

R v

d

R v

d i

h

h ,

* ,

, ,

=

Table 6.2 List of Initial Conditions and Assumptions 

1. Normalization for fluid and rod properties was done on the inlet conditions for the fluid, 

and the initial conditions for the rod. 

2. The flows were initialized on the inlet flow, Wi . 

3. Time constants for structures were defined in the text of the report. 

4. The temperature for a component is normalized by the expected maximum temperature 

variation for the component, such as 

T

T

T T r r

r CL sat

*

,

= −

 where Tr,CL is the centerline temperature and Tsat is the saturation temperature. 

5. The lengths were normalized on the full length of the bundle. 

6. Pressure drop was normalized on the velocity head of the fluid. 

7. The fluid momentum equation was normalized on the static head for the bundle. 

162
The total volume is the sum of the single phase and two phase volumes. Thus, 

 VV V 1 2 φ φ + = T (6-16) 

The time scale for the temporal terms is assumed to be the same for single phase and twophase flow. That is, the time constant is defined in terms of the inlet flow rate and the total fluid 

volume as 

τ

ρ

1 = i T

i

V

W (6-17) 

where τ1 is used to normalize the time rate of change terms on the left hand side of Equation 

6-15. 

Separate time constants are used to model the quenching of the heater rods, spacer grids and 

the housing. During the quenching, the convection heat transfer coefficient is about 5.6782 

kW/m2

-K (1000 Btu/hr-ft2-F). The Biot number is of the order of unity for all the heat structures 

with the exception of the spacer grids which has a Biot number much lower than 1.0. Therefore, 

in general, the conductivity across the heat structures cannot be neglected. For each structure 

the heat removal is characterized by a time constant: 

 heater rods τ 2 

 housing τ 3

 grids τ 4 

 dummy rods τ 5

The quench energy terms are normalized as follows: 

( ) Q cV

dT

dt

c VT T

c V

dT

dt qr r pr r

r q r i p r i r i r sat

r pr r

r q

, ,

, , ,, , , * ,

* * ,

*

* = = − ρ

ρ

τ

ρ

2 2 2

min

 (6-18) 

( ) Q cV

dT

dt

c VT T

c V

dT

dt qH H pH H

H q H i p H i H i H sat

H pH H

H q

, ,

, , ,, , , * ,

* * ,

*

* = = − ρ

ρ

τ

ρ

3 3 3

min

 (6-19) 

( ) Q cV

dT

dt

c VT T

c V

dT

dt qg g pg g

g q g i p g i g i g sat

g pg g

g q

, ,

, , ,, , , * ,

* * ,

*

* = = − ρ

ρ

τ

ρ

4 4 4

min

 (6-20) 

( ) Q cV

dT

dt

c VT T

c V

dT

dt q DR DR p DR DR

DR q DR i p DR i DR i sat

DR DR DR

DR q

, ,

, , ,, , ** * ,

*

* = = − ρ

ρ

τ

ρ

5 5 5

min

(6-21) 

Term 2, the temporal term representing the rate of change of energy storage within the control 

volume, becomes 

163
V d

dt

e V d

dt 2 v v vp v c T

1

2

1

φ φ () ( ρ ρ = Δ )

v

t

 (6-22) 

where 

e cT v p = Δ (6-23) 

and 

 

ΔT TT v v sa = − (6-24) 

Operating on each term in Equation 6-15 using the normalizing parameters from Table 6.1 and 

the ranges from Table 6.2 gives 

Wc T T V d

dt

c T

W cT T

V d

dt

c T

c VT T

c V

dT

dt

c VT T

c

i pi f i p

i v sat i p sat i v sat

i

v pv v

r i p r i r i r sat

r pr r

r q H i p H i H i H sat

H

, *

*

** * , , , , max, *

*

* ,* *

, , , , min, *

,

* * ,

*

*

, , , , min, *

() ( )

( )

( )

( ) ( )

− + − =

− + −

1

1

1 2

1

2 2 3

φ φ ρ

ρ

ρ

ρ

ρ

τ

ρ

ρ

τ

ρ

Δ Δ

pH H

H q

g i p g i g i g sat

g pg g

g q

DR i p DR i DR i sat

DR p DR DR

DR q

V

dT

dt

c VT T

c V

dT

dt

c VT T

c V

dT

dt

,

* * ,

*

*

, , , , min, * ,

* * ,

*

*

, , , , min *

,

* * ,

*

*

( )

( )

3

4 4

5 5

+ − +

−

ρ

τ

ρ

ρ

τ

ρ

++ − − {Q Q hA T T h A T T DP i, DP s r i r sat r r r v [ ( ) ( ) *

, max, ,

* ** *

2φ + (6-25) 

h A T T h AT T h A T T h AT T R r ( ) ( ) ( ) ( ) v i r i r sat R r

v rr v R rd i d i r sat R rd

d r sat , , , max, ,

* ** *

, , , max, ,

* ** * − − − −− ⎤

⎦

⎥

⎫

⎬

⎭

−

{[hA T T h A T T h A T T h A T T s H i H sat H H v H ( ) ( )] ( ) ( ) R v

H i H i H sat R vH , max, , HV H * ** *

, , , max, ,

* ** * − − + − ⎡

⎣

⎢ − ⎤

⎦

⎥ 2φ −

( ) ( ) {[ ( ) ( )] h A T T h A T T hA T T h A T T R H

d i d i H sat H R Hd , , , max, , , d H sat s g i g sat g g v g

* ** *

, max, ,

* ** * − − ⎡

⎣

⎢ ⎤

⎦

⎥

⎫

⎬

⎭

− − 2φ −

164
+ −− ( ) ( ) ( ) ( ) ⎤

⎦

⎥ − − ⎡

⎣

⎢ − ⎤

⎦

⎥

⎡

⎣

⎢

⎢

⎫

⎬

⎪

⎭

⎪

h A T T h AT T h A T T h AT T R v

g

g i g sat R v

g

gv g R g

d i d i g sat R gd

d g sat , , max, ,

* ** *

, , , max, ,

* ** *

−− − ( ) ( )] ( ) ( ) ⎡

⎣⎢

⎧

⎨

⎩ + − ⎡

⎣

⎢ ⎤

⎦

⎥ hA T T h A T T h A T T h A T T s DR i DR sat DR DR V DR − R v

DR i DR i DR sat R v

DR , max, , DR v DR

* ***

, , , max, ,

* ***

2φ −

( ) ( ) [ ( ) ( )] h A T T h A T T h A T T hA T T R DR

d i d i DR sat R DRd

d DR sat I i d i v sat I d v sat , , , max, ,

* ** * , , max, ** * * − − ⎤

⎦

⎥

⎡

⎣

⎢

⎫

⎬

⎭

+ − −

+ −− ( ) ( ) ( ) ( ) ⎡

⎣

⎢ ⎤

⎦

⎥ h A T T h A T T Wh hWh Wh h Wh + − −− R v

d i d i v sat R v

d d v sat i f i i i i s g o o , , , max, ,

* * * * * * * *

If we now divide all terms in Equation 6-25 by the “driver term” as first proposed by Wulff, one 

can obtain the normalized Pi time constants which represent the heat transfer processes in the 

rod bundle during reflood. The driver term selected is the initial decay power, QDPi , which is a 

test boundary condition. Therefore, each heat transfer process will be evaluated relative the 

initial bundle decay power. The resulting normalized Pi groups become: 

 

( ) Π1

1 = − = Wc T T

Q

i p i sat i

DPi

, φ fluid sensible energy / time

Initial decay power (6-26) 

Π2 =

−

=

Wi v sat i c p v sat i T Tsat

i DP Q i

ρ

ρ

, , ,, , ( ) max Vapor sensible energy / time

Initial decay power (6-27) 

Π 3

Rod quench energy / time

Initial decay power = − = ρ

τ

r i p r i r q i r q sat

DPi

cV T T

Q

, ,, ,, ,, ( ) max

2

 (6-28) 

Π 4 = − = ρ

τ

H i p H i H q i H q sat

DPi

cV T T

Q

, , , ,, , ( ) min,

3

Housing quench energy / time

Initial decay power (6-29) 

Π5

Grid quench energy / time

Initial decay power = − = ρ

τ

g i p g i g q i g q sat

DP

cV T T

Q i

, , , , , min, , ( )

4

 (6-30) 

Π6

Dead rod quench energy / time

Initial decay power = − = ρ

τ

DR i p DR i DR q i DR q sat

DP

cV T T

Q i

, , , , , min, , ( )

5

 (6-31) 

 

 

165
Π7

1 =

Q

Q

DP

DPi

φ

 (6-32) 

( ) Π8 = − = hA T T

Q

s r i r sat

DPi

, max, Convective heat rate from rods to mixture vapor

Initial decay power (6-33) 

( )

Π9 =

−

=

h AT T

Q

R r

v i ri r v

DPi

, , , max, Radiation heat rate from rods to vapor

Initial decay power (6-34) 

( )

Π10 =

−

=

h AT T

Q

R r

d i d i r sat

DPi

, , , max, Radiation heat rate from rod to drops

Initial decay power (6-35) 

( ) Π11 = − = hA T T

Q

s H i H sat

DPi

, max, Convective heat rate from mixture to housing

Initial decay power (6-36) 

 

( )

Π12 =

−

=

h AT T

Q

R v

H i Hi H v

DPi

, , , max, Radiative heat rate from vapor to housing

Initial decay power (6-37) 

( )

Π13 =

−

=

h AT T

Q

R H

d i d i H sat

DPi

, , , max, Radiation heat rate from housing to drops

Initial decay power (6-38) 

( ) Π14 = − = hA T T

Q

s g i sat

DPi

, max,g Convective heat rate from vapor to grids

Initial decay power (6-39) 

( )

Π15 =

−

=

h AT T

Q

R v

g

i g i v

DPi

, , , max,g Radiation heat rate from vapor to grids

Initial decay power (6-40) 

( )

Π16 =

−

=

h AT T

Q

R g

d i d i sat

DPi

, , , max,g Radiation heat rate from grids to drops

Initial decay power (6-41) 

( ) Π17 = − = hA T T

Q

s DR i DR sat

DPi

, max, Convective heat rate from vapor to dead rods

Initial decay power (6-42) 

166
( )

Π18 =

−

=

h AT T

Q

R v

DR i DR i DR v

DPi

, , , max, Radiation heat rate from vapor to dead rods

Initial decay power (6-43) 

( )

Π19 =

−

=

h AT T

Q

R DR

d i d i DR sat

DPi

, , , max, Radiation heat rate from dead rods to drops

Initial decay power (6-44) 

 

( ) Π20 = − = hAT T Ii d , max,v sat

QDPi

Interfacial heat transfer rate

Initial decay power (6-45) 

( )

Π21 =

−

=

h AT T R v

d i d i sat , , , max,v

QDPi

Radiation heat transfer from vapor to drops

Initial decay power (6-46) 

( ) ( ) Π22 = 1

− = − = Wh h

Q

Wc T T

Q

if i

DP

i pi f i

i i DP

,

Π (6-47) 

( ) Π23 = − = Wh h

Q

is g

DPi

Exit mixture energy / time

Initial decay power (6-48) 

Therefore, Equation 6-25 becomes 

Π Δ Π ΔΠ 1 1 ( ) ( )

1

1 2 2

1

3

2

V d

dt

cT V d

dt

c T

dT

dt p v v v

r q

φ φ ρ ρ φ ρ *

*

** * *

*

** * ,

*

* + =

+ + + ++ − Π ΠΠ Π 4 ( )

3

5

4

6

5

1 8 2

dT

dt

dT

dt

dT

dt

h AT T H q g q DR q

rr r v

,

*

*

,

*

*

, *

* ,

* ** *

φ

+ −− − − ΠΠ Π 9 1 h AT T h AT T h A T T ( ) 0 1 ( ) 1 2 ( ) R r

v rr v R rd , d r sat H H v H

* ** *

,

* ** *

,

* ** *

φ −

− − ΠΠ Π 12 h A T T h AT T h AT T ( ) + − 13 ( ) − 14 2 ( ) R v

H

Hv H R H

d d H sat g g v g ,

* ** *

,

* ** * , * ** *

φ − (6-49) 

− − ΠΠ Π 15h AT T h AT T h A T T ( ) + −− 16 ( ) 17 2 ( ) R v

g

gv g R g

d , d g sat DR DR v DR * ** *

,

* ** * , * ***

φ −

167
− − ΠΠΠ 18h A T T h A T T hA T T ( ) + − 19 ( ) + 20 ( ) R v

DR

DR v DR R DR

d

d DR sat I d v sat ,

* ***

,

* * * * ** * * −

+ −+ − Π Π 21 ( ) 1 23 h A T T Wh Wh R v

d

d v sat i i o o ,

* * * * ** ** Π

 

These Pi groups can be numerically calculated using the assumptions given in Table 6.2 for the 

heat transfer coefficients, heat flows and material properties. The results of the different Pi 

group calculations will be given in Section 6.4 of this report. 

Tables 6.3 and 6.4 summarize and compare the expected values of the fluid energy equation Pi 

groups of the RBHT Test Facility with those of a PWR and BWR respectively. Since the rod 

bundle geometry models a PWR assembly, it is expected that most of the Pi groups are 

preserved. However, since there is no housing in a PWR assembly, to ensure similarity the Pi 

groups which represent the heat transfer processes associated with the housing should be 

small. Since the test facility has a housing similar to a BWR channel, the same Pi groups 

derived for the RBHT Test Facility are present for a BWR fuel assembly. Their magnitudes are 

expected to be slightly different because of differences in material properties. 

Table 6.3 PWR Comparisons

Π Π 1 1 t PWR ≅ Should be similar since geometry is approximately correct and flows, 

powers are typical. 

Π Π 2 2 t PWR ≅ Similar to Π1 above, geometry is exact but power and flows are typical. 

Π Π 3 3 t PWR ≅ Not clear due to rod size and properties - need to check. 

Π Π 4 4 t PWR ≠ Distortion, as there is no housing in PWR. 

Π Π 5 5 t PWR ≈ Not clear how similar due to different materials and thicknesses (grids). 

Π Π 6 6 t PWR ≈ Not clear how similar due to different materials and thicknesses (dead or 

water rods). 

Π Π 7 7 t PWR = Controllable boundary conditions. 

Π Π 8 8 t PWR =

? Should be similar but geometry differences exist. 

Π Π 9 9 t PWR =

? Should be similar but geometry differences exist. 

Π Π 10 10 t PWR =

? Should be similar but geometry differences exist. 

Π Π 11 11 t PWR ≠ Distortion, as there is no housing in PWR. 

Π Π 12 12 t PWR ≠ Distortion, as there is no housing in PWR. 

168
Table 6.3 PWR Comparisons (Continued)

Π Π 13 13 t PWR ≠ Distortion, as there is no housing in PWR. 

Π Π 14 14 t PWR ≈

? Some differences due to grid designs, materials. 

Π Π 15 15 t PWR ≈

? Some differences due to grid designs, materials. 

Π Π 16 16 t PWR ≈

? Some differences due to grid designs, materials. 

Π Π 17 17 t PWR ≈

? Different materials, geometries, number - need to check. 

Π Π 18 18 t PWR ≅

? Different materials, geometries, number - need to check. 

Π Π 19 19 t PWR ≅

? Different materials, geometries, number - need to check. 

Π Π 20 20 t PWR ≈ Should be similar, as it is related to drops only and not materials, 

dimensions etc. 

Π Π 21 21 t PWR ≈ Should be similar, as it is related to drops only and not materials, 

dimensions etc. 

Π Π 23 23 t PWR ≈ Should be similar, but not exact due to geometry differences. 

Note: Some of the Pi groups can be made closer by adjusting the fluid conditions. Other Pi 

groups reflect the materials and geometry differences between the PWR and BWR 

assemblies so the simulation will only be approximate. 

Table 6.4 BWR Comparisons

Π Π 1 1 t BWR ≅ Should be similar since geometry is approximately correct (not sized for 

BWR) and flows, powers are typical. 

Π Π 2 2 t BWR ≅ Similar to Π1 above, geometry is exact but power and flows are typical. 

Π Π 3 3 t BWR ≅ Not clear due to rod size and properties - need to check. 

Π Π 4 4 t BWR ≅ Not clear how similar due to different materials and thicknesses (housing). 

Π Π 5 5 t BWR ≈ Not clear how similar due to different materials and thicknesses (grids). 

Π Π 6 6 t BWR ≈ Not clear how similar due to different materials and thicknesses (dead or 

water rods). 

Π Π 7 7 t BWR = Controllable boundary conditions. 

 

169
Table 6.4 BWR Comparisons (Continued)

Π Π 8 8 t BWR =

? Should be similar but geometry differences exist. 

Π Π 9 9 t BWR =

? Should be similar but geometry differences exist. 

Π Π 10 10 t BWR ≈

? Should be similar but geometry differences exist. 

Π Π 11 11 t BWR ≈

? Should be similar but housing thickness, material are different. 

Π Π 12 12 t BWR ≈

? Should be similar but housing thickness, material are different. 

Π Π 13 13 t BWR ≈ Should be similar but housing thickness, material are different. 

Π Π 14 14 t BWR ≈

? Some differences due to grid designs, materials. 

Π Π 15 15 t BWR ≈ Some differences due to grid designs, materials. 

Π Π 16 16 t BWR ≅

? Some differences due to grid designs, materials. 

Π Π 17 17 t BWR ≈

? Different materials, geometries, number - need to check. 

Π Π 18 18 t BWR ≅

? Different materials, geometries, number - need to check. 

Π Π 19 19 t BWR ≅

? Different materials, geometries, number - need to check. 

Π Π 20 20 t BWR ≈ Should be similar, as it is related to drops only and not materials, 

dimensions, etc. 

Π Π 21 21 t BWR ≈ Should be similar, as it is related to drops only and not materials, 

dimensions, etc. 

Π Π 23 23 t BWR ≈ Should be similar, but not exact due to geometry differences. 

Note: Some of the Pi groups can be made closer by adjusting the fluid conditions. Other Pi 

groups reflect the materials and geometry differences between the PWR and BWR 

assemblies so the simulation will only be approximate. 

170
6.3.2 Heater Rod (Fuel Rod) Energy Equation Scaling 

Equation 6-1 accounts for the energy release from the rods and other structures to the fluid and 

indicates some of the test distortions relative to a nuclear fuel assembly. The following analysis 

examines the behavior of the heater rod and a nuclear rod to determine the similarities and 

differences in their response to a reflood transient at or near the time that the peak cladding 

temperature would be calculated. In this situation, the quench front is approximately 2 or 3 ft 

below the peak temperature location such that there would be no axial conduction effects and 

one-dimensional radial heat transfer is sufficient. The analysis also considers the effects of the 

housing on the rod thermal response. 

Two heat transfer equations are developed for the rods; an equation which describes the 

transient fuel, or boron nitride (BN) and heating coil power generating region; and an equation 

for the cladding which reflects the rod interactions with the flow field, housing and other 

surfaces. The assumptions for the equation development include: 

• Analysis at one axial position in the bundle, 

• No axial conduction, that is, far from the quench front 

• Selected location on the rod is in dispersed flow film boiling, and the temperatures of the 

rod exceed Tmin, 

• A gap heat transfer coefficient couples the fuel pellet or boron nitride and heating coil, to 

the cladding, and 

• Heat generation is either in the fuel pellet region or in the boron nitride and heater coil 

region (BN). 

The radial conduction equation can be written for the fuel or BN region as 

 

ρ

∂

∂

∂

∂

∂

∂ f pf f

f

f

f

f f f gap i s ci c V

T

t rr

k r

T

r , − V QV h AT T ( )

⎛

⎝

⎜ ⎞

⎠

⎟ = ′′′ − − 1 (6-50) 

where Q′′′ is the volumetric heat generation for the fuel or BN region. f

A similar radial conduction equation can be written for the cladding as 

ρ ()( ∂

∂

∂

∂

∂

∂ c pc c

c

c

c

c gap i s ci c c co v c V

T

t rr

k r

T

r , − V h A T T hA T T ⎛

⎝

⎜ ⎞

⎠

⎟ = −− − 1

 (from pellet) (convective)

)

− −− − − − hAT T h A T T h A T T R R s co s ( ) R R H co H ( ) ( ) R hr cr R hr cr co hr co cr r

s rH , , , , , , , ,

(surface radiation) (housing radiation) (hot rod to cold rod radiation) (6-51) 

− −− −− hA T T h A T T h A T T lw lw co sat ( ) R r R d co sat ( ) R R v co v ( ) d r

v , , , ,

(liquid contact HT) (radiation to drops) (radiation to vapor) 

−

171
where the heat losses to the fluid, direct contact heat transfer, and the radiation heat transfer to 

the different components in the flow and bundle are indicated. This formulation allows rod-tohousing and rod to cold rod radiation heat transfer to occur. The heat transfer from the pellet or 

BN and heating coil to the cladding is given as 

172

q h AT T = − gap i s ci ( ) (6-52) 

Since the region of interest for the rod is assumed to be in dispersed flow film boiling, the local 

void fraction is greater than 90 percent such that there is allowable radiation heat transfer 

between the different components in the bundle. In this situation, the region of interest is also 

far from the quench front. 

The parameters for the normalization of Equations 6-50 and 6-51 are given in Table 6.5 and are 

similar to those used for the normalization of Equation 6-1. The individual temperature 

difference for the component temperature drop is shown in Table 6.5. In this fashion, the 

relative temperature differences are preserved. The time constant τ f is the fuel pellet and or BN 

region time constant. 

Table 6.5 Normalization Parameters for Rod Energy Equation

 A

A

A

 c

c

c

c

c

c

i

i

i i

p,c

* p c

pci

p,f

* p f

pfi

*

,

,

, ,

,

, ,

= = , , =

 h

h

h

h

h

h

h

h

h c

c

c i

gap

gap

gap i

R hr cr

R hr cr

R hr cr i

*

,

*

, ,

* ,

, ,

== = , , 

 k

k

k

k

k

k Q

Q

Q

 r

r

R f

f

f i

c

c

c i

f

f

f i f i

*

,

*

,

'''

'''

,

'''

*

,

,, , *== == 

 

( ) ( )

t

t

t

t

T

T

T T

T

T

T T

c f

c

c

ci co

f

f

f CL s

* *

* *

,

,

,

=

= − = −

τ τ = 

 

(For clad) (For fuel)

 

V

V

V

V

V

V c

c

c i

f

f

f i

c

c

c i

f

f

f i

*

,

*

,

*

,

*

,

,

,

= =

= =

 

ρ ρ

ρ

ρ

ρ

ρ
Using the definitions from Table 6.5 and substituting into Equation 6-50 gives 

ρ ( ) ( )

τ

ρ

∂

∂

∂

∂

∂

∂

f i p f i f i f CL s

f

f pf f

f o fi

f

f CL s

o

c i f

f

f

c VT T

c V

T

t

R k

R

T T

R

V

r r

k r

T

r

V , ,, , , *

,

* *

*

*

, ,

, * *

* *

*

*

* − − − ⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟ = 2

1 

Q Q f i f i f f gap i i i s ci gap i s ci , V V h A T Th AT T ( )( (6-53) "' , "' * , , * * * *−− − )

Equation 6-50 can be normalized by dividing each term in the equation by the “driver” term as 

recommended by Wulff. For this situation, the driver term is the initial power which is given as 

V Q fi fi , ,

* . Performing the division results in the different Pi groups for the pellet or BN region of 

the fuel or heater rod. The Pi groups are: 

( ) Π24 = −

′′′ = ρ

τ

f i p f i f CL s

f fi

cT T

Q

, ,, ,

,

Stored energy / time

Initial heat generation rate (6-54) 

( ) Π25 2 = − = kT T

R Q

f i f CL s

fi fi

, ,

, ,

'''

Clad heat conduction rate

Initial heat generation rate (6-55) 

Π26 = 1 V Q

V Q

fi fi

fi fi

, ,

"'

, ,

"' = (6-56) 

Π26 is identically unity since this was the driver term which was used to normalize the other Pi 

values. The normalization of the hgap term yields a Pi group which is identical to Π29. 

( ) Π29 = −

′′′ = h AT T

V Q

gap i i i s ci

fi fi

, ,

, ,

Heat transfer rate from pellet to clad 

Heat generation rate (6-57) 

The parameters used to normalize the clad conduction equation are also given in Table 6.5, 

where τc is the cladding time constant. Normalizing Equation 6-51 gives 

ρ ( )

τ

ρ

∂

∂

c i p c i c i ci co

c

c pc c c VT T

c

T

t

, ,, , * ,

*

*

*

− −

( ) 1 1

2 R

k T TV

r r

k r

T

r

V

i

c i ci co c i f

c

, , c * *

* *

*

*

* − ⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟ = ∂

∂

∂

∂

173
174

h A T T h A T T h A T T hA T T gap i i i s ci gap i s ci c i c i co sat c c co v , , ( ) ( ) ( )( − ) * * *

, , * * * − −− −

− − −− − h A T Th A T T h A T T h A T T ( ) ( ) ( ) ( ) R r

s

i R s i co s R r

s

R s co s R r

H i R H i co H R r

H , , , , , R H co H

* ,* *

, , , , ,

* ,* * − 

− − h A T Th A T T R hr ( ) ( ) cr i R hr cr i co hr co cr R hr cr R hr cr co hr co cr ,, ,, , , ,

*

,

*

, ,

*

− (6-58) 

−− − h A T T hA T T l l w i w i co sat w w co sat , , ( )( ) l l

* * *

− − h A T Th A T T ( ) ( ) R r

d i R r

d i f CL sat R r

d R r

d

co sat ,, ,, , ,

*

,

* * −

− − h A T Th A T T ( ) ( ) R r

v i R rv i f CL sat R rv R rv co v ,, ,, , ,

*

,

* * −

Equation 6-58 for the cladding can also be further normalized by dividing the coefficients by the 

driving term which is the rod initial heat generation rate. After this operation, the different Pi 

groups become: 

( ) Π27 = − = ρ

τ

c i p c i c i ci co

c fi fi

c VT T

Q V

, ,, ,

,

'''

,

Clad stored energy / time

Heat generation rate (6-59) 

( ) Π28 2

1 = − = R

k T TV

o Q V

c i ci co c i

fi fi

, ,

,

'''

,

Clad conduction heat rate

Heat generation rate (6-60) 

( ) Π29 = − = h AT T

V Q

gap i i i s ci

fi fi

, ,

, ,

"'

Heat transfer rate from pellet to clad 

Heat generation rate (6-61) 

( ) Π30 = − = hA T T

V Q

c i c i co sat

fi fi

, ,

, ,

*

Convective HT rate

Heat generation rate (6-62) 

( )

Π31 =

−

=

h A TT

V Q

R r

s i R rs i co s

fi fi

,, ,,

, ,

"'

Radiation HT rate to surfaces in bundle

Heat generation rate (6-63) 

( )

Π32 =

−

=

h A TT

V Q

R r

H i R rH i co H

fi fi

,, ,,

, ,

'''

Radiation HT rate to housing

Heat generation rate (6-64) 
Π33 =

−

=

h A TT

V Q

R hr cr i R hr cr i co hr co cr

fi fi

,, ,, , ,

, ,

'''

( ) Radiation HT rate from hot rods to cold rods

Heat generation rate (6-65) 

( ) Π34 = − = hA T T

V Q

w i w i co sat

fi fi

l l , ,

, ,

'''

Liquid contact HT rate

Heat generation rate (6-66) 

( )

Π35 =

−

=

h A TT

V Q

R r

d i R rd i co sat

fi fi

,, ,,

, ,

'''

Radiation HT rate to entrained drops

Heat generation rate (6-67) 

( )

Π36 =

−

=

h A TT

V Q

R r

v i R rv i co v

fi fi

,, ,,

, , '''

Radiation HT rate to vapor

Heat generation rate (6-68) 

One can replace the radiation heat transfer representation by a more complex model which will 

include the material dependent emissivity. The radiation heat transfer equations can also be 

replaced with a calculation of the heat flow by this path within the bundle. This will be presented 

in Section 7. 

The Pi groups presented in Equations 6-54 to 6-57 and 6-59 to 6-68 are valid for either a 

nuclear rod or a heater rod in a test bundle, though differences exist due to the difference in 

materials between the fuel rods and the electrical heater rods. Also, there is an additional term, 

Π 32, which represents the radiation from the hot rods to the test facility housing. There is no 

housing in a PWR fuel assembly. This is a distortion in the test facility relative to an infinitely 

sized PWR fuel assembly and will be addressed in Section 7 of this report. The housing effect 

must also be addressed in the analysis of the test data. Also, computer simulations of the test 

will require a structure model for the housing since the wall will communicate directly with the 

fluid and both directly and indirectly by radiation heat transfer with the heater rods in the interior 

of the bundle. 

6.3.3 Momentum Equation Scaling for the RBHT Test Facility 

The generalized one-dimensional integral form of the momentum equation is given by 

Shames (Ref. 11) and Wulff (Ref. 4) and is written for the entire test bundle as: 

∫ ∫ −

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ =− + −

e

i c i

i

e

e

c

e

c i

ei dz

g

WW g

gA A

dz

dt

dW

g

PP ρ

ρρ

22

2

1 11 (6-69) 

∫ + +

e

i c

T

ce gA

WK dzWW

gAD

f

2

2

2 2 ρ 2ρ

where the terms on the right hand side represent the 

• inertia effects of the fluid in the volume, 

• momentum flux of the fluid into and out of the volume, 

175
• gravitational forces, 

• frictional effects, and 

• form losses within the volume. 

The nomenclature is given at the end of this section for these equations. The momentum 

equation can be written for the complete bundle from the inlet to the exit. The flow in the bundle 

is single phase for some length and two-phase over the remaining length. The inlet is assumed 

to be single phase while the exit has a dispersed two-phase mixture. The saturation point is 

assumed to be at same location within the bundle as the quench front. Assuming that the 

saturation point is at the quench front is a reasonable simplification since for most reflood 

situations with low flooding rates (typically 0.0254 m/s, 1 in/s). The flow up to the quench front 

is assumed to be single phase while the flow downstream of the quench front is assumed to be 

in two-phase film boiling regime. Thus, the total bundle length can be split into a single phase 

region (from zi to zsat) and a two-phase region (from zsat to ze). 

It is also assumed that the mass flow rate is only time dependent, and does not vary across the 

bundle cross section or along the length (this is approximately true for low flooding rate 

situations of interest in which the exit flows nearly equal the inlet flows). For constant low 

flooding rate situations, a nearly constant flow process occurs. Most of the flow which is 

injected into the bundle becomes entrained and flows out of the bundle as a steam/droplet 

mixture. Figure 6.1 shows the mass balance on FLECHT-SEASET test 31504, a 0.0254 m/s, 1 

in/s, 40 psia, constant flooding rate test. Curve 1 represents the integrated injection, while 

curves 3 and 4 represent the integrated exit vapor and liquid flows respectively. The mass 

storage in the bundle is shown as curve 5 and is nearly horizontal indicating that only a portion 

of the injected water is stored in the bundle, while the remainder exits the bundle. 

If one examines the data at the very beginning of the test; this quasi-steady situation is not true 

and the rate of mass accumulation nearly equals the injection rate. However, once the quench 

front becomes developed, as seen in Figure 6.1, the flows are quasi-steady. 

Operating on the inertia term gives 

1 11

g

dW

dt

dz

A g

dW

dt A

dz dW

dt

L

A g c c i

e

i

e

T

c

= = ⎛

⎝

⎜ ⎞

⎠

⎟ ∫ ∫ 1 (6-70) 

where LT is the total length of the bundle. 

Operating on the momentum flux term gives 

1 1 1 1 1

2

2 2 2

2 g A

W W

g

W

c A

e

e

i

ρ ρ ρρ ic m

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟ −

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

= ⎡

⎣

⎢ ⎤

⎦

⎥

l

− (6-71) 

where the difference in the momentum flux is due to the density difference from the bundle inlet 

and exit. The density at the bundle exit is a mixture density (ρe = ρm) that reflects the two-phase 

flow behavior in the bundle during reflooding. This term is also called the acceleration pressure 

drop in two-phase flow. 

176
Figure 6.1 Mass Balance FLECHT–SEASET Run 31504. 

177
The gravity term is integrated along the length of the bundle and represents the single and twophase flow contributions to the total head in the bundle, therefore 

g

g

dz g

g

L g

g

dz

c i

e

c c

m

z

z

sat

e

∫ ρ ρ = + 1φ l ρ∫

f

 (6-72) 

where the single phase portion of the gravitational pressure drop uses an averaged fluid density 

from the subcooled inlet to the saturation density for the liquid, and the two-phase region uses a 

mixture density. 

The gravity term can be expanded in the two-phase region by representing the mixture density 

as 

ρ αρ α ρ m g = +− ( ) 1 (6-73) 

 

Inserting Equation 6-73 into Equation 6-72, and using an average void fraction in the two-phase 

region gives 

[ ( ) g

g

dz g

g

L g

g

L

c i

e

c c ∫ ρ ρ ρ α αρ = + +− 1φ l g f 1 ] 2φ (6-74) 

The frictional terms and the form pressure loss terms can be combined for both the single phase 

flow region as well as the two-phase flow region assuming that the mass flow is vertically 

upward in the test section (the absolute sign disappears). Operating on the single phase 

frictional term gives 

f

D Ag

W dz fL W

e c D gA z

z

e c i

sat

2 2 2

2 1

2

2 ρ ρ

φ

l l

∫ = (6-75) 

and for the two-phase frictional pressure drop, one obtains 

f

D Ag

W W dz fL W

e c D Ag z

z

fo

ef c sat

e

2 2 2

2

2

2

2 ρ

φ

ρ

φ

l

| | ∫ = (6-76) 

where 

φ φ

fo

z fo

z

e sat

sat

e

z z

2

2

= ∫

( − ) (6-77) 

is the average two-phase flow multiplier over the two-phase flow region. 

A similar approach can be used for the single and two-phase form losses in the bundle. The 

form losses represent the spacer grids within the bundle structure. Since the quench front is 

178
assumed to be at some intermediate position, there are a certain number of spacer grids which 

are in the single phase region and the remaining grids are in the two-phase region. There are 

typically eight grids in the rod bundle. The total form loss is given as 

K W

A g

nK W

A g

mK W

A g

T

c c

fo

f c

2

2

1

2

2

2

1

2

2 22 2 ρ ρ

φ

ρ

φ φ = +

l

 (6-78) 

where n and m are the number of grids in the single-phase and two-phase region respectively. 

The frictional and form losses can be combined for single and two-phase flow as 

1

2

1

2 2

1

1

2

2

2 2

1

2

ρ ρ

φ φ

φ

φ

φ

l A g

fL

D

nK W

A g

fL

D

mK W

c e f c

fo

e

+

⎡

⎣

⎢ ⎤

⎦

⎥ + +

⎧

⎨

⎩

⎫

⎬

⎭

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

 (6-79) 

Substituting Equations 6-70, 6-71, 6-74 and 6-79 into Equation 6-69 gives 

[ ( ) ] P P

g A

dW

dt

L

g

W

A

g

g

L g

g

L

c

T

cm c c

1 2 g f

2

2 1 2

1 1 11

−= + − 1 ⎛

⎝

⎜ ⎞

⎠

⎟ − + +−

⎡

⎣

⎢ ⎤

⎦

⎥ ρ ρ φ φ ρ ρ α αρ

l

l

+ +

⎡

⎣

⎢ ⎤

⎦

⎥ +

⎛

⎝

⎜ ⎞

⎠

⎟ ⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

W

A g

fL

D

nK W

A g

fL

D

mK

c e f c

fo

e

2

2

1

1

2

2

2 2

1 2 2 ρ ρ

φ φ

φ

φ

φ

l

+ (6-80) 

We can define the total frictional and form resistance for single-phase as 

R fL

D f nK

e 1

1

φ 1

φ = + φ (6-81) 

and for two-phase as 

R fL

D f fo mK

e 2

2 2

φ φ 1

φ = + φ

⎡

⎣

⎢ ⎤

⎦

⎥ (6-82) 

This equation can be normalized using the initial condition and boundary condition parameters 

from Table 6.2 and Table 6.6 as 

ΔP W

A g g

W

A

L L

V A

dW

dt

W

g A

W

A

i

ii c c

i

i i

T

B

i

ici m

* *

*

*

*

*

* * *

2

2

2 2

2 2

1 1 2

2

ρ ρ ρ ρ ρ = ⎛

⎝

⎜ ⎞

⎠

⎟ ⋅ + − ⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

l

1 

179
−+ + ( ( ) − ) ⎡

⎣

⎢ ⎤

⎦

⎥ g

g

L L g

g

L

c

T i

c

ρ ρ αρ ρα α ρ 1 2 φ φ eiT g 1 f * * * * * * * l L (6-83)

+ + [ ] [ ] W W

Ag A

R R

W W

Ag A

R R i

ii c

f f

i

ii cf

f f i i

2

2

2

2

2

2 1 1

2

2 2 1 2 2

*

* *

*

*

* *

*

ρ ρ ρ ρ

φ φ φ φ

l

The bundle volume VB = ALT can be used in equation 6-83. 

Table 6.6 Normalizing Parameters for Fluid Momentum Equation 

A A

A

L L

L

L

L

L

L

L

iT T L

*** * == = ,, , 1

1

2

2

φ

φ

φ

φ

T

=

( )

( )

ΔP

P P

W

g A

R

R

R

R

R

R

i

ci i

f

f

f

f

f

f i i

* * , ,

, ,

= −

⎧

⎨

⎪

⎩

⎪

⎫

⎬

⎪

⎭

⎪

= = 1 2

2

2 2

1

1

1

2

2

1

ρ

φ

φ

φ

φ

φ

φ

 *

where R refers to the total frictional and form resistance for the whole bundle in single phase f i ,1φ

flow. Thus all the (m + n) grids and the entire bundle is in single phase flow. 

W W

Wi

l

l

i

m m

i e

*** === ,, , ρ * = ρ

ρ

ρ

ρ

ρ

α

α

α

( ) 1 1 − = − α

α

α

*

e

t

t

V

W

i B

i

* = ⎛

⎝

⎜ ⎞

⎠

⎟ ρ

Collecting the different terms and dividing by gL

g

T i

c

ρ , the maximum gravitational driving head in 

the bundle as the “driving term” as recommended by Wulff gives 

W

A gL

P

W

A gL

dW

dt

L

A

W

A gL

W

A

i

ii T

i

ii T

i

ii T m

2

2 2

2

2 2

2

2 2

2

2 2

1 1 2

ρ ρ ρρ ρ

Δ * *

*

*

* * *

*

* = +−

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

⎛

⎝

⎜ ⎞

⎠

⎟

l

( ) (6-84) − + +− { [ ⎡

⎣

⎢ ⎤

⎦

⎥ L L 1 2 φ φ ρ α αρ α ρ e g 1 * * * ** * * l f ]}

+

⎛

⎝

⎜

⎜

⎜

⎞

⎠

⎟

⎟

⎟

+

⎛

⎝

⎜

⎜

⎜

⎞

⎠

⎟

⎟

⎟

W

A gL

R

W R

A

W

A gL

R

W R

A

i

ii T

f

f

l

i

ii T

f

f

f

i i

2

2 2

2

2 2 2 2 1

2

1

2 1

2

2

2

ρ ρ ρ ρ

φ

φ

φ

φ

* *

* *

* *

* *

180

where the Pi groups are given as: 
181

Π37

2

= = Wi Velocity

2 2 2ρii T A gL

 head

Gravity head (6-85) 

Π38

2

2 2 = = W

A gL

i

ii T ρ

Velocity head

Gravity head (6-86) 

 

Π39

2

= = Wi

2 2 A gL ii T ρ

Velocity head

Gravity head (6-87) 

Π (6-88) 40 = 1

Π41 = = α e

Vapor head

Total head (6-89) 

Π42 = = α e

Vapor head

Total head (6-90) 

 

Π43

2

= = W

R i Single phase resistance ( 2 2 2 1

ii T A gL f i ρ φ Gravity head 6-91) 

Π44

2

2 2 2 1 = = W

A gL

R i

ii T

f i ρ φ

Single phase resistance

Gravity head (6-92) 

ote that Π37, Π38, and Π39 are the same or are not independent and represent the velocity head 

41 and Π42 represent the single-phase and two-phase gravity head terms in the momentum 

e 

43 represents the ratio of the single phase frictional and form pressure losses in the bundle to 

omparing these terms to those for a PWR fuel assembly, differences can occur. If the spacer 

N

or kinetic energy of the flow relative to the maximum gravity head. Since inlet fluid conditions, 

geometry, and energy addition are preserved between the test and the PWR fuel assembly, the

PWR plant would have the same Pi groups and these in turn will have the same numerical 

value. Therefore, the test facility will correctly represent the inertia effects of the fluid, the 

momentum flux effects and the gravitational force effects. 

Π

equation, relative to the maximum gravity head in the bundle. The two Pi groups turn out to b

the same because of the normalization used. 

Π

the maximum gravitational head in the bundle. Π 44 represents the same ratio for the two-phase

region within the bundle. Again, because of the normalization used, the two Pi groups turn out 

to be the same. 

C

grids used in the test are prototypical, the form loss term will be the same for both the plant and 

the test. The frictional term, however, can be different since in the test there is a housing which 

adds additional wetted perimeter such that the hydraulic diameter is smaller for the same flow 

area. The smaller hydraulic diameter results in a lower Reynolds number for the same flow 
Table 6.7 Pi Groups for Fluid Energy Equation 

Πi Definition Ratio of

Π1 Wc T T

Q

i pi sat i

DPi

, ( ) − Single phase fluid sensible energy/tim

Initial decay power 

Π2 Wc TT

Q

i v sat i pv sat i v sat

i DPi

ρ

ρ

, , ,, , max, ( ) − Vapor sensible energy/time

Initial decay power 

Π3 ρ

τ

ri pri rqi rq sat

DP

cV T T

Q i

, ,, ,, max, , ( ) −

2

Rod quench energy/time

Initial decay power 

Π4 ρ

τ

Hi pHi Hqi Hq sat

DP

cV T T

Q i

, , , ,, min, , ( ) −

3

Housing quench energy/time

Initial decay power 

Π5 ρ

τ

gi pgi gqi gq sat

DP

cV T T

Q i

, ,, ,, min, , ( ) −

4

Grid quench energy/time

Initial decay power 

Π6 ρ

τ

DR i p DR i DR q i DR q sat

DP

cV T T

Q i

, , , ,, min, , ( ) −

5

Dead rod quench energy/time

Initial decay power 

Π7 Q

Q

DP

DPi

1φ

 = 1 

Heat generation rate

Initial decay power 

Π8 hA T T

Q

s ri r sat

DPi

, max, ( ) − Convective heat rate from rod to mixture 

Initial decay power 

182
Table 6.7 Pi Groups for Fluid Energy Equation (Continued) 

Πi Definition Ratio of

Π9 h AT T

Q

R r

v i ri r v

DPi

, , , max, ( ) − Radiation heat rate from rods to vapo

Initial decay power 

Π10 h AT T

Q

R r

d i di r sat

DPi

, , , max, ( ) − Radiation heat rate from rod to drops

Initial decay power 

Π11 hA T T

Q

s Hi H sat

DPi

, max, ( ) − Convective heat rate from mixture to hou

Initial decay power 

Π12 h AT T

Q

R v H i Hi H v

DPi

, , , max, ( ) − Radiation heat rate from vapor to hous

Initial decay power 

Π13 h AT T

Q

R H d i di H sat

DPi

, , , max, ( ) − Radiation heat rate from housing to dro

Initial decay power 

Π14 hA T T

Q

s gi g sat

DPi

, max, ( ) − Convective heat rate from vapor to gri

Initial decay power 

Π15 h AT T

Q

R v g i gi g v

DPi

, , , max, ( ) − Radiation heat rate from vapor to grid

Initial decay power 

Π16 h AT T

Q

R g

d i di g sat

DPi

, , , max, ( ) − Radiation heat rate from grids to drop

Initial decay power 

Π17 hA T T

Q

s DR i DR sat

DPi

, max, ( ) − Convective heat rate from vapor to dead 

Initial decay power 

183
Table 6.7 Pi Groups for Fluid Energy Equation (Continued) 

Πi Definition Ratio of

Π18 h AT T

Q

R v DR i DR i DR v

DPi

, , , max, ( ) − Radiation heat rate from vapor to dead 

Initial decay power 

Π19 h AT T

Q

R DRd i d i DR sat

DPi

, , , max, ( ) − Radiation heat rate from dead rods to dr

Initial decay power 

Π20 hAT T

Q

Ii d v sat

DPi

, max, ( ) − Interfacial heat transfer rate

Initial decay power 

Π21 h AT T

Q

R v

d i d v sat

DPi

, , max, ( ) − Radiation heat rate from vapor to drop

Initial decay power 

Π22 Wc T T

Q

i pi f i

DPi

, ( ) − Single phase fluid sensible energy

Initial decay power 

Π23 Wh h

Q

is g

DPi

( ) − Exit mixture energy/time

Initial decay power 

Π24

ρ ( ) τ fi pfi f CL s f fi cT T

Q

, ,, ,

,

"'

− Stored energy/time 

Initial heat generation rate 

Π25 kT T

R Q

fi f CL s

f fi

, ,

,

"'

( ) −

2

 Clad heat conduction rate 

Initial heat generation rate 

Π26 1 Initial power_____ 

Initial heat generation rate 

184
Table 6.7 Pi Groups for Rod Energy Equation (Continued) 

Πi Definition Ratio of

Π27

ρ

τ

ci ci pci ci co

fi fi c

Vc T T

V Q

, , ,,

, ,

"'

( ) − Clad stored energy/time

Heat generation rate 

Π28 kV T T

VQR

ci ci ci co

fi fi o

, ,

, ,

"'

( ) −

2

Clad heat conduction rate

Heat generation rate 

Π29 h AT T

V Q

gap i ii s ci

fi fi

, ,

, ,

"'

( ) − Heat transfer rate from pellet to clad

Heat generation rate 

Π30 hA T T

V Q

ci ci co sat

fi fi

, ,

, ,

"'

( ) − Convective HT rate

Heat generation rate 

Π31 h A TT

V Q

R r

s

i R r

s i co s

fi fi

,, ,,

, ,

"'

( ) − Radiation HT rate to surfaces in bund

Heat generation rate 

Π32 h A TT

V Q

R r

H i R r

H i co

H

fi fi

,, ,,

, ,

"'

( ) − Radiation HT rate to housing

Heat generation rate 

Π33 hA TT

V Q

R hr

cr

i R hr

cr i co hr co cr

fi fi

,, ,, , ,

, ,

"'

( ) − Radiation HT rate from hot rods to cold 

Heat generation rate 

Π34 hA T T

V Q

lw i lw i co sat

fi fi

, ,

, ,

"'

( ) − Liquid contact HT rate

Heat generation rate 

Π35 h A TT

V Q

R r

d i R r

d i co sat

fi fi

,, ,,

, ,

"'

( ) − Radiation HT rate to entrained drops

Fuel rod heat generation rate 

185
186

Table 6.7 Pi Groups for Rod Energy Equation (Continued) 

Πi Definition Ratio of

Π36 h A TT ( )

V Q

R r

v

i R r

v

i co v

fi fi

,, ,,

, ,

"'

− Radiation HT rate to vapor

Fuel rod heat generation rate 

Π Π 37 38 = = W

A gL

i

ii T

2

2 2 2ρ

Velocity head

Gravity head 

Π40 1 Maximum gravitational driving head

Total head 

Π Π 41 42 = αe Vapor head

Total head 

Π Π 43 44 = W

A gL

R i

ii T

f i

2

2 2 1 ρ φ

Single phase resistance

Gravity head 
187

condition and hence a higher friction factor. The effects of the non-prototypical hydraulic effect 

of the test section housing will be calculated in Section 6.6. All the Pi groups are presented in 

Table 6.7. 

6.4 Calculation of Pi Groups for Flow Energy Equation

6.4.1 Introduction 

The fluid energy equation includes 23 Pi groups which are defined in Section 6.1. Here, the 

numerical values of these groups are calculated for the RBHT Test Facility, the PWR bundle 

and BWR bundle. 

The RBHT reference conditions, given in Table 6.8 are similar to FLECHT-SEASET experiment 

(Run 31504) conditions. Hence, reference conditions used in the calculations are obtained from 

FLECHT-SEASET and then applied to the geometry and materials for each case (RBHT, PWR 

and BWR). 

Table 6.8 RBHT Program Conditions 

Flooding rate, m/s (in/s) 0.0254 (1.0) 

Pressure, bar (psia) 2.67788 (40) 

Inlet subcooling, degrees C (degrees F) 60 (140) 

kW/m (kW/ft) at peak power location 2.3 (0.7) 

Peaking factor 1.5 

The fluid energy equation represents the energy balance for the fluid in the entire bundle at a 

given time which is selected to be the PCT time (i.e., 125 s in Run 31504). Measured values 

are then averaged axially to obtain the values to be used in the calculations which are shown in 

Table 6.9. 

6.4.2 Calculation of Convective Heat Transfer Pi Groups 

The Pi groups for the fluid energy equation can be categorized mainly into quench energy 

terms, convective heat transfer terms and radiative heat transfer terms. The present section 

discusses the Pi groups of the fluid energy equation. 

6.4.2.1 Methodology used for Calculations: 

The following assumptions and simplifications were used in the analysis: 

1. Data from FLECHT-SEASET experiment (Run 31504) with conditions similar to the RBHT 

Test Facility were used; however, these values were applied to the RBHT Test Facility 

geometry and power shape. 
188

Table 6.9 Reference Conditions for the Fluid Energy Equation Pi Groups 

Exit Temperature, Te,

o

C (

o

F) 260 (500) 

Quench front location, m (ft) 1.2 (4.0) 

Average clad temperature, Tc,

o

C (

o

F) 898.88 (1650) 

Average housing temperature, TH,

o

C (

o

F) 246.11 (475) 

Average surface temperature, Ts,

o

C (

o

F) 246.11 (475) 

Fluid saturation temperature, Tsat,

o

C (

o

F) 130.55 (267) 

Average vapor temperature, Tvapor,

o

C (

o

F) 656.11 (1177) 

Average thimble temperature, Tthimble,

o

C (

o

F) 746.66 (1376) 

Average grid temperature, Tg, oC (

o

F) 746.66 (1376) 

Exit void fraction, αe 0.999 

2. The maximum temperature encountered in the run occurred at 125 s for channel 99. This 

was at an elevation of 1.98m (78 in). All other quantities from the FLECHT-SEASET, Run 

31504 were obtained at this time (125 s). 

3. The location of the quench front at 125 s was obtained from the plot of quench front 

location versus time in the FLECHT-SEASET report (Figure 6.6). At t = 125 s, the quench 

front was at the 1.2 m (4 ft) elevation. The quench front has been ‘frozen’ at this location 

for all calculations. In the calculation of the fluid energy equation Pi groups, all data used 

from FLECHT-SEASET report represents a snapshot in time, taken by freezing the quench 

front at that elevation (1.2 m [4 ft]). 

4. Time averaged values over 1.2 to 3.6 m (4 to 12 ft) of the heater rod clad temperature, 

vapor temperature and thimble temperature were used in the calculation of the Pi groups. 

For the housing temperature, the maximum value of the housing temperature at that time 

(125 s) was used to provide a more realistic estimate of the Pi group value. This value is 

410 degrees C (770 degrees F), obtained from the FLECHT SEASET report. The dummy 

rod temperature was taken to be the same as the maximum housing temperature. The 

grid temperature was set equal to the thimble temperature. 

5. The heat transfer coefficient value for convection, was the time Average value obtained 

from data above the quench front location to the exit of the test section. This value was 

referenced to the fluid saturation conditions (Tsat). 

6. The exit void fraction was assumed to be 0.999. 

7. Finally, the exit temperature was obtained from the FLECHT-SEASET plot for channel 199, 

which gives temperature of the vapor near the exit location 3.45 m (11.5 ft). Thus Texit = 

260 degrees C (500 degrees F). 

All values used in the calculations are summarized in Table 6.9. 
189

6.4.2.2 Numerical Input Quantities: 

Initial decay power: 

QDPi = 2.3 kW/m (0.7 kW/ft), is the initial rod decay power (40 s into a LOCA) at the peak power 

location, which is equivalent to a value of 5.6 kW/rod using a peaking factor of 1.50. With 45 

heated rods in the bundle, the total bundle power was 252 kW. 

Inlet conditions: 

Based on the information in Tables 6.8 and 6.9, the inlet properties were obtained from 

thermodynamic tables at a temperature of 52.77 degrees C (127 degrees F). 

Areas of rods, housing, grids and dead rods above the quench front (4 ft): 

a. The total rod area is calculated based on rod diameter 9.55 mm (0.374 in) and length 

above quench front 2.4 m (8 ft) for 45 heated rods. 

b. The housing area is obtained from the product of the inner perimeter of the housing and 

the length of housing above the quench front. 

c. The total grid area is calculated based on the product of the following: 

Area of each cell = 4 x pitch 12.6 mm (0.496 in) x height of the grid 38.1 mm (1.5 in) 

Number of cells per grid = 45 

Number of grids strops above quench front = 6 

d. The total dummy rod area is based on the dummy rod diameter 9.5 mm (0.374 in) and 

length above quench front 2.4 m (8 ft) for four dummy rods. 

6.4.2.3 Numerical Values of the Convection Pi groups: 

The Pi groups representing the energy storage terms are 

Π1 = 0.144 

Π2 = 0.0007 

 

For the convective energy terms for rods, housing, grids and dummy rods, a heat transfer 

coefficient of 56.78 W/m2

-K (10 Btu/hr-ft2-F) was used, based on the average from the FLECHTSEASET report (Run 31504) data. To give a more realistic value for the Pi group, Π11, instead 

of average value of housing temperature, the maximum housing temperature of 410 degrees C 

(770 degrees F) at PCT time (125 s), at the 6 ft elevation was used. Also, the maximum 

housing temperature 410 degrees C (770 degrees F) was for the value of Tmax of dummy rods. 

Using the above information and the calculated areas, the Pi values for the various convective 

heat transfer terms are: 
Π8 = 0.567 

Π11 = 0.055 

Π14 = 0.072 

Π17 = 0.019 

The Pi group for the interfacial heat transfer is 

( ) Π20 = − = hAT T

Q

I i d v sat

DPi

, max, Interfacial heat transfer rate

Initial decay power

where Ad represents the interfacial area, given by the product of area of a single drop times the 

number of drops. The number of drops is given by 

( ) N

d d =

6 1−

3

α

π (6-93) 

With a mean void fraction value of 0.995, and a drop diameter of 1.016 mm (0.04 in), the 

number of drops is 

 Nd = 9.104 drops/cm3

 (149.2 drops/in3) 

The quench front is at the 4 ft elevation, hence, the number of drops in the two-phase region 

which extends from the location of the quench front to the bundle exit is obtained by the product 

of the number of drops per unit volume times the volume above the quench front. 

 Flow area = 45.8 cm2

 (7.0987 in2) 

 

Hence, the total number of drops is calculated to be 101641. 

From the FLECHT-SEASET report (Page 6-26), the mean droplet velocity and mean vapor 

velocity are found as 

ud = 6555 215 . (. / m / sec ft sec)

uv = 13415 44 . ( / sec) m / sec ft

The Reynolds number for drop based on the relative velocity of drops and vapor is given as: 

( ) Red

vvd

v

du u =ρ −

μ (6-94) 

The droplet Reynolds Number is calculated to be 803.65. 

190
Taking a Prv = 1.04 from Collier and Thome (Ref. 12) and using the Lee-Ryley Correlation, the 

Nusselt number is 

Nud d = +2 0 74 0 5 1

3 . Re Pr . (6-95) 

h

Nu k

d I

d v

co = (6-96) 

where the thermal conductivity for vapor is obtained from Collier and Thomeas (Ref. 12) as

 kv = 0.02799027 W/m-K (0.01617 Btu/hr-ft-F) 

Based on these, 

Π20 = 0 43 . 

The flow energy Pi groups for exit energy are calculated assuming the exit mass flow is equal to 

the inlet mass flow. Value of saturated vapor enthalpy is used from thermodynamic tables at 

P = 40 psia. Thus 

Π Π 22 1 = = 0144 .

Π23 = 0121 .

From these, it is seen that the Pi groups representing the energy storage, the flow energy and 

convection from rod to vapor and the interfacial heat transfer terms are the dominant Pi groups. 

The other terms are very small by comparison. This clear distinction between the dominant 

terms and the others are in line with what is expected typically. 

 

( ) Π4

3

= − = ρ

τ

H i p H i H q i H q sat

DP

cV T T

Q i

, , , , , min, , Housing quench energy / time

Initial decay power

( ) Π5

4

= − = ρ

τ

g i p g i g q i g q sat

DP

cV T T

Q i

, , , , , min, , Grid quench energy / time

Initial decay power

( ) Π6

5

= − = ρ

τ

DR i p DR i DR q i DR q sat

DP

cV T T

Q i

, , , , , min, , Dead rod quench energy / time

Initial decay power

 

6.4.3 Quench Energy groups 

The Pi groups describing the heat transfer at the quench front for the rods, the housing, the 

grids and the surfaces (dummy rods) are the following: 

191
192

The calculation is based on the input data from in Tables 6.8 and 6.9 and the methodology used 

in Section 6.4.2.1. In addition, the following assumptions have been made to complete the 

calculation: 

• The same transition boiling heat transfer coefficient of hq,i = 5.678 kW/m2

-K (1000 

Btu/hr-ft2

-F) is assumed for the structures (rods, housing, grids and surfaces); 

• The same Tmin = 550 degrees C (1022 degrees F) is assumed for all surfaces; 

• The same axial quench front velocity uq is assumed for all the structures. 

where the same value of Tmin has been used for all surfaces since the material is all Inconel. 

The material properties and geometry data used in the calculation are summarized in the 

following tables (6.10, 6.11, 6.12, 6.13): 

 Table 6.10 Material Properties 

Material Reference 

Temperature (C) 

Density (kg/m3) Heat Capacity 

(J/kg-K) 

Conductivity 

(W/m-K) 

Inconel-600 1100 8254 696 24.7 

Boron Nitride 1100 1910 1500 86.3 

Monel K-500 1100 8470 531 34.4 

Uranium Dioxide 1100 9649 326 3.9 

Zircaloy-2 1100 6560 362 16.8 

Table 6.11 Electrical Rod Geometry

Material ri (mm, in) dri (mm, in) 

Boron Nitride 0, 0 1.7145, 0.0675 

Monel K-500 1.7145, 0.0675 1.143, 0.0450 

Boron Nitride 2.8575, 0.1125 1.1811, 0.0465 

Inconel-600 4.0386, 0.1590 0.7112, 0.0280 

Rod surface 4.7498, 0.1870 

Table 6.12 Nuclear Rod Geometry for PWR

Material ri (mm, in) dri (mm, in) 

Uranium Dioxide 0, 0 4.18084, 0.1646 

Zircaloy-2 4.18084, 0.1646 0.56896, 0.0224 

Rod surface 4.7498, 0.1870 
Table 6.13 Nuclear Rod Geometry for BWR

Material ri (mm, in) dri (mm, in) 

Uranium Dioxide 0, 0 5.199, 0.2047 

Zircaloy-4 5.199, 0.2047 0.810, 0.0319 

Rod surface 6.0198, 0.2370 

At first we need to calculate the volume of the rod which is quenching. This is related to the 

assumed quench front velocity vq and the heat structure time constant to release the stored 

energy: 

 

V Av r sr q = , τ 2 (6-97) 

where As,r is the cross section of one of the heater rods and is given as 

AND sr r r , = ⎛

⎝

⎜ ⎞

⎠

⎟ π

4

2 (6-98) 

This expression, when substituted in the definition of Π3 gives 

Π3 = ρ τ −

τ

r p r s r q r r sat

DP

c Av T T

Q i

, , , min, ( ) 2

2

 (6-99) 

Note that the time constant drops out. This is because, regardless the time constant, most of the 

stored energy will be released during the quenching time period. In other words, if the time 

constant is larger, then the energy release rate will be lower but the energy will be released by a 

larger volume as the quench front is advancing over the same time period. This follows from 

the assumption that the quench front velocity is constant. 

A similar procedure is used to calculate Π4; i.e., the energy released during quenching of the 

housing is 

Π4 = ρ −

τ

H i p H i H q i H q sat

DP

cV T T

Q i

, , , , , min, , ( )

3

 (6-100) 

Similarly for the grid 

Π5

4

= ρ −

τ

g i p g i g q i g q sat

DP

cV T T

Q i

, , , , , min, , ( ) (6-101) 

where 

A p s

s g, = ×

⎛

⎝

⎜ ⎞

⎠ 4 ⎟ ×

2

45 , (6-102) 

193
p is the pitch, and s is the strop thickness. 

Finally for the dummy (corner rods): 

Π6

5

= ρ −

τ

DR i p DR i DR q i DR q sat

DP

cV T T

Q i

, , , , , min, , ( )

 (6-103) 

where 

AND s DR DR DR , = ⎛

⎝

⎜ ⎞

⎠

⎟ π

4

2 (6-104) 

and NDR is the number of dead rods (in our case, 4). 

Details of the calculations are reported in Appendix B.7. The values of the Pi groups are the 

following: 

Π

Π

Π

Π

3

4

5

6

0 092

0 084

0 022

0 003

=

=

=

=

.

.

.

.

6.4.4 Thermal Radiation Heat Transfer Pi Group Calculations 

The Pi groups describing the radiative heat transfer to the fluid from the structures are: Π9 to 

Π16. These terms require particular attention because in order to obtain these values, the 

solution of a radiative surface network is required. Thermal radiation heat transfer takes place 

between the rod surfaces, between rod and housing, between any surface to steam and 

droplets and between steam and droplets directly. For a given temperature field (clad, dummy 

rods, housing, liquid and vapor) the heat rates among the surfaces, liquid and vapor are 

calculated by solving a radiation network lumped model (using the RADNET Fortran computer 

program). 

In this model, rods are lumped together and global surface view factors are calculated by 

combining single rod view factors obtained with the VUEFAC subroutine of the MOXY computer 

program (Ref. 11). Details of the view factors calculation are reported in Appendix B.1. 

To account for a radial temperature distribution in the bundle, a six node radiation network has 

been developed, where the heater rods are divided in hot rods and cold rods (Figure 6.2). The 

hot rods are considered to be either the single center rod, the inner 3x3 array, or the inner 5x5 

array. Sensitivity analyses (Appendix B.1) have been carried out and the inner 3x3 hot rods 

lumping approach was chosen to be the most appropriate. 

194
Figure 6.2 RBHT Layout. 

Figure 6.3 Six Node Radiation Network. 

The radiation network (Figure 6.3) resistances are calculated as described in Reference 8 and 

Appendix B.1 while the temperature at each network node surfaces is an input for the program. 

The node surface temperatures are calculated by averaging measured temperature in Run 

31504 of the FLECHT-SEASET experiments. These values are summarized in Table 6.9. 

Once the temperature is assigned to each radiative surface, the radiation network is solved for 

the heat rate (per unit length) between each node. In particular, the Pi groups concerned with 

radiation are redefined below: 

( ) ( )

Π9 =

−

=

h AT T −

Q

Qz z

Q

R r

v i ri r v

DP

r

v top q

i i DP

, , , max, '

 (6-105) 

195

 
( ) ( )

Π10 =

−

=

h AT T −

Q

Qz z

Q

R r

d i d i r sat

DP

r

d top q

i i DP

, , , max, '

 (6-106) 

 

 

( ) ( )

Π12 =

−

=

h AT T −

Q

Qz z

Q

R v

H i Hi H v

DP

v

H top q

i i DP

, , , max,

'

 (6-107) 

( ) ( )

Π13 =

−

=

h AT T −

Q

Qz z

Q

R H

d i d i H sat

DP

H

d top q

i i DP

, , , max, '

 (6-108) 

( )

Π

Δ

15 =

−

=

h AT T

Q

Q zN

Q

R v

g

i gi g v

DP

v

g

'

g g

i i DP

, , , max,

 (6-109) 

 

( )

Π

Δ

16 =

−

=

h AT T

Q

Q zN

Q

R g

d i d i g sat

DP

g

d

'

g g

i i DP

, , , max,

 (6-110) 

 

( ) ( )

Π18 =

−

=

h AT T −

Q

Qzz

Q

R,v

DR,i DR,i ,DR v

DP

DRv

' top q

i i DP

max

 (6-111) 

 

( ) ( )

Π19 =

−

=

h AT T −

Q

Qzz

Q

R DR

d i d i DR sat

DP

DR

d top q

i i DP

, , , max, '

 (6-112) 

( ) ( )

Π21 =

−

=

h AT T −

Q

Qz z

Q

R v

d i d v sat

DP

v

d top q

i i DP

, , max,

'

 (6-113) 

where 

ztop Elevation to the top of the bundle, 3.6 m (12 ft) 

zq Elevation of the quench front, 1.2 m at 125 s (4 ft at 125 s) 

Δzg Grid axial length, 38.1 mm (1.5 in) 

Ng Number of grids above quench front 

The solution of the radiation network provides the radiosity or emissive power in each node, 

then the values in each branch can be calculated by applying the definition 

196
Q

J J

R Q

J E

R ij

i j

ij

ij

i b

ij

= − = − or , j

 (6-114) 

The six node radiation network requires two clad temperature values: the hot rod temperature 

and the cold rod temperature. The temperature difference between the hot rods and the cold 

rods is estimated from the rod-to-rod (MOXY) radiation model and is 161 degrees F when a 3x3 

inner hot rods lumping approach in the bundle is assumed. Then the hot and cold rod 

temperature are calculated 

1650

45

369 == + T hr TT cr (6-115) 

and since 

−=Δ−= 161 hrcr TTTT hr

we obtain 

 

( )

( )

T

T

hr

cr

=

=

97055

88055

.

.

o

o

C 1779 F

C 1617 F

This completes the input data for the radiation network. The dimensionless group Π9 is the 

radiative energy from all the rods to the vapor and is expressed as 

Π

Δ

9 =

Q z

Q

r

v

DPi

'

 

where the numerator has the units of heat rate per unit length and is the sum of two 

contributions: energy from hot rods to vapor and energy from nominal rods to vapor. 

As already mentioned the difference Δz is the height above the quench front 

Δzz z = − top q

and 

 

Q QQ r

v v v ' ' = + 1 2'

The initial bundle decay power is 

QDPi = 252.0 kW

197
As results we obtain 

Π9

4 = 855 − . e

Similarly the Pi group for the radiative energy from the rod to the liquid droplets is calculated as 

Π

Δ

10 =

Q z

Q

r

d

DPi

'

where 

Q QQ r

d

d d

' ' = + 1 2

'

 

and 

Π10

2 = 7 06 − . e

The next two dimensionless groups represent the radiative heat transfer from the housing to the 

vapor and droplets, respectively 

Π

Δ

12 =

Q z

Q

v

H

DPi

'

and Π

Δ

13 =

Q z

Q

H

d

DPi

'

 

where 

Q Q v

H v

' ' = 4

 

Q Q H

d

d ' ' = 4

and then 

Π12

5 = −8 01 − . e

Π13

3 = 2 85 − . e

The next two Pi groups for the radiative energy from the grids to the fluid are calculated by 

solving a separate four node radiation network (Figure 6.4). The Pi groups are defined as 

198
Π

Δ

15 =

Q zN

Q

v

g

g g

DPi

'

and Π

Δ

16 =

Q zN

Q

g

d

g g

DPi

'

 

where 

Q

J T

R Q

J T

R v

g

v

v

g

d

d

d

' ' = , − = 2 − 4

2

2

4

2

σ σ

and J2 and R2v refer to the four node radiation network. The grid vertical length and the number 

of grids above the quench front are 

Δz N g g = = 1 6 .5in and 

Figure 6.4 Four Node Radiation Network. 

 

The rod-grid-liquid-vapor network resistances are calculated with the same procedure and 

equations described for the bundle six-node-radiation network. In this case there are only two 

unknowns (J1 and J2) which can be determined explicitly. Details of the calculation are reported 

in the Excel worksheet attached in Appendix B.2. The result is 

Π15

7 = 6 9 − . e

Π16 = 0 0016 .

Finally, the radiation energy from the surfaces (unheated rods) to the fluid are represented by 

 

199
Π

Δ

18 =

Q z

Q

v

DR

DPi

'

 and Π

Δ

19 =

Q z

Q

DR

d

DPi

'

where 

Q Q v

DR

v

' ' = 3 and Q Q DR

d

d

' ' = 3 

as results: 

Π18 and 5 = −322 − . e Π19

4 = 65 − . e

The last contribution to the radiative heat transfer is expressed by the interfacial radiation heat 

transfer 

Π

Δ

21 =

Q z

Q

v

d

DPi

'

which is determined directly from the network with the result that 

Π21

5 = 39 − . e

6.4.5 Summary 

Table 6.14 shows the numerical values of all the Pi groups for the fluid energy equation. As 

expected, stored energy, rod quench energy, convection from rod to vapor, interfacial heat 

transfer and flow energy terms are significant. The values of the radiation Pi groups are 

relatively small, thereby indicating the predominance of convection over radiation heat transfer. 

Though the rod quench energy term is significant, the housing, grid and the dummy rod quench 

energy terms are small. 

6.5 Calculations of Pi groups for the Rod Energy Equation 

6.5.1 Introduction 

The rod energy equation includes thirteen Pi groups (from Π24 to Π36) defined earlier. The 

numerical values of these groups are now calculated for the RBHT Test Facility. The reference 

conditions used in the calculation are obtained from the same FLECHT-SEASET experiment 

(Run 31504) used earlier and then applied to the geometry and materials for each case (RBHT, 

PWR and BWR).

The rod energy equation represents an energy balance at a given axial location within the 

dispersed flow film boiling region, far from the quench front at the time of the measured peak 

temperature. The conditions (temperature, heat transfer coefficients, etc.) are taken from 

FLECHT-SEASET (Run 31504) measured values at the time of PCT and at the PCT axial 

location. Since there are no data available for the dummy rods, their surface temperature is 

200
Table 6.14 Numerical Values of Pi Groups - Fluid Energy Equation 

201
Table 6.14 Numerical Values of Pi Groups - Fluid Energy Equation (Continued) 

202
Table 6.14 Numerical Values of Pi Groups - Fluid Energy Equation (Continued) 

203
assumed equal to the housing temperature. The complete list of data and assumptions is given 

in Table 6.15. 

6.5.2 Convection and Stored Energy Pi Groups 

The convection and stored energy Pi groups are Π24, Π25, Π26, Π27, Π28, Π29, Π30, and Π34. The 

values of the Pi groups are calculated for both the electric rod and the nuclear rod. The 

reference conditions and the input that is used in the calculation are tabulated in Table 6.15. 

Both types of rods are modeled as infinite cylinders. The temperature at the various locations 

such as centerline, surface, clad inside and clad outside surface are calculated simply by 

applying the concepts of conduction resistance for cylindrical geometries. 

Table 6.15 Reference Conditions for Rod Energy Equation Pi Groups 

Rod peak power, kW/m (kW/ft) 2.3 (0.7) 

PCT time (sec) 125 

PCT axial location, m (ft) 1.95 (6.5) 

Clad temperature (PCT), Tci, oC (F) 1148.88 (2100) 

Housing temperature, TH, oC (F) 426.66 (800) 

Surface temperature, Ts,

o

C (F) 426.66 (800) 

Saturation temperature, Tsat, oC (F) 130.55 (267) 

Vapor temperature, Tv, oC (F) 898.88 (1650) 

Gap heat transfer coefficient, kW/m2K (Btu/hr-ft2-F) 

hgap (Nuclear Rod) 

hgap (Electrical Rod) 

5.678 (1000) 

28.39 (5000) 

To account for the correct heat transfer, based on the maximum temperature difference (TCL - 

Tsat), the value of the heat transfer coefficient is taken to be h = 56.78 W/m2

-K (10 Btu/hr-ft -F). 

This is again based on the same FLECHT-SEASET (Run 31504) data. 

2

Also, to simulate the gap that exists between the inside of the clad and the fuel pellet or the 

boron nitride insulator, a gap heat transfer coefficient is used: 

hgap = 28.39 kW/m2K (5000 Btu/hr-ft2-F), for electrical rods 

 hgap = 5.678 kW/m2K (1000 Btu/hr-ft2-F), for nuclear rods 

which are representative values for these rods. 

The heat generation rate per unit volume, , is calculated from the kW/ft rating at peak 

location 2.3 kW/m (0.7 kW/ft) and the diameter of the fuel element, Df = 9.5 mm (0.374 in). We 

get = 1.469 x 108 W/m3

 (4329012.6 Btu/hr-ft3).

Qi

'''

Qi

'''

204
Material properties tabulated in Table 6.10 and the dimensions of the electrical rod from Table 

6.11 are used for the calculation of the Pi terms. 

The fuel time constant τ and clad time constant f τ c are obtained by solving a double-lumped 

model for the rod. Three time constants are calculated from these models that represent 

respectively the fuel resistance (UO2 or BN and Monel), the clad resistance and the film 

resistance. Results are reported in the following Table 6.16: 

 Table 6.16 Comparison of Calculated Time Constants 

Time constant (sec) RBHT PWR BWR 

Fuel, τf 0.55 3.99 5.98 

Clad, τc 0.36 0.68 1.15 

Film, τfilm 0.74 0.24 0.36 

The fuel time constant τ and clad time constant f τ c are used in groups Π24 and Π27, respectively. 

The calculation of the P34 group defining direct contact heat transfer requires some explanation,

( ) Π34 = − = hA T T

Q V

lw i lw i co sat

fi fi

, ,

,

''' ,

Liquid contact HT rate

Heat generation rate

To calculate the direct contact heat transfer for the dispersed droplet field, the Forsland 

Rohsenow correlation is used as follows 

( )( )( ) ( ) q ( g Hk

TT D dcht v T T f g fg

w sat g d

w sat ''

*

= − . . −

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥ 0 2 1276 1 − 2

3

3

1

4

α

ρ ρ

μ ) (6-116) 

In the calculations, it is assumed that the liquid is saturated such that H h . fg fg

* =

The properties are evaluated at 60 psia and the calculations are performed for different void 

fractions and wall superheats. The droplet area is calculated assuming a uniform distribution of 

drops. Only drops within a diameter of the rod can interact. The number of drops is given by 

( ) N

d d =

6 1−

3

α

π

 (6-117) 

With a mean void fraction value of 0.995, and a drop diameter of 0.04 in, the number of drops is 

calculated as 

 Nd = 9.104 drops/cm3 (149.2 drops/in3) 

205
206

The drops (max) that can interact with the rod are those which are within one drop diameter of 

the rod surface. 

 Rod diameter = 9.5 mm (0.374 in) 

 Rod diameter + diameter of two drops = 0.374 in + 2·(0.04 in) = 11.53 mm (0.454 in) 

 Area of the region occupied by two drops = (22/7)·(0.4542

 - 0.3742) = 33.55 mm2 

(0.052 in2

) 

 Subchannel area = (pitch)2

 - area of rod = 88.135 mm2 (0.13661 in2)

The area fraction of the drops that can hit the rod is the ratio of the area occupied by two drops 

to the subchannel area. 

 Area fraction = 0.052/0.13661 = 0.395 

From the information of the area fraction and the number of drops per cubic inch, the resultant 

number of drops that can contact the wall is calculated as 

 (0.395)·(149.2) = 59 drops. 

Since only one side of a drop contacts the rod, the total contact area is given as: 

 Total contact area = 0.5 (spherical area per drop)·(Resultant number of drops) = 

 95.66 mm2

 (0.14828 in2) 

Knowing all the values for the variables in equation 6-116, the heat flux is calculated for various 

values of (Tw - Tsat). From this, the heat transfer coefficient can also be calculated. For the Pi 

group calculation, the values of heat transfer coefficient, the contact area and the heat 

generation rate are known. The numerical value of the Pi group can be evaluated for various 

values of (Tco - Tsat), each time using the appropriate value of h. The value of Π34 tabulated in 

the result is for a temperature difference of 537.77 degrees C (1000 degrees F). The calculated 

Pi values are given in Table 6.17. 

Table 6.17 Convection and Stored Energy Pi Groups for Electrical/Nuclear Rod 

π group Electrical Rod Nuclear Rod PWR 

π24 0.965 1.180 

π25 0.182 0.182 

π26 1 1 

π27 0.110 0.04 

π28 0.016 0.016 

π29 0.73 0.73 

π30 0.73 0.73 

π34 0.005 0.005 
6.5.3 Thermal Radiation Heat Transfer Pi Groups 

The radiative heat transfer from the rod is expressed by the terms Π31, Π32, Π33, Π35, and Π36. 

The reference rod, for which the energy balance is described, is assumed to be a rod in the 

central region of the bundle, specifically in the inner 3x3 sub-array. These Pi groups describe 

the radiative heat transfer from the hot rod to dummy rods, to housing, to liquid droplets, to 

vapor and to the nominal rods in the outer region of the bundle. Due to the housing, the outer 

region of the bundle will be at a lower temperature compared to the inner region. This will 

cause a radial temperature distribution across the bundle which will drive rod-to-rod radiative 

heat transfer from the center region. A detailed model to address this phenomenon has been 

developed and is described in Section 7. 

The same phenomenon exists for the Pi groups for the rod equation, as 

 

( )

Π31 =

−

=

h A TT

Q V

Q

Q V

R r

s i R rs i co s

fi fi

r

s

fi fi

,, ,,

,

''' , , ''' ,

 (6-118) 

( )

Π32 =

−

=

h A TT

Q V

Q

Q V

R r

H i R rH i co H

fi fi

r

H

fi fi

,, ,,

,

'''

, ,

'''

,

 (6-119) 

( )

Π33 =

−

=

h A TT

Q V

Q

Q V

R hr cr i R hr cr i co hr co cr

fi fi

hr cr

fi fi

,, ,, , ,

,

''' , , ''' ,

 (6-120) 

( )

Π35 =

−

=

h A TT

Q V

Q

Q V

R r

d i R r

d i co sat

fi fi

r

d

fi fi

,, ,,

,

'''

, ,

'''

,

 (6-121) 

( )

Π36 =

−

=

h A TT

Q V

Q

Q V

R r

v i R rv i co v

fi fi

r

v

fi fi

,, ,,

,

'''

, ,

'''

,

 (6-122) 

These dimensionless groups are calculated by solving the six node radiative network already 

discussed in the previous section. In this case, a different set of boundary conditions is used 

from previously discussed (Table 6.2). 

The radiative heat transfer from the rod to the surfaces (unheated rods) is described by 

 

Π31 =

Q

Q V

r

s

fi fi ,

''' ,

207
where Qr/s and have both dimensions of heat rate per unit length. The heat rate Qr/s 

is the energy flowing from one of the hot rods (inner 3x3 sub-array) to the dummy rods and the 

normalization factor Q V is based to the peak power location: 

Q V fi fi ,

''' ,

f i,

'''

f i,

Q V = 0.7 kW/ft = 2296 W/m (6-123) fi fi ,

'''

,

From the network solution 

Q Q r

s

= 13

The heat rate is identically zero since the view factor from the inner 3x3 rods to the unheated 

rods at the corners is identically zero. As a consequence, the resistance R12 becomes infinite 

and 

Π31 = 0 0.

The same procedure is applied for the calculation of the next Pi group representing the direct 

radiative heat transfer from the rod to the housing 

 

Π32 =

Q

Q V

r

H

fi fi ,

'''

,

where 

Q Q r

H

= 14

which gives 

Π32 = 0 0272 .

The radiative heat transfer from the hot rod to the cold rods (rod-to-rod) radiation is expressed 

by 

Π33 =

Q

Q V

hr cr

fi fi ,

''' ,

where 

Q Q hr cr= 12

which gives 

208
Π33 = 0 388 .

The heat rate from the hot rod to the droplet and the vapor, respectively, is described by 

 

Π35 =

Q

Q V

r

d

fi fi ,

'''

,

Π36 =

Q

Q V

r

v

fi fi ,

''' ,

From the network, Qr/d and Qr/v are 

Q Q r

d

= 1l

Q Q r

v

= 1v

The calculated result becomes 

 

Π35 = 0154 .

Π36

4 = 7 88 − . e

The results of the calculations are summarized in Table 6.18. As seen in the table, the rod-torod radiative heat transfer (hot rod to cold rod) is the largest contribution. This term can also be 

seen as an indirect path for radiative heat transfer from the inner rods to the housing. In fact the 

housing reduces the temperature of the external rods because of radiation heat transfer. This 

generates a radial temperature gradient among the rods which drives energy from the inner 

region to the outer region of the bundle. This effect is more prototypical for a BWR than a PWR 

fuel assembly due to the fuel channel used for BWRs, and will be discussed further. 

This analysis overestimates the effect of the housing because the housing thermal resistance in 

the azimuthal direction is not considered since only one node is used to simulate the housing. 

To model this effect, the housing must be split in many separate surfaces with each surface 

thermally connected by azimuthal conductivity. This has been done in the more detailed 

COBRA-TF subchannel model described in Section 9. The COBRA-TF results indicate that the 

corners of the housing are at a lower temperature than the rest of the housing temperature 

predicted by the BUNDLE simple conduction model. In other words, for the same heat stored in 

the housing the more exposed portion of the housing surface will be at a higher temperature 

than predicted by a single surface model. This will reduce the heat removed by radiation from 

the heater rods. 

209
Table 6.18 Numerical Values of Pi Groups - Rod Energy Equation 

210
Table 6.18 Numerical Values of Pi Groups - Rod Energy Equation (Continued)

211
6.5.4 Summary 

The Pi groups obtained for the rod energy equation indicate that the significant terms are the 

convective heat transfer to the surrounding fluid, the radiation from hot rod to cold rod and 

radiation to entrained drops. Property differences between the electrical rod and the nuclear rod 

exist and hence the Pi groups involving the properties of the rods are different. One particular 

Pi group, Π24, is about 20 percent higher for the nuclear rod. This is because of the low thermal 

conductivity of UO2 and also due to the fact that at start up, a nuclear rod has very high amount 

of stored energy. The effect of this difference will be discussed in Section 7. 

6.6 Calculation of Pi Groups for Flow Momentum Equation

The flow momentum equation Pi groups are calculated using the given inlet conditions of 40 

psia, 140 degrees F subcooling, and flooding rate 25.4 mm/s (1 in/s) and flow area. The inlet is 

assumed to be single phase and the exit is dispersed two-phase mixture. The quench front is 

assumed to be at the 1.2 m (4 ft) elevation and two grids are underwater; therefore, there are 

six grids in the two phase region. Hydraulic diameter is calculated based on the wetted 

perimeter and flow area. Based on this hydraulic diameter, the Reynolds number and the single 

phase friction factor (f = 64/Re) are calculated. 

For two phase frictional pressure drop, all the two phase mixture is assumed to be liquid, so that 

a two-phase multiplier can be used. The exit void fraction is taken to be 0.999. For an average 

quality of 50 percent and low pressure conditions, it is appropriate to assume an average twophase flow multiplier, 2 φ fo , to be 100. 

Table 6.19 shows numerical values for all the Pi groups for the fluid momentum equation. 

Table 6.19 Fluid Momentum Pi Groups 

π Group Value 

π 37 = π 38 = π 39 8.9e-6

π 40 1 

π 41 = π 42 0.999 

π 43 = π 44 7.0e-4

The only Pi group of significance is Π40, which represents the liquid gravity head pressure drop. 

All other non dimensional groups are insignificant by comparison. This was expected since the 

differential pressure cells have been used to infer average void fraction in previous FLECHT 

and FLECHT-SEASET experiments because the frictional and acceleration effects are small. 

The calculated Pi groups, along with their definitions, are reported in Table 6.20. 

212
Table 6.20 Numerical Values of Pi Groups - Fluid Momentum Equation 

213
214

6.7 Calculation of PWR and BWR Pi Groups

6.7.1 Introduction 

Pi groups calculated for the RBHT Test Facility, a PWR and BWR assembly is given in 

Tables 6.14, 6.18 and 6.20. The values obtained were compared, and distortions due to 

scaling identified. Using this approach, it can be seen whether or not the RBHT Test 

Facility replicated prototypic behavior. The closer the values of the Pi group are for the 

test facility and the PWR or the BWR, the more similar is the behavior. The Pi groups 

which are not dependent on the material properties but only on the fluid conditions 

should be similar. Those Pi groups which are a function of the material properties will be 

different for the test facility and the PWR or the BWR, since the material properties are 

different. 

Table 6.3 compares the different Pi groups for the test facility and a PWR fuel assembly 

and indicates possible test distortions relative to the fuel assembly being modeled. 

These comparisons indicate that many of the Pi terms are preserved since the rod 

bundle geometry models that of a PWR fuel assembly and the initial conditions are 

preserved in the tests relative to the reactor. However, there is no housing in the PWR 

fuel assembly. So to ensure similarity, the Pi groups which represent the heat transfer 

processes associated with the housing must be small relative to the other transport 

terms in Equation 6-26. 

Similarly, Table 6.4 compares the Pi groups for the test facility to the Pi groups for the 

BWR fuel assembly. Since the BWR assembly has a channel surrounding the fuel rods, 

the same terms and Pi groups derived for the RBHT Test Facility are also present for the 

BWR fuel assembly. The terms can have different magnitudes since the materials are 

different between the test and the BWR fuel assembly. 

6.7.2 Calculation of Pi Groups for PWR 

The Pi groups for the fluid energy, which represent the flow energy, energy storage, 

convection to rods, housing, grids and dummy rods were evaluated for a PWR. Firstly, 

there is no housing for a PWR, hence the convection heat transfer from the vapor to the 

housing is zero. Those Pi groups which are dependent only on the flow conditions and 

independent of the material properties, will be the same for the test facility and the PWR, 

since the geometry, including the dimensions of rods, grids, etc. for the test facility and 

the PWR are the same. 

Therefore, the fluid energy storage, flow energy, and convection Pi groups are all 

identical for the PWR. Thus, the only Pi groups that will be different are the quench 

terms and those involving radiation heat transfer. 

The PWR quench energy groups Π3, Π4, Π5 and Π6 are calculated using the same 

method as for the RBHT Test Facility, however, the PWR core material properties and 

geometry are used (Zircaloy, UO2, etc.). Note that in this case the housing is not 

present and the scaling group describing the quench of the housing is zero by definition. 

The calculated values are reported in Table 6.14. 
The thermal radiation Pi groups for the PWR are calculated with a modified version of 

the RADNET computer program to account for the typical Westinghouse 17x17 rod 

bundle geometry. In a PWR, the housing is not present and only portion of the core 

section is considered. The situation assumed in the calculation is that of a hot assembly 

surrounded by eight colder assemblies as depicted in Figure 6.5. To reduce the size of 

the problem, this core portion (nine assemblies) is assumed to be 90 degrees 

symmetric. Moreover, because of the geometry, radiation from the hot assembly cannot 

penetrate beyond seven rows into the cold rods. This reduces the problem to a 15x15 

array. Thimble locations are described in the same Figure 6.5. At this point, the 

VUEFAC subroutine of the MOXY code is used to calculate the single rod-to-rod view 

factors matrix and these values are combined to produce the global view factors. The 

node surface areas are calculated in the computer program RADNET, as described in 

Appendix B.1. 

Figure 6.5 PWR Bundle Lumping Approach.

To simulate the absence of the housing in a PWR core, the resistances from each node 

to node 4 in the network are set to a very large number (practically infinite). Then the 

same node temperatures for the RBHT Test Facility are applied at the network external 

nodes and the program is solved for the radiosity in the other nodes. Finally, following 

the same procedure utilized for the RBHT case, the PWR fluid energy equation Pi 

groups for radiation heat transfer are calculated. 

215

The numerical values for PWR Pi groups for the radiation terms for the fluid energy and 

rod energy equations are shown in Tables 6.14 and 6.18. 
216

Similar to the RBHT, the fluid momentum Pi groups are calculated for the PWR and 

results are reported in Table 6.20. 

The Pi group for the interfacial heat transfer will be the same for the test facility, PWR 

and BWR. 

Comparing these terms to that for the test facility, minor differences can be seen. The 

spacer grids used in the test are prototypical, so the form loss term will be the same for 

both the plant and the test. The frictional term, however, can be different since in the 

test there is a housing which adds additional wetted perimeter such that the hydraulic 

diameter is smaller for the same flow area. The smaller hydraulic diameter results in a 

lower Reynolds number for the same flow condition and hence a higher friction factor, 

but the differences in the values are quite small. The emissivity of Inconel 600 is slightly 

lower than Zircaloy and this causes some differences in radiation terms. 

6.7.3 Calculation of Pi Groups for BWR 

The Pi groups for the fluid energy, which represent the flow energy, energy storage, 

convection to rods, housing, grids and dead rods have been evaluated for a BWR. 

Since the BWR fuel assembly is surrounded by a channel, which acts as a housing, the 

Pi groups related to the housing are not zero as in a PWR. It should be noted that the Pi 

groups which are dependent only on the flow conditions and independent of the material 

properties and geometry are the same for the RBHT Test Facility and the BWR fuel 

assembly. 

In the fluid energy equation, based on the above, it is evident that the Pi groups 

representing the fluid energy storage terms and, the flow energy terms, Π1, Π2, Π7, Π22

and Π23, will be the same as that of the test facility, as they depend only on the flow 

conditions. The interfacial heat transfer term, (Π20) will also be the same as it depends 

only on the fluid condition and the number of drops. The Pi groups for the convection to 

rod, housing, grid and dead rod will be different because of a different rod diameter for a 

BWR fuel rod. 

The stored energy and convection terms for the rod energy equation Pi groups for BWR 

are somewhat different because the dimensions of the rod is different for a BWR 

compared to a PWR. Also the time constants for the cladding and the fuel are higher for 

a BWR. These Pi groups are presented in Tables 6.14 and 6.18. 

 

The BWR quench energy groups are calculated by the same method used for the RBHT 

Test Facility, using BWR core material properties and geometry (Zircaloy, UO2, etc.). 

For simplicity, the same Tmin is assumed in the calculation for both Zircaloy and Inconel. 

Note that in this case the housing is represented by the channel walls. The quench 

energy Pi groups for the BWR are shown in Table 6.14. 

To calculate the thermal radiation Pi groups for the BWR, the RADNET computer 

program was modified to account for the different bundle geometry typical of a typical 

GE 8x8 rod bundle. In this case the housing is represented by the channel walls. The 

situation assumed in the calculation is a 4x4 hot assembly surrounded by two rows of 

colder assembly as depicted in Figure 6.6. The cold surfaces are the two water rod in 
the center of the channel. The VUEFAC subroutine of the MOXY code is used to 

calculate the single rod-to-rod view factors matrix and then by combining properly these 

values, the global view factors and node surface area are calculated in the RADNET 

computer program, as described in Appendix B.1 for the RBHT Test Facility. 

Figure 6.6 BWR Bundle Lumping Approach. 

The same node temperatures used for the RBHT Test Facility are applied at the network 

external nodes and the program solves for the radiosity in the other nodes. Finally, 

following the 

same procedure utilized for the RBHT case, we calculate the BWR fluid energy equation 

Pi groups for the radiation heat transfer. The numerical values are reported in Tables 

6.14 and 6.18. 

The Pi groups for the fluid momentum equation for the BWR will be the same as that of a 

PWR, based on the conditions of flooding rate of 1 in/s. 

6.8 Conclusions

The fluid energy equation, the rod energy equation and the bundle fluid momentum 

equations have been developed for the RBHT Test Facility. These equations were 

made dimensionless using the initial and boundary conditions such that dimensionless 

Pi groups were developed to examine similitude between the RBHT Test Facility and a 

PWR and a BWR fuel assembly. From the scaling analysis, it is found that the presence 

of a test housing leads to extra Pi groups for this structure relative to a PWR fuel 

assembly, thereby indicating that distortion in the test is possible. 

The test facility is actually a closer representation to a BWR fuel assembly which also 

has a Zircaloy channel or shroud surrounding the fuel rods. Therefore, for code 

modeling and validation purposes, the effect of the test housing must be modeled 

including the rod-to-rod and rod-to- housing radiation heat transfer. The housing effects 

must also be considered in the analysis of the test data to determine effect of radiation. 

217
218

The housing had a less important effect on the fluid momentum equation since it only 

affected the hydraulic diameter and resulting fluid Reynolds number and friction factor 

such that the frictional component of the fluid pressure drop would be somewhat larger 

than a PWR fuel assembly. Since the majority of the pressure drop in the bundle is due 

to the spacer grid form losses and the elevation head and since the prototypical grids 

are used in the test bundle, the hydraulic distortion is negligible. 

There also can be some difference in the PWR/BWR Pi groups relative to the test due to 

the material differences as seen in Tables 6.14, 6.18 and 6.20. These effects are 

relatively small and can be accounted for in the analysis of the data. 

Comparisons of the derived Pi groups for the test and a PWR and a BWR fuel assembly 

indicate that if prototypical fluid conditions are used in the tests, and the bundle 

geometry is retained, there is a very strong similarity between the bundle and the PWR 

and BWR fuel assemblies and the data should be applicable to either reactor fuel 

assembly type. 

6.9 References

1. Larson, T. K., et al, ”Scaling Criteria and Assessment of Semi-scale Mod-3 Scaling 

for Small-Break Loss of Coolant Transients,” EGG-SEMI-5121, 1980. 

2. Ishii, M. and I. Kataoka, “Scaling Criteria for LWRs under Single-Phase and TwoPhase Natural Circulation,” Proc. Joint ANS/NRC Meeting on Basic ThermalHydraulic Mechanisms in LWR Analysis, NUREG/CP-0043, Bethesda, MD, 1982. 

3. Zuber, N., “An Integrated Structure and Scaling Methodology for Severe Accident 

Analysis, Appendix D, A Hierarchical Two-Tiered Scaling Analysis”, NUREG/CR5809, 1991. 

4. Wulff, W., “Scaling of Thermal Hydraulic Systems,” Nuclear Engr. and Design, Vol 

163, pg. 359-395, 1996. 

5. Zuber, N., “Presentation at March 28, 1997 ACRS Thermal Hydraulic Phenomena 

Subcommittee Meeting,” Rockville, MD. 

6. Reyes, J. R., Hochreiter, L. E. and L. Lau, “AP600 Low Pressure Integral systems 

Test at Oregon State University, Facility Scaling Report,” WCAP-14270, 1995. 

7. Brown, W. L., Hochreiter, L. E. and M. J. Loftus, “AP600 Scaling and PIRT Closure 

Report”, WCAP-14727, 1997. 

8. Lee, N., Wong, S., Yeh, H.C. and L. E. Hochreiter, “PWR FLECHT-SEASET 

Unblocked Bundle Forced and Gravity Reflood Task Data Evaluation and Analysis 

Report,” NUREG/CR-2256, 1981. 

9. Mohr, C. L. et al., “Prototypic Thermal-Hydraulic Experiment in NRU to simulate 

Loss-of-Coolant Accidents,” NUREG/CR-1882, 1981. 
219

10. Kreith, F. and M. S. Bohn, “Principles of Heat Transfer,” Fourth Edition, Harper and 

Row Publishers, New York, 1986. 

11. Evans, D.R., “The MOXY Core Heat Transfer Program: View Factor Model 

Improvements,” RE-E-77-114, 1977. 

12. Collier, J. G. and J. R. Thome, “Convective Boiling and Condensation,” Oxford 

Science Publications, Oxford, 1994. 

13. “An Integrated Structure and Scaling Methodology for Severe Accident Technical 

Issue Resolution,” NRC Research, NUREG/CR - 5809, Nov 1991. 

14. Lewis, E. E., “Nuclear Power Reactor Safety,” John Wiley & Sons, New York, 1977. 
220
 

221

7. SECOND TIER SCALING FOR THE ROD BUNDLE HEAT 

TRANSFER TEST FACILITY 

7.1 Introduction

Following the two-tier scaling methodology approach, Section 6 examined the “Top Down” 

scaling of the RBHT Test Facility relative to a PWR fuel assembly as well as a BWR fuel 

assembly. The individual Pi groups were calculated from the normalized conservation 

equations for the test facility, a PWR fuel assembly and a BWR fuel assembly. The calculations 

indicated which terms in the conservation equations were dominant for each configuration. The 

ratio of the Pi group calculations for the test and either the PWR or BWR fuel assembly 

indicated where the test facility had possible scaling distortions. The distortions were larger for 

the representation of the PWR fuel assembly by the RBHT test facility as compared to a BWR 

fuel assembly since there is no fuel assembly channel in the PWR fuel assembly, as compared 

to the test facility, while the BWR fuel assembly contains a fuel channel. 

The top-down scaling analysis indicated three areas where scaling distortion could exist in the 

RBHT test facility relative to a PWR or BWR fuel assembly. They are: 

1. The presence of the housing which can act as a radiation and convection heat sink for the 

fluid and heater rods, as well as a heat source to the fluid as the housing quenches. The 

housing also changes the hydraulic diameter of the outer subchannels slightly such that 

there is lower flow in the outer subchannels, and correspondingly higher flow in the center of 

the bundle. However, this effect is small. 

2. The material differences between the electrical heater rods and the nuclear rods which 

include a gap between the fuel pellet and the cladding 

3. The material differences in the cladding which can affect the Tmin value and hence the 

quenching rate of the heater rods verses nuclear rods. Also included in this difference are 

the local effects of the surface, including roughness and oxide layer. 

The bottom-up scaling effort has been performed specifically to examine these differences so 

that identified distortions can be assessed and methods found to account for or minimize their 

effects in the testing, data reduction, and data analysis. In the bottom-up scaling approach, 

analysis was performed to determine the radiation heat transfer effects of the test section 

housing relative to an infinite size rod bundle. These calculations would tend to over-emphasize 

the distortion of the test relative to a PWR fuel assembly. The BWR fuel assembly channel is 

similar to that of the RBHT facility so the distortion is less. 

Calculations were also performed modeling a fuel rod, with its properties and the fuel- pellet gap 

as well as the electrical heater rod, to determine the heat released at quench as well as the 

stored energy effects and maximum temperatures and radial temperature distributions. 

The differences in cladding material on the value of Tmin were assessed by comparing Inconel 

and Zircaloy cladding quench data from different tests. These comparisons indicated that 

Zircaloy quenches at a higher temperature relative to stainless steel or Inconel cladding. 
The analysis and data comparisons for each of the identified areas of distortion are given in the 

remainder of this Section. 

7.2 Housing Effects and Studies

7.2.1 Introduction 

One of the main distortions of the RBHT facility compared to a PWR fuel assembly is the 

presence of the housing, which represents a heat sink for radiative heat transfer from the rods. 

The housing can also be a heat source for the fluid later into the transient because of the 

release of its stored energy during the quench time period. 

To address housing effects in more detail, a single rod-to-rod, rod-to-housing model based on 

the MOXY computer program (Ref. 1) was developed. MOXY was used to calculate the view 

factors matrix while a new program was written, called BUNDLE, to calculate the combined 

conduction-convection-radiation heat transfer in a cross section of the rod bundle. The 

BUNDLE program considers a cross section with each rod simulated individually, as well as the 

housing. 

Figure 7.1 Convective Heat Transfer Coefficient (FLECHT-SEASET Run 31504). 

The VUEFAC subroutine was extracted from the MOXY computer program and included in 

BUNDLE to calculate the view factors matrix. The program calculates the temperature field in 

the bundle cross section during the reflood transient. The model solves thermal conduction in 

the rods and the housing, convection heat transfer to the fluid and radiative heat transfer among 

 

222
 

223

the rods and the housing surfaces. Convection to the fluid is simulated by assigning the time 

history of the heat transfer coefficient estimated from the FLECHT-SEASET Run 31504 test 

data (Ref. 2), as shown in Figure 7.1. In addition, when the temperature in the hottest rod falls 

below Tmin, the heat transfer coefficient is set to a very large value 5678 W/m2

-K (1000 Btu/hrft2

-F) to force all the structures to quench at that time. 

The radiative heat transfer to the droplets and to the vapor is neglected in the BUNDLE program 

while fluid is assumed transparent to the radiation. The thermal radiation heat transfer between 

the surfaces and the fluid (steam and droplets) is considered in the simplified lumped parameter 

approach using the RADNET computer program described in Section 6.4.4. More details of the 

model as well as the computer program list can be found in Appendices C.1 and C.2. The base 

case was a 7x7 bundle with four zero power (dummy) rods in the corner of the array. The other 

parameters are given in Table 7.1. 

Table 7.1 Input Data 

Rod Power (kW/rod) 5.0 kW/ft. 

Power radial distribution Uniform 

Wall surface emissivity 0.80 

Bundle heat loss (hout), W/m2

-K (Btu/hr-ft2 -F) 0 

Fluid convective heat transfer coefficient (hin) See Figure 7.1 

Initial temperature dummy rods, o

C (oF) 232.22 (450) 

Initial temperature power rods, o

C (oF) 871.11 (1600) 

Initial (pre-heating) temperature, o

C (oF) 232.22 (450) 

Fluid temperature, o

C (oF) 147.5 (268) (Tsat) 

The heat transfer coefficient at the inside surface of the housing is assumed equal to the 

convective heat transfer coefficient used for the heater rods and is based on FLECHT-SEASET 

Test data. 

7.2.2 Results 

Figure 7.2 shows the clad temperature of the center rod, the inner 3x3 and 5x5 array averages, 

the housing and cold (dummy) rods surface temperature. The PCT temperature is reached at 

about 50 s while the maximum housing temperature is reached later at about 200 s. At about 

250 s the clad temperature at the hottest rod falls below Tmin and all structures are quenched. 

Note that the quenching time of the housing is larger than that for the other structures. Figure 

7.3 shows the heat rate (W/m) release from the rods to the housing and the heat released from 

the housing to the fluid. The heat transfer rate is very high when the housing quenches. Figure 

7.4 shows the same results with an expanded y-axis. The maximum heat transfer rate from the 

rods to the housing is about 25 percent of the heat generated in the bundle. The housing 
Figure 7.2 Wall Surface Temperature in the 7x7 Bundle (Base Case). 

Figure 7.3 Heat Rate To and From the Housing in the 7x7 Bundle (Base Case) 

(Bundle Linear Power = 103000 W/m). 

 

224
Figure 7.4 Clad Temperature Drop in the Inner 3x3 Array Because of Radiative Heat 

Transfer in a Finite Size Bundle Array. 

releases energy to the fluid early in transient by convection to the steam and later to the mixture 

during the quench time. 

The heat transfer from the rods to the fluid, particularly from the outer rods, can be a two-step 

process in which the energy first passes to the housing via radiation and then to the fluid by 

convection. This is described by Figure 7.4 which shows that the radiative heat rate from the 

rods to the housing reaches its maximum value of 24 kW/m at about 35 s, then 

decreasesalmost linearly to 2 kW/m at about 245 s, when quench occurs. In the same time 

period, the convective heat rate from the housing to the fluid rise from nearly 0 to about 15 

kW/m. Then the remaining energy stored in the housing is released during the quench period 

which last about 20-30 s. During quenching, the convective heat rate from the housing to the 

fluid increases to 400 kW/m. 

Note that the temperature gradient which develops radially across the bundle as a consequence 

of the presence of the housing is overestimated by these calculations because of the 

assumptions used. In reality, thermal radiation from the rods to the fluid (droplets and vapor) 

will tend to reduce the temperature of the inner rods, therefore, the heat transfer to the external 

rods and the housing will be lower than the calculated value. Another effect is the convective 

heat transfer coefficient, which is assumed uniform in the calculation. In reality, the convective 

heat transfer coefficient will be higher in the center region of the bundle. Again, this effect will 

reduce the temperature gradient across the bundle. 

 

225
 

226

tive 

the housing was estimated to be 10 to 20 percent of the 

onvective heat transfer depending on the flow conditions. Note that the FLECHT bundle was 

ensitivity studies were performed to the base case (Table 7.1) to optimize the facility designing 

llows: 

, 7x7,...,17x17,infinite) 

. radial power distribution

ed in the following and presented in Figures 7.5 through 7.10. 

r 

ted for 

ubrence represents the facility distortion when compared to the temperature 

xpected when the same boundary condition are applied in a real PWR core which is essentially 

dle 

re in the finite size bundle. Figure 7.4 shows that the quench time is anticipated 

y about 17 s in 5x5 bundle, by about 7-8 s in the 7x7 bundle and a smaller value for larger 

s 

1 bundle. 

temperature distortion experienced in a 7x7 bundle. In conclusion, when compared to the 

infinite bundle array, the 7x7 bundle is good compromise when low costs and scaling biases are 

Quasi steady-state calculations were carried out for the FLECHT 15x15 bundle using a radia

network approach (Ref. 3) similar to the one described in Section 6. In this case the radiative 

heat transfer from the inner rods to 

c

larger than the 7x7 RBHT bundle. 

S

by reducing the scaling bias where possible, as fo

1. bundle size (3x3, 5x5

2. housing thickness

3. housing pre-heating

4. surfaces emissivity

5

6. dummy rods (cold-surfaces) contribution

Results are summariz

7.2.2.1 Bundle Size

The calculation of the clad temperature for an infinite array with a constant radial powe

distribution results in a rod-to-rod temperature gradient which is zero since radiative heat 

transfer does not take place and the clad temperature is determined only by the fluid 

convection. An indication of the radiative heat transfer contribution for a finite array is the 

difference between the average clad temperature in the central rods sub-array as calcula

a finite size bundle and the same value calculated for an infinite size bundle. The selected s

array is the inner 3x3 rods and the temperature drop defined is ΔT∞ = ΔT∞ - T3x3 . This 

temperature diffe

e

an infinite array. 

Figure 7.4 shows the value of ΔT∞ for different bundle sizes (5x5, 7x7, 9x9 and 11x11). The 

time at which the quench is occurring is earlier in the finite bundle respect to the infinite bun

case. As a consequence, the significant clad temperature drop which is experience during the

quench is earlier than in the small bundle size. This effect is indicated in Figure 7.5, which 

shows the difference between the clad temperature in the hypothetical infinite bundle and the

clad temperatu

b

bundle sizes. 

Before the quenching, the maximum temperature distortion is reached between 150 and 200 

into the transient, depending on the bundle size. For the 7x7 bundle, a maximum value of 138 

degrees C (250 degrees F) is predicted, the maximum distortion decreases to 83 degrees C

(150 degrees F) for a 9x9 bundle and to 55.6 degrees C (100 degrees F) for an 11x1

For the 5x5 bundle size the maximum temperature distortion is up to 222.4 degrees C (400

degrees F) which is much larger than the 138 degrees C (250 degrees F) maximum 
Figure 7.5 Heat Rate To and From the Housing in the 7x7 Bundle (Base Case) 

(Bundle Linear Power = 103000 W/m). 

Figure 7.6 Inner 3x3 Rod Array Clad Temperature Bias in RBHT Bundle 

Housing Thickness Sensitivity. 

 

227
 

228

both a concern in the facility design. A larger bundle will provide a more prototypic behavior 

with a reduced temperature bias but the costs due to the additional rods increases dramatically. 

7.2.2.2 Housing Thickness

The housing is both a heat sink and a heat source during the reflood transient, and represents a 

bias which should be minimized by reducing its thickness to a minimum. The housing is a heat 

sink for the thermal radiation from the external rods and is a heat source to the fluid as the 

quench front approaches, as seen in Figure 7.5. The housing heat release is very large during 

quenching. A 6.35 mm (3 in) thick housing was chosen to provide enough strength for the 

facility operation. To quantify the effect of the housing thermal inertia, two sensitivity cases 

were run with 6.35 and 4.76 mm (3

/16 and 3 in) thick housing. Results shown in Figure 7.6 

indicate that in this range the solution is insensitive to the housing thickness. In conclusion the 

variation of the housing thermal inertia is negligible in the thickness range of interest. 

7.2.2.3 Housing Preheating 

To reduce the rod temperature drop introduced by the presence of the housing, the housing 

could be pre-heated before the reflood begins to reduce the radiative heat transfer between the 

rods and the housing during the early part of the reflood. An optimum preheating temperature 

value will exist. A high temperature reduces the radiative transfer between rods and housing; 

however, it increases the metal heat release to the fluid during quenching. The base case 

considered an initial housing temperature of 250 degrees C (450 degrees F) while the sensitivity 

case assumed an initial housing temperature of 556 degrees C (1000 degrees F). Results are 

shown in Figure 7.7. The temperature drop ΔΤ4 for the center 3x3 array is lower for higher preheating temperature, 556 degrees C (1000 degrees F), but the difference between the two 

cases is less than 40 degrees F, indicating that initial heating has a weak effect. 

7.2.2.4 Surface Emissivity

Some uncertainty exists in surface emissivity, which is a function of surface conditions 

(roughness, oxidation, etc.). Emissivity, in turn, affects radiative heat transfer. For oxidized 

Inconel-600, the literature provides emissivity values ranging from 0.7 and 0.9. A sensitivity 

analysis was performed to address this effect. Figure 7.8 shows that the temperature 

uncertainty introduced by the emissivity uncertainty is less than 11 degrees C (20 degrees F). 

7.2.2.5 Axial Power Distribution 

The base case considers a uniform radial profile with zero power in the four corner rods. The 

possibility of increasing the peripheral rods to provide a Ashield@ to rod-to-housing heat transfer 

was investigated. A 20 percent increase in power was applied to the external rods while 

keeping the same (5.0 kW/rod) power in the interior rods (i.e., the total power in the bundle 

increases by about 9 percent). Figure 7.9 shows that the maximum value of ΔΤ4 decreases of 

about 20 degrees F.
Figure 7.7 Inner 3x3 Rod Array Clad Temperature Bias in RBHT Bundle 

Housing Initial (Pre-Heating) Temperature Sensitivity. 

Figure 7.8 Inner 3x3 Rod Array Clad Temperature Bias in RBHT Bundle 

Wall Emmissivity Sensitivity. 

 

229
Figure 7.9 Inner 3x3 Rod Array Clad Temperature Bias in RBHT Bundle 

Radial Power Distribution Sensitivity. 

Figure 7.10 Inner 3x3 Rod Array Clad Temperature Bias in RBHT Bundle 

Dummy Rods Effect. 

 

230
 

231

7.2.2.6 Effect of the Corner Dummy Rods 

The effect of the dummy rods in the four corners of the bundle is shown in Figure 7.10. The 

calculation is based on the same rod power (5.0 kW/rod) and the total power of the bundle is the 

same of the previous sensitivity case (9 percent greater than the base case). The effect of the 

dummy rods is to decrease ΔΤ4 by about 10 degrees F. This is a secondary effect to the 

radiative heat transfer from the inner rods in the bundle. The conclusion from the six sensitivity 

studies is that the parameter of most importance is bundle size. A large gain (~50 percent) 

occurs in increasing the bundle size from 5x5 to 7x7. Further gains are made by increasing the 

bundle size to 11x11, however, the facility cost would increase accordingly by approximately a 

factor of four. The other parametric variations are small by comparison. 

7.3 Material Differences

7.3.1 Introduction 

Another issue which arose from the scaling analysis is the rod material differences. The 

electrical heater rods use Inconel-600 instead of Zircaloy for the clad and Boron Nitride instead 

of Uranium Dioxide. The electric power is generated only in an annulus area inside the rod 

where the heating element, Monel K-500, is located. Another difference is the gap conductance 

which is assumed to be 5679 W/m2

-K (1000 Btu/hr-ft2-F) for a nuclear rod and 28385 W/m2-K 

(5000 Btu/hr-ft2

-F) for the electrical rod. A detailed analysis was performed to quantify the 

transient temperature response distortion of an electrical rod when compared with a nuclear rod. 

The BUNDLE computer program was used to simulate a transient conduction problem for a 

single rod. The radiation heat transfer is turned off for this case. The transient was basically a 

step change in the convection heat transfer coefficient while keeping constant rod power and 

fluid temperature. The step change was applied after a steady-state was reached where the 

surface temperature is assumed to be at Tmin. This transient can be a simplified view of the 

quench process. Consistent with Section 6, Tmin was set to 550 degrees C (1022 degrees F). 

The initial convective heat transfer coefficient is calculated assuming a steady state condition 

where the rod surface temperature is exactly at Tmin. The conditions of the transient are given in 

Table 7.2. 

7.3.2 Rod Comparison 

Figure 7.11 shows the temperature profile at the initial steady state for both the heater rod and 

the nuclear rod with a clad surface temperature of 550 degrees C (1022 degrees F). The 

difference in the profiles is because of conductivity: UO2 is about a factor 20 lower than the 

BN/Monel conductivity; therefore, the nuclear rod has a higher centerline temperature than the 

electric rod for the same clad surface temperature. 

An additional contribution to the above difference is the gap conductance which larger for the 

heater rod by approximately a factor of five. This effect is shown in Figure 7.12. 
Table 7.2 Input Data 

Rod Power (kW/rod) 0.7 kW/ft. 

Fluid temperature, o

C (oF) 131 (267) 

Initial heat transfer coefficient, W/m2

-K (Btu/hr-ft2 -F) 183.4 (32.3) 

Final heat transfer coefficient, W/m2

-K (Btu/hr-ft2 -F) 5679 (1000) 

Initial Tclad = Tmin 550 (1022) 

Conductivity of UO2, W/m-K (Btu/hr-ft-F) 2.4 (1.4) 

Conductivity of BN, W/m-K (Btu/hr-ft-F) 85.9 (49.6) 

Gap Conductance (nuclear rod), W/m2

-K (Btu/hr-ft2 -F) 5679 (1000) 

Gap Conductance (electrical rod), W/m2

-K (Btu/hr-ft2 -F) 28385 (5000) 

Figure 7.11 Steady-State Temperature Profile. 

 

232
Figure 7.12 Electrical Rod Steady-State Temperature Profile Gap Resistance Sensitivity. 

The top-down analysis indicated that the stored energy in the fuel region is comparable between 

the nuclear rod and heater rod. On the other hand, more energy is stored in the Inconel 

cladding than Zircaloy cladding so that the total amount of stored energy is somewhat larger for 

the heater rod. The larger amount of energy which resides in the cladding of the heater rod is 

released quickly during quenching, as shown in Figure 7.13. Figure 7.14 shows the amount of 

stored energy released during the transient. This value was calculated by integrating over time 

the power released minus the power generated as: 

∫ −= t

o quench o))(( dtqtqE

where 

( )

( )

q t

q

t

o

o

=

=

=

Power released to the fluid

Rod Power 0.7kW / ft

Initiation of quench

Figure 7.14 shows that the electrical rod releases a larger amount of energy more quickly. The 

time constant for the energy release is consistent with that calculated with a simple doublelumped approach, described in Section 6. 

 

233
Figure 7.13 Rod Quenching. 

 

234

Figure 7.14 Rod Quench Energy Release. 
7.4 Surface Properties Differences

The surface properties which can affect the reflood behavior are the wall surface emissivity and 

the factors that determine minimum film boiling temperature Tmin. 

The Zircaloy surface emissivity can be slightly higher than the Inconel-600 even though the 

uncertainty in its real value is sometimes larger than the difference between the two materials. 

The wall emissivity depends on many factors such as temperature and oxidation of the surface. 

The effect of the wall emissivity on the rod-to-rod and rod-to-housing radiative heat transfer was 

addressed by the sensitivity analysis presented in Section 7.2. 

Figure 7.15 shows the distribution (Ref. 6) of experimental rewet temperatures based on 

Westinghouse G-1 and G-2 blowdown experiments (Refs. 7 and 8). A mean value of 536 

degrees C (998 degrees F) was found. Prototypic thermal hydraulic experiments (Ref. 9) for 

Zircaloy cladding indicate an average value of 575 degrees C (1068 degrees F). Zircaloy will 

quench at higher temperature than stainless steel or Inconel. 

Figure 7.15 Distribution of Measured Rewet Temperatures During 

Westinghouse G-1 and G-2 Blowdown Rod Bundle Experiments. 

7.5 Scaling Conclusions 

The three areas where scaling distortion could exist between the RBHT Test Facility and a PWR 

or BWR fuel assembly were indicated during the first tier scaling analysis described in Section 

6. Section 7 presented the bottoms-up scaling analysis and addressed these distortions in 

more detail. 

 

235
 

236

During the early part of reflood, the housing acts as both a radiation and convection heat sink 

for the fluid and heater rods, whereas with the approach of the quench front it acts as a heat 

source. The presence of the housing causes a radial temperature distribution across the bundle 

which in turn drives energy from the inner portion of the bundle to the housing. As a result, 

during the transient, the temperature in the inner region of the RBHT bundle is lower than the 

temperature in an ideal case. 

The effect of the housing is less important for a large bundle since the inner region is shielded 

by the outer region of the bundle. Sensitivity analyses were performed to quantify the housing 

distortion for different bundle sizes, from 5x5 to 11x11 arrays. The distortion decreases 

significantly when the bundle size is increased from 5x5 to 7x7, while for further increases the 

distortion reduction is progressively less and less significant. A 7x7 bundle size is a reasonable 

compromise between cost and scaling distortion. For a 7x7 array, the maximum temperature 

distortion to the inner 3x3 rod array with respect to an infinite (no-housing) bundle is about 121 

degrees C (250 degrees F). 

 Sensitivity studies were performed to evaluate the effects of the housing thickness, housing 

initial temperature, emissivity, radial power distribution and dummy rods contribution. These 

were found to be of second order importance. Their effect on the temperature in the center 

region is about 28 degrees C (50 degrees F) at most. 

The material differences between the electrical heater rods and the nuclear rod, which also 

includes a gap between the fuel pellet and the cladding, is the second major facility distortion. 

The analysis shows that the quench time can be affected by material properties. The stored 

energy is 15 percent larger in the heater rod compared with the nuclear rod. The amount of 

energy in the fuel region is similar. The difference resides in the Inconel cladding of the heater 

rod. The conductivity of the “fuel” region of the electrical rod is 20 times higher than the nuclear 

rod. Therefore, if we assume the same heat transfer coefficient at the quench front, the stored 

energy is released more rapidly in the heater rod versus the nuclear rod. This introduces a bias 

in the experiments which must be determined. This bias will be lower than predicted by this 

simplified analysis. In fact, if more energy is released to a given volume of liquid, the heat 

transfer coefficient will decrease and this will in turn reduce the heat release rate in the electric 

rod.

In addition, differences of the cladding material on the value of Tmin were assessed by 

comparing Inconel and Zircaloy cladding quench data from different tests. These comparisons 

indicated that there is a difference. The Zircaloy cladding will quench at a higher temperature 

relative to stainless steel or Inconel cladding. 

7.6 References

1. Evans, D. R., “The MOXY Core Heat Transfer Program: View Factor Model 

Improvements”, RE-E-77-114, February 1977. 

2. Lee, N., Wong, S., Yeh, H.C. and Hochreiter., L.E. - “PWR FLECHT-SEASET Unblocked 

Bundle, forced and gravity reflood task. Data evaluation and analysis report”. - WCAP9891, November 1981. 
 

237

3. Yao, S.C., Dodge, C. and Hochreiter, L.E., “A simple Method for Calculating Radiative Heat 

Transfer in Rod Bundles With Droplets and vapors as Absorbing Media” - (Technical Note), 

J. Heat Transfer 101, ASME, 736, 1979. 

4. Sun, K.H., et al., “Calculation of combined radiation and convection heat transfer in rod 

bundles under emergency cooling conditions”, - J. Heat Transfer 98, ASME, 4141-420, 

1976. 

5. Kreith, F. and Bohn, M.S. - “Principles of Heat Transfer (Fourth Edition)” - Harper & Row, 

Publishers Inc., New York, 1986.

6. Zhang J., Bajorek S. M., Kemper R M., Hochreiter L. E., “WCOBRA-TRAC Analysis of 

ORNL High Flow Rod Bundle Film Boiling Tests”, National Heat Transfer Conference, 

ANS-HTC- Vol. 10, Baltimore, MD, 1997.

7. Cunningham, J. P., et al., “ECCS Heat Transfer Experiments with Upper Head Injection,” 

WCAP-8100, Vols 1 & 2, October 1974 and January 1975.

8. Andreycheck, T. S., et al., “Blowdown Experiments with Upper Head Injection in G-2 

17x17 Rod Array Facility,” WCAP-8582, Vols 1 & 2, Jan. 1976 and Aug. 1976. 

9. Mohr, C. L., at al., “Prototypic Thermal Hydraulic Experiments in NRU to simulate LOCA”, 

NUREG-CR-1882.
 

238
239

8. Instrumentation Requirements for the Rod Bundle Heat Transfer 

Test Facility 

8.1 Introduction

The objective of the RBHT Program is to provide data on the key thermal-hydraulic phenomena 

of interest for dispersed flow film boiling and reflood heat transfer. Instrumentation requirements 

were developed to provide the needed data. The required information was identified in the 

PIRT given in Section 2. As the PIRT indicates, information is needed to develop and/or 

validate specific heat transfer and two-phase flow models. Since the objective is to develop the 

component models which comprise Areflood heat transfer,@ data will be obtained to view the 

component models as identified in the PIRT. 

One of the more important objectives of the RBHT Program is to obtain new information on the 

mechanism of liquid entrainment at the quench front. This requires detailed measurements of 

the void fraction, droplet size, droplet velocity, and local heat transfer from the heater rods. The 

liquid entrainment at the quench front and the resulting droplet field downstream is responsible 

for the improved cooling at the upper elevations in the rod bundle where the peak cladding 

temperature occurs. Codes currently have difficulty predicting the correct amount of liquid 

entrainment as well as the timing of the entrainment. The instrumentation used in the RBHT 

Program will help resolve this modeling issue. 

The instrumentation plan and layout will follow the lessons learned from the FLECHT (Ref. 1) 

and FLECHT-SEASET (Ref. 2) reflood heat transfer programs as well as the ACHILLES (Ref. 3) 

experimental program. Both sets of FLECHT experiments and the Rod Bundle Heat Transfer 

experiments are separate effects tests with prescribed boundary and initial conditions. While 

there are needs for very specific data, which is difficult to measure, proven instrumentation will 

be used with redundant measurement techniques where possible and developmental 

instrumentation will be verified using bench-top experiments before installing in the test bundle. 

In addition, bundle mass and energy balances will be used to calculate parameters of interest 

from the data. 

8.2 Instrumentation Requirements

Perhaps the most basic requirement is to perform transient mass and energy balances on the 

test facility. Inlet flow, pressure, coolant temperature, outlet vapor flow, pressure, and liquid flow 

will be measured. Since the reflood tests are transients, there will be mass accumulation within 

the bundle. The mass accumulation will be measured using sensitive differential pressure (DP) 

cells with fine axial spacing. This approach was used successfully in the FLECHT and 

FLECHT-SEASET programs and mass balances were typically within five percent. The DP 

resolution in the current facility is finer than FLECHT. 

To obtain an axial void fraction distribution requires the use of several different measurements. 

These include inlet and exit measurements of each phase and axial heat flux into the coolant. 

The axial quality distribution above the quench front and the amount of evaporation can be 

calculated from the data. Similarly, the void distribution along the heated bundle can also be 

determined to indicate the flow and heat transfer regimes and the information can be used to 

correlate the measured heat transfer data. 
240

The differential pressure drop measurements must be corrected for frictional pressure drop, as 

well as any acceleration pressure drop, to infer local void fraction. 

Since the quality is non-equilibrium, measurements of the true vapor temperature are needed as 

well as the wall heat flux into the fluid. Different techniques have been tried to measure the 

vapor temperature in a dispersed non-equilibrium two-phase flow as part of the FLECHTSEASET program (Ref. 2), as well as elsewhere (Refs. 4, 5, 6 and 7). The technique that 

appears to be best is the use of miniature thermocouples which are placed normal to the flow 

and which point into the flow. As the froth region approaches, the thermocouples will wet since 

the droplet number density increases as the void fraction decreases. Very small thermocouples 

have a fast response time to allow the thermocouple to recover rapidly from being wetted by 

entrained droplets. In this fashion, a reasonable measure of the non-equilibrium vapor 

temperature can be achieved. Therefore, ample miniature thermocouples will be placed into the 

different subchannels along the axial length of the bundle. In addition, since the spacer grids 

can promote improved cooling downstream of the spacer, fluid thermocouples will be placed at 

these locations. The local quality can be calculated wherever a local vapor temperature exists 

in the bundle. 

The experimental program will be structured to help separate the thermal-hydraulic phenomena 

which are observed during Areflood heat transfer. The test facility will be characterized 

hydraulically by measuring the rod bundle frictional losses. The spacer grid form losses will also 

be measured. Therefore, the two-phase differential pressure measurements can be corrected 

for frictional losses and form losses using single-phase data and an appropriate two-phase 

multiplier. Sufficient, sensitive, differential pressure cells will be arranged along the bundle to 

measure the rod bundle frictional losses and the grid losses over a range of Reynolds numbers. 

Radiation-only experiments will determine, in-situ, the fraction of radiation heat flux which is 

transmitted from the inner rods to the housing, unheated dummy rods, and the outer peripheral 

row of rods. Values of the heater rod emissivity will be obtained from independent 

measurements using the pre-production heater rods which were tested at similar conditions. 

This data will help validate a multi-node model radiation network which can then be used to 

calculate the portion of the total heat transfer due to radiation in the bundle during reflood. The 

convective or dispersed flow film boiling portion of the total measured heat transfer can then be 

calculated from the total measured heat transfer by subtracting out the radiation portion. The 

data will also be used to validate the detailed COBRA-TF subchannel radiation heat transfer 

model for the test facility. Therefore, there is a requirement for sufficient thermocouple 

instrumentation on the heater rods, housing, and the dead or support rods at different planes 

within the bundle. 

Electric heater rods will simulate fuel rods and will have the capability to simulate decay power 

at 40 seconds following reactor scram. These rods will have an internal heating coil with a 

prescribed axial power shape. Thermocouples will be placed along the rods to cover the 

complete axial length of the bundle. There will be thermocouples at specific elevations to obtain 

the radial temperature distribution dependence in the bundle. Heat flux will be determined from 

an inverse conduction calculation using the thermocouple data. In addition, the experiments are 

designed for computer code validation purposes; therefore, the thermocouples and the 

differential pressure cells will be arranged within the bundle with the following considerations: 

• The overall bundle energy distribution will be determined during the transient; 
241

• Thermocouples will be placed upstream and downstream of spacers to see their effects; 

• Thermocouples will be placed on the spacer grids to determine their temperature and 

quench time; 

• Thermocouples will be placed on the housing and dummy rods for rod-to-dummy rod, 

and rod-to-housing radiation heat transfer calculations; and 

• Thermocouples will be placed at the center of the differential pressure cell spans such 

that one can then more easily relate the measured heat transfer to the local void fraction. 

The experiments and instrumentation plan has been designed to allow a transient mass and 

energy balance to be performed. 

In addition to heat transfer and the vapor and structure temperatures, data are needed on the 

flow behavior in the test bundle. In the froth region, data are needed on local void fraction 

distribution, interfacial area, and droplet/liquid ligament size. Also in the dispersed flow regime, 

data are needed on the droplet size, velocity, and number density for wall-to-drop radiation heat 

transfer, and the vapor-to-drop radiation and convective heat transfer. There is also evidence 

that entrained droplets enhance the convective heat transfer (Refs. 1 and 2) either by increasing 

turbulence, adding a distributed heat sink, or both. There is a requirement, therefore, that data 

be obtained on drop sizes, velocities, and number densities, to characterize the droplet 

mechanics of the dispersed two-phase region so interfacial area and droplet Weber numbers 

can be calculated from the test data. If the vapor flow rates and temperatures are known from 

other measurements, slip or relative droplet velocity can be calculated from the drop velocity 

measurements. 

The flow regime must be characterized in the froth region where the liquid changes from 

continuous liquid dispersed droplet flow (continuous vapor). Therefore, the test section will 

require windows which will permit viewing and photographing the transient flow at important 

time periods in the transient. 

8.3 Proposed New Instrumentation

While the RBHT Program is not intended to be an instrumentation development program, 

several new techniques will be used to obtain the data needed as identified by the PIRT. A softgamma ray measuring devise or X-ray system will be used at selected fixed elevations along 

the lower portion of the bundle. The gamma densitometer will give chordal average densities of 

the two-phase flow mixture as the flow regime changes from a dispersed droplet flow to the froth 

region and finally to solid water. This technique has been used in the past for void fraction 

measurements in rod bundles as indicated in Reference 8. To minimize attenuation of the soft 

gamma ray, beryllium inserts will be used in the test housing instead of quartz. The transient 

gamma ray measurements will provide an independent validation of the void fraction obtained 

from the finely spaced differential pressure measurements. 

Droplet information has been traditionally obtained using high speed photography and laborious 

methods to obtain drop sizes and velocities, by examining droplet behavior frame-by-frame from 

the high speed film. Newer techniques will be used in the RBHT Program utilizing a pulsed 
242

laser technique in conjunction with a fine grid digital camera. This system is called a Laser 

Illuminated Digital Camera System (LIDCS). The pulsed laser provides backlighting as well as 

the focus volume for pictures in the center subchannels of the rod bundle. This measurement 

technique employs software to determine the droplet size spectrum, Sauter mean drop size, 

droplet velocities, drop velocity distribution and an estimate of the droplet number density. 

These data can be used to estimate the interfacial area of the entrained droplet phase. The 

pulsed laser and digital camera technique has not been applied to rod bundle heat transfer 

before; therefore, to verify the performance of the system and confirm the accuracy of the 

measurements, a series of Abench-top@ experiments are being performed to develop the data 

reduction and analysis methods to analyze the droplet data. 

There will also be new techniques used for more traditional measurements in the rod bundle. 

There will be very finely instrumented regions of differential pressure cells with three-inch spans 

along the bundle to calculate a more localized void fraction from the data in the froth region and 

dispersed regions. Note, however, that the dispersed region void fraction could be within the 

uncertainty of the pressure cell after corrections. These data will be used to help correlate the 

measured heat transfer with the local void fraction. There will also be miniature fluid 

thermocouples which will act as steam probes to measure the local vapor temperature. In 

addition there will also be traversing vapor measurements within the bundle at selected 

locations to give the subchannel local temperature. This technique will be verified in a small 

heated bench experiment. 

These techniques and measuring systems will provide new, more accurate, more reliable data 

for computer code model development and validation. 

8.4 Instrumentation Plan Comparison to the PIRT

The PIRT tables in Section 2 listed the key thermal-hydraulic models and or parameters which 

are needed for developing and validating component models which comprise reflood heat 

transfer. Most of the items identified in the PIRT tables can be measured directly. Some can be 

determined from analysis of the test data, and some can be determined from the literature, while 

others will not be fully separable from the measurements made. Tables 8.1 to 8.8 reproduce 

the PIRT tables from Section 2 and indicate how the specific phenomena will be measured. All 

PIRT items are given in these tables regardless of ranking; however, instrumentation and use of 

new measuring techniques have been oriented specifically to obtaining data for the highly 

ranked PIRT phenomena. 

As the tables indicate, nearly all the highly ranked phenomena will be measured directly or 

calculated from the experimental data. When a parameter is directly calculated from the 

experimental data, the calculation uses the transient mass and energy balance on the test 

section to calculate the radially averaged fluid properties. A code is not used at this stage of the 

analysis so the data analysis is independent of the code to be validated by the experiments. 

There will be some difficulties in measuring the effects of the different cladding used in the rod 

bundle experiments as compared to the Zircaloy cladding used in the fuel rods. This difference 

was discussed in the scaling analysis in Sections 6 and 7. The effects of the difference in the 

materials are small except for the minimum film boiling temperature. For this parameter, data 

from the literature, FLECHT tests with Zircaloy cladding (Ref. 9) and NRU experiments (Ref. 10)

can provide guidance on the most appropriate value to be used. A similar situation exists for 

the differences in the heater rod surface emissivity and the emissivity for Zircaloy rods. Here, 
243

Table 8.1 Single Phase Liquid Convective Heat Transfer in the Core Component During Reflood Below 

Process/Phenomena Ranking Basis RBHT Progr

Convective Heat Transfer M 1φ Convective H.T. data has been 

correlated for rod bundles, uncertainty will not affect PCT, can effect point of boiling.

Will measure Ts, Tf and power bel

forced convective H.T. or natural ccalculated. 

Geometry L Hydraulic diameter has been shown to 

be acceptable for pitch-to-diameter ratio of 1.3. 

Spacer Grids L Effects of spacers in 1φ convective H.T. 

are known effects known for natural convection. No impact on PCT uncertainty. 

Models exist for spacer H.T. multispacers will be measured with detplacement. 

Material Properties L Property effects are accounted for in 

analysis for 1φ H.T. Little uncertainty. 

Property effects can be calculated 

Liquid Velocity (Reynolds Number) 

M Determine convective heat transfer. Will measure total flow, Tw, Tf. Ca

from data and correlate. Local flofrom subchannel code (COBRA, Vcalculation. 

Liquid Subcooling M Liquid is heat sink. Fluid temperatures will be measur

probes; selected T/C=s can travers

Decay Power H Source of energy for rods, boundary 

condition for test. 

Will be simulated. 
244

Table 8.2 Subcooled and Saturated Boiling B Core Component Below the Quench Fro

Process/Phenomena Ranking Basis RBHT Instrumentation and 

Subcooled Boiling Heat Transfer and Heat Flux, Split of Energy Between Liquid and Vapor Production 

M A significant variation in the subcooled 

boiling heat transfer coefficient will not affect the PCT uncertainty since rod is quenched. 

Will measure rod temperature (surfactemperatures (selectively) and poweheat flux can be calculated. Bundle acalculated from an energy balance. Model which has a superposition of c

The RBHT can be used to test this tyboth Ts and q5 are measured. Howev

determine directly the heat flux split bboiling without using the correlation. 

Geometry, P/D, De L Boiling effects in rod bundles have been 

correlated for our P/d, De range with acceptable uncertainty. 

The void fraction will be measured alusing ΔP cells, and at fixed locations 

detector. 

Spacers L Locally enhances heat transfer; 

Correlations/ Models are available, acceptable uncertainty. 

Effects of spacer grids can be measuaxial T/C placement on the heater ro

Material Properties L Data exists for the range of conditions, 

little uncertainty. 

Local Void Fraction M Data exists for tubes and rod bundles. The void fraction will be measured al

using ΔP cells, and at fixed locations 

gamma ray detector. This is a difficuthe void is very low and attached to t

Liquid Subcooling M Determines the condensation of vapor, 

energy split. 

Subcooling will be measured with mitraversing T/C=s. 

Interfacial Heat Transfer Area 

M Determines net vapor generation. Movies can be taken at different pos

obtain interfacial area. 

Decay Power H Energy source for heat transfer. Will be simulated over a range of conSaturated Boiling Heat Transfer and Heat Flux 

M Similar to subcooled boiling, data is 

available for our P/D, De range. The uncertainty of Saturated Boiling H.T. coefficient will not significantly impact the PCT since rod is quenched. 

Rod wall temperature and heat flux was the fluid temperature (saturation). 

Geometry, P/D, De L Data exists in the range of P/D, De with 

acceptable uncertainties. 
245

Table 8.2 Subcooled and Saturated Boiling B Core Component Below the Quench Front (Co

Process/Phenomena Ranking Basis RBHT Instrumentation and 

Spacer Grids L Locally enhances heat transfer, 

Correlations/ Models are available, with acceptable uncertainty. 

The effect of the spacer grids can bheater rod thermocouples. 

Material Properties L Data exists for our range of conditions, 

little uncertainty. 

Local Void Fraction H Provides the fluid conditions as the flow 

enters the quench front region and total steam flow which effects the liquid entrainment. 

The void fraction will be measured ausing ΔP cells, and at fixed location

gamma ray detector. 

Decay Power H Source of energy for rods, boundary 

condition for the test. 

Will be simulated. 
246

Table 8.3 Quench Front Behavior in the Core Component

Process/Phenomena Ranking Basis RBHT Instrumentation a

Fuel/Heater Rod Materials, and Thickness. ρ, Cp, k, Rod Diameter 

H These properties effect the stored energy 

in the fuel/heater rod and its quench rate, uncertainty directly impacts PCT. 

Inconel Heater Rods will be usedwill be known from direct measur

Gap Heat Transfer Coefficient 

M Second largest resistance in fuel rod. 

Affects heat release rate from fuel pellet. 

Gap heat transfer coefficient has large uncertainty, but its impact on PCT is smaller since all stored energy is redistributed much earlier than reflood, timing may change however. 

Heater rods do have a gap like fuswagged. High gap conductivity (5000 Btu/Hr -ft2 -F since rods ar

cannot be directly simulated with 

Cladding Surface Effects • Oxides • Roughness • Materials • Tmin

• TCHF

H Since Zircaloy oxidizes, the oxide layer 

will quench sooner due to its low conductivity, compared to Inconel. Also roughness of oxide layer promotes quenching. The surface condition effects Tmin which is the point where quenching is 

initiated. Quenching is a quasi-steady two-dimensional process. Values of Tmin

and TCHF can be estimated. Large 

uncertainty but relatively less impact on PCT. 

Inconel will be used for the claddwill be performed. Other data on sought and compared to Inconel 

such that a simple model can tre

Separate bench tests will be perfTmin for different surfaces and ma

Transition Boiling Heat Transfer (surface - liquid contact heat transfer) 

H Determines the rate of heat release at 

Quench Front directly impacts PCT, large uncertainty. 

Depends on wall super heat. Lovalues, high super heats give low two-dimensional process. Estimthe closely spaced heater rod T/C

conduction effects as well as a twthe heat rod. Calculate heat flux methods. 

Steam Generation at Quench Front 

H It is the rapid amount of steam generation 

which creates the liquid entrainment, large uncertainty and impact on PCT. 

This is a quasi-steady two-dimen

generation rate can be calculated 

T/C=s, total energy and the bundlbalance. 
247

Table 8.3 Quench Front Behavior in the Core Component (Continued)

Process/Phenomena Ranking Basis RBHT Instrumentation a

TCHF H Clad temperature when the critical heat 

flux is obtained, Used to develop the boiling curve and transition boiling. 

Measured by heater rod T/C=s socorrection may be needed. 

Tmin H Clad temperature at minimum film boiling 

point, Demarcation between good and poor cooling is needed to develop boiling curve. 

Measured by heater rod T/C=s. Scorrection effects may be neededwill also be performed to measur

different surfaces. 

Surface Temperature H Cladding temperature indicates which 

heat transfer regime the surface is experiencing. 

Measured by heater rod T/C=s, mdimensional correction effects. 

Spacer Grid M Steam generation at the quench front is 

the dominant effect and the resulting heat transfer is very large, location could impact entrainment due to wetting of the grid and vapor acceleration through the grid. 

Axial placement of heater rod T/Cif any. 

Radiation Effects, Wall to Liquid, Vapor 

L The convective effects of the vapor 

generation dominates, wall temperatures are low. 

Can calculate from the data via eestimate. 

Decay Power M Stored energy is the primary source of 

energy for rods. 

Will be simulated in tests. 

Void Fraction/Flow Regime 

H Determines the wall heat transfer since 

large α results in dispersed flow, low α in film boiling. Directly impacts PCT. 

Void fraction will be measured (e

, and gamma densitometers, and 

Interfacial Area H Determines the initial configuration of the 

liquid as it enters the froth region directly impacts liquid/vapor heat transfer and resulting PCT downstream. 

Interfacial area can be estimated 

photography if windows remain dalso be measured with DP cells adensitometer. 

Fluid Temperature H Influences the quench rate and net vapor 

generation. Important for high flooding rates, with high subcooling. 

Local miniature fluid temperaturetemperature at many axial positio
248

Table 8.4 Two-Phase Froth (Transition) Region for Core Component

Process/Phenomena Ranking Basis RBHT Instrumentation a

Void Fraction/Flow Regime 

H Void fraction/flow regime helps determine 

the amount of vapor-liquid heat transfer, which affects the downstream vapor temperature at PCT, large uncertainty. 

Average void fraction will be meaVapor superheat will be estimateT/C=s. 

Liquid Entrainment H Significant generation of steam in the froth 

and quench regions helps create liquid entrainment. 

Can be calculated from the rod bhowever, assumption must be mtemperature. Mass stored in frotcells, and gamma measurements

Liquid Ligaments, Drop Sizes, Interfacial Area, Droplet Number Density 

H Liquid flow characteristics determine the 

interfacial heat transfer in the transition region as well as the dispersed flow region, large uncertainty. 

The flow regime, interfacial area, velocities will be estimated by higand laser measurements. 

Film Boiling Heat Transfer at Low Void Fraction Classical Film Boiling (Bromley) 

H Film boiling heat transfer is the sum of the 

effects listed below in the adjacent column. Each effect is calculated separately and is added together in a code calculation, large uncertainty. 

Will measure the total heat transwill be estimated from the bundle difference is the film boiling and dtransfer. 

Droplet Contact Heat Transfer 

H Wall temperature is low enough that some 

direct wall-to-liquid heat transfer is possible, with high heat transfer rates, large uncertainty. 

Some data exists on wall surfacethis component from total heat flu

Convective Vapor Heat Transfer 

M Vapor convective heat transfer relatively 

less important since the liquid content in the flow is large and the vapor velocities are low, but large uncertainty. 

Calculate from bundle energy bavapor temperatures, bundle exit total heat flux (corrected for radia

Interfacial Heat Transfer M Interfacial heat transfer effects are 

relatively small since the steam superheat 

is low, large uncertainty exists. 

Interfacial heat transfer will be intemperature measurements and bundle energy balance. 
249

Table 8.4 Two-Phase Froth (Transition) Region for Core Component (Continued)

Process/Phenomena Ranking Basis RBHT Instrumentation a

Radiation Heat Transfer to Liquid/Vapor 

M The radiation heat transfer effects are 

also small since the rod temperatures are low. 

Radiation tests will help isolatcomponents. Increased radiatdue to the two phase mixture wall-to-mixture radiation in adsurface radiation. 

Spacer Grids M The velocities and Reynolds numbers 

are low in this region such that droplet breakup and mixing are not as important. Drop deposition could occur. 

Axial placement of heater rod effects of spacers. 

Decay Power H Source of power for rods. Will be simulated.
250

Table 8.5 Dispersed Flow Region for Core Component 

Process/Phenomena Ranking Basis RBHT Instrumentation a

Decay Power H Energy source which determines the 

temperature of the heater rods, and energy to be removed by the coolant. 

Power is a controllable paramete

Fuel Rod/Heater Rod properties, ρ, Cp, k 

L Properties can be modeled. Stored energy 

release is not important at this time. 

Data on heater rod properties wimeasured. 

Dispersed Flow Film Boiling (Components given below) 

H Dispersed flow film boiling modeling has a 

high uncertainty which directly effects the PCT. 

Current plan for tests is to perforbalance to obtain local quality. Ttransfer will be calculated using sthat a 1φ convective correlation f

available. Specific tests will also effects of convective enhancemetransfer such that the different heshould be separable from the totmeasured in a reflood test. 

Convection to Superheated Vapor 

H Principal mode of heat transfer as indicated 

in FLECHT-SEASET experiments. 

Similar convective behavior is ex

tests, as in the FLECHT-SEASET spacer grids may have a larger evane design. 

Dispersed Phase Enhancement of Convective Flow 

H Preliminary models indicate that the 

enhancement can be over 50% in some cases. 

A series of separate tests will be this heat transfer effect which wilsingle-phase convection tests. 

Gap Heat Transfer L Controlling thermal resistance is dispersed 

flow film boiling heat transfer resistance. Large gap heat transfer uncertainties are not important, but fuel centerline temperature is affected. 

Heater rods will not simulate the not needed for this regime. 

Cladding Material L Cladding material in the tests is Inconel 

which has the same conductivity as Zircaloy. Nearly the same temperature drop will occur. 

Test will use Inconel. 

Oxidation Rate M Inconel will not oxidize while Zircaloy will, 

and create a secondary heat source at very high PCTs, Zircaloy reaction can be significant at high temperature. 

Oxidation not simulated in tests s
251

Table 8.5 Dispersed Flow Region for Core Component (Continued)

Process/Phenomena Ranking Basis RBHT Instrumentation a

Fuel Clad Swelling/Ballooning 

L Ballooning can divert flow from the 

PCT location above the ballooning region. The ballooned cladding usually is not the PCT location. Large uncertainty. 

Flow blockage is not simulateFLECHT-SEASET. Heat tran

Direct Wall Contact Heat Transfer 

L Wall temperatures are significantly 

above Tmin such that no contact is 

expected. 

Will verify no contact from the component cannot be directly RBHT tests but we can estimaSeparate small-scale tests are 

Droplet Dry Wall Contact M Iloeje indicates this heat transfer 

mechanism is less important than vapor convection. 

This component cannot be seheat flux data in the RBHT tesscale tests are needed. This in the measured total heat flux

Droplet-to-Vapor Interfacial Heat Transfer 

H Interfacial heat transfer reduces the 

vapor temperature, which is the heat sink for the wall. 

The axial vapor temperature dmeasured, and the bundle avecalculated to obtain the evaposizes and velocities will be me

Radiation Heat Transfer • Surfaces • Vapor • Droplets 

H/M H/M H/M 

Important at higher bundle elevations (H) where convective heat transfer is small since the vapor is highly superheated. Very important for BWR reflood with sprays and colder surrounding channel. Large uncertainty. 

Separate tests will be used to radiation behavior of the RBHconvection. The surface emisindependently measured. Rawill be calculated for the force
252

Table 8.6 Top Down Quench in Core Components

Process/Phenomena Ranking Basis RBHT Instrumentation a

Deentrainment of Film Flow 

L1 Film flow quenches the heater rod. High 

uncertainty. 

The top-down quench front will bdeentrainment of drops onto the measured. 

Sputtering Droplet Size and Velocity 

L Droplets are sputtered off at the quench 

front and reentrained upward. Since the sputtering front is above PCT location, no direct impact. Entrained, sputtered drops affect total liquid entrainment, as well as the steam production in the steam generators. 

If the top quench front progresseis within a viewing location then dcan be estimated from high-speemeasurements. Quench locationfrom heater rods T/C=s and hous

Fuel Rod/Heater Rod Properties for Stored Energy ρ, Cp, k. 

L1 These properties are important since they 

determine the heat release into the coolant. However, since this occurs above PCT level, no impact. 

Heater rod stored energy is apprthe fuel rod. The conductivity of than the fuel rod so heat is releas

Gap Heat Transfer L1 Affects the rate of energy release from 

fuel/heater rod. 

No gap heat transfer simulated. 

(1) Some of these individual items can be ranked as high (H) within the top down quenching process; however, the entire 

a PWR/BWR since it occurs downstream of the PCT location. 
253

Table 8.7 Preliminary PIRT for Variable Reflood Systems Effects Tests

Process/Phenomena Ranking Basis RBHT Instrumentation 

Upper Plenum - Entrainment/Deentrainment 

M Upper plenum will fill to a given mixture level 

after which the remaining flow will be entrained into the hot leg, large uncertainty. 

A non-scaled upper plenum wtests; it should be easier liquid plant. Differential pressure cestorage. 

Hot Leg - Entrainment, Deentrainment 

L Hot legs have a relatively small volume and 

liquid entering the hot leg will be entrained into the steam generator plena, medium uncertainty. 

Hot leg entrainment can be siseparator which will separate 

Pressurizer L Pressurizer is filled with steam and is not an 

active component-small uncertainty. 

Pressurizer will not be simulat

Steam Generators H The generators evaporate entrained droplets 

and superheat the steam such that the volumetric vapor flow increases (particularly at low pressure). The result is higher steam flow downstream of the generators, high uncertainty since a good model is needed. FLECHT-SEASET data exist. 

The steam generators will not aspects of the higher steam flwhen specifying the inlet floodpressure drop across simulatemeasured. 

Reactor Coolant Pumps H Largest resistance in the reactor coolant 

system, directly affects the core-flooding rate, low uncertainty. 

The resistance will be represe

approximate inlet flooding rate the system calculations. 

Cold Leg Accumulator Injection 

H Initial ECC flow into the bundle. Accumulator flow rates will be 

measured.

Cold Leg Pumped Injection H Pumped injection is the liquid source for 

majority of the reflood transient. 

Pumped injection will be simu

Pressure H Low pressure (~35 psia) significantly affects 

vapor volumetric flow steam binding decreases the bundle flooding rate. 

Pressure range will be simula

Injection Subcooling M/H Lower subcooling will result in more boiling 

below the quench front, additional vapor to vent. 

Subcooling range will be simu

Downcomer wall heat transfer 

H The heat transfer from the downcomer walls 

raises the ECC fluid temperature as it enters the core, resulting in more steam generation. 

Simulate affect by varying the 
254

Table 8.7 Preliminary PIRT for Variable Reflood Systems Effects Tests (Continued)

Process/Phenomena Ranking Basis RBHT Instrumentation a

Lower Plenum Wall Heat Transfer 

M Same effect as downcomer. Simulate the metal heat effect by 

temperature. A non-scaled uppesimulated in the tests; it should brelative to a plant. Differential prmass storage. 

Break L Excess ECC injection spills out of vessel, 

break ΔΡ helps pressurize reactor 

system. 

Break not simulated. 
255

Table 8.8 High Ranked BWR Core Phenomena 

Process/Phenomena Basis RBHT Instrumentation and Measuremen

Core Film Boiling PCT occurs in film boiling. Film boiling components will be measured by hea

T/C=s, data will be corrected for radiation. 

Upper Tie Plate CCFL Hot assembly is in cocurrent up-flow 

above CCFL limit. 

Similar behavior as PWR reflooding. 

Channel-bypass Leakage 

Flow bypass will help quench the BWR 

fuel channel. 

The housing in the RBHT test will approximate a channel, no leakage flow simulated; housing T/Cindicate quench location. 

Steam Cooling A portion of the dispersed flow film boiling 

heat transfer. 

Simulated in RBHT tests. 

Dryout Transition from nucleate boiling and film 

boiling. 

Not simulated in RBHT tests. 

Natural Circulation Flow Flow into the core and system pressure 

drops. 

Flow range can be simulated in RBHT, using pumflow. 

Flow Regime Determines the nature and details of the 

heat transfer in the core. 

Since pressures, heat flux, temperature, and flowsimulated, flow regimes will be representative,measurements of void fraction by cells, gamma densitometer, high speed photography. 

Fluid Mixing Determines the liquid temperature in the 

upper plenum for CCFL break down. 

Not simulated in RBHT, but hot assembly is calcube in upflow. 

Fuel Rod Quench Front Heat release from the quench front will 

determine entrainment to the upper region of the bundle. 

Heater rod T/C=s will indicate the quench front be

Decay Heat Energy source for heat transfer. Will simulate in RBHT as a boundary condition. Interfacial Shear Affects the void fraction and resulting 

droplet and liquid velocity in the entrained flow. 

Is not directly measured, can estimate for differenregimes from data. 

Rewet: Bottom Reflood BWR hot assembly refloods like PWR. Simulated in RBHT. Rewet Temperature Determines quench front location. RBHT will use different materials than fuel rod; be

tests will be used to support the RBHT data. 

Top Down Rewet Top of the hot assembly will rewet in a 

similar manner as PWR. 

Will be simulated in RBHT. 
256

Table 8.8 High Ranked BWR Core Phenomena (Continued)

Process/Phenomena Basis RBHT Instrumentation and Measuremen

Void Distribution Gives the liquid distribution in the bundle. Will be measured with differential pressure cells, 

densitometer, and/or x-ray techniques. 

Two-Phase Level Similar to quench front location, indicates 

location of nucleate and film boiling. 

Will be measured with heater rod T/C=s and differpressure cells to obtain axial void distribution.
257

however, the differences become smaller once the heater rod surface is oxidized. The 

emissivity of the oxidized surface approaches 0.9 for either metal. The determination of Tmin for 

different surface conditions and material types is a candidate for a bench-type test and analysis. 

In the dispersed flow film boiling region, the portion of the wall heat flux due to radiation heat 

transfer (to vapor, surfaces, housing, and droplets) can be separated from the measured total 

wall heat flux obtained from the inverse conduction calculation using the heater rod 

thermocouples. What cannot be easily separated from the remaining portion of the wall heat 

flux, in the froth flow regime, is the direct contact heat transfer. This mode of heat transfer 

occurs just above the quench front where the wall is near the minimum film boiling temperature. 

There have been models developed for this phenomenon by Forslund and Rohsenow (Ref. 11), 

Iloeji (Ref. 12) and Pederson (Ref. 13) and others (see Section 2) which can be used to 

separate this specific component from the remaining film boiling and convective heat transfer 

term. Different options and models will be used to assess the magnitude of this heat transfer 

component. For forced flooding experiments, instrumentation will be required to measure the 

variable flow into and out of the bundle. Previous experiments have concentrated on only the 

positive oscillatory flow (Ref. 14) such that there is no reverse flow out of the bundle. ERSEC 

(Ref. 14) are the closest tests which simulate positive and negative flows. The FLECHTSEASET tests simulated stepped flows which reflected the effects of the steam binding in 

PWRs. An injection scheme and measurement plan will be developed to measure the 

instantaneous flow into the bundle. 

8.5 Conclusions

The instrumentation requirements were developed using the PIRT tables as a guide for the 

important phenomena for the different test types, which the experiments must capture for code 

development and verification. The Rod Bundle Heat Transfer Test Facility will employ ample 

instrumentation proven to perform in previous rod bundle experiments. There will also be stateof-the-art instrumentation to measure details of the two-phase flow field in a non-intrusive 

manner. The combination of the different techniques provides a robust instrumentation plan for 

the Rod Bundle Heat Transfer program so the most important phenomena identified in the PIRT 

can be measured or calculated from the data. 

8.6 References

1. Lilly, G.P., Yeh, H.C., Hochreiter, L.E., and Yamaguchi, N., APWR FLECHT Skewed Profile 

Low Flooding Rate Test Series Evaluation Report,@ WCAP-9183. 

2. Lee, N., Wong, s., Yeh, H.C., and Hochreiter, L.E., APWR FLECHT-SEASET Unblocked 

Bundle, Forced and Gravity Reflood Task Data Evaluation and Analysis Report,@

NRC/EPRI/Westinghouse Report No. 10, WCAP-9891, NUREG/CR-2256, RPRI NP-2013, 

November 1981. 

3. Denham, M.K., Sowitt, D. and K.G. Pearson, AACHILLES Unballooned Cluster 

Experiments, Part I, Description of ACHILLES Rig Test Section and Experimental 

Procedures,@ AEEW-R2336, November 1989. 

4. Loftus, M.J., Hochreiter, L.E., Conway, C.E., Rosal, E.R., and Wenzel, A.H., ANonEquilibrium Vapor Temperature Measurements in Rod Bundle and Steam Generator Two-
258

Phase Flows,@ Proceedings of the Third CSNI Specialist Meeting on Transient Two-Phase 

Flow, March 1981. 

5. Ihle, P., and Rust, K., AInfluence of Spacers on the Heat Transfer During the Reflood 

Phase of a Pressured Water Reactor Loss of Coolant Accident,@ Nuclear Research Center, 

Karlsruhe, KFK Report 3178. September 1982. 

6. Lilly, G.P., Yeh, H.C., Hochreiter, L.E., and Yamaguchi, N., APWR FLECHT Cosine Low 

Flooding Rate Test Series Evaluation Report,@ WCAP-8838, 1977. 

7. Unal, C., AAn Experimental Study of Thermal Nonequilibrium Convective Boiling in PostCritical-Heat-Flux Region in Rod Bundles,@ Ph.D. Dissertation, Lehigh University, 1985. 

8. Jiang, Y and Rezkallah, K. S., AAn Experimental Study of the suitability of Using a Gamma 

Densitometer for Void Fraction Measurement in Gas-Liquid Flow in a Small Diameter 

Tube,@ Measurement Science and Technology, Vol. 4, pp. 496-505, 1993. 

9. Cadek, F.F., Dominicis, D.P., and R.H. Leyse, AFLECHT Final Report,@ WCAP-7665, April 

1971. 

10. Mohr, C.L., et.al., AData Report for Thermal-Hydraulic Experiment 2 (TH-2), NUREG/CR2526, PNL-4164, November 1982. 

11. Forslund, R.P., and Rohsenow, W.M., ADispersed Flow Film Boiling,@ J.Heat Trans. 90 (6), 

399-407, 1968. 

12. Iloeje, O.C., Plummer, D.N., Griffith, P., and Rohsenow, W.M., AAn Investigation of the 

Collapse and Surface Rewet in Film Boiling in Vertical Flow,@ J. Heat Trans. ,Vol. 97, pp. 

166-172, 1975. 

13. Pedersen, C.O., AThe Dynamics and Heat Transfer Characteristics of Water Droplets 

Impinging on a Heated Surface,@ Ph.D. Thesis, Carnegie Institute of Technology, 1967 

14. Clement, P., Deruaz, R., and Veteau, J.M., AReflooding of a PWR Bundle Effect of Inlet 

Flow Rate Oscillations and Spacer Grids,@ European Two-Phase Flow Group Meeting, 

Paris, June 1982. 
259

9. DEVELOPING A FACILITY INPUT MODEL 

9.1 Introduction

The COBRA-TF computer code (Refs. 1, 2 and 3) was used to model the RBHT Test Facility. 

The objective was to perform pre-test calculations to obtain information about the range of the 

parameters to expect during reflood transient. This analysis also provided a basis to develop 

the test matrix and indicate the maximum temperature conditions reached in the bundle for a 

given set of conditions. 

The COBRA-TF code was developed at the Pacific Northwest Laboratory under the sponsorship 

of the NRC to provide best-estimate thermal-hydraulic analyses of a LWR vessel during LOCAs. 

The two-phase flow is described with a two-fluid, three-field model. Thermal radiation and grid 

spacer effects are also included in the code, as well as a more detailed dispersed flow film 

boiling model as described in Section 4. The code was developed for use with either 

rectangular Cartesian or subchannel coordinates. 

Two COBRA-TF models of the RBHT Test Facility were developed: a two-channel model and a 

more detailed individual subchannel model. The two-channel model was used to examine the 

local fluid conditions within the test facility for comparison with a plant. This model does not 

account for rod-to-rod or rod-to-housing radiation heat transfer from the inner channel which 

exists in the test bundle. The model does account for the test section housing and calculates 

the convection heat transfer to the housing as well as the energy released from the housing as it 

quenches. 

A more detailed 1/8th sector of the test facility was modeled on a subchannel basis with each 

subchannel, individual heater rod surface, and the gap between rods uniquely modeled. The 

subchannel capability of COBRA-TF allows more accurate representation of small rod bundle 

arrays since each individual rod can be modeled with different surfaces for radiation heat 

transfer, so rod-to-rod and rod-to-housing radiation heat transfer can be modeled more 

accurately. In this fashion, the radial temperature gradient which develops due to the radiation 

heat losses to the test section housing can be simulated. There are specific experiments 

planned in the RBHT program to examine radiation-only heat transfer within the rod bundle and 

to the test section housing. The emissivities of the rods and housing will be measured. 

Both the two-channel and the subchannel model were used for pre-test analysis. Since the twochannel calculations run much quicker and are easier to analyze, the majority of the pre-test 

calculations used this model. The more detailed model was used selectively for specified tests

to examine the detail of the flow structure within the rod bundle. 

9.2 Two-Channel Model 

9.2.1 Input Deck Description 

The analysis considered a 7x7 rod array comprised of forty-five heater rods, four unheated rods, 

and the surrounding housing. The facility modeling approach was to divide the test facility into 

four sections and five fluid channels. As shown in Figure 9.1, channels one and five represent 

the lower and upper plenums, respectively. Channel two models the low end fitting of the rod 

bundle. The third element is the actual heated length of the rod bundle and contains two fluid 
channels. Channel three is the inner channel and encompasses a total of sixteen >hot= rods; this 

includes the nine center rods and summation of the fractional parts of the rods that lie on the 

channel=s boundary as shown in Figure 9.2. The second core channel, channel four, is 

comprised of the remaining twenty-nine heater rods, the four unheated rods, and the housing. 

Figure 9.1 RBHT - Partitioning of Sections, Channels and Gaps. 

Figure 9.2 RBHT - Test Section 7x7 Rod Bundle Array Cross Section. 

260
Three geometry types, hrod, tube and wall, were employed to represent the components of the 

test section. The hrod type signifies a solid cylinder and, thus, was employed to model the 

heater rods. As shown in Figure 9.3, successive layers of Boron Nitride, Monel K-500, Boron 

Nitride and Inconel 600 constitute the material composition of each rod. The unheated rods, of 

tube geometry, consist solely of Inconel 600. 

Figure 9.3 RBHT Heater Rod - Radial Dimensions, Materials and Noding Scheme. 

Figure 9.4 RBHT - Radial Dimensions, Materials and Noding Scheme. 

261
The housing was modeled as a single wall with a cross-sectional area and wetted perimeter 

equal to the sum of the four individual sides. Both radial and axial noding were specified in the 

input model. As seen in Figure 9.4, there are three radial nodes for the Inconel 600 unheated 

rods and housing. 

Radial noding in the heater rods is shown in Figure 9.3. The first two material segments of the 

rods (Boron Nitride and Monel K-500) both feature only one node, while three nodes each were 

allocated to the latter two segments. Axially, a total of twenty-eight nodes were specified, 

distributed as follows: two in the lower plenum, one in the lower end fitting, twenty-two in the 

heated length, and three in the upper plenum. Nodal boundaries in the heated length as shown 

in Figure 9.5 align with the grid locations, an ideal situation from a computational standpoint. 

Consequently, since the first grid is located 63.754 mm (2.51 in) from the bottom of the rod 

bundle, the first axial node in the heated length is 63.754 mm (2.51 in) from the bottom of the 

core. 

Figure 9.5 RBHT - Axial Dimensions and Nodal Scheme. 

262
The major approximation made by this input model was to neglect radiation heat transfer. 

COBRA-TF does not have the capability to calculate radiation effects across channel 

boundaries unless the individual subchannels are modeled. Rather, it can only calculate 

radiation within each channel in which the rods are lumped. Each rod within a channel is 

considered to be at the same temperature; therefore, wall-to-wall radiation effects within the 

channel boundaries are neglected. 

9.2.2 Results of Two-Channel Model 

At the time this report was written, work was still continuing, so the results presented in this 

section are preliminary. 

The analysis considered three flooding transients with different flooding rates: 20.32, 25.4 and 

38.1 mm/s (0.8, 1.0 and 1.5 in/s). A constant pressure (40 psia) was set in the upper plenum. 

The water inlet subcooling was 48.89 degrees C (120 degrees F). The axial power shape is 

shown in Figure 9.6 which is the axial shape to be used in the RBHT tests. The initial power 

was chosen to be 0.7 kW/ft at the peak power location of 2.7432 m (108 in) from the bottom of 

the heated length. The decay power factor is the ANS-1971 +20 percent and is shown in Figure 

9.7. This parameter will be ranged to cover the ANS-1979 decay heat standard as well as to 

provide overlap with existing data. In the actual experiments, the initial rod temperature will be 

determined by an adiabatic heat-up, not simulated in this analysis. The initial peak temperature 

was assumed to be 815 degrees C (1500 degrees F), and the local rod initial temperature was 

calculated based on the local power factor. The initial housing temperature was assumed to be 

a uniform value of 260 degrees C (500 degrees F). The simulation was carried out for 500 s. 

Figure 9.6 Axial Power Shape. 

The 25.4mm/s (1.0 in/s) flooding rate results are shown in Figures 9.8 through 9.15. Figure 9.8 

shows the quench front location versus time. The quench front rises relatively rapidly during the 

first 180 s, then it slows down. The average quench front velocity between 200 and 500 s is 

2.438 mm/s (0.096 in/s). Figure 9.9 shows the hot rod clad temperature at different elevations. 

The peak clad temperature (PCT) 1354 degrees C (2470 degrees F) is reached at about 170 s 

at the peak power location.

263
Figure 9.7 Power Decay. 

Figure 9.8 Quench Front - 1.0 in/s Reflooding Rate. 

The housing temperature at different elevations is given in Figure 9.10, showing that the 

maximum temperature is reached at the same heater rod peak locations. The axial distribution 

of hot rod temperature is shown in Figure 9.11. Figure 9.12 shows the vapor temperature at 

different locations above the quench front. The effect of the grids is to reduce the vapor 

temperature downstream of the grids and, as a consequence, this reduces the clad temperature 

at the same locations. This effect is visible in Figures 9.11 and 9.12. 

Figures 9.13 and 9.14 show respectively the vapor flow rate and the entrained liquid flow rate at 

the outlet of the bundle. An almost quasi-steady-state is reached at the end of the transient 

where the total of vapor, continuous liquid, and droplets flow rates almost matches the inlet 

subcooled liquid flow rate. 

264
Figure 9.9 Hot Rod Clad Temperature - 2.54 cm/s (1.0 in/s) Reflooding Rate. 

Figure 9.10 Housing Temperature - 2.54 cm/s (1.0 in/s) Reflooding Rate. 

265
Figure 9.11 Hot Rod Clad Temperature - 2.54 cm/s (1.0 in/s) Reflooding Rate. 

Figure 9.12 Vapor Temperature - 2.54 cm/s (1.0 in/s) Reflooding Rate. 

266
Figure 9.13 Vapor Flow Rate at Outlet of Rod Bundle - 2.54 cm/s (1.0 in/s) 

Reflooding Rate. 

Figure 9.14 Entrainment Flow Rate at Outlet of Rod Bundle - 2.54 cm/s (1.0 in/s) 

Reflooding Rate. 

267
Figure 9.15 Pressure at Inlet of Rod Bundle - 2.54 cm/s (1.0 in/s) Reflooding Rate. 

Finally, Figure 9.15 shows the pressure at the inlet of the bundle. Since pressure is fixed at 40 

psia at the outlet of the bundle, the inlet pressure is the result of the gravity head and pressure 

drop across the bundle. 

Similar results were obtained with the inlet flow rates of 20.3 mm/s (0.8 in/s) and 38.1 mm/s (1.5 

in/s). Results are not shown in detail for these two cases, but it is interesting to calculate the 

range of vapor Reynolds numbers in this range of flooding rate. Figures 9.16, 9.17 and 9.18 

show the vapor Reynolds number for respectively 20.3, 25.4 and 38.1 mm/s (0.8, 1.0 and 1.5 

in/s) cases. These figures indicate that the vapor Reynolds number can be within the laminar 

and transition regimes, as well as turbulent flow. 

The droplet Weber number was calculated for the 25.4 mm/s (1.0 in/s) flooding rate at 425 s into 

the transient when the flow conditions present a smooth, quasi-steady state behavior. The 

droplet Weber number is based on 

( ) We

uud vv e d = ρ −

σ

2

 (9-1) 

where the droplet diameter is calculated from the equation 

d

A d e

i

= 6α

 (9-2) 

The droplet Weber number is calculated just above the quench front and at the bundle outlet

using the variable values obtained from the code output shown in Table 9.1: 

268
Table 9.1 Weber Number Parameters at 425 s 

Symbol Description Value just above the 

quench front

Value at the top of the 

bundle

αe Entrainment phase void fraction 0.0029 0.0003 

ρv Vapor density, kg/m3

 (lbm/ft3) 0.9772 (0.061) 0.636 (0.0397) 

σ Surface tension, N/m (lbf/ft) 0.0535 (0.00366) 0.0535 (0.00366) 

uv Vapor velocity, m/s (ft/s) 5.94 (19.49) 16.67 (54.69) 

ue Entrainment phase (droplet) velocity, 

m/s (ft/s) 

1.109 (3.64) 11.433 (37.51) 

Ai Interface Area (ft2

/ft3) 9.79 1.48 

The calculated value of the Weber number ranges from 7.4 just above the quench front to 3.9 at 

the top of the bundle. 

Figure 9.16 Vapor Reynolds Number - 2.032 cm/s (0.8 in/s) Reflooding Rate. 

269
Figure 9.17 Vapor Reynolds Number - 2.54 cm/s (1.0 in/s) Reflooding Rate. 

Figure 9.18 Vapor Reynolds Number - 3.81 cm/s (1.5 in/s) Reflooding Rate. 

270
9.3 Individual Subchannel Model 

9.3.1 Input Deck Description 

A detailed COBRA-TF subchannel model of the RBHT test section was developed to examine 

the effects of rod-to-rod and rod-to-housing radiation as well as the subchannel flow behavior 

during refloods. The RBHT test section is assumed to have 1/8 symmetry which enables 

COBRA-TF to model the bundle with ten rods, ten channels, 12 gaps, and four wall sections, as 

seen in Figure 9.19. Each rod is divided into four surfaces with each surface oriented towards a 

channel. The heater rod surfaces are connected thermally by azimuthal conduction heat flow 

paths. Partial rods have less then four surfaces, with the number dependent upon rod 

orientation. The composition and noding of the rods and housing are identical to the description 

of the two-channel model in Section 9.2. 

Figure 9.19 Nodal Diagram for Subchannel Model. 

The subchannel model uses the same power profile and linear power densities as the twochannel model, the peak linear power being at 2.7432 m (108 in) and 2,297 W/m (0.7 kW/ft). 

The axial noding of the test section is identical to the two-channel model described in Section 

9.2 with 22 nodes and eight spacer grids except the test section contains ten, not two channels. 

The plenum is modeled at the top and bottom of the test section to provide inlet and exit 

boundary conditions. An intermediate section with three channels is used to link the test section 

to the plenums; COBRA-TF does not allow more than six channels to be directly linked to one 

channel. Figure 9.20 shows the axial nodal diagram for the subchannel model. 

Each rod is modeled with four separate surfaces. The COBRA-TF radiation model exchanges 

radiation between surfaces of the rods and surfaces in the four adjoining channels, and the 

271
Figure 9.20 Axial Nodal Diagram for Subchannel Model. 

channel walls through the rod gaps. Because of the symmetry planes (1/8 symmetry) the net 

radiation across a line of symmetry is zero. The azimuthal conduction model allows heat to be 

conducted around the rods from hot surfaces oriented toward the center of the bundle to the 

cold surfaces nearer the bundle housing. 

Initial temperature distributions in the test section are taken from a COBRA run from which the 

bundle is initially at saturation, 130 degrees C (267 degrees F), and heated about 110 s until 

the peak rod temperature is 870 degrees C (1600 degrees F). This procedure is the prescribed 

pre-test heatup phase. 

9.3.2 Results of Subchannel Model 

To determine the effect of the housing on the bundle temperature distribution, the subchannel 

model was run with and without the ten radiation channels. The inlet conditions were set to zero 

such that the bundle was heated in an adiabatic manner in a stagnant steam environment. 

However, as the bundle was heated, steam convective currents developed and steam was 

released from the top pressure boundary to maintain the system pressure at 40 psia. Also, the 

bundle underwent convective heat transfer from the hot rods to the unheated surfaces because 

natural circulation paths were set in motion between grid spans. 

The bundle was heated for 50 s to obtain the peak rod temperature at 870 degrees C (1600 

degrees F). The results presented in Figure 9.21 are taken at the peak power location at the 

end of the 50 s heat-up. All temperature information on Figure 9.21 is in Celsius. 

272
Initial temperatures at the peak location were: 

Heated Rods: 870 degrees C (1600 degrees F) 

Corner Rod: 340 degrees C (645 degrees F) 

Housing: 250 degrees C (482 degrees F) 

Figure 9.21 Temperature Distributions after 50 s Heatup (in degrees C). 

These results confirm the assumption that the central 5x5 array of rods can be assumed to be at 

the same temperature. For the central rods the maximum temperature difference is 39 degrees 

273
274

C (70 degrees F). The outermost row of rods is quite effective in shielding the remainder of the 

rods. 

The detailed subchannel model will be used to selectively analyze the test facility to establish 

the exact test facility test conditions. 

9.4 Conclusions 

Two COBRA-TF models were developed for the RBHT Test Facility. A two-channel model 

represents the 7x7 rod bundle by splitting the bundle into two channels. One channel describes 

the inner, hotter rods and another describes the peripheral rods. The peripheral rods (in this 

case) are colder due to the presence of the housing, which provides a heat sink because of 

convective heat transfer. The two-channel model does not include radiation heat transfer. This 

was modeled with a more detailed subchannel model. 

The detailed subchannel model was developed. The adiabatic heat-up phase for the RBHT 

Test Facility was simulated. Results show that radiation heat transfer is especially important for 

the rods facing the housing. The central 5x5 array of rods have practically uniform temperature 

with a maximum temperature difference of 39 degrees C (70 degrees F). The outer most row of 

rods is quite effective in shielding the remainder of the rods. 

These preliminary results show the values of parameters to be expected during reflood of the 

RBHT bundle and provide the range of fluid vapor Reynolds and droplet Weber numbers for 

those conditions which should be compared with expected conditions in PWR and/or BWR 

reflood. 

9.5 References

1. C. Y. Paik et al., “Analysis of FLECHT SEASET 163-Rod Blocked Bundle Data Using 

COBRA-TF,” NUREG/CR-4166, 1975. 

2. Thurgood, M. J., et al., “COBRA-TRAC: A Thermal-Hydraulic Code for Transient Analysis 

of Nuclear Reactor Vessels and Primary Coolant Systems,” NUREG/CR-3046 (PNL 4385), 

Volumes 1-5, 1982. 

3. Wheeler, C. L., et al., “COBRA-IV-I: An Interim Version of COBRA for Thermal Hydraulic 

Analysis of Rod Bundle Nuclear Fuel Elements and Cores,” BNWL- 1962, 1973. 
275

10. ROD BUNDLE HEAT TRANSFER TEST MATRIX 

10.1 Introduction

A test matrix for the RBHT tests was developed. The range of conditions is given and the 

objectives for the proposed tests are described. Some of the proposed tests were compared to 

the conditions and types of tests described in Section 3 to show how the proposed tests overlap 

and complement the existing database. The strategy in developing the test matrix was to use a 

"building block" approach in which simpler experiments are performed first to quantify a 

particular heat transfer mechanism. Additional complications of two-phase flow film boiling 

behavior are added in later experiments. The proposed test conditions bracket those expected 

in postulated LOCA. 

10.2 Types of Tests Which are Proposed

The types of tests proposed include: 

1. Steady-state liquid flow characterization tests to determine the rod bundle frictional pressure 

drop and the spacer grid loss coefficients. These tests will provide the bundle-specific 

hydraulic information to be used in the TRAC and COBRA-TF models. 

2. Heat loss experiments to characterize the facility heat loss to the environment. These tests 

will provide the heat loss boundary information to be modeled in the COBRA-TF model, and 

to verify the scaling calculations for heat losses. 

3. Radiation-only tests with an evacuated rod bundle. These tests will be performed over a 

range of rod bundle powers to achieve a wide range of heater rod surface temperatures, 

characteristic of those expected for dispersed flow film boiling. The bundle will be 

evacuated such that heat transfer will be by radiation only with no convective currents within 

the bundle. These tests will characterize the rod-to-rod and rod-to-housing radiation heat 

transfer. The objective will use the measured emissivities to characterize the rod bundle 

and housing surfaces such that the radiation heat transfer component can be subtracted 

from the total dispersed flow film boiling transfer as well as to verify that the outer row of 

heater rods effectively shields the inner 5x5 rows of rods. These tests will provide the data 

for the rod-to-rod and rod-to-surface radiation heat transfer models in TRAC and COBRATF. Modeling of this type of tests has been successfully performed using COBRA-TF in the 

past (Refs. 1 and 2). 

4. Subcooled and saturated boiling experiments at low flows and low pressure. The objectives 

will be to provide data which can be utilized to validate the boiling models and correlations 

currently used. The experiments will be conducted in a steady-state manner and the heat 

transfer and void distributions will be measured along the rod bundle. 

5. Convective steam cooling tests over a wide range of Reynolds numbers to determine the 

single-phase convective heat transfer in superheated steam. The analysis of the FLECHTSEASET 161 rod bundle data (Ref. 3) indicates that for low flooding rates where the vapor 

becomes highly superheated, the vapor Reynolds numbers can decrease sufficiently to the 

laminar flow or transition flow regime. Therefore, these tests will characterize single-phase 

convective heat transfer cooling without the complications of a dispersed droplet field. Data 
276

from these tests will be compared to rod bundle steam cooling data from the ORNL tests 

(Ref. 4) and the FLECHT-SEASET tests (Ref. 5), and other data sets for consistency. 

6. Steam cooling tests with injected droplets at the entrance of the test bundle. A droplet 

injection system will be designed to inject drops of a known initial size and velocity into the 

heated rod bundle subchannels over a range of liquid flows such that quasi-steady state 

dispersed flow film boiling experiments can be conducted. An estimate of the droplet flow 

can be made from the FLECHT-SEASET 161 rod bundle tests as well as calculations from 

COBRA-TF. The objective of these experiments will be to examine the effects of a highly 

dispersed phase of entrained liquid droplets on convective heat transfer within the rod 

bundle. 

These tests will be simpler to analyze since the additional effects of the rod quench front 

movement, quench heat release and generation of the entrainment will be minimized. Since 

these tests will be quasi-steady, the Laser-Illuminated Digital Camera Systems (LIDCS) can 

be used at selected elevations to track the droplets and measure their size and velocity 

distributions, such that the change of the droplet interfacial area can be measured and 

compared to predictions. 

The LIDCS can be positioned upstream and downstream of spacer grids to determine the 

grid effects on the drop field. Also, local vapor temperature will be measured from steam 

probes, as well as the exit liquid and vapor temperature flow. From this, a mass and energy 

balance can be written for the bundle to calculate the quality change along the bundle, and 

therefore the axial steam flow. Radiation heat transfer can be calculated using the 

measured rod and surface temperatures, and this value can be subtracted from the 

measured total heater rod wall heat flux, resulting in the dispersed flow film boiling 

contribution to the total wall heat flux. The convective heat flux can then be compared to the 

single-phase convective heat flux based on the steam cooling tests to determine under what 

conditions convective heat transfer enhancement is enhanced by the evaporating droplets in 

the flow. A similar approach was used in the analysis of the FLECHT-SEASET 161 rod 

bundle experiments, but the lack of separate radiation only tests and good single-phase 

steam cooling tests resulted in significant data scatter. The inclusion of the radiation only 

and the steam cooling tests will reduce the uncertainties in the data analysis as well as the 

modeling uncertainties to avoid compensating errors as much as possible. These tests 

represent a unique contribution to the rod bundle dispersed flow film boiling literature. 

7. Forced reflooding experiments will be performed to compliment the existing data, as 

determined from Task 2. The forced reflooding tests will also overlap the steam cooling and 

the droplet injection two-phase experiments. The forced reflooding experiments will contain 

all the elements of the experiments performed earlier with the additional complications of the 

heater rod quench front movement, quench heat release, and entrainment expected for 

reactor conditions, for a prescribed set of initial and boundary conditions. 

The focus of these experiments is to examine entrainment at the quench front within the 

froth region. The LIDCS and gamma densitometers will be used to determine the flow 

regime and the behavior of the entrained phase over a range of pressure, inlet flow, inlet 

subcooling, heater rod power, and heater rod initial temperatures. In addition, the data 

above the quench front can be analyzed in the same fashion as the FLECHT-SEASET 161 

rod bundle data and the steam cooling tests with droplet injection to determine the wall heat 

flux components due to radiation heat transfer and film boiling. 
277

These tests will serve as validation experiments for the models to be developed from the 

simpler component tests described above. Some of the data for selected tests can be 

designed as "blind" test data to be released to only the NRC for blind test predictions for the 

merged TRAC computer code. The COBRA-TF model developed in Task 8 will be used for 

pre-test calculations to determine the test matrix conditions for these experiments. 

8. Gravity reflood experiments or variable inlet injection experiments will also be performed. 

These experiments will examine the system response on the inlet-flooding rate into the test 

bundle and the resulting heat transfer within the bundle. In the experiments described 

above, inlet flow conditions are prescribed boundary conditions. Actual inlet flow in a 

reactor system is a dependent parameter which depends upon the steam generation rate 

within the core, driving head in the downcomer, and pressure losses in the reactor piping, 

steam generators and pumps. The resistances for the generator, pump, and associated 

piping will be simulated using an orifice at the test section outlet. The parameters of interest 

are the orifice resistance, injection flow rate into the downcomer, initial rod bundle 

temperature, inlet subcooling, and rod bundle power levels. There will be a LaserIlluminated Digital Camera System and gamma densitometer data to examine the gravity 

flow behavior within the bundle, effects of the spacer grids, and resulting entrainment. The 

tests will be modeled using COBRA-TF, which will have been improved as part of the 

program effort. 

10.3 Range of Conditions Considered for the Experiments

The range of conditions used to establish the test matrix covers the postulated calculated 

reflood transit. Typical calculated reflood conditions were obtained from Westinghouse (Ref. 5), 

Framatome (Ref. 6), and Siemens (Ref. 7). Westinghouse compared the ranges of existing 

data to their model to show that it had been tested over the range of model application. 

The composite table of all the predicted conditions from the reactor vendor calculations is given 

in Table 10.1. The table is subdivided into each of the different heat transfer regimes and the 

range of the calculated plant conditions is given for each. As can be seen, there is a large 

variation in parameters such as liquid and vapor Reynolds number, liquid subcooling and vapor 

superheat. The range of pressures is small since all plants reflood at low pressures. The 

Westinghouse plant parameters were extracted from best-estimate WCOBRA/TRAC 

calculations, while the plant parameters from Framatome and Siemens were taken from their 

Appendix K evaluation model calculations. 

The liquid Reynolds number was based on the inlet flow and the bottom cell in the bundle which 

was single phase liquid. The vapor Reynolds number was based on the local vapor superheat, 

and the calculated vapor flow rate in the dispersed flow film-boiling region of the bundle. The 

wall superheat is from the calculated peak cladding temperature for the calculation. The liquid 

subcooling and the vapor superheat are also given. 

Using Table 10.1 as a guide, a test matrix was developed to capture most of the range of 

conditions which the vendor and NRC safety analysis computer codes are required to calculate. 

Not all the heater rod temperature conditions will be directly simulated in the RBHT test program 

since many of the test conditions are at very high heater rod temperatures (>1093 degrees C, 

>2000 degrees F) which can limit the lifetime of the heater rods. Since the RBHT test program 

strategy is to reuse the expensive heater rods in two bundles builds, the very high temperature 

tests will be conducted in the second bundle build. Also, data are available from the FLECHT-
278

SEASET program in which several tests were run at very high temperatures, near or at the 

licensing limit, which can be used with the RBHT data to cover the full range of calculated 

conditions for reflood heat transfer model development. 

Table 10.1 Range of PWR Reflood Conditions 

Heat Transfer Regime PWR Range of Conditions 

Single Phase Liquid

Rel 5500 - 25000 

P (bar) [psia] 1.38 - 3.10 [20 - 45] 

Tsub = Tsat - Tl (oC) [oF] < 44 [< 80]

Single Phase Vapor

Rev 2500 - 9500

P (bar) [psia] 1.38 - 3.10 [20 - 45]

Tsat = Tv - Tsat (oC) [oF] 333 - 778 [600 - 1400]

Subcooled Boiling

Rel 5500 - 25000

P (bar) [psia] 1.38 - 3.10 [20 - 45]

Tsub = Tsat - Tl (oC) [oF] < 44 [<80]

Saturated Nucleate Boiling

Rel 5500 - 25000

P (bar) [psia] 1.38 - 3.10 [20 - 45]

Tsat = Tw - Tsat (oC) [oF] 2.78 - 16.7 [5 - 30]

Transition Boiling

Rel 5500 - 25000 

Rev 2500 - 9500 

P (bar) [psia] 1.38 - 3.10 [20 - 45]

Tsub = Tsat - Tl (oC) [oF] 0 - 44 [0 - 80]

Inverted Annular Film Boiling

P (bar) [psia] 1.38 - 3.10 [20 - 45]

Tsat = Tv - Tsat (oC) [oF] 222 - 333 [400 - 600]

Tsub = Tsat - Tl (oC) [oF] 0 - 11.1 [0 - 20]

Dispersed Flow Film Boiling

Rev 2500 - 9500

P (bar) [psia] 1.38 - 3.10 [20 - 45]

T = Tw - Tsat (oC) [oF] 222 - 1056 [400 - 1900]

Tsub = Tsat - Tl (oC) [oF] 0 [0]

Tv = Tw - Tv (oC) [oF] < 1000 [<1800]

The other source for the test conditions are those conditions obtained from the analysis of the 

FLECHT-SEASET test data and the earlier FLECHT Cosine (Ref. 8) and the FLECHT Skewed 

(Ref. 9) reports. In these tests, a mass and energy balance was used to calculate the axial 

quality behavior along the test bundle at different times using the non-equilibrium steam vapor 

temperature measurements. The vapor Reynolds number, void fraction, calculated quality, and 

rod temperatures are shown in Figures 10.1 to 10.3 for FLECHT-SEASET test 31504, which is a 

25.4 mm/s (1 in/s) flooding rate test at 2.76 bars (40 psia), 66.7 degrees C (120 degrees F) inlet 

subcooling, peak power of 2.3 kW/m (0.7 kW/ft) and an initial cladding temperature of 871 

degrees C (1600 degrees F). As the figures indicate, the high vapor temperatures result in very 

low vapor Reynolds numbers, well within the laminar region. The vapor Reynolds number is 

approximately proportional to 1/Tv

2

 such that as the vapor superheats, the Reynolds number 

decreases, even for relatively high vapor velocities (Ref. 3). 
279

10.4 Proposed Preliminary Test Matrix

A preliminary test matrix for the RBHT Test Facility is given in this section. A sufficient number 

of COBRA-TF calculations have been performed to specify the range of conditions for the tests 

as an envelope for the test facility design. Therefore, parameters such at flows, temperature 

limits, pressures, and powers have been broadly specified for the facility design to specify 

thermal-hydraulic conditions which provide data. 

The Tests are divided into the same classifications as given in Section 10.2 and reflect the 

building-block approach for characterizing the test facility as well as minimizing the duty on the 

heater rods. 

1. Steady-state flow characterization of the test facility, designed to provide the detailed 

pressure drop and loss coefficient information of the test facility so the facility can be 

modeled accurately. The Reynolds number range of interest covers laminar, transition, and 

fully turbulent ranges; therefore, the grid loss coefficients will be a strong function of the 

Reynolds number. The tests will be performed with the rod bundle unpowered, at 

approximately 2.68 bars (40 psia), and using subcooled water. The Reynolds number range 

that will be investigated is 1500 - 25000. Several tests and repeat tests, approximately 25 

valid tests total, will be performed to characterize the grid loss coefficients, rod bundle 

frictional losses and the total bundle pressure loss. 

2. Heat loss experiments to determine the heat loss characteristics of the facility. These tests 

will be performed in two steps. The first series of tests will be with the rod bundle 

unpowered using the hot water from the accumulator tank at 1.34 bars (Tsat = 108.9 degrees 

C) [20 psia (Tsat = 228 degrees F)], and 4.02 bars (Tsat = 145 degrees C) [60 psia (Tsat = 293 

degrees F)]. The bundle will be filled with hot water and the temperature distribution, as a 

function of time will be measured. The heat losses will be calculated from the data. 

Approximately three valid tests will be performed with an additional repeat test. The higher 

temperature heat loss data will be obtained as part of the radiation only and steam cooling 

tests. It should be noted that all heated tests will have sufficient instrumentation to 

characterize the heat losses. 

3. Radiation only tests with the facility evacuated to minimize free convection currents within 

the rod bundle. These tests will be used to characterize the rod-to-rod and rod-to-housing 

heat transfer within the bundle, and to verify the radiation heat losses given in Sections 6 

and 7. These tests will be performed using a constant power calculated to give maximum 

temperatures of 260, 538, and 816 degrees C at 2.76 bars (500, 1000, and 1500 degrees F 

at 40 psia) in a quasi-steady fashion. The tests will provide data for heat loss calculations. 

Heat loss should equal the bundle power if the temperature is constant. Pre-test 

calculations using both MOXY and COBRA-TF will be performed to estimate the target 

power level for the given peak temperature. Approximately six tests with repeat tests will be 

performed. 

4. Subcooled and saturated steady-state boiling experiments will be performed over a range of 

inlet subcooling, from approximately -17-27 degrees C (1 - 80 degrees F), with a pressure 

range of 1.34 to 4.02 bars (20 to 60 psia). The liquid flow rate and temperature will be 

varied to cover the liquid Reynolds range from approximately 4000 to 30000. The heater 

rods will be powered and the test section total power needed to develop boiling will be 

calculated using COBRA-IV or VIPRE-II subchannel codes. Simpler calculations will also be 
280

performed as a check. The heater rods should not exceed critical heat flux since the 

objective is to investigate stable nucleate and saturated boiling. Approximately 30 tests will 

be performed including repeat tests. The specific test matrix will be completed after the pretest calculations have been performed for the range of conditions. 

5. Convective steam cooling steady-state tests over a wide range of vapor Reynolds numbers 

from 1500 to 30000 with pressure variations from 1.34 to 4.02 bars (20 to 60 psia). As with 

the boiling tests in Part 4 above, pre-test predictions of the steam cooling tests will be made 

using COBRA-IV and/or VIPRE-II subchannel codes to help determine the test power. 

Simpler calculations will also be performed as a check. The bundle will be heated to a 

maximum temperature of 538 degrees C (1000 degrees F) to determine the consequence of 

temperature on the steam physical properties; i.e., the local Reynolds number. The tests 

will also be analyzed using the subchannel vapor temperature measurements with COBRAIV and/or VIPRE-II. The data will be reduced to obtain local heat transfer and Reynolds 

numbers. Approximately 30 tests will be performed after the pre-test predictions have been 

performed. 

6. Steady-state dispersed flow film boiling tests in which droplets, of known size and velocity, 

are injected into the steam flow for the same conditions as the steam only convective 

cooling tests. The test conditions will be preserved between these two different experiments 

to determine the effects of the droplets on the flow and resulting heat transfer behavior. The 

amount of the liquid flow will be estimated from the FLECHT-SEASET data and scaled 

appropriately for the RBHT Test Facility. The same scaling logic will have already been 

used for the 3x3 heated bench test. The heated bench test will have already been 

performed to qualify the LIDCS, which will measure the drop size and velocity. The range of 

vapor Reynolds numbers is the same as the steam cooling tests, from 1500 - 30000. The 

pressure will be varied from 1.34 to 4.02 bars (20 to 60 psia), and the initial drop size will be 

varied from approximately 0.5 to 1.52 mm (0.02 to 0.06 in). The initial drop velocity will be 

estimated from COBRA-TF pre-test calculations and from FLECHT-SEASET data. The 

initial drop velocity is a function of the inlet quality to be simulated. The rod bundle will be 

heated and the maximum temperature will be kept below 816 degrees C (1500 degrees F), 

with most tests temperatures peaking at 538 degrees C (1000 degrees F) to prolong the 

bundle life. 

7. Forced reflood experiments over a range of inlet flooding rates, which will correspond to 

liquid Reynolds of approximately 4000 to 25000 and vapor Reynolds numbers from 1500 to 

30000. The tests will be performed over the pressure range of 1.34 to 4.02 bars (20 to 60 

psia) with inlet subcoolings of approximately 2.78 to 66.7 degrees C (5 to 120 degrees F), 

and peak rod powers chosen not to exceed 1000 degrees C (1800 degrees F). The initial 

temperatures and powers will be determined by pre-test predictions using COBRA-TF. The 

code calculations will also be used to verify the range of Reynolds numbers within the 

bundle. There will be approximately 20 forced reflood tests. 

8. Gravity reflood and or variable reflood tests. The purpose is to examine the effect of 

variable inlet flow on entrained liquid which is carried to upper regions of the bundle. In a 

PWR, the inlet flow initially surges into the core as the downcomer fills and its head 

increases. The two-phase froth front and liquid continuous flow regime can penetrate 

further into the bundle than the quench front to produce inverted annular film boiling. 

However, the head in the core region quickly comes in equilibrium with the downcomer head 

and the flow into the bundle decreases. The water in the bundle quickly heats and boils and 
281

entrainment from the bundle increases. Water above the quench front tends to be entrained 

and carried through the bundle, providing improved cooling at the upper elevations. 

These tests will use a stepped variable inlet flooding rate and will vary the flooding rate time 

history, inlet subcooling and the system pressure. The variable flooding rate tests will be 

integrated into the forced flooding experiments so that the final low flooding rate period will 

overlap with the forced flooding rate tests. Approximately five tests are planned. 

10.5 Conclusions

Eight different types of experiments have been planned for the RBHT Test Facility to 

characterize the facility as well as to obtain data on dispersed flow film boiling. The experiments 

cover the ranges of conditions which best estimate and Appendix K reflood models are required 

to calculate. Hydraulic heat loss characterization experiments will be conducted. Single phase 

liquid boiling experiments, radiation only experiments, and single phase steam convection heat 

transfer experiments will also be performed to characterize the facility. In this fashion, the 

modeling uncertainties of the test facility are reduced. 

The tests are structured in a building block approach to separate and understand the 

components of dispersed flow film boiling, so there is less of a chance of compensating error 

being applied in a specific heat transfer mode. 

The precise test conditions will be developed. There is a need to perform further pre-test 

predictions to select the range of rod powers and initial temperatures to provide the data needed 

while at the same time, to minimize the duty on the heater rods. The facility design envelope is 

sufficiently broad to be able to perform tests over a wide range of initial and boundary 

conditions. 

10.6 References

1. Chiou, J. S. and L. E. Hochreiter, ACombined Radiation and Dispersed Flow Film Boiling in 

a BWR Rod Bundle with Top Spray,@ Proceedings of 26th National Heat Transfer 

Conference, Philadelphia, PA, 1989. 

2. Hochreiter, L.E. and J. S. Chiou, ACOBRA-TF Analysis of SVEA Spray Cooling 

Experiments,@ Proceedings of 26th National Heat Transfer Conference, Philadelphia, PA, 

1989. 

3. Lee, N., S. Wong, H. C. Yeh, and L. E. Hochreiter, APWR FLECHT-SEASET Unblocked 

Bundle, Forced and Gravity Reflood Test Data Evaluation and Analysis Report,@

NUREG/CR-2256, 1981. 

4. Yoder, G., et al, ADispersed Flow Film Boiling in Rod Bundle Geometry, Steady-State Heat 

Transfer Data and Correlation Comparisons,@ NUREG/CR-2435, 1982. 

5. Bajorek, S. M., Letter to L.E. Hochreiter on ACalculated Range of Conditions for PWR 

Reflood Transients,@ June 1998. 
282

6. Nithianandan, C.K., Framatome Technologies, Letter to L.E. Hochreiter on ACalculated 

Range of Conditions for PWR Reflood Transients,@ September 1998. 

7. O=Dell, L., Siemens, Letter to L.E. Hochreiter on ACalculated Range of Conditions for PWR 

Reflood Transients,@ September 1998. 

8. Lilly, G.P., H. C. Yen, L. E. Hochreiter, and N. Yamaguchi, APWR FLECHT Cosine Low 

Flooding Rate Test Series Evaluation Report@, WCAP-8838, 1977. 

9. Lilly, G.P., H. C. Yeh, L. E. Hochreiter, and N. Yamaguchi, APWR FLECHT Skewed Profile 

Low Flooding Rate Test Series Evaluation Report,@ WCAP-9183, 1977. 
11. Test Facility Design 

11.1 Introduction

The RBHT Test Facility is designed to conduct systematic separate-effects tests under wellcontrolled conditions in order to generate fundamental rod bundle heat transfer data including 

single phase steam cooling tests, low flow boiling tests, steam flow tests with injected droplets 

and inverted annular film boiling and dispersed flow film boiling heat transfer. The facility is 

capable of operating in both forced and variable flow reflood modes covering wide ranges of 

flow and heat transfer conditions at pressures from 1.34 to 4.02 bars (20 psia to 60 psia). 

11.2 General Design Description

The RBHT Test Facility consists of the following major components, shown schematically in 

Figure 11.1: 

• A test section consisting of a lower plenum, a low-mass housing containing the heater 

rod bundle, and an upper plenum 

• Coolant injection and steam injection systems 

• Closely coupled phase separation and liquid collection systems 

• An injection system 

• A pressure fluctuation damping tank and steam exhaust piping 

Figure 11.1 RBHT Test Facility Schematic. 

283
11.3 Detailed Component Design Description

The various components of the RBHT Test Facility are described in the following paragraphs. 

All components are well insulated to minimize heat losses to the environment. 

11.3.1 Test Section

The test section consists of the heater rod bundle, the flow housing, and the lower and upper 

plenums, as shown in Figure 11.2. 

Figure 11.2 Test Section Isometric View. 

The heater rod bundle simulates a small portion of a 17x17 reactor fuel assembly. The 

electrically powered heater rods have a diameter of 9.5 mm (0.374 inches) arranged in a 7x7 

array with a 12.598 mm (0.496 in) pitch, as shown in Figure 11.3. The heater rod specifications 

are listed in Table 11.1. The bundle has 45 heater rods and four unheated corner rods. The 

corner rods are used to support the bundle grids and the grid and fluid thermocouple leads. The 

support rods are made from Inconel 600 tubing having a diameter of 9.525 mm (0.375 in), a wall 

thickness of 2.108 mm (0.083 in), and have a length of 3.96 m (156 in). The heater rods are 

284
Table 11.1 General Specifications

Operating Pressure 

Maximum Sheath Temperature 

200 psi 

220 degrees F 

Heater Rod (Schematic Drawing) 

Design Power 

Design Voltage 

Design Current 

Design Resistance (@ 1000 degrees F) 

Electrical Resistance (@ 70 degress F) 

Axial Power Profile 

10.0 kW 

57V 

175.4A 

0.325 Ω

0.306 Ω " 5 percent 

Linear 0.5/1.5/0.5 

(See Figure 11.5) 

Heated Length 144 in 

Average Linear Power 

Peak Linear Power 

0.83 kW/ft 

1.25kW/ft 

Outside Diameter 

Overall Sheath Length 

Electrode Length 

Electrode Diameter 

Extension Length - Top 

0.374 " 0.002 in 

172 in 

8 in 

0.230 " 0.002 in 

8 " 0.25 in 

Sheath Surface Finish As Swaged 

(63 Fin or better) 

Figure 11.3 Rod Bundle Cross Sectional View. 

285
Figure 11.4 Heater Rod. 

Figure 11.5 Heater Rod Axial Power Profile. 

286

single ended and consist of a Monel 500 electrical resistance element filled and surrounded by 

hot pressed boron nitride (BN) insulation, and enclosed in an Inconel 600 cladding, as shown in 

Figure 11.4. This material was chosen for its high strength and low thermal expansion 

coefficient at high temperatures, which minimizes rod bowing and failure at high temperature 

operating conditions since it was desired to reuse the heater rods for a second bundle build. 

The heater rods have a 3.657 m (12 ft) heated length with a skewed axial power profile, as 

shown in Figure 11.5, with the peak power located at the 2.74 m (9 ft) elevation. The maximumto-average power ratio (Pmin/Pavg) is 1.5 and the minimum-to-average power ratio (Pmin/Pavg) is 

0.5 at both ends of the heated length. The bundle has a uniform radial power distribution. 
Power to each rod is provided by a 60 volt, 12,600 amp, 750 kW DC power supply. Each rod is 

rated for 10 kW, and designed to operate at 13.8 bars (200 psig) at a maximum temperature of 

1204 degrees C (2200 degrees F), but because of its solid construction can be operated at up 

to 103.4 bars (1500 psig). Each rod is instrumented with eight 0.508 mm (20 mil) diameter 

ungrounded thermocouples attached to the inside surface of the Inconel sheath at various 

locations. All of the thermocouple leads exit at the heater rod bottom end. Thermocouple 

specifications are shown in Table 11.2. The Inconel 600 thermocouple sheath is compatible 

with the heater rod cladding and housing material to reduce thermal expansion and minimize 

the possibility of thermocouple failure during the thermocycling operations. 

Table 11.2 Thermocouple Specifications

Type Premium grade ANSI Type K 

Diameter 0.02 in 

Sheath Inconel 600 

Insulation MgO 

Junction Ungrounded, BN backfilled 

Length Up to 18 ft 

Resistance, Lead to Sheath 1x1011 Ω at 50 V 

Length beyond Heater Sheath 48 in 

Figure 11.6 Low-Melt Reservoir. 

287
The rod bundle has eight grids located 0.522 m (20.55 in) apart except for the spacing between 

the first and second grids, which are 588.26 mm (23.16 in) apart. The first grid is located 

101.854 mm (4.01 in) above the bottom of the heated length. The grid elevations are similar to 

the ones found in a 17x17 fuel assembly. The grids, in conjunction with the corner support rods, 

form the heater rod bundle support structure. The heater rod top extensions are attached to the 

2.4 cm (1 in) thick nickel ground plate by means of a Morse taper that provides a good electrical 

contact. The heater rod bottom extension and copper electrode extend through the lower 

plenum-O ring pressure seal plate. The copper electrodes, which are 5.842 mm (0.230 in) in 

diameter and 203 mm (8 in) long, extend through holes drilled in the low-melt reservoir shown in 

Figure 11.6. This reservoir serves as the electrical power supply positive side connection. It 

contains a low temperature melting alloy that melts at about 71.11 degrees C (160 degrees F) 

which is an excellent conductor, thus providing a good electrical contact to each heater rod. 

The flow housing provides the pressure and flow boundary for the heater rod bundle. It has a 

square geometry. Its nominal inside dimensions are 90.17 mm2

 (3.55 in2), and wall thickness 

6.35 mm (0.25 in), as shown in Figure 11.7. The housing is made out of Inconel 600, the same 

material used for the heater rod cladding and thermocouple sheaths. As pointed out previously, 

the high strength of Inconel 600 at elevated temperatures will minimize housing distortion during 

testing. The 6.35 mm (0.25 in) wall thickness is the minimum allowable for operating at 4.0 bars 

(60 psia) and 537.77 degrees C (1000 degrees F), taking into consideration the cutouts to 

accommodate the large windows and the numerous pressure and temperature penetrations 

through the walls. The empty housing has a flow area of 81.29 cm2

 (12.60 in2). With the rod 

bundle in place the flow area is 45.80 cm2

 (7.1 in2). This area is 8.2 percent larger than the 

ideal flow area of a 7x7 rod bundle configuration. The excess flow area is due to the flow 

housing inside dimensional tolerance and the space needed to insert the rod bundle in the 

housing. The gap between the outer rods and the flow housing inner wall is 2.54 mm (0.1 in) 

wide. 

Figure 11.7 Low Mass Flow Housing Assembly. 

288
The flow housing has six pairs of windows. Each window provides a 50.8x292.1 mm (2x11.5 in) 

viewing area. Each pair of windows is placed 180 degrees apart and located axially at 

elevations overlapping rod bundle spacer grids, thus providing a viewing area about 88.9 mm 

(3.5 in) below and 152.4 mm (6 in) above the corresponding spacer grids. The windows will 

facilitate the measurement of droplet size and velocity using a Laser Illuminated Digital Camera 

System (LIDCS). The two-phase void fraction will be measured using a X-ray densitometer, as 

well as sensitive differential pressure (DP) cells. In addition, high speed movies using diffused 

back lighting can be taken during the experiments, if desired, for visualization and flow regime 

information. The windows are made out of optical grade fused quartz and are mounted on the 

housing by means of a bolted flange and Thermiculite high temperature gasketing material, as 

shown in Figure 11.8. 

Figure 11.8 Housing Window. 

The flow housing has 22 pressure taps located at various elevations, as shown in Figure 11.7. 

The pressure taps are connected to sensitive DP cells, providing measurements to calculate 

single-phase friction losses for determining bare rod bundle and grid loss coefficients. Nine of 

these pressure taps are located about 76.2 mm (3 in) apart to provide detailed void fraction 

measurements in the froth region above the quench front. The flow housing is supported from 

the nickel plate and upper plenum, allowing it to freely expand downward, thus minimizing 

thermal buckling and distortion. 

289
11.3.2 Lower Plenum

The lower plenum is attached to the bottom of the flow housing. The lower plenum is made out 

of nominal 203.2 mm (8 in) schedule 40, 304 stainless steel pipe with an inside diameter of 

201.6 mm (7.937 in), a height of 203.2 mm (8 in), and a volume of 6569.5 cm3

 (0.232 ft3), as 

shown in Figure 11.9. The lower plenum is used as a reservoir for the coolant prior to injection 

into the rod bundle during reflood. It connects to the injection water line and steam cooling line. 

It has two penetrations for thermocouples monitoring the coolant temperature prior and during 

reflood, and a pressure tap for static and differential pressure measurements. 

 

 Figure 11.9 Lower Plenum. Figure 11.10 Lower Plenum Flow Baffle. 

The lower plenum also has four Conax fittings with multiple probes sealing glands for the bundle 

grid, steam probes, and support rod wall thermocouple extensions that are routed through the 

bottom of the rod bundle. It contains a flow baffle, which is attached to the flow housing bottom 

flange. The flow baffle has a square geometry, similar to the flow housing, as shown in Figure 

11.10. The flow baffle wall has numerous small diameter holes that act as a flow distributor and 

flow straightener to provide an even flow distribution into the rod bundle. 

11.3.3 Upper Plenum

The upper plenum serves as the first stage for phase separation and liquid collection of the twophase effluent exiting the rod bundle. The liquid phase separates due to the sudden expansion 

from the bundle to the larger plenum flow area. The de-entrained liquid is collected around the 

flow housing extension in the upper plenum. The extension acts as a weir preventing the 

separated liquid from falling back into the heater rod bundle. The upper plenum vessel 

configuration is shown in Figure 11.11. The vessel is made from a 203.2 mm (8 in) 304 

stainless steel pipe with an inside diameter of 201.6 mm (7.937 in) and a height of 304.8 mm 

(12 in). It has a volume of 9825.95 cm3

 (0.347 ft3). The plenum has a 76.2 mm (3 in) pipe 

flanged connection to the steam separator and two penetrations for fluid thermocouples. It is 

covered with a 203.2 mm (8 in) 304 stainless steel blind flange. This flange has a 25.4 mm 

290
 Figure 11.11 Upper Plenum. Figure 11.12 Exhaust Line Baffle. 

 

 Figure 11.13 Large Carryover Tank. Figure 11.14 Small Carryover Tank. 

291
292

(1 in) penetration for steam injection, venting, and connecting the safety relief valve and rupture 

disc assembly. It also has a pressure tap penetration for static and differential pressure 

measurements. In addition, the upper plenum contains an exhaust line baffle, shown in Figure 

11.12. The baffle is used to further de-entrain water from the steam, and prevents water 

dripping from the upper plenum cover flange to be carried out by the exhaust steam. The baffle 

has a 76.2 mm (3 in) flange connection at one end. It is inserted through the upper plenum exit 

nozzle, and it is bolted between the nozzle flange and the flange of the pipe going to the steam 

separator. 

11.3.4 Carryover Tanks

The de-entrained liquid from the upper plenum drains into the top of a 25.6 mm (1 in) tube which 

extends inside a small carryover tank to detect and measure the carryover liquid as soon as

possible. This tank, shown in Figure 11.14, is connected close coupled in series with a larger 

carryover tank, shown in Figure 11.13, which collects and measures the amount of liquid 

overflow from the smaller carryover tank. The small carryover tank has a volume of about 

4247.53 mm3 (0.15 ft3

) to more accurately measure the water being collected as a function of 

time. This tank is made from a 76.2 mm (3 in) schedule 40 pipe having an overall length of 

0.9144 m (36 in) including the end caps. The large carryover tank is made from a 101.6 mm (4 

in) schedule 40 pipe with a bottom end cap and top flanges having an overall length of 152.4 

mm (6 ft) and a capacity of 15007.9 mm3

 (0.53 feet3). Each tank is connected with 25.4 mm (1 

in) flexible hose, and has a 1 in drain tube, and 9.525 mm (3/8 in) tubes with wall penetrations 

for installing fluid and level meters. 

11.3.5 Steam Separator and Collection Tanks

The wet steam exhausted from the upper plenum flows through a steam separator (or dryer), 

shown in Figure 11.15, where carryover liquid droplets are further separated from the steam. 

The droplets are collected in a small collection tank, shown in Figure 11.16, attached to the 

bottom of the steam separator. The steam separator relies on centrifugal force action to provide 

99 percent dry steam. The separated liquid is drained into a collection tank where a DP cell is 

used as a level meter to measure the liquid accumulation. The steam separator is fabricated 

from a 355.6 mm (14 in) diameter 316 stainless steel pipes and is 914.4 mm (36 in) long. It has 

50.8 mm (2 in) connecting nozzles, a 25.4 mm (1 in) drain, and a 12.7 mm (0.5 in) top vent. It 

also has two pressure taps for liquid level measurements and two 38.1 mm (1.5 in) side nozzle 

connections. The drain tank is a small vessel with a capacity of 0.0113 m3

 (0.4 ft3). It is made 

from a 101.6 mm (4 in) schedule 10, 304 stainless steel pipe with an overall length of 121.9 mm 

(48 in), including both end caps. It has a 25.4 mm (1 in) drain nozzle, a 25.4 mm (1 in) pipe top 

connection to the steam separator, pressure taps and fluid thermocouple connections. 

11.3.6 Pressure Oscillation Damping Tank 

The dry steam from the steam separator flows into a pressure oscillation-damping tank. As its 

name implies, it is used to dampen pressure oscillations in the upper plenum caused by rapidly 

oscillating steam generation rates in the heater rod bundle during reflood. This effect is coupled 

to the characteristics of the pressure control valve, which is located downstream in the steam 

exhaust line. It is desirable to have a smooth pressure control in order to minimize uncertainties

when calculating mass balances, steam generation rates, and heat transfer coefficients in the 

heater rod bundle, and avoid the pressure control valve causing oscillations in the bundle as it 

cycles. The tank has a volume of 0.227 m3

 (8 ft3), which is approximately equal to the total 
Figure 11.15 Steam Separator. 

Figure 11.16 Steam Separator Collection Tank. 

293
Figure 11.17 Pressure Oscillation Damping Tank. 

volume of the rest of the test facility. This design criterion was used successfully in the 

ACHILLES reflood test facility (Refs. 1, 2, 3, 4, 5 and 6). The pressure tank is fabricated from a 

355.6 mm (14 in), 304 stainless steel standard schedule pipe by 2.59 m (102 in) long, as shown 

in Figure 11.17. Inside the tank is a 76.2 mm (3 in), schedule 40, 304 stainless steel pipe that 

provides a tortuous path for the steam flow to expand into a large volume, thus damping 

pressure oscillations. The inlet and outlet nozzles are 76.2 mm (3 in) in diameter with flanges. 

The vent and drain lines are made of 25.4 mm (1 in) pipe. There are 9.53 mm (3/8 in) tube 

penetrations for a fluid thermocouple and two static pressure taps. The tank walls are heated 

with clamp-on strip heaters up to about 10 degrees above saturation temperatures to prevent 

steam condensation. 

11.3.7 Exhaust Piping

The steam flowing out of the pressure oscillation-damping tank is exhausted through a 76.2 mm 

(3 in) schedule 40, 304 stainless steel pipes, shown schematically in Figure 11.20. The exhaust 

line has a Vortex flowmeter, a 76.2 mm (3 in) V-Ball pressure control valve, and a muffler at the 

exit to minimize the noise caused by steam blowing into the atmosphere. The pressure control 

valve is activated by a signal from a static pressure transmitter located on the upper plenum. 

294
The line is also instrumented with a static pressure transmitter, fluid thermocouples, and outer 

wall thermocouples. The 76.2 mm (3 in) line has flow-straightening vanes which reduce the 

pipe length requirements upstream of the Vortex meter in order to obtain accurate flow 

measurements. This line has strapped-on electrical heaters to keep the wall temperature about 

11.11 degrees C (20 degrees F) above saturation to insure that single-phase steam flow 

measurements are made by the Vortex flowmeter. 

Figure 11.18 Injection Water Supply Tank. 

295
296

11.3.8 Injection Water Supply Tank

The injection water system consists of a water supply tank, a circulating pump, and 

interconnecting lines to the test section lower plenum. The water supply tank, shown in Figure 

1118, has a capacity of 200 gal. It is designed for 4.0 bar (60 psia) and 154.44 degrees C (310 

degrees F). The tank is equipped with a submersible electrical heater to heat the injection water 

to specified test temperatures. The tank is pressurized by a nitrogen supply system, which 

regulates the over-pressure needed for the forced flooding injection tests. The tank has inlet 

and outlet nozzles, pressure taps for level measurements, fluid and wall thermocouples. Water 

from the tank can be circulated through the test section by a centrifugal pump with a capacity up 

to 250 gpm which is needed to perform liquid single-phase flow tests. 

11.3.9 Water Injection Line

The water injection line, shown schematically on Figure 11.20, consists of a 50.8 mm (2 in) 

diameter 304 stainless steel tubing with a 2.7686 mm (0.109 in) wall. It is rated for 60 psia (4.0 

bar) and 154.44 degrees C (310 degrees F) service. This line has a Coriolis Effect type 

flowmeter, a V-ball control valve, a quick opening solenoid valve, and appropriate shut-off and 

drain valves. It also has penetrations for static pressure and fluid thermocouples, and outside 

wall thermocouples. The line has tracer electrical cable type heater to maintain the water being 

injected at the proper test inlet temperatures. The water injection line can also be extended to 

the downcomer during gravity reflood tests. 

11.3.10 Steam Supply

A boiler with a capacity of 2613 kg (5760 lbs) per hour at 10 bar (150 psia) provides steam for 

the single phase steam cooling , pressure drop and water droplet injection tests. It also 

provides steam for preheating the test components prior to testing. The boiler is connected to 

the lower plenum by means of a 50.8 mm (2 in), 304 stainless steel tube. It is equipped with a 

Vortex flowmeter to measure steam flows, fluid and wall thermocouples, a V-ball control valve, 

and a quick acting solenoid valve. The boiler is also connected to the upper plenum to provide 

steam for preheating the test components prior to testing. 

11.3.11 Droplet Injection System

A system to inject water droplets into the test section has been included in the RBHT design. 

The droplet injection system consists of six 2.38 mm (3/32 in) O.D. stainless steel tubes 

entering through the test section at the 1.295 m (51 in) elevation. The tubes run perpendicular 

to the heater rods and penetrate through both sides of the housing as seen in Figure 11.19. 

The tubes can be easily removed when not needed so they do not interfere with other types of 

tests. Water is supplied to the injector tubes from the injection water supply tank as described 

in Section 11.3.8 and a series of small holes are drilled in the tubes to inject water directly into 

each of the 36 subchannels. 

11.4 Test Facility Instrumentation

The test facility instrumentation is designed to measure temperatures, power, flows, liquid 

levels, pressures, void fractions, and droplet sizes, distribution, and drop velocities. The vapor 

velocity cannot be directly measured in a two-phase dispersed flow, but it can be calculated at 
Figure 11.19 Droplet Injection Schematic. 

different axial positions from the data. Overall and transient mass and energy balances, mass 

inventories, carryover liquid and steam flows as a function of time can be calculated. Heater rod 

power, temperature, and fluid temperature are used to calculate heat fluxes and heat transfer 

coefficients, quench times, rod bundle energy losses, convective and radiation heat transfer to 

steam, droplets, grids, support rods, and housing. Effects of grids, support rods and housing 

behavior during reflood can be determined. Void fraction can be determined from the pressure 

drop measurements below the quench front and in the froth level above the quench front. The 

laser illuminated digital camera measurements are used to determine droplet entrainment 

behavior and droplet effects on heat transfer, and steam desuperheating above the quench 

front.

11.4.1 Loop Instrumentation and Controls

Loop instrumentation is shown schematically in Figure 11.20, and the instrumentation and data 

acquisition channels are listed in Table 11.3. There are 61 instrumentation channels assigned 

to the collection of electrical power, fluid and wall temperatures, levels, flows, differential 

pressures, and static pressure measurements. The injection water supply tank has three fluid 

and three wall thermocouples to monitor water and wall temperatures during heat-up prior to 

testing. A DP transmitter used as a level meter to determine water mass in the tank and mass 

depletion during reflood testing. A static pressure transmitter which monitors the nitrogen 

overpressure and controls the nitrogen flow needed to maintain a constant pressure during 

forced injection reflood tests. 

The water injection line is equipped with a Coriolis Effect Micromotion flowmeter that directly 

measures mass flows up to 454 kg/min (1000 lbs/min) with an accuracy of plus or minus eleven 

hundredths of a percent (±0.11 percent) of the flow rate. The steam line has a Rosemount 

Vortex shedding flowmeter to measure flow up to 7.08 m3

/min (250 ft3/min) with an accuracy of 

plus or minus 65 hundredths of a percent (±0.65 percent) of the flow rate. Each flowmeter is 

connected through a pneumatic controller to a V-ball flow control valve. Each line has a fluid 

thermocouple to measure water or steam temperature during heat-up and forced injection

297
Figure 11.20 Loop Instrumentation Schematic. 

testing. The injection line has three wall thermocouples to monitor wall temperatures during 

heat-up and during testing. One of these thermocouples in conjunction with a temperature 

controller regulates the power to an electrical heating cable wrapped around the injection line. 

The heating cable is used to heat-up the injection line wall and to maintain the injection water at 

the required injection temperature. 

The carryover tank instrumentation consists of one fluid thermocouple, three wall 

thermocouples, and a liquid level meter which measures the amount of carryover liquid being 

collected during testing. In addition, a DP transmitter is connected from the top of the carryover 

tank to the upper plenum to determine the static pressure in the carryover tank. 

The steam separator and drain tank are instrumented with two wall thermocouples to monitor 

wall temperatures during heat-up. The drain tank has a fluid thermocouple to measure 

temperatures of de-entrained liquid being collected during testing. The volume of de-entrained 

water is measured with a level meter connected across the drain tank. A DP transmitter is 

connected between the steam separator and upper plenum. 

The pressure oscillation damping tank has three wall thermocouples which are used to monitor 

vessel walls during heat-up, and to insure that the vessel wall is at a temperature above 

saturation to prevent condensation. One wall thermocouple in conjunction with a temperature 

controller monitors the power applied to clamp-on heaters that heat up the tank to the desired 

wall temperature. 

298
299

The exhaust line is equipped with a Rosemount Vortex shedding flowmeter which, in 

conjunction with a static pressure transmitter and fluid thermocouple measurements, is used to 

calculate steam volumetric flows up to 7.08 m3

/min (250 ft3/min). The flowmeter has an 

accuracy of plus or minus 65 hundredths of a percent (±0.65 percent) of the flow rate. The 

exhaust line also has wall thermocouples to measure pipe wall temperatures. One wall 

thermocouple in conjunction with a temperature control regulates the power going to clamp-on 

heaters which are used for heating the pipe walls up to a temperature above saturation of about 

11 degrees C (~20 degrees F) to prevent steam condensation and to insure accurate single 

phase steam flow measurements. The exhaust line has a V-ball pressure control valve this 

valve is controlled by a static pressure transmitter through a pneumatic controller connected to 

the top of the upper plenum in order to maintain constant test section pressure during testing. 

11.4.2 Test Section Instrumentation

The test section is heavily instrumented to obtain the data described at the beginning of Section 

11.4. 

The test section instrumentation consists of the heater rod bundle and flow housing, the lower 

plenum, and the upper plenum groups. The heater rod bundle and flow housing instrumentation 

is shown schematically in Figure 11.21 and listed in Table 11.3. Figure 11.21 shows the 

instrumentation axial locations in relation to heater rod heated length, heater axial power profile, 

grids, housing pressure taps, and windows. 

Five grids have thermocouples attached to their surfaces in order to determine quenching 

behavior during reflood. Eight groups of heater rods have thermocouples at different elevations 

to cover, as much as possible, the entire rod bundle heated length. The radial location of each 

heater rod group is shown in Figure 11.22. The radial locations of instrumentation rods were 

chosen in order to be able to characterize heat transfer of hot rods simulated by the center rods, 

rod-to-rod and rod-to-housing radiation heat transfer. For this purpose, heater rod 

thermocouples, steam probes, and housing wall thermocouples are located at the same 

elevations. In addition, symmetrical location of the same group of instrumented heater rods will 

help in the data analysis and will determine any anomalies in the radial flow distribution through 

the rod bundle. Rod thermocouples are also placed at varying distances downstream from a 

grid to determine the decreasing heat transfer gradient between grid spans. The steam probe 

or fluid thermocouples are located at short distances upstream and downstream of a grid to 

determine the effect of water droplets being shattered by the grids on droplet size and 

distribution, and the de-superheating effect on steam temperatures in the disperse flow regime. 

The vapor or steam temperature will be measured using miniature thermocouples which are 

attached to the spacer grids or are used for traversing. These are very small bare 

thermocouples that have a fast response time such that they can follow the vapor temperature 

accurately in a dispersed, non-equilibrium, two-phase flow. As the froth front approaches, the 

number and sizes of the droplets increase which can lead to wetting of these thermocouples. 

Experiments performed as part of the FLECHT-SEASET program indicated that very small bare 

thermocouples would provide reliable vapor superheat ready for the longest time period until 

they quench as the froth region approached. While the Lehigh vapor probe was considered, it is 

too large and causes a flow distribution effect which is not typical of the bundle. The Lehigh 

probe would block 68 percent of the gap between adjacent heat rods. The effect of the probe 

would be to distort the data downstream of the sensing location. Such flow distribution
Figure 11.21 Rod Bundle and Housing Instrumentation Axial Locations. 

300
Table 11.3 Instrumentation and Data Acquisition Channel List 

CHAN NAME PANEL/ Slot, SCP CHAN NAME PANEL/ Slot, SCP

INPUT # & SCP # INPUT # & SCP #

497 Pnl1-Therm2S 1-0 1-E1508A-0 499 Pnl3-Therm2S 3-0 2-E1508A-0

418 Lg CT fl 1-1 1-E1508A-0 392 U Plen wall-b 3-1 2-E1508A-0

419 Lg CT wall-t 1-2 1-E1508A-0 399 Sup Tnk fl-t 3-2 2-E1508A-0

420 Lg CT wall-m 1-3 1-E1508A-0 400 Sup Tnk fl-m 3-3 2-E1508A-0

421 Lg CT wall-b 1-4 1-E1508A-0 401 Sup Tnk fl-b 3-4 2-E1508A-0

422 Sm CT fl 1-5 1-E1508A-0 402 Sup Tnk wall-t 3-5 2-E1508A-0

423 Sm CT wall-t 1-6 1-E1508A-0 403 Sup Tnk wall-m 3-6 2-E1508A-0

424 Sm CT wall-b 1-7 1-E1508A-0 404 Sup Tnk wall-b 3-7 2-E1508A-0

1 HR_B1-48.1 1-8 1-E1508A-1 49 HR_B2-4.2 3-8 2-E1508A-1

2 HR_B1-63.9 1-9 1-E1508A-1 50 HR_B2-11.2 3-9 2-E1508A-1

3 HR_B1-68.9 1-10 1-E1508A-1 51 HR_B2-16.2 3-10 2-E1508A-1

4 HR_B1-79.7 1-11 1-E1508A-1 52 HR_B2-23.2 3-11 2-E1508A-1

5 HR_B1-97.3 1-12 1-E1508A-1 53 HR_B2-29.2 3-12 2-E1508A-1

6 HR_B1-114.9 1-13 1-E1508A-1 54 HR_B2-33.2 3-13 2-E1508A-1

7 HR_B1-126.6 1-14 1-E1508A-1 55 HR_B2-35.2 3-14 2-E1508A-1

8 HR_B1-139.3 1-15 1-E1508A-1 56 HR_B2-38.2 3-15 2-E1508A-1

9 HR_D1-48.1 1-16 1-E1508A-2 57 HR_C2-41.2 3-16 2-E1508A-2

10 HR_D1-63.9 1-17 1-E1508A-2 58 HR_C2-53.1 3-17 2-E1508A-2

11 HR_D1-68.9 1-18 1-E1508A-2 59 HR_C2-55.1 3-18 2-E1508A-2

12 HR_D1-79.7 1-19 1-E1508A-2 60 HR_C2-58 3-19 2-E1508A-2

13 HR_D1-97.3 1-20 1-E1508A-2 61 HR_C2-63.9 3-20 2-E1508A-2

14 HR_D1-114.9 1-21 1-E1508A-2 62 HR_C2-73.8 3-21 2-E1508A-2

15 HR_D1-126.6 1-22 1-E1508A-2 63 HR_C2-75.7 3-22 2-E1508A-2

16 HR_D1-139.3 1-23 1-E1508A-2 64 HR_C2-76.7 3-23 2-E1508A-2

17 HR_F7-48.1 1-24 1-E1508A-3 65 HR_D2-103.2 3-24 2-E1508A-3

18 HR_F7-63.9 1-25 1-E1508A-3 66 HR_D2-106.1 3-25 2-E1508A-3

19 HR_F7-68.9 1-26 1-E1508A-3 67 HR_D2-112.9 3-26 2-E1508A-3

20 HR_F7-79.7 1-27 1-E1508A-3 68 HR_D2-114.9 3-27 2-E1508A-3

21 HR_F7-97.3 1-28 1-E1508A-3 69 HR_D2-116.8 3-28 2-E1508A-3

22 HR_F7-114.9 1-29 1-E1508A-3 70 HR_D2-120.7 3-29 2-E1508A-3

23 HR_F7-126.6 1-30 1-E1508A-3 71 HR_D2-124.6 3-30 2-E1508A-3

24 HR_F7-139.3 1-31 1-E1508A-3 72 HR_D2-128.5 3-31 2-E1508A-3

SLOT 1 SLOT 2

301
Table 11.3 Instrumentation and Data Acquisition Channel List (Continued) 

CHAN NAME PANEL/ Slot, SCP CHAN NAME PANEL/ Slot, SCP

INPUT # & SCP # INPUT # & SCP #

498 Pnl2-Therm2S 2-32 1-E1508A-4 500 Pnl4-Therm2S 4-32 2-E1508A-4

385 L Plen fl-t 2-33 1-E1508A-4 407 Sup Ln fl 4-33 2-E1508A-4

386 L Plen fl-b 2-34 1-E1508A-4 408 Sup Ln wall 4-34 2-E1508A-4

387 L Plen wall-t 2-35 1-E1508A-4 409 Sup Ln wall 4-35 2-E1508A-4

388 L Plen wall-b 2-36 1-E1508A-4 410 Sup Ln wall 4-36 2-E1508A-4

389 U Plen fl-t 2-37 1-E1508A-4 414 St Sup fl 4-37 2-E1508A-4

390 U Plen fl-b 2-38 1-E1508A-4 415 St Sup wall 4-38 2-E1508A-4

391 U Plen wall-t 2-39 1-E1508A-4 428 St Sep fl 4-39 2-E1508A-4

25 HR_D7-48.1 2-40 1-E1508A-5 73 HR_E2-50.1 4-40 2-E1508A-5

26 HR_D7-63.9 2-41 1-E1508A-5 74 HR_E2-54.1 4-41 2-E1508A-5

27 HR_D7-68.9 2-42 1-E1508A-5 75 HR_E2-57 4-42 2-E1508A-5

28 HR_D7-79.7 2-43 1-E1508A-5 76 HR_E2-60 4-43 2-E1508A-5

29 HR_D7-97.3 2-44 1-E1508A-5 77 HR_E2-65.9 4-44 2-E1508A-5

30 HR_D7-114.9 2-45 1-E1508A-5 78 HR_E2-69.8 4-45 2-E1508A-5

31 HR_D7-126.6 2-46 1-E1508A-5 79 HR_E2-72.8 4-46 2-E1508A-5

32 HR_D7-139.3 2-47 1-E1508A-5 80 HR_E2-74.8 4-47 2-E1508A-5

33 HR_A6-48.1 2-48 1-E1508A-6 81 HR_F2-4.2 4-48 2-E1508A-6

34 HR_A6-63.9 2-49 1-E1508A-6 82 HR_F2-11.2 4-49 2-E1508A-6

35 HR_A6-68.9 2-50 1-E1508A-6 83 HR_F2-16.2 4-50 2-E1508A-6

36 HR_A6-79.7 2-51 1-E1508A-6 84 HR_F2-23.2 4-51 2-E1508A-6

37 HR_A6-97.3 2-52 1-E1508A-6 85 HR_F2-29.2 4-52 2-E1508A-6

38 HR_A6-114.9 2-53 1-E1508A-6 86 HR_F2-33.2 4-53 2-E1508A-6

39 HR_A6-126.6 2-54 1-E1508A-6 87 HR_F2-35.2 4-54 2-E1508A-6

40 HR_A6-139.3 2-55 1-E1508A-6 88 HR_F2-38.2 4-55 2-E1508A-6

41 HR_A4-48.1 2-56 1-E1508A-7 89 HR_F3-50.1 4-56 2-E1508A-7

42 HR_A4-63.9 2-57 1-E1508A-7 90 HR_F3-54.1 4-57 2-E1508A-7

43 HR_A4-68.9 2-58 1-E1508A-7 91 HR_F3-57 4-58 2-E1508A-7

44 HR_A4-79.7 2-59 1-E1508A-7 92 HR_F3-60 4-59 2-E1508A-7

45 HR_A4-97.3 2-60 1-E1508A-7 93 HR_F3-65.9 4-60 2-E1508A-7

46 HR_A4-114.9 2-61 1-E1508A-7 94 HR_F3-69.8 4-61 2-E1508A-7

47 HR_A4-126.6 2-62 1-E1508A-7 95 HR_F3-72.8 4-62 2-E1508A-7

48 HR_A4-139.3 2-63 1-E1508A-7 96 HR_F3-74.8 4-63 2-E1508A-7

SLOT 1 SLOT 2

302
Table 11.3 Instrumentation and Data Acquisition Channel List (Continued) 

CHAN NAME PANEL/ Slot, SCP CHAN NAME PANEL/ Slot, SCP

INPUT # & SCP # INPUT # & SCP #

501 Pnl5-Therm2S 5-0 3-E1508A-0 503 Pnl7-Therm2S 7-0 4-E1508A-0

429 St Sep wall-t 5-1 3-E1508A-0 453 Qtz Win4-B 7-1 4-E1508A-0

430 St Sep wall-b 5-2 3-E1508A-0 454 Qtz Win5-A 7-2 4-E1508A-0

431 St Sep Dr wall-t 5-3 3-E1508A-0 455 Qtz Win5-B 7-3 4-E1508A-0

432 St Sep Dr wall-b 5-4 3-E1508A-0 456 Qtz Win6-A 7-4 4-E1508A-0

435 Acc wall-t 5-5 3-E1508A-0 457 Qtz Win6-B 7-5 4-E1508A-0

436 Acc wall-m 5-6 3-E1508A-0 440 Ex Pipe fl 7-6 4-E1508A-0

437 Acc wall-b 5-7 3-E1508A-0 441 Ex Pipe wall 7-7 4-E1508A-0

97 HR_F4-79.7 5-8 3-E1508A-1 145 HR_B6-4.2 7-8 4-E1508A-1

98 HR_F4-85.5 5-9 3-E1508A-1 146 HR_B6-11.2 7-9 4-E1508A-1

99 HR_F4-88.5 5-10 3-E1508A-1 147 HR_B6-16.2 7-10 4-E1508A-1

100 HR_F4-92.4 5-11 3-E1508A-1 148 HR_B6-23.2 7-11 4-E1508A-1

101 HR_F4-94.4 5-12 3-E1508A-1 149 HR_B6-29.2 7-12 4-E1508A-1

102 HR_F4-97.3 5-13 3-E1508A-1 150 HR_B6-33.2 7-13 4-E1508A-1

103 HR_F4-109 5-14 3-E1508A-1 151 HR_B6-35.2 7-14 4-E1508A-1

104 HR_F4-111.4 5-15 3-E1508A-1 152 HR_B6-38.2 7-15 4-E1508A-1

105 HR_F5-41.2 5-16 3-E1508A-2 153 HR_B5-41.2 7-16 4-E1508A-2

106 HR_F5-53.1 5-17 3-E1508A-2 154 HR_B5-53.1 7-17 4-E1508A-2

107 HR_F5-55.1 5-18 3-E1508A-2 155 HR_B5-55.1 7-18 4-E1508A-2

108 HR_F5-58 5-19 3-E1508A-2 156 HR_B5-58 7-19 4-E1508A-2

109 HR_F5-63.9 5-20 3-E1508A-2 157 HR_B5-63.9 7-20 4-E1508A-2

110 HR_F5-73.8 5-21 3-E1508A-2 158 HR_B5-73.8 7-21 4-E1508A-2

111 HR_F5-75.7 5-22 3-E1508A-2 159 HR_B5-75.7 7-22 4-E1508A-2

112 HR_F5-76.7 5-23 3-E1508A-2 160 HR_B5-76.7 7-23 4-E1508A-2

113 HR_F6-4.2 5-24 3-E1508A-3 161 HR_B4-88.5 7-24 4-E1508A-3

114 HR_F6-11.2 5-25 3-E1508A-3 162 HR_B4-91.4 7-25 4-E1508A-3

115 HR_F6-16.2 5-26 3-E1508A-3 163 HR_B4-93.4 7-26 4-E1508A-3

116 HR_F6-23.2 5-27 3-E1508A-3 164 HR_B4-95.3 7-27 4-E1508A-3

117 HR_F6-29.2 5-28 3-E1508A-3 165 HR_B4-100.2 7-28 4-E1508A-3

118 HR_F6-33.2 5-29 3-E1508A-3 166 HR_B4-106.1 7-29 4-E1508A-3

119 HR_F6-35.2 5-30 3-E1508A-3 167 HR_B4-111 7-30 4-E1508A-3

120 HR_F6-38.2 5-31 3-E1508A-3 168 HR_B4-142.2 7-31 4-E1508A-3

SLOT 3 SLOT 4

303
Table 11.3 Instrumentation and Data Acquisition Channel List (Continued) 

CHAN NAME PANEL/ Slot, SCP CHAN NAME PANEL/ Slot, SCP

INPUT # & SCP # INPUT # & SCP #

502 Pnl6-Therm2S 6-32 3-E1508A-4 504 Pnl8-Therm2S 8-32 4-E1508A-4

446 Qtz Win1-A 6-33 3-E1508A-4 442 Ex Pipe wall 8-33 4-E1508A-4

447 Qtz Win1-B 6-34 3-E1508A-4 443 Ex Pipe wall 8-34 4-E1508A-4

448 Qtz Win2-A 6-35 3-E1508A-4 394 Pwr Sup W 8-35 4-E1508A-4

449 Qtz Win2-B 6-36 3-E1508A-4 395 Pwr Sup V 8-36 4-E1508A-4

450 Qtz Win3-A 6-37 3-E1508A-4 396 Pwr Sup Cur 8-37 4-E1508A-4

451 Qtz Win3-B 6-38 3-E1508A-4 397 Test Sect V 8-38 4-E1508A-4

452 Qtz Win4-A 6-39 3-E1508A-4 398 Test Sect Cur 8-39 4-E1508A-4

121 HR_E6-50.1 6-40 3-E1508A-5 169 HR_B3-50.1 8-40 4-E1508A-5

122 HR_E6-54.1 6-41 3-E1508A-5 170 HR_B3-54.1 8-41 4-E1508A-5

123 HR_E6-57 6-42 3-E1508A-5 171 HR_B3-57 8-42 4-E1508A-5

124 HR_E6-60 6-43 3-E1508A-5 172 HR_B3-60 8-43 4-E1508A-5

125 HR_E6-65.9 6-44 3-E1508A-5 173 HR_B3-65.9 8-44 4-E1508A-5

126 HR_E6-69.8 6-45 3-E1508A-5 174 HR_B3-69.8 8-45 4-E1508A-5

127 HR_E6-72.8 6-46 3-E1508A-5 175 HR_B3-72.8 8-46 4-E1508A-5

128 HR_E6-74.8 6-47 3-E1508A-5 176 HR_B3-74.8 8-47 4-E1508A-5

129 HR_D6-103.2 6-48 3-E1508A-6 177 HR_C3-79.7 8-48 4-E1508A-6

130 HR_D6-106.1 6-49 3-E1508A-6 178 HR_C3-85.5 8-49 4-E1508A-6

131 HR_D6-112.9 6-50 3-E1508A-6 179 HR_C3-88.5 8-50 4-E1508A-6

132 HR_D6-114.9 6-51 3-E1508A-6 180 HR_C3-92.4 8-51 4-E1508A-6

133 HR_D6-116.8 6-52 3-E1508A-6 181 HR_C3-94.4 8-52 4-E1508A-6

134 HR_D6-120.7 6-53 3-E1508A-6 182 HR_C3-97.3 8-53 4-E1508A-6

135 HR_D6-124.6 6-54 3-E1508A-6 183 HR_C3-109 8-54 4-E1508A-6

136 HR_D6-128.5 6-55 3-E1508A-6 184 HR_C3-111.4 8-55 4-E1508A-6

137 HR_C6-41.2 6-56 3-E1508A-7 185 HR_D3-88.5 8-56 4-E1508A-7

138 HR_C6-53.1 6-57 3-E1508A-7 186 HR_D3-91.4 8-57 4-E1508A-7

139 HR_C6-55.1 6-58 3-E1508A-7 187 HR_D3-93.4 8-58 4-E1508A-7

140 HR_C6-58 6-59 3-E1508A-7 188 HR_D3-95.3 8-59 4-E1508A-7

141 HR_C6-63.9 6-60 3-E1508A-7 189 HR_D3-100.2 8-60 4-E1508A-7

142 HR_C6-73.8 6-61 3-E1508A-7 190 HR_D3-106.1 8-61 4-E1508A-7

143 HR_C6-75.7 6-62 3-E1508A-7 191 HR_D3-111 8-62 4-E1508A-7

144 HR_C6-76.7 6-63 3-E1508A-7 192 HR_D3-142.2 8-63 4-E1508A-7

SLOT 3 SLOT 4

304
Table 11.3 Instrumentation and Data Acquisition Channel List (Continued) 

CHAN NAME PANEL/ Slot, SCP CHAN NAME PANEL/ Slot, SCP

INPUT # & SCP # INPUT # & SCP #

505 Pnl9-Therm2S 9-0 5-E1508A-0 507 Pnl11-Therm2S 11-0 6-E1508A-0

393 UP Exit P 9-1 5-E1508A-0 425 CT-UP DP 11-1 6-E1508A-0

406 Sup Tnk Pr 9-2 5-E1508A-0 433 St Sep-UP DP 11-2 6-E1508A-0

411 Sup Ln Pr 9-3 5-E1508A-0 438 St Sup-Acc DP 11-3 6-E1508A-0

416 St Sup Pr 9-4 5-E1508A-0 362 FH DP-(0-144) 11-4 6-E1508A-0

439 Acc Pr 9-5 5-E1508A-0 363 FH DP-(0-12) 11-5 6-E1508A-0

444 Ex Pipe Pr 9-6 5-E1508A-0 364 FH DP-(12-25) 11-6 6-E1508A-0

412 Sup Ln FM 9-7 5-E1508A-0 365 FH DP-(25-37) 11-7 6-E1508A-0

193 HR_E3-63.9 9-8 5-E1508A-1 241 HR_D4-50.1 11-8 6-E1508A-1

194 HR_E3-113.9 9-9 5-E1508A-1 242 HR_D4-54.1 11-9 6-E1508A-1

195 HR_E3-115.8 9-10 5-E1508A-1 243 HR_D4-57 11-10 6-E1508A-1

196 HR_E3-118.8 9-11 5-E1508A-1 244 HR_D4-60 11-11 6-E1508A-1

197 HR_E3-122.7 9-12 5-E1508A-1 245 HR_D4-65.9 11-12 6-E1508A-1

198 HR_E3-126.6 9-13 5-E1508A-1 246 HR_D4-69.8 11-13 6-E1508A-1

199 HR_E3-131.5 9-14 5-E1508A-1 247 HR_D4-72.8 11-14 6-E1508A-1

200 HR_E3-135.4 9-15 5-E1508A-1 248 HR_D4-74.8 11-15 6-E1508A-1

201 HR_E4-88.5 9-16 5-E1508A-2 249 GRD2-fl-D-4/d2-b2 11-16 6-E1508A-2

202 HR_E4-91.4 9-17 5-E1508A-2 250 GRD2-wall-D-4/a-2 11-17 6-E1508A-2

203 HR_E4-93.4 9-18 5-E1508A-2 251 GRD3-fl-D-4/d2-b2 11-18 6-E1508A-2

204 HR_E4-95.3 9-19 5-E1508A-2 252 GRD3-fl-D-2/d1-b2 11-19 6-E1508A-2

205 HR_E4-100.2 9-20 5-E1508A-2 253 GRD3-fl-D-6/c3-b2 11-20 6-E1508A-2

206 HR_E4-106.1 9-21 5-E1508A-2 254 GRD3-wall-E-3/c-1 11-21 6-E1508A-2

207 HR_E4-111 9-22 5-E1508A-2 255 GRD3-wall-D-4/a-2 11-22 6-E1508A-2

208 HR_E4-142.2 9-23 5-E1508A-2 256 GRD3-wall-C-5/d-3 11-23 6-E1508A-2

209 HR_E5-63.9 9-24 5-E1508A-3 257 GRD4-fl-D-4/d2-b2 11-24 6-E1508A-3

210 HR_E5-113.9 9-25 5-E1508A-3 258 GRD4-fl-D-2/d1-b2 11-25 6-E1508A-3

211 HR_E5-115.8 9-26 5-E1508A-3 259 GRD4-fl-D-6/c3-b2 11-26 6-E1508A-3

212 HR_E5-118.8 9-27 5-E1508A-3 260 GRD4-wall-E-3/c-1 11-27 6-E1508A-3

213 HR_E5-122.7 9-28 5-E1508A-3 261 GRD4-wall-D-4/a-2 11-28 6-E1508A-3

214 HR_E5-126.6 9-29 5-E1508A-3 262 GRD4-wall-C-5/d-3 11-29 6-E1508A-3

215 HR_E5-131.5 9-30 5-E1508A-3 263 GRD5-fl-D-4/d2-b2 11-30 6-E1508A-3

216 HR_E5-135.4 9-31 5-E1508A-3 264 GRD5-fl-D-2/d1-b2 11-31 6-E1508A-3

SLOT 5 SLOT 6

305
Table 11.3 Instrumentation and Data Acquisition Channel List (Continued) 

CHAN NAME PANEL/ Slot, SCP CHAN NAME PANEL/ Slot, SCP

INPUT # & SCP # INPUT # & SCP #

506 Pnl10-Therm2S 10-32 5-E1508A-4 508 Pnl12-Therm2S 12-32 6-E1508A-4

413 Drop Inj FM 10-33 5-E1508A-4 265 GRD5-fl-D-6/c3-b2 12-33 6-E1508A-4

417 St Sup FM 10-34 5-E1508A-4 266 GRD5-wall-E-3/c-1 12-34 6-E1508A-4

445 Ex Pipe FM 10-35 5-E1508A-4 267 GRD5-wall-D-4/a-2 12-35 6-E1508A-4

405 Sup Tnk Lvl 10-36 5-E1508A-4 268 GRD5-wall-C-5/d-3 12-36 6-E1508A-4

426 Lg CT Lvl 10-37 5-E1508A-4 269 GRD6-fl-D-4/d2-b2 12-37 6-E1508A-4

427 Sm CT Lvl 10-38 5-E1508A-4 270 GRD6-fl-B-4/c2-a1 12-38 6-E1508A-4

434 St Sep Lvl 10-39 5-E1508A-4 271 GRD6-fl-F-4/c2-b3 12-39 6-E1508A-4

217 HR_D5-88.5 10-40 5-E1508A-5 272 GRD6-wall-E-3/c-1 12-40 6-E1508A-5

218 HR_D5-91.4 10-41 5-E1508A-5 273 GRD6-wall-D-4/a-2 12-41 6-E1508A-5

219 HR_D5-93.4 10-42 5-E1508A-5 274 GRD6-wall-G-4/b-3 12-42 6-E1508A-5

220 HR_D5-95.3 10-43 5-E1508A-5 275 GRD6-wall-C-5/d-3 12-43 6-E1508A-5

221 HR_D5-100.2 10-44 5-E1508A-5 276 GRD7-fl-D-4/d2-b2 12-44 6-E1508A-5

222 HR_D5-106.1 10-45 5-E1508A-5 277 GRD7-fl-D-2/d1-b2 12-45 6-E1508A-5

223 HR_D5-111 10-46 5-E1508A-5 278 GRD7-fl-D-6/c3-b2 12-46 6-E1508A-5

224 HR_D5-142.2 10-47 5-E1508A-5 279 GRD7-wall-D-4/a-2 12-47 6-E1508A-5

225 HR_C5-63.9 10-48 5-E1508A-6 280 SPR1-37.2 12-48 6-E1508A-6

226 HR_C5-113.9 10-49 5-E1508A-6 281 SPR1-59.1 12-49 6-E1508A-6

227 HR_C5-115.8 10-50 5-E1508A-6 282 SPR1-76.8 12-50 6-E1508A-6

228 HR_C5-118.8 10-51 5-E1508A-6 283 SPR1-90.7 12-51 6-E1508A-6

229 HR_C5-122.7 10-52 5-E1508A-6 284 SPR1-96.6 12-52 6-E1508A-6

230 HR_C5-126.6 10-53 5-E1508A-6 285 SPR1-102.5 12-53 6-E1508A-6

231 HR_C5-131.5 10-54 5-E1508A-6 286 SPR1-114.4 12-54 6-E1508A-6

232 HR_C5-135.4 10-55 5-E1508A-6 287 SPR1-138.2 12-55 6-E1508A-6

233 HR_C4-88.5 10-56 5-E1508A-7 288 SPR13-37.2 12-56 6-E1508A-7

234 HR_C4-91.4 10-57 5-E1508A-7 289 SPR13-59.1 12-57 6-E1508A-7

235 HR_C4-93.4 10-58 5-E1508A-7 290 SPR13-76.8 12-58 6-E1508A-7

236 HR_C4-95.3 10-59 5-E1508A-7 291 SPR13-90.7 12-59 6-E1508A-7

237 HR_C4-100.2 10-60 5-E1508A-7 292 SPR13-96.6 12-60 6-E1508A-7

238 HR_C4-106.1 10-61 5-E1508A-7 293 SPR13-102.5 12-61 6-E1508A-7

239 HR_C4-111 10-62 5-E1508A-7 294 SPR13-114.4 12-62 6-E1508A-7

240 HR_C4-142.2 10-63 5-E1508A-7 295 SPR13-138.2 12-63 6-E1508A-7

SLOT 5 SLOT 6

306
Table 11.3 Instrumentation and Data Acquisition Channel List (Continued) 

CHAN NAME PANEL/ Slot, SCP CHAN NAME PANEL/ Slot, SCP

INPUT # & SCP # INPUT # & SCP #

509 Pnl13-Therm2S 13-0 7-E1508A-0 511 Pnl15-Therm2S 15-0 8-E1508A-0

296 ST. PR-R1-16.2-A 13-1 7-E1508A-0 358 FH24-wall-129.25 15-1 8-E1508A-0

297 ST. PR-R1-16.2-B 13-2 7-E1508A-0 359 FH25-wall-135.18 15-2 8-E1508A-0

298 ST. PR-R1-16.2-C 13-3 7-E1508A-0 360 RB-IF1-fl-(-1)-A 15-3 8-E1508A-0

299 ST. PR-R2-37-A 13-4 7-E1508A-0 361 RB-IF2-fl-(-1)-B 15-4 8-E1508A-0

300 ST. PR-R2-37-B 13-5 7-E1508A-0 366 FH DP-(37-43) 15-5 8-E1508A-0

301 ST. PR-R2-37-C 13-6 7-E1508A-0 367 FH DP-(43-46) 15-6 8-E1508A-0

302 ST. PR-R3-55-A 13-7 7-E1508A-0 368 FH DP-(46-53) 15-7 8-E1508A-0

303 ST. PR-R3-55-B 13-8 7-E1508A-1 369 FH DP-(53-57) 15-8 8-E1508A-1

304 ST. PR-R3-55-C 13-9 7-E1508A-1 370 FH DP-(57-60) 15-9 8-E1508A-1

305 ST. PR-R4-60-A 13-10 7-E1508A-1 371 FH DP-(60-63) 15-10 8-E1508A-1

306 ST. PR-R4-60-B 13-11 7-E1508A-1 372 FH DP-(63-67) 15-11 8-E1508A-1

307 ST. PR-R4-60-C 13-12 7-E1508A-1 373 FH DP-(67-72) 15-12 8-E1508A-1

308 ST. PR-R5-73.81-A 13-13 7-E1508A-1 374 FH DP-(72-75) 15-13 8-E1508A-1

309 ST. PR-R5-73.81-B 13-14 7-E1508A-1 375 FH DP-(75-78) 15-14 8-E1508A-1

310 ST. PR-R5-73.81-C 13-15 7-E1508A-1 376 FH DP-(78-81) 15-15 8-E1508A-1

311 ST. PR-R6-76-A 13-16 7-E1508A-2 377 FH DP-(81-85) 15-16 8-E1508A-2

312 ST. PR-R6-76-B 13-17 7-E1508A-2 378 FH DP-(85-93) 15-17 8-E1508A-2

313 ST. PR-R6-76-C 13-18 7-E1508A-2 379 FH DP-(93-97) 15-18 8-E1508A-2

314 ST. PR-R7-79.7-A 13-19 7-E1508A-2 380 FH DP-(97-100) 15-19 8-E1508A-2

315 ST. PR-R7-79.7-B 13-20 7-E1508A-2 381 FH DP-(100-108) 15-20 8-E1508A-2

316 ST. PR-R7-79.7-C 13-21 7-E1508A-2 382 FH DP-(108-120) 15-21 8-E1508A-2

317 ST. PR-R8-93.53-A 13-22 7-E1508A-2 383 FH DP-(120-133) 15-22 8-E1508A-2

318 ST. PR-R8-93.53-B 13-23 7-E1508A-2 384 FH DP-(133-144) 15-23 8-E1508A-2

319 ST. PR-R8-93.53-C 13-24 7-E1508A-3 458 Rem Close 15-24 8-E1535A-3

320 ST. PR-R9-96-A 13-25 7-E1508A-3 459 Rem Start/Stop 15-25 8-E1535A-3

321 ST. PR-R9-96-B 13-26 7-E1508A-3 460 Rem Reset 15-26 8-E1535A-3

322 ST. PR-R9-96-C 13-27 7-E1508A-3 461 RELAY 3 - NO 15-27 8-E1535A-3

323 ST. PR-R10-100-A 13-28 7-E1508A-3 462 I/O Disc 15-28 8-E1535A-3

324 ST. PR-R10-100-B 13-29 7-E1508A-3 463 Pull-Up+/I/O Disc- 15-29 8-E1535A-3

325 ST. PR-R10-100-C 13-30 7-E1508A-3 464 Not Available 15-30 8-E1535A-3

326 ST. PR-R11-115.39-A 13-31 7-E1508A-3 465 Not Available 15-31 8-E1535A-3

SLOT 7 SLOT 8

307
Table 11.3 Instrumentation and Data Acquisition Channel List (Continued) 

CHAN NAME PANEL/ Slot, SCP CHAN NAME PANEL/ Slot, SCP

INPUT # & SCP # INPUT # & SCP #

510 Pnl14-Therm2S 14-32 7-E1508A-4 512 Pnl16-Therm2S 16-32 8-E1508A-4

327 ST. PR-R11-115.39-B 14-33 7-E1508A-4 482 Spare1 16-33 8-E1508A-4

328 ST. PR-R11-115.39-C 14-34 7-E1508A-4 483 Spare2 16-34 8-E1508A-4

329 ST. PR-R12-120-A 14-35 7-E1508A-4 484 Spare3 16-35 8-E1508A-4

330 ST. PR-R12-120-B 14-36 7-E1508A-4 485 Spare4 16-36 8-E1508A-4

331 ST. PR-R12-120-C 14-37 7-E1508A-4 486 Spare5 16-37 8-E1508A-4

332 ST. PR-R13-136-A 14-38 7-E1508A-4 487 Spare6 16-38 8-E1508A-4

333 ST. PR-R13-136-B 14-39 7-E1508A-4 488 Spare7 16-39 8-E1508A-4

334 ST. PR-R13-136-C 14-40 7-E1508A-5 489 Spare8 16-40 8-E1508A-5

335 FH1-wall-10.1 14-41 7-E1508A-5 490 Spare9 16-41 8-E1508A-5

336 FH2-wall-22 14-42 7-E1508A-5 491 Spare10 16-42 8-E1508A-5

337 FH3-wall-37 14-43 7-E1508A-5 492 Spare11 16-43 8-E1508A-5

338 FH4-wall-42.95 14-44 7-E1508A-5 493 Spare12 16-44 8-E1508A-5

339 FH5-wall-46.93 14-45 7-E1508A-5 494 Spare13 16-45 8-E1508A-5

340 FH6-wall-52.9 14-46 7-E1508A-5 495 Spare14 16-46 8-E1508A-5

341 FH7-wall-55.87 14-47 7-E1508A-5 496 Spare15 16-47 8-E1508A-5

342 FH8-wall-61.85 14-48 7-E1508A-6 466 PS-PWR OUTA 16-48 8-E1532A-6

343 FH9-wall-67.83 14-49 7-E1508A-6 467 PS-PWR OUTB 16-49 8-E1532A-6

344 FH10-wall-70.82 14-50 7-E1508A-6 468 IF RATEA 16-50 8-E1532A-6

345 FH11-wall-73.81 14-51 7-E1508A-6 469 IF RATEB 16-51 8-E1532A-6

346 FH12-wall-78.78 14-52 7-E1508A-6 470 CNTL3A 16-52 8-E1532A-6

347 FH13-wall-84.7 14-53 7-E1508A-6 471 CNTL3B 16-53 8-E1532A-6

348 FH14-wall-87.65 14-54 7-E1508A-6 472 CNTL4A 16-54 8-E1532A-6

349 FH15-wall-90.55 14-55 7-E1508A-6 473 CNTL4B 16-55 8-E1532A-6

350 FH16-wall-93.53 14-56 7-E1508A-7 474 CNTL5A 16-56 8-E1532A-7

351 FH17-wall-96.5 14-57 7-E1508A-7 475 CNTL5B 16-57 8-E1532A-7

352 FH18-wall-102.48 14-58 7-E1508A-7 476 CNTL6A 16-58 8-E1532A-7

353 FH19-wall-108.43 14-59 7-E1508A-7 477 CNTL6B 16-59 8-E1532A-7

354 FH20-wall-110.43 14-60 7-E1508A-7 478 CNTL7A 16-60 8-E1532A-7

355 FH21-wall-111.42 14-61 7-E1508A-7 479 CNTL7B 16-61 8-E1532A-7

356 FH22-wall-116.38 14-62 7-E1508A-7 480 CNTL8A 16-62 8-E1532A-7

357 FH23-wall-120.3 14-63 7-E1508A-7 481 CNTL8B 16-63 8-E1532A-7

SLOT 7 SLOT 8

308
Figure 11.22 Instrumented Heater Rod Radial Locations. 

effects were observed in the Lehigh data as well as the INEL single tube data which used these 

probes. 

In addition, there will be traversing vapor temperature measurement probes mounted on rakes 

with multiple thermocouples. The traversing steam probe rakes will be installed at the mid span 

between grids at the upper rod bundle elevations. The steam probes will measure steam 

temperatures in the rod bundle flow subchannels and the gap between the heater rods during 

the dispersed flow regime. The conceptual design of a tranversing steam probe rake is shown 

in Figure 11.23. Each rake consists of three 0.381 mm (15 mil) diameter ungrounded 

thermocouples mounted on a 0.356 mm (14 mil) thick by 6.35 mm (3 in) wide inconel strip. The 

thermocouples are spaced 12.6 mm (0.496 inch) apart which correspond to the heater rod 

spacing in the bundle. The thermocouple tips are located facing the steam flow. A 2.39 mm (94 

mil) diameter tube attached to the strip is used to traverse the steam probe rake across the rod 

bundle. This tube also carries the thermocouples leads outside the flow housing through a 

extension tube and a pressure seal arrangement. This instrument is now in the development 

phase and will be tested in the nine rod bundle bench test prior to installing it on the large rod 

bundle. 

Two fluid thermocouples are placed 24.5 mm (1 in) below the bottom of the bundle heated 

length such that injection water temperatures are monitored prior and when reflood is started. 

There are 22 DP transmitters are connected to the housing wall pressure taps providing 

measurements to calculate single phase bare bundle and grid friction losses, bundle mass 

inventory and void fraction during reflood. Nine DP cells are connected to pressure taps located 

76.2 mm (3 in) apart to provide detail mass inventory, and void fraction data in the froth region 

above the quench front. In addition, heater rod and housing wall thermocouples are placed at 

the pressure tap mid spans locations to determine convective and radiant heat 

309
Figure 11.23 Traversing Steam Probe Rake. 

transfer coefficients in the froth region where the differential pressure cells will give the average 

void fraction. 

As described in Section 11.3.1, the flow housing has six pairs of windows at the following 

elevations: 685.8, 1193.8, 1752.6, 2260.6, 2768.6, 3302.0 and 3962.4 mm (27, 47, 69, 89, 109, 

130 and 156 in). Each pair of windows are 180 degrees apart. The window lenses are made 

from optical grade fused quartz and provide a 50.8x292.1 mm (2x11.5 in) viewing area. The 

windows are positioned about 88.9 mm (3.5 in) below and 152.4 mm (6 in) above grid numbers 

2, 3, 4, 5, 6 and 7. The windows will be preheated to prevent wetting during the time when 

dispersed flow is occurring and LCDS measurements are being made. The windows will be 

heated using infrared heaters on each window and by pulsing the rod bundle for preheating the 

flow housing walls. The infrared heaters will be removed just before a test is started. Two 

significant measurements above and below the grid can be made through the windows: void 

fraction measurements with a Gamma Densitometer, and entrained water droplet size, velocity, 

and distribution with the LIDCS. High speed movies can also be shot through this window to 

observe the different two-phase flow regimes during testing. 

There can be up to three densitometers or an x-ray detector located at different elevations 

during testing. The bottom densitometer will measure void fractions as the quench front 

approaches this location, while the other densitometers will measure void fraction in the 

dispersed flow regimes. 

The Gamma Densitometer system which could be used is shown schematically in Figure 11.24. 

There are three systems each at different elevations consisting of an AM 241, 120 mCi, 59.5 

KeV gamma ray source, a Reuter-Stokes gas proportional counter, a preamplifier and an 

amplifier, high voltage power supply, a single channel analyzer, and a rate meter. The radiation 

beam intensity is measured across the center gap among the bundle heater rods. The beam is 

310
Figure 11.24 Densitometer Schematic. 

passed through a small beryllium window fabricated from an S 200F alloy sheet. These 

windows are mounted on a metal plate that replaces the glass window lenses. The 

densitometer provides a cordial average void fraction across the bundle. The three 

densitometers are located at various elevations during a test. 

A droplet imaging system known as VisiSizer has been developed in conjunction with Oxford 

Lasers of Acton, MA, to measure the size and velocity of water droplets entrained in the steam 

flow of the RBHT test section. VisiSizer uses a pulsed infrared laser to image water droplets on 

a 1000x1000 pixel high-resolution black and white digital camera through a set of windows in 

the bundle housing. The LIDCS setup used for VisiSizer is shown schematically in Figure 

11.25. 

A digital system such as VisiSizer was chosen over conventional high-speed cameras because 

of issues with reliability and speed of data acquisition. A high-speed camera is capable of only 

a few seconds of imaging and is a tedious process that does not give instantaneous results. 

Each frame of a standard imaging technique would need to be analyzed by hand. The VisiSizer 

system is capable of analyzing 12 to 13 frames per second for an indefinite period of time. Film 

from the FLECHT-SEASET tests show much less image quality than images taken with 

VisiSizer in the experiments performed so far. However, VisiSizer is incapable of measuring 

anything other than complete droplets. This makes it an inadequate tool for gathering 

information about the entrainment front where there are ligaments and other unusual water 

behavior. Therefore, it is still a possibility that a high-speed camera will be used in tandem with 

VisiSizer for preliminary RBHT tests. 

An infrared laser is used with the system because it is capable of passing through the quartz 

viewing windows and being absorbed by the water droplets entrained in the steam flow. 

311
Figure 11.25 Laser Illuminated Digital Camera System Setup 

Because the infrared rays are absorbed by the water droplets, the resulting droplet shadows 

can be recorded by the digital camera. So far, there has been no effect of laser light scattering 

from rods to droplets. Pictures taken in and out of the rod bundle have the same imaging 

characteristics, droplet analyzing capability, and clarity. A band pass laser light filter 

is placed in front of the digital camera to eliminate non-infrared light from other sources and an 

anti-glare attachment is used to eliminate any illumination interference from outside the viewing 

area. In addition, rod bundle geometry has little effect in the measurement of droplet 

distributions and velocities. 

The frames captured by the camera are fed back to a computer at approximately 12 to 13 

frames per second. The software can analyze each frame for droplet size and velocity and write 

the recorded data to a size and velocity data array. The software program determines droplet 

sizes by determining the area of black versus white pixels in each droplet image. Once the 

droplet area is determined, the program calculates the perimeter of the droplet image to 

determine the sphereosity of the droplet. The VisiSizer system is capable of determining the 

surface area based on diameter of any and all droplets. At any droplet concentration that is 

measurable with the system, an accurate measure of the total droplet surface area can be 

obtained. So far, number fluxes of up to six droplets per frame in velocity mode (12 droplet 

images) have been analyzed successfully with the droplets in a very narrow viewing area. 

There is the capability to increase this droplet number flux by several times using larger and 

multiple viewing areas. 

Operating the laser in a double pulse mode enables the VisiSizer system to measure both 

droplet diameter and velocity for a particular probe volume. The laser pulses twice with a 

312
known pulse delay (on the order of 1 ms) while the camera shutter remains open, creating two 

images in the same frame of each droplet. The distance between images is then determined 

and the velocity calculated. These velocity characteristics are enough to characterize the 

behavior of the flow despite the fact that the droplets are only captured in a single frame. 

The local distribution of droplets will be determined for a known probe volume governed by the 

software settings. Droplets that lie out of this probe volume on either side of the line of sight will 

be rejected based on focus. The opposite sides of the probe volume will be set by the spacing 

of the rods in the bundle. Each droplet is recorded in a two-dimensional array according to size 

and velocity. The droplet sizes are recorded in lognormal bins while the velocity bin size is user 

defined. Data for the transient reflood experiments is recorded in user defined quasi-steady 

state time periods. At the end of each time period the data is saved and a new array is opened. 

Arrays characterized by similar droplets populations can then be combined for better statistical 

results. 

The VisiSizer will enable the experimenters to collect a vast amount of information about the 

droplet flow in the test section. The information will be collected in an easy to handle data array 

and all information will be written to a CD-ROM to ensure the information will be available for 

later use. 

The droplet injection system described in Section 11.3.12 has been constructed so that RBHT 

can collect steady state information on droplet behavior. The injection system creates droplets 

of a known size and flow rate in the test section. The injection tubes are easily removed and 

replaced. This enables multiple injection sizes to be used as needed. The flow rate of the 

injection is controlled through a series of valves and flow meters. These factors should allow for 

the production of various droplet sizes. VisiSizer can study the droplet flow and distribution 

before a grid and then the system can be moved to image droplets immediately after the grid 

with the same conditions. In this way the effects of a spacer grid on the droplet diameter 

distribution can be determined. 

The four corner support rods are unheated, they are used to support the bundle grids and to 

support grid and steam probes thermocouple leads going out of the bundle. These rods are 

instrumented with eight thermocouples attached at various elevations corresponding to heater 

rods and housing wall thermocouples. The purpose of this arrangement is to quantify radiation 

heat transfer losses to unheated surfaces and determine their behavior during reflood. 

The DC power supply can be controlled by regulating the voltage, current, or total power output. 

The voltage drop across the heater rod bundle is measured by a voltmeter connected to voltage 

taps at the Low-Melt pot and the Nickel Ground Plate. The electrical current is measured by a 

copper shunt calibrated for 15,000 amps proportional to an output signal of 0-50 mV. 

The Lower Plenum is instrumented with two fluid and two wall thermocouples. The fluid 

thermocouples monitor the injection water temperature prior and during testing. The wall 

thermocouples measure the vessel wall during heat-up and testing. One of the wall 

thermocouples in conjunction with a temperature controller regulates electrical power to clampon heater rods to maintain the vessel wall at inlet temperatures. 

The Upper Plenum is also instrumented with two fluid thermocouples and two wall 

thermocouples. The fluid thermocouples measure steam and carryover liquid during testing. 

The wall thermocouples monitor vessel wall temperatures during heat-up and testing. The 

313
Upper Plenum is also instrumented with a static pressure transmitter which measures and 

controls the test section pressure during testing. 

11.4.3 Data Acquisition System

The control and data acquisition system provides control functions and data collection functions 

for the RBHT Test Facility. This system consists of two parts, the computer and display 

terminals residing in the control room, and the VXI mainframe and terminal panels residing in 

the test facility. The two parts are connected via an industry standard IEEE 1394 (Firewire) 

serial control and data interface. 

The computer provides the display, control, and data storage functions. It has the capability of 

displaying control function setpoints and process variables, and critical operating parameters 

during tests, along with selected variables such as various rod temperatures displayed in realtime during the experiment. This system will provide dial, meter, and strip-chart functions as 

required. The computer collects and saves data from the various instruments, such as voltage, 

current, pressure, level, flow, and temperature; and provides control functions such as heater 

rod power, injection water pressure, upper and lower plenum temperature, etc. 

The instrumentation part of this system, residing in the test facility, consists of an industry 

standard VXI mainframe (Vme bus with extensions for Instrumentation) from Hewlett-Packard 

(HP E8401A), and a set of terminal panels (HP E1586A). The VXI mainframe contains a 

Firewire controller card (HP E8491A) and several (currently seven) state-of-the-art data 

acquisition and control cards (HP E1419A). The terminal panels provide the isothermal 

reference junctions needed for the thermocouples, as well as the voltage and current-loop 

input/output (i/o) interface to the RBHT Test Facility. These terminal panels are connected to 

the HP E1419A cards with SCSI cables. Seven cards yield a capability of 448 i/o. The VXI 

mainframe can hold up to 12 cards, and the Firewire interface can support up to 16 mainframes. 

Each E1419A card can support up to eight signal conditioning plug-ons (scp=s), conditioning 

eight channels each. Each E1509A scp contains low-pass antialiasing filters, fixed at 7 Hz. 

Because of this, the scan rate for each channel must be greater than or equal to the Nyquist 

rate of 14 Hz. The maximum a/d conversion rate on each HP E1419A card is nominally 100 

kHz, but is controlled to the rate the user requires. The seven cards can be synchronized to 

perform the scans simultaneously. The theoretical maximum scan rate for each channel (on 

any individual card) is 100,000/64 = 1,562.5 Hz, if all 64 channels are scanned. (Note that the 

actual scan rate would be less because of multiplexer switching, amplifier settling times due to 

gain changes, etc. There are different scp=s available from HP providing different filter values to 

scan at these rates.) The normal data-scanning rate will be 2 Hz during the majority of the 

tests, but this rate can be increased to 10 Hz for specific times during testing.

11.5 RBHT Test Facility Improvement

Significant improvements related to other rod bundle testing programs, listed in Section 3.0 

Literature Review have been incorporated in the RBHT Test Facility. These improvements are: 

• A low mass square flow housing design which better fits a square rod bundle array and 

minimizes the housing mass and the excess rod bundle flow area. 

314
• The six pairs of windows which provide large viewing areas below and above grid 

locations, making it possible to observe and make void fraction and droplet 

measurements during reflood testing. 

• The possible use of Densitometers or X-ray detectors to obtain void fraction 

measurements in the subcooled, quench, and froth level regions. 

• The use of a Laser Illuminated Digital Camera System to measure entrained water 

droplets sizes, distribution, and velocities in the dispersed flow regions. 

• The use of a traversing steam probe rake to measure simultaneously steam 

temperatures in the flow subchannel and in the rod-to-rod gap. 

• DP transmitter axially located 3 in apart in conjunction with heater rod and flow housing 

wall thermocouples to obtain detailed void fraction and heat transfer information. 

• Water droplets injection system in conjunction steam injection to study the droplet-steam 

cooling effects on heat transfer and grids. 

• Addition of a large pressure oscillation-damping tank to minimize test section oscillations 

observed in the FLECHT and FLECHT-SEASET tests. 

• The incorporation of closely coupled liquid collection tanks and piping to reduce delay 

times for liquid collection. 

11.6 Conclusions

The RBHT Test Facility has been designed as a flexible rod bundle separate-effects test facility 

which can be used to perform single-phase and two-phase experiments under well-controlled 

laboratory conditions to generate fundamental reflood heat transfer data. The facility is capable 

of operating in both forced and variable reflood modes covering wide ranges of flow and heat 

transfer conditions at pressures up to 4.02 bars (60 psia). It is heavily instrumented to meet all 

the instrumentation requirements developed under Task 7. It can be used to conduct all types 

of the planned experiments according to the test matrix developed under Task 9. It is 

considered that the RBHT Test Facility with its robust instrumentation represents a unique NRC 

facility for the in-depth studies of the highly ranked reflood phenomena identified in the PIRT 

table developed under Task 1, and will produce the data and analysis needed to refine reflood 

heat transfer models in the current safety analysis computer codes. 

11.7 References

1. Denham, M.K., D. Jowitt, and K.G. Pearson, AACHILLES Unballooned Cluster 

Experiments, Part 1: Description of the ACHILLES Rig, Test Section, and Experimental 

Procedures,@ AEEW-R2336, Winfrith Technology Centre (Commercial in Confidence), Nov. 

1989. 

2. Denham, M.K. and K.G. Pearson, AACHILLES Unballooned Cluster Experiments, Part 2: 

Single Phase Flow Experiments,@ AEEW-R2337, Winfrith Technology Centre (Commercial 

in Confidence), May 1989. 

315
316

3. Pearson, K.G. and M.K. Denham, AACHILLES Unballooned Cluster Experiments, Part 3: 

Low Flooding Rate Reflood Experiments,@ AEEW-R2339, Winfrith Technology Centre 

(Commercial in Confidence), June 1989. 

4. Pearson, K.G. and M.K. Denham, AACHILLES Unballooned Cluster Experiments, Part 4: 

Low Pressure Level Swell Experiments,@ AEEW-R2339, Winfrith Technology Centre 

(Commercial in Confidence), July 1989. 

5. Dore, P. and M.K. Denham, AACHILLES Unballooned Cluster Experiments, Part 5: Best 

Estimate Experiments,@ AEEW-R2412, Winfrith Technology Centre (Commercial in 

Confidence), July 1990. 

6. Dore, P. and D.S. Dhuga, AACHILLES Unballooned Cluster Experiments, Part 6: Flow 

Distribution Experiments,@ AEA-RS-1064, Winfrith Technology Centre (Commercial in 

Confidence), December 1991.
317

12. CONCLUSIONS 

The initial phase of the RBHT Program, which aims at designing a flexible, well-instrumented 

rod bundle test facility for conducting reflood experiments to aid in the development of dispersed 

flow film boiling models for the NRC=s thermal-hydraulics code, was completed and documented 

in this report. Based upon the results obtained in the initial phase, i.e., Tasks 1 through 10, the 

following are concluded: 

1. The thermal-hydraulics heat transfer phenomena that dominates the reflood transient is 

dispersed flow film boiling, which is the limiting (lowest heat transfer from fuel to fluid) heat 

transfer situation for the LOCA transient. The RBHT Program will emphasize this phase in 

providing specific experimental data and associated analysis to improve the understanding 

of the dispersed flow film boiling region. 

2. The heat transfer rates in the dispersed flow film-boiling region are very low, and several 

competing mechanisms are responsible for the total wall heat flux. No single mechanism 

dominates the heat transfer process such that all the competing mechanisms must be 

modeled with roughly equal precision. Separate-effect data at the subcomponent levels 

isolating the particular contribution of each competing mechanism to the total wall heat flux 

will be simulated in the RBHT Test Facility. 

3. The single largest uncertainty in predicting the dispersed film boiling heat transfer is the 

liquid entrainment from the froth region just above the quench front. In this region, the 

steam generation from the rod quenching results in very large vapor velocities which 

entrain and shear liquid ligaments into droplets. The entrained droplets provide cooling by 

several different mechanisms in the upper elevations of the rod bundle where the resulting 

peak clad temperatures occur. To address the liquid entrainment and resulting droplet 

flow, specific tests are planned which will isolate the droplet behavior. Also, state-of-theart instrumentation will be used to obtain drop size and velocities as well as the local void 

fraction. 

4. The RBHT Test Facility is designed to permit separate-effect component experiments 

isolating each highly ranked reflood phenomenon as best as possible so as to permit 

model development for particular phenomenon and to minimize the risk of introducing 

compensating error in the advanced reflood model package. 

5. The proposed experiments to be performed in the RBHT Test Facility will provide new data 

on reflood heat transfer as well as supplementing existing data for model development and 

code validation. They will also focus on the improvements of specific best-estimate 

thermal-hydraulics models of importance to the highly ranked phenomena rather than 

identifying licensing margin. 

6. Results of the two-tier scaling analysis indicate that if prototypical fluid conditions are used 

in the tests and the bundle geometry is retained by using the prototypical spacer grids, 

there is very strong similarity between the RBHT test bundle and the PWR and BWR fuel 

assemblies. The data to be obtained in the RBHT Test Facility should be applicable to 

either reactor fuel assembly type. 

7. The effects of the gap conductance and the rod materials differences between electrical 
318

and nuclear fuel rods are small with the possible exception of the minimum film boiling 

temperature. Other literature or bench type tests can determine the appropriate value for 

fuel rod cladding. The presence of a test housing in the proposed RBHT facility can lead 

to some distortion in the tests and it should be accounted for in the test analyses. 

8. One important objective of the program is to obtain new information on the mechanism of 

liquid entrainment at the quench front as the resulting droplet field downstream is 

responsible for the improved cooling at the upper elevations in the rod bundle where the 

clad temperature peaks. The instrumentation requirements will include detailed 

measurements of the local void fraction, droplet size, droplet velocity, and droplet number 

density in the droplet field. 

9. To determine the local heat transfer, a reliable measurement of the non-equilibrium vapor 

temperature is needed. This has been included in the instrumentation requirements. 

Instrumentation will also be placed upstream and downstream of the spacer grids to see 

their effects. Additional instrumentation requirements have been identified using the PIRTs 

as a guide for the important phenomena for the different test types which the experiments 

must capture for the code development and validation. 

10. The instrumentation plan developed in the RBHT Program, which involves the use of 

ample instrumentation proven to perform in previous rod bundle experiments as well as 

state-of-the-art instrumentation specifically developed for dispersed two-phase flow 

measurements, represents a robust diagnostic plan that allows all the highly ranked 

phenomena to be either directly measured or calculated directly from the experimental 

data. 

11. The RBHT Test Facility meets all the instrumentation requirements developed in Task 7 

and can be used to conduct all of the planned experiments according to the test matrix 

developed in Task 9. It presents a unique NRC facility that can be used to provide new 

data at the subcomponent levels for the fundamental assessment of the physical behavior 

upon which the code constitutive heat transfer and flow models are based. 

12. In addition to obtaining separate-effect reflood data, the RBHT Test Facility is designed to 

perform mechanistic studies of the highly ranked phenomena to develop new or improved 

models for implementation in the NRC merged code. Thus, it will aid in the refinement of 

the NRC=s thermal-hydraulics code and will help maintain the NRC=s leadership in the 

reactor thermal-hydraulics safety analysis area. 
A-1

APPENDIX A1. LITERATURE REVIEW

Appendix A1: FLECHT Low Flooding Rate Cosine Test Series 

Dates When Tests Were Performed: 1974 - 1975 

References:

R1 Rosal, E. R. et al, AFLECHT Low Flooding Rate Cosine Test Series Data Report,@

WCAP-8651, Dec 1975. 

R2 Lilly, G.P.,Yeh, H. C.,Hochreiter, L. E., and N. Yamaguchi, APWR FLECHT Cosine Low 

Flooding rate Test Series Evaluation Report,@ WCAP-8838, March 1977. 

Availability of Data: 

Plots of selected data exist in the data report in R1. The raw data and reduced and analyzed 

data exists at Westinghouse on CDC 6600 and 7600 Magnetic tapes. This data has been in 

storage at the Westinghouse facilities. Microfiche of the raw data and analyzed data exist at the 

Westinghouse Engineering offices in Monroeville, PA. It is not clear if any of this data was put 

on the INEL data bank. 

Test Facility Description, Types of Tests 

The FLECHT Low Flooding Rate Cosine Test Series was a continuation of the FLECHT reflood 

heat transfer program started in the late 1960's and focused on low forced flooding rates tests at 

low pressures to provide a broader data range for the Appendix K licensing basis during the 

reflood period. The overall objective of the test program was to obtain data that would be useful 

for calculating the reflood behavior of PWRs following a postulated Loss Of Coolant Accident. 

The tests were performed using a 10x10 rod bundle with 91 active electrical heater rods and 

nine guide tube thimbles in which instrumentation was placed. The rod bundle was placed 

inside a thick walled 19.05 mm (0.75 in square housing which was heated externally for the 

tests. There was excess flow area around the bundle such that the housing had to be heated to 

preserve the correct power-to-flow area of a PWR fuel assembly. The heater rods were 10.72 

mm (0.422 in) in diameter and were arranged on a square pitch of 14.3 mm (0.563 in) and had a 

heated length of 3.66 m (12 ft). The electrical heater rods used a 1.66 cosine power distribution 

which was approximated by different pitch heating coils. The facility layout is shown in Figure 

A1.1 and the bundle geometry is given in Figure A1.2 from R2. A radial power distribution was 

used in these experiments to simulate or bound the rod-to-rod power distribution in a PWR fuel 

assembly. One feature which was unique in this test series is that there were a large number of 

variable inlet flooding rates tests performed to better simulate the gravity reflood behavior of the 

PWR. There were also low initial clad temperature test performed to simulate lower power 

regions in the core that could have quenched during blowdown or during Upper Head Injection 

which was a newer high-pressure accumulator installed on PWRs which had Ice Condenser 

Containment. 
A-2

The ranges of conditions include: 

Constant Flooding Rates 10.16 - 38.1 mm/s (0.4 - 1.5 in/s) 

Upper Plenum Pressure 172.37 - 413.685 kPa (25 - 60 psia) 

Initial Clad Temperature 148.88 - 871.11 degrees C (300 - 1600 degrees F) 

(At Peak Location) 

Initial Peak Power 1.673 - 3.1167 kW/m (0.51 - 0.95 kW/ft) 

(At Peak Location) 

Inlet Subcooling 11.11 - 100 degrees C (20 180 degrees F) 

Variable Inlet Flooding Rate Ranged from 0.3048 m/s (12 in/s) for 5 s and 20.32 mm/s 

(0.8 in/s) onward, to 50.8 mm/s (2 in/s) for 20 s and 25.4 

mm/s (1 in/s) onward 

Continuously Variable Flooding There were two tests which simulated the average variable 

flooding rate from the FLECHT-SEASET Phase B systems 

tests. 

Housing Temperature Tests Housing initial temperature varied from 140 - 371.11 

degrees C (284 - 700 degrees F) 

FLECHT Repeat Tests There were six repeat tests of previously performed 

FLECHT reflood tests. 

Bundle and Housing Three different housing temperatures were used 

Stored Energy Tests 

Supplemental Entrainment These were entrainment tests with several disconnected 

heater rods and failed rods over a range of flooding rates 

and pressures to provide additional data. 

Instrumentation and Data From Tests 

The heater rods were instrumented with several thermocouples to measure the inside cladding 

surface temperature. The heat flux from the cladding surface was calculated form the 

thermocouple response using an inverse conduction computer program called DATAR. This 

program should still exist at Westinghouse and has been replaced by an improved version 

called DATARH. The thimbles shown in Figure A2.2 were unheated tubes which receive radiant 

heat from the heater rods. The temperatures of the thimbles were measured using 

thermocouples welded to the inside of the tubes. Housing temperatures were measured along 

the length of the housing to characterize its heat release as the bundle quenched. The inlet flow 

and water temperature were measured as well as the pressure in the exit or upper plenum. 

There were separators and collection tanks at the exit of the test section such that the existing 

steam and water flows could be separated and individually measured. There were also 

sensitive differential pressure cells every two feet along the housing to measure the bundle 
A-3

mass storage. The spacing is too sparse to obtain an accurate indication of local void fraction, 

however, the cells will indicate the mass stored in the bundle. 

One of the more important pieces of data is the steam probe measurements at the 2.1366, 

3.048 and 3.81 m (7, 10 and 12.5 ft) elevations. These were shielded aspirating thermocouples 

which could measure the vapor superheat until the quench front would approach and fill the 

probe with water. The steam probes indicated the high degree of superheat in the dispersed 

two-phase flow above the quench front. 

This FLECHT Test Series was the first to perform a mass and energy balance down the test 

section to determine the local quality conditions and the split of the heat transfer between 

radiation to drops, vapor and housing, and steam convection with entrained droplets. There are 

calculated values of the real quality for seven tests which span the matrix at different times in 

the transient. The analysis indicated, for the first time, that the convection is enhanced when 

droplets are entrained. The analysis also indicated the importance of the radiation heat transfer. 

The Appendix A in Reference 1 gives the details of the calculational method. 

Conclusions 

The FLECHT Low Flooding Rate Cosine tests do have some data which would be of interest for 

improved reflood modeling. In addition to the heater rod temperatures, the measurement of the 

vapor temperature at the 2.1366, 3.048 and 3.81 m (7, 10 and 12.5 ft) elevations are of value 

since these data indicate the degree of non-equilibrium within the flow. The pressure drop 

measurements are too coarse to be used as an indicator of the void fraction within the bundle. 

However, these measurements can be used to indicate the mass rate of accumulation within the 

bundle such that a complete mass balance can be calculated from the data for the tests. 

The conditions which were simulated are also useful from a code analysis and validation effort 

since a large range of conditions were simulated, in particular a variable inlet flooding rate and a 

continuously variable inlet flooding rate which simulates gravity reflooding. These experiments 

would be useful to assess the code performance. 

This is not sufficient data to make code model changes without the potential for compensating 

error. More detailed data is needed which identify code calculated parameters such as vapor 

superheat, convective enhancement, radiation to drops, rods, vapor and housing, droplet sizes 

and velocities along the bundle, and the void distribution in the froth region. These types of 

measurements are missing such that the code can only be compared to the cladding 

temperatures, quench front, and the overall mass balance. 

Therefore while these tests are useful in determining the overall reflood heat transfer, they 

provide very limited data which can be used to assess the reflood phenomena which was 

identified in the PIRT. Therefore, limited effort should be spent modeling these tests. 
Figure A1.1 FLECHT Low Flooding Rate Test Configuration. 

A-4
Figure A1.2 Rod Bundle Instrumentation for FLECHT Low Flooding Rate Tests.

A-5
 A-6

APPENDIX A2. LITERATURE REVIEW

Appendix A2: FLECHT Low Flooding Rate Skewed Test Series 

Dates When Tests Were Performed: 1976-1977 

References:

R3 Rosal, E. R. et al, “FLECHT Low Flooding Rate Skewed Test Series Data Report,” 

WCAP-9108, May 1977. 

R4 Lilly, G. P., Yeh, H. C., Dodge, C. E., and S. Wong, “PWR FLECHT Skewed Profile Low 

Flooding Rate Test Series Evaluation Report,” WCAP-9183, Nov. 1997. 

 

Availability of Data:

Plots and tables of selected data are given in R3 for the different tests. Some of the basic 

quantities which were measured and calculated from the bundle mass and energy balance 

(given in R4) such as the local non-equilibrium quality, portion of the rod energy which is due to 

radiation and convective film boiling, and energy absorbed by the drops above the quench front. 

Two skewed power tests and one low flooding rate cosine test were analyzed in detail, which 

can be used for computer code comparison purposes. A heat transfer correlation was also 

developed which was a function of the distance above the quench front and is given in 

Reference R4. The skewed profile data was also compared to the cosine power shape data for 

the same test conditions. 

The raw test data and the analyzed test data are available at Westinghouse on CDC 7600 

magnetic tapes. Some selected tests have been brought forward to the new UNIX system at 

Westinghouse. Microfiche exist for the measured data as well as the analyzed test data at 

Westinghouse Engineering Offices in Monroeville, PA. It is believed that some of the transient 

temperature data were placed in the NRC data bank at INEL. 

 

Test Facility Description, Types of Tests

The FLECHT Low Flooding Rate Skewed Tests were a continuation of the FLECHT Low 

Flooding Rate Cosine Tests which were performed in the 1975 time frame. The rod diameter 

used was 10.719 mm (0.422 in) on a square pitch of 14.33 mm (0.563 in). These tests were 

intended to provide data for supporting the Appendix K reflood heat transfer models for different 

possible axial power shapes for analysis of the Loss Of Coolant Accident. 

There were two unique differences in the skewed tests as compared to the earlier cosine tests. 

The axial power shape was skewed to the top of the bundle with a peak of 1.35 at 3.048 m (10 

ft), and a low mass circular housing was used for the first time in the FLECHT program. 

The test facility is shown in Figure A2.1 and is similar to that for the low flooding rate cosine 

tests. The power shape is shown in Figure A2.2 and the bundle cross section is given in Figure 

A2.3. The bundle contained 105 electrical heater rods, six guide tube thimbles, eight metal filler 

rods and the ANC liquid level probe. The use of the filler rods permitted the square pitch rod 

array to fit into the circular housing with a minimum of excess flow area. There was additional 
 A-7

instrumentation added to the skewed test facility as compared to the low flooding rate cosine 

tests. There was more extensive thermocouple instrumentation within the bundle, there were 

differential pressure cells every foot instead of every two feet, close coupled tanks were 

attached to the upper plenum to collect and separate the liquid entrainment, and a more reliable 

exit flow measurement was used to measure the exiting steam flow from the bundle. 

There was a radial power profile which was similar to the low flooding rate cosine bundle as 

seen in Figure A2.3. There were instrumented control rod guide tubes and aspirating steam 

probes in the rod bundle. The steam probes were at 2.1336, 3.048 and 3.3528 m (7, 10 and 11 

ft). Selected guide tube thimbles were also instrumented with wall thermocouples. 

The range of conditions which were investigated were similar to the low flooding rate cosine 

tests and included: 

Constant Flooding Rate 17.78 - 152.4 mm/s (0.7 - 6.0 in/s) 

Upper Plenum Pressure 137.896 - 413.685 kPa (20 - 60 psia) 

Initial Clad Temperature 263.89 - 871.11 degrees C (507 - 1600 degrees F) 

(At Peak Location) 

Initial Peak Power 1.4764 - 3.3808 kW/m (0.45 - 1.0 kW/ft) 

(At Peak Location) 

Inlet Subcooling 4.44 - 55.55 degrees C (8 - 100 degrees F) 

Variable Inlet Flooding Rate Ranged from 152.4 mm/s (6 in/s) for 5 seconds 

 to 20.32 mm/s (0.8 in/s), to 38.1 mm/s (1.5 in/s) for 100 s 

 to 12.7 mm/s (0.5 in/s) onward 

Cosine Overlap Tests Tests were performed to overlap Cosine and 

 Skewed test conditions 

Hot and Cold Channel Tests Tests were performed with portions of the bundle 

 hot and the remainder cold 

Transient Pressure and Tests were performed in which the inlet flow, system 

Subcooling Tests pressure, and the inlet subcooling varied with time 

There were also repeat tests which were performed to insure that the bundle geometry was not 

distorted. There were a total of 75 powered experiments. Very early on in the program, two 

heater rods failed at the beginning of testing. As the number of thermal cycles increased in the 

test bundle, additional heater rods failed later. 

Instrumentation and Data From Tests

The electrical heater rods were instrumented with several thermocouples at the different 

elevation which gave good coverage for the length of the bundle. However, there were no 

thermocouples placed around the spacer grids which would indicate a spacer grid effect on the 

two-phase flow. The liquid carried out of the test section was measured as well as the exiting 
 A-8

steam vapor. The mass storage within the test section was also measured using delta P cells at 

one-foot intervals along the length of the housing. From these measurements, a transient mass 

balance could be performed on the test to help validate the data. Typically the mass balances 

were within five percent. 

There were three aspirating steam probes at the 2.1336, 3.048 and 3.3528 m (7, 10 and 11 ft) 

elevations, as well as the exit pipe of the test section, to verify that the steam flow measurement 

was single phase. Using the flow measurements at the bundle exit, the actual steam nonequilibrium temperature, and the integrated wall heat flux between the steam probe locations; 

an energy balance can be performed to obtain the local quality and therefore the local steam 

and liquid flow. The change in the calculated quality indicates how much of the rod bundle 

surface heat flux goes into evaporating the entrained liquid droplets. The calculation was 

carried to the quench front where the vapor temperature was assumed to be the average of the 

rod temperature and the saturation temperature. 

A simple radiation network was developed to separate the radiation heat transfer component 

from the total measured wall heat flux on the heater rods. Knowing the total wall heat flux, and 

subtracting the radiation heat flux, the convective wall heat flux can be determined. In the 

dispersed flow film boiling, this is the heat flux to the superheated vapor which contains 

entrained liquid droplets. The Nusselt number for the convective flux was calculated and 

compared to the Nusselt number that typical single-phase correlations would predict. It was 

observed that the convective Nusselt number calculated from the test data lied significantly 

above the limits calculated with conventional single phase convective correlations. Also, since 

the flow was superheated steam at low pressure, the calculated vapor Reynolds number was 

quite small, from 1500 to 10,000. These data and that of the low flooding rate cosine tests 

indicated that the presence of entrained liquid droplets could enhance the convective nature of 

the single phase vapor significantly at low vapor Reynolds numbers. 

Conclusions

The FLECHT Low Flooding Rate Skewed Power Tests do have data which would be of interest 

for improved computer code modeling for the reflood heat transfer process. In particular, the 

different axial power shape used in these tests is very useful for assessing computer codes 

which may have been “tuned” to a cosine power shape. The pressure drop measurements are 

improved in the skewed bundle tests such that a more local void fraction (one-foot increments), 

can be determined and used to assess the local heat transfer. The void fractions and overall 

pressure drop are also used in the test bundle mass balances along with the inlet flows and exit 

flows. Typically the mass balances were within five percent. 

There were a large number of experiments which were performed over a wide range of 

conditions, some of which specifically over-lapped with the low flooding rate cosine tests. 

These overlap experiments are particularly useful for code validation purposes, since the 

accuracy of the computer code predictions for different axial power shapes can be assessed. A 

Best-Estimate computer code must be able to calculate a range of different axial power shapes 

to determine the most limiting shape. 

While the data from the skewed series of experiments as well as the data analysis of these tests 

was improved over the low flooding rate cosine tests; there was still the lack of sufficient vapor 

temperature distribution and information in the test bundle such that the axial distribution of the 

local qualities could be more accurately determined. The data was analyzed to determine the 
 A-9

heat flux split between radiation heat transfer and convective-dispersed flow film boiling heat 

transfer using a simplified radiation network approach. When the resulting convective-film 

boiling heat transfer (from the data) was compared to calculated single phase heat transfer 

correlation at the same vapor Reynolds number, the calculated data convective-film boiling 

transfer was significantly higher. Since the single phase correlation used the measured vapor 

temperature and the calculated vapor flow rate from the quality and energy balance, it is 

believed that the improved heat transfer is due to the presence of the entrained droplets which 

can add to the turbulence level in the flow at the low vapor Reynolds numbers. This 

phenomenon of enhanced convective-dispersed flow film boiling was identified in this report as 

well as in the low flooding rate report. 

Therefore, the Low Flooding Rate Skewed Power reflood tests are useful in determining the 

overall heat transfer processes and some of individual models and phenomena which 

compromise the reflood heat transfer process. 
Figure A2.1 FLECHT Low Flooding Rate Test Facility Schematic.

A-10
Figure A2.2 FLECHT Low Flooding Rate Test Power Shape. 

A-11
Figure A2.3 FLECHT Low Flooding Rate Test Rod Bundle Cross Section. 

A-12
 A-13

APPENDIX A3. LITERATURE REVIEW

Test Facility Name: Westinghouse FLECHT-SEASET 21-Rod Bundle Test Facility. 

Dates When Tests Were Performed: 1977-1982 

References:

R5 M. J. Loftus, et. al., APWR FLECHT SEASET 21-Rod Bundle Flow Blockage Task Data 

and Analysis Report,@ NUREG/CR-2444, EPRI NP-2014, ECAP-992, Vol. 1 and Vol. 2, 

September 1982. 

Availability of Data: 

Volume 1 contains data and limited analysis from the 21-Rod Bundle FLECHT-SEASET 

Program. Volume 2 contains sampling of data tables and plots collected for the unblocked 

bundle (Configuration A) and five blocked bundle configurations, (B, C, D, E and F). All the 

valid measured data are available in the NRC data bank. 

Test Facility Description, Types of Tests

Low forced flooding rate, gravity reflood, and single phase flow tests were performed in the 21-

Rod bundle FLECHT-SEASET Test Facility. The overall objectives of these tests were to 

determine effects of various flow blockages of reflooding behavior and to aid in 

development/assessment of computational models in predicting reflooding behavior of flow 

blockage configurations for the 163-Rod flow blockage bundle test. 

The tests were performed using a 5x5 rod bundle array typical of a 17x17 power fuel assembly. 

The bundle contained 21 active electrical heater rods and four triangular shaped filler strips 

placed at the corners in order to minimize excess flow areas due to the circular low mass flow 

housing as shown in Figure A3.1. The heater rods were 0.0095 m (0.374 in) in diameter and 

3.24 m in length. The electrical heater rods used a 1.66 peak to average axial power 

distribution with a chopped cosine shape, which was approximately simulated by different pitch 

coils in the electrical heating element. The heater rod bundle had a uniform radial power profile. 

Spacer grids were of a simple egg-crate style installed 0.533 m (21 in) apart. The tests were 

conducted in a heavily instrumented facility as indicated in the reference Reports. 

Four types of tests were conducted: hydraulic characteristics tests, steam cooling tests, forced 

reflood tests, and gravity reflood tests. The hydraulic characteristics tests were performed to 

determine the pressure losses associated with rod friction, grids, and blockage sleeves. The 

steam cooling tests were performed to measure single-phase heat transfer effects of unblocked 

and blocked configurations. Forced reflood tests were performed to measure the two-phase 

flow heat transfer effects of unblocked configurations. The gravity reflood tests were performed 

to measure heat transfer effects during the PWR-simulated gravity reflood injection for 

unblocked and blocked configurations. 
Figure A3.1 Schematic of the Test Bundle. 

The range of conditions included: 

Constant Flooding Rates: 10.2 - 152 mm/s (0.4 - 6.0 in/s) 

Upper Plenum Pressure: 0.14 - 0.28 MPa (20 - 40 psia) 

Initial Clad Temperature: 260 - 871 degrees C ( 500 - 1600 degrees F) 

(At Peak Location) 

Inlet Subcooling: 3 - 78 degrees C (5 - 140 degrees F) 

Variable Steps in Flooding Rates: 20 - 152 mm/s (0.8 - 6.8 in/s) 

Injection Gravity Reflood: 0.09 - 0.82 kg/s (0.2 - 1.8 lb/s) 

(Variable Steps) 

Housing Temperature Tests: 222 - 546 degrees C (431 - 1015 degrees F 

(At Peak Location) 

Repeat Tests: There were 2 repeat tests of the Unblocked 

 Configuration (A) 

Conclusions 

Comparisons of calculated and measured temperatures generally showed good agreement. 

Nusselt numbers calculated from the steam cooling data were compared with the Dittus-Boelter 

heat transfer correlation as a function of Reynolds number. The results showed that, in general, 

the Dittus-Boelter correlation under predicts the heat transfer coefficient for Reynolds numbers 

less than 2500 and is in agreement for values about Reynolds numbers greater than 10,000. 

Comparisons of the FLECHT-SEASET 21-Rod Bundle tests with the Rod Bundle PIRT are 

given in Tables A3.1 to A3.4. 

 A-14
A-15

Figure A3.2 21-Rod Bundle Flow Blockage Task Instrumentation Schematic Diagram
A-16

Table A3.1 Assessment of FLECHT-SEASET Unblocked 21-Rod Bundle Test to RBHT PIRT: Disperse

Core Component 
A-17

Table A3.2 Assessment of FLECHT-SEASET Unblocked 21-Rod Bundle Test to RBHT PIRT: Top Dow

Components

Process/Phenomena Ranking Basis FLECHT-SEA

De-entrainment of film flow Sputtering droplet size and velocity Fuel rod/heater rod properties for stored energy: ρ, cp and k. 

Gap heat transfer 

L1

L 

L1L1

The film flow is the heat sink needed to quench the heater rod. This has high uncertainty. The droplets are sputtered off at the quench front and are then re-entrained upward. Since the sputtering front is above the PCT location, no impact. The entrained sputtered drops do not affect the total liquid entrainment into the reactor system, as well as the steam production, in the steam generators. These properties are important since they determine the heat release into the coolant. However, since this occurs above the PCT level, no impact. Affects the rate of energy release from the fuel/heater rod. 

Top down quensome tests. Details at top qmeasured. Ontransfer was meHeater rod propNo gap in heate

Note: Some of these individual items can be ranked as High (H) within the top down quenching process; howevranked as low (L) for a PWR/BWR since it occurs downstream of the PCT location. 
A-18

Table A3.3 Assessment of FLECHT-SEASET Unblocked 21-Rod Bundle Test to RBHT P

Preliminary PIRT for Gravity Reflood Systems Effects Tests

Process/Phenomena Ranking Basis FLECHT-SEASE

Upper PlenumEntrainment/Deentrainment Hot leg - Entrainment, de-entrainment. Pressurizer Steam Generators Reactor Coolant Pumps Cold leg accumulator injection Cold leg pumped injection 

M 

L L 

H H H H 

The plenum will fill to a given void fraction after which the remaining flow will be entrained into the hot leg, large uncertainty. The hot legs have a small volume and any liquid swept with the hot leg will be entrained into the steam generator plenums, medium uncertainty. Pressurizer is filled with steam and is not an active component, small uncertainty. The generators evaporate entrained droplets and superheat the steam releases (particularly at low pressures). The result is a higher steam flow downstream of the generators. High uncertainty since a good model is needed. FLECHT-SEASET data exists for reflood. This is the largest resistance in the reactor coolant system which directly affects the core flooding ratelow uncertainty. Initial ECC flow into the bundle. Pumped injection maintains the core cooling for the majority of the reflood transient. 

Not measured. Not measured. Not measured. Not measured. Not measured. Not measured. Variabsimulated to model acinjections, also continuflooding rate tests werNot measured, variablto model accumulator also continuous by vartests were performed. Low pressure (20 psia
A-19

Table A3.3 Assessment of FLECHT-SEASET Unblocked 21-Rod Bundle Test to RBHT P

Preliminary PIRT for Gravity Reflood Systems Effects Tests (Continued)

Process/Phenomena Ranking Basis FLECHT-SEASE

Pressure Injection Subcooling Downcomer Wall Heat Transfer Lower Plenum Wall Heat Transfer Break 

H 

M/H 

H 

M 

L 

Low pressure (20 psia) significantly impacts the increased vapor volume flow rate, which decreases the bundle flooding rate. Lower subcooling will result in boiling below quench front such that there is additional vapor to vent. The heat transfer from the downcomer walls can raise the ECC fluid temprature as it enters the core, resulting in more steam generation. Source effect as downcomer but less severe. Excess ECC injection spills, but break ΔP helps pressurize reactor system. 

Low pressure (20 psiaLow subcooling simulaNot measured. Not measured. Not measured. 
A-20

Table A3.4 Assessment of FLECHT- SEASET Unblocked 21-Rod Bundle Test to RBHT PIRT: High R

Phenomena

Process/Phenomena Basis FLECHT-SEASET 

Core Film Boiling Upper Tie Plate CCFL Channel-Bypass Leakage Steam Cooling Dryout Natural Circulation Flow Flow Regime Fluid Mixing Fuel Rod Quench Front Decay Heat Interfacial Shear Rewet: Bottom Reflood 

PCT is determined in film boiling period. Hot assembly is in co-current flow above CCFL limit. Flow bypass will help quench the BWR fuel assembly core. A portion of the dispersed flow film boiling heat transfer. Transition from nucleate boiling and film boiling. Flow into the core and system pressure drops. Determines the nature and details of the heat transfer in the core. Determines the liquid temperature in the upper plenum for CCFL break down. Heat release from the quench front will determine entrainment to the upper region of the bundle. Energy source for heat transfer. Affects the void fraction and the resulting droplet and liquid velocity in the entrained flow. BWR hot assembly refloods like PWR. 

Total heat transfer is meNot applicable. Not applicable. Steam cooling heat transdata. Quench front is measureNot measured. Not measured. Not measured. Quench front data existsMeasured as initial/bounNot measured. Total reflood heat transfe
A-21

Table A3.4 Assessment of FLECHT- SEASET Unblocked 21-Rod Bundle Test to RBHT PIRT: High R

Phenomena (Continued)

Process/Phenomena Basis FLECHT-SEASET 

Rewet Temperature Top Down Rewet Void Distribution Two-Phase Level 

Determines the quench front point on the fuel rod. Top of the hot assembly fuel will rewet in a similar manner as PWR. Gives the liquid distribution in the bundle. Similar to quench front location, indicates the location of nucleate and film boiling. 

Quench temperature meTop down rewet quench Not measured. Measured by rod TC’s. measured, two phase levcells. 
A-22

APPENDIX A4. LITERATURE REVIEW 

Appendix A4: FLECHT-SEASET 161-Rod Unblocked Bundle Tests 

Dates When Tests Were Performed: 1981-1982 

References: 

R6 Loftus, M. J., et al,@ PWR FLECHT-SEASET Unblocked Bundle Forced and Gravity 

Reflood Task Data Report,@ NUREG/CR-1532, September 1981. 

R7 Lee, N. ,Wong, S., Yeh, H.C., and Hochreiter, L.E., APWR FLECHT-SEASET Unblocked 

Bundle Forced and Gravity Task, Data Evaluation and Analysis Report,@ NUREG/CR2256, February 1982. 

R8 Wong, S. and Hochreiter, L.E., APWR FLECHT-SEASET Analysis of Unblocked Bundle 

Steam-Cooling and Boil-off Tests,@ NUREG/CR-1533, May 1981. 

Availability of Data: 

Plots and tables of selected data are given in R6 for each of the tests. These tests are similar to 

the Low Flooding Rate Cosine Tests excepting that the rod array used in the FLECHT-SEASET 

tests used the newer 17x17 array while the Low Flooding Rate Cosine and Skewed Power 

Tests used the older 15x15 rod array. There are selected tests which were analyzed in detail in 

Reference 2, particularly Test 31504 which is a 40 psia, 1 in/s constant reflood test. There was 

additional instrumentation on the test bundle which permitted more accurate mass and energy 

balances for the two-phase dispersed flow region of the bundle. There were also several highspeed movies of the different tests taken at the three, six and nine-foot windows. The drop 

diameter and droplet velocities were obtained and are given in R7. A heat transfer correlation 

was developed as a function of the distance from the quench front for both the 15x15 and 17x17 

rod bundle geometry. 

The raw data in engineering units is available from the NRC Data Bank for selected tests. All 

the data exists at Westinghouse on Microfiche, including the analyzed data. The analyzed data 

and the row data in engineering units also exists at Westinghouse in storage on older computer 

tapes. It is not clear at this time if the data can be assessed. 

Test Facility Description, Types of Tests 

The FLECHT-SEASET Unblocked Bundle tests were the first publicly available reflood 

experiments on the newer 17x17 fuel array which was adopted by the utilities in the 1980's. 

This fuel array used fuel rod of approximately 9.5 mm (0.374 in) on a square pitch of 12.60 mm 

(0.496 in). 

The experiments used a 1.66 chopped cosine power shape which was the same as the 

FLECHT Low Flooding Rate Cosine Tests. The tests were used to help confirm the 

conservatism in the Appendix K rule as well as to be used for reflood safety analysis computer 

code assessment. Two of the experiments were also used as US Standard Problem 9 in which 
A-23

different parties predicted two FLECHT-SEASET unblocked bundle reflood transients. The 

unblocked bundle tests were also used as a basis for determining the effects of flow blockage 

within the rod bundle which simulated the ballooning and bursting of the Zircaloy cladding. 

The majority of the tests were separate effects constant and or variable reflood tests. There 

were also limited gravity reflood scoping experiments as well. In addition, there were boil-off 

and steam cooling tests performed as well as given in R8. 

The 161-rod bundle unblocked bundle did have problems with the electrical heater rod. The 

new smaller diameter rods, with smaller inside wall thermocouples, proved to be less reliable 

then the previous larger 10.719 mm (0.422 in) diameter rods. Several of the heater rod 

thermocouples failed in the initial transient tests such that the bundle instrumentation became 

degraded. Consequently, the 161-rod bundle was rebuilt by replacing heater rods 

approximately one-half way into the testing program. Those individuals using the test data must 

verify the proper channel and rod location since new rods were used in several different 

locations. The full channel list for all tests is given in R6. 

The 161-rod bundle also used the thin wall circular housing so as to minimize the housing 

radiation heat sink effects as well as the housing heat release effects. Figure A4.1 shows the 

cross-section of the rod bundle and Figure A4.2 shows the facility flow diagram. The majority of 

these tests were conducted with a uniform radial power profile for ease of analysis, as well as 

obtaining a statistical distribution for the hot spot temperatures and heat transfer coefficient. 

The 161-rod bundle was much more heavily instrumented as compared to the previous 

FLECHT test bundles. Most of the heater rods were instrumented and would have eight 

thermocouples per rod. Rods were located in symmetric positions such that complete coverage 

over the bundle length was achieved. The differential pressure cells were located one foot apart 

as in the skewed bundle tests and the data was used to determine the mass balance as well as 

for the average void fraction over the given cell span. There was no specific thermocouple 

placement relative to the grids, and the spacer grids were not instrumented; however, the axial 

placement was sufficiently fine that the data does indicate the heat transfer improvements 

caused by the spacer grids. The FLECHT egg-crate spacer grids were used and are the same 

as those used in previous FLECHT tests. One of the objectives of the 161 rod bundle tests was 

to provide improved data for the development and validation of safety analysis computer codes. 

To this end, there were additional aspirating steam probes added to the guide tube thimbles. 

Some of the steam probes aspirated the flow out the bottom of the bundle while other probes 

aspirated out the top of the bundle. It was discovered that the bottom probes would not indicate 

the true steam temperature since they were more easily wetted during the transient. The 

probes which are regarded as unreliable are given in R6. 

The range of conditions which were examined was similar to the Low Flooding Rate FLECHT 

tests and included: 

Constant Flooding Rates 11.43 - 154.94 mm/s (0.45 - 6.1 in/s) 

Upper Plenum Pressure 137.895 - 413.685 kPa (20 - 60 psia) 

Initial Clad Temperature 256.66 - 1118.33 degrees C (494 - 2045 degrees F) 

(At Peak Location) 
A-24

Initial Peak Power 1.312 - 3.2808 kW/m (0.40 - 1.0 kW/ft) 

(At Peak Location) 

Radial Power Distribution Uniform - FLECHT 

Similar to FLECHT Tests 

Inlet Liquid Temperature 51.11 - 125 degrees C (124 - 257 degrees F) 

Variable Flooding Rate Tests 161.544 mm/s (6.36 in/s) for 5 s; 

20.828 mm/s (0.82 in/s) onward; 

165.862 mm/s (6.53 in/s) for 5 s; 

24.892 mm/s (0.98 in/s) for 25 s; 

15.748 mm/s (6.36 in/s) onward 

Gravity Injection Tests 147.32 mm/s (5.8 in/s) for 15 s; 

19.94 mm/s (0.785 in/s) onward 

There were other tests performed such as hot and cold channel tests to examine the effects of 

liquid entrainment, repeat tests to verify that the bundle was performing in a repeatable manner 

overlap tests with the previously performed 15x15 cosine experiments and steam cooling tests. 

The steam cooling tests are given in Reference 3 and investigated the steam cooling in the 

bundle over a Reynolds number range of approximately 1500 to 25000. The test matrix for this 

test series is given as Table A4.1, along with the measured peak cladding temperatures. 

There was a significant number of power cycles performed on the test bundle which led to 

heater rod distortion at the end of the test program. An analysis was performed to determine 

when the effects of distortion became evident in the data. This analysis is given in Reference 1 

and should be consulted when modeling the tests from this program such that only valid data is 

used. 

High-speed movies were taken for a number of tests at the three, six, and nine-foot windows 

with camera speeds up to 2000 frames/sec. The movie data was reduced and analyzed to 

obtain droplet size and velocity data which was then compared to values from the literature as 

well as calculations. It was found that a log-normal distribution fit the droplet diameter data 

reasonably well while there was no real correlation of the droplet velocity with the droplet 

diameter or any other parameter. 

An empirical reflood heat transfer correlation was developed from the 161-rod bundle 

experiments. The heat transfer correlation was a function of the distance above the quench 

front as well as the bundle initial conditions of power, pressure, flooding rate, inlet subcooling, 

and initial power. This correlation was used to predict the heat transfer above the quench. In 

addition, a quench front correlation was also developed such that given a set of system 

conditions; the dispersed flow film boiling heat transfer above the quench front in the PCT 

region could be predicted. The correlation was also used the older 15x15 FLECHT Low 

Flooding Rate Cosine and Skewed Power test data for developing the correlation. 

The unique area that the 161-rod bundle tests addressed was the analysis of the test data 

above the quench front in the film boiling region. The analysis methods which were first 

developed as part of the FLECHT Low Flooding Rate Test Series were expanded upon in the 
A-25

FLECHT-SEASET program. There was increased instrumentation for axial vapor temperature 

measurements along the test bundle which could then be used with the exit flow measurements 

to calculate the local actual quality in the test bundle, from an energy balance, such that the 

local liquid and vapor velocities could be determined. From the calculations of the vapor flows, 

velocities, and temperatures, the local vapor Reynolds number could be calculated such that a 

convective heat transfer could be predicted from different single-phase correlations. The effects 

of the vapor superheat on the calculated Reynolds number were significant since superheated 

steam flows at 15.24 m/s (50 ft/s) could result in a Reynolds number in the laminar regime. The 

results from the energy balance were also used with the high-speed movie from the analysis of 

the droplet data to calculate the void fraction in the flow. The measured void fraction from the 

differential pressure cells is not as accurate in the highly dispersed flow regime when the flow 

has very little liquid content. 

The wall heat flux was also decomposed using a six node radiation heat transfer network such 

that the radiation heat transfer from the inner hot rods, outer cold rods, guide tube thimbles, 

housing, droplets, and vapor could be calculated. Once the radiation component of the hot rods 

was calculated, the convective-dispersed flow film boiling portion of the rod heat transfer could 

be determined by subtracting the calculated radiation heat transfer from the measured total heat 

transfer which was calculated from an inverse conduction calculation using the heater rod 

thermocouple and local power. The convective-dispersed flow film boiling heat transfer was 

also compared to the single phase heat transfer one would predict using the same vapor 

Reynolds number, wall temperature and vapor temperature conditions. As with the FLECHT 

tests, the convective dispersed flow heat transfer data gave much higher values of the Nusselt 

number when compared to the Nusselt number calculated form the same conditions for a 

single-phase vapor. The interpretation of this difference is that the droplets are acting to 

enhance the heat transfer in the flow by acting as additional turbulence promoters, as well as 

temperature sinks which change the local bulk temperature profile. The comparisons indicate 

that the droplet effects are the greatest at the lowest vapor Reynolds numbers where the natural 

turbulence in the flow is the smallest. Therefore, the drops could be promoting increased 

turbulence in the flow which provides for increased heat transfer. It was also observed that as 

the liquid content of the flow increased, the difference between the convective dispersed flow 

film boiling heat transfer and the predicted single phase heat transfer also increased. 

The 161-rod bundle tests also clearly showed that two different two-phase regions exist above 

the quench front. A lower void fraction, liquid rich froth or transition region, exists at and just 

above the quench front for the forced flooding tests. The length of this region depends on the 

flooding rate value relative to the quench velocity. The larger the flooding rates relative to the 

quench velocity (which is conduction controlled), the longer the froth region. The froth region 

was observed and appears as liquid ligaments which are sheared into increasingly smaller 

droplets from the steam flow generated at the quench front and the higher wall temperature in 

the quench front region. The vapor shearing effects generate the entrained droplets which then 

provide cooling at the upper elevations of the test bundle in the non-equilibrium dispersed flow 

film-boiling regime. 

Conclusions

The FLECHT-SEASET 161-rod unblocked bundle experiments represent the best reflood 

experiments which were performed. It was recognized in the test planning that data was 
A-26

needed for advanced reflood computer code development such that an effort was made to 

obtain additional local heat transfer and fluid flow data in addition to the total heater rod heat 

transfer data for an empirical correlation. The mass balances on the tests were generally very 

good such that the data can be used with confidence, however, one must be careful of the 

vapor measurements as indicated earlier since some of the steam probes did not function as 

desired. Also because of heater rod problems, the bundle was rebuilt so that channel 

designation relative to specific heater rods may have changed. These changes are 

documented in the reports such that the user can correctly obtain the data for a given test. 

The analysis for the test data is the most complete of all the FLECHT test series. Test 31504 

was analyzed in detail with several plots given in the reports which can be used for computer 

code validation. There is also an amount of very good droplet size and velocity information 

which can also be used for computer code validation. If all the data is used for the validation, 

not just the heater rod temperatures, one can more realistically assess a computer code reflood 

heat transfer model since the test measurements include the rod surface temperature, vapor 

temperature, drop size, drop velocity as well as the local quality, void fraction, and heat flux split 

between radiation heat transfer and convective dispersed flow film boiling heat transfer. 

Two of the FLECHT-SEASET tests were used as US Standard Problem 9 for the purposes of 

code validation. It is strongly recommended that these data be used for validating the NRC 

merged code. 
A-27

Figure A4.1 FLECHT-SEASET Rod Bundle Cross Section. 
Figure A4.2 FLECHT-SEASET Facility Flow Diagram. 

A-28
A-29

Table A4.1 FLECHT-SEASET Unblocked Bundle Reflood Test Data Summary 
Table A4.1 FLECHT-SEASET Unblocked Bundle Reflood Test Data Summary (Continu

A-30
Table A4.1 FLECHT-SEASET Unblocked Bundle Reflood Test Data Summary (Continu

A-31
A-32

Table A4.1 FLECHT-SEASET Unblocked Bundle Reflood Test Data Summary (Continu
A-33

Table A4.1 FLECHT-SEASET Unblocked Bundle Reflood Test Data Summary (Continu
A-34

Table A4.1 FLECHT-SEASET Unblocked Bundle Reflood Test Data Summary (Continu
A-35

APPENDIX A5. LITERATURE REVIEW 

Test Facility Name: FEBA - Flooding Experiments with Blocked Arrays. 

Dates When Tests Were Performed: 1977 

References:

R9 P. Ihle, K. Rust, “FEBA - Flooding Experiments with Blocked Arrays Evaluation Report,” 

KfK 3657, March 1984. 

R10 P. Ihle, K. Rust, “FEBA - Flooding Experiments with Blocked Arrays Data Report 1, 

Test Series I through IV,” KfK 3658, March 1984. 

R11 P. Ihle, K. Rust, “FEBA - Flooding Experiments with Blocked Arrays Data Report 2, 

Test Series V through VIII,” KfK 3659, March 1984. 

Availability of Data:

Reduced instrument responses are presented in References R9 to R11 in a variable versus 

time plot format. Tables and figures describing instrument locations are provided. Results are 

presented in ‘almost SI’ units. A listing of computer channel numbers and of data identification 

are available on tapes or in the USNRC/RSR Data Bank. 

Test Facility Description, Types of Tests

The test facility is designed for a separate effect test program involving a constant flooding rate 

and a constant back pressure to allow investigation of the influence of coolant channel 

blockages independently of system effect. 

Figure A5.1 shows a scheme of the test facility. The coolant water is stored in tank and during 

operation the flow is forced into the bundle with a back pressure control system. A 1x5 as well 

as 5x5 rod array are placed in a full length stainless steel housing which have a wall thickness 

of 1/4 in. The heater rods were 10.75 mm (0.423 in) in diameter and were arranged on a 

square pitch of 14.3 mm (0.563 in) and had a heated length of 3.90 m (12.8 ft) for the 5x5 rod 

bundle tests and 2.9 m (9.5 ft) for the 1x5 rod bundle tests. The axial power profile is shown in 

Figure A5.2. Top-down quenching was prevented in the experiments by using a particular 

upper plenum design (Figure A5.3). 

The ranges of conditions include: 

Constant Mass Flow Rate 2.0 - 9.5 cm/s (0.8 - 3.7 in/s) 

Pressure 2.0 - 6.2 bar (29.4 - 91.1 psia) 

Initial Clad Temperature 368 - 794 degrees C (694 - 1461 degrees F) 

Power Axial Peak Factor 1.19 
A-36

Initial Average Power 120 percent ANS: 40s after Reactor Trip 

Inlet Temperature 40 - 125 degrees C (104 - 257 degrees F) 

Initial Housing Temperature 275 - 760 degrees C (527 - 1400 degrees F) 

Flow Blockage Ratio 0, 62, 90 and 90+62 percent 

Flow Blockage Geometry Various 

The FEBA 5x5 rod bundle program consisted of eight test series with different grid spacer and 

sleeve blockage arrays within the bundle (Figure A5.4). Series I tests are baseline tests with 

undisturbed bundle geometry. Series II tests investigate the grid spacer effect on the axial 

temperature profile at bundle mid-plane. Series III and IV tests consider 90 and 62 percent 

blockage at bundle midplane respectively. Series V tests consider both the blockage and the 

grid spacer effects while Series VI tests have double blockage and investigate on the possibility 

of a hot region between the two blockages. Finally Series VII and VIII tests investigate on 

cooling enhancement downstream the blockages. 

Instrumentation and Data From Tests

Thermocouples (Chromel-Alumel) are imbedded in each of the rods as shown in Figure A5.5 

and A5.6. They are used to measure cladding, sleeve, grid spacers and housing temperatures 

at different locations (Figure A5.7). Fluid temperatures were measured with three different 

thermocouples (Figure A5.8) and probes in order to provide information about two separate 

phases. The signals of all three fluid thermocouples indicated roughly same temperature during 

most part of reflood. Radiation effect for the unshielded thermocouple was not detected 

however shielding let to earlier quenching of the shielded thermocouples. Pressure and 

pressure differences were measured with pressure transducers. In addition to inlet and outlet 

pressure, the pressure differences along the midplane as well as along both the lower and 

upper portion of the bundle were measured. The flooding rate was measured with a turbine flow 

meter. The amount of water carry over was measured continuously by a pressure transducer 

on the water collecting tank. All data were digitally recorded with a scan frequency of 10 Hz. 

The water level rising in the lower plenum at the onset of reflood was detected by 

thermocouples. In some tests high-frequency probes were used to detect the presence of water 

in the flow channel. 

Conclusions

The FEBA experiments provide very good information concerning the separate effect of grids 

and blocked bundle regions on the heat transfer during reflood. Separate tests were run with 

the same boundary conditions with and without grids, with and without blockage to address this 

effect. On the other hand, very little effort has been dedicated to investigating the single 

thermal-hydraulic process involved in the heat transfer during reflood (droplets behavior, 

entrainment, etc.). This does not provide sufficient data to develop and validate mechanistic 

models to be used in best-estimate code. 
A-37

Figure A5.1 FEBA Test Facility. 
A-38

Figure A5.2 Axial Power Profile. 

Figure A5.3 Upper Bundle End and Upper Plenum.
A-39

Figure A5.4 5x5 Rod Bundle, Test Matrix for Series I Through VIII. 
A-40

Figure A5.5 Rod Geometry and Location of Thermocouple. 
A-41

Figure A5.6 Radial and Axial Location of Cladding, Fluid and Housing 

T/C’s for Test Series I.
A-42

Figure A5.7 Axial Locations of Various Thermocouples in 5x5 Rod Bundle. 
A-43

Figure A5.8 5-Rod Row: Comparison of Different Fluid Temperature Measuring Device
A-44

Table A5.1 Assessment of FEBA Test to RBHT PIRT: Single Phase Liquid Convective Heat Tra

Core Component During Reflood Below the Quench Front
A-45

Table A5.2 Assessment of FEBA Test to RBHT PIRT: Subcooled and Saturated Boiling i

Core Component Below the Quench Front 
A-46

Table A5.3 Assessment of FEBA Tests to RBHT PIRT: Quench Front Behavior in the Core Co
A-47

Table A5.3 Assessment of FEBA Tests to RBHT PIRT: Quench Front Behavior in the Core Compon
A-48

Table A5.4 Assessment of FEBA Tests to RBHT PIRT: Froth Region for the Core Compo
A-49

Table A5.5 Assessment of FEBA Tests to RBHT PIRT: Dispersed Flow Region for the Core C

Process/Phenomena Ranking Basis F

Radiation Heat Transfer to: - Surfaces - Vapor - Droplets Gap Heat Transfer Cladding Material Reaction Rate Fuel Clad Swelling/Ballooning 

M/H M/H M/H 

L L 

M 

L 

This is important at higher bundle elevations (H) where the convective heat transfer is small since the vapor is highly superheated. Very important for BWR reflood with spays and colder surrounding can. Large uncertainty. Controlling thermal resistance is the dispersed flow film boiling heat transfer resistance. The large gap heat transfer uncertainties can be accepted, but fuel centerline temperature will be impacted. Cladding material use din the tests is Inconel which has the same thermal conductivity as zircaloy. Nearly the same temperature drop will occur. Inconel will not react while zircaloy will react and create a secondary heat source at very high PCTs. Zirc reaction can be significant. Ballooning can divert flow from the PCT location above the ballooning region. The ballooned cladding usually is not the PCT location. Large uncertainty. 

Radiation heat tranconsidered in data A 0.5 mm gap is prsleeve in the blockeexperiments. Rod temperature were mUsed Ni-Cr 80-20 cNot present. The effect of clad bextensively investigmain issue of FEBA campaign. Large aavailable. 
A-50

Table A5.6 Assessment of FEBA Tests to RBHT PIRT: Top Down Quench in Core Compo

Process/Phenomena Ranking Basis 

De-Entrainment of Film Flow Sputtering Droplet Size and Velocity Fuel Rod/Heater Rod Properties for Stored Energy: r, cp, k. 

Gap Heat Transfer 

L1

L 

L1L1

The film flow is the heat sink needed to quench the heater rod. This has high uncertainty. The droplets are sputtered off at the quench front and are then re-entrained upward. Since the sputtering front is above the PCT location, no impact. The entrained sputtered drops do affect the total liquid entrainment into the reactor system, as well as the steam production in the steam generators. These properties are important since they determine the heat release into the coolant. However, since this occurs above PCT level, no impact. Affects the rate of energy releases from the fuel/heater rod. 

Top down quprevented in Not applicablquenching waNot applicablquenching waNot applicablquenching wa

Note: Some of these individual items can be ranked as high (H) within the top down quenching process; however, the entirfor a PWR/BWR since it occurs downstream of the PCT location. 
A-51

Table A5.7 Assessment of FEBA Tests to RBHT Preliminary PIRT for Gravity Reflood Systems E

Process/Phenomena Ranking Basis 

Upper PlenumEntrainment/De-Entrainment Hot Leg - Entrainment, De-Entrainment. Pressurizer Steam Generators Reactor Coolant Pumps Cold Leg Accumulator Injection Cold Leg Pumped Injection Pressure Injection Subcooling Downcomer Wall Heat Transfer Lower Plenum Wall Heat Transfer Break 

M 

L L 

H H H H H 

M/H 

H 

M 

L 

The plenum will fill to a given void fraction after which the remaining flow will be entrained into the hot leg, large uncertainty. The hot legs have a small volume and any liquid swept with the hot leg will be entrained into the steam generator plenums, medium uncertainty. Pressurizer is filled with steam and is not an active component, small uncertainty. The generators evaporate entrained droplets and superheat the steam releases (particularly at low pressures). The result is a higher steam flow downstream of the generators. High uncertainty since a good model is 

needed. FLECHT-SEASET data exists for reflood. This is the largest resistance in the reactor coolant system which directly 

affects the core flooding rate- low uncertainty. Initial ECC flow into the bundle. Pumped injection maintains the core cooling for the majority of the reflood 

transient. Low pressure (20 psia) significantly impacts the increased vapor volume flow rate, which decreases the bundle flooding rate. Lower subcooling will result in boiling below quench front such that there is additional vapor to vent. The heat transfer from the downcomer walls can raise the ECC fluid temprature as it enters the core, resulting in more steam generation. Source effect as downcomer but less severe. Excess ECC injection spills, but break ΔP helps pressurize reactor system. 
A-52

Table A5.8 Assessment of FEBA Tests to RBHT PIRT for High Ranked BWR Core Pheno

Process/Phenomena Basis FEB

Core Film Boiling Upper Tie Plate CCFL Channel-Bypass Leakage Steam Cooling Dryout Natural Circulation Flow Flow Regime Fluid Mixing Fuel Rod Quench Front Decay Heat Interfacial Shear Rewet: Bottom Reflood Rewet Temperature Top Down Rewet 

PCT is determined in film boiling period. Hot assembly is in co-current flow above CCFL limit. Flow bypass will help quench the BWR fuel assembly core. A portion of the dispersed flow film boiling heat transfer. Transition from nucleate boiling and film boiling. Flow into the core and system pressure drops. Determines the nature and details of the heat transfer in the core. Determines the liquid temperature in the upper plenum for CCFL break down. Heat release from the quench front will determine entrainment to the upper region of the bundle. Energy source for heat transfer. Effects the void fraction and the resulting droplet and liquid velocity in the entrained flow. BWR hot assembly refloods like PWR. Determines the quench front point on the fuel rod. Top of the hot assembly fuel will rewet in a similar manner as PWR. 

Total heat transfer is meNot applicable. Not applicable. Steam cooling heat transdata. Quench front is measureNot applicable. Movies exist to determinNot applicable. Quench front data existsMeasured as initial/bounNot measured. Total reflood heat transfeQuench temperature meTop down rewet quench 
A-53

Table A5.8 Assessment of FEBA Tests to RBHT PIRT for High Ranked BWR Core Phenomena 

Process/Phenomena Basis FEB

Void Distribution Two-Phase Level 

Gives the liquid distribution in the bundle. Similar to quench front location, indicates the location of nucleate and film boiling. 

Not measured. Measured by rod TC’s. measured, two-phase lecells. 
A-54

APPENDIX A6. LITERATURE REVIEW 

Test Facility Name: Oak Ridge National Laboratory Thermal-Hydraulic Test Facility (THTF). 

Dates when tests were performed: 1980 - 1982. 

References: 

R12 Mullins, C. B., et al., AORNL Rod Bundle Heat Transfer Test Data,@ NUREG/CR - 2525, 

Vol. 1 to Vol. 5, 1982. 

R13 Yoder, G. L., et al., ADispersed Flow Film Boiling in Rod Bundle Geometry - Steady State 

Heat Transfer Data and Correlations Comparisons,@ NUREG/CR - 24351, 1982. 

Availability of Data: 

Reduced instrument responses are presented in Reference R12 for transient film boiling in 

upflow. Microfiche of the reduced data in graphical form exist along with three types of tables to 

assist the reader in using the data. The first table lists instrumentation in terms of instrument 

function, type and location. The second table lists instruments in the order they appear 

graphically in the microfiche. The third table lists instruments alphabetically in terms of the 

instrument application number (IAN). In addition to the transient data, steady state data exist in 

Reference R13 for dispersed flow film boiling. The data are presented in two separate sets of 

tables, one in SI units and the other in English units, listing fluid conditions, surface conditions 

and correlation - predicted versus experimentally determined heat transfer coefficients. 

Test Facility Description, Types of Tests 

Both the transient and steady state experiments were performed in the Thermal-Hydraulic Test 

Facility (THTF), as shown in Figure A6.1. The THTF was a heavily instrumented non-nuclear 

pressurized water loop containing 64 full-length rods arranged in an 8x8 bundle; 60 of the rods 

were electrically heated (see Figure A6.2). The rod diameter was 0.0095 m (0.374 in) and the 

rod pitch was 0.0127 m (0.501 in) on a square lattice, typical of PWRs with 17xl7 fuel rod 

assemblies. Figure A6.3 shows a simplified cross section of a typical fuel rod simulator. The 

axial and radial power profile was flat. The heated length of the bundle was 3.66 m (12 ft) and 

there were eight spacer grids in the heated length, as shown in Figure A6.4. The spacer grids 

were of the egg crate type installed 0.61 m (2 ft) apart. 

Two types of tests were performed, one transient and the other steady state. The transient 

tests were initiated by breaking the outlet rupture disk assembly. Although the THTF had a 

rupture disk assembly at the inlet, it was not employed to assure a unidirectional flow up through 

the test section. At the same time the outlet rupture disk was broken, the pump was tripped and 
A-55

Figure A6.1. THTF System with Instrumented Spool Pieces Labeled. 
A-56

 

Figure A6.2. Identification of THTF Heater Rods, Subchannel Location, 

and Inactive Rods in THTF Heater Bundle. 

Figure A6.3. Cross-Section of a Typical Fuel Rod Simulator. 
A-57

Figure A6.4. Axial Locations of Spacer Grid and Thermocouples. 
A-58

bundle power was ramped up to about 6-8 MW. After the initial power ramped up, the bundle 

power remained at this high level until most of the sheath temperatures at level G in the bundle 

reached 811 degrees K (1000 degrees F). The bundle power was then ramped down to 

maintain high rod sheath temperatures in the upper bundle without reaching the safety limit of 

1116 degrees K (1550 degrees F). All test series including test 3.03.6AR, test 3.06.6B and test 

3.08.6C were conducted under reactor accident-type conditions to obtain transient film boiling 

data. The ranges of conditions are given are given below: 

Test 3.03.6AR 

Mass Velocity 136 B 502 kg/m2

s (1x105 to 3.7x105 lbm/hr - ft2) 

Quality 23 B 100 percent 

Pressure 5 B 10 MPa (700 B 1500 psi) 

Heat Flux 158 B 1000 kW/m2

 (5x104 to 3.2x105 Btu/hr - ft2) 

Test 3.06.6B 

Mass Velocity 136 B 610 kg/m2

s (1x105 to 4.5x105 lbm/hr - ft2) 

Quality 5 B 100 percent 

Pressure 6 B 13 MPa (875 B 1900 psi) 

Heat Flux 158 B 630 kW/m2

 (5x104 to 2x105 Btu/hr - ft2) 

Test 3.08.6C 

Mass Velocity 330 B 1090 kg/m2

s (2.4x105 to 8x105 lbm/hr - ft2) 

Quality 35 B 100 percent 

Pressure 6.6 B 11.7 MPa (950 B 1700 psi) 

Heat Flux 160 B 1100 kW/m2

 (5x104 to 3.5x105 Btu/hr-ft2) 

In the steady state tests, the working fluid flowed from the pump through two control values, 

past the inlet rupture disk assembly and through a vertical spool piece before it entered the 

external downcomer. The working fluid then flowed through two spool pieced in the downcomer 

and entered the test section. The fluid was heated as it flowed along the rods within the test 

section. It then left the test section from the upper plenum, past through the three outlet spool 

pieces and the heat exchangers, and returned to the pump. During the run, the loop was 

adjusted to provide the desired inlet fluid temperature and inlet pressure. The bundle power 

was then increased until the dryout point was at the desired position in the bundle. The steady 

state operating conditions were assumed to have been reached when the operating pressure 

and rod surface temperatures stabilized. A total of 22 steady-state tests were performed. The 

ranges of conditions were: 

Mass Velocity 226 B 806 kg/m2

s (1.66x105 to 5.94x105 lbm/hr - ft2) 

Quality 0 B 100 percent 

Pressure 4.4 B 13.4 MPa (635 B 1938 psi) 

Heat Flux 320 B 940 kW/m2

 (1x105 to 3x105 Btu/hr - ft2) 
A-59

Instrumentation and Data from Tests 

The bundle was fully instrumented with thermocouples at various axial locations (i.e., at A, B, C, 

D, E, F and G levels) to measure the rod temperatures and in-bundle fluid temperatures. At 

each axial location where a rod had thermocouples, there were three individual thermocouples 

spaced azimuthally around the rod. In-bundle fluid temperatures were measured using 

thermocouples extending a short distance from the rod surface into the fluid as well as 

thermocouples mounted on the spacer grids. Rods 36 and 46 also contained gamma 

densitometer instrumentation for measuring in-bundle fluid density. Two flow measurement 

sites were positioned at each end of the test section containing the rod bundle. Differential 

pressure and pressure instrumentation was made at various locations along the heated bundle. 

In addition, there was instrumentation located in the entire piping system including the outlet 

nozzle, vertical outlet and external downcomer spool pieces. 

In the transient tests, local bundle fluid conditions were calculated with the homogeneous twophase flow and thermodynamic equilibrium thermal-hydraulics code RLPSFLUX. The transient 

data were compared to six existing film boiling correlations. Results of the comparisons were 

presented in Reference R12. In the steady state tests, mass and energy conservation 

relationship were used to calculate equilibrium fluid conditions within the rod bundle. These 

fluid conditions, along with calculated rod surface temperatures, were used to evaluate the six 

film boiling correlations as well as single-phase vapor correlation. Results of the comparisons 

were presented in Reference R13. In addition to the dispersed flow film boiling data, results 

were also obtained for the spacer grid effects, which had beneficial influence on the heat 

transfer due to a boundary layer breakup-rebuild process at the grids. 

Conclusions 

The ONRL/THTF tests provide both transient and steady state film boiling heat transfer data in 

rod bundle geometry. In general, the steady state results support the conclusions reached in 

the analysis of the transient results. The experimentally determined heat transfer coefficients 

may be useful as they have been compared to various existing heat transfer correlations. It is 

found that the Dougall-Rohsenow correlation often overpredicts the heat transfer coefficient 

whereas the Groeneveld-Delorme correlation tends to underpredict the heat fluxes near dryout 

but improves as distance from dryout increases. On the other hand, the Groeneveld 5.7, 

Groeneveld 5.9 and Condie-Bengston IV correlations give better agreement with the 

experimental data. 

It should be noted that although the steady state and the transient data appear to be consistent 

with each other, the bundle fluid conditions in both cases are determined from mass and energy 

conservation consideration based on the assumption of thermodynamic equilibrium. However, 

non-equilibrium conditions probably exist within the bundle. Thus, a more sophisticated 

calculational method accounting for the effect of non-equilibrium is needed to determine the 

actual bundle fluid conditions. Non-equilibrium also implies that liquid droplets can be present in 

the flow when equilibrium qualities are calculated to be larger than unity. 
A-60

The ORNL/THTF tests have been focused on the case of dispersed flow film boiling in upflow 

under high-pressure high-temperature conditions. The data may provide some relevant 

information in the dispersed flow region for core component in the RBHT PIRT Table 5. 

However, the results are not applicable to single phase liquid corrective heat transfer in the core 

component during reflood below the quench front (RBHT PIRT Table 1), subcooled and 

saturated boiling in the core component below the quench front (RBHT PIRT Table 2), quench 

front behavior in the core component (RBHT PIRT Table 3), froth region for the core component 

(RBHT PIRT Table 4), top down quench in core component (RBHT PIRT Table 6), and gravity 

reflood system effects (RBHT PIRT Table 7). 

Even in the dispersed flow region, the ORNL/THFT data must be used with caution. This is 

because the pressure range of 4.4 - 13.4 MPa (635 - 1938 psi) explored in the THTF tests is 

very high, more characteristic of a PWR or BWR blowdown situation. Thus the results may not 

be directly applicable to transient stage of reflood heat transfer in rod bundles. 
A-61

Table A6.1 Assessment of ORNL/THTF Data to RBHT PIRT: Dispersed Flow Region for 

Component
A-62

Table A6.1 Assessment of ORNL/THTF Data to RBHT PIRT: Dispersed Flow Region for 

Component (Continued)
A-63

APPENDIX A7. LITERATURE REVIEW 

Test Facility Name: FRIGG-2 36-Rod Loop (Sweden) 

Dates When Tests Were Performed: 1965-1968 

References: 

R14 Becker, K. M., Flinta, J., and Nylund, O., ADynamic and Static Burnout Studies for the 

Full Scale 36-Rod Marviken Fuel Element in the 8 MW Loop FRIGG,@ Paper presented 

at the Symposium on Two-Phase Flow Dynamics, Eindhoven, September 1967. 

R15 Nylund, O., et al., AMeasurements of Hydrodynamic Characteristics, Instability 

Thresholds, and Burnout Limits for 6-Rod Clusters in Natural and Forced Circulation,@

ASEA and AB Atomenergi Report FRIGG-1, 1967. 

R16 Nylund, O., Becker, K. M., Eklund, R., Gelius, O., Haga, I., Herngorg, G., Rouhani, Z., 

and Akerhielm, F., AHydrodynamic and Heat Transfer Measurements on a Full Scale 

Simulated 36-Rod Marviken Fuel Element with Uniform Heat Flux Distribution,@ ASEA 

and AB Atomenergi Report FRIGG-2, 1968. 

Availability of Data: 

The experimental investigation simulates the fuel element of a Swedish heavy water cooled 

Marviken BVRR with 35 uniformly heated heater rods and a unheated (but larger in diameter) 

center rod simulating the control rod. Experimental data available from the FRIGG-2 tests, all 

under pressures up to 50 bar (711 psi), are single- and two-phase pressure drops; burnout (or 

critical heat flux) in natural and forced circulation; natural circulation mass velocity as a function 

of total power and inlet subcooling; the stability limit; as well as the details about the system 

during transient conditions. Additionally, a unique output of the FRIGG-2 tests is the axial and 

radial void distributions measured by the Cobalt-60 gamma-ray densitometer system. The 

results have been compared to data obtained from in the previous six-rod tests (R15, FRIGG- 1) 

and to predictions with existing correlations and models. All pressure drop data are consistently 

agreeable between FRIGG-2, FRIGG-1, and actual Marviken conditions. The natural circulation 

burnout value is very close to that of forced circulation, but both are about 20 percent low 

compared to predictions by the Becker correlation. This is believed to be due to the unfavorable 

conditions in the inner subchannels of the uniformly heated bundle. The results of natural 

circulation mass velocity, stability limit, and transient behavior at different power levels agree 

well with the calculation. Calculations indicate that the conditions in a real Marviken boiling 

channel are somewhat more favorable than in the FRIGG-2 experiment. This suggests that 

sufficient margins against burnout and hydrodynamic instability are present in the Marviken 

reactor. 
A-64

Test Facility Description, Types of Tests

The primary purpose of FRIGG-2 tests was to obtain the burnout values of the 36-rod bundle at 

different mass fluxes and inlet subcoolings to simulate the core conditions of a Marviken BWR. 

The geometric features of the test section are: 

 

Number of heated rods: 35 Rod diameter: 13.8 mm (0.5433 in) 

Number of unheated rods: 1 Unheated rod dia.: 20 mm (0.7874 in) 

Circular housing diameter: 160 mm (6.30 in) Number of spacers: 8 

Average hydraulic dia.: 26.9 mm (1.06 in) Heated hydraulic dia.: 36.6 mm (1.44 in) 

Heated length (uniform): 4375 mm (172 in) No. of burnout T/C's: 4 

Tests were run with 35 rods electrically heated and one center rod unheated. Both the axial and 

radial power profiles are uniform. A cross-sectional view of the test section is shown in Figure 

A7.1, indicating the placement pattern of the unheated center rod and 35 heated rods in three 

orbital rows. The flow diagram of the FRIGG-2 loop is shown in Figure A7.2. For burnout tests 

FRIGG-2 requires a significant DC electrical power: 80 MW, 80 kA, and DC voltage regulation 

from 0 to 200 V. The heater rods were of a type with coaxial feeder rod eliminating the 

electromagnetic forces between the rods. Most of the heat is produced in the 0.8 mm stainless 

steel canning of the rod, which is isolated from the center copper conductor. This means that 

the reactor fuel time constant (or heat capacity) is not correctly simulated. There are four 

electrically isolated burnout detectors (or thermocouples) measuring temperatures at different 

elevations and there wires running axially along the inside surface of the stainless steel canning. 

If a burnout event is detected by any of the burnout detectors in the bundle, the DC power 

applied to the bundled would be immediately reduced by 20 percent within 0.1 s and the 

histories of all important fluid and thermal parameters are recorded. These burnout conditions 

are the primary objective of the FRIGG-2 tests. 

A secondary but important test of FRIGG-2 is the void fraction measurement in both the axial 

and radial directions of the bundle. The measurement system comprises one gamma source, 

Co-60, and four scintillation detectors with adjustable collimators. The pulses from the detectors 

are amplified, analyzed and counted in separate scalars built into the data collection system. 

The penetration paths of the four gamma beams can be changed between three prefixed radial 

positions within the bundle. The void at a certain level is thus evaluated from the twelve 

measurements covering different parts of the bundle. This gives a rather good cross sectional 

mean value of the void and also information about the radial void distribution. The void 

measurement system is moved up and down the test section by means of an electric elevator 

that allows for axial void distribution measurement. 

Other instrumentation includes: Chromel-alumel thermocouples for fluid temperature 

distribution measurement; fast response differential pressure (DP) cells with venturi units and 

turbine flow meters for mass velocity measurement; and impedance void gauge to measure the 

outlet quality. Standard single and two-phase pressure drops at all test conditions are also 

measured using differential and absolute pressure sensors. 
A-65

 

Figure A7.1. 36-Rod Bundle of the FRIGG-2. 
A-66

 

Figure A7.2. Flow Diagram of the FRIGG-2 Loop.
A-67

The ranges of test conditions include: 

Single-Phase (Cold) Mass Flux 840 - 3195 kg/m2

-s (0.618 B 2.35x106 lbm/ft2-hr) 

Two-Phase Mass Flux 366 - 1492 kg/m2

-s (0.269 B 1.098x106 lbm/ft2-hr) 

Pressure 50 bar (711 psi) 

Rod Temperature measured with thermocouples serving as burnout 

 detectors 

Average Heat Flux 8.1 - 103 W/cm2

 (0.0257 B 0.326x106 Btu/ft2-hr) 

Exit Quality 2.2 - 51.5 percent 

)Tsub 2.4 - 29.4 degrees C 

Flow Regimes Liquid 1-N, bubbly, transition, annular (typical of BWR). 

Void Fraction 0 - 100 percent 

Instrumentation and Data from Tests 

Each of the heater rods was instrumented with four thermocouples. These thermocouples are 

primarily for burnout detectors and thus calibration is not necessary. Neither was any 

visualization view port provided, such that the identification of flow regimes was based on 

empirical correlations from the state of local quality. Heat transfer information were mainly 

derived from the voltage and current parameters of the DC power system, thus only global heat 

flux (rather than local heat flux) were obtained. Although the heater rods were pushed to the 

burnout limits in order to obtain the critical heat flux (CHF), the normal BWR operating mass flux 

range was maintained. Therefore the post-LOCA reflood (or blowdown) scenarios were not 

addressed, neither were the radiation heat transfer and dispersed flow film boiling phenomena 

as normally encountered in a uncovered core during reflood. However, the FRIGG-2 gammaray densitometer experiments provided valuable information on the axial and radial distribution 

of void faction. It could facilitate the physical correlation between void fraction, local quality, and 

interfacial slip. 

Extensive single and two-phase flow pressure drop data were obtained in the FRIGG-2 tests. 

These pressure drop data are specific to the Marviken reactor core condition, but have 

compared favorably with the Martinelli-Nelson and Becker correlations. 

 The only complete natural circulation curve was also obtained at conditions close to the 

Marviken reactor's. However, by far, the most important data obtained from the FRIGG-2 tests 

are the CHF data for the particular fuel type and grid spacer pattern, as well as the void fraction 

distribution of the 36-rod bundle. 

Conclusions 

For the burnout experiments in FRIGG-2, all independent parameters (mass flux, inlet 

subcooling, pressure, and power to the bundle) have been carefully and independently 

controlled. Due to the uniform axial and radial power profiles of FRIGG-2, which resulted in a 

less favorable heat transfer condition in FRIGG-2 as compared to the actual Marviken core, the 
A-68

measured burnout data were approximately 20 percent lower than those predicted. This points 

out the major deficiency of the uniform power profiles of FRIGG-2. Follow-up tests using the 

actual Marviken reactor's power profiles have been suggested and recognized. 

The natural circulation mass flow rate in Marviken is 10-15 percent above the experimental 

values of FRIGG-2 in the power range of interest, while there is a close agreement between the 

calculated and measured FRIGG-2 flows. The differences are attributed to the Marviken's 

coolant (heavy water); larger radial heat loss of Marviken channel; and distributed power profiles 

of Marviken fuel assembly. 

Although the FRIGG-2 facility has improved our understanding of the burnout limits and natural 

circulation flows of a simulated Marviken core, it did not address the heat transfer phenomena 

associated with post-LOCA reflood conditions, in which the quench front progression, froth 

region propagation, and dispersed flow film boiling are of major interest. However, the relevant 

heat transfer information of FRIGG-2 is assessed against the RBHT PIRT in the following 

Tables A7.1 through A7.3: 
A-69

Table A7.1 Assessment of FRIGG-2 36-Rod Bundle Test to RBHT PIRT: Single Phase L

Convective Heat Transfer in the Core Component During Reflood Below the Quench Fr
A-70

Table A7.2 Assessment of FRIGG-2 36-Rod Bundle Test to RBHT PIRT: Subcooled an

Saturated Boiling in the Core Component During Reflood Below the Quench Front 
A-71

Table A7.3 Assessment of FRIGG-2 36-Rod Bundle Test to RBHT PIRT for 

High Ranked BWR Core Phenomena 
A-72

APPENDIX A8. LITERATURE REVIEW 

Test Facility Name: General Electric 9-Rod Bundle Facility 

Dates When Tests Were Performed: 1968-1970 

References: 

R17 Lahey, R. T., and Schraub, F. A., AMixing, Flow Regimes, and Void Fraction for TwoPhase Flow in Rod Bundles,@ Two-Phase Flow and Heat Transfer in Rod Bundles, 

ASME, Nov. 1969. 

R18 Lahey, R. T., Shiralkar, B. S., and Radcliff, D. W., ATwo-Phase Flow and Heat Transfer 

in Multirod Geometries: Subchannel and Pressure Drop Measurements in a Nine-rod 

Bundle for Diabatic and Adiabatic Conditions,@ GEAP-13049, AEC, 1968. 

Availability of Data: 

In the 3x3 9-rod bundle configuration for typical BWR operating conditions, there are three types 

of geometrical subchannels: comer, side, and center subchannels. Subchannels are also 

classified into hot (locally heated), cold (unheated), and uniform (uniformly heated) 

subchannels. Data for all test points are available in tabulated form for all types of subchannel. 

Bundle average mass flux, bundle average exit quality, measured subchannel mass flux, and 

subchannel quality are tabulated against the test points in Refereces R17 and R18. Substantial 

differential pressure drop data for both single- and two-phase flows are available in the same 

references. Other reduced or analyzed data are also available in graphic format that include: 

subchannel quality-vs-average quality; subchannel energy flux-vs-subchannel mass flux; 

subchannel quality-vs-subchannel type; subchannel mass flux-vs-subchannel type; etc. Singlephase friction factors are graphed against the Reynolds number, while two-phase friction 

multipliers are graphed against flow quality and favorably compared with the Martinelli-Nelson 

correlation. 

Test Facility Description, Types of Tests 

The primary purpose of this investigation was to obtain the mass flux and enthalpy distribution in 

a simulated rod bundle for a BWR. The geometric features of the test section are: 

Number of rods 9 Rod diameter 14.48 mm (0.570 in) 

Radius of channel corner 10.16 mm (0.400 in) Rod-rod clearance 4.287 mm (0.168 in) 

Rod-wall clearance 3.429 mm (0.135 in) Hydraulic diameter 12.04 mm (0.474 in) 

Heated length 1.83 m (72 in) 
A-73

Tests were run with all nine rods electrically heated. The radial local peaking was either uniform 

or a peaking pattern typical of BWR conditions. A cross-sectional view of the test section is 

shown in Figure A8.1, indicating the corner, side, and center subchannels. One of the unique 

features of the facility is that provisions are made for bringing static and differential pressure 

lines at the same axial location but for different subchannels. To measure the flow in any given 

subchannel, that subchannel is isolated at some point from the rest of the channel. The 

subchannel flow, also referred as sample flow as shown in Figure A8.2, can then be taken 

through special ducting to another point outside the test section, where both the flow rate and 

enthalpy can be measured. Flow splinters made of thin metal sheets are used to separate and 

isolate flow of a subchannel at the end of the heated length. Such an isolated flow is guided 

through a tube before passing out the test section flange and entering a heat exchanger 

(calorimeter) as shown in Figure A8.2. The condensed flow is monitored by a turbine flow meter 

for subchannel flow measurement. 

The sample enthalpy was determined by a heat balance on the calorimeter. For this purpose, 

the cooling water flow and temperature rise are carefully measured to provide as accurate 

energy information as possible. The outlet thermocouples are inserted beyond a right- angle 

bend in the piping to ensure good mixing in the water. Pressure drop measurements were also 

made during both single- and two-phase tests. All pressure drop measurements were 

corrected-for the hydrostatic head in the pressure tap lines based on the average density of 

water between the relevant pressure taps. 

The ranges of test conditions include: 

Single-Phase (Cold) Mass Flux 422.67 - 3089.21 kg/m2

-sec (0.311 - 2.273x106 lbm/ft2-hr) 

Two-Phase Mass Flux 505.58 - 1603.72 kg/m2

-sec (0.372 - 1.180x106 lbm/ft2-hr) 

Pressure 75.84 - 82.74 bar (1100 - 1200 psi) 

Rod Temperature not measured 

Average Heat Flux 690.63 - 2513.4 kW/m2

-K (0.219 - 0.797x106 Btu/ft2-hr) 

Exit Quality 3.1 - 44.4 percent 

)hsub 674.54 - 1239.76 kJ/kg (290 - 533 Btu/lbm) 

Flow Regimes Liquid 1-N, bubbly, transition, annular 

Instrumentation and Data from Tests 

The heater rods were not instrumented with thermocouples. Thus, little local heat transfer 

information could be obtained. Neither was any visualization view port provided, such that the 

identification of flow regimes was based on empirical correlations from the state of local quality. 

Since the heater rods were sufficiently cooled under the normal BWR operating conditions and 

the issues of DNB and LOCA/reflood were not addressed, radiation heat transfer was not a 

important factor. However, flow and enthalpy distributions among the subchannels that are 

unique to BWR conditions were carefully measured and addressed. The tests were able to 

measure flow, enthalpy, and derive local quality in each individual subchannel. Thus the facility 

can yield some significant information on the heterogeneous flow core, of which the cross flow 

phenomenon is of importance. 
A-74

Figure A8.1 Positions of Pressure Taps for Setting Isokinetic Conditions. 

Figure A8.2 Schematic of Loop Showing Sampling Circuit. 
A-75

While the heater rods were uniformly heated in the axial direction, the radial power distribution 

was controlled by peaking the individual transformers. Thus the flow, enthalpy, and quality 

distributions across the subchannels due to radial power peaking were also unique output of the 

facility. 

Pressure drop data for single (cold) and two-phase flow tests were obtained for frictional loss 

correlation. At the same axial locations, cross-flow phenomenon (between subchannels) was 

interpreted from the pressure differential between subchannels (non-isokinetic cases). 

Conclusions 

Subchannel test data were taken for a 9-rod bundle in typical BWR operating conditions. In 

general the following observations are made: 

1. The corner subchannel runs a mass flux and quality below the bundle average values. 

2. The side subchannel has mass flux and quality approximately equal to or slightly less than 

the bundle average. 

3. The center subchannel has both mass flux and quality above the bundle average values. 

4. There is an observable, though somewhat inconsistent, tendency for the subchannels to 

approach bundle average condition in the regions of slug-annular flow-regime transition. 

5. The effect of heat flux on subchannel enthalpy distribution was small for low flows, but 

showed a strong effect at the high flows. 

6. The effect of the bundle average mass flux on subchannel mass flux distribution was to 

increase the mass flux in the comer and center subchannels, and decrease the mass flux in 

the side subchannels, as the bundle average mass flux was increased. 

7. The effect of heat flux on subchannel mass flux distribution was to decrease the mass flux in 

the comer subchannel but leave the mass flux in other subchannels relatively unchanged. 

8. The adiabatic single-phase friction factor for the clean 9-rod bundle under consideration was 

slightly higher than the smooth-tube friction factor, for all Reynolds numbers. 

9. The two-phase friction drop multiplier showed only a very minor flow effect, and the data 

was well correlated by the classical Martinelli-Nelson curve. 

Although this facility and work improved our understanding of subchannel flow and energy 

diversions in typical BWR conditions, it did not address the heat transfer phenomena associated 

with post-LOCA reflood conditions, in which the quench front progression, froth region 

propagation, and dispersed flow film boiling are of major interest. However, the relevant heat 

transfer information is assessed against the RBHT PIRT in the following Tables A8.1 and A8.2: 
A-76

Table A8.1 Assessment of General Electric 9-Rod Bundle Tests to RBHT PIRT: 

Subcooled and Saturated Boiling in the Core Component Below the Quench Front 
A-77

Table A8.2 Assessment of General Electric 9-Rod Bundle Tests to RBHT PIRT 

for High Ranked BWR Core Phenomena 
A-78

APPENDIX A9. LITERATURE REVIEW

Test Facility Name: PNL LOCA Simulation Program at NRU Reactor, Chalk River, Canada 

Dates When Tests Were Performed: October 1980 - November 1981 

References: 

R19 C. L. Mohr, et. al., AData Report for Thermal-Hydraulic Experiment 2 (TH-2)@, 

NUREC/CR-2526, PNL-4164, November 1982. 

R20 C. L. Mohr, et. al., AData Report for Thermal-Hydraulic Experiment 3 (TH-3)@, 

NUREC/CR-2527, PNL-4165, March 1983. 

Availability of Data: 

Graphical data demonstrating fuel cladding temperature control using the preset reflood flow 

and temperature feedback. Photographs of guard and test fuel used are shown. Data in 

graphical form on the test assembly temperatures, cooling flow and the neutronic environment 

are also presented. Data is available in both SI and British units. Microfiche of the entire report 

is available with NTIS. 

Test Facility Description, Types of Tests 

The TH-2 included 14 tests. A schematic of the test train used is depicted in Figure A9.1. The 

fuel assembly consists of a 6x6 segment of a 17x17 PWR fuel assembly with four corner rods 

removed, providing a basic fuel array of 32 rods. The 20 guard rods in the outer row reduced 

the heat net heat transfer from the inner test rods during the test. All the inner 12 test fuel rods 

were arranged in cruciform pattern. All the 32 unpressurized fuel rods were filled with helium. 

The core configuration is shown in Figure A9.2. 

The following table gives the test fuel rod design variables: 

Cladding Material Zircaloy-4 

Cladding Outside Diameter (OD) 0.963 cm (0.379 in) 

Cladding Inside Diameter (ID) 0.841 cm (0.331 in) 

Pitch (Rod to Rod) 1.275 cm (0.502 in) 

Fuel Pellet OD 0.826 cm (0.325 in) 

Fuel Pellet Length 0.953 cm (0.375 in) 

Active Fuel Length 3.66 m (12 ft) 

The TH-2 experiment included a preconditioning phase and 14 successive tests, each having a 

pre-transient and transient phase. The average test assembly fuel rod power during 

preconditioning was ~18.7 kW/m (5.7 kW/ft) with the U-2 loop providing water cooling; this was 

also used for the TH-3 experiment. System loop pressure was held at 8.63 MPa (1250 psia). 

The pre-transient stage for the TH-3 tests was conducted with the steam cooling provided by 

the U-1 loop at a mass flow rate of ~0.379 kg/s (~3000 lbm/hr) and a reactor power of ~7.4 MW. 
A-79

Figure A9.1 Schematic of NRU Loss-of-Coolant Accident Test Train. 

This enabled the total assembly power to remain constant, even though the peak cladding 

temperature varied from test to test. The transient phase of TH-3 commenced when the steam 

coolant flow was reduced from ~3000 lbm/hr to 0, with the reactor power being maintained at 

about 7.4 MW. No preconditioning operation was conducted for the TH-3 experiment. 

The test conditions measured during the TH-2 and TH-3 experiments are described in Tables 

A9.1 and A9.2, respectively. 

Instrumentation and Data from Tests

The instrumentation for the TH-2 experiment included: 24 self-powered neutron detectors 

(SPNDs), 115 fuel rod thermocouples, 18 steam probe thermocouples and four closure head 

thermocouples. The instrumentation was located at 21 elevations along the test train assembly. 

These are shown in Figure A9.3. 
A-80

Figure A9.2 NRU Reactor Core Configuration. 

The instrumentation for the TH-3 experiment included: 24 SPNDs, 69 fuel rods thermocouples, 

four hanger thermocouples and four closure head thermocouples. The instrumentation was 

located at 22 elevations along the test train assembly. These are shown in the Figure A9.4. 

Thermal-hydraulic data was obtained by turbine flowmeters and thermocouples. Local coolant 

temperatures were measured with steam probe thermocouples that protruded into the coolant 

channel and with thermocouples attached to the shroud. Azimuthal temperature variations 

were measured by thermocouples located at the fuel centerline and attached to the inside of the 

cladding surface. The cladding temperature was monitored by cladding thermocouples that 

were spot welded to the interior cladding surface. 
A-81

Figure A9.3 Instrumentation Levels in the TH-2 Test Assembly. 

The SPNDs provided neutron flux measurements within the fuel bundle. These measurements 

were made at opposite corners of the stainless steel shroud at several elevations, ranging from 

13.3 - 139.3 in above the bottom of the fuel column. The SPNDs provide a measure of the 

radial neutron flux gradient and neutron flux distribution over the vertical axis of the test 

assembly. These could also detect the coolant density variations (through flux changes) 

associated with the quench front that passed each SPND during the reflood phase of the 

transient. The instrument signals were monitored on a real-time basis with the DACS (Data 

Acquisition and Control System). The recorded data characterized the coolant flow rates, 

temperature neutron flux and operating history. 

The reflood flow measurement system included a Fisher-Porter turbine flowmeter in the high 

flow rate and a series connected Barton and Fisher-Porter turbine flowmeters in the parallel low 

flow rate line. Steam probe temperature history provided independent measurements of the 

reflood coolant level in the test assembly. 
A-82

Figure A9.4 Instrumentation Levels in the TH-3 Test Assembly. 

Conclusions

These tests give the average fuel rod cladding temperatures during pre-conditioning, pretransient and transient phases. Also available are the test coolant and shroud temperatures. 

However, these tests do not have enough data to make code model changes without the 

potential for compensating errors. Many of the heat transfer phenomena such as droplet to 

vapor interfacial heat transfer, dry wall contact are not simulated, though overall wall heat 

transfer is measured. Therefore, while these tests are useful in simulating the overall reflood 

heat transfer, they provide limited data which can be used to assess the reflood phenomena 

which was identified in the PIRT table for the RBHT Program. 
A-83

Table A9.1 Measured Conditions for the TH-2 Experiment(1)
A-84

Table A9.1 Measured Conditions for the TH-2 Experiment (Continued) 
A-85

Table A9.2 Measured Conditions for the TH-3 Experiment
A-86

Table A9.3 Assessment of NRU Inpile Reflood Data to RBHT PIRT: Dispersed Flow Region for Co
A-87

Table A9.3 Assessment of NRU Inpile Reflood Data to RBHT PIRT: Dispersed Flow Region for Co

(Continued) 
A-88

Table A9.4 Assessment of NRU Inpile Reflood Data to RBHT PIRT: High Ranked BWR Core P

Process/Phenomena Basis NRU Inpile R

Core Film Boiling Upper Tie Plate CCFL Channel-Bypass Leakage Steam Cooling Dryout Natural Circulation Flow Flow Regime Fluid Mixing Fuel Rod Quench Front Decay Heat Interfacial Shear Rewet: Bottom Reflood Rewet Temperature 

PCT is determined in film boiling period. Hot assembly is in co-current flow above CCFL limit. Flow bypass will help quench the BWR fuel assembly core. A portion of the dispersed flow film boiling heat transfer. Transition from nucleate boiling and film boiling. Flow into the core and system pressure drops. Determines the nature and details of the heat transfer in the core. Determines the liquid temperature in the upper plenum for CCFL break down. Heat release from the quench front will determine entrainment to the upper region of the bundle. Energy source for heat transfer. Affects the void fraction and the resulting droplet and liquid velocity in the entrained flow. BWR hot assembly refloods like PWR. Determines the quench front point on the fuel rod. 

PCT is determined in Not simulated. Not simulated. Simulated but overall measured. Quench front location Not applicable. Dispersed flow film boNot applicable. Simulated with nucleaSimulated. Not measured. Measured. Measured. 
A-89

Table A9.4 Assessment of NRU Inpile Reflood Data to RBHT PIRT: High Ranked BWR Core Phenom

Process/Phenomena Basis NRU Inpile R

Top Down Rewet Void Distribution Two-Phase Level 

Top of the hot assembly fuel will rewet in a similar manner as PWR. Gives the liquid distribution in the bundle. Similar to quench front location, indicates the location of nucleate and film boiling. 

Not measured. Not measured. Measured. 
A-90

APPENDIX A10. LITERATURE REVIEW 

Appendix A10: ACHILLES Reflood Heat Transfer Tests 

Dates when Tests Were Performed: 1989 - 1991 

References: 

R21 Denham, M. K., Jowitt, D., and K. G. Pearson, AACHILLES Unballooned Cluster 

Experiments, Part 1: Description of the ACHILLES Rig, Test Section, and Experimental 

Procedures,@ AEEW-R2336, Winfrith Technology Centre (Commercial in Confidence), 

November 1989. 

R22 Denham, M. K., and K. G. Pearson, AACHILLES Unballooned Cluster Experiments, Part 

2: Single Phase Flow Experiments,@ AEEW-R2337, Winfrith Technology Centre 

(Commercial in Confidence), May 1989. 

R23 K.G. Pearson and M. K. Denham, A ACHILLES Unballooned Cluster Experiments, Part 

3: Low Flooding Rate Reflood Experiments,@ AEEW-R2338, Winfrith Technology Centre 

(Commercial in Confidence), June 1989. 

R24 K.G. Pearson and M.K. Denham, AACHILLES Unballooned Cluster Experiments, Part 4: 

Low Pressure Level Swell Experiments,@ AEEW-R2339, Winfrith Technology Centre 

(Commercial in Confidence), July 1989. 

R25 Dore, P and M.K. Denham, AACHILLES Unballooned Cluster Experiments, Part 5: Best 

Estimate Experiments,@ AEEW-R2412, Winfrith Technology Centre, (Commercial in 

confidence), July 1990. 

R26 Dore, P. and D.S. Dhuga, AACHILLES Unballooned Cluster Experiments, Part 6: Flow 

Distribution Experiments,@ AEA-RS-1064, Winfrith Technology Centre (Commercial in 

Confidence), December 1991. 

Availability of Data: 

The ACHILLES experiments were performed as part of the safety case for PWRs in the United 

Kingdom. The ACHILLES tests were funded by the Central Electricity Generating Board 

(CEGB) and were performed by the United Kingdom Atomic Energy Authority (UKAEA) at the 

Winfrith Laboratories. The data does have some release restrictions and is not unlimitedly 

available to the general public. However, more recently, data has been released to interested 

parties and governments as part of cooperative data exchange. Some of the data was used for 

an International Standard Problem. Westinghouse has been able to obtain some of the data 

directly from the CEGB provided that reference was given to the CEGB in the reports prepared 

by Westinghouse. Therefore, the data should be available to the Nuclear Regulatory 

Commission. 
A-91

Test Facility Description, Types of Tests

The ACHILLES tests were specifically conducted to support the PWR (Sizewell) safety case in 

the United Kingdom in the late 1980's and early 1990's. Since these tests were performed after 

the FLECHT-SEASET tests, the authors had made some improvements which are of value for 

the current Rod Bundle Heat Transfer Program. The testing consisted of specific test series 

which were used to examine specific safety issues and safety analysis issues. Specifically, 

experiments were performed to examine: 

• Low reflooding rate behavior similar to FLECHT-SEASET and FLECHT, 

• Best-Estimate Reflood tests were performed to assess a realistic LOCA transient, 

• Single-phase flow distribution tests were performed to examine the flow uniformity and 

single-phase heat transfer within the rod bundle, and 

• Low-pressure level swell experiments were also performed to validate drift flux/void 

fraction relationships. 

There were also gravity feed reflood tests with loop resistance simulated, and variable injection 

reflood tests which simulated evaluation model type system response. There were also 

oscillating inlet flow injection tests. 

One of the purposes of the ACHILLES test program was to examine the heat transfer 

performance of a fuel assembly with high blockages caused by the swelling of the zirc cladding 

(sausage ballooning problem). This issue had been resolved in the U.S. but it still remained as 

an open item in the United Kingdom safety case for the PWR. The reports given in the review 

only discuss the unblocked or unballooned configuration of the test program. There is a 

continuation of the ACHILLES test program which specifically examines flow blockages of up to 

80 percent to address the clad swelling issues during a LOCA. These tests will not be 

discussed here. 

The ACHILLES bundle is shown in Figure A10.1 and contains a total of 69 heater rods of 9.5 

mm (0.374 in) in diameter on a square pitch of 12.6 mm (0.496 in) and have 3.66 m (12 ft) of 

heated length. ACHILLES used production Inconel mixing vane grids supplied by 

Westinghouse. All rods were heated in ACHILLES such that there was no simulation of the 

guide tube thimbles in the bundle such as in the FLECHT-SEASET experiments. However, 

experiments were performed in ACHILLES to examine the effects of increased surface-tosurface radiation heat transfer by performing tests with selective unpowered heater rods. 

Figure A10.2 indicates the flow loop schematic for the ACHILLES facility. There was ample 

flexibility built into the test facility such that both single phase, two-phase, forced reflood 

injections could be performed, as well as oscillatory injection and gravity injection tests with little 

facility modifications. The test bundle was contained within a circular shroud of wall thickness of 

6.5 mm (0.26 in) and a pressure capability of 6 bars (approximately 90 psia). There were no 

filler rods in the test bundle design which resulted in excess flow area for the square array of 

rods within the circular housing. To compensate for the excess flow area and to better simulate 

an infinite array of fuel rods, the ACHILLES housing was heated with zonal heaters which had a 
A-92

Figure A10.1 Cross Section of ACHILLES 69-Rod Bundle. 

total power of 46 kW. These heaters provided a similar axial temperature distribution as the 

heater rods. 

The heater rods were manufactured by RAMA corporation, the same company that made the 

FLECHT-SEASET heater rods. A chopped cosine power shape with a peak-to-average of 1.4 

was used. These rods used Inconel cladding, and could have up to six thermocouples per rod 

installed. The axial distribution of the heater rod thermocouples and the other instrumentation is 

shown in Figure A10.3. One unique feature of the ACHILLES bundle is that the instrumentation 

plan was developed with the idea of examining the heat transfer effects of the spacer grids both 

upstream and downstream of the grids. 
A-93

Figure A10.2 Schematic of ACHILLES Flow Loop. 

The grids used were Inconel production 17x17 spacer grids with mixing vanes. These grids 

were instrumented with 0.5 mm (0.20 in) thermocouples which were attached to the grids using 

Inconel shim stock which was spot-welded to the spacer. The attachment method was 

designed to minimize the flow disturbance and the effects of the thermocouple lead leading to 

early grid rewet. Each grid had two thermocouples attached to the spacer at the top and lower 

edges at different radial positions. The data indicates that this installation method worked well 

and only one-grid thermocouples failed. 

The vapor temperature was measured in the rod bundle at different axial location, up steam and 

down stream of spacer grids using 1 mm (0.040 in) thermocouples which were swagged to a tip 

size of 0.5 mm (0.020 in). There is an uncertainly analysis given in the report which indicates 

that f or the conditions used in the ACHILLES tests, the vapor temperature uncertainty is only 

13 degrees C (23.4 degrees F) which is consistent with the uncertainty which was derived in the 

FLECHT-SEASET program. It is mentioned in Reference R22 that the vapor temperature 

measurements did have an effect on the entrained droplets with the probe causing additional 
A-94

Figure A10.3 Axial Locations in Test Section. 

droplet breakup and slowing down of larger droplets. There is insufficient data presented to 

draw an independent conclusion of these effects. 

There were additional pressure taps placed along the shroud such that the pressure drops 

across the spacer grids were obtained as well as the frictional pressure drop in the rod bundle 

section. The pressure drop information was used to infer void fraction; however, there was no 

frictional or acceleration pressure drop corrections to the data such that the void fractions given 

for ACHILLES are lower then those expected. 
A-95

The shroud had windows at the mid-plane for photographic purposes with the view being 

through specific rows of heater rods. The windows were very small such that they could be 

heated by the rods during heat-up before each test. The windows were set back from the inside 

edge to avoid direct droplet impact which would have caused the window to wet. From the 

report, it appears that the windows would stay dry until the quench front was within the grid span 

where the windows were located. One could interpret this as having the top of the froth front 

approaching the window before the window wetted. 

Tests were performed using a four-cylinder piston pump which superimposed an oscillating flow 

on the forced flooding rate. The period and magnitude of the flow and oscillation frequency 

could be adjusted for different sensitivity tests. The bi-directional flow probe showed reverse 

flow, but is not clear if Areal@ reverse flow occurred. One significant observation is that with 

oscillatory flow, the grids quickly rewet as compared to constant forced injection flow. The same 

situation occurred for initially high injection flows. 

An improved photographic droplet diameter and velocity measuring technique was developed 

as part of the ACHILLES program in which a pulse of green light was shined into the open 

camera shutter, followed by a pulse of red light. The duration of each pulse was short and there 

was a fixed time between the two pulses. This approach produced two images of a droplet 

which were of different color such that the drop size and velocity could be inferred from the 

prints. The filming rate was 100 frames/s; clips of shots were taken during a given test. Two 

cameras were also able to focus on different subchannels such that a reasonable droplet 

distribution across the bundle could be determined. It was observed that the droplet flow was 

not uniform with more liquid in the outermost channel near the wall. The outermost channel has 

the larger hydraulic diameter and hence the greater steam flows as compared to the inner 

regions of the bundle which could explain the observed trend. The report included droplet 

distribution plots for selected tests. 

The test matrix for the low flooding rate tests is given in Table A10.1. One parameter to note is 

that they purposely controlled the power such that very high heater rod temperatures never 

occurred and the maximum temperatures were very similar. Details of the reference test and 

the effects for the different sensitivity tests are given in Reference R23. The temperature rise 

values were different. Table A10.2 gives the test numbers for the droplet distribution 

experiments. Table A10.3 gives the conditions for the single-phase air flow distribution 

experiments and for the voidage distribution experiments. Each series of tests is discussed in 

Reference R22. The test matrix for the best-estimate or realistic Reflood tests is given in Table 

A10.4 from Reference R25. 

The authors did perform a similar analysis as in the FLECHT and FLECHT-SEASET tests in 

which the actual quality was calculated at the bundle cross sections where vapor measurements 

existed. The same or similar exit flow measurements were made in the ACHILLES tests as in 

the FLECHT and FLECHT-SEASET tests such that a bundle heat and mass balance could be 

determined. However, the authors did not attempt to separate the radiation component from the 

total measured heat transfer such that their estimates of the convective dispersed flow film 

boiling heat transfer results in higher heat transfer coefficients then would be the case in the 

FLECHT and FLECHT-SEASET experiments. However, very similar trends were observed, 

with very low vapor Reynolds number flows and enhancement of the dispersed flow film boiling 

heat transfer above the single phase convection heat transfer limit for the same fluid conditions. 
A-96

The effects of the spacer grids were analyzed and a correlation was suggested for the 

convective enhancement of the local heat transfer downstream of the grid. There were also 

some very informative plots of the vapor temperatures and the spacer grid temperatures which 

showed that when the grid quenches, the vapor temperature downstream of the grid decreases. 

The axial distribution of the heater rod thermocouples gave an excellent indication of the quench 

front along the bundle. These authors did display their data more as axial plots for different time 

periods such that additional information good be obtained with fewer figures. Variable reflood 

rates, oscillatory flooding rates, and stepped flooding rates would easily quench the spacer grids 

and they remained wetted throughout the transient. The very high flooding rates also quenched 

the miniature thermocouples used to measure the vapor temperature. Some of these 

thermocouples could dry out later in the tests and would indicate the presence of superheated 

vapor. 

The best-estimate tests had more favorable test initial conditions such that the heat transfer was 

higher and the bundle would quench more easily. The same or similar phenomenon was 

observed in these tests excepting that the transients were shorter and the temperatures were 

lower. 

Single-phase heat transfer and flow tests were also conducted using air as the fluid. A specially 

constructed hot film probe was used for the air velocity distribution which confirmed that a 

bypass effect was occurring in the ACHILLES bundle due to the large excess flow area located 

on the outside edge of the bundle between the heater rods and the shroud. Single-phase 

effects of the spacer grids were also determined and compared to a previous correlation. We 

need to verify the axial distribution of the thermocouples in the RBHT test to make sure that we 

can detect the decaying heat transfer trend downstream of the spacer grids. 

One of the more unique data obtained in the ACHILLES program is the droplet or liquid 

distribution across the bundle using the photographic technique. Again, this distribution is 

distorted and shows more liquid at the edge of the bundle where the steam mass flow is higher 

due to the increased bypass flow at this location. The opposite would be expected in an infinite 

bundle since the center rods would be hotter creating a thermal syphon which should result in 

increased entrainment. 

Conclusions 

The ACHILLES Reflood experiments potentially represent some of the best reflood data 

available for computer code validation. However, a two-channel model which includes 

crossflow should be used to represent the inner region of the bundle which has the correct flow 

are per rod, while an outer channel would represent the outer region of the bundle where there 

is excess flow area. Also, the computer code would have to model the housing or shroud which 

also supplies energy to the fluid. Computer codes such as the TRAC- P series, and COBRA-TF 

and COBRA-TRAC have the ability to model these effects. However, the flow diversion, excess 

flow area, and housing heat release effects must be assessed as test distortions. Also, if they 

are first order effects, it will be difficult to determine what models in the candidate code need 

improving since the test distortions could mask the model requirements resulting in 

compensating error being introduced into the code. 
A-97

There is some unique data from the ACHILLES tests which are not available from other tests 

such as the subchannel droplet distribution data, spacer grid loss coefficient data, 

instrumentated spacer grid and local fluid temperature data, along with very finely spaced 

heater rod thermocouple data which shows the heat transfer effects of the spacer grids and 

quench front. The differential pressure data was taken using small spans both between grids 

and across spacer grids. This data needs to be corrected for frictional pressure drop and 

acceleration pressure drop in order to be used for inferring the local void fraction. Once this is 

performed, the local heat transfer can then be correlated with the void fraction. 

The tests cover a wide range of conditions which are equally applicable to evaluation of model 

calculations as well as best-estimate reflood conditions such that an ample set of data is 

available. Also the tests include oscillating inlet flow, stepped forced flooding rate tests, and 

gravity reflood tests. 

It is strongly recommended that these data be screened and selected ACHILLES tests be 

obtained from CEGB and added to the NRC data bank and analyzed with the TRAC-M code 

and COBRA-TF. These tests can also be used for comparison purposes with the Rod Bundle 

Heat Transfer Tests. 
A-98

Table A10.1 Summary of Low Flooding Rate Reflood Experiments 
A-99

Table A10.2 Droplet Distribution Experiments 
A-100

Table A10.3 Airflow and Voidage Distribution Experiments 
A-101

Table 10A.4 Summary of Best Estimate Reflood Experiments 
A-102

APPENDIX A11. LITERATURE REVIEW 

Appendix A11: Lehigh 9-Rod Bundle Tests

Dates When Tests Were Performed: 1982 - 1986 

References: 

R27 Tuzla, K., Unal, C., Badr, O., Neti, S., Chen, J.C., AThermodynamic Nonequilibrium in 

Post-Critical-Heat-Flux Boiling in a Rod Bundle,@ NUREG-CR 5095, Vol. 1-4, June 1998. 

R28 Unal C., Tuzla, K., Badr, O., Neti, S., Chen, J.C., AConvective Boiling in a Rod Bundle: 

Traverse Variation of Vapor Superheat Temperature Under Stabilized post-CHF 

Conditions,@ Int. J. Heat and Mass Transfer, Vol. 34, No. 7, pp. 1695-1706, 1991. 

Availability of Data: 

The data for these experiments is contained in Volumes 2 - 4 of Reference R27. Raw data are 

not available from the original source. 

Test Facility Description, Types of Tests 

The rods were 9.5 mm (0.374 in) in diameter and were arranged in a square pitch of 12.6 mm 

(0.496 in) as shown in Figure A11.1. The actual test section of the facility was 1.22 m (4 ft) long 

with one spacer grid located at 0.762 m (30 in) from the bottom as shown in Figure A11.2. The 

rods had a linear power profile to provide a constant heat flux over the length of the test section. 

Each subchannel had the same wetted perimeter and this resulted in about 39 percent of 

excess flow area in the bundle. The excess flow area was to account for the housing effect. 

Coolant Mass Flow Rate 6.6x10-4 - 0.1694 kg/s (3x10-4 - 0.077 lbm/s) 

Inlet Subcooling 40 - 0.55 degrees C (72 - 1 degrees F) 

Pressure 102.042 - 119.97 kPa (14.8 - 17.4 psi) 

Initial Shroud Temperature 301.67 - 398.89 degrees C (575 - 750 degrees F) 

Initial Rod Temperature 593.33 degrees C (1100 degrees F) 

Heat Flux 5 - 4312 kW/m2 

Linear Heat Generation 1.3123 to 11.483 kW/m (0.4 to 3.5 kW/ft) 

(Constant Over the Length) 

Constant Flooding Rates 1.016 to 4.064 mm/s (0.04 to 0.16 in/s) 
A-103

Figure A11.1 Cross-Sectional View of Test Bundle. 

Figure A11.2 Schematic of Test Section Support System. 
A-104

Instrumentation and Data From Tests 

There were eight thermocouples imbedded in each of the nine heater rods at 152.4 mm (6 in) 

intervals. Due to limitations of the data collection system, only 80 channels could be monitored 

for any given test. The arrangement of thermocouple elevations has one disturbing 

shortcoming. There are no thermocouples located at identical elevations and angles to allow for 

checking of the symmetry of the test section. The pressure cells were spaced too far apart to 

be able to make a calculation of the void fraction. Two aspirating steam probes were located at 

609.6 mm (24 in) and 965.2 mm (38 in), respectively. These probes were traversed through the 

bundle in several experiments to measure the traverse variation of vapor superheat. The vapor 

temperature difference was reduced from 120 to 40 degrees C superheat when the inlet quality 

was increased from 0.04 to 0.40. Effects of dispersed droplet cooling were evident after the grid 

as well. 

The data presented in Figures A11.3 to A11.7 and Tables A11.1 to A11.4 shows a pronounced 

effect caused by the spacer grid located at the 762 mm (30 in) elevation. This information might 

be used in evaluating the effects of spacer grids in two-phase-dispersed droplet flow. The data 

also showed a small error caused by the steam probes. 

Conclusions 

This series of tests is of limited use to the RBHT Program. The information gathered using a 

traversing steam probe is the most significant contribution. 

Figure A11.3 Sample Plot of Temperature and Steam Quality Data for the 

Stabilized Quench Front Experiments. 
A-105

Figure A11.4 Sample Plot of Heat Flux and Steam Quality Data for the 

Advancing Quench Front Experiments. 

Figure A11.5 Sample Plot of Rod and Steam Temperature Data for the 

Advancing Quench Front Experiments. 
A-106

Figure A11.6 Typical Transverse Vapor Temperature Profiles for Various Vapor Qualities. 

Figure A11.7 Typical Transverse Vapor Temperature Profiles Downstream 

of the Grid Spacer. 
A-107

Table A11.1 Sample Tabulation of a Stabilized Quench Front Data Point 

(See Table A11.2 for Nomenclature) 
A-108

Table A11.2 Definition of Parameters Used in Table A11.1 

QRS = shroud heat flux (local) 

TR 1 = surface temperature of test rod number 1 

TR 3 = surface temperature of test rod number 3 

TR 4 = surface temperature of test rod number 4 

TR 5 = surface temperature of test rod number 5 

TR 6 = surface temperature of test rod number 6 

TR 7 = surface temperature of test rod number 7 

TR 8 = surface temperature of test rod number 8 

TR 9 = surface temperature of test rod number 9 

TS = shroud surface temperature 

TV 1 = vapor temperature obtained from first probe 

TV 2 = vapor temperature obtained from second probe 

XA 1 = actual quality at the first vapor probe location 

XA 2 = actual quality at the second vapor probe location 

XE = equilibrium quality 

XE 1 = equilibrium quality at the first vapor probe location 

XE 2 = equilibrium quality at the second vapor probe location 

ZS = shroud axial location (reference to hot-patch inlet) 

ZT = Test section axial location (reference to hot-patch inlet) 
A-109

Table A11.3 Sample Tabulation of an Advancing Quench Front Data Point 

(See Table A11.4 for Nomenclature) 
A-110

Table A11.4 Definition of Parameters Used in Table A11.3 

DEV = device 

DIS = distance 

QRS = shroud=s heat flux (local value) 

QUAL = equilibrium quality 

R1 = test rod #1 

R3 = test rod #3 

R4 = test rod #4 

R6 = test rod #6 

R7 = test rod #7 

R8 = test rod #8 

SH = shroud 

TR 1 = surface temperature of test rod number #1 

TR 3 = surface temperature of test rod number #3 

TR 4 = surface temperature of test rod number #4 

TR 6 = surface temperature of test rod number #6 

TR 7 = surface temperature of test rod number #7 

TR 8 = surface temperature of test rod number #8 

TS = surface temperature of the shroud 

TV1 = vapor temperature of first vapor probe elevation 

TV2 = vapor temperature of second vapor probe elevation 

XA 1 = actual quality at the first vapor probe location 

XA 2 = actual quality at the second vapor probe location 

XE = equilibrium quality 

XE 1 = equilibrium quality at the first vapor probe location 

XE 2 = equilibrium quality at the second vapor probe location 

ZS = shroud axial location (reference to hot-patch outlet) 

ZT = test section axial location (reference to hot-patch outlet) 
APPENDIX B1. RADIATION HEAT TRANSFER NETWORK AND 

CALCULATION OF PI GROUPS 

Description of the Radiation Network

In order to calculate the radiative heat transfer from the rods to the surfaces and the housing, a 

six node radiation network (Figure 6.3) has been developed which includes radiation heat 

transfer to droplets and vapor. The network resistances discussed in Section 7 (Refs. 7-2, 7-3 

and 7-4) are defined as follows: 

i

w A

Rii w ε

ε

1− = 1

( )( ) ijivl

ij

FA

R

11 −−= εε

1

( ) ivl

il

A

R

1−= εε

1

( ) ilv

iv

A

R

1 −= εε

1 

∑=

=

4

1

1

i

ivl

lv

A

R

εε

where 

Ai radiating area per unit length for the i-th radiating wall surface 

Fij view factor from node >i= to node >j=

εw wall emissivity 

εl, εv drop and vapor emissivity 

The view factors are calculated by summing up single rod-to-rod, rod-to-housing and rod-tosurfaces view factors which are calculated with the VIEWFAC subroutine of MOXY computer 

program (Ref. 7-1): 

, 49

1

49

1

12 ∑

∑

∑

=

= = j

i

i

i

iji

A

FA

F where and 

CR = jj CR ≠ ji ( are the cold rods indices) CR j

B-1
, 49

1

49

1

13 ∑

∑

∑

=

= = j

i

i

i

iji

A

FA

F where and 

S = jj CRS ≠ , jji ( are surfaces indices: 1,7,43,49) Sj

∑

∑

=

= = 49

1

49

1

14

i

i

i

iNi

A

FA

F , where CRS ≠ , jji

, 49

1

49

1

23 ∑

∑

∑

=

= = j

i

i

i

iji

A

FA

F where S = jj and CR = ji

 

∑

∑

=

= = 49

1

49

1

24

i

i

i

iNi

A

FA

F , where CR = ji

+++ AAAA 494371

7711 4343 4949

34

FAFAFAFA F N N ++ N + N =

 

Assuming that the droplet and vapor media are optically thin, the drop and vapor emissivities εl

and εv are calculated with the following formula: 

La ml

l e− ε 1−=

La mv

v e− ε 1−=

where the beam length Lm is defined as follows for rod bundle geometry: 

m = 85.0 DL h

Assuming the droplets in the geometric scattering regime, the liquid absorption coefficient is 

calculated by the following formula which is based on Reference 7-4 with the additional 

assumption of considering a single drop size group (Sauter mean diameter): 

 l d a nd

2 = π.0185

B-2
where d is the drop Sauter mean drop diameter (m) while the number of droplet per unit volume 

nd is calculated from the void fraction: 

3 .

)1(6

d

nd

π

−α =

where the Sauter mean diameter and the void fractions are inputs in the program. The vapor 

absorption coefficient av is calculated with the following formula: 

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

− ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ ⋅= −

2 4

5 555 555 66.181084.9

w w

v TT

a P

 

where P is the pressure (kPa) and Tw is the wall temperature (K). 

Solution of the Radiation Network

Kirchhoff Law is applied to nodes 1, 2, 3 and 4: 

0.0 . . .

1

4

1

1

4

1

13

41

13

31

12

21

11

4

1 = − + − + − + − + − + −

v

v

l

hr l

R

TJ

R

TJ

R

JJ

R

JJ

R

JJ

R

σ TJ σ σ

0.0 . . .

2

4

2

2

4

2

24

42

23

32

12

12

22

4

2 = − + − + − + − + − + −

v

v

l

cr l

R

TJ

R

TJ

R

JJ

R

JJ

R

JJ

R

σ TJ σ σ

 0.0 . . .

3

4

3

3

4

3

34

43

23

23

13

13

33

4

3 = − + − + − + − + − + −

v

v

l

s l

R

TJ

R

TJ

R

JJ

R

JJ

R

JJ

R

σ TJ σ σ

0.0 . . .

4

4

4

4

4

4

34

34

24

24

14

14

44

4

4 = − + − + − + − + − + −

v

v

l

h l

R

TJ

R

TJ

R

JJ

R

JJ

R

JJ

R

σ TJ σ σ

where are the radiosities in the network nodes. i J

For a given temperature field (Thr, Tcr, Ts, Th, Tl and Tv), the equations are solved for the 

unknowns (J1, J2, J3 and J4). Then the heat rate across each resistance in the network can be 

calculated as: 

ij

ij

ij R

JJ

Q − =

B-3
The previous procedure has been implemented in the Fortran program called RADNET 

attached in Appendix B5. 

Another input to the RADNET computer program is how hot versus cold rods are lumped 

together in the bundle. It can be recognized that for given boundary conditions, the result is 

dependent on how hot and cold rods are lumped together in the model. Sensitivity studies have 

carried out where the hot rods sub-array has been assumed to be the central rod, the inner 3x3 

array or the inner 5x5 array. For example, the Pi group π30 (see later) calculated with the three 

different lumping approaches is: 

π ,30 cr = 567.0

π x33,30 = 388.0

π x55,30 = 345.0

It is important to note that this is the group affected most while the effect of different lumping 

approach on the other groups is less important. Results from the detailed rod-to-rod model 

calculations discussed in Section 7 show that the temperature is practically uniform in the inner 

3x3 array while the temperature drops in the periphery due to the effect of the housing. Thus, 

the inner 3x3 hot rods lumping approach is the most appropriate and was chosen in the 

dimensionless groups calculation. 

B-4
B-5

APPENDIX B2. ROD GRID RADIATION NETWORK FOR RBHT 

Inputs 

H grid 1.5 in 0.0381 m

N grids 6

rod diameter 0.374 in 0.0094996 m

rods pitch 0.496062992 in 0.0126 m

rod power 5.6 kW

pressure 40 psia 272.1088435 kPa

liquid temperature 267 F 403.6955556 K

vapor temperature 1177 F 909.2511111 K

rod temperature 1650 F 1172.028889 K

grid temperature 1376 F 1019.806667 K

void fraction 0.995

droplets Sauter mean diameter 0.001 m

wall emissivity 0.8 

Calculation 

bundle hydraulic diameter 0.011789932 m

droplet density 9554140.127 Ndrp/m3

liquid absorption coefficient 5.55 m-1

beam length 0.010021442 m

liquid emissivity 0.054100549 

vapor absorption coefficient 0.182435145 m-1

vapor emissivity 0.000542019 

rod area (based on Hgrid) Ar 1.76154 in2 0.001136475 m2

grid area (per rod) Ag 2.976 in2 0.001919996 m2

1/R11 0.004545901 

1/R22 0.007679985 

1/R12 0.001074409 

1/R1L 6.14506E-05 

1/R1V 5.82665E-07 

1/R2L 0.000103817 

1/R2V 9.84373E-07 

1/RLV 8.96264E-08 

A11 0.005682342 

A22 0.008859194 

A12=A21 -8.96264E-08 

C1 486.4733384 

C2 471.1878606 
B-6

APPENDIX B3. ROD GRID RADIATION NETWORK FOR PWR 

Inputs 

H grid 1.5 in 0.0381 m 

N grids 6 

rod diameter 0.374 in 0.0094996 m 

rods pitch 0.496063 in 0.0126 m 

rod power 5.6 kW 

pressure 40 psia 272.10884 kPa 

liquid temperature 267 F 403.69556 K 

vapor temperature 1177 F 909.25111 K 

rod temperature 1650 F 1172.0289 K 

grid temperature 1376 F 1019.8067 K 

void fraction 0.995 

droplets Sauter mean diameter 0.001 m 

wall emissivity 0.9 

Calculation 

bundle hydraulic diameter 0.0117899 m 

droplet density 9554140.1 Ndrp/m3

liquid absorption coefficient 5.55 m-1

beam length 0.0100214 m 

liquid emissivity 0.0541005 

vapor absorption coefficient 0.1824351 m-1

vapor emissivity 0.000542 

rod area (based on Hgrid) Ar 1.76154 in2 0.0011365 m2

grid area (per rod) Ag 2.976 in2 0.00192 m2

1/R11 0.0102283 

1/R22 0.01728 

1/R12 0.0010744 

1/R1L 6.145E-05 

1/R1V 5.827E-07 

1/R2L 0.0001038 

1/R2V 9.844E-07 

1/RLV 8.963E-08 

A11 0.0113647 

A22 0.0184592 

A12=A21 -8.963E-08 

C1 1094.4211 

C2 1059.9296 
B-7

APPENDIX B4. ROD GRID RADIATION NETWORK FOR BWR 

Inputs 

H grid 1.5 in 0.0381 m

N grids 6

rod diameter 0.4830709 in 0.01227 m

rods pitch 0.6377953 in 0.0162 m

rod power 5.6 kW

pressure 40 psia 272.10884 kPa

liquid temperature 267 F 403.69556 K

vapor temperature 1177 F 909.25111 K

rod temperature 1650 F 1172.0289 K

grid temperature 1376 F 1019.8067 K

void fraction 0.995

droplets Sauter mean diameter 0.001 m

wall emissivity 0.9 

Calculation 

bundle hydraulic diameter 0.0149768 m

droplet density 9554140.1 Ndrp/m3

liquid absorption coefficient 5.55 m-1

beam length 0.0127303 m

liquid emissivity 0.068215 

vapor absorption coefficient 0.1824351 m-1

vapor emissivity 0.000868 

rod area (based on Hgrid) Ar 2.2752638 in2 0.0014679 m2

grid area (per rod) Ag 2.976 in2 0.00192 m2

1/R11 0.0132112 

1/R22 0.01728 

1/R12 0.0013666 

1/R1L 0.0001 

1/R1V 1.187E-06 

1/R2L 0.0001309 

1/R2V 1.553E-06 

1/RLV 2.006E-07 

A11 0.014679 

A22 0.018779 

A12=A21 -2.006E-07 

C1 1413.6388 

C2 1059.9923 
B-8

APPENDIX B5. FORTRAN PROGRAM RADNET 

program radnet 

c 

 dimension f(50,50),area(50) 

 dimension pir(50) 

 dimension ir(50) 

c 

 common/cgauss/ a(10,10),b(10),c(10),na 

 common/temp/t(10),eb(10),tl,tv,ebl,ebv,q(10) 

 common/resist/ r(10,10) 

c 

 data sig/5.67E-08/ 

 data pi/3.141592654/ 

c 

c......input values 

 nhot=9 

 trmed=1650.0 

 thr=2100.0 

 ts=800.0 

 th=800.0 

 tl=267.0 

 tv=1650.0 

 hqch=4.0 

 qrod=2296.6 

c 

 hcore=12.0 

 qtot=qrod*45.0 

 qhr=qrod*float(nhot) 

 nsurf=4 

 nrod=49 

 ncold=nrod-nhot-nsurf 

 n=nrod+1 

 drod=0.0095 

 dh=0.01178 

 dtemp=155.0 

 if (nhot.eq.9) dtemp=161.0 

 if (nhot.eq.25) dtemp=170.0 

 if (thr.eq.0.0) thr=trmed+ncold*dtemp/float(ncold+nhot) 

 tcr=thr-dtemp 

 write(6,*) thr,tcr 

c 

c......pressure in psia 

 press=40.0 

 alp=0.995 

 dd=0.001 

 ew=0.8 

 timax=500.0 

c 

c......end of inputs 

c 

 do 301 i=1,49 

 ir(i)=2 

 301 continue 
B-9

 if (nhot.eq.1) then 

 ir(25)=1 

 endif 

 if (nhot.eq.9) then 

 ir(17)=1 

 ir(18)=1 

 ir(19)=1 

 ir(24)=1 

 ir(26)=1 

 ir(31)=1 

 ir(32)=1 

 ir(33)=1 

 endif 

 if (nhot.eq.25) then 

 ir(9)=1 

 ir(10)=1 

 ir(11)=1 

 ir(12)=1 

 ir(13)=1 

 ir(16)=1 

 ir(20)=1 

 ir(23)=1 

 ir(27)=1 

 ir(27)=1 

 ir(30)=1 

 ir(34)=1 

 ir(37)=1 

 ir(38)=1 

 ir(39)=1 

 ir(40)=1 

 ir(41)=1 

 endif 

c 

 ir(1)=3 

 ir(7)=3 

 ir(43)=3 

 ir(49)=3 

c 

 shrod=float(nhot)*pi*drod 

 scrod=float(ncold)*pi*drod 

 ssrf=float(nsurf)*pi*drod 

 shou=0.3607 

 nd=6.0*(1.0-alp)/(pi*dd**3.0) 

 al=0.185*nd*pi*dd**2.0 

 press=press*100.0/14.7 

c 

c......calculate global view factors with inner hot rods array considered 

c 

 do 11 i=1,n 

 do 12 j=1,n 

 read(9,*) ni,nj,f(i,j) 

 12 continue 

 read(9,*) area(i) 

 11 continue 

c 
B-10

 fhrcr=0.0 

 do 101 j=1,nrod 

 fsum=0.0 

 asum=0.0 

 if (ir(j).ne.2) goto 101 

 do 102 i=1,nrod 

 if (ir(i).ne.1) goto 102 

 fsum=fsum+area(i)*f(i,j) 

 asum=asum+area(i) 

 102 continue 

 fhrcr=fhrcr+fsum/asum 

 101 continue 

c 

 fsum=0.0 

 asum=0.0 

 fhrh=0.0 

 do 202 i=1,nrod 

 if (ir(i).ne.1) goto 202 

 fsum=fsum+area(i)*f(i,n) 

 asum=asum+area(i) 

 202 continue 

 fhrh=fsum/asum 

c 

 fsum=0.0 

 asum=0.0 

 fcrh=0.0 

 do 302 i=1,nrod 

 if (ir(i).ne.2) goto 302 

 fsum=fsum+area(i)*f(i,n) 

 asum=asum+area(i) 

 302 continue 

 fcrh=fsum/asum 

c 

 fhrs=0.0 

 do 401 j=1,nrod 

 fsum=0.0 

 asum=0.0 

 if (ir(j).ne.3) goto 401 

 do 402 i=1,nrod 

 if (ir(i).ne.1) goto 402 

 fsum=fsum+area(i)*f(i,j) 

 asum=asum+area(i) 

 402 continue 

 fhrs=fhrs+fsum/asum 

 401 continue 

c 

 fcrs=0.0 

 do 501 j=1,nrod 

 fsum=0.0 

 asum=0.0 

 if (ir(j).ne.3) goto 501 

 do 502 i=1,nrod 

 if (ir(i).ne.2) goto 502 

 fsum=fsum+area(i)*f(i,j) 

 asum=asum+area(i) 
B-11

 502 continue 

 fcrs=fcrs+fsum/asum 

 501 continue 

c 

 asum=area(1)+area(7)+area(43)+area(49) 

 fs1=area(1)*f(1,n) 

 fs2=area(7)*f(7,n) 

 fs3=area(43)*f(43,n) 

 fs4=area(49)*f(49,n) 

 fsh=(fs1+fs2+fs3+fs4)/asum 

c 

c......calculate network resistances 

c 

 ebl=sig*tl**4.0 

 ebv=sig*tv**4.0 

 av=9.84e-5*press*(18.66*(555.0/tv)**2.0 - (555.0/tv)**4.0) 

 xlm=0.85*dh 

 el=1.0-exp(-al*xlm) 

 ev=1.0-exp(-av*xlm) 

 r(1,1)=(1.0-ew)/(ew*shrod) 

 r(1,2)=1.0/((1.0-el)*(1.0-ev)*shrod*fhrcr) 

 r(1,3)=1.0/((1.0-el)*(1.0-ev)*shrod*fhrs) 

 r(1,4)=1.0/((1.0-el)*(1.0-ev)*shrod*fhrh) 

 r(1,5)=1.0/(el*(1.0-ev)*shrod) 

 r(1,6)=1.0/(ev*(1.0-el)*shrod) 

c 

 r(2,1)=r(1,2) 

 r(2,2)=(1.0-ew)/(ew*scrod) 

 r(2,3)=1.0/((1.0-el)*(1.0-ev)*scrod*fcrs) 

 r(2,4)=1.0/((1.0-el)*(1.0-ev)*scrod*fcrh) 

 r(2,5)=1.0/(el*(1.0-ev)*scrod) 

 r(2,6)=1.0/(ev*(1.0-el)*scrod) 

c 

 r(3,1)=r(1,3) 

 r(3,2)=r(2,3) 

 r(3,3)=(1.0-ew)/(ew*ssrf) 

 r(3,4)=1.0/((1.0-el)*(1.0-ev)*ssrf*fsh) 

 r(3,5)=1.0/(el*(1.0-ev)*ssrf) 

 r(3,6)=1.0/(ev*(1.0-el)*ssrf) 

c 

 r(4,1)=r(1,4) 

 r(4,2)=r(2,4) 

 r(4,3)=r(3,4) 

 r(4,4)=(1.0-ew)/(ew*shou) 

 r(4,5)=1.0/(el*(1.0-ev)*shou) 

 r(4,6)=1.0/(ev*(1.0-el)*shou) 

c 

 r(5,1)=r(1,5) 

 r(5,2)=r(2,5) 

 r(5,3)=r(3,5) 

 r(5,4)=r(4,5) 

 r(5,5)=0.0 

 r(5,6)=1.0/(ev*el*(shrod+scrod+ssrf+shou)) 

c 

 r(6,1)=r(1,6) 
B-12

 r(6,2)=r(2,6) 

 r(6,3)=r(3,6) 

 r(6,4)=r(4,6) 

 r(6,5)=r(5,6) 

 r(6,6)=0.0 

c 

 na=4 

c 

 t(1)=273.14+(thr-32.0)/1.8 

 t(2)=273.14+(tcr-32.0)/1.8 

 t(3)=273.14+(ts-32.0)/1.8 

 t(4)=273.14+(th-32.0)/1.8 

 t(5)=273.14+(tl-32.0)/1.8 

 t(6)=273.14+(tv-32.0)/1.8 

 do 10 i=1,6 

 eb(i)=sig*t(i)**4.0 

 10 continue 

c 

 call matrix 

 call gauss 

c 

 do 351 i=1,na 

 q(i)=(c(i)-eb(i))/r(i,i) 

 351 continue 

 q(5)=0.0 

 q(6)=0.0 

 do 352 i=1,na 

 q(5)=q(5)+(c(i)-eb(5))/r(i,5) 

 q(6)=q(6)+(c(i)-eb(6))/r(i,6) 

 352 continue 

 qvl=(eb(6)-eb(5))/r(5,6) 

 q(5)=q(5)+qvl 

 q(6)=q(6)-qvl 

c 

 q12=(c(1)-c(2))/r(1,2) 

 q13=(c(1)-c(3))/r(1,3) 

 q23=(c(2)-c(3))/r(2,3) 

 q14=(c(1)-c(4))/r(1,4) 

 q24=(c(2)-c(4))/r(2,4) 

 q1l=(c(1)-eb(5))/r(1,5) 

 q1v=(c(1)-eb(6))/r(1,6) 

 q2l=(c(2)-eb(5))/r(2,5) 

 q2v=(c(2)-eb(6))/r(2,6) 

 q3l=(c(3)-eb(5))/r(3,5) 

 q3v=(c(3)-eb(6))/r(3,6) 

 q4l=(c(4)-eb(5))/r(4,5) 

 q4v=(c(4)-eb(6))/r(4,6) 

c 

c......pi groups in the flow energy equation 

 pir(1)=(q1v+q2v)/qtot 

 pir(2)=(q1l+q2l)/qtot 

 pir(3)=q4v/qtot 

 pir(4)=q4l/qtot 

 pir(5)=q3v/qtot 

 pir(6)=q3l/qtot 
B-13

pir(7)=qvl/qtot 

c 

c......pi groups in the rod energy equation 

 pir(8)=q13/qhr 

 pir(9)=q14/qhr 

 pir(10)=q12/qhr 

 pir(11)=q1l/qhr 

 pir(12)=q1v/qhr 

c 

c......correction to account for the above quench length 

 corf=(hcore-hqch)/hcore 

 do 701 i=1,7 

 pir(i)=pir(i)*corf 

 701 continue 

c 

 write(6,*) 'RV = ', pir(1) 

 write(6,*) 'RL = ', pir(2) 

 write(6,*) 'HV = ', pir(3) 

 write(6,*) 'HL = ', pir(4) 

 write(6,*) 'SV = ', pir(5) 

 write(6,*) 'SL = ', pir(6) 

 write(6,*) 'VL = ', pir(7) 

 write(6,*) 

 write(6,*) 'RS = ', pir(8) 

 write(6,*) 'RH = ', pir(9) 

 write(6,*) 'RR = ', pir(10) 

 write(6,*) 'RL = ', pir(11) 

 write(6,*) 'RV = ', pir(12) 

c 

 stop 

 end 

c 

c 

 subroutine matrix 

c 

 common/cgauss/ a(10,10),b(10),c(10),na 

 common/temp/t(10),eb(10),tl,tv,ebl,ebv,q(10) 

 common/resist/ r(10,10) 

c 

 do 10 i=1,na 

 b(i)=0.0 

 do 10 j=1,na 

 a(i,j)=0.0 

 10 continue 

c 

 do 101 i=1,na 

 b(i)=eb(i)/r(i,i)+ebl/r(i,5)+ebv/r(i,6) 

 do 102 j=1,na 

 if (i.ne.j) then 

 a(i,j)=-1.0/r(i,j) 

 else 

 do 103 k=1,6 

 a(i,i)=a(i,i)+1.0/r(i,k) 

 103 continue 

 endif 
B-14

 102 continue 

 101 continue 

c 

 return 

 end 

c 

c 

 subroutine gauss 

c 

 common/cgauss/ a(10,10),b(10),c(10),na 

c 

 k=1 

 20 temp = 1.0/a(k,k) 

 j=k 

 30 a(k,j) = a(k,j)*temp 

 if (j.eq.na) goto 40 

 j=j+1 

 goto 30 

 40 b(k) = b(k)*temp 

 j=k+1 

 50 temp = a(j,k) 

 l=k 

 60 a(j,l) = a(j,l)-a(k,l)*temp 

 if (l.eq.na) goto 70 

 l=l+1 

 goto 60 

 70 b(j) = b(j)-b(k)*temp 

 if (j.eq.na) goto 80 

 j=j+1 

 goto 50 

 80 if (k.eq.na-1) goto 90 

 k=k+1 

 goto 20 

 90 continue 

 c(na) = b(na)/a(na,na) 

 i=1 

 120 sum = 0.0 

 j=na-i+1 

 100 sum = sum+a(na-i,j)*c(j) 

 if (j.eq.na) goto 110 

 j=j+1 

 goto 100 

 110 c(na-i) = b(na-i)-sum 

 if (i.eq.na-1) goto 130 

 i=i+1 

 goto 120 

 130 continue 

c 

 return 

 end 

c 
APPENDIX C1. BUNDLE MODEL DESCRIPTION 

A full model of a square lattice rod bundle was developed to calculate the cross section 

temperature distribution during the reflood transient. The model includes the rod-to-rod and rodto-housing thermal radiation heat transfer as well as the radial heat conduction in the rods and 

the housing. The convection heat transfer between rods and fluid as well as housing and fluid is 

simulated by inputting a convective heat transfer coefficient time history. The fluid temperature 

is another input value and it is kept constant during the transient. 

The view factor matrix is calculated with the VUEFAC subroutine of MOXY computer program 

(Ref. 7-1). The conduction heat transfer is computed in each of the fuel rods, subject to the 

transient heat flux boundary condition of combined convection and radiation heat transfer. The 

radiative heat transfer computations are based on assumptions of gray and diffuse surfaces. 

The model neglects absorption, emission, or scattering of radiation by steam and droplets 

contained between surfaces. The radiation heat transfer between the surfaces and vapor was 

taken into account in the lumped model described in Section 6 (RADNET computer program). 

Conductive Heat Transfer 

The heat conduction in fuel rods, solid inactive rods and housing is computed by numerical 

integration of the one-dimensional Fourier heat conduction equation: 

1

r r

kr T

r

q c

T

t p

∂

∂

∂

∂ ρ

∂

∂

⎛

⎝

⎜ ⎞

⎠

⎟ + = "'

where q’’’ is zero for the inactive rods. The equation is discretized as follows: 

( ) ρ

π

c V

t

T TQ k p n n T T n n ,1 1

1

1

11 1

2 1 2

Δ 2

+ − =+

⎡ −

⎣

⎢

⎢

⎤

⎦

⎥

⎥

( ) ρ

π

c V

t

T T Q kr

dr T T

dr

k r

dr T T

dr

pi i

i

n

i

n

i ii

i i

n

i

n

i

i i

i i

n

i

n

i

,

Δ

+ +

−

− −

−

− =+ +

⎛

⎝

⎜ ⎞

⎠

⎟

⎛ −

⎝

⎜

⎜

⎞

⎠

⎟

⎟ − − ⎛

⎝

⎜ ⎞

⎠

⎟

⎛ −

⎝

⎜

⎜

⎞

⎠

⎟

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

1 1

1

1 1

1

2

2 2

C-1
( ) [ ] ( ) ρ

π π

c V

t

T TQ kr

dr T T

dr r q hT T pN N

N

n

N

n

N NN

N N

n

N

n

N

N rod

n

N

n

f

,

Δ

+

−

− −

−

−=− − ⎛

⎝

⎜ ⎞

⎠

⎟

⎛ −

⎝

⎜

⎜

⎞

⎠

⎟

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

− +− 1

1

1 1

1

2

2

2

where 

V r dr dr ( ) dr dr

i ii i

i i = ++

⎡ −

⎣

⎢

⎢

⎤

⎦

⎥

⎥ − − π 1

2

1

2

4

The equation for the heat conduction in the housing is: 

∂

∂

∂

∂ ρ

∂

x ∂

k T

x

q c

T

t p

⎛

⎝

⎜ ⎞

⎠

⎟ + = "'

Again, this is solved numerically with the following equations: 

( ) ( ) ρc dx

t

T Tk

T T

dx

hTT p n n n n

loss

n

out

,1

1

1

1 1

2 1

1 Δ

+ − = ⎛ −

⎝

⎜

⎜

⎞

⎠

⎟

⎟ − −

( ) ρc dx

t

T Tk

T T

dx

k

T T

dx

p i

i

n in ii

n

i

n

i

i

n

i

n ,

Δ

+ + − − − = ⎛ −

⎝

⎜

⎜

⎞

⎠

⎟

⎟ − ⎛ −

⎝

⎜

⎜

⎞

⎠

⎟

⎟ 1 1

1

1

( ) ( ) ρc dx

t

TT k

T T

dx hT T q p N

N

n Nn NN

n

N

n

N

n f ra

, n

Δ

+ − − − =− ⎛ −

⎝

⎜

⎜

⎞

⎠

⎟

⎟ − −− 1

1

1

d

E i ε

Once the radiative heat rate is calculated from the radiation transport equations, the 

previous equations are solved for the temperature field at time tn+1.

n qrad

Radiative Heat Transfer 

The equations governing the radiative heat transfer are the following: 

 (i = 1, 2, ... N) J F ( ) J i ij

j

N

1 j ib

1

−− = 1

=

ε ∑ ,

where 

Ji radiosity of the ith surface 

Eb,i blackbody emissive power of the ith surface 

Fij view factor matrix 

Ei emissivity of the ith surface 

Once the temperature field is known by solving the conduction equation at time tn the emissive 

power Eb,i can be calculated. Then the previous system is solved for the radiosities Ji and the 

radiative heat fluxes at time tn are calculated from the following equation: 

C-2
)( 1 1, , iib

i

n i

rad q − JE − = ε

ε

The radiative heat fluxes are applied as the wall boundary condition for the conduction equation 

which is used to evaluate the temperature field at time tn+1. 

The program herein presented can operate also in a steady state mode. In this case the 

conduction equation is not solved while the temperature field is calculated iteratively. The 

source list of the Fortran program called BUNDLE is attached in Appendix C2. 

C-3
C-4

APPENDIX C2. FORTRAN PROGRAM BUNDLE 

program bundle 

c 

 implicit double precision (a-h,o-z) 

 dimension d(1000),pwf(1000) 

 dimension a(1001,1001),b(1001) 

c 

 common /vf/ f(1001,1001),area(1001) 

 common/heat/q(1001),qrad(1001),qconv(1001),temp(1001), 

 + emiss(1001),bs(1001),qold(1001) 

 common/heat1/tfad,tenvad,h,hout,hmin,qct,qrt,qt 

 common/geoint/nrod,n,nl 

 common/geo/vrod(1000) 

 common/temp/told(1001) 

 common/converg/alfa 

 common/printc/tpcv,nprt1,nprt2,imod 

c 

 common/trans1/regsze(4),ql(1000),qr(1000),tr(1000,100),th(100) 

 common/trans2/ndreg,ndx,ndr,npc,np1,ntab,ntab2,ifrad,inuc 

 common/trans3/dt,tmax,time,tft,s,tenv,hloss,qavg,htrs,trst, 

 + tdst,thst,tmin,fdcy,hgap 

 common/trans4/tme(100),hft(100),tmep(100),pdcy(100),tmix(100) 

c 

 data pi/3.141592654/ 

 data sig/5.67D-08/ 

c 

 open(unit=8,file='bd.inp') 

 open(unit=11,file='bd.out') 

 open(unit=12,file='bd.dmp') 

 open(unit=13,file='bd.flx') 

c 

 write(11,800) 

 write(12,600) 

 write(13,700) 

 read(8,*) nl 

 write(11,812) nl,nl 

 read(8,*) inuc 

 read(8,*) dd,p,drh 

 write(11,801) dd 

 write(11,802) p 

 write(11,803) drh 

 read(8,*) pwavg 

 write(11,804) pwavg 

 read(8,*) emirod,emihs 

 write(11,805) emirod 

 write(11,806) emihs 

 read(8,*) hf,tf,tmin 

 write(11,807) hf 

 write(11,808) tf 

 hf=hf*5.679 

 tf=(tf-32.0)*5.0/9.0 + 273.14 
C-5

 tmin=(tmin-32.0)*5.0/9.0 + 273.14 

read(8,*) hloss,tenv 

 write(11,809) hloss 

 write(11,810) tenv 

 hloss=hloss*5.679 

 tenv=(tenv-32.0)*5.0/9.0 + 273.14 

 read(8,*) s 

 write(11,813) s 

 s=s*0.0254 

c 

 hmin=0.2 

c 

 write(11,811) 

 nrod=nl*nl 

 n=nrod+1 

 k1=1 

 k2=k1+nl-1 

 do 500 i=1,nl 

 read(8,*) (pwf(k),k=k1,k2) 

 write(11,903) (pwf(k),k=k1,k2) 

 k1=k1+nl 

 k2=k2+nl 

 500 continue 

c 

 read(8,*) err 

 read(8,*) imod,ifrad 

c 

 if (imod.eq.0) goto 510 

c 

c.....read transient data 

 read(8,*) dt,tmax,nprt1,nprt2 

 read(8,*) (regsze(i),i=1,4) 

 do 505 i=1,4 

 regsze(i)=regsze(i)*0.0254 

 rsum=rsum+regsze(i) 

 vrod(i)=(rsum**2.0-(rsum-regsze(i))**2.0)*pi 

 505 continue 

 read(8,*) hgap 

 hgap=hgap*5.679 

 read(8,*) ndreg,ndx 

c read(8,*) tft 

c tft=(tft-32.0)*5.0/9.0 + 273.14 

 read(8,*) ntab 

 do 507 i=1,ntab 

 read(8,*) tme(i),hft(i),tmix(i) 

 hft(i)=hft(i)*5.679 

 tmix(i)=(tmix(i)-32.0)*5.0/9.0 + 273.14 

 507 continue 

 read(8,*) ntab2 

 do 508 i=1,ntab2 

 read(8,*) tmep(i),pdcy(i) 

 508 continue 

 read(8,*) trst,tdst,thst 

 trst=(trst-32.0)*5.0/9.0 + 273.14 
C-6

 tdst=(tdst-32.0)*5.0/9.0 + 273.14 

 thst=(thst-32.0)*5.0/9.0 + 273.14 

c 

c 

c....'pwavg' is the radial average power in kW/ft 

c 

 510 feet=0.3048 

 pwl=pwavg*1000./feet 

 tpcv=tf+pwl/(hf*pi*dd*0.0254) 

c 

 call vufac(nl,dd,p,drh) 

c 

 do 301 i=1,n 

 do 302 j=1,n 

 302 continue 

 area(i)=area(i)*0.0254 

 301 continue 

c 

 do 401 i=1,nrod 

 d(i)=dd*0.0254 

 ql(i)=pwf(i)*pwl 

 emiss(i)=emirod 

 401 continue 

 emiss(n)=emihs 

 qavg=pwl/(pi*d(1)) 

c 

 if (imod.eq.1) goto 2000 

c 

c.....Set dimensionless variables 

c 

 tfad=(sig*tf**4.0d0/qavg)**0.25d0 

 tenvad=(sig*tenv**4.0d0/qavg)**0.25d0 

 tguess=tfad 

 h=hf/(qavg**0.75d0 * sig**0.25d0) 

 hout=hloss/(qavg**0.75d0 * sig**0.25d0) 

 do 501 i=1,nrod 

 q(i)=pwf(i) 

 501 continue 

 q(n)=0.0 

c 

c.....Start Iteration loop 

c 

 if (h.lt.hmin) then 

 alfa=1.0 

 nitmax=1000 

 goto 150 

 endif 

c 

 write(6,*) 'ALFA = ?' 

 read (6,*) alfa 

 write(6,*) 'NITER = ?' 

 read (6,*) nitmax 

c 

 150 niter=0 
C-7

c 

c.....Initial guess for temperature 

c 

 do 201 i=1,n 

 temp(i)=tfad 

 201 continue 

c 

1001 niter=niter+1 

c 

 call rads 

 call conv 

c 

c.....check for convergence 

 eps=0.0 

 elast=0.0 

 do 240 i=1,n 

 tnew=temp(i) 

 eps=abs(tnew-told(i)) 

 eps=max(elast,eps) 

 elast=eps 

 told(i)=tnew 

 240 continue 

 write(6,*) niter,eps 

 if (niter.gt.nitmax) goto 1002 

 if (eps.gt.err) goto 1001 

1002 continue 

 goto 2100 

c 

c.....transient calculation 

c 

2000 call trans 

 goto 9001 

c 

c.....print results steady state 

c 

2100 call print 

c 

c 

 600 format(5x,'TIME',4x,'TCR-1',4x,'TCR-N',4x,'TWR-N',4x,'T0R-N', 

 + 4x,'THO-1',4x,'THO-N',4x,'TN3x3',4x,'TN5x5',4x,'TN7x7',/) 

 700 format(5x,'TIME',3x,'Q-RtoH',3x,'Q-RtoF',3x,'Q-HtoF',3x, 

 + 'Q-LOSS',3x,'T-RODS',3x,'T-SURF',3x,'T-HOUS',//) 

 800 format(/,40x,'CALCULATION RBHT', 

 + //,3x,'INPUT DATA') 

 801 format(3x,'Rod Diameter (in) = ',F8.3) 

 802 format(3x,'Rods Array Pitch (in) = ',F8.3) 

 803 format(3x,'Distance Rods-to-Housing (in) = ',F8.3) 

 804 format(3x,'Rod Average Power (kW) = ',F8.3) 

 805 format(3x,'Rod Surface Emissivity (-) = ',F8.3) 

 806 format(3x,'Housing Surface Emissivity (-) = ',F8.3) 

 807 format(3x,'Bundle Covection H.T.C. (Btu/hr-F-ft2)= ',F8.3) 

 808 format(3x,'Fluid Temperature (F) = ',F8.3) 

 
C-8

809 format(3x,'Housing Heat Losses H.T.C. (Btu/hr-F-ft2)= ',F8.3) 

 810 format(3x,'Enviroment Temperature (F) = ',F8.3) 

 811 format(//,3x,'RODS POWER FACTOR',///) 

 812 format(//,3x,'Bundle Array Size (-) = ',3x, 

 + I2,'x',I2) 

 813 format(3x,'Housing Thickness (in) = ',F8.3) 

 903 format(20(1x,F7.2)) 

c 

9001 stop 

 end 

c 

c***************************************************************** 

c 

 subroutine trans 

c 

 implicit double precision (a-h,o-z) 

c 

 common/trans1/regsze(4),ql(1000),qr(1000),tr(1000,100),th(100) 

 common/trans2/ndreg,ndx,ndr,npc,np1,ntab,ntab2,ifrad,inuc 

 common/trans3/dt,tmax,time,tft,s,tenv,hloss,qavg,htrs,trst, 

 + tdst,thst,tmin,fdcy,hgap 

 common/trans4/tme(100),hft(100),tmep(100),pdcy(100),tmix(100) 

 common/heat/q(1001),qrad(1001),qconv(1001),temp(1001), 

 + emiss(1001),bs(1001),qold(1001) 

 common/geoint/nrod,n,nl 

 common /vf/ f(1001,1001),area(1001) 

 common/printc/tpcv,nprt1,nprt2,imod 

c 

 dimension trf(1000,100),thf(100) 

c 

 data pi/3.141592654/ 

 data sig/5.67D-08/ 

c 

 ndr=4*ndreg 

 npc=ndr+1 

 ndt1=0 

 ndt2=0 

 ic=(nl**2.0+1)/2.0 

 iw=ic-(nl-1)/2.0 

c 

c.....initial condition 

c 

 do 10 j=1,nrod 

 qr(j)=0.0 

 do 10 i=1,npc 

 tr(j,i)=trst 

 if (ql(j).eq.0.0) tr(j,i)=tdst 

 10 continue 

 do 11 i=1,ndx+1 

 th(i)=thst 

11 continue 

 qr(n)=0.0 

c 

 100 call interp(tme,hft,time,htrs,ntab) 
C-9

 if (tr(ic,npc).lt.tmin) htrs=5600.0 

 call interp(tme,tmix,time,tft,ntab) 

 call interp(tmep,pdcy,time,fdcy,ntab2) 

 call trod 

 call thous 

c 

 qrf=0.0 

 do 102 i=1,nrod 

 tw=tr(i,npc) 

 temp(i)=(sig*tw**4.0d0/qavg)**0.25d0 

 qrf=qrf+htrs*area(i)*(tw-tft) 

 102 continue 

 temp(n)=(sig*th(np1)**4.0d0/qavg)**0.25d0 

 qhf=htrs*area(n)*(th(ndx+1)-tft) 

 qloss=hloss*area(n)*(th(1)-tenv) 

c 

 if(ifrad.eq.0) goto 210 

c 

c.....turn off radiation after quench 

 if(htrs.ge.5600.0) then 

 qrh=0.0 

 do 141 i=1,n 

 qr(i)=0.0 

 141 continue 

 goto 210 

 endif 

c 

 call rads 

c 

c.....calculate new radiation fluxes qrad 

c 

 do 201 i=1,n 

 qr(i)=(temp(i)**4.0d0 - bs(i))*qavg*emiss(i)/(1.0d0-emiss(i)) 

 201 continue 

 qrh=-qr(n)*area(n) 

c 

 210 time=time+dt 

 ndt1=ndt1+1 

 ndt2=ndt2+1 

 if(ndt1.eq.nprt1) then 

 write(6,*) time,htrs,tr(ic,npc) 

 do 301 i=1,nrod 

 do 302 j=1,npc 

 trf(i,j)=(tr(i,j)-273.14)*9.0/5.0 + 32.0 

 302 continue 

 301 continue 

 do 303 i=1,np1 

 thf(i)=(th(i)-273.14)*9.0/5.0 + 32.0 

 303 continue 

c 

c.....3x3 Taverage 

 tsum=0.0 

 is3=ic-nl-1 

 do 402 k=1,3 
C-10

 do 401 i=is3,is3+2 

 tsum=tsum+trf(i,npc) 

 401 continue 

 is3=is3+nl 

 402 continue 

 t33=tsum/9.0 

c 

c.....5x5 Taverage 

 tsum=0.0 

 is5=ic-2*nl-2 

 do 404 k=1,5 

 do 403 i=is5,is5+4 

 tsum=tsum+trf(i,npc) 

 403 continue 

 is5=is5+nl 

 404 continue 

 t55=tsum/25.0 

c 

c.....7x7 Taverage 

 tsum=0.0 

 n7=0 

 is7=ic-3*nl-3 

 do 406 k=1,7 

 do 405 i=is7,is7+6 

 if (ql(i).eq.0.0) goto 405 

 tsum=tsum+trf(i,npc) 

 n7=n7+1 

 405 continue 

 is7=is7+nl 

 406 continue 

 t77=tsum/n7 

c 

c.....Hot-Rods Taverage 

 tsum1=0.0 

 tsum2=0.0 

 ndum=0 

 do 407 i=1,nrod 

 if (ql(i).eq.0.0) then 

 tsum2=tsum2+trf(i,npc) 

 ndum=ndum+1 

 goto 407 

 endif 

 tsum1=tsum1+trf(i,npc) 

 407 continue 

 thot=tsum1/float(nrod-ndum) 

 tcold=tsum2/float(ndum) 

c 

 write(12,601) time,trf(ic,1),trf(ic,npc),trf(22,npc), 

 + trf(1,npc),thf(1),thf(np1),t33,t55,t77 

 write(13,701) time,qrh,qrf,qhf,qloss,thot,tcold,thf(np1) 

 ndt1=0 

 endif 

 if(ndt2.eq.nprt2) then 

 call print 
C-11

 ndt2=0 

 endif 

c 

 if(time.lt.tmax) goto 100 

c 

 return 

c 

 601 format(10(1x,F8.2)) 

 701 format(8(1x,F9.0)) 

c 

 end 

c 

c***************************************************************** 

c 

 subroutine rads 

c 

 implicit double precision (a-h,o-z) 

c 

 common /vf/ f(1001,1001),area(1001) 

 common/heat/q(1001),qrad(1001),qconv(1001),temp(1001), 

 + emiss(1001),bs(1001),qold(1001) 

 common/geoint/nrod,n,nl 

c 

 dimension a(1001,1001),b(1001),c(1001) 

c 

 do 205 i=1,n 

 do 204 j=1,n 

 204 a(i,j) =-f(i,j)*(1.0d0-emiss(i)) 

 a(i,i)=a(i,i)+1.0 

 205 continue 

 do 206 i=1,n 

 b(i)=emiss(i)*temp(i)**4.0d0 

 206 continue 

c 

 call gauss(a,n,b,bs) 

c 

 return 

 end 

c 

c***************************************************************** 

c 

 subroutine conv 

c 

 implicit double precision (a-h,o-z) 

c 

 common /vf/ f(1001,1001),area(1001) 

 common/heat/q(1001),qrad(1001),qconv(1001),temp(1001), 

 + emiss(1001),bs(1001),qold(1001) 

 common/heat1/tfad,tenvad,h,hout,hmin,qct,qrt,qt 

 common/geoint/nrod,n,nl 

 common/temp/told(1001) 

 common/converg/alfa 

c 

 data sig/5.67D-08/ 
C-12

c 

 qct=0.0 

 qrt=0.0 

 qt=0.0 

c 

 do 102 i=1,n 

 sumbs=0.0d0 

 do 101 j=1,n 

 sumbs=sumbs+f(i,j)*bs(j) 

 101 continue 

c 

c.....special case: radiation dominated cases 

 if (h.lt.hmin) then 

 eb=q(i)*(1.0d0-emiss(i))/emiss(i) + bs(i) 

 temp(i)=eb**0.25d0 

 goto 102 

 endif 

c 

 temp(i)=tfad + (q(i)-bs(i)+sumbs)/h 

 102 continue 

 c1=(h*tfad+hout*tout)/(h+hout) 

 c2=1.0d0/(h+hout) 

 temp(n)=c1+c2*(sumbs-bs(n)) 

c 

c.....underrelaxation 

 do 103 i=1,n 

 temp(i)=(1.0d0-alfa)*told(i) + alfa*temp(i) 

 103 continue 

c 

 do 105 i=1,n 

 qconv(i)=h*(temp(i)-tfad) 

 qrad(i)=q(i)-qconv(i) 

 qrt=qrt+qrad(i)*area(i) 

 qt=qt+q(i)*area(i) 

 qct=qct+qconv(i)*area(i) 

 105 continue 

 if (h.lt.hmin) temp(n)=tenvad+qt/(hout*area(n)) 

c 

 return 

 end 

c 

c***************************************************************** 

c 

 subroutine gauss(a,na,b,c) 

c 

 implicit double precision (a-h,o-z) 

 dimension a(1001,1001),b(1001),c(1001) 

c 

 k=1 

 20 tmp = 1.d0/a(k,k) 

 j=k 

 30 a(k,j) = a(k,j)*tmp 

 if (j.eq.na) goto 40 

 j=j+1 
C-13

 goto 30 

 40 b(k) = b(k)*tmp 

 j=k+1 

 50 tmp = a(j,k) 

 l=k 

 60 a(j,l) = a(j,l)-a(k,l)*tmp 

 if (l.eq.na) goto 70 

 l=l+1 

 goto 60 

 70 b(j) = b(j)-b(k)*tmp 

 if (j.eq.na) goto 80 

 j=j+1 

 goto 50 

 80 if (k.eq.na-1) goto 90 

 k=k+1 

 goto 20 

 90 continue 

 c(na) = b(na)/a(na,na) 

 i=1 

 120 sum = 0.0 

 j=na-i+1 

 100 sum = sum+a(na-i,j)*c(j) 

 if (j.eq.na) goto 110 

 j=j+1 

 goto 100 

 110 c(na-i) = b(na-i)-sum 

 if (i.eq.na-1) goto 130 

 i=i+1 

 goto 120 

 130 continue 

c 

 return 

 end 

c 

c***************************************************************** 

c 

 subroutine trod 

c 

 implicit double precision (a-h,o-z) 

c 

 common/trans1/regsze(4),ql(1000),qr(1000),tr(1000,100),th(100) 

 common/trans2/ndreg,ndx,ndr,npc,np1,ntab,ntab2,ifrad,inuc 

 common/trans3/dt,tmax,time,tft,s,tenv,hloss,qavg,htrs,trst, 

 + tdst,thst,tmin,fdcy,hgap 

 common/trans4/tme(100),hft(100),tmep(100),pdcy(100),tmix(100) 

 common/heat/q(1001),qrad(1001),qconv(1001),temp(1001), 

 + emiss(1001),bs(1001),qold(1001) 

 common/geoint/nrod,n,nl 

 common/geo/vrod(1000) 

c 

 dimension cd(100),cp(100),t(100),qh(100),ddr(100) 

c 

 data pi/3.141592654/ 

c 
C-14

 do 201 j=1,nrod 

c 

 do 10 i=1,npc 

 t(i)=tr(j,i) 

 qh(i)=0.0 

 10 continue 

 i1=ndreg+2 

 i2=ndreg*2 

 do 20 i=i1,i2 

 qh(i)=ql(j)*fdcy/float(ndreg-1) 

 20 continue 

 qvnuc=0.0 

 if (inuc.ne.0) qvnuc=fdcy*ql(j)/(vrod(1)+vrod(2)+vrod(3)) 

 

c 

c.....calculation properties 

c 

 ireg=1 

 jr=1 

 do 50 i=1,ndr 

 ddr(i)=regsze(ireg)/float(ndreg) 

 tn=t(i) 

 call prop(tn,ireg,cnd,cpm,inuc) 

 if (ql(j).eq.0.0) call prop(tn,4,cnd,cpm,inuc) 

 if (i.eq.(ndreg*3+1).and.hgap.ne.0) 

 + cnd=cnd*hgap*ddr(i)/(cnd+hgap*ddr(i)) 

 cd(i)=cnd 

 cp(i)=cpm 

 if (jr.eq.ndreg) then 

 jr=0 

 ireg=ireg+1 

 endif 

 jr=jr+1 

 50 continue 

c 

c.....calculation conduction in rod 

c.....centerline, inner regions, clad surface 

c 

 r=0.0 

c 

 dr=ddr(1) 

 vol=0.25*pi*dr**2.0 

 a=cd(1)*0.5*(t(2)-t(1)) 

 c=dt/(cp(1)*vol) 

 if (inuc.ne.0) qh(1)=qvnuc*vol 

 t(1)=t(1)+(qh(1)+2.0*pi*a)*c 

c 

 r=ddr(1) 

 do 101 i=2,ndr 

 drm1=ddr(i-1) 

 dr=ddr(i) 

 vol=pi*(r*(drm1+dr) + (dr**2.0-drm1**2.0)/4.0) 

 vol2=pi*(r*drm1-(drm1**2.0)/4.0) 

 if (inuc.ne.0) then 
C-15

 qh(i)=qvnuc*vol 

 if (i.gt.ndreg*3) qh(i)=qvnuc*vol2 

 if (i.gt.ndreg*3+1) qh(i)=0.0 

 endif 

 a=cd(i)*(r+dr/2.0)*(t(i+1)-t(i))/dr 

 b=cd(i-1)*(r-drm1/2.0)*(t(i)-t(i-1))/drm1 

 c=dt/(cp(i)*vol) 

 t(i)=t(i)+(qh(i)+2.0*pi*(a-b))*c 

 r=r+dr 

 101 continue 

c 

 vol=pi*(r*dr - 0.25*dr**2.0) 

 a=-cd(ndr)*(r-dr/2.0)*(t(npc)-t(npc-1))/dr 

 b=r*(qr(j) + htrs*(t(npc)-tft)) 

 c=dt/(cp(ndr)*vol) 

 t(npc)=t(npc)+(qh(npc)+2.0*pi*(a-b))*c 

c 

 do 151 i=1,npc 

 tr(j,i)=t(i) 

 151 continue 

c 

 201 continue 

c 

 return 

 end 

c 

c***************************************************************** 

c 

 subroutine thous 

c 

 implicit double precision (a-h,o-z) 

c 

 common/trans1/regsze(4),ql(1000),qr(1000),tr(1000,100),th(100) 

 common/trans2/ndreg,ndx,ndr,npc,np1,ntab,ntab2,ifrad,inuc 

 common/trans3/dt,tmax,time,tft,s,tenv,hloss,qavg,htrs,trst, 

 + tdst,thst,tmin,fdcy,hgap 

 common/trans4/tme(100),hft(100),tmep(100),pdcy(100),tmix(100) 

 common/heat/q(1001),qrad(1001),qconv(1001),temp(1001), 

 + emiss(1001),bs(1001),qold(1001) 

 common/geoint/nrod,n,nl 

c 

 dimension cd(100),cp(100),t(100) 

c 

 data pi/3.141592654/ 

c 

 dx=s/float(ndx) 

 np1=ndx+1 

c 

c.....calculation properties 

c 

 ireg=4 

 do 50 i=1,ndx 

 tt=th(i) 

 call prop(tt,ireg,cnd,cpm,inuc) 
C-16

 cd(i)=cnd 

 cp(i)=cpm 

 50 continue 

c 

c.....calculation conduction in the housing wall 

c 

 a=2.0*cd(1)*(th(2)-th(1))/dx 

 b=hloss*(th(1)-tenv) 

 c=dt/(cp(1)*dx) 

 th(1)=th(1)+(a-b)*c 

c 

 do 101 i=2,ndx 

 a=2.0*cd(i)*(th(i+1)-th(i))/dx 

 b=2.0*cd(i-1)*(th(i)-th(i-1))/dx 

 c=dt/(cp(i)*dx) 

 th(i)=th(i)+(a-b)*c 

 r=r+dr 

 101 continue 

c 

 a=-2.0*cd(ndx)*(th(np1)-th(np1-1))/dx 

 b=htrs*(th(np1)-tft) 

 c=dt/(cp(ndx)*dx) 

 th(np1)=th(np1)+(a-b-qr(n))*c 

c 

 return 

 end 

c 

c***************************************************************** 

c 

 subroutine prop(tk,ireg,cnd,cpm,inuc) 

c 

 implicit double precision (a-h,o-z) 

c 

 t=tk-273.14 

c 

c.....nuclear rod 

c 

 if (inuc.eq.0) goto 100 

 if (ireg.eq.4) goto 110 

c 

c.....uranium dioxide 

 rho=9649.0 

 cnd=2.45 

 cpm=333.0*rho 

 return 

c 

c.....zircalloy 

 110 rho=6560.0 

 a=1.461e-2 

 b=12.092 

 cnd=a*t+b 

 cpm=347.0*rho 

 return 

c 
C-17

c.....region 1 and 3 - BN 

c 

 100 if (ireg.ne.3.and.ireg.ne.1) goto 101 

 rho=1910.0 

 a=-0.061356 

 b=122.734 

 cnd=a*t + b 

 cpm=1500*rho 

 return 

c 

c.....region 2 - Heater 

 101 if (ireg.ne.2) goto 102 

 rho=8470.0 

 a=4.7742e-10 

 b=-1.1151e-6 

 c=5.2571e-4 

 d=4.0755e-1 

 cpm=1000.0*(a*t**3.0+b*t**2.0+c*t+d)*rho 

 a=2.8263e-2 

 b=17.583 

 cnd=a*t+b 

 return 

c 

c.....region 4 - Clad - Inconel 600 

c 

 102 rho=8270.0 

 a=4.7427e-4 

 b=4.1430e-1 

 cpm=1000.0*(a*t+b)*rho 

 a=1.6972e-2 

 b=14.599 

 cnd=a*t+b 

 cnd=15.0 

 return 

c 

 end 

c 

c 

c*********************************************************** 

c 

 subroutine print 

c 

 implicit double precision (a-h,o-z) 

c 

 common/heat/q(1001),qrad(1001),qconv(1001),temp(1001), 

 + emiss(1001),bs(1001),qold(1001) 

 common/trans3/dt,tmax,time,tft,s,tenv,hloss,qavg,htrs,trst, 

 + tdst,thst,tmin,fdcy,hgap 

 common/trans4/tme(100),hft(100),tmep(100),pdcy(100),tmix(100) 

 common/printc/tpcv,nprt1,nprt2,imod 

 

common/geoint/nrod,n,nl 

c 

 data sig/5.67D-08/ 
C-18

c 

c.....print results 

 if (imod.eq.0) write(11,900) 

 if (imod.eq.1) write(11,904) time 

 do 250 i=1,n 

 temp(i)=temp(i)/(sig/qavg)**0.25d0 

c 

c.....conversion to british units 

 temp(i)=(temp(i)-273.14)*9.0/5.0 + 32.0 

c 

 250 continue 

c 

 k1=1 

 k2=k1+nl-1 

 do 600 i=1,nl 

 write(11,903) (temp(k),k=k1,k2) 

 k1=k1+nl 

 k2=k2+nl 

 600 continue 

 write(11,901) temp(n) 

 tpcv=(tpcv-273.14)*9.0/5.0 + 32.0 

 if (imod.eq.0) write(11,902) tpcv 

c 

 return 

c 

 900 format(///,3x,'RESULTS STEADY STATE', 

 + //,3x,'RODS SURFACE TEMPERATURE (F)',//) 

 904 format(///,'***********************************************', 

 + /,3x,'RESULTS AT TIME (sec) = ',F7.2, 

 + //,3x,'RODS SURFACE TEMPERATURE (F)',//) 

 901 format(/,3x,'HOUSING TEMPERATURE (INSIDE WALL) (F) = ',F7.2) 

 902 format(//,3x,'Rod Surf. Temp. for infinite array at SS (F) = ', 

 + F7.2) 

 903 format(20(1x,F7.2)) 

c 

 end 

c 

c 

c***************************************************************** 

c 

 subroutine vufac(nmx,dd,p,drh) 

C 

c the subroutine is based 

C VUFAC 12/06/78 D.R.EVANS 

c and modified by C. Frepoli 3/10/98 

c the symmentry logic (MIRRIM, ISWAP etc.) is deleted 

c 

 implicit double precision (a-h,o-z) 

C 

c DIMENSION AREA(226),R0(225) 

 dimension r0(1000) 
C-19

 COMMON /VF/ F(1001,1001),area(1001) 

 COMMON /RI/ RIJ(1001,1001) 

c 

 data nf,npt,n,na/1001,200,37,37/ 

 data pi/3.14159265358979323846/ 

 

c 

 xlh=p*float(nmx-1)+dd+2.0*drh 

c 

 nlim=nmx 

 n2=nmx*nmx +1 

 nl=nmx 

 nl=8 

 nl1=nmx 

 ahs=xlh*4.0 

c 

 NP=N2-1 

 

 TWOPI=2.*PI 

 

 DO 1700 I=1,NP 

 

 r0(i)=dd/2.0 

 AREA(I)=TWOPI*R0(I) 

 

1700 CONTINUE 

 

 AREA(N2)=ahs 

c 

 CALL VFAC(F,AREA,AEA,SCALFC,BB,R0,IROW,JCOL,MIRRIM,P,PI,N, 

 1NF,NLIM,N2,NA,NSYM,NL,NL1,NPT) 

 

c 

 do 998 i=1,n2 

 do 997 j=1,n2 

 write(9,*) i,j,f(i,j) 

 997 continue 

 write(9,*) area(i) 

 998 continue 

c 

 return 

 END 

 

c 

C****** FIJ 12/12/78 D.R.EVANS 

 SUBROUTINE FIJ(F,R,P,PI,M,NPT,L,SOURCE,IX,IY,L1,L2,IRC,IA) 

 implicit double precision (a-h,o-z) 

 DIMENSION F(M,1),R(1),XA(2,100),YA(2,100),RA(2,100) 

 COMMON /RI/ RIJ(1001,1001) 

INTEGER SOURCE,TARGET,UPPER(14),LOWER(14) 

 

 LOGICAL SKIP 

 

 DATA XA(1,1),YA(1,1)/2*0.D0/ 
C-20

 DATA SKIP/.FALSE./ 

 IF(SKIP) GO TO 10 

 SKIP=.TRUE. 

 RNPT=1.D0/NPT 

 DELTA=2.D0*PI*RNPT 

 

 RDELT=1.D0/DELTA 

 

 PIO2=.5D0*PI 

 

10 CONTINUE 

 

 IF(IRC-2) 12,16,20 

 

12 CONTINUE 

 

C ROWS 

 

 IF(IA.EQ.2) GO TO 14 

 

C ADJACENT ROW 

 

 IXY=IX 

 

 K2=L 

 

 K3=1 

 

 GO TO 24 

 

 14 CONTINUE 

 

C ROWS BEYOND ADJACENT ROW 

 

 IXY=IY 

 

 IYX=IX 

 I3=1 

 

 K2=0 

 

 K3=L 

 GO TO 24 

 16 CONTINUE 

C HIGHER-NUMBERED COLUMNS 

 IF(IA.EQ.2) GO TO 18 

C ADJACENT COLUMN 

 

 K2=1 

 GO TO 22 

 18 CONTINUE 

C COLUMNS BEYOND ADJACENT COLUMN 

 IXY=IX 

 IYX=IY 

 
C-21

 I3=L 

 K2=0 

 K3=1 

 GO TO 24 

 20 CONTINUE 

C LOWER-NUMBERED COLUMNS 

 K2=-1 

 22 CONTINUE 

 IXY=IY 

 K3=L 

 24 CONTINUE 

C COMPUTE SHADOWING ROD NUMBERS 

 

 KMI=L2-IXY 

 

 IF(KMI.LT.0) KMI=L1-IXY 

 KMIABS=IABS(KMI) 

 TARGET=SOURCE+K2+K3*KMI 

 I2=K3*ISIGN(1,KMI) 

 IF(IA.EQ.2) GO TO 30 

C ADJACENT ROW AND COLUMNS 

 K4=KMIABS 

 GO TO 40 

 30 CONTINUE 

 

C ROWS AND COLUMNS BEYOND ADJACENT 

 

 K4=KMIABS-1 

 UPPER(1)=0 

 LOWER(KMIABS)=0 

 K5=0 

 40 CONTINUE 

 DO 70 I=1,K4 

 LOWER(I)=SOURCE+I2*I 

 

 IF(IA.EQ.2) GO TO 60 

 

 UPPER(I)=TARGET-I2*(KMIABS-I+1) 

 GO TO 70 

 60 CONTINUE 

 UPPER(I+1)=LOWER(I)+I3 

 IF(IYX.EQ.L) UPPER(I+1)=0 

70 CONTINUE 

 

 K=KMIABS+1 

 

C SET RADII AND COORDINATES OF SOURCE,TARGET, AND ALL POTENTIAL 

C SHADOWING RODS 

 

 R1=R(SOURCE) 

 

 RA(1,1)=R1 

 RA(2,K)=R(TARGET) 

C XA(2,1)=0.D0 

 XA(2,1)=0.E0 
C-22

 YA(2,1)=P 

 DO 230 I=1,KMIABS 

 FI=I 

 PTFI=P*FI 

 

 IP1=I+1 

 

 XA(1,IP1)=PTFI 

C YA(1,IP1)=0.D0 

 YA(1,IP1)=0.E0 

 XA(2,IP1)=PTFI 

 YA(2,IP1)=P 

 IF(LOWER(I).EQ.0) GO TO 200 

 RA(1,IP1)=R(LOWER(I)) 

 GO TO 210 

 200 CONTINUE 

C RA(1,IP1)=0.D0 

 RA(1,IP1)=0.E0 

 

 210 CONTINUE 

 IF(UPPER(I).EQ.0) GO TO 220 

 

 RA(2,I)=R(UPPER(I)) 

 GO TO 230 

 

 220 CONTINUE 

 

C RA(2,I)=0.D0 

 RA(2,I)=0.E0 

 230 CONTINUE 

 DO 700 K1=L1,L2 

 KMI=K1-IXY 

 KMIABS=IABS(KMI) 

 TARGET=SOURCE+K2+K3*KMI 

 K=KMIABS+1 

 IF(IA.EQ.2) GO TO 235 

 Y1=YA(2,K) 

 R2=RA(2,K) 

 K4=KMIABS 

 GO TO 238 

 235 CONTINUE 

 IF(R(SOURCE).LE.R(LOWER(1)).AND. 

 * R(LOWER(KMIABS-1)).GE.R(TARGET)) GO TO 700 

 

C Y1=0.D0 

 

 Y1=0.E0 

 

 R2=R(TARGET) 

 K4=KMIABS-1 

 238 CONTINUE 

 X1=XA(2,K) 

 FKMI=KMIABS-1 

C DIAG=FKMI**2+1.D0 

 DIAG=FKMI**2+1.E0 
C-23

C RR12=1.D0/(P*DSQRT(DIAG)) 

 RR12=1.E0/(P* SQRT(DIAG)) 

 

 TEMP=P*SQRT((FLOAT(KMIABS))**2+1.) 

 

 RIJ(SOURCE,TARGET)=TEMP-0.5*(R(SOURCE)+R(TARGET)) 

C I1=RDELT*(PI-DARCOS((R1+R2)*RR12)-DATAN2(1.D0,FKMI)) 

 I1=RDELT*(PI- ACOS((R1+R2)*RR12)- ATAN2(1.E0,FKMI)) 

 240 CONTINUE 

C COMPUTE VIEW FACTOR 

 VIEWFC=0. 

 DO 500 IPT=I1,NPT 

 XIPT = IPT - 1 

 THETA = DELTA * XIPT 

C XV=-R1*DCOS(THETA) 

 XV=-R1* COS(THETA) 

C YV=R1*DSIN(THETA) 

 YV=R1* SIN(THETA) 

C DETERMINE IF (XV,YV) CAN SEE THE TARGET ROD 

 

 IF(XV*X1+YV*Y1.LE.R1*(R1-R2)) GO TO 500 

 

C TS IS THE TANGENT TO THE SOURCE ROD AT (XV,YV) 

C TS=DATAN2(-XV,YV) 

 TS= ATAN2(-XV,YV) 

C COMPUTE TANGENTS TO TARGET ROD 

C T1 IS THE LOWER TANGENT TO THE TARGET ROD 

C T2 IS THE UPPER TANGENT TO THE TARGET ROD 

 X1MXP=X1-XV 

 Y1MYP=Y1-YV 

 RSQ=X1MXP**2+Y1MYP**2 

 

C S=DSQRT(RSQ-R2**2) 

 

 S= SQRT(RSQ-R2**2) 

C RRSQ=1.D0/RSQ 

 RRSQ=1.E0/RSQ 

 SORSQ=S*RRSQ 

 R1ORSQ=R2*RRSQ 

 

 A=SORSQ*X1MXP 

 

 B=R1ORSQ*Y1MYP 

 C=SORSQ*Y1MYP 

 D=R1ORSQ*X1MXP 

 XTAMXP=S*(A-B) 

 YTAMYP=S*(C+D) 

 

 XTBMXP=S*(A+B) 

 

 YTBMYP=S*(C-D) 

 

C T2=DATAN2(YTAMYP,XTAMXP) 

 T2= ATAN2(YTAMYP,XTAMXP) 

C T1=DATAN2(YTBMYP,XTBMXP) 
C-24

 T1= ATAN2(YTBMYP,XTBMXP) 

 

C COMPUTE TANGENTS THROUGH (XV,YV) TO SHADOWING RODS 

 

C FIND MINIMUM UPPER SHADOWING AND MAXIMUM LOWER SHADOWING 

 DO 300 J=1,2 

 

 DO 300 I=1,K4 

 

 RB=RA(J,I+2-J) 

 IF(RB.EQ.0.) GO TO 300 

 XB=XA(J,I+2-J) 

 YB=YA(J,I+2-J) 

 X1MXP=XB-XV 

 Y1MYP=YB-YV 

 RSQ=X1MXP**2+Y1MYP**2 

C S=DSQRT(RSQ-RB**2) 

 

 S= SQRT(RSQ-RB**2) 

 

 IF(S.EQ.0.) GO TO 260 

C RRSQ=1.D0/RSQ 

 RRSQ=1.E0/RSQ 

 SORSQ=S*RRSQ 

 R1ORSQ=RB*RRSQ 

 A=SORSQ*X1MXP 

 B=R1ORSQ*Y1MYP 

 C=SORSQ*Y1MYP 

 D=R1ORSQ*X1MXP 

 

 IF(J.EQ.2) GO TO 250 

 

C UPPER TANGENTS TO LOWER SHADOWING RODS 

 XTAMXP=S*(A-B) 

 YTAMYP=S*(C+D) 

 TA=DATAN2(YTAMYP,XTAMXP) 

c TA= ATAN2(YTAMYP,XTAMXP) 

 T1=DMAX1(TA,T1) 

c T1=AMAX1(TA,T1) 

 GO TO 300 

 

 250 CONTINUE 

C LOWER TANGENTS TO UPPER SHADOWING RODS 

 XTBMXP=S*(A+B) 

 YTBMYP=S*(C-D) 

 TB=DATAN2(YTBMYP,XTBMXP) 

c TB= ATAN2(YTBMYP,XTBMXP) 

 T2=DMIN1(TB,T2) 

c T2=AMIN1(TB,T2) 

 GO TO 300 

260 CONTINUE 

 

 IF(J.EQ.2) GO TO 270 

 

 T1=DMAX1(PIO2,T1) 
C-25

c T1=AMAX1(PIO2,T1) 

 GO TO 300 

 270 CONTINUE 

 T2=DMIN1(0.D0,T2) 

c T2=AMIN1(0.E0,T2) 

 300 CONTINUE 

 IF (T1 .GE. T2) GO TO 490 

 IF (T1 .LT. TS .OR. T1 .GE. TS + PI) GO TO 320 

 PHI1 = T1 - TS 

 GO TO 350 

 320 CONTINUE 

 PHI1 = 0. 

 IF (T1 .GE. TS) PHI1 = PI 

 350 CONTINUE 

 IF (T2 .LT. TS .OR. T2 .GE. TS + PI) GO TO 370 

 

 PHI2 = T2 - TS 

 

 GO TO 380 

 370 CONTINUE 

 PHI2 = 0. 

 IF (T2 .GE. TS) PHI2 = PI 

 380 CONTINUE 

C CONFIG=.5D0*(DCOS(PHI1)-DCOS(PHI2)) 

 CONFIG=.5E0*( COS(PHI1)- COS(PHI2)) 

 VIEWFC=VIEWFC+CONFIG 

 GO TO 500 

 490 CONTINUE 

 IF(VIEWFC.NE.0.) GO TO 510 

 500 CONTINUE 

 510 CONTINUE 

 IF(IA.EQ.1) GO TO 550 

 IF(K5.EQ.1) GO TO 540 

 FSAVE=VIEWFC 

 K5=K5+1 

 DO 530 I=1,K4 

 IF(IYX.EQ.1) GO TO 520 

 UPPER(I+1)=LOWER(I)-I3 

 RA(2,I+1)=R(UPPER(I+1)) 

 GO TO 530 

 520 CONTINUE 

C RA(2,I+1)=0.D0 

 RA(2,I+1)=0.E0 

 

530 CONTINUE 

 

 GO TO 240 

 540 CONTINUE 

 VIEWFC=VIEWFC+FSAVE 

 K5=0 

 DO 545 I=1,K4 

 IF(IYX.EQ.L) GO TO 542 

 UPPER(I+1)=LOWER(I)+I3 

 RA(2,I+1)=R(UPPER(I+1)) 

 GO TO 545 
C-26

 542 CONTINUE 

C RA(2,I+1)=0.D0 

 RA(2,I+1)=0.E0 

 545 CONTINUE 

 550 CONTINUE 

 F(SOURCE,TARGET)=VIEWFC*RNPT 

 700 CONTINUE 

 RETURN 

 END 

c 

C****** PATHLEN 12/14/78 D.R.EVANS 

 

 SUBROUTINE PATHLEN(R,DELTAX,P,N2,L) 

 

 implicit double precision (a-h,o-z) 

 DIMENSION F(15),R(1) 

 

 COMMON /RI/ RIJ(1001,1001) 

 

 INTEGER SOURCE 

 REAL L1,L2,L3,L4 

 

 DATA F/0.5,0.086740,0.013966,0.001517,0.000424,0.000172, 

 

 1 0.000088,0.000048,0.000034,6*0./ 

C COMPUTE PATH LENGTHS FROM RODS TO CANISTER 

 DO 100 IX=1,L 

 DO 100 IY=1,L 

 SOURCE=IY+(IX-1)*L 

 HALFR1=0.5*R(SOURCE) 

C PATH OND 

 L1=P*FLOAT(IX-1)+DELTAX-HALFR1 

C PATH TWO 

 L2=P*FLOAT(L-IX)+DELTAX-HALFR1 

C PATH THREE 

 L3=P*FLOAT(IY-1)+DELTAX-HALFR1 

C PATH FOUR 

 

 L4=P*FLOAT(L-IY)+DELTAX-HALFR1 

 

C PATH LENGTH IS THE VIEW-FACTOR-WEIGHTED MEAN OF FOUR 

C CONTRIBUTIONS 

 RIJ(SOURCE,N2)=(L1*F(IX) 

 1 +L2*F(L-IX+1) 

 2 +L3*F(IY) 

 3 +L4*F(L-IY+1)) / 

 4 (F(IX) 

 5 +F(L-IX+1) 

 6 +F(IY) 

 7 +F(L-IY+1)) 

100 CONTINUE 

 

 RETURN 

 

 END 
C-27

c 

C****** STRING 12/12/78 D.R.EVANS 

 

 SUBROUTINE STRING(F,R,P,PI,M,L,SOURCE,IX,IY) 

 

 implicit double precision (a-h,o-z) 

 DIMENSION F(M,1),R(1) 

 COMMON /RI/ RIJ(1001,1001) 

 DIMENSION TIN(1000,4),THET(1000,4),TEX(1000,2),ALPH(1000,2) 

 INTEGER SOURCE,TARGET 

 LOGICAL SKIP 

 DATA SKIP/.FALSE./,PP/0./ 

 IF(SKIP) GO TO 10 

 SKIP=.TRUE. 

C RPI=1.D0/PI 

 RPI=1.E0/PI 

C PIO2=.5D0*PI 

 PIO2=.5E0*PI 

C PIO4=.5D0*PIO2 

 PIO4=.5E0*PIO2 

 10 CONTINUE 

 IF(PP.EQ.P) GO TO 20 

 PP=P 

 PSQ=P**2 

C R13SQ=2.D0*PSQ 

 R13SQ=2.E0*PSQ 

C RR13=1.D0/DSQRT(R13SQ) 

 RR13=1.E0/ SQRT(R13SQ) 

C RP=1.D0/P 

 

 RP=1.E0/P 

 

 20 CONTINUE 

 

C COMPUTE TANGENT LENGTHS AND ANGLES FOR CROSSED STRING METHOD 

 

 IF(IX.GT.1.OR.IY.EQ.L) GO TO 145 

 

 J1=SOURCE 

 J2=SOURCE+L-2 

 DO 140 I=J1,J2 

 R1=R(I) 

 R2=R(I+1) 

 R3=R(I+1+L) 

 R4=R(I+L) 

 R2MR3=R2-R3 

 

 R4MR3=R4-R3 

 

C TIN13=DSQRT(R13SQ-(R1+R3)**2) 

 

 TIN13= SQRT(R13SQ-(R1+R3)**2) 

C TIN23=DSQRT(PSQ-(R2+R3)**2) 

 TIN23= SQRT(PSQ-(R2+R3)**2) 

C TIN34=DSQRT(PSQ-(R3+R4)**2) 
C-28

 TIN34= SQRT(PSQ-(R3+R4)**2) 

C TIN24=DSQRT(R13SQ-(R2+R4)**2) 

 TIN24= SQRT(R13SQ-(R2+R4)**2) 

 TIN(I,2)=TIN13 

 TIN(I+1,3)=TIN23 

 TIN(I+L,1)=TIN34 

 TIN(I+1,4)=TIN24 

C THET(I,2)=DARSIN(TIN13*RR13) 

 THET(I,2)= ASIN(TIN13*RR13) 

C THET(I+1,3)=DARSIN(TIN23*RP) 

 THET(I+1,3)= ASIN(TIN23*RP) 

C THET(I+L,1)=DARSIN(TIN34*RP) 

 THET(I+L,1)= ASIN(TIN34*RP) 

C THET(I+1,4)=DARSIN(TIN24*RR13) 

 THET(I+1,4)= ASIN(TIN24*RR13) 

 IF(R2MR3.EQ.0.) GO TO 100 

C ALPH(I+1,2)=DARCOS(R2MR3*RP) 

 

 ALPH(I+1,2)= ACOS(R2MR3*RP) 

 

C TEX(I+1,2)=DSQRT(PSQ-R2MR3**2) 

 TEX(I+1,2)= SQRT(PSQ-R2MR3**2) 

 GO TO 105 

 100 CONTINUE 

 ALPH(I+1,2)=PIO2 

 TEX(I+1,2)=P 

 105 CONTINUE 

 IF(R4MR3.EQ.0.) GO TO 110 

C ALPH(I+L,1)=DARCOS(R4MR3*RP) 

 ALPH(I+L,1)= ACOS(R4MR3*RP) 

C TEX(I+L,1)=DSQRT(PSQ-R4MR3**2) 

 TEX(I+L,1)= SQRT(PSQ-R4MR3**2) 

 GO TO 115 

 110 CONTINUE 

 ALPH(I+L,1)=PIO2 

 TEX(I+L,1)=P 

 115 CONTINUE 

 IF(I.GT.J1) GO TO 130 

 R1MR4=R1-R4 

C TIN14=DSQRT(PSQ-(R1+R4)**2) 

 TIN14= SQRT(PSQ-(R1+R4)**2) 

 TIN(I,3)=TIN14 

C THET(I,3)=DARSIN(TIN14*RP) 

 THET(I,3)= ASIN(TIN14*RP) 

 IF(R1MR4.EQ.0.) GO TO 120 

 

C ALPH(I,2)=DARCOS(R1MR4*RP) 

 

 ALPH(I,2)= ACOS(R1MR4*RP) 

C TEX(I,2)=DSQRT(PSQ-R1MR4**2) 

 TEX(I,2)= SQRT(PSQ-R1MR4**2) 

 GO TO 125 

 120 CONTINUE 

 ALPH(I,2)=PIO2 

 TEX(I,2)=P 
 125 CONTINUE 

 130 CONTINUE 

 IF(IY.GT.1) GO TO 140 

 R1MR2=R1-R2 

C TIN12=DSQRT(PSQ-(R1+R2)**2) 

 TIN12= SQRT(PSQ-(R1+R2)**2) 

 TIN(I,1)=TIN12 

C THET(I,1)=DARSIN(TIN12*RP) 

 THET(I,1)= ASIN(TIN12*RP) 

 IF(R1MR2.EQ.0.) GO TO 135 

C ALPH(I,1)=DARCOS(R1MR2*RP) 

 ALPH(I,1)= ACOS(R1MR2*RP) 

C TEX(I,1)=DSQRT(PSQ-R1MR2**2) 

 TEX(I,1)= SQRT(PSQ-R1MR2**2) 

 GO TO 140 

 135 CONTINUE 

 ALPH(I,1)=PIO2 

 TEX(I,1)=P 

 

 140 CONTINUE 

 

 145 CONTINUE 

C COMPUTE ADJACENT AND DIAGONAL ROD VIEW FACTORS 

C USING CROSSED STRING METHOD 

C COMPUTE ADJACENT ROD VIEW FACTORS 

 R1=R(SOURCE) 

 DO 150 I=1,2 

 IF(IX.EQ.L.AND.I.EQ.1) GO TO 150 

 IF(IY.EQ.L.AND.I.EQ.2) GO TO 150 

 TARGET=SOURCE+L**(I-1) 

 R2=R(TARGET) 

 CROLEN=TIN(SOURCE,2**I-1)+R1*ALPH(SOURCE,I) 

D +R2*(PI-ALPH(SOURCE,I))-(R1+R2)*THET(SOURCE,2**I-1) 

 

 CROMUN=CROLEN-TEX(SOURCE,I) 

 

C F(SOURCE,TARGET)=.5D0*RPI*CROMUN/R1 

 F(SOURCE,TARGET)=.5E0*RPI*CROMUN/R1 

 RIJ(SOURCE,TARGET)=P-0.5*(R1+R2) 

 IF(IY.NE.IX) GO TO 150 

 

 F(SOURCE,SOURCE+L)=F(SOURCE,TARGET) 

 

 RIJ(SOURCE,SOURCE+L)=RIJ(SOURCE,TARGET) 

 GO TO 152 

 150 CONTINUE 

 

 152 CONTINUE 

 IF(IY.EQ.L) GO TO 190 

C COMPUTE DIAGONAL ROD VIEW FACTORS 

 DO 185 I=1,2 

 IF(IX.EQ.1.AND.I.EQ.1) GO TO 185 

 IF(IX.EQ.L.AND.I.EQ.2) GO TO 185 

 MORP1=(-1)**I 

C-29

 M1ORZ=I-2 
C-30

 TARGET=SOURCE+L+MORP1 

 R2=R(SOURCE+MORP1) 

 R3=R(TARGET) 

 R4=R(SOURCE+L) 

 TIN12=TIN(SOURCE+M1ORZ,1) 

 THET12=THET(SOURCE+M1ORZ,1) 

 TIN13=TIN(SOURCE,2**(3-I)) 

 THET13=THET(SOURCE,2**(3-I)) 

 TIN14=TIN(SOURCE,3) 

 THET14=THET(SOURCE,3) 

 TIN23=TIN(SOURCE+MORP1,3) 

 THET23=THET(SOURCE+MORP1,3) 

 TIN34=TIN(SOURCE+L+M1ORZ,1) 

 THET34=THET(SOURCE+L+M1ORZ,1) 

 PSI2=PIO2-THET12-THET23 

 PSI4=PIO2-THET14-THET34 

 IF(PSI2.GT.0.) GO TO 155 

 

 R1MR3=R1-R3 

C ALPH31=DARCOS(R1MR3*RR13) 

 ALPH31= ACOS(R1MR3*RR13) 

 PSI312=ALPH31-THET13 

 PSI132=PI-ALPH31-THET13 

C TIN12=DSQRT(R13SQ-R1MR3**2) 

 TIN12= SQRT(R13SQ-R1MR3**2) 

C TIN23=0.D0 

 TIN23=0.E0 

C PSI2=0.D0 

 PSI2=0.E0 

 GO TO 160 

 155 CONTINUE 

 PSI312=PIO4+THET12-THET13 

 PSI132=PIO4+THET23-THET13 

160 CONTINUE 

 

 IF(PSI4.GT.0.) GO TO 175 

 

 IF(PSI2.LE.0.) GO TO 165 

 R1MR3=R1-R3 

C ALPH31=DARCOS(R1MR3*RR13) 

 ALPH31= ACOS(R1MR3*RR13) 

 PSI314=ALPH31-THET13 

 PSI134=PI-ALPH31-THET13 

C TIN14=DSQRT(R13SQ-R1MR3**2) 

 TIN14= SQRT(R13SQ-R1MR3**2) 

 GO TO 170 

 

 165 CONTINUE 

 PSI314=PSI312 

 PSI134=PSI132 

 TIN14=TIN12 

 170 CONTINUE 

C TIN34=0.D0 

 TIN34=0.E0 

C PSI4=0.D0 
C-31

 PSI4=0.E0 

 GO TO 180 

 175 CONTINUE 

 PSI314=PIO4+THET14-THET13 

 

 PSI134=PIO4+THET34-THET13 

 

 180 CONTINUE 

C CROLEN=2.D0*TIN13+R1*(PSI312+PSI314)+R3*(PSI132+PSI134) 

 CROLEN=2.E0*TIN13+R1*(PSI312+PSI314)+R3*(PSI132+PSI134) 

 UNCLEN=TIN12+TIN23+TIN34+TIN14+R2*PSI2+R4*PSI4 

 CROMUN=CROLEN-UNCLEN 

C F(SOURCE,TARGET)=.25D0*RPI*CROMUN/R1 

 F(SOURCE,TARGET)=.25E0*RPI*CROMUN/R1 

 RIJ(SOURCE,TARGET)=SQRT(R13SQ)-0.5*(R1+R3) 

 185 CONTINUE 

 190 CONTINUE 

 RETURN 

 END 

c 

C****** VFAC 12/12/78 D.R.EVANS 

 

 SUBROUTINE VFAC(F,AREA,E,SCALFC,B,R0,IROW,JCOL,MIRRIM,P,PI,N, 

1 M,L,N2,NA,NSYM,NL,NL1,NPT) 

 

 implicit double precision (a-h,o-z) 

 DIMENSION F(M,1),AREA(1),E(1),SCALFC(1),B(NA,1),IROW(1), 

 1 JCOL(1),MIRRIM(20,1),R0(1) 

 COMMON /RI/ RIJ(1001,1001) 

 INTEGER ROD,TARGET 

 

 NP=N2-1 

 SL=0.25*AREA(N2) 

 

C SL IS THE DISTANCE BETWEEN OPPOSITE SIDES OF THE CANISTER 

 

 DELTAX=0.5*(SL-P*FLOAT(L-1)) 

 

C DELTAX IS THE DISTANCE FROM THE CENTER OF AN EDGE ROD TO 

 

C THE ADJACENT FACE OF THE CANISTER 

 

C CALCULATE THE PATH LENGTH FROM ROD TO CANISTER 

 

 CALL PATHLEN(R0,DELTAX,P,N2,L) 

 

C 

C GENERATE UPPER DIAGONAL PORTION OF VIEW FACTOR MATRIX 

 

 DO 50 IY=1,L 

 

 IYP2=IY+2 

 

 IYP1=IY+1 

 
C-32

 DO 45 IX=1,L 

 

 IYMIX=IY-IX 

 

 IXP2=IX+2 

 

 ROD=IX+L*(IY-1) 

 

C ZERO OUT MATRIX 

 

 DO 10 KK=ROD,NP 

 F(ROD,KK)=0. 

 RIJ(ROD,KK)=0. 

 10 CONTINUE 

 

C ADJACENT AND DIAGONAL ROD VIEW FACTORS BY CROSSED STRING 

 

C METHOD 

 

 CALL STRING(F,R0,P,PI,M,L,ROD,IX,IY) 

 

 IF(IY.EQ.L) GO TO 40 

 

C MORE-DISTANT VIEW FACTORS BY MODIFIED VIEWPIN METHOD 

C HIGHER-NUMBERED ROWS 

C ADJACENT ROW 

 K1=IX-NL 

 IF(K1.LE.0) K1=1 

 IXM2=IX-2 

 IF(IXM2.LT.K1) GO TO 12 

 CALL FIJ(F,R0,P,PI,M,NPT,L,ROD,IX,IY,K1,IXM2,1,1) 

 12 CONTINUE 

 K2=IX+NL 

 IF(K2.GT.L) K2=L 

 IF(K2.LT.IXP2) GO TO 14 

 

 CALL FIJ(F,R0,P,PI,M,NPT,L,ROD,IX,IY,IXP2,K2,1,1) 

 

 14 CONTINUE 

 IF(IYMIX.NE.0) GO TO 20 

 DO 15 KK=K1,K2 

 IF(KK.LT.IX.OR.KK.EQ.IYP1) GO TO 15 

 TARGET=KK+L*IY 

 ITARG2=IYP1+(KK-1)*L 

 RIJ(ROD,ITARG2)=RIJ(ROD,TARGET) 

 F(ROD,ITARG2)=F(ROD,TARGET) 

 15 CONTINUE 

 20 CONTINUE 

 IF(IYP1.GE.L) GO TO 40 

C ROWS BEYOND ADJACENT ROW 

 K2=IY+NL1 

 IF(K2.GT.L) K2=L 

 

 IF(K2.LT.IYP2) GO TO 24 

 
C-33

 CALL FIJ(F,R0,P,PI,M,NPT,L,ROD,IX,IY,IYP2,K2,1,2) 

 IF(IYMIX.NE.0) GO TO 24 

 DO 21 KK=IYP2,K2 

 TARGET=ROD+(KK-IY)*L 

 ITARG2=ROD+KK-IY 

 F(ROD,ITARG2)=F(ROD,TARGET) 

 21 CONTINUE 

 24 CONTINUE 

 IF(IX.EQ.1) GO TO 34 

C LOWER-NUMBERED ADJACENT COLUMN 

 K2=IY+NL 

 IF(K2.GT.L) K2=L 

 

 IF(K2.LT.IYP2) GO TO 40 

 

 CALL FIJ(F,R0,P,PI,M,NPT,L,ROD,IX,IY,IYP2,K2,3,1) 

 34 CONTINUE 

 IF(IYMIX.EQ.0) GO TO 45 

 IF(IX.EQ.L) GO TO 45 

C HIGHER-NUMBERED COLUMNS 

C ADJACENT COLUMN 

 CALL FIJ(F,R0,P,PI,M,NPT,L,ROD,IX,IY,IYP2,K2,2,1) 

40 CONTINUE 

 

 IF(IX.EQ.L-1) GO TO 45 

 

C COLUMNS BEYOND ADJACENT COLUMN 

 K2=IX+NL1 

 IF(K2.GT.L) K2=L 

 IF(K2.LT.IXP2) GO TO 44 

 CALL FIJ(F,R0,P,PI,M,NPT,L,ROD,IX,IY,IXP2,K2,2,2) 

 44 CONTINUE 

 45 CONTINUE 

 

 50 CONTINUE 

c 

C FILL VIEW FACTOR MATRIX 

 

 DO 225 I=1,NP 

 DO 225 J=I,NP 

 RIJ(J,I)=RIJ(I,J) 

 225 F(J,I)=F(I,J)*AREA(I)/AREA(J) 

 SUMA=1. 

 DO 230 I=1,NP 

 SUM=1. 

 DO 235 J=1,NP 

 235 SUM=SUM-F(I,J) 

 F(I,N2)=SUM 

 RIJ(N2,I)=RIJ(I,N2) 

 

 F(N2,I)=F(I,N2)*AREA(I)/AREA(N2) 

 

 230 SUMA=SUMA-F(N2,I) 

 F(N2,N2)=SUMA 

 RIJ(N2,N2)=0.25*SL 
C-34

c 

 RETURN 

 

 END 

c 

c 

c************************************************ 

c 

 SUBROUTINE INTERP(X,Y,X1,Y1,N) 

c 

 implicit double precision (a-h,o-z) 

c 

 dimension x(100),y(100) 

c 

 DO 100 I=1,n 

 I1=I 

 IF(X(I1)-X1) 100,100,200 

 100 CONTINUE 

 200 Y1=Y(I1-1)+((X1-X(I1-1))/(X(I1)-X(I1-1)))*(Y(I1)-Y(I1-1)) 

 RETURN 

 END 

 
D-1

APPENDIX D1. COBRA-TF LISTINGS 

Introduction

Appendix D2 contains an input listing from the two-channel model of COBRA-TF and associated 

input processing as well as the output for time zero. A full listing of the sub-channel model is 

not given because the listing is too large because the file is too large, instead only the input file 

is given here. 

Appendix D3 contains the input deck for the sub-channel model. 
D-2

APPENDIX D2. TWO-CHANNEL MODEL LISTING 

1********************************* input file listing *********************************  12345678901234567890123456789012345678901234567890123456789012345678901234567890  1 0  2 0 0.0  3 .001 10 40  4 1   RBHT Bundle 7x7 Rods ** **  5 1 1  6 40.0 1170. 0.0 0.466 124. 0.0 .9999 1.0  7 air .0001  8 2 5  9 144.8671.74 0 7.22  10 27.22071.74  11 32.17918.79  12 45.04052.95  13 550.2471.74 7.22 0  14 3 1  15 1 3 41.952 1.38 2.0 0.0 0 0 1.0 0 0  16 16. 0.0  17 0  18 4 4 1 0  19 1 1 2 4.0  20 1 2 1  21 2 1 1 5.75  22 2 3 4 1  23 3 2 22 2.51 10  24 2 2.51 3 7.72 4 7.72 5 7.72 6 6.85  25 20 6.85 21 6.85 22 6.85 22 6.85 23 6.85  26 3 5 2  27 4 5 2  28 4 1 3 4.0  29 5 5 3 4  30 2  12345678901234567890123456789012345678901234567890123456789012345678901234567890  31 50  32 7 8 1 1 1 1 1 0 0 0 
D-3

 33 1.2 2 2 3  34 1.2 5 2 3  35 1.2 8 2 3  36 1.2 11 2 3  37 1.2 14 2 3  38 1.2 17 2 3  39 1.2 20 2 3  40 1.2 23 2 3  41 1 8 2 1 1.4 .2952 1.5 1.984  42 2 5 8 11 14 17 20 23  43 3 16. 1 1  44 4 33. 2 1  45 8 3 1 2 2 0 0 0 1  46 1 1 1 2 0.05 16. 1.0 5000. 1 

 47 3 1.0  48 2 1 1 2 0.05 29.0 1.0 5000. 1  49 4 1.0  50 3 2 0 2 0.05 4. 0.0 5000. 1  51 4 1.0  52 1 3 14.20 14.20 1.0 4 0. 90.0  53 1 2 0 4  54 1 2  55 13.75 521.0 121.75 1563. 157.75 502.0 169.76 502.0  56 2 1 1 2  57 3  58 -1  59 13.75 521.0 169.0 521.  60 9 3  12345678901234567890123456789012345678901234567890123456789012345678901234567890  61 1 hrod .374 0.0 4 0  62 1 2.0685 0.0 1 3 .044 1.0 3 2.0545 0.0 3 1 .02 0.0  63 2 tube .374 .209 1 0  64 3 1.0825 0.0  65 3 wall 14.20 .250 1 0  66 3 1 .250  67 10 3  68 1 17 516.7  69 32. .1010 8.1400 70. .1030 8.340  70 212. .1110 9.090 392. .1210 10.04 
D-4

 71 500. .1270 10.60 572. 0.131 10.98  72 752. .1410 11.93 932. 0.151 12.88  73 1000. 0.158 13.23 1112. 0.166 13.82  74 1292. 0.178 14.77 1472. 0.191 15.72  75 1500. 0.193 15.86 1652. 0.204 16.66  76 1832. 0.216 17.61 2012. 0.229 18.56  77 2192. 0.241 19.50  78 2 14 119.  79 212. .16587 67.37 392. .22014 63.827  80 572. .26263 60.28 752. .29590 56.737  81 932. .32194 53.19 1112. .34233 49.646  82 1292. .35829 46.10 1472. .37078 42.555  83 1652. .38056 39.01 1832. .38822 35.464  84 2012. .39421 31.92 2192. .39891 28.375  85 2372. .40259 24.83 2552. .40546 21.284  86 3 10 528.8  87 70.0 .10000 10.083 200. 0.107 11.333  88 400. .11400 13.00 600. 0.117 14.833  89 800. .120 16.50 1000. 0.125 18.333  90 1200. .132 20.00 1400. 0.141 21.833  12345678901234567890123456789012345678901234567890123456789012345678901234567890  91 1600. 0.157 23.50 1800. 0.186 25.167  92 11 1 25  93 1 5  94 13.75 0.5 121.75 1.50 157.75 0.5 157.76 0.0  95 168.0 0.0  96 0.0 1. 17.5 .921 35.0 .8704 52.5 .8326  97 70. .803 87.5 .7755 105.0 .7512 122.5 .7302  98 140. .714 157.5 .6973 175.0 .6837 192.5 .6710  99 220. .652 255.0 .6332 290.0 .6167 325.0 .6017  100 360. .588 395.0 .5769 430.0 .5656 465.0 .5562  101 500. .547 535.0 .5444 570.0 .5304 605.0 .5243  102 1000. .002  103 13 2 0 2 0 0  104 3 3  105 0.0 0.0 0.1 .801500. .80  106 0.0 1.0 0.2 1.01500. 1.0  107 1 1 2 1 0 .260 92.05 40.0  108 124. 1.0.9999.0001 
D-5

 109  110 5 5 1 0 0 40.0 1170.0 40.0  111 124. 1.0.9999.0001  112  113 14 5 0 0 0 0 1 2  114 0  115 0  116  117 500 0 0  118 .0002 .015 500. 1.0 99999.  119 5. 1. 800. 800.  120 -.001 .005 5.0 1.0 200.  12345678901234567890123456789012345678901234567890123456789012345678901234567890  121 10. 10. 500. 500.  122  123  124  125  126  127  128  129 1  cobra_tf date 19980803 time 00:00:00 1 main control parameters are:  restart time step . . . . . . . . . . . 0  simulation start time . . . . . . . . . .000  outer iteration convergence limit . . . .0010000  maximum number of inner iterations . . 40  maximum number of outer iterations . . 10  1 1 0 0 0 0 0 0 0 0 0  2 5 0 0 0 0 0 0 0 0 0  3 1 0 0 0 0 0 0 0 0 0  4 4 1 0 0 0 0 0 0 0 0  7 8 1 1 1 1 1 0 0 0 0  8 3 1 2 2 0 0 0 1 0 0  9 3 0 0 0 0 0 0 0 0 0 
D-6

 10 3 0 0 0 0 0 0 0 0 0  11 1 25 0 0 0 0 0 0 0 0  13 2 0 2 0 0 0 0 0 0 0  14 5 0 0 0 0 1 2 0 0 0  0 0 0 0 0 0 0 0 0 0 0 1 input summary    Test 31504 Bundle Rod 7x7 ** **  general information  ******************* 0 initial system operating pressure (psi) . . . 40.00000  initial system steam/water enthalpy . . . . .1170.00000  initial noncondensable gas enthalpy . . . . . 124.00000  initial liquid volume fraction . . . . . .00000  mass flux for initialization (lb/ft**2-sec) . . .00000  average linear heat rate (kw/ft) . . . . . . . .46600  total axial length (inches). . . . . . . . . . 174.71997  total no. of axial nodes . . . . . . . . . . . 28 1  initial volume fractions of vapor and noncondensable gases 1  100.00000 percent of the total system volume is initially filled with vapor and/or noncondensable gases. the fracti of this gas volume occupied by water vapor and each noncondensable gas is as follows:  steam .9999 air .00010 1  subchannel data  nominal wetted momentum momentum axial variation tables  subchannel channel area perimeter area area continuity momentum wetted  id. no. (in**2) (in.) (bottom) (top) area area perimeter  ---------------------------------------------------------------------------------------------------- 
D-7

 1 44.8600 71.740 44.8600 7.2200 0 0 0  2 7.2200 71.740 7.2200 7.2200 0 0 0  3 2.1790 18.790 2.1790 2.1790 0 0 0  4 5.0400 52.950 5.0400 5.0400 0 0 0  5 50.2400 71.740 7.2200 50.2400 0 0 0 0 1 ************************************************************************************************************************  grid spacer data  model selection grid quench front heat transfer to fluid 1  (0=off,1=on) drop breakup at grid spacer 1  grid enhancement of single phase vapor convection 1  grid type 1 material type index, 1  grid length [in] 1.500  grid perimeter [in] 1.984  fraction of channel blocked .295  loss coefficient multiplier 1.400  axial levels containing grid type 1  2 5 8 11 14 17 20 23  grid located no. of grids fuel rod - surface index pairs surrounding grid  in channel in channel  ------------ ------------ ------------------------------------------------------------------  3 16.000 1 - 1 0 - 0 0 - 0 0 - 0 0 - 0 0 - 0  4 33.000 2 - 1 0 - 0 0 - 0 0 - 0 0 - 0 0 - 0 0 0 data for lateral momentum convected by axial velocities at section boundries  channel node gap gap area node gap gap area node gap gap area node gap gap ar no. no. below above no. below above no. below above no. below above 
D-8

0  ***************************************************************************************************************************** channel thermal connection input data  -------------------------------------  channel no. fuel rod - surface index pairs heat slab indices  ----------- ------------------------------------------------------------ ----------------------------------------  3 1 - 1 0 - 0 0 - 0 0 - 0 0 - 0 0 - 0 0 0 0 0 0 0 0 0  4 2 - 1 3 - 1 0 - 0 0 - 0 0 - 0 0 - 0 -1 0 0 0 0 0 0 0  ***************************************************************************************************************************** 0  gap data  gap gap centroid loss frict. gap gap sign gaps which face this gap variation  no. ik jk width distance coeff. flag below above modifier ii side jj side table  1 3 4 1.952 1.380 2.000 .00 0 0 1.000 0 0 0 0 0 0 0 1  channel splitting data - axial level 1 of 4  number no. of cell length  of channels nodes (nominal)  1 2 .3333  channel channels above channels below  ---------------------------- ----------------------------  1 2 0 0 0 0 0 1 0 0 0 0 0 1  channel splitting data - axial level 2 of 4 
D-9

 number no. of cell length  of channels nodes (nominal)  1 1 .4792  channel channels above channels below  ---------------------------- ----------------------------  2 3 4 0 0 0 0 1 0 0 0 0 0  variable axial noding  ---------------------  node length node length node length node length node length  no. (ft) no. (ft) no. (ft) no. (ft) no. (ft)  ---- ------ ---- ------ ---- ------ ---- ------ ---- ------  2 .4792 1  channel splitting data - axial level 3 of 4  number no. of cell length  of channels nodes (nominal)  2 22 .5643  channel channels above channels below  ---------------------------- ----------------------------  3 5 0 0 0 0 0 2 0 0 0 0 0  4 5 0 0 0 0 0 2 0 0 0 0 0  variable axial noding  ---------------------  node length node length node length node length node length  no. (ft) no. (ft) no. (ft) no. (ft) no. (ft)  ---- ------ ---- ------ ---- ------ ---- ------ ---- ------  2 .2092 3 .6433 4 .6433 5 .6433 6 .5708  7 .5708 8 .5708 9 .5708 10 .5708 11 .5708  12 .5708 13 .5708 14 .5708 15 .5708 16 .5708  17 .5708 18 .5708 19 .5708 20 .5708 21 .5708 
D-10

 22 .5708 23 .5708 1  channel splitting data - axial level 4 of 4  number no. of cell length  of channels nodes (nominal)  1 3 .3333  channel channels above channels below  ---------------------------- ----------------------------  5 5 0 0 0 0 0 3 4 0 0 0 0  variable axial noding  ---------------------  node length node length node length node length node length  no. (ft) no. (ft) no. (ft) no. (ft) no. (ft)  ---- ------ ---- ------ ---- ------ ---- ------ ---- ------  2 .3333 3 .3333 4 .3333  simultaneous solution group information  no. of last cell number in each group  groups  1 50 1  *****************************************************************************************************************************  fuel rod and heat slab model input  no. of fuel rods = 3 no. of fuel rod surfaces = 3  no. of heat slabs = 1  *****************************************************************************************************************************  fuel rod model input 
D-11

 fuel rod axial location geometry conductor radial power axial power renoding minimum r index (in.) - ( in.) type type factor profile flag node size multiplier  -------- ------------ -- -------- --------- ------------ ----------- -------- --------- ----------  1 13.75 - 162.72 hrod 1 1.000 1 2 .0500 16.000  2 13.75 - 162.72 hrod 1 1.000 1 2 .0500 29.000  3 13.75 - 162.72 tube 2 .000 0 2 .0500 4.000  heat slab model input  heat slab ch annel connection - heated perimeter geometry conductor slab  index inside outside type type multiplier  --------- ------------ ------------- -------- --------- ----------  1 4 - 14.20 0 - 14.20 wall 3 1.000  ----------------------------------------------------------------------------------------------------------------------------- 

 conductor geometry description 

 no. of geometry types = 3  -----------------------------------------------------------------------------------------------------------------------------  type 1 - hrod cylindrical heater rod ----------------------------------------------------------------------------  rod diameter .3740 (in.)  inside diameter .0000 (in.)  no. of nodes (total) 8  material index (oxide) 0  radial noding information  node material radial node boundaries power  no. index location (inside) (outside) fraction  ---- -------- -------- -------- --------- --------  1 2 .0484 .0000 .0685 .00000  2 3 .0931 .0685 .1125 1.00000 
D-12

 3 2 .1219 .1125 .1307 .00000  4 2 .1400 .1307 .1488 .00000  5 2 .1582 .1488 .1670 .00000  6 1 .1710 .1670 .1750 .00000  7 1 .1790 .1750 .1830 .00000  8 1 .1870 .1830 .1870 .00000  type 2 - tube tube conductor geometry --------------------------------------------------------------------------- 

 outside diameter .3740 (in.)  inside diameter .2090 (in.)  no. of nodes (total) 3  material index (inside) 0  material index (outside) 0  radial noding information  node material radial node boundaries power  no. index location (inside) (outside) fraction  ---- -------- -------- -------- --------- --------  1 1 .1045 .1045 .1251 .00000  2 1 .1472 .1251 .1664 .00000  3 1 .1870 .1664 .1870 .00000  type 3 - wall flat plate conductor geometry --------------------------------------------------------------------- 

 wall perimeter 14.2000 (in.)  wall thickness .2500 (in.)  no. of nodes (total) 3  material index (inside) 0  material index(outside) 0  radial noding information  node material radial node boundaries power  no. index location (inside) (outside) fraction  ---- -------- -------- -------- --------- --------  1 1 .0000 .0000 .0625 .00000  2 1 .1250 .0625 .1875 .00000 
D-13

 3 1 .2500 .1875 .2500 .00000  ------------------------------------------------------------------------------------------------------------------------  material property tables  ------------------------  material type - 1 cold state density = 516.700 (lbm/ft3)  temperature (f) specific heat (btu/lbm-f) conductivity (btu/hr-ft-f)  32.0 .10100 8.140  70.0 .10300 8.340  212.0 .11100 9.090  392.0 .12100 10.040  500.0 .12700 10.600  572.0 .13100 10.980  752.0 .14100 11.930  932.0 .15100 12.880  1000.0 .15800 13.230  1112.0 .16600 13.820  212.0 .16587 67.370  392.0 .22014 63.827  572.0 .26263 60.280  752.0 .29590 56.737  932.0 .32194 53.190  1112.0 .34233 49.646  1292.0 .35829 46.100  material type - 2 cold state density = 119.000 (lbm/ft3)  temperature (f) specific heat (btu/lbm-f) conductivity (btu/hr-ft-f)  212.0 .16587 67.370  392.0 .22014 63.827  572.0 .26263 60.280  752.0 .29590 56.737  932.0 .32194 53.190 
D-14

 1112.0 .34233 49.646  1292.0 .35829 46.100  1472.0 .37078 42.555  1652.0 .38056 39.010  1832.0 .38822 35.464  70.0 .10000 10.083  200.0 .10700 11.333  400.0 .11400 13.000  600.0 .11700 14.833  material type - 3 cold state density = 528.800 (lbm/ft3)  temperature (f) specific heat (btu/lbm-f) conductivity (btu/hr-ft-f)  70.0 .10000 10.083  200.0 .10700 11.333  400.0 .11400 13.000  600.0 .11700 14.833  800.0 .12000 16.500  1000.0 .12500 18.333  1200.0 .13200 20.000  1400.0 .14100 21.833  1600.0 .15700 23.500  1800.0 .18600 25.167  ------------------------------------------------------------------------------------------------------------------------  axial power profile tables  --------------------------  axial profile no. 1 - used by rod nos. = 1 2  rod node no. axial location (in.) fluid node no. axial power factor  ------------ -------------------- -------------- ------------------  1 13.75 5 .5029  2 15.01 5 .5145  3 20.12 6 .5590  4 27.84 7 .6305  5 35.56 8 .7019 
D-15

 6 42.84 9 .7694  7 49.69 10 .8328  8 56.54 11 .8962  9 63.39 12 .9597  10 70.24 13 1.0231  11 77.09 14 1.0865  12 83.94 15 1.1500  13 90.79 16 1.2134  14 97.64 17 1.2768  15 104.49 18 1.3402  16 111.34 19 1.4037  17 118.19 20 1.4671  18 125.04 21 1.4084  19 131.89 22 1.2182  20 138.74 23 1.0279  21 145.59 24 .8376  22 152.44 25 .6474  23 159.29 26 .1930  24 162.72 26 .0000  this table integrates to .9689 over a heated length of 148.97 (in.)  ------------------------------------------------------------------------------------------------------------------------  power forcing function table  ----------------------------  transient time (secs) power factor  --------------------- ------------  .0000 1.0000  17.5000 .9210  35.0000 .8704  52.5000 .8326  70.0000 .8030  87.5000 .7755  105.0000 .7512  122.5000 .7302  140.0000 .7140  157.5000 .6973  175.0000 .6837 
D-16

 192.5000 .6710  220.0000 .6520  255.0000 .6332  290.0000 .6167  325.0000 .6017  360.0000 .5880  395.0000 .5769  430.0000 .5656  465.0000 .5562  500.0000 .5470  535.0000 .5444  570.0000 .5304  605.0000 .5243  1000.0000 .0020  ------------------------------------------------------------------------------------------------------------------------ 1 forcing function tables 0 table 1  time forcing time forcing time forcing time forcing time forcing  coord. factor coord. factor coord. factor coord. factor coord. factor  .000 .000 .100 .800 1500.000 .800 0 table 2  time forcing time forcing time forcing time forcing time forcing  coord. factor coord. factor coord. factor coord. factor coord. factor  .000 1.000 .200 1.000 1500.000 1.000 1 axial and/or injection boundary conditions  boundary type property specification  -------------------------------- ----------------------  1= pressure and enthalpy (axial) . . . . . . . pressure  2= flow and ehthalpy (axial) . . . . . . . . . mass flow 
D-17

 3= zero axial flow . . . . . . . . . . . . . . zero  4= injected flow and enthalpy . . . . . . . . injected flow  5= pressure sink and enthalpy . . . . . . . . sink pressure  boundary specified  channel axial type property  index node (see above) (see above) enthalpy  1 1 2 .26 92.05  5 5 1 40.00 1170.00 0  zero crossflow boundary conditions  gap axial  index node  5 channels will be printed  1 2 3 4 5 0 3 rods will be printed  1 2 3 0 1 gaps will be printed  1 0 ***** graphics dump data ******************************************************************************************  initial run  maximum number of graphics (check against dimension of indcmp array --  dumps . . . . . . . . . . . . . . 500 must not exceed it.)  normal vessel dump selected 1 trac major edit  time = 0.000E+00 seconds delt = 0.000E+00 seconds time steps = 0 oitno= 0 
D-18

 last minimum number of inner iterations was 0 at step 0  current convergence limits and limitation counts  delamx delemx delrmx delvmx delcmx delpmx  0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00  0 0 0 0 0 0  cptime = 0.000E+00 0 channel results date 19980803 time 00:00:00   Test 31504 Bundle Rod 7x7 ** **  ******************************************************************************************************************************** simulation time = .00000 seconds fluid properties for channel 1  node dist. pressure velocity void fraction flow rate flow heat added gama 

 no. (ft.) (psi) (ft/sec) (lbm/s) reg. (btu/s) (lbm/s)  liquid vapor entr. liquid vapor entr. liquid vapor entr. liquid vapor  3 .67 40.009 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 2 .33 40.010 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 1 .00 40.010 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 node dist. enthalpy density net  no. (ft.) (btu/lbm) (lbm/ft3) entrain  -------------------------------------------------------------------------- -------------------------------  vapor hg vapor-hg liquid hf liq. - hf mixture liquid vapor mixture  3 .67 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09446 .0945 . 2 .33 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09446 .0945 . 1 .00 1170.00 1169.77 .23 236.13 236.15 -.02 1169.25 58.29915 .09446 .0945 . * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  node dist. mixture mixture -- relative velocities -- area vap./liq. vap./drop -------- grid spacers --------  no. flow rate velocity vap. - liq. vap. - entr. interfacial interfacial grid temperature percent  drag drag type degf quenched  3 .67 .00 .00 .00 .00 .0501 .0010 .0010 0 .00 .000  2 .33 .00 .00 .00 .00 .3115 .0010 .0010 0 .00 .000  1 .00 .00 .00 .00 .00 .3115 .0010 .0010 0 .00 .000  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  node dist. hashl hascl hashv hascv drop ai ai source sent sdent qradd qradv snkld gams
D-19

 3 .67 347.3965 34.7397 3.4740 34.7397 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E

.0000E+00  2 .33 347.3965 34.7397 3.4740 34.7397 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  1 .00 347.3965 34.7397 3.4740 34.7397 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00 0 -------------------------------- gas volumetric analysis --------------------------------  hmgas rmgas steam air diam-ld diam-sd flow-sd veloc-sd gamsd  3 .67 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .00 2 .33 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .00 1 .00 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .00 ********************************************************************************************************************************0 channel results date 19980803 time 00:00:00   Test 31504 Bundle Rod 7x7 ** **  ******************************************************************************************************************************** simulation time = .00000 seconds fluid properties for channel 2  node dist. pressure velocity void fraction flow rate flow heat added gama 

 no. (ft.) (psi) (ft/sec) (lbm/s) reg. (btu/s) (lbm/s)  liquid vapor entr. liquid vapor entr. liquid vapor entr. liquid vapor  2 1.15 40.009 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 1 .67 40.009 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 node dist. enthalpy density net  no. (ft.) (btu/lbm) (lbm/ft3) entrain  -------------------------------------------------------------------------- -------------------------------  vapor hg vapor-hg liquid hf liq. - hf mixture liquid vapor mixture  2 1.15 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09446 .0945  1 .67 1170.00 1169.77 .23 236.13 236.14 -.01 1169.22 58.29915 .09446 .0945 . * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  node dist. mixture mixture -- relative velocities -- area vap./liq. vap./drop -------- grid spacers --------  no. flow rate velocity vap. - liq. vap. - entr. interfacial interfacial grid temperature percent  drag drag type degf quenched  2 1.15 .00 .00 .00 .00 .0501 .0010 .0010 0 .00 .000  1 .67 .00 .00 .00 .00 .0501 .0010 .0010 0 .00 .000 
D-20

 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  node dist. hashl hascl hashv hascv drop ai ai source sent sdent qradd qradv snkld gams 2 1.15 80.3732 8.0373 .8037 8.0373 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  1 .67 80.3732 8.0373 .8037 8.0373 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+0.0000E+00 0 -------------------------------- gas volumetric analysis --------------------------------  hmgas rmgas steam air diam-ld diam-sd flow-sd veloc-sd gamsd  2 1.15 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 1 .67 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .00 ********************************************************************************************************************************0 channel results date 19980803 time 00:00:00   Test 31504 Bundle Rod 7x7 ** **  ******************************************************************************************************************************** simulation time = .00000 seconds fluid properties for channel 3  node dist. pressure velocity void fraction flow rate flow heat added gama 

 no. (ft.) (psi) (ft/sec) (lbm/s) reg. (btu/s) (lbm/s)  liquid vapor entr. liquid vapor entr. liquid vapor entr. liquid vapor  23 13.56 40.001 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 22 12.99 40.001 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 21 12.42 40.002 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 20 11.85 40.002 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 19 11.28 40.003 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 18 10.71 40.003 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 17 10.13 40.003 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 16 9.56 40.004 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 15 8.99 40.004 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 14 8.42 40.004 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 13 7.85 40.005 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 12 7.28 40.005 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 11 6.71 40.006 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 10 6.14 40.006 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 9 5.57 40.006 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 8 5.00 40.007 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 7 4.43 40.007 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 6 3.86 40.007 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 5 3.28 40.008 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0
D-21

 4 2.64 40.008 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 3 2.00 40.009 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 2 1.36 40.009 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 1 1.15 40.009 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 node dist. enthalpy density net  no. (ft.) (btu/lbm) (lbm/ft3) entrain  -------------------------------------------------------------------------- -------------------------------  vapor hg vapor-hg liquid hf liq. - hf mixture liquid vapor mixture  23 13.56 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  22 12.99 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  21 12.42 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  20 11.85 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  19 11.28 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  18 10.71 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  17 10.13 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09444 .0945  16 9.56 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09444 .0945  15 8.99 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09444 .0945  14 8.42 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09444 .0945  13 7.85 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  12 7.28 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  11 6.71 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  10 6.14 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  9 5.57 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  8 5.00 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  7 4.43 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  6 3.86 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  5 3.28 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  4 2.64 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  3 2.00 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  2 1.36 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09446 .0945  1 1.15 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09446 .0945  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  node dist. mixture mixture -- relative velocities -- area vap./liq. vap./drop -------- grid spacers --------  no. flow rate velocity vap. - liq. vap. - entr. interfacial interfacial grid temperature percent  drag drag type degf quenched 
D-22

 23 13.56 .00 .00 .00 .00 .0151 .0010 .0010 1 .00 .000  22 12.99 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  21 12.42 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  20 11.85 .00 .00 .00 .00 .0151 .0010 .0010 1 502.00 .000  19 11.28 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  18 10.71 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  17 10.13 .00 .00 .00 .00 .0151 .0010 .0010 1 1062.12 .000  16 9.56 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  15 8.99 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  14 8.42 .00 .00 .00 .00 .0151 .0010 .0010 1 1528.70 .000  13 7.85 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  12 7.28 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  11 6.71 .00 .00 .00 .00 .0151 .0010 .0010 1 1330.43 .000  10 6.14 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  9 5.57 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  8 5.00 .00 .00 .00 .00 .0151 .0010 .0010 1 1132.16 .000  7 4.43 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  6 3.86 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  5 3.28 .00 .00 .00 .00 .0151 .0010 .0010 1 933.89 .000  4 2.64 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  3 2.00 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  2 1.36 .00 .00 .00 .00 .0151 .0010 .0010 1 731.43 .000  1 1.15 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  node dist. hashl hascl hashv hascv drop ai ai source sent sdent qradd qradv snkld gams 23 13.56 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00  22 12.99 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00  21 12.42 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00  20 11.85 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00  19 11.28 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00 
D-23

 18 10.71 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00  17 10.13 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00  16 9.56 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000

.0000E+00  15 8.99 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00  14 8.42 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00  13 7.85 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00  12 7.28 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00  11 6.71 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00  10 6.14 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00  9 5.57 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  8 5.00 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  7 4.43 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  6 3.86 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  5 3.28 124.3412 12.4341 1.2434 12.4341 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  4 2.64 124.3412 12.4341 1.2434 12.4341 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  3 2.00 124.3412 12.4341 1.2434 12.4341 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  2 1.36 40.4270 4.0427 .4043 4.0427 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  1 1.15 40.4270 4.0427 .4043 4.0427 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00 0 -------------------------------- gas volumetric analysis --------------------------------  hmgas rmgas steam air diam-ld diam-sd flow-sd veloc-sd gamsd  23 13.56 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .
D-24

 22 12.99 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 21 12.42 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 20 11.85 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 19 11.28 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 18 10.71 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 17 10.13 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 16 9.56 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 15 8.99 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 14 8.42 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 13 7.85 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 12 7.28 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 11 6.71 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 10 6.14 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 9 5.57 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 8 5.00 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 7 4.43 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 6 3.86 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 5 3.28 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 4 2.64 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 3 2.00 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 2 1.36 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 1 1.15 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 ********************************************************************************************************************************0 channel results date 19980803 time 00:00:00   Test 31504 Bundle Rod 7x7 ** **  ******************************************************************************************************************************** simulation time = .00000 seconds fluid properties for channel 4  node dist. pressure velocity void fraction flow rate flow heat added gama 

 no. (ft.) (psi) (ft/sec) (lbm/s) reg. (btu/s) (lbm/s)  liquid vapor entr. liquid vapor entr. liquid vapor entr. liquid vapor  23 13.56 40.001 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 22 12.99 40.001 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 21 12.42 40.002 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 20 11.85 40.002 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 19 11.28 40.003 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 18 10.71 40.003 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 17 10.13 40.003 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 16 9.56 40.004 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+
D-25

 15 8.99 40.004 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 14 8.42 40.004 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 13 7.85 40.005 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 12 7.28 40.005 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 11 6.71 40.006 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 10 6.14 40.006 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 9 5.57 40.006 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 8 5.00 40.007 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 7 4.43 40.007 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 6 3.86 40.007 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 5 3.28 40.008 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 4 2.64 40.008 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 3 2.00 40.009 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 2 1.36 40.009 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 1 1.15 40.009 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 node dist. enthalpy density net  no. (ft.) (btu/lbm) (lbm/ft3) entrain  -------------------------------------------------------------------------- -------------------------------  vapor hg vapor-hg liquid hf liq. - hf mixture liquid vapor mixture  23 13.56 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  22 12.99 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  21 12.42 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  20 11.85 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  19 11.28 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  18 10.71 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  17 10.13 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09444 .0945  16 9.56 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09444 .0945  15 8.99 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09444 .0945  14 8.42 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09444 .0945  13 7.85 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  12 7.28 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  11 6.71 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  10 6.14 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  9 5.57 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  8 5.00 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  7 4.43 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  6 3.86 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945 
D-26

 5 3.28 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  4 2.64 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  3 2.00 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  2 1.36 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09446 .0945  1 1.15 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09446 .0945 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * node dist. mixture mixture -- relative velocities -- area vap./liq. vap./drop -------- grid spacers --------  no. flow rate velocity vap. - liq. vap. - entr. interfacial interfacial grid temperature percent  drag drag type degf quenched  23 13.56 .00 .00 .00 .00 .0350 .0010 .0010 1 .00 .000  22 12.99 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  21 12.42 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  20 11.85 .00 .00 .00 .00 .0350 .0010 .0010 1 502.00 .000  19 11.28 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  18 10.71 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  17 10.13 .00 .00 .00 .00 .0350 .0010 .0010 1 1062.12 .000  16 9.56 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  15 8.99 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  14 8.42 .00 .00 .00 .00 .0350 .0010 .0010 1 1528.70 .000  13 7.85 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  12 7.28 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  11 6.71 .00 .00 .00 .00 .0350 .0010 .0010 1 1330.43 .000  10 6.14 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  9 5.57 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  8 5.00 .00 .00 .00 .00 .0350 .0010 .0010 1 1132.16 .000  7 4.43 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  6 3.86 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  5 3.28 .00 .00 .00 .00 .0350 .0010 .0010 1 933.89 .000  4 2.64 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  3 2.00 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  2 1.36 .00 .00 .00 .00 .0350 .0010 .0010 1 731.43 .000  1 1.15 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * node dist. hashl hascl hashv hascv drop ai ai source sent sdent qradd qradv snkld gams
D-27

 23 13.56 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  22 12.99 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  21 12.42 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  20 11.85 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  19 11.28 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  18 10.71 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  17 10.13 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  16 9.56 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  15 8.99 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  14 8.42 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  13 7.85 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  12 7.28 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  11 6.71 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  10 6.14 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  9 5.57 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  8 5.00 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  7 4.43 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  6 3.86 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  5 3.28 102.0585 10.2059 1.0206 10.2059 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00 
D-28

 4 2.64 102.0585 10.2059 1.0206 10.2059 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  3 2.00 102.0585 10.2059 1.0206 10.2059 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  2 1.36 33.1822 3.3182 .3318 3.3182 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  1 1.15 33.1822 3.3182 .3318 3.3182 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00 0 -------------------------------- gas volumetric analysis --------------------------------  hmgas rmgas steam air diam-ld diam-sd flow-sd veloc-sd gamsd  23 13.56 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 22 12.99 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 21 12.42 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 20 11.85 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 19 11.28 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 18 10.71 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 17 10.13 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 16 9.56 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 15 8.99 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 14 8.42 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 13 7.85 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 12 7.28 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 11 6.71 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 10 6.14 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 9 5.57 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 8 5.00 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 7 4.43 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 6 3.86 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 5 3.28 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 4 2.64 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 3 2.00 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 2 1.36 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 1 1.15 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 ********************************************************************************************************************************0 channel results date 19980803 time 00:00:00   Test 31504 Bundle Rod 7x7 ** **  ******************************************************************************************************************************** simulation time = .00000 seconds fluid properties for channel 5  node dist. pressure velocity void fraction flow rate flow heat added gama 
D-29

 no. (ft.) (psi) (ft/sec) (lbm/s) reg. (btu/s) (lbm/s)  liquid vapor entr. liquid vapor entr. liquid vapor entr. liquid vapor  4 14.56 40.000 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 3 14.23 40.000 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 2 13.89 40.001 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 1 13.56 40.001 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ node dist. enthalpy density net  no. (ft.) (btu/lbm) (lbm/ft3) entrain  -------------------------------------------------------------------------- -------------------------------  vapor hg vapor-hg liquid hf liq. - hf mixture liquid vapor mixture  4 14.56 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09443 .0945  3 14.23 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  2 13.89 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  1 13.56 1170.00 1169.77 .23 236.13 236.13 .00 1169.29 58.29915 .09444 .0945  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  node dist. mixture mixture -- relative velocities -- area vap./liq. vap./drop -------- grid spacers --------  no. flow rate velocity vap. - liq. vap. - entr. interfacial interfacial grid temperature percent  drag drag type degf quenched  4 14.56 .00 .00 .00 .00 .3489 .0010 .0010 0 .00 .000  3 14.23 .00 .00 .00 .00 .3489 .0010 .0010 0 .00 .000  2 13.89 .00 .00 .00 .00 .3489 .0010 .0010 0 .00 .000  1 13.56 .00 .00 .00 .00 .0501 .0010 .0010 0 .00 .000  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  node dist. hashl hascl hashv hascv drop ai ai source sent sdent qradd qradv snkld gams 4 14.56 389.0593 38.9059 3.8906 38.9059 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000

.0000E+00  3 14.23 389.0593 38.9059 3.8906 38.9059 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00  2 13.89 389.0593 38.9059 3.8906 38.9059 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00 
D-30

 1 13.56 389.0593 38.9059 3.8906 38.9059 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000

.0000E+00 0 -------------------------------- gas volumetric analysis --------------------------------  hmgas rmgas steam air diam-ld diam-sd flow-sd veloc-sd gamsd  4 14.56 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0

 3 14.23 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0

 2 13.89 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0

 1 13.56 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0

 ********************************************************************************************************************************1 rod results date 1998 0803 time 00:0 0:00    Test 31504 Bundle Rod 7x7 ** **  ******************************************************************************************************************************** heater rod number 1 simulation time = .00 seconds  surface no. 1 of 1  -------------------- conducts heat to channels 3 0 0 0 0 0 geometry type = 1  and azimuthally to surfaces 1 and 1 no. of radial nodes = 8  ******************************************************************************************************************************** rod axial fluid temperatures surface heat heater rod temperatues,  node location (deg-f) heat flux transfer (deg-f)  no. (in.) liquid vapor (b/h-ft2) mode surface center  ---- -------- ------ ----- --------- -------- ------- ------  24 162.72 .0 .0 .0000E+00 502.00 502.00 .0000E+00  23 * 159.29 .0 .0 .0000E+00 502.00 502.00 .0000E+00  22 * 152.44 .0 .0 .0000E+00 658.35 658.35 .0000E+00  21 * 145.59 .0 .0 .0000E+00 860.24 860.24 .0000E+00  20 * 138.74 .0 .0 .0000E+00 1062.12 1062.12 .0000E+00  19 * 131.89 .0 .0 .0000E+00 1264.00 1264.00 .0000E+00  18 * 125.04 .0 .0 .0000E+00 1465.89 1465.89 .0000E+00  17 * 118.19 .0 .0 .0000E+00 1528.70 1528.70 .0000E+00  16 * 111.34 .0 .0 .0000E+00 1462.61 1462.61 .0000E+00  15 * 104.49 .0 .0 .0000E+00 1396.52 1396.52 .0000E+00  14 * 97.64 .0 .0 .0000E+00 1330.43 1330.43 .0000E+00  13 * 90.79 .0 .0 .0000E+00 1264.34 1264.34 .0000E+00 
D-31

 12 * 83.94 .0 .0 .0000E+00 1198.25 1198.25 .0000E+00  11 * 77.09 .0 .0 .0000E+00 1132.16 1132.16 .0000E+00  10 * 70.24 .0 .0 .0000E+00 1066.07 1066.07 .0000E+00  9 * 63.39 .0 .0 .0000E+00 999.98 999.98 .0000E+00  8 * 56.54 .0 .0 .0000E+00 933.89 933.89 .0000E+00  7 * 49.69 .0 .0 .0000E+00 867.80 867.80 .0000E+00  6 * 42.84 .0 .0 .0000E+00 801.71 801.71 .0000E+00  5 * 35.56 .0 .0 .0000E+00 731.43 731.43 .0000E+00  4 * 27.84 .0 .0 .0000E+00 656.94 656.94 .0000E+00  3 * 20.12 .0 .0 .0000E+00 582.46 582.46 .0000E+00  2 * 15.01 .0 .0 .0000E+00 533.11 533.11 .0000E+00  1 13.75 .0 .0 .0000E+00 521.00 521.00 .0000E+00  rod axial ---------------------------------rod temperatures (deg-f)---------------------------------  node location radii in inches  no. (in.) .0484 .0931 .1219 .1400 .1582 .1710 .1790 .1870  ---- -------- ------ ------ ------ ------ ------ ------ ------ ------ ------ ------  23 * 159.29 502.0 502.0 502.0 502.0 502.0 502.0 502.0 502.0  22 * 152.44 658.4 658.4 658.4 658.4 658.4 658.4 658.4 658.4  21 * 145.59 860.2 860.2 860.2 860.2 860.2 860.2 860.2 860.2  20 * 138.74 1062.1 1062.1 1062.1 1062.1 1062.1 1062.1 1062.1 1062.1  19 * 131.89 1264.0 1264.0 1264.0 1264.0 1264.0 1264.0 1264.0 1264.0  18 * 125.04 1465.9 1465.9 1465.9 1465.9 1465.9 1465.9 1465.9 1465.9  17 * 118.19 1528.7 1528.7 1528.7 1528.7 1528.7 1528.7 1528.7 1528.7  16 * 111.34 1462.6 1462.6 1462.6 1462.6 1462.6 1462.6 1462.6 1462.6  15 * 104.49 1396.5 1396.5 1396.5 1396.5 1396.5 1396.5 1396.5 1396.5  14 * 97.64 1330.4 1330.4 1330.4 1330.4 1330.4 1330.4 1330.4 1330.4  13 * 90.79 1264.3 1264.3 1264.3 1264.3 1264.3 1264.3 1264.3 1264.3  12 * 83.94 1198.3 1198.3 1198.3 1198.3 1198.3 1198.3 1198.3 1198.3  11 * 77.09 1132.2 1132.2 1132.2 1132.2 1132.2 1132.2 1132.2 1132.2  10 * 70.24 1066.1 1066.1 1066.1 1066.1 1066.1 1066.1 1066.1 1066.1  9 * 63.39 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0  8 * 56.54 933.9 933.9 933.9 933.9 933.9 933.9 933.9 933.9  7 * 49.69 867.8 867.8 867.8 867.8 867.8 867.8 867.8 867.8  6 * 42.84 801.7 801.7 801.7 801.7 801.7 801.7 801.7 801.7  5 * 35.56 731.4 731.4 731.4 731.4 731.4 731.4 731.4 731.4 
D-32

 4 * 27.84 656.9 656.9 656.9 656.9 656.9 656.9 656.9 656.9  3 * 20.12 582.5 582.5 582.5 582.5 582.5 582.5 582.5 582.5  2 * 15.01 533.1 533.1 533.1 533.1 533.1 533.1 533.1 533.1  ******************************************************************************************************************************** heater rod number 2 simulation time = .00 seconds  surface no. 1 of 1  -------------------- conducts heat to channels 4 0 0 0 0 0 geometry type = 1  and azimuthally to surfaces 1 and 1 no. of radial nodes = 8  ******************************************************************************************************************************** rod axial fluid temperatures surface heat heater rod temperatues,  node location (deg-f) heat flux transfer (deg-f)  no. (in.) liquid vapor (b/h-ft2) mode surface center  ---- -------- ------ ----- --------- -------- ------- ------  24 162.72 .0 .0 .0000E+00 502.00 502.00 .0000E+00  23 * 159.29 .0 .0 .0000E+00 502.00 502.00 .0000E+00  22 * 152.44 .0 .0 .0000E+00 658.35 658.35 .0000E+00  21 * 145.59 .0 .0 .0000E+00 860.24 860.24 .0000E+00  20 * 138.74 .0 .0 .0000E+00 1062.12 1062.12 .0000E+00  19 * 131.89 .0 .0 .0000E+00 1264.00 1264.00 .0000E+00  18 * 125.04 .0 .0 .0000E+00 1465.89 1465.89 .0000E+00  17 * 118.19 .0 .0 .0000E+00 1528.70 1528.70 .0000E+00  16 * 111.34 .0 .0 .0000E+00 1462.61 1462.61 .0000E+00  15 * 104.49 .0 .0 .0000E+00 1396.52 1396.52 .0000E+00  14 * 97.64 .0 .0 .0000E+00 1330.43 1330.43 .0000E+00  13 * 90.79 .0 .0 .0000E+00 1264.34 1264.34 .0000E+00  12 * 83.94 .0 .0 .0000E+00 1198.25 1198.25 .0000E+00  11 * 77.09 .0 .0 .0000E+00 1132.16 1132.16 .0000E+00  10 * 70.24 .0 .0 .0000E+00 1066.07 1066.07 .0000E+00  9 * 63.39 .0 .0 .0000E+00 999.98 999.98 .0000E+00  8 * 56.54 .0 .0 .0000E+00 933.89 933.89 .0000E+00  7 * 49.69 .0 .0 .0000E+00 867.80 867.80 .0000E+00  6 * 42.84 .0 .0 .0000E+00 801.71 801.71 .0000E+00  5 * 35.56 .0 .0 .0000E+00 731.43 731.43 .0000E+00  4 * 27.84 .0 .0 .0000E+00 656.94 656.94 .0000E+00 
D-33

 3 * 20.12 .0 .0 .0000E+00 582.46 582.46 .0000E+00  2 * 15.01 .0 .0 .0000E+00 533.11 533.11 .0000E+00  1 13.75 .0 .0 .0000E+00 521.00 521.00 .0000E+00  rod axial ---------------------------------rod temperatures (deg-f)---------------------------------  node location radii in inches  no. (in.) .0484 .0931 .1219 .1400 .1582 .1710 .1790 .1870  ---- -------- ------ ------ ------ ------ ------ ------ ------ ------ ------ ------  23 * 159.29 502.0 502.0 502.0 502.0 502.0 502.0 502.0 502.0  22 * 152.44 658.4 658.4 658.4 658.4 658.4 658.4 658.4 658.4  21 * 145.59 860.2 860.2 860.2 860.2 860.2 860.2 860.2 860.2  20 * 138.74 1062.1 1062.1 1062.1 1062.1 1062.1 1062.1 1062.1 1062.1  19 * 131.89 1264.0 1264.0 1264.0 1264.0 1264.0 1264.0 1264.0 1264.0  18 * 125.04 1465.9 1465.9 1465.9 1465.9 1465.9 1465.9 1465.9 1465.9  17 * 118.19 1528.7 1528.7 1528.7 1528.7 1528.7 1528.7 1528.7 1528.7  16 * 111.34 1462.6 1462.6 1462.6 1462.6 1462.6 1462.6 1462.6 1462.6  15 * 104.49 1396.5 1396.5 1396.5 1396.5 1396.5 1396.5 1396.5 1396.5  14 * 97.64 1330.4 1330.4 1330.4 1330.4 1330.4 1330.4 1330.4 1330.4  13 * 90.79 1264.3 1264.3 1264.3 1264.3 1264.3 1264.3 1264.3 1264.3  12 * 83.94 1198.3 1198.3 1198.3 1198.3 1198.3 1198.3 1198.3 1198.3  11 * 77.09 1132.2 1132.2 1132.2 1132.2 1132.2 1132.2 1132.2 1132.2  10 * 70.24 1066.1 1066.1 1066.1 1066.1 1066.1 1066.1 1066.1 1066.1  9 * 63.39 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0  8 * 56.54 933.9 933.9 933.9 933.9 933.9 933.9 933.9 933.9  7 * 49.69 867.8 867.8 867.8 867.8 867.8 867.8 867.8 867.8  6 * 42.84 801.7 801.7 801.7 801.7 801.7 801.7 801.7 801.7  5 * 35.56 731.4 731.4 731.4 731.4 731.4 731.4 731.4 731.4  4 * 27.84 656.9 656.9 656.9 656.9 656.9 656.9 656.9 656.9  3 * 20.12 582.5 582.5 582.5 582.5 582.5 582.5 582.5 582.5  2 * 15.01 533.1 533.1 533.1 533.1 533.1 533.1 533.1 533.1  ******************************************************************************************************************************** cylindrical tube rod no. 3 simulation time = .00 seconds  surface no. 1 of 1  ------------------------ conducts heat to channels 4 0 0 0 0 0 geometry type = 2  and azimuthally to surfaces 1 and 1 no. of radial nodes = 3 
D-34

 ******************************************************************************************************************************** rod axial *---------------- outside surface ----------------* *---------------- inside surface ----------------*  node location heat flux h.t. **** temperatures (deg-f)   ** ** temperatures (deg-f) **** h.t. heat flux 

 no. (in.) (b/h-ft2) mode wall vapor liquid liquid vapor wall mode (b/h-ftl)  ---- -------- --------- ---- ------- ------- ------- ------- ------- -------  24 162.72 .0000E+00 521.00 .00 .00 521.00 .0000E+00  23 * 159.29 .0000E+00 521.00 .00 .00 521.00 .0000E+00  22 * 152.44 .0000E+00 521.00 .00 .00 521.00 .0000E+00  21 * 145.59 .0000E+00 521.00 .00 .00 521.00 .0000E+00  20 * 138.74 .0000E+00 521.00 .00 .00 521.00 .0000E+00  19 * 131.89 .0000E+00 521.00 .00 .00 521.00 .0000E+00  18 * 125.04 .0000E+00 521.00 .00 .00 521.00 .0000E+00  17 * 118.19 .0000E+00 521.00 .00 .00 521.00 .0000E+00  16 * 111.34 .0000E+00 521.00 .00 .00 521.00 .0000E+00  15 * 104.49 .0000E+00 521.00 .00 .00 521.00 .0000E+00  14 * 97.64 .0000E+00 521.00 .00 .00 521.00 .0000E+00  13 * 90.79 .0000E+00 521.00 .00 .00 521.00 .0000E+00  12 * 83.94 .0000E+00 521.00 .00 .00 521.00 .0000E+00  11 * 77.09 .0000E+00 521.00 .00 .00 521.00 .0000E+00  10 * 70.24 .0000E+00 521.00 .00 .00 521.00 .0000E+00  9 * 63.39 .0000E+00 521.00 .00 .00 521.00 .0000E+00  8 * 56.54 .0000E+00 521.00 .00 .00 521.00 .0000E+00  7 * 49.69 .0000E+00 521.00 .00 .00 521.00 .0000E+00  6 * 42.84 .0000E+00 521.00 .00 .00 521.00 .0000E+00  5 * 35.56 .0000E+00 521.00 .00 .00 521.00 .0000E+00  4 * 27.84 .0000E+00 521.00 .00 .00 521.00 .0000E+00  3 * 20.12 .0000E+00 521.00 .00 .00 521.00 .0000E+00  2 * 15.01 .0000E+00 521.00 .00 .00 521.00 .0000E+00  1 13.75 .0000E+00 521.00 .00 .00 521.00 .0000E+00  ********************************************************************************************************************************1 heat slab results date 1998 0803 time 00:0 0:00    Test 31504 Bundle Rod 7x7 ** **  ********************************************************************************************************************************
D-35

 heat slab no. 1 (wall) simulation time = .00 seconds  fluid channel on inside surface = 4  fluid channel on outside surface = 0  geometry type = 3 

no. of nodes = 3 

 ******************************************************************************************************************************** rod axial *---------------- outside surface ----------------* *---------------- inside surface ----------------*  node location heat flux h.t. **** temperatures (deg-f)   ** ** temperatures (deg-f)   h.t. heat flux 

 no. (in.) (b/h-ft2) mode wall vapor liquid liquid vapor wall mode (b/h-ftl)  ---- -------- --------- ---- ------- ------- ------- ------- ------- -------  23 159.29 .0000E+00 521.00 .00 .00 521.00 .0000E+00  22 152.44 .0000E+00 521.00 .00 .00 521.00 .0000E+00  21 145.59 .0000E+00 521.00 .00 .00 521.00 .0000E+00  20 138.74 .0000E+00 521.00 .00 .00 521.00 .0000E+00  19 131.89 .0000E+00 521.00 .00 .00 521.00 .0000E+00  18 125.04 .0000E+00 521.00 .00 .00 521.00 .0000E+00  17 118.19 .0000E+00 521.00 .00 .00 521.00 .0000E+00  16 111.34 .0000E+00 521.00 .00 .00 521.00 .0000E+00  15 104.49 .0000E+00 521.00 .00 .00 521.00 .0000E+00  14 97.64 .0000E+00 521.00 .00 .00 521.00 .0000E+00  13 90.79 .0000E+00 521.00 .00 .00 521.00 .0000E+00  12 83.94 .0000E+00 521.00 .00 .00 521.00 .0000E+00  11 77.09 .0000E+00 521.00 .00 .00 521.00 .0000E+00  10 70.24 .0000E+00 521.00 .00 .00 521.00 .0000E+00  9 63.39 .0000E+00 521.00 .00 .00 521.00 .0000E+00  8 56.54 .0000E+00 521.00 .00 .00 521.00 .0000E+00  7 49.69 .0000E+00 521.00 .00 .00 521.00 .0000E+00  6 42.84 .0000E+00 521.00 .00 .00 521.00 .0000E+00  5 35.56 .0000E+00 521.00 .00 .00 521.00 .0000E+00  4 27.84 .0000E+00 521.00 .00 .00 521.00 .0000E+00  3 20.12 .0000E+00 521.00 .00 .00 521.00 .0000E+00  2 15.01 .0000E+00 521.00 .00 .00 521.00 .0000E+00  ** ******************************************************************************************************************************
D-36

1 lateral drift results date 1998 0803 time 00:0 0:00  case 0   Test 31504 Bundle Rod 7x7 ** **  ******************************************************************************************************************************** simulation time = .00000 seconds summary for gap 1 connecting channel 3 to channel 4  --- axial --- -------- crossflows -------- ------------ velocities ------------ pressure void fraction flow  range (lb/sec) diff. area  (in.) liquid vapor entrained liquid vapor entrained pii-pjj ii jj  13.8- 16.3 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .034  16.3- 24.0 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .105  24.0- 31.7 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .105  31.7- 39.4 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .105  39.4- 46.3 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  46.3- 53.1 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  53.1- 60.0 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  60.0- 66.8 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  66.8- 73.7 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  73.7- 80.5 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  80.5- 87.4 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  87.4- 94.2 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  94.2-101.1 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  101.1-107.9 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  107.9-114.8 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  114.8-121.6 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  121.6-128.5 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  128.5-135.3 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  135.3-142.2 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  142.2-149.0 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  149.0-155.9 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  155.9-162.7 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093 1 injection boundary conditions date 1998 0803 time 00:0 0:00  case 0   Test 31504 Bundle Rod 7x7 ** **  ******************************************************************************************************************************** simulation time = .00000 seconds 
D-37

 channel node wginjt wlinjt hginjt hlinjt  no. no. lbm/sec lbm/sec btu/lbm btu/lbm  *************************************************************************  * new time domain reached *  * minimum maximum time long short graphics dump *  * time time domain edit edit edit *  * step step end interval interval interval interval *  * *  * 2.000E-04 1.500E-02 5.000E+02 5.000E+00 8.000E+02 1.000E+00 8.000E+02 *  *************************************************************************  time step ratio = 1.000E+00  * * * * * saved graphics data at time .0000 * * * * * * * * * * *  * * * * * saved graphics data at time .9868 * * * * * * * * * * *  * * * * * saved graphics data at time 1.9918 * * * * * * * * * * *  * * * * * saved graphics data at time 2.9968 * * * * * * * * * * *  * * * * * saved graphics data at time 4.0018 * * * * * * * * * * * 
D-38

APPENDIX D3. SUB-CHANNEL MODEL INPUT DECK 

 0 

 0 0.0 

 .001 5 40 

 1 ****** Sub-Channel Model of RBHT 7x7 Bundle ****** 

 1 1 

 40.0 1169.77 0.0 .46667 124. 0.0 .9999 1.0 

air .0001 

 2 18 

 1.0681.5875 0.0 0.0 1 

 23 1 0 

 2.13621.175 0.0 0.0 3 

 23 1 0 23 2 0 23 3 0 

 3.0681.5875 0.0 0.0 2 

 23 2 0 23 4 0 

 4.13621.175 0.0 0.0 3 

 23 3 0 23 5 0 23 7 0 

 5.13621.175 0.0 0.0 4 

 23 4 0 23 5 0 23 6 0 23 8 0 

 6.0681.5875 0.0 0.0 2 

 23 6 0 23 9 0 

 7.08741.083 0.0 0.0 2 

 23 7 0 23 10 0 

 8.08741.083 0.0 0.0 3 

 23 8 0 23 10 0 23 11 0 

 9.08741.083 0.0 0.0 3 

 23 9 0 23 11 0 23 12 0 

 10.0275.4339 0.0 0.0 1 

 23 12 0 

 11.4920 1.01 0.0 0.0 1 

 3 13 0 

 12.6150 1.01 0.0 0.0 2 

 3 13 0 3 14 0 

 13.50941.775 0.0 0.0 1 

 3 14 0 

 14.27242.350 0.0 0.0 2 

 3 15 3 3 15 4 

 15.34052.938 0.0 0.0 5 

 3 15 3 3 15 4 3 16 7 3 16 8 3 16 9 

 16.28973.683 0.0 0.0 3 

 3 16 7 3 16 8 3 16 9 

 175.60710.69 0.0.9026 2 

 3 0 15 3 0 16 

 186.2803.5001.616 0.0 0 

 3 16 

 1 1 20.1220.496 0.5 0.0 0 0 1.0 1 3 

 1. 0.0 

 2 2 30.1220.496 0.5 0.0 0 0 1.0 0 4 

 1. 0.0 

 3 2 40.1220.496 0.5 0.0 0 0 1.0 1 7 

 1. 0.0 

 4 3 50.1220.496 0.5 0.0 0 0 1.0 2 8 
D-39

 1. 0.0 

 5 4 50.1220.496 0.5 0.0 0 0 1.0 0 6 

 1. 0.0 

 6 5 60.1220.496 0.5 0.0 0 0 1.0 5 9 

 1. 0.0 

 7 4 70.122.3915 0.5 0.0 0 0 1.0 3 -1 

 1. 0.0 

 8 5 80.122.3915 0.5 0.0 0 0 1.0 4 -1 

 1. 0.0 

 9 6 90.122.3915 0.5 0.0 0 0 1.0 6 -1 

 1. 0.0 

 10 7 80.1000.496 0.5 0.5 0 0 1.0 0 11 

 1. 0.0 

 11 8 90.1000.496 0.5 0.5 0 0 1.0 10 12 

 1. 0.0 

 12 9 100.100.3915 0.5 0.5 0 0 1.0 11 -1 

 1. 0.0 

 13 11 120.9920.744 0.0 0.0 0 0 1.0 0 14 

 1. 0.0 

 14 12 131.4880.496 0.0 0.0 0 0 1.0 13 0 

 1. 0.0 

 15 14 150.1220.744 0.5 0.0 0 0 1.0 0 16 

 2. 0.0 

 16 15 160.1220.496 0.5 0.0 0 0 1.0 15 0 

 3. 0.0 

 18 

 1 2 1 2 2 1 2 4 3 3 5 2 

 4 5 2 4 6 4 5 4 3 5 8 7 

 6 6 4 6 9 8 7 10 5 8 10 5 

 8 11 6 9 11 6 9 12 9 10 8 7 

 11 9 8 12 12 9 

 4 5 1 0 

 1 1 2 4.0 

 17 14 15 16 17 

 2 3 2 2.875 

 14 1 2 3 17 

 15 4 5 6 17 

 16 7 8 9 10 17 

 3 10 22 2.51 5 

 2 2.51 3 7.72 5 7.72 6 6.85 23 6.85 

 1 11 14 

 2 11 14 

 3 11 14 

 4 12 15 

 5 12 15 

 6 12 15 

 7 13 16 

 8 13 16 

 9 13 16 

 10 13 16 

 4 3 2 4.0 

 11 18 1 2 3 

 12 18 4 5 6 

 13 18 7 8 9 10 

 5 1 1 4.0 
D-40

 18 18 11 12 13 

 18 

 235 

 7 8 1 1 1 1 1 0 0 0 

 1.2 2 1 2 3 4 5 6 7 8 9 10 

 1.2 5 1 2 3 4 5 6 7 8 9 10 

 1.2 8 1 2 3 4 5 6 7 8 9 10 

 1.2 11 1 2 3 4 5 6 7 8 9 10 

 1.2 14 1 2 3 4 5 6 7 8 9 10 

 1.2 17 1 2 3 4 5 6 7 8 9 10 

 1.2 20 1 2 3 4 5 6 7 8 9 10 

 1.2 23 1 2 3 4 5 6 7 8 9 10 

 1 8 10 1 1.4 .2952 1.5 1.984 

 2 5 8 11 14 17 20 23 

 1 0.5 1 1 2 1 3 1 

 2 1.0 2 2 3 2 4 1 5 1 

 3 0.5 3 3 5 2 6 1 

 4 1.0 4 2 5 4 7 1 8 1 

 5 1.0 5 3 6 2 8 2 9 1 

 6 0.5 6 3 9 2 10 1 

 7 0.75 7 2 8 4 

 8 0.75 8 3 9 4 

 9 0.75 9 3 10 2 

 10 0.50 10 3 

 8 10 4 3 3 10 6 31 1 

 1 1 1 2 0.05 1. 1.0 0. 1 0. 

 1 .125 

 2 1 1 2 0.05 1. 1.0 0. 1 0. 

 1 .25 2 .25 

 3 1 1 2 0.05 1. 1.0 0. 1 0. 

 1 .125 2 .25 3 .125 

 4 1 1 2 0.05 1. 1.0 0. 1 0. 

 2 .25 4 .25 

 5 1 1 2 0.05 1. 1.0 0. 1 0. 

 2 .25 3 .25 5 .25 4 .25 

 6 1 1 2 0.05 1. 1.0 0. 1 0. 

 3 .125 5 .25 6 .125 

 7 1 1 2 0.05 1. 1.0 0. 1 0. 

 4 .25 7 .25 

 8 1 1 2 0.05 1. 1.0 0. 1 0. 

 4 .25 5 .25 8 .25 7 .25 

 9 1 1 2 0.05 1. 1.0 0. 1 0. 

 5 .25 6 .25 9 .25 8 .25 

 10 2 0 2 0.05 1. 0.0 0. 1 0. 

 6 .125 9 .25 10 .125 

 1 3 0.496 0.496 1.0 7 0. 90.0 

 2 3 0.496 0.496 1.0 8 0. 90.0 

 3 3 0.496 0.496 1.0 9 0. 90.0 

 4 3 0.537 0.287 1.0 10 0. 90.0 

 1 9 0 4 

 1 2 3 4 5 6 7 8 9 

 13.75 822.0 121.75 1600. 157.75 858.0 168.76 858.0 

 2 1 0 4 

 10 

 13.75 372.0 121.75 645.0 157.75 383.0 168.76 383.0 
D-41

 3 0 4 4 

 -1 -2 -3 -4 

 13.75 322.0 121.75 482.0 157.75 327.0 168.76 327.0 

 1 1 -1 20 0 1.0 1.0 1.0 1.0 1.0 

 1 2 4 2 1 2 4 2 1 2 4 2 3 5 9 7 

 3 7 9 5 

 2 2 -1 20 0 1.0 1.0 1.0 1.0 1.0 

 3 5 9 7 2 1 2 4 3 7 9 5 8 12 18 16 

 6 10 13 10 

 3 3 -1 20 0 1.0 1.0 1.0 1.0 1.0 

 6 10 13 10 5 3 7 9 5 9 7 3 11 14 22 19 

 11 19 22 14 

 4 4 2 19 0 1.0 1.0 1.0 1.0 1.0 

 8 12 18 16 7 3 5 9 8 16 18 12 17 21 -1 11 

 14 22 19 

 5 5 2 19 0 1.0 1.0 1.0 1.0 1.0 

 11 14 22 19 10 6 10 13 12 18 16 8 20 25 -2 15 

 23 26 23 

 6 6 3 18 0 1.0 1.0 1.0 1.0 1.0 

 15 23 26 23 14 11 19 22 14 22 19 11 24 27 -3 24 

 -3 27 

 7 7 4 13 0 1.0 1.0 1.0 1.0 1.0 

 17 21 -1 16 8 12 18 17 -1 21 20 25 -2 

 8 8 4 13 0 1.0 1.0 1.0 1.0 1.0 

 20 25 -2 19 11 14 22 21 -1 17 24 27 -3 

 9 9 5 12 0 1.0 1.0 1.0 1.0 1.0 

 24 27 -3 23 15 23 26 25 -2 20 28 -4 

 10 10 6 8 0 1.0 1.0 1.0 1.0 1.0 

 28 -4 27 24 -3 27 -3 24 

 -1 

 .374 .8 .374 .496 

 -2 

 .374 .8 .100 .496 0.0 0.0 .8 .374 

 -3 

 .374 .8 .100 .496 0.0 0.0 .8 .374 

 -4 

 .374 .8 .100 .496 0.0 .248 .8 .374 

 -5 

 .374 .8 .100 .496 0.0 .248 .8 .374 

 -6 

 .374 .8 .100 .496 0.0 .248 .8 .374 
D-42

 9 3 

 1 hrod .374 0.0 4 0 

 1 2.0675 0.0 1 3 .045 1.0 3 2.0465 0.0 3 1.0280 0.0 

 2 tube .375 .209 1 0 

 3 1 .083 0.0 

 3 wall .496 .250 1 0 0 

 3 1 .250 

 10 3 

 1 12 528.8 Inco 

 212. .111 9.09 392. .121 10.04 

 572. .131 10.98 752. .141 11.93 

 932. .151 12.88 1112. .166 13.82 

 1292. .178 14.77 1472. .191 15.72 

 1652. .204 16.66 1832. .216 17.61 

 2012. .229 18.56 2192 .241 19.50 

 2 14 119.2 BN 

 212. .16587 67.37 392. .22015 63.87 

 572. .26264 60.28 752. .29590 56.74 

 932. .32194 53.19 1112. .34233 49.65 

 1292. .35829 46.10 1472. .37078 42.56 

 1652. .38057 39.01 1832. .38822 35.47 

 2012. .39421 31.92 2192. .39891 28.37 

 2372. .40259 24.83 2552. .40546 21.28 

 3 10 528.8 Mon 

 70. .100 10.083 200. .107 11.333 

 400. .114 13.000 600. .117 14.833 

 800. .120 16.500 1000. .125 18.333 

 1200. .132 20.000 1400. .141 21.833 

 1600. .157 23.500 1800. .186 25.167 

 11 1 25 

 1 4 

 13.75 .5 121.75 1.5 157.75 .5 157.76 0.0 

 0.0 1. 17.5 .921 35.0 .8704 52.5 .8326 

 70. .803 87.5 .7755 105.0 .7512 122.5 .7302 

 140. .714 157.5 .6973 175.0 .6837 192.5 .6710 

 220. .652 255.0 .6332 290.0 .6167 325.0 .6017 

 360. .588 395.0 .5769 430.0 .5656 465.0 .5562 

 500. .547 535.0 .5444 570.0 .5304 605.0 .5243 

 1000. .002 

 13 2 0 1 0 0 

 3 3 

 0.0 0.0 0.1 1.01500. 1.0 

 17 1 2 1 0 .0321610 95.3047 40.0 

 124. 1.0.9999.0001 

 18 4 1 0 0 40. 1169.7685 40.0 

 124. 1.0.9999.0001 

 14 5 0 0 0 0 0 0 

 0 

 0 

 300 0 0 

 .00001 .00110 0.2 1.0 99000.0 
D-43

 .19 50.0 100.0 50.0 0 

 .00001 .00200 50.0 1.0 99000.0 

 25.0 50.0 100.0 5.0 0 

 -.00001 .00100 300.0 1.0 99000.0 

 5.0 5.0 100.0 5.0 0 

 -.001 
D-44