NUREG-2208

Validation of Computational 

Fluid Dynamics Methods 

Using Prototypic Light Water 

Reactor Spent Fuel Assembly 

Thermal-Hydraulic Data

Office of Nuclear Regulatory Research

NUREG-2208

Validation of Computational 

Fluid Dynamics Methods 

Using Prototypic Light Water 

Reactor Spent Fuel Assembly 

Thermal-Hydraulic Data

Office of Nuclear Regulatory Research

Manuscript Completed: November 2016

Date Published: March 2017 

Prepared by: 

G. Zigh

S. Gonzalez 

iii

ABSTRACT

Applicants submit spent nuclear fuel dry storage cask designs to the U.S. Nuclear Regulatory

Commission (NRC) for certification under Title 10 of the Code of Federal Regulations 

(10 CFR) Part 72, “Licensing Requirements for the Independent Storage of Spent Nuclear Fuel, 

High-Level Radioactive Waste, and Reactor-Related Greater Than Class C Waste.” The NRC 

staff performs its technical review of these designs in accordance with 10 CFR Part 72 and 

NUREG-1536, “Standard Review Plan for Spent Fuel Dry Storage Systems at a General License

Facility,” Revision 1, issued July 2010. To ensure that the cask and fuel material temperatures of 

the dry cask storage system remain within the allowable limits or criteria for normal, off-normal,

and accident conditions, the NRC staff performs a thermal review as part of the technical review.

Recent applications increasingly have used thermal-hydraulic analyses using computational fluid 

dynamics (CFD) codes (e.g., ANSYS FLUENT) to demonstrate the adequacy of the thermal 

design. The NRC Office of Nuclear Material Safety and Safeguards asked the NRC Office of 

Nuclear Regulatory Research to perform validation studies of the FLUENT CFD code to assist it in 

making regulatory decisions to ensure adequate protection for storage and transportation casks. 

The validation studies were based on preignition data (separate effect tests) obtained from the 

following previous studies:

• NUREG/CR-7143, “Characterization of Thermal-Hydraulic and Ignition Phenomena in 

Prototypic, Full-Length Boiling Water Reactor Spent Fuel Pool Assemblies After a 

Postulates Complete Loss-of Coolant Accident,” issued March 2013

• NUREG/CR-7215, “Spent Fuel Pool Project Phase I: Pre-Ignition and Ignition Testing of a 

Single Commercial 17x17 Pressurized Water Reactor Spent Fuel Assembly under 

Complete Loss of Coolant Accident Conditions,” issued April 2016

• NUREG/CR-7216, “Spent Fuel Pool Project Phase II: Pre-Ignition and Ignition Testing of 

a 1x4 Commercial 17x17 Pressurized Water Reactor Spent Fuel Assemblies under 

Complete Loss of Coolant Accident Conditions,” issued April 2016

The fuel assembly experimental data from these studies provided reliable information for various 

fuel assembly heat loads that can be used to validate the analytical methods. Combined with 

current methods to determine modeling and application uncertainty, the measured data offered 

additional confirmation on the adequacy of the applied analytical methods. 

The research summarized in this report relates to the CFD validation studies performed for a 

single test assembly of a full-length commercial 17x17 pressurized-water reactor (PWR) fuel 

bundle; a 17x17 PWR 1x4 configuration where the center fuel assembly was electrically heated 

and the four surrounding assemblies were unheated; and, a single test assembly for a full-length 

commercial 9x9 boiling-water reactor fuel bundle. For each of these configurations, a detailed 

and porous media model were developed to validate the results based on the experimental data 

and conducted parametric studies to assess model sensitivity. The grid conversion index method 

published by the American Society of Mechanical Engineers (ASME), “Standard for Verification 

and Validation in Computational Fluid Dynamics and Heat Transfer,” was used to calculate the 

discretization uncertainty of the model. 

v

CONTENTS

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

LIST OF FIGURES......................................................................................... ...............vii

LIST OF TABLES ................................................................................................................................xi

EXECUTIVE SUMMARY ...................................................................................................................xiii

ABBREVIATIONS...............................................................................................................................xv

1 INTRODUCTION...........................................................................................................................1-1

1.1 Pressurized-Water Reactor Single Assembly.......................................................................1-1

1.2 Pressurized-Water Reactor 1x4 Assembly Configuration ....................................................1-2

1.3 Boiling-Water Reactor Single Assembly ...............................................................................1-4

1.4 Computational Fluid Dynamics Model...................................................................................1-6

2 COMPUTATIONAL FLUID DYNAMICS MODELING.................................................................2-1

2.1 Detailed Model.......................................................................................................................2-1

2.2 Porous Model.........................................................................................................................2-8

3 RESULTS AND DISCUSSION.....................................................................................................3-1

3.1 Pressurized-Water Reactor Single Assembly (Cell 2: 223.4 mm)........................................3-1

3.1.1 Power—1 kW (Steady State)......................................................................................3-1

3.1.2 Power—1 kW (Transient)............................................................................................3-5

3.1.3 Power—0.5 kW (Steady State).................................................................................3-13

3.2 Pressurized-Water Reactor Single Assembly (Cell 1: 221.3 mm)......................................3-15

3.2.1 Power—1 kW (Steady State)....................................................................................3-15

3.2.2 Power—1 kW (Transient)..........................................................................................3-17

3.3 Pressurized-Water Reactor 1x4 Assembly Configuration ..................................................3-18

3.3.1 Power—1 kW (Steady State)....................................................................................3-18

3.3.2 Power—1 kW (Transient)..........................................................................................3-21

3.4 Boiling-Water Reactor Single Assembly .............................................................................3-26

3.4.1 Power—1,369 W (Steady State) ..............................................................................3-26

3.4.2 Power—1,369 W (Transient) ....................................................................................3-28

3.4.3 Power—2,236 W (Steady State) ..............................................................................3-32

4 COMPUTATIONAL FLUID DYNAMICS DISCRETIZATION ERROR ANALYSIS 

(GRID CONVERGENCE INDEX) .................................................................................................4-1

4.1 Peak Cladding Temperature .................................................................................................4-3

4.2 Mass Flow Rate.....................................................................................................................4-4

5 CONCLUSION...............................................................................................................................5-1

6 REFERENCES..............................................................................................................................6-1

vii

LIST OF FIGURES

Figure 1-1 Various components in a typical 17x17 PWR fuel assembly .................................. 1-1

Figure 1-2 Layout of the Phase II test assembly ...................................................................... 1-2

Figure 1-3 Dimensions of the as-built pool rack and the design insulation thickness............... 1-3

Figure 1-4 Arrangement of insulation, radiation barriers, and external thermocouples ............ 1-5

Figure 1-5 Arrangement of drain holes..................................................................................... 1-5

Figure 1-6 CFD PWR single assembly cross sections of the detailed and porous models...... 1-6

Figure 2-1 Detailed PWR single assembly (Cell 2 illustrated)—boundary conditions .............. 2-1

Figure 2-2 Detailed PWR single assembly top and bottom views (Cell 2 illustrated)—

 boundary conditions................................................................................................ 2-2

Figure 2-3 Detailed BWR single assembly—boundary conditions (1/4 symmetry) .................. 2-2

Figure 2-4 Detailed BWR single assembly top and bottom views—boundary conditions ........ 2-3

Figure 2-5 Detailed PWR 1x4 configuration—boundary conditions ......................................... 2-3

Figure 2-6 Detailed PWR 1x4 configuration top and bottom views—boundary conditions ...... 2-3

Figure 2-7 2D model to calclulate keff for PWR single assembly (Cell 1 shown) ...................... 2-9

Figure 2-8 2D model to calclulate keff for 1x4 PWR configuration (peripheral assembly)....... 2-10

Figure 2-9 Porous PWR single assembly (Cell 2 illustrated)—boundary conditions .............. 2-17

Figure 2-10 Porous PWR single assembly top and bottom views (Cell 2 illustrated)—

 boundary conditions.............................................................................................. 2-17

Figure 2-11 Porous PWR 1x4 configuration—boundary conditions ......................................... 2-18

Figure 2-12 Porous PWR 1x4 configuration top and bottom views—boundary conditions ...... 2-18

Figure 2-13 Porous BWR single assembly—boundary conditions........................................... 2-19

Figure 2-14 Porous BWR single assembly top and bottom views—boundary conditions........ 2-19

Figure 3-1 Detailed configuration—PWR single assembly Cell 2............................................. 3-2

Figure 3-2 Porous configuration—PWR single assembly Cell 2 .............................................. 3-2

Figure 3-3 Porous configuration for extended models—PWR single assembly Cell 2............. 3-3

Figure 3-4 PWR Cell 2 steady-state PCT as a function of height at 1 kW................................ 3-4

Figure 3-5 PWR Cell 2 steady-state pool cell wall maximum temperature as a function 

 of height at 1 kW..................................................................................................... 3-4

Figure 3-6 PWR Cell 2 steady-state exterior wall maximum temperature as a function 

 of height at 1 kW..................................................................................................... 3-5

Figure 3-7 PWR Cell 2 PCT as a function of time at 1 kW....................................................... 3-6

Figure 3-8 PWR Cell 2 mass flow rate as a function of time at 1 kW ....................................... 3-6

Figure 3-9 PWR Cell 2 pool cell wall maximum temperature as a function of time at 1 kW..... 3-7

Figure 3-10 PWR Cell 2 exterior wall maximum temperature as a function of time at 1 kW ...... 3-7

Figure 3-11 PWR Cell 2 PCT as a function of height at 1 kW at 20 hours ................................. 3-8

Figure 3-12 PWR Cell 2 pool cell wall maximum temperature as a function of height at 

 1 kW at 20 hours...................................................................................................... 3-8

Figure 3-13 PWR Cell 2 exterior wall maximum temperature as a function of height at 

 1 kW at 20 hours..................................................................................................... 3-9

Figure 3-14 PWR Cell 2 PCT as a function of time at 1 kW..................................................... 3-10

Figure 3-15 PWR Cell 2 mass flow rate as a function of time at 1 kW ..................................... 3-10

Figure 3-16 PWR Cell 2 pool cell wall maximum temperature as a function of time at 1 kW... 3-11

Figure 3-17 PWR Cell 2 exterior wall maximum temperature as a function of time at 1 kW .... 3-11

Figure 3-18 PWR Cell 2 PCT as a function of height at 1 kW at 20 hours ............................... 3-12

Figure 3-19 PWR Cell 2 pool cell wall maximum temperature as a function of height at 

 1 kW at 20 hours.................................................................................................... 3-12

Figure 3-20 PWR Cell 2 exterior wall maximum temperature as a function of height at 

 1 kW at 20 hours.................................................................................................... 3-13
viii

Figure 3-21 PWR Cell 2 steady-state PCT as a function of height at 0.5 kW........................... 3-14

Figure 3-22 PWR Cell 2 steady-state pool cell wall maximum temperature as a function 

 of height at 0.5 kW................................................................................................ 3-14

Figure 3-23 PWR Cell 2 steady-state exterior wall maximum temperature as a function 

 of height at 0.5 kW................................................................................................. 3-15

Figure 3-24 PWR Cell 1 steady-state PCT as a function of height at 1 kW.............................. 3-16

Figure 3-25 PWR Cell 1 steady-state pool cell wall temperature as a function off height 

 at 1 kW..................................................................................................................3-16

Figure 3-26 PWR Cell 1 PCT as a function of time at 1 kW..................................................... 3-17

Figure 3-27 PWR Cell 1 mass flow rate as a function of time at 1 kW ..................................... 3-17

Figure 3-28 PWR 1x4 configuration—steady-state center assembly PCT as a function 

 of height at 1 kW................................................................................................... 3-19

Figure 3-29 PWR 1x4 configuration—steady-state peripheral assembly PCT as a function 

 of height at 1 kW................................................................................................... 3-19

Figure 3-30 PWR 1x4 configuration—steady-state outer pool cell wall maximum 

 temperature as a function of height at 1 kW ......................................................... 3-20

Figure 3-31 PWR 1x4 configuration—steady-state exterior wall maximum temperature 

 as a function of height at 1 kW.............................................................................. 3-20

Figure 3-32 PWR 1x4 configuration—PCT location in peripheral assembly ............................ 3-21

Figure 3-33 PWR 1x4 configuration—center assembly PCT as a function of time at 1 kW..... 3-22

Figure 3-34 PWR 1x4 configuration—center assembly mass flow rate as a function of 

 time at 1 kW.......................................................................................................... 3-22

Figure 3-35 PWR 1x4 configuration—peripheral assembly PCT as a function of time at 

 1 kW.......................................................................................................................3-23

Figure 3-36 PWR 1x4 configuration—peripheral assembly mass flow rate as a function 

 of time at 1 kW...................................................................................................... 3-23

Figure 3-37 PWR 1x4 configuration—exterior wall maximum temperature as a function 

 of time at 1 kW...................................................................................................... 3-24

Figure 3-38 PWR 1x4 configuration—center assembly PCT as a function of height at 

 1 kW at 24 hours.................................................................................................... 3-25

Figure 3-39 PWR 1x4 configuration—peripheral assembly PCT as a function of height 

 at 1 kW at 24 hours............................................................................................... 3-25

Figure 3-40 PWR 1x4 configuration—exterior wall maximum temperature as a function 

 of height at 1 kW at 24 hours................................................................................ 3-26

Figure 3-41 BWR steady-state PCT as a function of height at 1,369 W .................................. 3-27

Figure 3-42 BWR steady-state pool cell wall maximum temperature as a function of 

 height at 1,369 W.................................................................................................. 3-27

Figure 3-43 BWR steady-state exterior wall maximum temperature as a function of

 height at 1,369 W.................................................................................................. 3-28

Figure 3-44 BWR PCT as a function of time at 1,369 W.......................................................... 3-28

Figure 3-45 BWR inlet bundle mass flow rate as a function of time at 1,369 W....................... 3-29

Figure 3-46 BWR inlet drain mass flow rate as a function of time at 1,369 W.......................... 3-29

Figure 3-47 BWR pool cell wall maximum temperature as a function of time at 1,369 W........ 3-30

Figure 3-48 BWR exterior wall maximum temperature as a function of time at 1,369 W......... 3-30

Figure 3-49 BWR PCT as a function of height at 1,369 W at 12 hours.................................... 3-31

Figure 3-50 BWR pool cell wall maximum temperature as a function of height at 1,369 W 

 at 12 hours............................................................................................................ 3-31

Figure 3-51 BWR exterior wall maximum temperature as a function of height at 1,369 W 

 at 12 hours............................................................................................................ 3-32

Figure 3-52 BWR steady-state PCT as a function of height at 2,236 W .................................. 3-33
ix

Figure 3-53 BWR steady-state pool cell wall maximum temperature as a function of 

 height at 2,236 W.................................................................................................. 3-33

Figure 3-54 BWR steady-state exterior wall maximum temperature as a function of 

 height at 2,236 W.................................................................................................. 3-34

xi

LIST OF TABLES

Table 1-1 Summary of Assembly Hydraulic Characteristics for Storage Cell 1 and Cell 2....... 1-1

Table 1-2 Hydraulic Dimensions for the Center Assembly, Average Peripheral Assembly, 

 and the Cross-Flow Path ......................................................................................... 1-4

Table 1-3 Dimensions of Assembly Components in the 9x9 BWR........................................... 1-4

Table 2-1 Detailed PWR Assemblies—Materials ..................................................................... 2-4

Table 2-2 Detailed BWR Assembly—Materials........................................................................ 2-4

Table 2-3 Density of Materials.................................................................................................. 2-4

Table 2-4 Heat Capacity of Air ................................................................................................. 2-5

Table 2-5 Thermal Conductivity of Air ...................................................................................... 2-5

Table 2-6 Viscosity of Air.......................................................................................................... 2-5

Table 2-7 Heat Capacity of Zircaloy-2 ...................................................................................... 2-5

Table 2-8 Thermal Conductivity of Zircaloy-2........................................................................... 2-5

Table 2-9 Heat Capacity of Steel.............................................................................................. 2-6

Table 2-10 Thermal Conductivity of Steel .................................................................................. 2-6

Table 2-11 Heat Capacity of the Surrogate Fuel in the Heated Assembly ................................. 2-6

Table 2-12 Thermal Conductivity of the Surrogate Fuel in the Heated Assembly...................... 2-6

Table 2-13 Heat Capacity of the Surrogate Fuel in the Unheated Assemblies .......................... 2-7

Table 2-14 Thermal Conductivity of the Surrogate Fuel in the Unheated Assemblies ............... 2-7

Table 2-15 Heat Capacity of Aluminum...................................................................................... 2-7

Table 2-16 Thermal Conductivity of Aluminum........................................................................... 2-7

Table 2-17 Heat Capacity of Incoloy .......................................................................................... 2-7

Table 2-18 Thermal Conductivity of Incoloy ............................................................................... 2-8

Table 2-19 Heat Capacity of Kaowool........................................................................................ 2-8

Table 2-20 Thermal Conductivity of Kaowool............................................................................. 2-8

Table 2-21 Predicted and TRW Radial keff Comparison........................................................... 2-10

Table 2-22 PWR Cell 1 Porous Model—Radial keff .................................................................. 2-11

Table 2-23 PWR Cell 1 Porous Model—Axial keff..................................................................... 2-11

Table 2-24 PWR Cell 2 Porous Model—Radial keff .................................................................. 2-11

Table 2-25 PWR Cell 2 Porous Model—Axial keff..................................................................... 2-11

Table 2-26 1x4 PWR Center Assembly Porous Model—Radial keff ......................................... 2-12

Table 2-27 1x4 PWR Center Assembly Porous Model—Axial keff............................................ 2-12

Table 2-28 1x4 PWR Peripheral Assembly Porous Model—Radial keff.................................... 2-12

Table 2-29 1x4 PWR Peripheral Assembly Porous Model—Axial keff ...................................... 2-12

Table 2-30 BWR Fully Populated Cladding Region Porous Model—Radial keff ....................... 2-12

Table 2-31 BWR Fully Populated Cladding Region Porous Model—Axial keff.......................... 2-13

Table 2-32 BWR Partially Populated Cladding Region Porous Model—Radial keff .................. 2-13

Table 2-33 BWR Partially Populated Cladding Region Porous Model—Axial keff .................... 2-13

Table 2-34 Equivalent Porous Model Density .......................................................................... 2-14

Table 2-35 PWR Cell 1 Porous Model—Heat Capacity ........................................................... 2-14

Table 2-36 PWR Cell 2 Porous Model—Heat Capacity ........................................................... 2-14

Table 2-37 1x4 PWR Center Porous Model—Heat Capacity................................................... 2-15

Table 2-38 1x4 PWR Peripheral Assembly Porous Model—Heat Capacity............................. 2-15

Table 2-39 BWR Fully Populated Cladding Region Porous Model—Heat Capacity ................ 2-15

Table 2-40 BWR Partially Populated Cladding Region Porous Model—Heat Capacity........... 2-15

Table 2-41 Friction Coefficient—PWR Assemblies .................................................................. 2-16

Table 2-42 Friction Coefficient—BWR Assemblies .................................................................. 2-16

Table 3-1 PWR Single Assembly Cell 2—Models.................................................................... 3-1

Table 3-2 PWR Cell 2 Steady-State Summary Results at 1 kW .............................................. 3-3
xii

Table 3-3 PWR Cell 2 Steady-State Convected Heat and Heat Transfer Coefficient 

 at 1 kW.....................................................................................................................3-3

Table 3-4 PWR Single Assembly Cell 2—PCT and Mass Flow rate at 1 kW at 20 Hours ....... 3-7

Table 3-5 PWR Single Assembly Cell 2 (Thermal Mass)—PCT and Mass Flow rate at 

 1 kW at 20 hours..................................................................................................... 3-11

Table 3-6 PWR Cell 2 Steady-State Mass Flow Rate at 0.5 kW............................................ 3-14

Table 3-7 PWR Single Assemble Cell 1—Models.................................................................. 3-15

Table 3-8 PWR Cell 1 Steady-State Mass Flow Rate at 1 kW............................................... 3-16

Table 3-9 PWR 1x4 Configuration—Models........................................................................... 3-18

Table 3-10 PWR 1x4 Configuration—Steady-State Mass Flow Rate at 1 kW ......................... 3-18

Table 3-11 PWR 1x4 Configuration—PCT and Mass Flow Rate at 1 kW at 24 Hours ............ 3-24

Table 3-12 BWR Single Assembly—Models ............................................................................ 3-26

Table 3-13 BWR Steady-State Mass Flow Rate at 1,369 W.................................................... 3-27

Table 3-14 WR Single Assembly—PCT and Mass Flow Rate at 1,369 W at 12 Hours ........... 3-31

Table 3-15 BWR Steady-State Mass Flow Rate at 2,236 W.................................................... 3-32

Table 4-1 Total Number of Cells for Different Grid Levels........................................................ 4-2

Table 4-2 Combinations ........................................................................................................... 4-3

Table 4-3 Mesh Level Ratios.................................................................................................... 4-3

Table 4-4 Computed Maximum Temperature........................................................................... 4-3

Table 4-5 PCT—GCI for Calculated Order of Accuracy ........................................................... 4-3

Table 4-6 PCT—GCI for Formal Order of Accuracy................................................................. 4-3

Table 4-7 Computed Mass Flow Rate...................................................................................... 4-4

Table 4-8 Mass Flow Rate—GCI for Calculated Order of Accuracy ........................................ 4-4

Table 4-9 Mass Flow Rate—GCI for Formal Order of Accuracy .............................................. 4-4
xiii

EXECUTIVE SUMMARY

Computational fluid dynamics (CFD) technologies are rapidly expanding, with a large database of 

proven capabilities. The driving force for program development generally is not the nuclear 

community, as it was for the classical thermal-hydraulic system codes. Nevertheless, many 

applications overlap with those associated with the nuclear industry, and in particular, dry cask 

applications: flows in complex geometries, mixing in stratified fluids, flow separation and 

reattachment, turbulence, multiphase phenomena, chemical species interaction, and combustion. 

Consequently, practitioners in areas related to dry cask applications can benefit from 

advancements in the technology taking place elsewhere. However, because of the complexity of 

modern commercial CFD packages, careful input preparation and solution of model equations are 

essential to avoiding errors.

In 2003, the U.S. Nuclear Regulatory Commission (NRC) undertook an experimental program to 

address thermal-hydraulic conditions and zirconium fire propagation during a complete loss of 

coolant event in a boiling-water reactor (BWR) spent fuel pool. The accident conditions of interest 

for the spent fuel pool were simulated in a full-scale prototypic fashion (electrically heated, 

prototypic BWR 9x9 assemblies in a prototypic spent fuel pool rack) so that the results closely 

represented actual fuel assembly responses. These experiments are summarized in 

NUREG/CR-7143, “Characterization of Thermal-Hydraulic and Ignition Phenomena in Prototypic, 

Full-Length Boiling Water Reactor Spent Fuel Pool Assemblies After a Postulated Complete Lossof-Coolant Accident,” issued March 2013.

Similarly, in 2009, the NRC, in collaboration with the Organisation for Economic Co-operation and 

Development/Nuclear Energy Agency (OECD/NEA) and 12 international partners signed an 

agreement called the “OECD/NEA Sandia Fuel Project—An Experimental Programme and 

Related Analyses for the Characterization of Hydraulic and Ignition Phenomena of Prototypic 

Water Reactor Fuel Assemblies.” This program defined an experimental test matrix, experimental 

conditions, and the parameters to be examined. The overall objective was to perform a highly 

detailed thermal-hydraulic characterization of a full-length pressurized-water reactor (PWR; 

17x17) commercial fuel assembly mockup to provide data for the direct validation of severe 

accident computer codes. These experiments are summarized in NUREG/CR-7215, “Spent Fuel 

Pool Project Phase 1: Pre-Ignition and Ignition Testing of a Single Commercial 17x17 

Pressurized Water Reactor Spent Fuel Assembly under Complete Loss of Coolant Accident 

Conditions,” issued April 2016, and NUREG/CR-7216, “Spent Fuel Pool Project Phase II: PreIgnition and Ignition Testing of a 1x4 Commercial 17x17 Pressurized Water Reactor Spent Fuel 

Assemblies under Complete Loss of Coolant Accident Conditions,” issued April 2016.

The experiments for both the BWR and the PWR assemblies were conducted in two phases: 

Phase I focused on a single, heated assembly and Phase II consisted of a single, heated 

assembly surrounded by four unheated assemblies representing a 1x4 loading pattern. 

Both phases included separate effect tests (i.e., preignition tests) and integral effects tests 

(i.e., ignition tests). The experiments in the separate effect tests were designed to investigate 

heat transfer and flow phenomena (i.e., naturally induced mass flow). The temperature values 

reached in these tests were below the ignition point of the cladding. As such, these tests were 

nondestructive. The experiments in the integral effects tests were conducted to reach the onset of 

cladding fire. As such, these tests led to the destruction of the assemblies. Both phases were 

conducted using a uniform axial power profile with electrically heated rods at multiple decay 

powers. 
xiv

This NUREG summarizes the efforts to validate the ANSYS FLUENT code using experimental 

data collected in the separate effects tests. The data of interest for these nondestructive tests 

were measured temperatures throughout the fuel assembly and induced mass flow rate. Detailed 

and porous CFD models were created for each assembly configuration including a single, heated 

full-length 17x17 PWR fuel bundle; a single, heated 17x17 PWR assembly surrounded by four 

unheated similar assemblies in a 1x4 loading pattern; and, a single, heated full-length 9x9 BWR 

fuel bundle. 

Steady-state and transient simulations were performed at different decay power values. Peak 

cladding temperature, exterior wall temperature, and mass flow rate from CFD predictions were 

compared to the experimental data. 

The CFD results and experimental data for PCT and air mass flow rate agreed favorably within 

the calculated experimental and CFD numerical uncertainties range. The results demonstrate that 

ANSYS Fluent modeling can be used to demonstrate the safety of dry cask storage and 

transportation.
xv

ABBREVIATIONS

2D two dimensional

BWR boiling-water reactor

CFD computational fluid dynamics

CFR Code of Federal Regulations

DH hydraulic diameter

ft foot/feet

GCI grid convergence index

ID inner dimension

in. inch(es)

J joule(s)

K Kelvin

keff effective thermal conductivity

kg kilogram(s)

kW kilowatt(s)

m meter(s)

MgO magnesium oxide

mm millimeter(s)

NRC U.S. Nuclear Regulatory Commission

OD outer dimension

OECD/NEA Organisation for Economic Co-operation and 

Development/Nuclear Energy Agency

PCT peak cladding temperature

PWR pressurized-water reactor

TRW TRW Environmental Safety Systems, Inc.

U.S. United States

V&V verification and validation

W watt(s)

1-1 

1 INTRODUCTION

1.1 Pressurized-Water Reactor Single Assembly

The testing in Phase I of the Spent Fuel Pool Project focused on axial heating and burn 

propagation. The near-prototypic test assembly was constructed to represent a commercial 

17x17 pressurized-water reactor (PWR) fuel bundle. Figure 1-1 illustrates the various 

components comprising a typical 17x17 PWR assembly. The main structural component of the 

assembly is the core skeleton, which consists of 11 spacers permanently attached to 25 guide 

tubes. The 264 fuel rods pass through the spacers and are held captive in the assembly by the 

top and bottom nozzles.

Figure 1-1 Various components in a typical 17x17 PWR fuel assembly

The single full-length, electrically heated PWR assembly was fabricated using prototypic, 

commercial 17x17 PWR components and 9.50-millimeter (mm) (0.374-inch (in.)) heater rods 

made from 11.18-mm (0.44-in.) Zircaloy-2 tubing. The as-built heater rod diameter of 9.50 mm 

(0.374 in.) is slightly smaller than the typical PWR design value of 9.53 mm (0.375 in.) but is not 

expected to significantly affect system hydraulics. 

The tests were performed using a uniform power profile with electrically heated rods. A 0.1524-

meter (m) (6-in.) layer of Kaowool insulation was installed around the pool cell and then wrapped

with a 0.9 mm (0.036 in.) thick sheet of stainless steel. 

During the tests, the assembly cooled by natural circulation, and the pressure and air inlet 

temperature maintained the local ambient conditions.

The tests were performed for two storage pool cell sizes. Table 1-1 presents a summary of the 

hydraulic characteristics of the cells. 

Table 1-1 Summary of Assembly Hydraulic Characteristics for Storage Cell 1 and Cell 2

Description Cell 1 Cell 2

Inner Dimension (mm/in) 221.3/8.71 223.4/8.80

Flow Area (m2/in2) 0.0273/4.2e-5 0.0283/4.4e-5

Hydraulic diameter, DH (mm/in) 11.2/0.441 11.6/0.457

Spacer

Bottom 

nozzle

Guide 

tubes Top 

nozzle

Spacer
1-2

NUREG-7215, “Spent Fuel Project Phase I: Pre-Ignition and Ignition Testing of a Single 

Commercial 17x17 Pressurized Water Reactor Spent Fuel Assembly under Complete Loss of 

Coolant Accident Conditions,” issued April 2016, contains further details of the test conditions, 

such as thermocouple and hot wire anemometer layout.

1.2 Pressurized-Water Reactor 1x4 Assembly Configuration 

The testing in Phase II of the Spent Fuel Pool Project focused on axial and transverse heating 

propagation from the center to the peripheral bundles of the full-length assemblies with the same 

components as used for Phase I. The fuel assemblies were arranged in a pool rack with the 

heated assembly in the center pool cell as shown in Figure 1-2. The four unheated peripheral fuel 

assemblies shared a cell wall with the center assembly, representing older spent fuel. All mock 

fuel assemblies were constructed with zirconium alloy cladding and prototypic structural 

components. The center assembly was constructed with electrically resistive heaters. The 

thermal mass of the compacted magnesium oxide (MgO) powder used to make the electric heater 

matched the prototypic uranium oxide spent fuel as demonstrated in the boiling-water reactor 

(BWR) study (NUREG/CR-7143, “Characterization of Thermal-Hydraulic and Ignition Phenomena 

in Prototypic, Full-Length Boiling Water Reactor Spent Fuel Pool Assemblies After a Postulated 

Complete Loss-of-Coolant Accident,” issued March 2013). The peripheral assemblies were 

loaded with MgO pellets in order to closely match the thermal mass of spent fuel. A series of 

preignition tests were conducted to build a database of the thermal-hydraulic response of fuel 

below ignition temperatures. 

The main structural component of the assembly is the core skeleton, which consists of 11 spacers 

permanently attached to 25 guide tubes. The 264 fuel rods pass through the spacers and are 

held captive in the assembly by the top and bottom nozzles.

Figure 1-2 Layout of the Phase II test assembly

The four peripheral PWR assemblies were fabricated using prototypic, commercial 17x17 PWR 

components including a skeleton, top and bottom nozzles, 9.50-mm (0.374-in.) outer dimension

by 0.57-mm (0.0225-in.) wall tubing, top and bottom end plugs, and plenum springs. The center 

heated PWR assembly was fabricated using prototypic, commercial 17x17 PWR components and 

9.53-mm (0.375-in.) outer dimension heater rods made from 11.18-mm (0.44-in.) zirconium alloy 

tubing supplied by an industrial vendor. The wall thickness of the Zircaloy-2 cladding measured
1-3 

approximately 0.71 mm (0.028 in.) and was relatively unchanged by the heater fabrication 

process. The spent fuel rod simulators for Phase II had a linear power profile and a maximum 

output of 31.1 watts (W)/m (9.5 W/foot (ft)), which was twice that expected to produce ignition.

The pool rack for the 17x17 PWR fuel assemblies incorporates pool cells with an inner dimension 

of 224.5 mm (8.84 in.). As with the Phase I pool cells, the Phase II pool rack was constructed of 

1.91-mm (0.075-in.)-thick stainless steel material. Figure 1-3 shows the actual inner dimensions 

of each of the pool cells. The inner dimension of the center cell used in this experiment was 

224.2 mm (8.83 in.), which is nearly identical to the 224.5-mm (8.84-in.) inner dimension of the 

pool rack. The as-built peripheral cells are slightly smaller than the design, with an average inner 

dimension of 222.7 mm (8.77 in.), or less than a 1 percent difference. Figure 1-3 also shows the 

insulation scheme for Phase II. The corner cells were filled with high-temperature insulation. The 

entire assembly was surrounded by approximately 152.4 mm (6 in.) of the same high-temperature 

insulation. A stainless steel thermal radiation barrier was installed around the external insulation. 

Table 1-2 summarizes the hydraulic characteristics.

Figure 1-3 Dimensions of the as-built pool rack and the design insulation thickness

North

South

West East

222.65

222.65

222.65

222.65 224.2

Corner 

cells filled 

w/ 

insulation

152.4

Insulation

(All dimensions in mm)
1-4

Table 1-2 Hydraulic Dimensions for the Center Assembly, Average Peripheral Assembly, 

and the Cross-Flow Path

Description Center Peripheral Cross-Flow Path

Inner Dimension (mm/in.) 224.2/8.83 222.65/8.77 8.7/0.34

Flow Area (m2/in.2) 0.0287/44.49 0.0283/43.87 5.89E-5/0.0913

Hydraulic diameter, DH (mm/in.) 11.7/0.46 11.6/0.46 8.7/0.34

NUREG/CR-7216, “Spent Fuel Project Phase II: Pre-Ignition and Ignition Testing of a 1x4 

Commercial 17x17 Pressurized Water Reactor Spent Fuel Assemblies under Complete Loss of 

Coolant Accident Conditions,” issued April 2016, has further details about the instrumentation, 

including the hot wire anemometers, oxygen sensors, residual gas analyzer, strain gauges, and 

thermocouples.

1.3 Boiling-Water Reactor Single Assembly

The prototypic 9x9 BWR assembly includes the top and bottom tie plates, spacers, water rods, 

channel box, and all related assembly hardware. Incoloy heater rods were substituted for the fuel 

rod pins for heated testing. The diameter of the Incoloy heaters was slightly smaller than that of 

the prototypic pins, 1.09x10-2 m versus 1.12x10-2 m. Table 1-3 lists the dimensions of the 

assembly components.

Table 1-3 Dimensions of Assembly Components in the 9x9 BWR

Description

Lower (Fully Populated) 

Section

Upper (Partially Populated) 

Section

Number of Pins 74 66

Pin Diameter (m) 1.09x10-2 1.09x10-2

Pin Pitch (m) 1.44x10-2 1.44x10-2

Pin Separation (m) 3.48x10-3 3.48x10-3

Water Rod OD (main section) (m) 2.49x10-2 2.49x10-2

Water Rod ID (m) 2.34x10-2 2.34x10-2

Storage Cell Dimension Dcell (mm) 132.6 132.6

Flow Area, A Assembly (m2) 0.0098 0.0106

DH, Ref. (m) 0.0119 0.0141

A stainless steel enclosure housed the entire fuel assembly, simulating the rack walls of a spent 

fuel pool. This enclosure was then insulated with 0.15 m (6 in.) of Fiberfrax Durablanket® type S

insulation. Two radiation barriers, consisting of stainless steel shim stock, were placed at 0.075-m 

(3-in.) intervals, as shown in Figure 1-4.
1-5 

Figure 1-4 Arrangement of insulation, radiation barriers, and external thermocouples

Data using closed bypass and open drain holes were used for the validation effort. Bypass holes 

are part the BWR 9x9 configuration. The drain holes simulate the flow from the plenum and other 

assemblies. Figure 1-5 shows the drain holes at the bottom side of the BWR single assembly.

Figure 1-5 Arrangement of drain holes

NUREG/CR-7143 contains more details about the instrumentation.

The 1x4 BWR experimental setup consisted of five shortened assemblies, recreating the top 

1.22-m (4-ft.) section. For this testing, airflow rates and inlet temperature were controlled for the 

center and peripheral assemblies. The mass flow was not naturally induced (i.e., forced flow) in 
1-6 

the assemblies, which is not prototypical for dry cask applications. Therefore, this validation effort 

did not include this part of the experiment. 

1.4 Computational Fluid Dynamics Model

Detailed and porous media simulations were performed for each of the aforementioned preignition 

tests using ANSYS FLUENT. As an example, Figure 1-6 shows a cross section of the CFD PWR 

single assembly detailed and porous models. Both models used 1/8th symmetry boundary 

conditions to reduce the modeling efforts.

 Detailed Model Porous Model

Figure 1-6 CFD PWR single assembly cross sections of the detailed and porous models

The PWR and BWR detailed models explicitly represent each component of the assemblies, 

including fuel rods, cladding, guide tubes, grid spacers, neutron absorbers in the peripheral 

assemblies, and bottom and top nozzles. The porous media model in the PWR assemblies was 

representative of the fuel, cladding, fluid within the pool cell, grid spacers and guide tubes. In the 

BWR assemblies, the porous media represented the fuel, cladding, water rods, and the flow within 

the channel box and grid spacers. Use of porous media involves representing the absence of 

these components with an equivalent frictional and inertial hydraulic loss, equivalent thermal 

conductivity, equivalent density, and equivalent heat capacity. 

FLUENT, Version 16, was used for the validation in this NUREG. 

Fuel rods

Guide tubes

Pool cell

Insulation

Pool cell

Insulation

Porous media
2-1 

2 COMPUTATIONAL FLUID DYNAMICS MODELING

2.1 Detailed Model

Geometry and mesh models were generated for a single PWR assembly, single BWR assembly, 

and 1x4 PWR configuration. The model’s boundary conditions represented the existing 

conditions during the experiment. Figure 2-1 through Figure 2-6 show a schematic of the 

boundary conditions applied to the detailed models. The model used a pressure inlet boundary at 

the entry of the assembly (shown in blue), pressure outlet at the exit (shown in red) and applied a 

volumetric heat source in the volume occupied by MgO powder. The flow regime through the 

assembly was modeled as laminar, as the corresponding Reynolds number based on the 

hydraulic diameter was below 200. The model used an operating pressure of 84,000 Pa, which 

corresponded to the altitude of the location of the experiment. To reduce the extent of the 

analyzed control volume, the model considered symmetry. As such, the PWR assemblies for the 

Phase 1 and Phase 2 simulations used 1/8th symmetry (shown in the figures in yellow), and the 

BWR single assembly simulation used 1/4th symmetry. In the BWR assembly, the drain holes 

were modeled by adding an inlet at the bottom of the assembly, as shown in Figure 2-4, using an 

inlet vent boundary condition (shown in blue) with a loss coefficient of 0.42 to represent minor 

losses from the experimental drain holes arrangement shown in Figure 1-5. 

Figure 2-1 Detailed PWR single assembly (Cell 2 illustrated)—boundary conditions
2-2 

Figure 2-2 Detailed PWR single assembly top and bottom views (Cell 2 illustrated)—

boundary conditions

Figure 2-3 Detailed BWR single assembly—boundary conditions (1/4 symmetry)
2-3 

Figure 2-4 Detailed BWR single assembly top and bottom views—boundary conditions

Figure 2-5 Detailed PWR 1x4 configuration—boundary conditions

Figure 2-6 Detailed PWR 1x4 configuration top and bottom views—boundary conditions
2-4

Table 2-1 and Table 2-2 summarize the materials of each component in the assembly. Table 2-3

shows the material densities with the exception of air, which was modeled as an ideal gas. All 

other physical properties for the materials used were implemented as function of temperature, as 

seen in Table 2-4 through Table 2-20.

Table 2-1 Detailed PWR Assemblies—Materials

Component Material

Surrogate Fuel (heated assembly) Magnesium Oxide Powder and Nichrome

Surrogate Fuel (unheated assembly) Magnesium Oxide Pellets

Cladding Zircaloy-2

Guide Tubes Zircaloy-2

Fluid Air

Grid Spacers Zircaloy-2

Insulation Kaowool

Cell Wall Steel

Exterior Wall Steel

Neutron Absorber Aluminum

Table 2-2 Detailed BWR Assembly—Materials

Component Material

Surrogate Fuel Magnesium Oxide Powder and Nichrome

Cladding Incoloy

Water Rod Zircaloy-2

Fluid Air

Grid Spacers Zircalo-2

Insulation Kaowool

Channel Box Zircaloy-2

Cell Wall Steel

Exterior Wall Steel

Table 2-3 Density of Materials

Material Density (kg/m3)

Zirconium 6,500

Steel 8,030

Magnesium Oxide powder and Nichrome 2,913

Magnesium Oxide Pellets 2,720

Aluminum 2,702

Inconel 8,000

Kaowool 96
2-5

Table 2-4 Heat Capacity of Air

Temperature (K) cp (J/kg-K)

250 1,007

500 1,030

800 1,091

1,000 1,141

1,600 1,248

Table 2-5 Thermal Conductivity of Air

Temperature (K) k (W/m-K)

250 0.0223

500 0.0373

800 0.0573

1,000 0.0667

1,600 0.106

Table 2-6 Viscosity of Air

Temperature (K) μ (kg/m-s)

250 1.6E-5

500 2.7E-5

800 3.7E-5

1,000 4.24E-5

1,600 5.84E-5

Table 2-7 Heat Capacity of Zircaloy-2

Temperature (K) cp (J/kg-K)

273 275

400 302

640 331

1,090 375

1,093 505

Table 2-8 Thermal Conductivity of Zircaloy-2

Temperature (K) k (W/m-K)

273 12.1

473 14.5

673 17

873 19.9

1,073 23.1
2-6

Table 2-9 Heat Capacity of Steel

Temperature (K) cp (J/kg-K)

200 402

400 526

600 554

800 581

1,000 608

1,200 640

1,500 682

Table 2-10 Thermal Conductivity of Steel

Temperature (K) k (W/m-K)

273 16

398 17

498 19

800 22.6

1,000 25.4

1,200 28

1,500 31.7

Table 2-11 Heat Capacity of the Surrogate Fuel in the Heated Assembly

Temperature (K) cp (J/kg-K)

273 848

400 100

600 1,111

800 1,167

1,000 1,209

1,145 1,228

Table 2-12 Thermal Conductivity of the Surrogate Fuel in the Heated Assembly

Temperature (K) k (W/m-K)

273 400

400 12.8

600 15.3

800 17.6

1,000 19.7

1,100 20.6
2-7

Table 2-13 Heat Capacity of the Surrogate Fuel in the Unheated Assemblies

Temperature (K) cp (J/kg-K)

273 892.4

400 1,058

600 1,176

800 1,234

1,000 1,272

Table 2-14 Thermal Conductivity of the Surrogate Fuel in the Unheated Assemblies

Temperature (K) k (W/m-K)

273 1.73

400 1.88

600 2.06

800 2.2

1,000 2.28

1,100 2.3

Table 2-15 Heat Capacity of Aluminum

Temperature (K) cp (J/kg-K)

100 482

200 798

400 949

600 1,033

800 1,146

Table 2-16 Thermal Conductivity of Aluminum

Temperature (K) k (W/m-K)

100 302

200 237

400 240

600 231

800 218

Table 2-17 Heat Capacity of Incoloy

Temperature (K) cp (J/kg-K)

298 428

473 435

673 450

873 469

1,073 488
2-8

Table 2-18 Thermal Conductivity of Incoloy

Temperature (K) k (W/m-K)

298 11.5

473 14.3

673 17.4

873 20.6

1,073 23.8

Table 2-19 Heat Capacity of Kaowool

Temperature (K) cp (J/kg-K)

273 788

473 862

673 928

873 985

1,073 1,030

1,273 1,090

1,473 1,100

Table 2-20 Thermal Conductivity of Kaowool

Temperature (K) k (W/m-K)

273 0.0208

473 0.0502

673 0.088

873 0.134

1,073 0.188

1,273 0.251

1,473 0.322

2.2 Porous Model

All dry cask applicants favor the use of the porous model, or media method, since it simplifies the 

configuration and saves on processing time. As such, the porous media method was chosen for 

validation to test its robustness and predictive capabilities. The use of this model involves input to 

make up for the simplifications made in the geometry. Simplifications, such as fuel rods, grid 

spacers, and any assembly’s intricacies, are replaced by a volume filled with porous media with 

an equivalent flow resistance. Additionally, the combination of radiation and conduction heat 

transfer within that volume is represented by an effective thermal conductivity (keff). To 

accomplish this task, a two-dimensional (2D) model representing the detailed cross section of an 

assembly explicitly showing fuel rods was used (as shown in Figure 2-7) to obtain keff for different 

temperature boundary conditions. The TRW Environmental Safety Systems, Inc. (TRW) report, 

“Spent Nuclear Fuel Effective Thermal Conductivity,” dated July 11, 1996, describes the keff

approach in detail.

Figure 2-7 shows the CFD 2D model with 1/8th symmetry used to calculate the radial effective 

thermal conductivity for the PWR cell 1 single assembly configuration. The model shows all the 
2-9 

components in the assembly including fuel, cladding, guide tubes, and cell wall. This model used 

symmetry as well as constant wall temperature as boundary conditions.

Figure 2-7 2D model to calclulate keff for PWR single assembly (Cell 1 shown)

Similarly, 2D models were developed for each configuration that was validated to calculate the 

effective thermal conductivity as a function of temperature. In these models, the boundary 

conditions consisted of the fuel rods surrounded by the pool cell wall. Multiple runs at different 

powers for each assembly configuration were performed in order to generate a “database” that 

would represent the temperature range to which each assembly would be exposed. Equation 2-1 

and Equation 2-2 show the radial and axial components of the effective conductivity in the PWR 

and BWR single assembly configurations and the center assembly in the 1x4 PWR configuration. 

Equation 2-2 and Equation 2-3 were applied to the peripheral assembly configuration since the 

heat source was not coming from the center of assembly itself like the other assemblies, but 

rather from the wall next to the center assembly. 

 kkeeeeee(rrrrrrrrrrrr) = 00. 22222222 ∗ QQ

∗LL ∗(TTpp −TTee eeee)

 Equation 2–1 

kkeeeeee( aa ) = ∑ kk ∗ AA _rrrrrrrrrr nn Equation 2–2 

 kkeeeeee(rrrrrrrrrrrr) = QQ∗ΔΔΔΔ

AA∗ΔΔ Equation 2–3 

Where:

keff = The effective thermal conductivity

Q = the power

La = the active length of the assembly

Tpeak = the maximum temperature in the assembly

Tedge = the constant boundary condition temperature at the edge of the assembly

ki = the thermal conductivity of the material

Ai_ratio = the area ratio

Δy = the width of the assembly

A = the cross sectional area

ΔT = the difference in temperature between the hot wall and the assembly 

temperature area weighted average.
2-10

In order to verify the effective conductivity values obtained with this model, the results were 

compared with the results from the TRW report. The values in the TRW report were obtained 

using a finite element method. Table 2-21 summarizes the results of this comparison. 

Table 2-21 Predicted and TRW Radial keff Comparison

Temperature (Kelvin) Keff (W/m*K) Keff (W/m*K) (calculated 

based on TRW report data)

298 0.4061 0.3987

473 0.6676 0.6763

673 1.1346 1.1890

Similarly, Figure 2-8 shows the 2D model used to calculate the effective radial thermal 

conductivity for the peripheral assembly in the 1x4 configuration. The model shows half of one of 

the peripheral assemblies, representing 1/8th of all the peripheral assemblies. This model applied 

constant heat flux on the hot wall, constant temperature at the opposing wall, and symmetry.

Figure 2-8 2D model to calclulate keff for 1x4 PWR configuration (peripheral assembly)
2-11

Table 2-22 through Table 2-33 summarize the results for all configurations.

Table 2-22 PWR Cell 1 Porous Model—Radial keff

Temperature (Kelvin) Keff (W/m*K)

293 0.0846

312 0.0928

394 0.1308

465 0.1841

545 0.2622

631 0.3721

Table 2-23 PWR Cell 1 Porous Model—Axial keff

Temperature (Kelvin) Keff (W/m*K)

273 4.5186

400 5.1989

600 6.1722

800 7.0880

1,000 7.9906

1,100 8.4468

Table 2-24 PWR Cell 2 Porous Model—Radial keff

Temperature (Kelvin) Keff (W/m*K)

292 0.0967

311 0.1078

348 0.129

385 0.1523

456 0.2248

537 0.3343

580 0.4064

Table 2-25 PWR Cell 2 Porous Model—Axial keff

Temperature (Kelvin) Keff (W/m*K)

273 4.43

400 5.1

600 6.06

800 6.96

1,000 7.84

1,100 8.29
2-12

Table 2-26 1x4 PWR Center Assembly Porous Model—Radial keff

Temperature (Kelvin) Keff (W/m*K)

293 0.0867

312 0.0959

389 0.1357

459 0.1962

539 0.2866

Table 2-27 1x4 PWR Center Assembly Porous Model—Axial keff

Temperature (Kelvin) Keff (W/m*K)

273 4.21

400 4.8443

600 5.7517

800 6.6053

1,000 7.4466

1,100 7.8718

Table 2-28 1x4 PWR Peripheral Assembly Porous Model—Radial keff

Temperature (Kelvin) Keff (W/m*K)

293 0.1999

318 0.2664

348 0.3596

410 0.4601

Table 2-29 1x4 PWR Peripheral Assembly Porous Model—Axial keff

Temperature (Kelvin) Keff (W/m*K)

273 1.6066

400 1.8287

600 2.1162

800 2.3817

1,000 2.6573

1,100 2.8125

Table 2-30 BWR Fully Populated Cladding Region Porous Model—Radial keff

Temperature (Kelvin) Keff (W/m*K)

297 0.0981

324 0.1113

423 0.1576

489 0.215

564 0.2975

646 0.4121

733 0.5653
2-13

Table 2-31 BWR Fully Populated Cladding Region Porous Model—Axial keff

Temperature (Kelvin) Keff (W/m*K)

273 4.5002

400 5.2028

600 6.2560

800 7.2618

1,000 8.2211

1,100 8.8762

Table 2-32 BWR Partially Populated Cladding Region Porous Model—Radial keff

Temperature (Kelvin) Keff (W/m*K)

294 0.0959

321 0.11

410 0.155

478 0.2166

555 0.3061

639 0.4315

728 0.5998

Table 2-33 BWR Partially Populated Cladding Region Porous Model—Axial keff

Temperature (Kelvin) Keff (W/m*K)

273 4.0248

400 4.6537

600 5.5962

800 6.4961

1,000 7.3546

1,100 7.7621

The equivalent density for the porous models was calculated as shown in . 

ρρ = ∑ ρρnn ∗ AA _rrrrrrrrrr Equation 2–4

Where:

ρ = the density

Aratio = the area ratio

Table 2-34 lists the values used for each of the models.
2-14

Table 2-34 lists the values used for each of the models.

Table 2-34 Equivalent Porous Model Density

Assembly Configuration Density (kg/m3)

PWR single assembly (Cell 1) 1,562

PWR single assembly (Cell 2) 1,533

PWR 1x4 configuration (center assembly) 1,455

PWR 1x4 configuration (peripheral assembly) 1,355

BWR single assembly (fully populated rods 

region)

1,680

BWR single assembly (partially populated rods 

region)

1,503

The equivalent heat capacity for each porous model was calculated using Equation 2-5. 

ccpp = ∑ ccpp_ii ∗ mmii_rrrrrr rr nn

ii ; mmii_rrrrrr rr = (ρρii∗AAiirrrrrr rr)

ρρ Equation 2-5

Where:

cp = the heat capacity

mratio = the mass ratio

Aratio = the area ratio

Table 2-35 to Table 2-40 illustrates the results and values used for each porous configuration.

Table 2-35 PWR Cell 1 Porous Model—Heat Capacity

Temperature (Kelvin) cp (J/kg*K))

273 571

400 662

600 731

800 770

1,000 801

Table 2-36 PWR Cell 2 Porous Model—Heat Capacity

Temperature (Kelvin) cp (J/kg*K))

273 571

400 662

600 731

800 770

1,000 801
2-15

Table 2-37 1x4 PWR Center Porous Model—Heat Capacity

Temperature (Kelvin) cp (J/kg*K))

273 571

400 662

600 731

800 770

1,000 801

Table 2-38 1x4 PWR Peripheral Assembly Porous Model—Heat Capacity

Temperature (Kelvin) cp (J/kg*K))

273 621

400 726

600 802

800 844

1,000 874

Table 2-39 BWR Fully Populated Cladding Region Porous Model—Heat Capacity

Temperature (Kelvin) cp (J/kg*K))

273 641

400 723

600 786

800 824

1,000 855

Table 2-40 BWR Partially Populated Cladding Region Porous Model—Heat Capacity

Temperature (Kelvin) cp (J/kg*K))

273 640

400 721

600 785

800 823

1,000 853

Another important parameter for the porous media model was the frictional coefficient for each 

assembly configuration. Three methods were used to calculate the friction coefficient. The first 

two methods used are shown in Equation 2-6 and Equation 2-7. The values for the variables in 

these equations were obtained from ANSYS FLUENT simulations of the detailed model for both 

the heated and isothermal models, respectively. 

DD = 4∗ττww

μ∗VV aaaa aaaaaa _pp ∗DDhyyyy

Equation 2-6

DD = ΔΔΔΔ

μ∗LL∗VV aaaa aaaaaa _pp

Equation 2-7
2-16

Where:

DD = the friction coefficient

ττww = the shear stress at the wall

μ = the viscosity

Vavg_inlet_por = the average inlet velocity for the porous model

Dhyd = the hydraulic diameter

ΔP = the pressure difference

L = the length of the assembly

The frictional coefficient obtained from either Equation 2-6 or Equation 2-7 was used as an initial 

input for the third method. The third method used the comparison of the peak cladding 

temperature (PCT) obtained from the detailed and porous models. The frictional coefficient of the 

porous media model was changed until the PCT matched. Table 2-41 and Table 2-42 show the 

values used for the porous model for each configuration using the third method.

Table 2-41 Friction Coefficient—PWR Assemblies

Power

(kW)

Single Assembly

Cell 1

Single Assembly

Cell 2

1x4 Configuration

Center Assembly

1x4 configuration 

Peripheral Assembly

0.5 1,005,000

1 1,120,000 992,000 1,120,000 800,000

Table 2-42 Friction Coefficient—BWR Assemblies

Power (kW) Single Assembly 

1.369 547,000

2.236 529,000

The boundary conditions were representative of those present during the experiment. Figure 2-9

to Figure 2-14 show a schematic of the boundary conditions. Pressure inlet was used at the inlet 

(shown in blue), pressure outlet at the exit (shown in red), and volumetric heat source was used in 

the volume occupied by MgO powder. Laminar flow was assumed inside the assembly, as the 

Reynolds number was below 200. An operating pressure of 84,000 Pa and symmetry (shown in 

yellow) were used to reduce the extent of the analyzed control volume. The drain holes in the 

BWR assembly were represented in the porous model in the same manner as previously 

discussed in the detailed model. Section 2.1 provides more details.
2-17

Figure 2-9 Porous PWR single assembly (Cell 2 illustrated)—boundary conditions

Figure 2-10 Porous PWR single assembly top and bottom views (Cell 2 illustrated)—

boundary conditions
2-18

Figure 2-11 Porous PWR 1x4 configuration—boundary conditions

Figure 2-12 Porous PWR 1x4 configuration top and bottom views—boundary conditions
2-19

Figure 2-13 Porous BWR single assembly—boundary conditions

Figure 2-14 Porous BWR single assembly top and bottom views—boundary conditions

3-1

3 RESULTS AND DISCUSSION 

3.1 Pressurized-Water Reactor Single Assembly (Cell 2: 223.4 mm)

The tables and graphs in this section summarize the results for a single PWR assembly with a cell 

size inner dimension of 223.4 mm (8.8 in.). Table 3-1 summarizes the scenarios modeled in this 

section. Section 3.1.1 includes a detailed description of the purpose for each of these models. 

This explanation provides the basis for all other models throughout this report.

Table 3-1 PWR Single Assembly Cell 2—Models

Model Steady State Transient

Power (kW) 1 0.5 1

Detailed

Porous

Extended Porous (laminar)

Extended Porous (turbulent)

Detailed (MgO - 3,204 (kg/m3))

Detailed (MgO -1,747 (kg/m3))

3.1.1 Power—1 kW (Steady State)

Three configurations were used to obtain the correct heat transfer coefficient at the external 

boundary. The first two configurations, which were used in the rest of this report, included only 

the insulated assembly without the surroundings, as shown in Figure 3-1 and Figure 3-2. These 

two configurations used model and porous media, respectively. Table 3-2 summarizes the results 

from these models including PCT, mass flow rate through the assembly, and the exterior wall 

temperature. The heat transfer interaction of the insulated assembly with the surroundings 

through the outside walls (i.e., external and top walls) was modeled using a heat transfer 

correlation. Table 3-3 shows the heat transfer coefficients for all these cases. The heat transfer 

coefficient correlations used for the vertical and horizontal walls came from Rohsenow 

et al. (1998) and Bergman et al. (2011). Radiation heat transfer was also included at these 

boundaries. The third configuration included the surroundings and used the porous media model, 

as depicted in Figure 3-3. Both laminar and turbulent flow models were considered to model the 

flow of the surroundings for this configuration to test the effect of the flow regime. The predictions 

in this section were undertaken to check the heat transfer boundary condition at the external wall 

of the first two configurations. This could be done simply by comparing the PCT temperature, air 

mass flow rate entering the assembly, and the external wall temperature of these models, as 

shown in Table 3-2, or by calculating the heat transfer coefficient from the extended model shown 

in Table 3-3. Figure 3-4 through Figure 3-6 summarize the results obtained for each of these 

configurations and models. Cell wall temperature profiles were used to compare the CFD 

modeling approaches (i.e., detailed vs. porous modeling), as Figure 3-5 shows. The same 

approach was taken for all other configurations in the NUREG.
3-2 

Figure 3-1 Detailed configuration—PWR single assembly Cell 2 

Figure 3-2 Porous configuration—PWR single assembly Cell 2 
3-3 

Figure 3-3 Porous configuration for extended models—PWR single assembly Cell 2

Table 3-2 PWR Cell 2 Steady-State Summary Results at 1 kW

Model PCT 

(K)

Mass Flow Rate 

(kg/s)

Exterior Wall 

Temperature (K)

Detailed 533 0.00048 310

Porous 533 0.00047 311

Porous Extended 

(laminar)

530 0.00047 312

Porous Extended 

(turbulent)

530 0.00048 312

Experiment at 

20 hours

525 0.00052 310

Table 3-3 PWR Cell 2 Steady-State Convected Heat and Heat Transfer Coefficient at 1 kW

Model Exterior Wall 

Convected Heat 

(W)

Exterior Wall 

Heat Transfer 

Coefficient 

(W/m2.K)

Top Wall 

Convected Heat 

(W)

Top Wall Heat 

Transfer 

Coefficient 

(W/m2.K)

Detailed 8.4 (from 

Correlations)

1.89 (from 

Correlations)

1.02 (from 

Correlations)

5.52 (from 

Correlations)

Porous 9.1 (from 

Correlations)

1.88 (from 

Correlations)

0.93 (from 

Correlations)

 5.15 (from 

Correlations)

Porous 

Extended 

(laminar)

8.9 (from CFD 

predictions)

1.84 (from CFD 

predictions)

0.69 (from CFD 

predictions)

2.76 (from CFD 

predictions)

Porous 

Extended 

(turbulent)

8.9 (from CFD 

predictions)

1.85 (from CFD 

predictions)

0.82 (from CFD 

predictions)

3.32 (from CFD 

predictions)
3-4

Figure 3-4 PWR Cell 2 steady-state PCT as a function of height at 1 kW

Figure 3-5 PWR Cell 2 steady-state pool cell wall maximum temperature as a function of 

height at 1 kW

275

325

375

425

475

525

575

0 1 2 3 4

Temperature (K)

Height (m)

Experimental

Detailed

Porous

Porous Extended

(Laminar)

Porous Extended

(Turbulent)

290

340

390

440

490

540

0 1 2 3 4

Temperature (K)

Height (m)

Porous

Porous Extended

(Laminar)

Porous Extended

(Turbulent)

Detailed
3-5

Figure 3-6 PWR Cell 2 steady-state exterior wall maximum temperature as a function of 

height at 1 kW

Table 3-2 and Table 3-3 results show that the heat transfer correlations used in the nonextended 

models predicted very well the heat transfer at the walls surrounding the insulated assembly. This 

is also apparent in Figure 3-4 through Figure 3-6 when comparing the models. As shown in these

figures, the effect of turbulence on the extended models is negligible.

The porous model predicted the profiles of the PCT, external wall, and cell wall favorably, as 

shown in Figure 3-4 through Figure 3-6. In addition, the porous media model predictions were 

slightly more conservative than the detailed model. As such, the choice for the porous media 

parameters, as explained in Section 2.2, such as frictional factor and the effective heat 

conductivity, are justified. The initial guess of the friction factor was obtained from the isothermal 

pressure drop method or the isothermal shear stress method. The final tunning of the friction 

factor was obtained by comparing the PCT values between the porous and the detailed models. 

Further, the experimental data in these plots are shown at the last time step (20 hours). The CFD 

models for the detailed and the porous models predicted very closely the profile of the PCT and 

the external wall temperature obtained in the experiment. Any discrepancy between the 

experimental data and the CFD predictions can be attributed to the fact that steady state was not 

yet reached in the final step of the experiment as well as the uncertainty from both the experiment 

and grid convergence index (GCI) calculations (see Section 4 ).

3.1.2 Power—1 kW (Transient)

Figure 3-7 through Figure 3-13 show that CFD predictions matched the experimental data profile 

for the PCT, mass flow rate, pool cell wall, and external wall temperature closely. The predictions 

obtained from CFD also matched the profiles of the experimental data for the PCT and external 

wall temperature at 20 hours (see Table 3-4 and Figure 3-11 through Figure 3-13). Any 

discrepancy between the CFD predictions and experimental data may be attributed to the 

uncertainty of the thermal mass (i.e., ρ*cp, where ρ is the density and cp is the specific heat 

capacity) used in the CFD predictions. Section 3.1.2.1 provide a more detailed analysis of this 

discrepancy. As a general highlight, the higher the thermal mass, the more resistance to heat 

290

295

300

305

310

315

320

0 1 2 3 4

Temperature (K)

Height (m)

Experimental

Detailed

Porous

Porous Extended

(Laminar)

Porous Extended

(Turbulent)
3-6

transfer and the lower the temperature. Additionally, this discrepancy can be attributed to the 

uncertainty of measurement and CFD discretization error (see Section 4 ). Another fact that can 

lead to this discrepancy is the possibility of leakage through the top of the 25 guide tubes. The 

tops of the guide tubes were fitted with spherical objects. This type of seal leaks quickly as the 

assembly is heated. As such, potential air flow rate can lower the temperature of the experimental 

setup. 

Figure 3-7 PWR Cell 2 PCT as a function of time at 1 kW

Figure 3-8 PWR Cell 2 mass flow rate as a function of time at 1 kW

290

340

390

440

490

540

0 10 20 30 40

Temperature (K)

Time (hrs)

Experiment

Detailed

Porous

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0 10 20 30 40

Mass Flow Rate (kg/s)

Time (hrs)

Experiment

Detailed

Porous

Uncertainty
3-7

Figure 3-9 PWR Cell 2 pool cell wall maximum temperature as a function of time at 1 kW

Figure 3-10 PWR Cell 2 exterior wall maximum temperature as a function of time at 1 kW

Table 3-4 PWR Single Assembly Cell 2—PCT and Mass Flow rate at 1 kW at 20 Hours

Model PCT (K) Mass Flow Rate (kg/s)

Experiment 525 0.00053

Detailed 529 0.00048

Porous 532 0.00047

250

300

350

400

450

500

550

0 10 20 30 40

Temperature (K)

Time (hrs)

Experiment

Porous

Detailed

298

300

302

304

306

308

310

312

0 10 20 30 40

Temperature (K)

Time (hrs)

Experiment

Porous

Detailed
3-8

Figure 3-11 PWR Cell 2 PCT as a function of height at 1 kW at 20 hours

Figure 3-12 PWR Cell 2 pool cell wall maximum temperature as a function of height at 1 kW 

at 20 hours

290

340

390

440

490

540

590

0 1 2 3 4

Temperature (K)

Height (m)

Experiment

Detailed

Porous

290

340

390

440

490

540

0 1 2 3 4 5

Temperature (K)

Height (m)

Porous

Detailed
3-9

Figure 3-13 PWR Cell 2 exterior wall maximum temperature as a function of height at 1 kW at 

20 hours

As seen in the figures for the power of 1 kilowatt (kW) for both the transient and steady analyses, 

the porous media model predictions matched the detailed model predictions and the experimental 

data closely. The close prediction is the result of using the right friction factor. In all porous media 

models, the difference in friction factor values obtained from the 3 methods mentioned in 

Section 2.2 was negligible. As such, the initial guess of the friction factor was obtained from the 

isothermal pressure drop method or the isothermal shear stress method. The final tuning of the 

friction factor was obtained by comparing the PCT values with the porous and the detailed 

models. 

3.1.2.1 Thermal Mass Uncertainty 

Figure 3-11 and Table 3-4 show that the PCT at 20 hours predicted by CFD is slightly higher than 

the experimental data. Therefore, sensitivity study was performed by increasing and decreasing 

the thermal mass of the MgO of the detailed model. The density was first increased to 

3,204 kg/m3

, keeping cp unchanged. The density was then decreased to 1,747 kg/m3, also 

keeping cp unchanged. Figure 3-14 through Figure 3-20 show the results of this sensitivity study. 

298

300

302

304

306

308

310

312

0 1 2 3 4

Temperature (K)

Height (m)

Experiment

Detailed

Porous
3-10

Figure 3-14 PWR Cell 2 PCT as a function of time at 1 kW

Figure 3-15 PWR Cell 2 mass flow rate as a function of time at 1 kW

290

340

390

440

490

540

0 10 20 30

Temperature (K)

Time (hrs)

Experiment

Detailed

Detailed (MgO - 3,204

kg/m^3)

Detailed (MgO - 1747

kg/m^3)

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0 10 20 30

Mass Flow Rate (kg/s)

Time (hrs)

Experiment

Detailed

Detailed (MgO - 3,204

kg/m^3)

Uncertainty

Detailed (MgO - 1747

kg/m^3)
3-11

Figure 3-16 PWR Cell 2 pool cell wall maximum temperature as a function of time at 1 kW

Figure 3-17 PWR Cell 2 exterior wall maximum temperature as a function of time at 1 kW

Table 3-5 PWR Single Assembly Cell 2 (Thermal Mass)—PCT and Mass Flow rate at 1 kW at 

20 hours

Model PCT (K) Mass Flow Rate (kg/s)

Experiment 525 0.00053

Detailed 529 0.00048

Detailed (MgO - 3,204 (kg/m3)) 527 0.00048

Detailed (MgO - 1,747 (kg/m3)) 532 0.00048

250

300

350

400

450

500

550

0 10 20 30

Temperature (K)

Time (hrs)

Experiment

Detailed

Detailed (MgO - 3,204

kg/m^3)

Detailed (MgO - 1747

kg/m^3)

298

300

302

304

306

308

310

312

0 10 20 30

Temperature (K)

Time (hrs)

Experiment

Detailed

Detailed (MgO - 3,204

kg/m^3)

Detailed (MgO - 1747

kg/m^3)
3-12

Figure 3-18 PWR Cell 2 PCT as a function of height at 1 kW at 20 hours

Figure 3-19 PWR Cell 2 pool cell wall maximum temperature as a function of height at 1 kW 

at 20 hours

290

340

390

440

490

540

590

0 1 2 3 4

Temperature (K)

Height (m)

Experiment

Detailed

Detailed (MgO - 3,204

kg/m^3)

Detailed (MgO - 1747

kg/m^3)

290

340

390

440

490

540

0 1 2 3 4 5

Temperature (K)

Height (m)

Detailed

Detailed (MgO - 3,204

kg/m^3)

Detailed (MgO - 1747

kg/m^3)
3-13

Figure 3-20 PWR Cell 2 exterior wall maximum temperature as a function of height at 1 kW at 

20 hours

The results in this sensitivity study shows that steady state was not yet reached, as the 

temperature is still a function of the thermal mass of the fuel used. As Figure 3-14 shows, the 

variation of the thermal mass did envelope the experimental data. This will attest that the thermal 

mass can influence the transient thermal response of the fuel assembly.

3.1.3 Power—0.5 kW (Steady State)

Table 3-6 shows that steady state was reached at the end of the experiment (i.e., 19 hours) by 

looking at the rate of change of PCT and mass flow rate with time.

Figure 3-21 through Figure 3-23 show that CFD predictions matched the profile the experimental 

data of the PCT, mass flow rate, pool cell wall temperature, and external wall temperature closely 

and favorably. The predictions obtained from CFD also matched the profiles of the experimental 

data for PCT and external wall temperature at time of 19 hours. Any discrepancy between the 

CFD predictions and experimental data can be attributed to the uncertainty of measurement and 

CFD discretization error, as shown in Section 4 .

Figure 3-21 through Figure 3-23 also show that the porous media model predictions matched the 

detailed model predictions and the experimental data closely. The close prediction is the result of 

using the right friction factor. In all the porous media models, the difference in friction factor 

values obtained from the three methods mentioned in Section 2.2 were negligible. As such, the 

initial guess of the friction factor obtained from the isothermal pressure drop method or the 

isothermal shear stress method was a good prediction. The final tuning of the friction factor was 

performed using the PCT values between the porous and the detailed models. 

298

300

302

304

306

308

310

312

0 1 2 3 4

Temperature (K)

Height (m)

Experiment

Detailed

Detailed (MgO - 3,204

kg/m^3)

Detailed (MgO - 1747

kg/m^3)
3-14

Table 3-6 PWR Cell 2 Steady-State Mass Flow Rate at 0.5 kW

Model PCT (K) Mass Flow Rate 

(kg/s)

Exterior Wall 

Temperature (K)

Detailed 434 0.00042 304

Porous 434 0.00041 304

Experiment at 19 

hours

432 0.00042 304

Figure 3-21 PWR Cell 2 steady-state PCT as a function of height at 0.5 kW

Figure 3-22 PWR Cell 2 steady-state pool cell wall maximum temperature as a function of 

height at 0.5 kW

290

310

330

350

370

390

410

430

450

0 1 2 3 4

Temperature (K)

Height (m)

Experimental

Detailed

Porous

290

310

330

350

370

390

410

430

0 1 2 3 4

Temperature (K)

Height (m)

Porous

Detailed
3-15

Figure 3-23 PWR Cell 2 steady-state exterior wall maximum temperature as a function of 

height at 0.5 kW

3.2 Pressurized-Water Reactor Single Assembly (Cell 1: 221.3 mm)

The tables and graphs in this section summarize the results for a single PWR assembly with a cell 

size inner dimension of 221.3 mm (8.7 in.). Table 3-7 summarizes the scenarios modeled in this 

section. Sections 3.2.1 and 3.2.2 summarize the PWR Cell 1 assembly experiment and CFD 

results for steady-state and transient runs. 

Table 3-7 PWR Single Assemble Cell 1—Models

Model Steady State Transient

Power (kW) 1 1

Detailed

Porous

3.2.1 Power—1 kW (Steady State)

Figure 3-24 and Figure 3-25 show the PCT and pool cell wall temperature as a function of height. 

As the experiment had not yet reached steady state, the PCT predictions in Figure 3-24 are 

slightly higher than the experimental data. Table 3-8 also reflects slightly higher predictions than 

experimental data. Figure 3-24 and Figure 3-25 show that the predictions from both the detailed 

and porous models agree favorably.

290

295

300

305

310

315

320

0 1 2 3 4

Temperature (K)

Height (m)

Experimental

Detailed

Porous
3-16

Table 3-8 PWR Cell 1 Steady-State Mass Flow Rate at 1 kW

Model PCT (K) Mass Flow Rate 

(kg/s)

Exterior Wall 

Temperature (K)

Detailed 560 0.00041 312

Porous 560 0.00041 312

Experiment at 20 hours 545 0.00045 314

Figure 3-24 PWR Cell 1 steady-state PCT as a function of height at 1 kW

Figure 3-25 PWR Cell 1 steady-state pool cell wall temperature as a function off height at 

1 kW

290.0

340.0

390.0

440.0

490.0

540.0

590.0

0 1 2 3 4

Temeperature (K)

Height (m)

Experiment

Porous

Detailed

290

340

390

440

490

540

590

0 1 2 3 4

Temperature (K)

Height (m)

Detailed

Porous
3-17

3.2.2 Power—1 kW (Transient)

The CFD prediction in this section was obtained by using only porous media model, as it is the 

method of choice for the dry cask applicants. Additionally, the discrepancy between the detailed 

and porous models is minimal, as shown in Section 3.2.1. Figure 3-26 and Figure 3-27 show the 

PCT and mass flow rate as a function of time. Any discrepancy between the prediction using the 

porous model and the experimental data can be attributed to the measurement errors as well as 

the discretization error summarized in Section 4 .

Figure 3-26 PWR Cell 1 PCT as a function of time at 1 kW

Figure 3-27 PWR Cell 1 mass flow rate as a function of time at 1 kW

250

300

350

400

450

500

550

600

0 5 10 15 20 25

Temperature (K)

Time (hrs)

Porous

Experiment

-0.0001

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0 5 10 15 20 25

Mass Flow Rate (kg/s)

Time (hrs)

Experiment

Porous

Uncertainty
3-18

3.3 Pressurized-Water Reactor 1x4 Assembly Configuration

The tables and graphs in this section summarize the results for a PWR 1x4 assembly. Table 3-9 

summarizes the scenarios modeled in this section.

Table 3-9 PWR 1x4 Configuration—Models

Model Steady State Transient

Power (kW) 1 1

Detailed

Porous

3.3.1 Power—1 kW (Steady State)

Figure 3-28 through Figure 3-31 show the steady-state CFD predictions and the experiment at 

24 hours. The results of the experimental data show that the center assembly PCT and mass 

flow rate reached the steady conditions, but the peripheral assembly did not. This was concluded 

by looking at the rate of change of these variables as a function of time (see Figure 3-33 through 

Figure 3-37 in Section 3.3.2 ).

Table 3-10 shows that the CFD predictions matched the experimental data within the 

experimental error for the center assembly. As the peripheral assembly was still losing heat at 

24 hours (i.e., not yet reaching steady state), both the PCT and the mass flow rate were lower 

than the steady-state CFD predictions.

Figure 3-28 and Figure 3-31 show PCT and external wall temperature as a function of height. 

There is good agreement between the CFD prediction and experimental data. Figure 3-29 shows 

the PCT as function of height of the peripheral assembly for the steady CFD predictions using the 

detailed and porous models and the experimental data at 24 hours. The discrepancies between 

the predictions and the experimental data are mainly because steady state was not reached in the 

peripheral assembly. In addition, the porous media model predicted higher PCT than the 

corresponding detailed model, as the porous model PCT is obtained at the peripheral hot cell wall, 

whereas the detailed model PCT is in the center of the first row cladding, as shown in Figure 3-32.

Table 3-10 PWR 1x4 Configuration—Steady-State Mass Flow Rate at 1 kW

Model Temperature (K) Mass Flow Rate (kg/s)

Center 

Assembly 

PCT (K)

Peripheral 

Assembly 

PCT (K)

Exterior 

Wall (K)

Center 

Assembly

Peripheral 

Assembly

Detailed 472 375 300 0.00040 0.00095

Porous 473 380 300 0.00040 0.00096

Experiment 

at 24 hours

470 367 300 0.00044 0.00087
3-19

Figure 3-28 PWR 1x4 configuration—steady-state center assembly PCT as a function of 

height at 1 kW

Figure 3-29 PWR 1x4 configuration—steady-state peripheral assembly PCT as a function of 

height at 1 kW

273

323

373

423

473

523

0 1 2 3 4 5

Temperature (K)

Height (m)

Detailed

Porous

Experiment

290

300

310

320

330

340

350

360

370

380

390

0 1 2 3 4 5

Temperature (K)

Height (m)

Detailed

Porous

Experiment
3-20

Figure 3-30 PWR 1x4 configuration—steady-state outer pool cell wall maximum temperature 

as a function of height at 1 kW

Figure 3-31 PWR 1x4 configuration—steady-state exterior wall maximum temperature as a 

function of height at 1 kW

290

300

310

320

330

340

350

360

0 1 2 3 4 5

Temperature (K)

Height (m)

Detailed

Porous

290

292

294

296

298

300

302

0 1 2 3 4 5

Temperature (K)

Height (m)

Detailed

Porous

Experiment
3-21

Figure 3-32 PWR 1x4 configuration—PCT location in peripheral assembly

3.3.2 Power—1 kW (Transient)

Figure 3-33 through Figure 3-37 show the center assembly PCT, center assembly mass flow rate, 

peripheral assembly PCT, peripheral assembly mass flow rate, and the exterior wall temperature 

as a function of time. The CFD predictions for both the detailed and porous media models and 

the experimental data agree favorably. Any discrepancy between the predictions and the data 

can be attributed to the experimental errors, discretization errors, and the thermal mass 

uncertainty. Figure 3-35 shows that the porous media model predicted slightly higher PCT for the 

peripheral assembly than the detailed model. This can be attributed to the modeling differences 

between the two models. The PCT in the porous media is obtained at the hot peripheral cell wall, 

whereas the PCT in the detailed model is obtained on cladding, as shown in Figure 3-32. 
3-22

Figure 3-33 PWR 1x4 configuration—center assembly PCT as a function of time at 1 kW

Figure 3-34 PWR 1x4 configuration—center assembly mass flow rate as a function of time at 

1 kW

250

300

350

400

450

500

0 5 10 15 20 25 30

Temperature (K)

Time (hrs)

Experiment

Porous

Detailed

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0 5 10 15 20 25 30

Mass Flow Rate (kg/s)

Time (hrs)

Experiment

Porous

Detailed

Uncertainty
3-23

Figure 3-35 PWR 1x4 configuration—peripheral assembly PCT as a function of time at 1 kW

Figure 3-36 PWR 1x4 configuration—peripheral assembly mass flow rate as a function of 

time at 1 kW

250

270

290

310

330

350

370

390

0 5 10 15 20 25 30

Temperature (K)

Time (hrs)

Experiment

Porous

Detailed

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.001

0 5 10 15 20 25 30

Mass Flow Rate (kg/s)

Time (hrs)

Experiment

Porous

Detailed

Uncertainty
3-24

Figure 3-37 PWR 1x4 configuration—exterior wall maximum temperature as a function of 

time at 1 kW

Figure 3-38 through Figure 3-40 show the PCT of the center assembly, peripheral assembly, and 

the exterior wall temperature at 24 hours for the CFD predictions using the detailed and the 

porous models and the experimental data. Figure 3-38 and Figure 3-410 show that the 

predictions agree favorably with the experimental data. Figure 3-39 shows that the peripheral 

assembly PCT predicted by the porous media model is slightly higher than the detailed model 

because of the modeling difference. Table 3-11 shows good agreement between the two CFD 

models and the experimental data, considering the experimental and discretization errors.

Table 3-11 PWR 1x4 Configuration—PCT and Mass Flow Rate at 1 kW at 24 Hours

Model Center Assembly Peripheral Assembly

PCT (K) Mass Flow Rate 

(kg/s)

PCT (K) Mass Flow Rate (kg/s)

Experiment 470 0.00044 367 0.00087

Detailed 467 0.00040 363 0.00090

Porous 469 0.00040 369 0.00090

273

278

283

288

293

298

303

0 5 10 15 20 25 30

Temperature (K)

Time (hrs)

Experiment

Porous

Detailed
3-25

Figure 3-38 PWR 1x4 configuration—center assembly PCT as a function of height at 1 kW at 

24 hours

Figure 3-39 PWR 1x4 configuration—peripheral assembly PCT as a function of height at 

1 kW at 24 hours

273

323

373

423

473

523

0 1 2 3 4 5

Temperature (K)

Height (m)

Experiment

Porous

Detailed

273

293

313

333

353

373

393

0 1 2 3 4 5

Temperature (K)

Height (m)

Experiment

Porous

Detailed
3-26

Figure 3-40 PWR 1x4 configuration—exterior wall maximum temperature as a function of 

height at 1 kW at 24 hours

3.4 Boiling-Water Reactor Single Assembly

This section discusses the results obtained in the experiment, using the detailed and porous CFD 

models. Both CFD models used 1/4th symmetry. Table 3-12 summarizes the scenarios modeled 

in this section.

Table 3-12 BWR Single Assembly—Models

Models Steady State Transient

Power (W) 1,369 2,236 1,369

Detailed

Porous

3.4.1 Power—1,369 W (Steady State)

Table 3-13 shows the PCT, mass flow rate through the assembly, drain mass flow rate, and the 

exterior wall temperature for the steady-state case. The table also has the corresponding 

experimental values at 13 hours. Temperature values from the experiment clearly did not reach 

steady state; therefore, the figures do not include the temperature values. On the other hand, 

mass flow through the assembly and the drains already reached the steady-state values as can 

be seen in Figure 3-45 and Figure 3-46 in Section 3.4.2 .

The mass flow rate through the assembly and drains obtained from CFD compare favorably with 

the experimental data. Figure 3-41 through Figure 3-43 show the variation of PCT, pool cell wall 

temperature, and exterior wall temperature as a function of height for the CFD detailed and 

porous media models. The predictions from the CFD are consistent, considering the 

discretization error and the differences in the two models. 

273

278

283

288

293

298

303

0 1 2 3 4 5

Temperature (K)

Height (m)

Experiment

Porous

Detailed
3-27

Table 3-13 BWR Steady-State Mass Flow Rate at 1,369 W

Model PCT (K) Mass Flow Rate (kg/s) Exterior Wall 

Assembly Drain Hole Temperature (K)

Detailed 637 0.00055 0.00040 314

Porous 637 0.00059 0.00039 314

Experiment 

at 13 hours

631 0.00060 0.00040 311

Figure 3-41 BWR steady-state PCT as a function of height at 1,369 W

Figure 3-42 BWR steady-state pool cell wall maximum temperature as a function of height at 

1,369 W

250

300

350

400

450

500

550

600

650

700

0 1 2 3 4 5

Temperature (K)

Height (m)

Detailed

Porous

250

300

350

400

450

500

550

600

650

0 1 2 3 4 5

Temperature (K)

Height (m)

Detailed

Porous
3-28

Figure 3-43 BWR steady-state exterior wall maximum temperature as a function of height at 

1,369 W

3.4.2 Power—1,369 W (Transient)

Figure 3-44 through Figure 3-48 show the PCT, mass flow rate through the assembly, drain mass 

flow rate, cell wall temperature, and the exterior wall temperature as a function of time. The 

predictions from both CFD models agree favorably with the experimental data, considering the 

measurement uncertainty, discretization error, and thermal mass uncertainty. 

Figure 3-44 BWR PCT as a function of time at 1,369 W

300

302

304

306

308

310

312

314

316

0 1 2 3 4 5

Temperature (K)

Height (m)

Detailed

Porous

250.0

300.0

350.0

400.0

450.0

500.0

550.0

600.0

650.0

700.0

0 5 10 15

Temperature (K)

Time (hrs)

Experiment

Detailed

Porous
3-29

Figure 3-45 BWR inlet bundle mass flow rate as a function of time at 1,369 W

Figure 3-46 BWR inlet drain mass flow rate as a function of time at 1,369 W

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0 5 10 15

Mass Flow Rate (kg/s)

Time (hrs)

Experiment

Detailed

Uncertainty

Porous

-0.00005

0

0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

0.00035

0.0004

0.00045

0.0005

0 5 10 15

Mass Flow Rate (kg/s)

Time (hrs)

Experiment

Detailed

Uncertainty

Porous
3-30

Figure 3-47 BWR pool cell wall maximum temperature as a function of time at 1,369 W

Figure 3-48 BWR exterior wall maximum temperature as a function of time at 1,369 W

Table 3-14 summarizes the PCT, mass flow rate through the assembly, and the drain mass flow 

rate for the experiment and both CFD models at 12 hours. The CFD predictions from both the 

detailed and the porous models, shown in Figure 3-49 through Figure 3-51, agree favorably with

the experimental data, considering the uncertainties from measurements, discretization, and 

thermal mass. 

250.0

300.0

350.0

400.0

450.0

500.0

550.0

600.0

650.0

0 5 10 15

Temperature (K)

Time (hrs)

Experiment

Porous

Detailed

296.0

298.0

300.0

302.0

304.0

306.0

308.0

310.0

312.0

314.0

0 5 10 15

Temeprature (K)

Time (hrs)

Experiment

Detailed

Porous
3-31

Table 3-14 BWR Single Assembly—PCT and Mass Flow Rate at 1,369 W at 12 Hours

Model PCT (K) Mass Flow Rate (kg/s)

Assembly Drain Hole

Experiment 629 0.00060 0.00040

Detailed 627 0.00055 0.00040

Porous 632 0.00059 0.00039

Figure 3-49 BWR PCT as a function of height at 1,369 W at 12 hours

Figure 3-50 BWR pool cell wall maximum temperature as a function of height at 1,369 W at 

12 hours

250

300

350

400

450

500

550

600

650

700

0.0 1.0 2.0 3.0 4.0 5.0

Temperature (K)

Height (m)

Experiment

Detailed

Porous

250

300

350

400

450

500

550

600

0 1 2 3 4 5

Temperature (K)

Height (m)

Detailed

Porous
3-32

Figure 3-51 BWR exterior wall maximum temperature as a function of height at 1,369 W at 

12 hours

3.4.3 Power—2,236 W (Steady State)

Table 3-15 shows the PCT, mass flow rate through the assembly, drain mass flow rate, and the 

exterior wall temperature for the steady-state case. The table also has the corresponding 

experimental values at 13 hours. Temperature values from the experiment clearly did not reach 

steady state; therefore, the figures do not include the temperature values. On the other hand, 

mass flow through the assembly and the drains already reached the steady-state values. The 

mass flow rate through the assembly and drains obtained from the CFD compare favorably with 

the experimental data. Figure 3-52 through Figure 3-54 show the variation of PCT, pool cell wall 

temperature, and exterior wall temperature as a function of height for the CFD detailed and 

porous media models. The two CFD model predictions are consistent, considering the 

discretization error and the differences in the two models. 

Table 3-15 BWR Steady-State Mass Flow Rate at 2,236 W

Model PCT (K) Mass Flow Rate (kg/s) Exterior Wall 

Assembly Drain Hole Temperature (K)

Detailed 817.8 0.00051 0.00041 328

Porous 818.2 0.00055 0.00041 327

Experiment 

at 13 hours

792 0.00057 0.00041 320

296

298

300

302

304

306

308

310

312

314

0 1 2 3 4 5

Temperature (K)

Height (m)

Experiment

Porous

Detailed
3-33

Figure 3-52 BWR steady-state PCT as a function of height at 2,236 W

Figure 3-53 BWR steady-state pool cell wall maximum temperature as a function of height at 

2,236 W

250

350

450

550

650

750

850

0 1 2 3 4 5

Temperature (K)

Height (m)

Detailed

Porous

250

350

450

550

650

750

850

0 1 2 3 4 5

Temperature (K)

Height (m)

Detailed

Porous
3-34

Figure 3-54 BWR steady-state exterior wall maximum temperature as a function of height at 

2,236 W

300

305

310

315

320

325

330

0 1 2 3 4 5

Temperature (K)

Height (m)

Detailed

Porous
4-1

4 COMPUTATIONAL FLUID DYNAMICS DISCRETIZATION ERROR 

ANALYSIS (GRID CONVERGENCE INDEX)

The credibility and predictive capability of CFD has been greatly enhanced and can be considered 

a reliable tool for engineering analysis if the numerical errors and uncertainties present in the 

solution can be reliably estimated. Error and uncertainty for a solver and a solution is formally 

estimated through a verification and validation process. In 2009, the American Society of 

Mechanical Engineers published a standard, “Standard for Verification and Validation in 

Computational Fluid Dynamics and Heat Transfer,” explaining the procedures for code 

verification, solution verification, and validation of CFD studies. The general objective of the 

verification and validation process is to estimate the accuracy of a numerical solution. 

Validation is the process used to determine whether a model accurately represents the physical 

phenomena of interest to obtain an estimate of modeling uncertainty. This is primarily done by 

comparing simulated results with suitable experimental data. Verification deals with the 

uncertainty of the solution that can be attributed to numerical error, irrespective of how well the 

solution represents the actual physical process it models. A verification study consists of two 

components: code verification and solution verification. Code verification is used to demonstrate 

that the mathematical equations are correctly programmed. It ensures that the solver is free of 

any coding error and that the solution algorithm has been implemented correctly. In general, 

developers perform code verification based on evaluation of a known problem by the solver. In 

contrast, solution verification does not deal with the correctness of a code, but involves estimation 

of the numerical error or uncertainty for specific simulation results performed by users of a code. 

Discretization errors and iteration errors are the two main sources of numerical error. The solution 

verification process is also known as numerical error estimation.

This section presents the methodology and results from the numerical error estimation analysis 

performed for the PWR Cell 1 single assembly configuration. For this study, the GCI was 

determined for two representative target variables. These target variables included PCT and 

mass flow rate through the assembly.

Four mesh levels were used to calculate the GCI. The additional meshes were developed based 

on systematic refinement or coarsening of a baseline mesh. The approach for mesh refinement 

and coarsening used in this study was adopted from the guidelines for best practice use of CFD 

for dry storage cask analysis from NUREG-2152, “Computational Fluid Dynamics Best Practice 

Guidelines for Dry Cask Applications,” issued March 2013, to determine the approach for mesh 

refinement and coarsening used in this study. They used Equation 4-1 through Equation 4-8 to 

calculate the GCI.

h = �

1

NN ∗ ∑ (ΔΔΔΔ) NN

ii=1 �

1

3 Equation 4-1

Where:

h = the grid size

ΔΔΔΔ = the volume of the ith cell

N = the total number of cells used for the computations.

Three sets of grids were selected as part of the study. Table 4-1 summarizes these sets.
4-2

Table 4-1 Total Number of Cells for Different Grid Levels

Level Cell Number

1 (finest) 67,000

2 20,636

3 6,750

4 (coarsest) 1,980

To calculate the apparent order of accuracy, p, let h1<h2<h3, r21=h2/h1, and r32=h3/h2. 

pp = 1

ln(rr21) ∗ �ln �

εε32

εε21

� + qq(pp)� Equation 4-2

qq(pp) = ln �

rr21

pp −ss

rr32

pp −ss

� Equation 4-3

ss = 1 ∗ ssssssss �

εε32

εε21

� Equation 4-4

where 32 3 2 ε = φ −φ , 21 2 1 ε = φ − φ , φk denoting the solution of the target variable φ on the kth grid. 

Note that q(p) = 0 for r = const. Equation 4-2 can be solved using fixed-point iteration, with the 

initial guess equal to the first term. The absolute value in Equation 4-2 is necessary to ensure 

extrapolation towards h=0. Negative values of 32 21 ε ε < 0 are an indication of oscillatory 

convergence. If possible, the percentage occurrence of oscillatory convergence should also be 

reported if agreement of the observed apparent order with the formal order of the scheme used 

can be taken as a good indication of the grids being in the asymptotic range; the converse should 

not necessarily be taken as a sign of unsatisfactory calculations. It should be noted that if either

32 3 2 ε = φ − φ or 21 2 1 ε = φ − φ is “very close” to zero, the above procedure would not work. This might 

be an indication of oscillatory convergence or, in rare situations, may indicate that the “exact” 

solution has been attained. In such cases, if possible, calculations with additional grid refinement 

may be performed; if not, the results may be reported as such.

The extrapolated values can be calculated using the following equation:

∅eeee

21 = rr21

pp ∅1−∅2

rr21

pp −1 Equation 4-5

Similarly, ∅eeee

32 was calculated.

The approximate relative errors were calculated, respectively:

ee21 = �

∅1−∅2

∅1

� Equation 4-6

Finally, the relative GCI was calculated using the following equation:

GGGGGGff

21 = 3ee21

rr21

pp −1 Equation 4-7
4-3

The absolute error and GCI is obtained by using the following equation:

ee21 = |∅1 − ∅2| Equation 4-8

Table 4-2 and Table 4-3 summarize the three combinations and mesh level ratios used for the 

calculation of the GCI.

Table 4-2 Combinations

Combination 1 Combination 2 Combination 3

Mesh level 1 1 1

Mesh level 2 2 3

Mesh level 3 4 4

Table 4-3 Mesh Level Ratios

Mesh Level ratio Combination 1 Combination 2 Combination 3

r21 1.48 1.48

r32 1.45

r42 2.18

r31 2.15

r43 1.51

4.1 Peak Cladding Temperature

Table 4-4 through Table 4-6 summarize the GCI results for the PCT. 

Table 4-4 Computed Maximum Temperature

Level Temperature (K)

1 (finest) 560.2

2 559.8

3 559.3

4 (coarsest) 558.4

Table 4-5 PCT—GCI for Calculated Order of Accuracy

Combination 1 Combination 2 Combination 3

Order of accuracy (p) 0.3 0.8 1.1

GCI-abs (K) 9.8 11.2 2.0

GCI-relative (%) 1.8 2.0 0.4

Table 4-6 PCT—GCI for Formal Order of Accuracy

Combination 1 Combination 2 Combination 3

Order of accuracy (p) 1 1 1

GCI-abs (K) 2.8 8.4 2.3

GCI-relative (%) 0.5 1.5 0.4
4-4

4.2 Mass Flow Rate

Table 4-7 through Table 4-9 summarize the GCI results for the mass flow rate.

Table 4-7 Computed Mass Flow Rate

Level Mass flow rate (kg/s)

1 (finest) 0.000413

2 0.000414

3 0.000415

4 (coarsest) 0.000416

Table 4-8 Mass Flow Rate—GCI for Calculated Order of Accuracy

Combination 1 Combination 2 Combination 3

Order of accuracy (p) 0.6 2.8 0.5

GCI-abs (kg/s) 1.0E-05 2.4E-06 4.2E-06

GCI-relative (%) 2.5 0.6 1.0

Table 4-9 Mass Flow Rate—GCI for Formal Order of Accuracy

Combination 1 Combination 2 Combination 3

Order of accuracy (p) 1 1 1

GCI-abs (kg/s) 5.6E-06 9.9E-06 1.8E-06

GCI-relative (%) 1.4 2.4 0.4
5-1

5 CONCLUSION

The data obtained from the experiments for the single 17x17 PWR and 9x9 BWR assemblies and 

17x17 PWR in a 1x4 configuration array provided valuable data for the validation of ANSYS 

FLUENT 16.0 for dry cask applications. The results in Section 3 of this report show good 

agreement between the experimental results and the CFD predictions, including both the detailed 

and porous media models. Data including temperature profiles at different locations such as PCT, 

pool cell wall, exterior wall temperature, and mass flow rate through the assembly were used for 

comparison.

Methods to calculate friction factors for the porous media model were developed and tested. The 

friction factor used in the porous media model as implemented in this investigation provided 

satisfactory CFD predictions. The CFD predictions showed that the friction factor increases as the 

pool cell size or the decay heat source decreases. keff which includes both the conduction and 

radiation model was tested, and proved effective for use in the porous media model. The tests 

also showed that the thermal mass can affect the transient data. In addition, selecting the correct 

heat transfer coefficient at the exterior wall of the control volume allowed the exclusion of the 

ambient volume from the calculation domain, reducing the computational effort and processing 

time. The results indicated that porous media model is capable to model the thermal response of 

an assembly when using the proper input.

The analysis also showed the importance of calculating the error obtained from an experiment as 

well as the CFD predictions. The validation in this study did not deal with modeling errors, as the 

study did not consider turbulence modeling. The air flowing through the assembly was in laminar 

regime for all the cases considered. The only error considered in the CFD predictions performed 

in this study was the discretization error (i.e., solution verification) or GCI evaluation.

Four levels of meshes were generated to perform the GCI calculations. The variables selected for 

the GCI analysis were PCT and mass flow rate. Computed data obtained from simulation runs 

using different grid levels showed little variation. The discretization error for the PCT and air mass 

flow rate was 2 percent and 2.5 percent, respectively.

The staff recommends that the lessons and guidelines discovered from this work be added to the 

NUREG-2152, “Computational Fluid Dynamics Best Practice Guidelines for Dry Cask 

Applications.”

6-1

6 REFERENCES

American Society of Mechanical Engineers (ASME), “Standard for Verification and Validation in 

Computational Fluid Dynamics and Heat Transfer,” V&V 20-2009.

ANSYS, Inc., ANSYS FLUENT Theory Guide Version 14.5, Canonsburg, PA, 2012a.

ANSYS, Inc., ANSYS FLUENT User Guide Version 14.5, Canonsburg, PA, 2012b.

Bergman, T.L.; Lavine, A.S.; Incropera, F.P.; and DeWitt, D.P., Fundamentals of Heat and Mass 

Transfer, Seventh Edition, John Wiley & Sons New York City, New York, 2011.

Celik, I.B.; Ghia, U.; Roache, P.J.; Freitas, C.J.; Coleman, H.; and Raad, E., “Procedure for 

Estimation and Reporting of Uncertainty Due to Discretization in CFD Applications,” ASME

Journal of Fluids Engineering (Special Publication), Vol. 130, 2008.

Celik I., and Karatekin, O., “Numerical Experiments on Application of Richardson Extrapolation 

With Nonuniform Grids,” ASME Journal of Fluids Engineering, Vol. 119, No 3, pp. 584–590, 1997.

Kays, W., and Crawford, M., Convective Heat and Mass Transfer, McGraw-Hill Publishing 

Company, NY, 1980.

Oberkampf, W.L., and Roy, C.J., Verification and Validation in Scientific Computing, Cambridge 

University Press, Cambridge, Massachusetts, 2010.

Phillips, T.S., and Roy, C., “Evaluation of Extrapolation-Based Discretization Error and Uncertainty 

Estimators,” AIAA-2011-215, Proceedings of the 49th AIAA Aerospace Sciences Meeting,

including the New Horizons Forum and Aerospace Exposition, American Institute of Aeronautics 

and Astronautics, Orlando, Florida, January 4–7, 2011.

Rezende, H.C.; Santos, A.A.; Navarro, M.A.; and Jordao, E., “Verification and Validation of a 

Thermal Stratification Experiment CFD Simulation,” Nuclear Engineering and Design, Vol. 248, 

pp. 72–81, 2012.

Rohsenow, W.M.; Hartnett, J.P.; and Cho, Y.I., Handbook of Heat Transfer, 3rd Edition, McGrawHill, New York, New York, 1998.

Sucec, J., Heat Transfer, William C. Brown Publishers, Dubuque, IA, 1985.

TRW Environmental Safety Systems, Inc., “Spent Nuclear Fuel Effective Thermal Conductivity 

Report,” prepared for U.S. Department of Energy, July 11, 1996.

U.S. Nuclear Regulatory Commission, NUREG-2152, “Computational Fluid Dynamics Best 

Practice Guidelines for Dry Cask Applications,” Washington, DC, March 2013.

U.S. Nuclear Regulatory Commission, NUREG/CR-7143, “Characterization of Thermal-Hydraulic 

and Ignition Phenomena in Prototypic, Full-Length Boiling Water Reactor Spent Fuel Pool 

Assemblies After a Postulated Complete Loss-of-Coolant Accident,” Washington, DC, 

March 2013.
6-2

U.S. Nuclear Regulatory Commission, NUREG/CR-7215, “Spent Fuel Project Phase I: 

Pre-Ignition and Ignition Testing of a Single Commercial 17x17 Pressurized Water Reactor Spent 

Fuel Assembly under Complete Loss of Coolant Accident Conditions,” Washington, DC, 

April 2016.

U.S. Nuclear Regulatory Commission, NUREG/CR-7216, “Spent Fuel Project Phase II: 

Pre-Ignition and Ignition Testing of a 1x4 Commercial 17x17 Pressurized Water Reactor Spent 

Fuel Assemblies under Complete Loss of Coolant Accident Conditions,” Washington, DC, 

April 2016.
NUREG-2208

Ghani Zigh, Sergio Gonzalez

Division of Systems Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001 

Division of Spent Fuel Management

Office of Nuclear Material Safety and Safeguards

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001 

The research summarized in this report relates to the CFD validation studies performed for a single test 

assembly of a full-length commercial 17x17 Pressurized Water Reactor (PWR) fuel bundle, a 17X17 PWR 

1x4 configuration where the center fuel assembly was electrically heated and the four surrounding 

assemblies were unheated and a single test assembly for a full-length commercial 9X9 Boiling Water 

Reactor (BWR) fuel bundle. For each of these configurations, a detailed and porous media model was 

developed in order to validate the results based on the experimental data. Parametric studies were 

conducted to assess model sensitivity. The grid conversion index (GCI) method published by the American 

Society of Mechanical Engineers (ASME) standard Verification and Validation (V&V) 20-2009 was used to 

calculate the discretization uncertainty of the model.

CFD, Validation of Thermal-Hydraulic Data using ANSYS Fluent, GCI

March 2017

Technical

Validation of Computational Fluid Dynamics Methods Using Prototypic Light 

Water Reactor Spent Fuel Assembly Thermal-Hydraulic Data





NUREG-2208 Validation of Computational Fluid Dynamics Methods Using Prototypic Light Water Reactor 

Spent Fuel Assembly Thermal-Hydraulic Data

March 2017