NUREG/IA-0462

Uncertainty and Sensitivity Investigations 

with TRACE-SUSA and TRACE-DAKOTA 

by Means of Post-test Calculations of 

NUPEC BFBT Experiments 

Prepared by:

Wadim Jaeger, Victor Hugo Sanchez Espinoza*

Francisco Javier Montero Mayorga, Cears Queral**

*Karlsruher Institute of Technology (KIT)

Institute for Neutron Physics and Reactor Technology (INR)

Hermann-von-Helmholtz-Platz 1

76344, Eggenstein-Leopoldshafen, Germany

**Universidad Politecnica de Madrd,

Departmento de Sistemas Energeticos ETSI Minas

28003 Madrid, Alenza 4, Spain

Kirk Tien, NRC Project Manager 

Division of Systems Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission 

Washington, DC 20555-0001 

Manuscript Completed: January 2014

Date Published: August 2017

Published by 

U.S. Nuclear Regulatory Commission

NUREG/IA-0462

Prepared by:

Wadim Jaeger, Victor Hugo Sanchez Espinoza*

Francisco Javier Montero Mayorga, Cears Queral**

*Karlsruher Institute of Technology (KIT)

Institute for Neutron Physics and Reactor Technology (INR)

Hermann-von-Helmholtz-Platz 1

76344, Eggenstein-Leopoldshafen, Germany

**Universidad Politecnica de Madrd,

Departmento de Sistemas Energeticos ETSI Minas

28003 Madrid, Alenza 4, Spain

Kirk Tien, NRC Project Manager 

Division of Systems Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001 

Manuscript Completed: January 2014

Date Published: August 2017

Published by 

U.S. Nuclear Regulatory Commission

Uncertainty and Sensitivity Investigations 

with TRACE-SUSA and TRACE-DAKOTA 

by Means of Post-test Calculations of 

NUPEC BFBT Experiments 

iii 

ABSTRACT 

Uncertainty and sensitivity investigations are performed with TRACE-SUSA and with TRACEDAKOTA for thermal hydraulic simulations of selected BWR related experimental scenarios 

based on the NUPEC BFBT data base. Steady state as well as transient scenarios are selected 

to conduct a comprehensive investigation of BWR like phenomena. The steady state 

investigations include single and two phase flow pressure drop analyses, axial void fraction 

profiles and critical power predictions. The pressure losses and the void fractions are also 

predicted during two postulated BWR transients; a turbine trip and a trip of a re-circulation pump. 

The average error for the pressure losses, the void fractions and the critical power scenarios is in 

the order of ± 5 %. Parameters of the input and of the source code are selected for the uncertainty 

and sensitivity study. By means of sensitivity coefficients, a quantitative way of evaluating the 

system response is given. The analysis shows that even small variations can cause a rather large 

spread of the output parameter(s). The investigations show also that the width of the predicted 

uncertainty band is a function of parameters like the inlet sub cooling or the hydraulic diameter. 

In addition, shortcomings of the thermal hydraulic code/modeling or of the uncertainty and 

sensitivity tool(s) are given in order to help to improve the prediction capabilities. 

v 

FOREWORD 

This assessment report deals with the application of the system code TRACE in combination with 

SUSA and DAKOTA for the quantification of uncertainties related to input and boundary 

conditions and empirical models. The subject of this report is the post-test analyses of 

experiments performed within the NUPEC BFBT benchmark which is related to BWRs. The 

results predicted by TRACE are in code agreement to the experiments and the associated 

uncertainty and sensitivity study quantifies the importance of the input and source code 

parameters on selected output parameters. Such studies help to identify areas for improvement 

of the system code but also help to better understand the physical feedbacks between different 

parameters. 

vii 

CONTENTS

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

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

FIGURES ....................................................................................................................................xi

TABLES .................................................................................................................................. xvii

EXECUTIVE SUMMARY ..........................................................................................................xix

ACKNOWLEDGMENTS ...........................................................................................................xxi

ABBREVIATIONS ..................................................................................................................xxiii

NOMENCLATURE ..................................................................................................................xxv

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

1.1 Motivation ..................................................................................................................1-1

1.2 Scope of the Report ...................................................................................................1-2

1.3 Structure and Content of the Report .........................................................................1-2

2 UNCERTAINTIES IN NUCLEAR SAFETY INVESTIGATIONS ....................................... 2-1

2.1 Generalities ................................................................................................................2-1

2.2 Conservative Approach versus Best Estimate Plus Uncertainties ............................2-1

2.3 Sources of Uncertainties ............................................................................................2-4

2.4 Uncertainty Methods ..................................................................................................2-5

3 NUPEC BFBT BENCHMARK ........................................................................................... 3-1

3.1 General Remarks........................................................................................................3-1

3.2 Test Facility ................................................................................................................3-2

3.3 Assembly and Heat Rod Design ................................................................................3-4

3.4 Pressure Drop Evaluation ..........................................................................................3-6

3.5 Void Fraction Evaluation ............................................................................................3-8

3.6 Critical Power Evaluation ............................................................................................3-9

4 CODES AND PROGRAMS .............................................................................................. 4-1

4.1 TRACE .......................................................................................................................4-1

4.1.1 General Remarks and Main Features ..........................................................4-1

4.1.2 Numerical Methodology ................................................................................4-2

4.1.3 Field Equations ............................................................................................4-2

4.1.4 Closure Relations .........................................................................................4-4

4.1.5 Validation Process .......................................................................................4-9

4.2 SUSA.........................................................................................................................4-10

4.2.1 Generalities ................................................................................................4-10
viii 

4.2.2 Probability Density Function and Other Statistical Parameters ..................4-11

4.2.3 Number of Samples ....................................................................................4-14

4.2.4 Sampling .....................................................................................................4-16

4.2.5 Statistical Measures....................................................................................4-17

4.3 DAKOTA ...................................................................................................................4-21

4.4 SNAP........................................................................................................................4-22

5 APPLIED UNCERTAINTY AND SENSITIVITY METHODOLOGY.................................... 5-1

5.1 General Remarks........................................................................................................5-1

5.2 Uncertainty and Sensitivity Study with TRACE-SUSA ...............................................5-1

5.2.1 General Procedure .......................................................................................5-1

5.2.2 How to Run SUSA: The Sampling ................................................................5-3

5.2.3 How to Generate n TRACE Input Files ........................................................5-4

5.2.4 How to Run SUSA: The Analysis ...............................................................5-12

5.3 Uncertainty and Sensitivity Study with TRACE-DAKOTA ........................................5-13

5.3.1 Assignment of Uncertain Parameters.........................................................5-13

5.3.2 PDF and Monte Carlo Sampling .................................................................5-18

5.3.3 Data Extraction ...........................................................................................5-20

6 RESULTS OF THE UNCERTAINTY AND SENSITIVITY ANALYSES .............................. 6-1

6.1 Modeling......................................................................................................................6-1

6.2 Uncertain Parameters .................................................................................................6-2

6.3 Pressure Drop Analyses .............................................................................................6-3

6.3.1 Single Phase Flow Pressure Drop ................................................................6-3

6.3.2 Two-Phase Flow Pressure Differenc ...........................................................6-15

6.4 Void Fraction Analyses ..............................................................................................6-29

6.5 Critical Power Analyses ..............................................................................................6-57

6.6 Transient analyses .....................................................................................................6-67

6.6.1 Results for the Pressure Drop ......................................................................6-70

6.6.2 Results for the Void Fraction .......................................................................6-72

7 SUMMARY AND CONCLUSION ....................................................................................... 7-1

7.1 Summary ......................................................................................................................7-1

7.2 Discussion ....................................................................................................................7-2

7.3 Fields of Improvement ..................................................................................................7-2

7.4 Conclusion ....................................................................................................................7-3

7.5 Outlook..........................................................................................................................7-3

8 REFERENCES .................................................................................................................... 8-1

APPENDIX A TRACE.INP ........................................................................................................A-1
ix

APPENDIX B TRACE.OUT ..................................................................................................B-1

APPENDIX C MEDUSA.PRN ...............................................................................................C-1

APPENDIX D SAMPLE.DAT ................................................................................................D-1

APPENDIX E DATA EXTRACTION .....................................................................................E-1

APPENDIX F EQUUS.PRN .................................................................................................. F-1

APPENDIX G SAMOS.PRN ................................................................................................. G-1

APPENDIX H DAKOTA REPORT ........................................................................................H-1

xi

FIGURES 

Figure 1 Conservative Calculation versus Best Estimate .................................................... 2-2

Figure 2 Safety Margins ...................................................................................................... 2-3

Figure 3 Uncertainty Methods ............................................................................................. 2-5

Figure 4 Propagation of Input Errors [2] .............................................................................. 2-6

Figure 5 Output Error Extrapolation [2] ............................................................................... 2-6

Figure 6 NUPEC BFBT Benchmark Organization ............................................................... 3-2

Figure 7 Schematic Diagram of the Test Facility ................................................................. 3-2

Figure 8 Cross Section of the BWR Fuel Assembly Test Section ........................................ 3-3

Figure 9 Fuel Assembly 4/C2A and Radial Power Profile .................................................... 3-5

Figure 10 Axial Power Profile for Assembly C2A................................................................... 3-5

Figure 11 Heater Rod Design ............................................................................................... 3-6

Figure 12 Location of the Pressure Sensors ......................................................................... 3-7

Figure 13 Ferrule Spacer Type (Top Left: Top View; Bottom Left: 3D View; Top Right: 

Radial Dimensions; Bottom Right Axial Dimensions) ............................................ 3-8

Figure 14 Arrangement of the Void Fraction Measurement Devices ..................................... 3-9

Figure 15 Thermocouple Position during Critical Power Measurement ............................... 3-10

Figure 16 Mapping of the Regime Dependent Parameters for Energy Conservation [7]........ 4-5

Figure 17 Mapping of the Regime Dependent Parameters Momentum Conservation [7] ...... 4-5

Figure 18 Mapping of the Regime Dependent Parameters for Mass Conservation [7] .......... 4-6

Figure 19 Pre-CHF Heat Transfer Selection Logic in TRACE [5] .......................................... 4-7

Figure 20 Flowchart of the TRACE Development Process for LWRs .................................... 4-9

Figure 21 TRACE Validation Matrix for LWRs ..................................................................... 4-10

Figure 22 Normal Distribution with 2 Known Quantiles ....................................................... 4-13

Figure 23 Definition of the Tolerance Interval ...................................................................... 4-15

Figure 24 Comparison of Latin Hypercube Sampling (left side) and Random Sampling 

(right side) Regarding the Sampling Distribution ................................................. 4-17

Figure 25 Meaning of Statistical Correlation [14] ................................................................. 4-20

Figure 26 Coupling Scheme between DAKOTA and a Simulation Code ............................. 4-22

Figure 27 SNAP Architecture [25] ....................................................................................... 4-23

Figure 28 Model Editor ....................................................................................................... 4-24

Figure 29 Configuration Tool .............................................................................................. 4-25

Figure 30 Job Status ........................................................................................................... 4-25

Figure 31 Flow Chart of the TRACE-SUSA Interface [26] ..................................................... 5-2

Figure 32 SUSA Main Data Sheet for the Single-Phase Pressure Drop Analysis .................. 5-4

Figure 33 DAKOTA Reference Implementation Process Diagram ...................................... 5-14

Figure 34 Adding Uncertainty Stream to Existing TRACE Job Stream ................................ 5-15

Figure 35 Single Step TRACE Stream ................................................................................ 5-15

Figure 36 Job Stream Window with Added Uncertainty Step .............................................. 5-16

Figure 37 Unfolded Numerics Item in SNAP with Two New Parameters ............................. 5-16

Figure 38 Fill with Initial Coolant Mass Flow Rate Assigned as an Uncertain Parameter .... 5-17

Figure 39 Control Block for the System Pressure with Assigned Shared Real (uncertain) 

Value .................................................................................................................. 5-18

Figure 40 New Variable Reference to Assign PDF's ........................................................... 5-19

Figure 41 Assigned Distribution Type for Mass Flow Rate and Pressure ............................ 5-19

Figure 42 Parameters of the PDF's ..................................................................................... 5-20

Figure 43 Definition of the Sampling Method and Size ........................................................ 5-21
xii

Figure 44 Job Stream with DAKOTA Uncertainty and a Single TRACE Input File ............... 5-21

Figure 45 AptPlot Data Extraction Scripting Window ........................................................... 5-22

Figure 46 Job Stream with Multiple TRACE Input Files ....................................................... 5-22

Figure 47 Job Stream Window with Steady State and Transient Uncertainty Models .......... 5-23

Figure 48 Example of an Uncertainty Analysis of a Specific Variable .................................. 5-23

Figure 49 TRACE Model of the BFBT Assembly ................................................................... 6-1

Figure 50 Input and Boundary Conditions for the Single-Phase Flow Pressure Drop 

Cases ................................................................................................................... 6-3

Figure 51 Relative Error of the Local Single-Phase Flow Pressure Drop for Selected 

Cases ................................................................................................................... 6-6

Figure 52 Calculated versus Measured Pressure Drop for the Single-Phase Flow 

Reference Cases .................................................................................................. 6-7

Figure 53 Percental Error of the Reference Values Compared to the Experimental Data 

for Single-Phase Flow Cases ................................................................................ 6-7

Figure 54 Error as Function of the Single-Phase Flow Pressure Drop .................................. 6-8

Figure 55 Comparison of the Experimental and Predicted Pressure Drops for the SinglePhase Flow Cases in Absolute Values .................................................................. 6-9

Figure 56 Comparison of the Experimental and Predicted Pressure Drops for the SinglePhase Flow Cases in Relative Values ................................................................... 6-9

Figure 57 Sensitivity Coefficients for the Single-Phase Flow Pressure Drop Analysis with 

TRACE-SUSA..................................................................................................... 6-12

Figure 58 Sensitivity Coefficients for the Single-Phase Flow Pressure Drop Analysis with 

TRACE-DAKOTA ................................................................................................ 6-12

Figure 59 Ranking of the Uncertain Parameters for the Single-Phase Flow Pressure Drop 

Analysis with TRACE-SUSA ............................................................................... 6-13

Figure 60 Ranking of the Uncertain Parameters for the Single-Phase Flow Pressure Drop 

Analysis with TRACE-DAKOTA .......................................................................... 6-13

Figure 61 Input and Boundary for the Two-Phase Flow Pressure Drop Cases .................... 6-16

Figure 62 Relative Error of the Local Two-Phase Flow Pressure Drop for Selected 

Cases (1) ............................................................................................................ 6-19

Figure 63 Relative Error of the Local Two-Phase Flow Pressure Drop for Selected 

Cases (2) ............................................................................................................ 6-20

Figure 64 Calculated versus Measured Pressure Drop for the Two-Phase Flow 

Reference Cases ................................................................................................ 6-21

Figure 65 Percental Error of the Reference Values Compared to the Experimental Data 

for the Two-Phase Flow Cases ........................................................................... 6-22

Figure 66 Error as Function of the Two-Phase Flow Pressure Difference ........................... 6-22

Figure 67 Comparison of the Experimental and Predicted Pressure Drops for the 

Two- Phase Flow Cases in Absolute Values ....................................................... 6-23

Figure 68 Comparison of the Experimental and Predicted Pressure Drops 

for the Two- Phase Flow Cases in Relative Values ..............................................6-24

Figure 69 Sensitivity Coefficients for the Two-Phase Flow Pressure Drop Analysis with 

TRACE-SUSA..................................................................................................... 6-26

Figure 70 Sensitivity Coefficients for the Two-Phase Flow Pressure Drop Analysis with 

TRACE-DAKOTA ................................................................................................ 6-26

Figure 71 Ranking of the Uncertain Parameters for the Two-Phase Flow Pressure Drop 

Analysis with TRACE-SUSA ............................................................................... 6-27

Figure 72 Ranking of the Uncertain Parameters for the Two-Phase Flow Pressure Drop 

Analysis with TRACE-DAKOTA .......................................................................... 6-27

Figure 73 Input and Boundary Conditions for the Steady State Void Fraction 

Measurements .................................................................................................... 6-30
xiii

Figure 74 Calculated versus Measured Outlet Void Fractions ................................................. 6-33

Figure 75 Percental Error of the Reference Values Compared to the Experimental Data 

for the Outlet Void Fraction ..................................................................................... 6-33

Figure 76 Error as a Function of the Void Fraction .................................................................. 6-34

Figure 77 Comparison of the Experimental and Outlet Void Fractions in Absolute Values...... 6-35

Figure 78 Comparison of the Experimental and Predicted Outlet Void Fractions 

in Relative Values................................................................................................... 6-35

Figure 79 Sensitivity Coefficients for the Outlet Void Fraction Analysis with TRACESUSA...................................................................................................................... 6-39

Figure 80 Sensitivity Coefficients for the Outlet Void Fraction Analysis with TRACEDAKOTA ................................................................................................................. 6-39

Figure 81 Sensitivity Coefficients for Inlet Temperature and Power versus the 

Outlet Void Fraction .................................................................................................. 6-40

Figure 82 Ranking of the Uncertain Parameters for the Outlet Void Fraction with TRACESUSA...................................................................................................................... 6-40

Figure 83 Ranking of the Uncertain Parameters for the Outlet Void Fraction with TRACEDAKOTA ................................................................................................................. 6-41

Figure 84 Axial Void Fraction for Cases 4101-01 - 4101-08 (x-axes = Axial Location [m]; yaxes = Void Fraction; Black Circles = Original Experimental Data; Red Diamonds 

= Corrected Experimental Data; Red Line = Uncertainty Range; Black Line = 

Mean Value of the Calculations) ............................................................................. 6-45

Figure 85 Axial Void Fraction for Cases 4101-09 - 4101-16 (x-axes = Axial Location [m]; yaxes = Void Fraction; Black Circles = Original Experimental Data; Red Diamonds 

= Corrected Experimental Data; Red Line = Uncertainty Range; Black Line = 

Mean Value of the Calculations) ............................................................................. 6-46

Figure 86 Axial Void Fraction for Cases 4101-17 - 4101-24 (x-axes = Axial Location [m]; yaxes = Void Fraction; Black Circles = Original Experimental Data; Red Diamonds 

= Corrected Experimental Data; Red Line = Uncertainty Range; Black Line = 

Mean Value of the Calculations) ............................................................................. 6-47

Figure 87 Axial Void Fraction for Cases 4101-25 - 4101-32 (x-axes = Axial Location [m]; yaxes = Void Fraction; Black Circles = Original Experimental Data; Red Diamonds 

= Corrected Experimental Data; Red Line = Uncertainty Range; Black Line = 

Mean Value of the Calculations) ............................................................................. 6-48

Figure 88 Axial Void Fraction for Cases 4101-33 - 4101-40 (x-axes = Axial Location [m]; yaxes = Void Fraction; Black Circles = Original Experimental Data; Red Diamonds 

= Corrected Experimental Data; Red Line = Uncertainty Range; Black Line = 

Mean Value of the Calculations) ............................................................................. 6-49

Figure 89 Axial Void Fraction for Cases 4101-41 - 4101-48 (x-axes = Axial Location [m]; yaxes = Void Fraction; Black Circles = Original Experimental Data; Red Diamonds 

= Corrected Experimental Data; Red Line = Uncertainty Range; Black Line = 

Mean Value of the Calculations) ............................................................................. 6-50

Figure 90 Axial Void Fraction for Cases 4101-49 - 4101-56 (x-axes = Axial Location [m]; yaxes = Void Fraction; Black Circles = Original Experimental Data; Red Diamonds 

= Corrected Experimental Data; Red Line = Uncertainty Range; Black Line = 

Mean Value of the Calculations) ............................................................................. 6-51

Figure 91 Axial Void Fraction for Cases 4101-57 - 4101-64 (x-axes = Axial Location [m]; yaxes = Void Fraction; Black Circles = Original Experimental Data; Red Diamonds 

= Corrected Experimental Data; Red Line = Uncertainty Range; Black Line = 

Mean Value of the Calculations) ............................................................................. 6-52
xiv

Figure 92 Axial Void Fraction for Cases 4101-65 - 4101-72 (x-axes = Axial Location [m]; yaxes = Void Fraction; Black Circles = Original Experimental Data; Red Diamonds 

= Corrected Experimental Data; Red Line = Uncertainty Range; Black Line = 

Mean Value of the Calculations) .............................................................................. 6-53

Figure 93 Axial Void Fraction for Cases 4101-73 - 4101-80 (x-axes = Axial Location [m]; yaxes = Void Fraction; Black Circles = Original Experimental Data; Red Diamonds 

= Corrected Experimental Data; Red Line = Uncertainty Range; Black Line = 

Mean Value of the Calculations) ......................................................................... .....6-54

Figure 94 Axial Void Fraction for Cases 4101-81 - 4101-86 (x-axes = Axial Location [m]; yaxes = Void Fraction; Black Circles = Original Experimental Data; Red Diamonds 

= Corrected Experimental Data; Red Line = Uncertainty Range; Black Line = 

Mean Value of the Calculations) .............................................................................. 6-55

Figure 95 Comparison of the Axial Void Fraction Predicted with TRACE-SUSA and

TRACE-DAKOTA for Case 4101-04 ........................................................................ 6-56

Figure 96 Comparison of the Axial Void Fraction Predicted with TRACE-SUSA and

TRACE-DAKOTA for Case 4101-18 ........................................................................ 6-56

Figure 97 Input and Boundary Conditions for the Critical Power Cases ................................... 6-57

Figure 98 Calculated versus Measured Critical Power ............................................................. 6-60

Figure 99 Percental Error of the Reference Values Compared to the Experimental Data 

for the Critical Power Cases ..................................................................................... 6-60

Figure 100 Error as Function of the Critical Power ..................................................................... 6-61

Figure 101 Comparison of the Experimental and Predicted Critical Power in Absolute 

Values...................................................................................................................... 6-61

Figure 102 Comparison of the Experimental and Predicted Pressure Drops for Critical 

Power in Relative Values ......................................................................................... 6-62

Figure 103 Sensitivity Coefficients for the Critical Power Analysis with TRACE-SUSA............... 6-65

Figure 104 Ranking of the Uncertain Parameters for the Critical Power Analysis with 

TRACE-SUSA.......................................................................................................... 6-65

Figure 105 Inlet Temperature Evolution During the Transients ................................................... 6-68

Figure 106 Bundle Mass Flow Rate Evolution During the Transients ......................................... 6-69

Figure 107 Outlet Pressure Evolution During the Transients ...................................................... 6-69

Figure 108 Assembly Power Evolution During the Transients .................................................... 6-70

Figure 109 Pressure Drop During the Turbine Trip Transient ..................................................... 6-71

Figure 110 Pressure Drop During the Re-Circulation Pump Trip ................................................ 6-71

Figure 111 Sensitivity Coefficients for the Transient Pressure Drop Analysis with SUSA ........... 6-73

Figure 112 Void Fraction Predictions with Uncertainty Band Compared to Original and 

Corrected Turbine Trip Measurements for the First Densitometer at 682 mm .......... 6-74

Figure 113 Void Fraction Predictions with Uncertainty Band Compared to Original and

Corrected Turbine Trip Measurements for the Second Densitometer at 1706 mm ... 6-74

Figure 114 Void Fraction Predictions with Uncertainty Band Compared to Original and 

Corrected Turbine Trip Measurements for the Third Densitometer at 2730 mm ....... 6-75

Figure 115 Deviation of the Fredictions from the Corrected Turbine Trip Measurements for 

all Three Densitometer Positions ............................................................................. 6-76

Figure 116 Void Fraction Predictions with Uncertainty Band Compared to Original and

Corrected Re-Circulation Pump Trip Measurements for the First 

Densitometer at 68 mm ............................................................................................ 6-77

Figure 117 Void Fraction Predictions with Uncertainty Band Compared to Original and

Corrected Re-Circulation Pump Trip Measurements for the Second 

Densitometer at 1706 mm ........................................................................................ 6-77
xv

Figure 118 Void Fraction Predictions with Uncertainty Band Compared to Original and

Corrected Re-Circulation Pump Trip Measurements for the Third 

Densitometer at 2730 mm ........................................................................................ 6-78

Figure 119 Deviation of the Predictions from the corrected Re-Circulation Pump Trip 

Measurements for all Three Densitometer Positions ................................................ 6-79

Figure 120 Sensitivity Coefficients for the Void Fraction Related to the Turbine Trip with 

SUSA....................................................................................................................... 6-80

Figure 121 Sensitivity Coefficients for the Void Fraction Related to the Re-Circulation 

Pump Trip with SUSA .............................................................................................. 6-80

xvii

TABLES 

Table 1 Safety Analysis Options for Licensing Purposes ................................................... 2-4

Table 2 Geometrical Data of the Considered Fuel Assembly Types .................................. 3-4

Table 3 Numerical Differences between Legacy Codes like TRACE and Future Code

Systems ................................................................................................................ 4-3

Table 4 Required Parameters for the Closure of the Field Equations [7] ............................ 4-4

Table 5 Minimum Sample Size (N) for the One-sided Tolerance Limit (l + u = 1) ............. 4-16

Table 6 Minimum Sample Size (N) for the Two-sided Tolerance Limit (l + u = 2) ............. 4-16

Table 7 Dependency of Correlation as Function of the Sensitivity Coefficient .................. 4-19

Table 8 PDF Characteristics for Mass Flow and Pressure ............................................... 5-18

Table 9 Uncertain Parameters, Range and Distribution for TRACE-SUSA ........................ 6-2

Table 10 Uncertain Parameters, Range and Distribution for TRACE-DAKOTA ................... 6-2

Table 11 Input and Boundary Conditions for the Single-Phase Flow Pressure Drop

Cases ......................................................................................................................6-4

Table 12 Local Single-Phase Flow Pressure Drop Measurements ...................................... 6-5

Table 13 Percental Error of the Predicted Local Single-Phase Flow Compared to the 

Measurements ...................................................................................................... 6-5

Table 14 Results of the Uncertainty Analysis for the Single-Phase Flow Pressure 

Drops with TRACE-SUSA................................................................................... 6-10

Table 15 Results of the Uncertainty Analysis for the Single-Phase Flow Pressure 

Drops with TRACE-DAKOTA ................................................................................ 6-11

Table 16 Pearson's Momentum Correlation Coefficients for the Single-Phase 

Flow Pressure Drop Cases with TRACE-SUSA.................................................. 6-14

Table 17 Pearson's Momentum Correlation Coefficients for the Single-Phase 

Flow Pressure Drop Cases with TRACE-DAKOTA ............................................. 6-15

Table 18 Input and Boundary Conditions for the Two-Phase Flow Pressure Drop Cases .. 6-16

Table 19 Local Two-Phase Flow Pressure Drop Measurements ........................................ 6-17

Table 20 Percental Error of the Predicted Local Two-Phase Flow Compared to the 

Measurements .................................................................................................... 6-18

Table 21 Results of the Uncertainty Analysis for the Two-Phase flow Pressure 

Drops with TRACE-SUSA................................................................................... 6-24

Table 22 Results of the Uncertainty Analysis for the Two-Phase Flow Pressure 

Drops with TRACE-DAKOTA ............................................................................... 6-25

Table 23 Pearson's Momentum Correlation Coefficients for the Two-Phase 

Flow Pressure Drop Cases with TRACE-SUSA.................................................. 6-28

Table 24 Pearson's Momentum Correlation Coefficients for the Two-Phase 

Flow Pressure Drop Cases with TRACE-DAKOTA ............................................. 6-29

Table 25 Input and Boundary Conditions for the Steady State Void Fraction

Measurements .................................................................................................... 6-30

Table 26 Results of the Uncertainty Analysis for the Outlet Void Fraction with 

TRACE-SUSA..................................................................................................... 6-36

Table 27 Results of the Uncertainty Analysis for the Outlet Void Fraction with TRACE

DAKOTA ............................................................................................................. 6-37

Table 28 Pearson's Momentum Correlation Coefficients for the Outlet Void Fraction 

Cases with TRACE-SUSA .................................................................................. 6-41

Table 29 Pearson's Momentum Correlation Coefficients for Outlet Void Fraction 

Cases with TRACE-DAKOTA ............................................................................. 6-43

Table 30 Input and Boundary Conditions for the Critical Power Cases .............................. 6-57
xviii

Table 31 Results of the Uncertainty Analysis for the Critical Power with TRACE-SUSA .... 6-62

Table 32 Pearson's Momentum Correlation Coefficients for the Critical Power 

Cases with TRACE-SUSA .................................................................................. 6-66

Table 33 Summary of the Uncertainty and Sensitivity Investigations.................................... 7-1
xix

EXECUTIVE SUMMARY 

The scope of this report is to present TRACE results related to the post-test analyses of the 

NUPEC BWR Full-size Fine mesh Bundle Test (BFBT) benchmark. First of all, the investigations 

are valuable for the ongoing validation process of the best estimate system code. Second, the 

application of uncertainty and sensitivity methods together with TRACE helps to identify which 

parameters have the highest influence on the system behavior during various test scenarios. 

Therefore, the tools SUSA and DAKOTA are used for the quantification of input and boundary 

uncertainties as well as uncertainties related to source code parameters. 

The quantification of uncertainties in the process of safety related investigations with best 

estimate thermal hydraulic codes is the latest step on the path to enhance the safety of nuclear 

installations. By means of best estimate codes more realistic values can be predicted for safety 

relevant parameters like the peak cladding temperature or the DNB. With the help of uncertainty 

analyses the influence of input parameter uncertainties can be considered (material properties, 

decay heat curve, temperature and mass flow rate profiles, etc.). Instead of one calculation as 

with conservative codes or best estimate codes without uncertainty, several calculations are 

necessary to show that not only the reference or best estimate case is within acceptance limits 

but also the combination of extremes (lowest mass flow rate possible combined with highest 

power possible). 

In the context of this report several stationary and transient scenarios have been evaluated. A 

short summary of the investigation and findings is given hereafter 

 Steady state scenarios:

o Single-phase pressure drop: During this investigation 36 different combinations of

system pressure, mass flow rate and inlet temperature have been investigated to

evaluate the single-phase pressure drop. Thereby, typical BWR conditions are

considered (70 bar, 560 K) as well as low pressure (2 bar) low temperature (310

K) cases. The overall evaluation yields an average error of less than 7 %. The

largest discrepancies are found for the cases with the lowest mass flow rate.

Deviations of up to 35 % are found. But in these cases the pressure drop is

extremely small and amounts to just 1000 Pa. The most important parameters for

the uncertainty and sensitivity analysis are related to geometrical uncertainties

(exact hydraulic diameter of the bundle, form loss coefficients).

o Two-phase flow pressure differences: Concerning the two-phase flow cases, 33

combinations of pressure, inlet sub-cooling, mass flow rate and assembly power

are studied. The overall error is smaller as for the single phase cases and is less

than 5 %. The reason for the lower deviation in two-phase flow then in single-phase

flow might be origin from the different formalism. For single phase flow it is the

pressure drop with considered geodetic height change while for the two-phase flow

cases it is just the pressure difference between inlet and outlet. Therefore, also

higher values are reported than for single phase flow and the problem of low

pressure drop measurement is not pronounced. Parameters like the inlet

temperature and the hydraulic diameter have the highest influence on the twophase flow pressure difference.Void fraction:
xx

o Critical power: 79 parameter combinations (pressure, inlet sub-cooling and mass

flow rate) are taken into account in this exercise. The comparison results in an

average error of less than 4 %. One finding is that with increasing critical power,

the deviations between experiment and calculations are getting lower. Main

parameter of interest for the uncertainty and sensitivity study is the inlet

temperature and the mass flow rate. Even though the error is less than 4 % the

investigation/results must be treated with caution. During the uncertainty analysis

the coefficient of determination (R2) is calculated and serves, to some extent, as a

figure of merit. For the three previous sub-tasks, this value is close to unity,

indicating the quality of the investigation. For the critical power cases, values

between 0.15 and 0.8 are found. Furthermore, some of the critical powers could

not have been calculated with TRACE due to code failure.

 Transient scenarios

o Turbine trip: By means of variation of the inlet temperature, bundle mass flow rate,

outlet pressure and assembly power, a postulated turbine trip in a BWR is

simulated. The turbine isolation valve is closed and the pressure increases

immediately. The pressure wave propagates through the core and results in a

decrease of the void fraction. Due to the better moderation the power increases.

To minimize the consequences of such an event the pump speed is reduced. Less

mas flow rate results in an increase of the void fraction. The higher void (lower

density) causes the power to drop. The calculated void fraction as a function of the

transient time is compared to the experimental data for three axial elevations. The

comparison shows a good agreement.

o Re-circulation pump trip: During this simulated accident the pump speed is

reduced that the mass flow rate decreases to 1/3 of the nominal mass flow. This

will cause an increase of the void fraction which will, in turn, causes the power to

drop due to the lower moderation. The mass flow rate is reset to the nominal value

after approximately 30 seconds. The void fraction comparison shows a relatively

good agreement to the experiment.

The performed investigation proofed that TRACE is very well able to model BWR fuel assemblies 

during different stationary and transient scenarios. The comparison to the experimental data 

showed a general good agreement. The applied uncertainty and sensitivity methods are in good 

agreement to each other, which is mainly due to their identical approach. These studies helped 

to quantifiy the influence of the input parameters on the output parameters. This information is 

valuable for the further development of the TRACE system code. 
xxi

ACKNOWLEDGMENTS 

This work has been performed during a collaboration of the Karlsruhe Institute of Technology and 

the Universidad Politecnica de Madrid. The authors like to thank to the Program "Nuclear Safety 

Research" of KIT for the financial support of the Research Topic "Multiphysics Methodologies for 

Reactor Dynamics and Safety" and the Deutscher Akademischer Austauschdienst (DAAD), which 

provided the funding for the exchange of UPM scientists to KIT. 

Furthermore, the authors highly appreciate the help and support of Nico Trost, Jorge Perez, Uwe 

Imke, and Javier Jimenez Escalante. A special thanks goes to Professor Rafael Macián-Juan for 

providing modules and routines for the data manipulation in the context of SUSA application. 

Parts of this work have been submitted to international conferences and journals prior to the 

compilation of the present document. These are: 

W. Jaeger, J. Perez Manes, U. Imke, J. Jimenez Escalate and V. Sanchez Espinoza, “Validation 

and comparison of two-phase flow modeling capabilities of CFD, sub channel and system codes 

by means of post-test calculations of BFBT transient tests”. Nuclear Engineering and Design, Vol 

263, pp 313-326, 2013. 

W. Jaeger, V. Sanchez Espinoza, F. Montero Mayorga und C. Queral, „Uncertainty and Sensitivity 

Studies with TRACE-SUSA and TRACE-DAKOTA by means of steady state BFBT Data“.Science 

and Technology of Nuclear Installations, Vol 2013, Article ID 610598, 2013. 

W. Jaeger, V. Sanchez Espinoza, F. Montero Mayorga und C. Queral, „Uncertainty and Sensitivity 

Studies with TRACE-SUSA and TRACE-DAKOTA by means of transient BFBT Data“.Science 

and Technology of Nuclear Installations, Vol 2013, Article ID 565246, 2013. 

F. Montero Mayorga, W. Jaeger and V. Sanchez Espinoza, “Análisis de Incertidumbre y 

Sensibilidad con TRACE-SUSA y TRACE-DAKOTA - Aplicación a NUPEC BFBT” (in spanish). 

Annual Meeting of the Spanish Nuclear Society, Caceres, Spain, October 17-19, 2012. 

xxiii

ABBREVIATIONS 

AEAW Atomic Energy Authority Winfrith 

BFBT BWR Full-size Fine mesh Bundle Test 

BWR Boiling Water Reactor 

CAMP Code Application and Maintenance Program 

CHF Critical Heat Flux 

CSAU Code Scaling, Applicability and Uncertainty

CT Computer Tomography 

DAAD Deutscher Akademischer Austausch Dienst 

DAKOTA Design Analysis Kit for Optimization and Terascale Application 

DBA Design Basis Accident 

DRM Deterministic Realistic Method 

ENUSA Empresa Nacional del Uranio, SA 

GRS Gesellschaft fuer Anlagen- und Reaktorsicherheit mbH 

IAEA International Atomic Energy Agency 

INR Institute for Neutron physics and Reactor technology 

IPSN Institut de Protection et de Sûreté Nucléaire 

KIT Karlsruhe Institute of Technology 

LOCA Loss Of Coolant Accident 

LWR Light Water Reactor 

METI Japanese Ministry of Economy, Trade and Industry 

NEA Nuclear Energy Agency 

NUPEC Nuclear Power Engineering Corporation 

OECD Organization for Economic Co-operation and Development 

PCC Partial Correlation Coefficient 

PCT Peak Cladding Temperature 

PDF Probability Density Function 

PSA Probabilistic Safety Assessment 

PWR Pressurized Water Reactor 

RELAP Reactor Excursion and Leak Analysis Program 

SETS Stability-Enhancing Two Step 

SNAP Symbolic Nuclear Analysis Package 

SRC Standardized Regression Coefficient 

SUSA Software system for Uncertainty and Sensitivity Analysis 

TDMA Tri-Diagonal Matrix Algorithm 

TH Thermal Hydraulics 

TRACE TRAC/RELAP Advanced Computational Engine 

UMAE Uncertainty Methodology based on Accuracy Extrapolation 

UPM Universidad Politecnica de Madrid 

US NRC US Nuclear Regulatory Commission 

xxv

NOMENCLATURE 

Symbol Name of quantity Value Unit

A Area - m2

Cov Covariance - - 

E Expected value - - 

F Force term - - 

N Sample size - - 

Nu Nusselt number, Nu = f(Re, Pr) - - 

P Pressure ratio - - 

P Probability - - 

Pe Peclet number, Pe = Re·Pr - - 

Pr Prandtl number, Pr = cp·η·k-1- - 

R Rank - - 

R

2 Coefficient of determination - - 

Re Reynolds number, Re = ρ·v·l·η-1- - 

St Stanton number, St = Nu·Re-1·Pr-1- - 

T Temperature - K 

V Volume - m3

X Input variable - - 

X Random variable - - 

Y Output variable - - 

c Drag coefficient - - 

cp Specific heat - J·kg-1·K-1

d Diameter - m 

e Internal Energy - W 

f Friction factor - - 

g Acceleration of Gravity - m·s-2

h Enthalpy - kJ·kg-1

h Heat transfer coefficient - W·m-2·K-1

h0 Reference heat transfer coefficient, Eq. (4.14) 5600 W·m-2·K-1

i Index - - 

j Index - - 

k Thermal conductivity - W·m-1·K-1

p Pressure - Pa

p Pitch - m 

p Probability content - - 

q Heat flux - W·m-2

q0’’ Reference heat flux, Eq. (4.14) 20000 W·m-2

r Pearson’s product momentum correlation coefficient - - 

s Standard deviation - - 

s

2 Variance - - 

t Time - s 

v Velocity - m·s-1

y Output - - 

y̅ Mean - - 

ΔTliquid Twall - Tliquid - K 

ΔTsaturation Twall - Tsaturation - K 
xxvi

Greek 

Γ Mass transfer rate - - 

Δ Wall roughness - m 

α Void fraction - - 

β Confidence interval - - 

β Blomqvist’s medial correlation coefficient - - 

η Dynamic viscosity - Pa·s 

ρ Density - kg·m-3

ρ Spearman’s rank correlation coefficient - - 

σ Standard deviation - - 

σ

2 Variance - - 

μ Mean - - 

τ Kenadall’s tau - - 

Subscript 

dg Droplet-to-gas 

dl Droplet-to-liquid 

g Gas 

i Interface 

i index 

ig Interface-to-gas 

il Interface-to-liquid 

l Liquid 

r Reduced 

wg Wall-to-gas 

wl Wall-to-liquid 

x Related to an input quantity 

y Related to an output quantity 
1-1

1 INTRODUCTION 

1.1 Motivation 

Uncertainty and sensitivity (U+S) analysis related to nuclear design and safety investigations gain 

more and more importance. That is a necessary step since the codes which are used in 

combination with U+S analysis have been changed from conservative codes to best estimate 

codes. Conservative codes used conservative approaches in order to account for shortcomings 

and uncertainties of the used models. Best estimate codes are now using the best empirical 

models. But these models are nevertheless affected by uncertainties and inaccuracies. These 

uncertainties are related to material properties, input and boundary conditions and as well as 

physical models. Therefore, it is necessary to account for them by means of combined U+S when 

using best estimate codes. The methods to be used to perform that kind of analysis are at a 

mature level and the community reached a certain experience in order to provide realistic and 

reliable results. Besides the fact that the application of thermal hydraulic best estimate codes with 

the purpose of licensing issues has to be accompanied by the quantification of uncertainties, 

these studies help also to identify areas of further research. In addition, it can be determined to 

which extend certain models are sensitive to variations of e.g. input and boundary conditions. This 

information is helpful to address improvement of these models and to show how the computational 

implementation of empirical models is performing. 

A prerequisite for best estimate + uncertainty quantification is the validation and verification of the 

best estimate simulation tool. Since best estimate tools are based, usually, on empirical 

correlations within a computational framework, it is mandatory to proof that the used correlations 

and models are implemented in a proper way and that they are only applied if the simulation 

condition fit with their range of validity. Verification can be therefore defined, with simple words, 

as the assessment whether a given correlation is implemented/solved correctly. This is an issue 

for the mathematical/computational quality management of computer codes. Validation can 

simply be defined as the test whether or not the correct correlation is used. This is a check of the 

physical nature of the problem to be investigated and the correlation which is used for (parts of) 

the simulation. Usually, both tasks go hand in hand since the process of validation requires 

sometimes to improve or to replace models since they are wrong or obsolete. In case new models 

need to be implemented or existing models are about to get updated, the verification is one major 

part of such tasks. 

Besides the best estimate codes, the applied uncertainty method must be also checked for 

appropriateness. One major difference is that the results of thermal hydraulic obtained during 

validation and verification can be compared to experimental or analytical data. Each of the major 

thermal hydraulic best estimate code like TRACE has its validation matrix. Such a matrix consists 

of several hundred experiments. These experiments cover small scale single effect test but also 

large scale integral plant tests. For the uncertainty methods, no validation matrix or qualification 

procedure exists. 

In the present report, the thermal hydraulic best estimate code TRACE is used for the post test 

analysis of experiments related to BWR fuel assembly. Results of these experiments are provided 

by the NUPEC in the frame of the BFBT (BWR Full-Size Fine Mesh Bundle Test) endorsed by 

the OECD/NEA. TRACE is well validated for the present simulation conditions and therefore can 

be applied as is without performing validation and verification work prior to the study. Concerning 
1-2

the U+S analysis, the programs SUSA and DAKOTA are used. SUSA is chosen on the one hand 

because it has been used successfully in the past and provides a reference tool in order to be 

compared with a new one such as DAKOTA. On the other hand DAKOTA is used as a second 

reference in order to perform a code-to-code comparison. Moreover, DAKOTA has been provided 

with a graphical user interface which is used for the input generation, manipulation and execution 

of TRACE simulations. Therefore, an automatized interaction already exists. Furthermore, the 

application of one best estimate code with two U+S analysis tools has the advantage that the user 

effect related to the modeling of the BWR fuel assembly can be excluded. Usually, the application 

of different thermo hydraulic codes or even the same code by different users will result in different 

representations of the object to be investigated. That, by itself, can cause differences and 

inaccuracies in the model results. Additional, with the application of the same code the influence 

of e.g. different physical models or material properties is excluded from the analysis. The only 

reason for different results presented in this report will arise from the different U+S tools and their 

interaction with TRACE. 

1.2 Scope of the Report 

The scope of this report can be divided into two major tasks. Task 1 is to provide an overview of 

uncertainties and related consideration especially when dealing with thermal hydraulic system 

codes like TRACE. In addition, the presented working methodology for the TRACE-SUSA study 

and the TRACE-DAKOTA study can be used as a guide book for future investigations. 

The second task is to present the results related to the post test calculations of BFBT experiments 

for pressure losses, void fraction and critical power during steady state and transient conditions. 

1.3 Structure and Content of the Report 

The report is divided into several sections. The second section deals with the uncertainties, their 

origin and methods to account for them. Section three gives an overview on the BFBT benchmark. 

The experimental facility is explained in detail as well as the different measurement devises 

installed for the different experiments. The fourth section covers the codes and programs which 

are used. In particular, the structure of the TRACE code is given and the theoretical fundamentals 

of the SUSA/DAKOTA are explained. Section five presents the applied uncertainty 

methodologies. This section can be considered as a guidebook for future U+S analysis with SUSA 

and with DAKOTA. The sixth section presents the actual U+S analysis. Results are presented for 

1) steady state single and two phase flow pressure drops, void fraction and critical power

measurements and 2) for transient void fraction and pressure drop measurements following two 

representative BWR transients. 
2-1

2 UNCERTAINTIES IN NUCLEAR SAFETY INVESTIGATIONS 

2.1 Generalities 

Uncertainties are the lack of certainties which are caused by inappropriate data and missing 

information. In general, uncertainties can be divided into two groups: stochastic or statistical 

uncertainties and epistemic or systematic uncertainties. 

Stochastic or statistical uncertainties are results of a random variability of the values of the 

variable that describe the system and its boundary conditions, also known as input variables to 

the model, and the lack of precision of the code’s physical models. 

Epistemic or systematic uncertainties are related due to the lack of knowledge, whether realized 

or not by the analyst. For instance, the real degree of variability of the input variables are not 

completely known, and an approximation is necessary, or that the physical models lack the 

description of some process or mechanism with more or less relevance in the quality of the 

predictions of the model. 

2.2 Conservative Approach versus Best Estimate Plus Uncertainties 

In the frame of safety related investigations of nuclear installations it has to be demonstrated that 

during normal and off-normal operation: the reactivity can be controlled, the heat can be removed 

from the system and that no radioactivity is released into the environment. The demonstration is 

done by simulation of the actual plant during normal and off-normal operation. 

With the development of nuclear technology, computer programs have been developed to 

describe the phenomena taking place in a nuclear reactor. But since some of these phenomena 

are of complex physical nature and elude from a comprehensive description, the models of the 

computer programs are afflicted with uncertainties or with a bias. In order to avoid a too optimistic 

prediction of vital safety parameters, safety factors have been introduced into the programs. 

These codes follow a conservative approach. 

Since the beginning of the nuclear safety simulation tools development the knowledge concerning 

the involved phenomena has increased, the computational capabilities are growing and the 

measurement and instrumentation techniques have improved. Hence, the conservatism in the 

codes has been reduced step by step. The actual safety analysis tools related to thermal hydraulic 

are nowadays best estimate codes referring to the fact that the best available empirical model is 

used to describe a certain phenomenon. A qualitative comparison of a peak cladding temperature 

as a function of time during a LOCA transient is depicted in Figure 1. 

Nevertheless, the models are afflicted by uncertainties since the experiments which have been 

used to derive the models are itself subject of uncertainties. About the sources of uncertainties 

please see the next sub section. That will ultimately lead to values which are characterized by an 

uncertainty band. 
2-2

Figure 1 Conservative Calculation versus Best Estimate 

Figure 2 is a more general overview of conservative and best estimate calculations and their 

margins to acceptance and failure criteria. As one can see, the best estimate result is expressed 

as a range of possible solutions. It is the purpose of uncertainty studies to prove that the upper or 

lower band limits are not exceeding or undershooting the acceptance limits. 

The remaining margin between the conservative prediction and the upper (or lower) value of the 

best estimate plus uncertainty investigation to the acceptance criterion is called margin. 

Intentionally, it is the aim to reduce that margin to its minimum. The safety is guaranteed by 

maintaining the margin which is defined as the distance between the failure limit, e.g. cladding 

fragilisation, and the acceptance criterion. That margin does not only consider a “safe distance” 

to failure but also the uncertainty which comes along with determining the failure limit(s). 

In case the conservative and best estimate plus uncertainty investigation would aim for the same, 

e.g., peak cladding temperature the conservative investigation would be characterized by e.g., a 

lower linear heating rate, meaning lower power level since the distance to the acceptance limit is 

smaller for the conservative code. 
2-3

Figure 2 Safety Margins 

The IAEA [1] defines the safety margins as: 

"Safety Margins are the differences in physical units between the established safety 

limits/criteria of assigned parameters associated with failures or changes of a system 

or component or with a phenomenon under consideration, and the calculated values 

of those parameters. Safety limits may be the limiting value used in the design or 

established for plant operation. Safety limits ... shall not be exceeded during normal 

operations including anticipated operational occurrences. The terminology safety 

criterion is generally associated with the assigned parameter for design basis 

accidents (DBAs). The values of acceptance limits or criteria are stipulated by national 

regulatory bodies, not to be exceeded during DBAs. The regulatory limits or criteria 

may be the same or more restrictive than what the plant is designed for. Therefore, 

for practical purposes, the safety margin is usually understood as the difference in 

physical units between the regulatory acceptance criteria and the results provided by 

the calculation of the relevant plant parameter. ...“

and

"...The probabilistic safety margins may be defined as the difference between the 

established probabilistic safety targets acceptable to the regulatory body and the 

calculated value of the risk parameter taking into account uncertainties in failure data, 

modeling of common cause failures, human actions etc. and other uncertainties in 

knowledge. ..." 

Since the computer codes underwent a transition from conservative to best estimate the safety 

analysis with respect to licensing purposes changes, too. 

Table 1 gives an overview about the different approaches [1]. 
2-4

Table 1 Safety Analysis Options for Licensing Purposes 

Applied Code Input and boundary 

conditions 

Assumptions on 

system availability Approach 

Conservative Conservative Conservative Deterministic 

Best estimate Conservative Conservative Deterministic 

Best estimate 

+ uncertainty 

Realistic 

+ uncertainty Conservative Deterministic 

Best estimate 

+ uncertainty 

Realistic 

+ uncertainty PSA based Deterministic + probabilistic 

The option assuming a best estimate code and conservative assumptions regarding the initial and 

boundary conditions as well as the system availability is the preferred option for safety analyses. 

The safety of a system can be demonstrated with a single calculation. Recently, the option with a 

realistic input taking also into account the uncertainties is considered more frequently since the 

other analyses are too conservative and in some cases and due to e.g. power upgrades the 

acceptance criteria can be reached. This requires several calculations to demonstrate safety for 

a given condition. Option two is used in Germany while in the USA either option one or option 

three must be applied [2]. Most times it is a question of time and money whether option one or 

three is followed. 

2.3 Sources of Uncertainties 

According to the IAEA safety report no. 52 [2], the origin of the uncertainties can be divided into 

five groups: Code or model uncertainties, representation uncertainties, scaling uncertainties, plant 

uncertainties and user effects. 

The code or model uncertainties are related to the field equations and the corresponding empirical 

closure laws. Furthermore, uncertainties can be attributed to: the correlations or physical models 

(e.g. the wall to fluid heat transfer or the interface friction), material data (e.g. thermal conductivity, 

dynamic viscosity of coolants or of structure materials), or geometrical averaging at a cross 

section or volume scale (one value per cell or cell interface). 

The uncertainties related and caused by the modeling of the facility or plant to be investigated are 

called representative uncertainties. A real set-up has to be transferred into a code readable input 

deck. Most codes have several components available allowing the description of the plant in great 

detail. Nevertheless, a 1-to-1 copy from a real system into an input deck is not possible. This can 

be related to the geometrical representation. For instance, asymmetries can hardly be modeled 

since the nodalization approaches are rigid. Another example is the representation of the pressure 

losses which is done by form loss coefficients. These are based on empirical formulations, 

tabulated for different parameter combinations. 

The third group considers the uncertainties related to scaling issues. The model or experiment is 

usually of smaller geometrical size than the real plant. In addition, boundary and initial conditions 

like temperature or pressure might be different in the experiment and the plant. The underlying 

physical phenomena are the same but the aforementioned differences introduce uncertainties. 

The uncertainties with respect to initial and boundary conditions are called plant uncertainties. 

Not all data of a nuclear power plant are available for setting up a model. But the missing 

information, however, can alter the results dramatically. Besides the pure operational parameters 
2-5

such as water level in the pressurizer or radial mass flow rate distributions at the core inlet 

geometrical parameters are unknown. These could be the pin and pellet dimensions in hot state. 

Moreover, parameters such as the gap conductance and the fuel composition after a certain burnup are also subject of uncertainties. Especially during transients, these parameters have an 

influence on e.g. the peak cladding temperature. 

The user effect is the last group of uncertainties. These uncertainties can be caused by different 

approaches users follow, which will yield different results even if both/all users made no mistakes 

and their assumptions are reasonable. Nevertheless, due to the user knowledge and experience 

the users can do mistakes while creating a model. To build a full plant model several hundreds of 

components and control blocks are required. Each of these components or controllers requires 

various information and multiple numbers have to be entered. It is likely that mistakes appear, 

causing not necessarily the code to crush but to predict wrong numbers. 

Based on the mentioned sources of uncertainties it is impossible that predictions with best 

estimate system codes are free of uncertainties. 

2.4 Uncertainty Methods 

The majority of the practical and applied uncertainty methods follow either an input error 

propagation approach or an output error extrapolation approach. An overview of selected 

uncertainty methods is given in Figure 3. 

Figure 3 Uncertainty Methods 
2-6

The input error propagation approach considers the uncertainties of, e.g., initial and boundary 

conditions, the geometry, the material data and the physical models. These uncertainties will be 

propagated through the code calculation and will cause, for their part, the uncertainties of the 

output. A graphical sketch is shown in Figure 4. That requires detailed information about the 

uncertainty of each and single parameter (e.g. uncertainty range, distribution, correlation 

between two or more parameters). 

The output error extrapolation approach does not consider the uncertainties of specific 

parameters. Instead, it extrapolates the uncertainties of relevant output parameters from an 

experiment to a real plant. That requires a comprehensive data base of experiments, which are 

focused on the same specific phenomena as during the investigation of the plant (e.g. reflood 

after LOCA). An illustration of that approach is given in Figure 5. 

Figure 4 Propagation of Input Errors [2] 

Figure 5 Output Error Extrapolation [2] 
3-1

3 NUPEC BFBT BENCHMARK 

3.1 General Remarks 

The objective of the OECD/NRC BWR Full-size Fine-Mesh Bundle Test (BFBT) benchmark is 

to understand the phenomena taking place during two-phase flow and to improve two-phase 

flow models needed for sub channel analysis [3]. In the frame of an international project the data 

base of the NUPEC has been made available to benchmark participants. The benchmark team 

consists of international experts in the field of modeling and validation as well as two-phase flow. 

Figure 6 shows the organization team formed by NUPEC Nuclear Power Engineering 

Corporation), JNES (Japan Nuclear Energy Safety organization) and the Pennsylvania State 

University. That benchmark has been approved as an international project by METI (Japanese 

Ministry of Economy, Trade and Industry), OECD/NEA and the U.S. NRC (United States Nuclear 

Regulatory Commission). 

By means of the NUPEC database, benchmark participants can assess the two-phase flow 

models of their codes. Based on the results, the models can be modified in order to represent 

the experimental data. In addition, the results obtained with the different codes can be compared 

to each other. Thereby, the different physical models can be compared and conclusions can be 

drawn regarding the appropriateness of the models. 

The benchmark is divided into two phases with the following sub division. 

 Phase I – Void distribution benchmark

o Exercise 1 – Steady-state sub-channel grade benchmark, where sub-channel,

meso- and microscopic approaches can be used;

o Exercise 2 – Steady-state microscopic grade benchmark, where meso- and

microscopic approaches and molecular dynamics can be utilized;

o Exercise 3 – transient macroscopic grade benchmark, where a sub-channel

approach can be applied;

o Exercise 4 – uncertainty analysis of the void distribution benchmark.

 Phase II – Critical power benchmark

o Exercise 0 – Steady-state pressure drop benchmark;

o Exercise 1 – Steady-state benchmark, which applies a one-dimensional approach

with BT correlations and a sub-channel mechanistic approach;

o Exercise 2 – transient benchmark, which applies a one-dimensional approach

with BT correlations and a sub-channel mechanistic approach.

The advantage of the NUPEC database related to BWRs is that full-size mock-ups of current 

BWR fuel assemblies have been used during the experimental phase, conducted from 1987 to 

1995 in Japan. 

Pictures and drawings showing the test facility, the test section, the assembly, etc. are taken 

from the specifications [3]. 
3-2

Figure 6 NUPEC BFBT Benchmark Organization 

3.2 Test Facility 

The test facility is shown in Figure 7. The description of the test facility is taken verbatim from 

the specifications [3]. The test section which holds the mock-ups of the BWR fuel assemblies is 

shown in Figure 8. 

Figure 7 Schematic Diagram of the Test Facility 
3-3

Water is circulated by the circulation pump (1) and the coolant flow rate is controlled by the 

three valves (3) of different sizes. The inlet fluid temperature for the test section (5) is 

controlled by a direct-heating tubular pre-heater (4). Sub-cooled coolant flows upward into the 

test bundle (5), where it is heated and becomes a two-phase mixture. The steam is separated 

from the steam-water mixture in the separator (7) and is condensed using a spray of subcooled water in the steam drum (8). The condensed water is then returned to the circulation 

pump (1). The system pressure in both steady and transient state is controlled by spray lines 

(9), which have four different-sized valves. The pressurizer (6) controls the system pressure 

when the test assembly power is low. The spray pump (10) forces a spray into the steamdrum after water is cooled with two air-cooled heat exchangers (11). With the test facility 

operational conditions of up to 10.3 MPa, 315°C, 12 MW and 75 t/h could have been realized. 

Figure 8 Cross Section of the BWR Fuel Assembly Test Section 
3-4

3.3 Assembly and Heat Rod Design 

In general, two different types of fuel assemblies can be investigated, a current (1980s) 8X8 and 

a high burn-up 8X8 assembly. The mock-ups consist of electrically heated rods which are 

arranged like in an 8X8 fuel assembly. Geometrical data of the fuel assemblies are given in 

Table 2. Assembly type four with a uniform axial power profile is used for the stationary 

investigations related to pressure drop, void fraction and critical power. For the transient 

analyses, assembly type C2A with a cosine shaped axial power profile is used. 

A drawing of the fuel assembly layout of the considered assemblies is given on the left side of 

Figure 9 along with the radial power profile, right side. The axial power profile can be found in 

Figure 10. 

Table 2 Geometrical Data of the Considered Fuel Assembly Types 

Parameter [unit] Value 

Assembly type [-] 4 C2A 

Investigation condition steady state transient 

Number of fuel rods [-] 60

Outer diameter [mm] 12.3 

Rod pitch [mm] 16.2 

Heated length [mm] 3708 (100%) 

Number of water rods [-] 1 

Channel box inner width [mm] 132.5 

Channel box corner radius [mm] 8 

In channel flow area [mm2] 9463

Number of spacers [-] 7 

Spacer type [-] Ferrule 

Spacer form loss coefficient [-] 1.2 

Spacer location (from bottom) [mm] 455, 967, 1479, 1991, 2503, 3015, 3527 

Heater outer diameter [mm] 7.3 

Heater material [-] Nichrome 

Insulator outer diameter [mm] 9.7 

Insulator material [-] Boron nitride 

Cladding thickness [mm] 1.3 

Cladding material [-] Inconel 600/beryllium 

Axial power profile [-] uniform cosine 
3-5

Figure 9 Fuel Assembly 4/C2A and Radial Power Profile 

Figure 10 Axial Power Profile for Assembly C2A 

The heat rod design and structure is depicted in Figure 11. The dimensions of the heater rods 

are identical to regular fuel rods. The heater rods consist of three layers. The central one is the 

heater layer made from Nichrome. The middle layer is made from boron nitride and has the 

function of an insulator. The last and outer layer is made of Inconel. 
3-6

Figure 11 Heater Rod Design 

3.4 Pressure Drop Evaluation 

During the exercise 3 of phase 1 and exercise 0 of phase 2, absolute and differential pressures 

were measured. Diaphragm transducers have been used in both cases. The locations of the 

pressure taps are shown in Figure 12. Nine differential pressure tabs are installed to measure 

the pressure drop e.g. across the spacer grids, dpT1, dpT2, dpT6 and dpT8, or of the whole 

bundle, dpT9. These taps have been employed for exercise 0 of phase 2. During exercise 3 of 

phase 1, the absolute pressure sensors, PTN010 and PTN007, are used and the difference 

between them is taken as the pressure loss. 

During exercise 0 of phase 2, prior to the critical power measurements, several single and twophase flow conditions have been analyzed with respect to the pressure loss. During the transient 

scenarios in exercise 3 of phase 1 only two-phase flow pressure losses have been investigated. 

As Figure 12shows, 7 spacer grids are installed along the heated length of 3708 mm. A ferrule 

type spacer grid, Figure 13, is used for the high burn up 8x8 assemblies (4 and C2A). The form 

loss coefficient is 1.2 according to the specifications. 
3-7

Figure 12 Location of the Pressure Sensors 
3-8

Figure 13 Ferrule Spacer Type (Top Left: Top View; Bottom Left: 3D View; Top Right:

Radial Dimensions; Bottom Right Axial Dimensions

3.5 Void Fraction Evaluation 

The void fraction at various combinations of pressure, mass flow rate, inlet sub-cooling and 

power has been recorded during all exercises of phase 1. Figure 14 indicates the positions of 

the void fraction measurement devices. Two different types have been use. The first one is an 

X-ray CT (computational tomography) scanner which consists of an X-ray tube and 512 

detectors, located at 3758 mm (850 mm above the top of the heated section). The whole 

arrangement can be rotated around the bundle. With this detector and the applied measurement 

technique a spatial resolution of 0.3 x 0.3 mm was achieved. These fine mesh results have been 

exclusively provided for the steady state scenarios where it was possible to rotate the detector 

in order to precisely measure the void fraction. During transient conditions, the X-ray CT scanner 

has been used too but it has not been rotated in order to repeat the measurements to obtain fine 

mesh data. These data are called chordal averaged void fraction. 

The second device consists of one X-ray tube and one detector. Three of these devices have 

been placed at 682, 1706 and 2730 mm. The X-ray tube and the arrangements have been 

moved in lateral direction since only a thin beam is penetrating the test section. Cross-sectional 

averaged void fractions have been recorded during the transients where the device was not 

moved. 
3-9

Figure 14 Arrangement of the Void Fraction Measurement Devices 

3.6 Critical Power Evaluation 

During phase 2, critical power measurements were taken. The assembly power has been 

increased slowly and the surface temperatures of the rods were monitored, making it a quasitransient experiment. The positions of the thermo couples are shown in Figure 15. About the 

definition when critical power was reached the specification states the following:

“The critical power was defined when the peak rod surface temperature became 

14°C higher than the steady-state temperature level before the dry-out occurred. 

The dry-out was observed in the peak power rod located at the peripheral row 
3-10

adjacent to the channel box. The boiling transition was always observed just 

upstream of the spacer.”

Figure 15 Thermocouple Position during Critical Power Measurement 
4-1

4 CODES AND PROGRAMS 

4.1 TRACE 

The explanations and discussion that follow in this sub section have been pulled, almost entirely 

verbatim, from the Ph.D. thesis of W. Jäger [4]. 

4.1.1 General Remarks and Main Features 

The system code TRACE (TRAC/RELAP Advanced Computational Engine) is one of the latest 

developments for the investigations of the thermal hydraulic of light water reactors (LWR) and the 

current thermo-hydraulic reference code of the U.S. NRC. The span of application ranges from 

investigations of normal operation behavior to the analyses of accidental scenarios (e.g., loss of 

flow or loss of coolant). TRACE has also been used to design and evaluate experimental test-rigs 

supporting the research related to LWR’s. For this application range TRACE has been widely 

used in the nuclear community but nevertheless the validation, as well as the developing process, 

is still ongoing to increase the confidence of the code calculation. 

In the frame of an international project - Code Application and Maintenance Program (CAMP) - 

codes of the U.S. NRC (e.g., TRACE, RELAP5) are distributed to the CAMP partners, to assess 

their capabilities. TRACE combines the capabilities of four major system codes (TRAC-P, TRACB, RELAP5 and RAMONA) and is envisaged to replace them in the near future. The U.S. NRC 

describes TRACE as follows [5]: 

"TRACE has been designed to perform best-estimate analysis of loss-of-coolant 

accidents (LOCAs), operational transients, and other accident scenarios in 

pressurized light-water reactors (PWRs) and boiling light-water reactors (BWRs). It 

can also model phenomena occurring in experimental facilities designed to simulate 

transients in reactor systems. Models used include multidimensional two-phase flow, 

non equilibrium thermo-dynamics, generalized heat transfer, re flood, level tracking, 

and reactor kinetics. Automatic steady-state and dump/restart capabilities are also 

provided." 

The main numerical features of TRACE are: 

 Partial differential equations for two-phase flow and heat transfer are solved using a finite

volume method.

 Heat transfer equations use a semi-implicit time differencing procedure.

 Fluid-dynamics equations in the components (1D or 3D) use either a multi-step time

differencing procedure or a semi-implicit time differencing procedure.

 The coupled, nonlinear equations for the hydrodynamic phenomena using finite difference

equations are solved by the Newton-Raphson iteration method.

 Resulting linearized equations are solved by direct matrix inversion.
4-2

TRACE follows a component-based approach to model a reactor system or an experimental 

facility. Nearly all components employed in a reactor system are represented in TRACE. The 

component itself can be nodalized as demanded by the user. Also, several types of the 

component are available. The following components can be used in TRACE: BREAK (pressure 

boundary), CHAN (BWR FAs), CONTAN (containment), EXTERIOR (needed for parallel 

execution of TRACE), FILL (mass flow and temperature boundary condition), FLPOWER (fluid 

power), HEATR (feed water heater), HTSTR (heat structure), JETP (jet pumps), PIPE (piping 

system), PLENUM, POWER, PRIZER (pressurizer), PUMP, RADENC (radiation enclosure), 

SEPD (separator), TEE, TURB (turbine), VALVE and VESSEL (3D). The VESSEL component 

can be used to model components where 3D phenomena take place like the reactor pressure 

vessel (RPV) or a storage tank. The VESSEL can also be separated into RPV typical 

components like downcomer, lower and upper plenum, and the core. 

4.1.2 Numerical Methodology 

A comparison between numerical methods used for current legacy codes like TRACE and future 

code systems are given by Nourgaliev [6], see Table 3. The numerical architecture of codes like 

TRACE and RELAP corresponds to the state-of-the-art of the 1970/80. Nowadays, more 

advanced mathematical methods are available to handle time and space discretization 

problems. Also new developments concerning program languages have been made by means 

of object oriented programming. Therefore, it is foreseen that the existing codes will be 

replaced by codes based on advanced physical, numerical and computational methods. The 

closure relations in the current TH system codes needed to solve the field equations are 

based on empirical models derived from experiments. Due to the complexity of certain 

experimental investigations, the derived correlations are valid for a narrow range of parameters 

only. Examples are the flow regime maps in the system and sub channel codes. For each flow 

regime (depending on mass flux and void fraction) a set of correlations is needed. In system 

codes, the size of the control volume is rather big ranging from centimeter to meter. Hence, 

some small scale physical phenomena (e.g., turbulence, boiling effects) cannot be taken into 

account because of time and space averaging techniques in the codes. To describe these 

phenomena, models based on first principles are needed. Instead of empirical correlations, the 

phenomena will be described by mechanistic models, i.e. based on nature laws if feasible. 

4.1.3 Field Equations 

The set of equations in TRACE are based on single-phase Navier-Stokes equation for each 

phase and additional jump conditions between the phases. The set of two-fluid, two-phase 

conservation equations are obtained by time and volume averaging techniques. Six partial 

differential equations, to describe the mass, energy and momentum conservation for the liquid 

and the gas field, are implemented into TRACE. Concerning non-condensables in the gas phase, 

a single momentum and a single energy conservation equation for the gas mixture is used. For 

the conservation of mass, one equation for each component of the gas field is used [5]. 
4-3

Table 3 Numerical Differences between Legacy Codes like TRACE and Future Code

Systems 

Legacy codes New developments Remarks 

Time discretization 

Semi-implicit Fully implicit 1st order does not allow to 

quantify numerical 

discretization uncertainties 

Nearly-implicit L-stable 

SETS Runge-Kutta 

Operator split High order 

1st order 

Space discretization 

Staggered-grid Finite-volume 1st order does not allow to 

quantify numerical 

discretization uncertainties 

Donor-cell Finite-elements 

Upwind Discontinuous Galerkin 

1st order Godunov based 

Collocated grid 

Linear algebra 

Direct solvers Efficient iterative linear and 

Sparse Gaussian elimination nonlinear solvers 

TDMA Krylov method 

Scale as ≈ N3 Multigrid 

Scale as ≈ N·log (N) 

Programming 

Serial Parallel (MPI) 

FORTRAN legacy Object-oriented (C++, Java 

The six partial differential equations for mass, energy and momentum conservation in the TRACE 

code are given below whereas the equations for the mass conservation are [5]. 

∂[(1 − α) ∙ ρl

]

∂t

+ ∇[(1 − α) ∙ ρl∙ vl⃗ ] = −Γ

(1)

∂[α ∙ ρg]

∂t

+ ∇[α ∙ ρg∙ vg⃗⃗⃗ ] = Γ (2)

The conservation of energy is based on a formulation with the internal energy 

∂ [(1 − α) ∙ ρl∙ (el +

vl

2

2

)]

∂t

+ ∇ [(1 − α) ∙ ρl∙ (el +

p

ρl

+

vl

2

2

) ∙ vl

⃗ ]

= qil + qwl + qdl + (1 − α) ∙ ρl∙ ⃗g ∙ vl⃗ − Γ ∙ hl

′ + (Fi

⃗ + Fwl ⃗⃗⃗⃗⃗⃗ ) ∙ vl

⃗ 

(3)

∂ [α ∙ ρg∙ (eg +

vg

2

2

)]

∂t

+ ∇ [α ∙ ρg∙ (eg +

p

ρg

+

vg

2

2

) ∙ vg

⃗⃗⃗ ]

= qig + qwg + qdg + α ∙ ρg∙ ⃗g ∙ vg⃗⃗⃗ − Γ ∙ hg

′ + (Fg

⃗ + Fwg⃗⃗⃗⃗⃗⃗⃗ ) ∙ vg

⃗⃗⃗ 

(4)
4-4

Conservation of momentum for the two phases writes as follows 

∂[(1 − α) ∙ ρl∙ vl⃗ ]

∂t

+ ∇(1 − α) ∙ ρl∙ vl⃗ ∙ vl⃗ + (1 − α) ∙ ∇p

= Fi

⃗ + Fwl ⃗⃗⃗⃗⃗⃗ + (1 − α) ∙ ρl

∙ ⃗g − Γ ∙ vi⃗ 

(5)

∂[α ∙ ρg∙ vg⃗⃗⃗ ]

∂t

+ ∇α ∙ ρg∙ vg⃗⃗⃗ ∙ vg⃗⃗⃗ + α ∙ ∇p = −Fi

⃗ + Fwg⃗⃗⃗⃗⃗⃗⃗ + α ∙ ρg

∙ ⃗g − Γ ∙ vi⃗ 

(6)

The force terms Fi, Fwl and Fwg rely on friction coefficients fi, fwl and fwg, and are cast in the 

following equations. 

Fi = fi∙ (vg⃗⃗⃗ − vl⃗ ) ∙ |vg⃗⃗⃗ − vl⃗ |

(7)

Fwl = −fwl ∙ vl⃗ ∙ |vl⃗ |

(8)

Fwg = −fwg ∙ vg⃗⃗⃗ ∙ |vg⃗⃗⃗ |

(9)

4.1.4 Closure Relations 

As one can see, it is necessary to provide additional information to close the above given 

correlations. Therefore, 10 parameters have been defined. These parameters are: the interfacial 

area, the interfacial mass transfer rate, the interfacial drag coefficient, the wall drag coefficient for 

both phases, the interfacial heat transfer coefficient for both phases, the heat transfer coefficient 

for the liquid-to-gas sensible heat transfer, and the wall heat transfer coefficients for both phases. 

Table 4 gives an overview of the flow and heat transfer regime dependent parameters required 

for solving the field equations. The relationship between the field equations and the closure 

parameters is illustrated in Figure 16 - Figure 18. 

Table 4 Required Parameters for the Closure of the Field Equations [7] 

Par. Mass Energy Momentum

Liquid Gas Liquid Gas Liquid Gas

Ai X X - X X X

Γ X X - X X X

ci - - - - X X

cwl - - - - X -

cwg - - - - - X

hil X X - X X X

hig X X - X X X

hgl - - - X - -

hwl X X X X X X

hwg - - X X - -
4-5

Figure 16 Mapping of the Regime Dependent Parameters for Energy Conservation [7] 

Figure 17 Mapping of the Regime Dependent Parameters Momentum Conservation [7] 

For the present investigation the heat transfer regime is pre-CHF more precisely nucleate boiling. 

The selection logic for pre-CHF scenarios is given in Figure 19. Depending on the void fraction 

and the bulk and wall temperatures, the position on the boiling curve is determined and the 

corresponding correlations/models are called. The nucleate boiling model takes into account pool 

boiling, based on Gorenflo [8] and forced convection flow, based on El-Genk [9]. For the sake of 

completeness, the considered physical models are given hereafter. 
4-6

Figure 18 Mapping of the Regime Dependent Parameters for Mass Conservation [7] 

qnucleate boiling

′′ = (qforced convection

′′ 3

+ (qpool boiling

′′ − qboiling initiation′′ )

3

)

1

3

(10)

qforced convection

′′ = hforced convection ∙ ∆Tliquid (11)

hforced convection = (

k

dhydraulic) ∙ [0.028 ∙ (

ppin

dpin) − 0.006] ∙ Re0.8

∙ Pr0.4

(12)

qpool boiling

′′ = hpool boiling ∙ ∆Tsaturation (13)

hpool boiling = (

h0 ∙ Fp

q0

′′ )

(

1

1−n

)

∙ ∆Tsaturation

(

n

1−n

)

∙

(14)

with 

Fp = 1.73 ∙ Pr

0.27 + (6.1 +

0.68

1 − Pr

) ∙ Pr

2

(15)

n = 0.9 + 0.3 ∙ Pr

0.15

(16)
4-7

Figure 19 Pre-CHF Heat Transfer Selection Logic in TRACE [5] 
4-8

where h0 is a reference heat transfer coefficient (5600 W/m2·K), q0

′′ is a reference heat flux (20000 

W/m2) and Pr is the reduced pressure quantity (Pr =

p

pcritical ⁄ )

qboiling initiation

′′ = qpool boiling′′ (Tonset nucleate boiling)

(17)

The wall heat transfer coefficient for subcooled boiling is calculated with the same models as for 

nucleate boiling but with a vapor generation fraction by means of temperatures. 

hliquid boiling =

fsub cooled ∙ (qnucleate boiling

′′ − qforced convection

′′ )

∆Tsaturation (18)

hwall =

qforced convection

′′ + (1 − fsub cooled) ∙ qnucleate boiling

′′

∆Tliquid (19)

fsub cooled = MAX (0,

Tliquid − Tbubble detachment

Tsaturation − Tbubble detachment

)

(20)

Tbubble detachment = Tsaturation −

qnucleate boiling

′′ − dhydraulic

Pe ∙ St (21)

where Pe is the Peclet number which is the maximum of either 70000 or the product of Reynolds 

number and Prandtl number, St is the Stanton number which is considered to be 0.0065 for sub 

cooled boiling Tbubble detachment is the temperature at which bubble detachment occurs. 

In addition, TRACE uses flow regime dependent wall drag models. For void fractions lower than 

0.8 the bubbly/slug flow regime with nucleation is used to determine the wall drag coefficient. 

Cwall→liquid = f ∙

2 ∙ ρliquid

dhydraulic

∙ (1 + Cnucleate boiling)

2

(22)

where f is the single-phase friction factor based on Churchill [10] and (1+Cnucleate boiling)2 is the 

two phase flow multiplier related to nucleate boiling. 

fsingle−phase = 2 ∙ [(

8

Re)

12

+

1

(a + b)

1.5

]

1

12

(23)

a =

{

 

 

 

 

2.457 ∙ ln

[

 

 

 

 

1

(

7

Re)

0.9

+ 0.27 ∙ (

∆

dhydraulic

)

]

 

 

 

 

}

 

 

 

 

16

(24)
4-9

b = (37530

Re )

16

(25) 

Cnucleate boiling = MIN{2.0, 155 ∙ (

dbubble

dhydraulic) ∙ [α ∙ (1 − α)]

0.62}

(26) 

4.1.5 Validation Process 

Since TRACE is a tool for the analysis of LWRs, an assessment matrix, as well as a validation 

matrix, has been developed to improve and validate TRACE. The development process of TRACE 

related to LWRs is summarized in Figure 20 [11]. Many experimental facilities exist and the results 

have been used for the purpose of assessment and validation. Figure 21 shows the assessment 

matrix of the U.S. NRC and the assessment matrix consists of more than 400 individual 

experiments [11]. 

Figure 20 Flowchart of the TRACE Development Process for LWRs 
4-10

Figure 21 TRACE Validation Matrix for LWRs 

4.2 SUSA 

4.2.1 Generalities 

The program system SUSA (Software for Uncertainty and Sensitivity Analysis) of the GRS 

(Gesellschaft fuer Anlagen- und Reaktorsicherheit mbH) [12, 13] can be used in general to 

evaluate the uncertainty of results and the sensitivity concerning input and boundary parameter 

variations. In particular, with respect to the uncertainty evaluation, SUSA can provide the range 

of output parameters and margins of upper and lower bounds to acceptance limits or safety 

criteria. For the sensitivity evaluation, SUSA can be used to identify important parameters based 

on sensitivity coefficients and corresponding ranks. Furthermore, these results can be used as 

feedback to code and physical model developments and to experimental investigations. Due to 

its programming in Visual Basic as an Add-on for Microsoft Excel, SUSA can be used for various 

problems including thermal hydraulics and neutron physics. 

SUSA follows the input error propagation approach. The uncertainties in the input deck or the 

source code of any program (assuming source code is accessible) will be treated as stochastic 

variables. The deterministic code transforms the stochastic input into a stochastic output. 

Thereby, the uncertainties in the input will be propagated to the output. By means of statistical 

methods uncertainty information of selected output parameters will be extracted from the output. 

A mathematical formulation of this paragraph is given in the following equation [14]. 
4-11

(

(X)1

(X)2

⋮

(X)N

) = (

(X1, ... , Xk)1

(X1, ... , Xk)2

⋮

(X1, ... , Xk)N

) → (

(x1, ... , xk)1

(x1, ... , xk)2

⋮

(x1, ... , xk)N

) → (

Code[(x1, ... , xk

)1

]

Code[(x1, ... , xk

)2

]

⋮

Code[(x1, ... , xk

)N]

) → ⋯

... → (

(y1, ... , ym)1

(y1, ... , ym)2

⋮

(y1, ... , ym)N

) = (

Code[(X)1

]

Code[(X)2

]

⋮

Code[(X)N]

) → (

(Y)1

(Y)2

⋮

(Y)N

)

(27)

4.2.2 Probability Density Function and Other Statistical Parameters 

For a comprehensive understanding of the SUSA methodology some statistical parameters will 

be introduced and explained. Reference of this section can be given, if not indicated otherwise to 

[15]. First, a function is defined that assigns a real number to a point in a sample space. That 

function is called random variable. The probability of a random variable which corresponds to the 

individual values assumed by the random variable equals the sum of the probability associated 

with the values of the set which is: 

P(a < X < b) = ∑ P(X = x)

a<x<b

(28)

The random variable can be described by the probability density function (PDF) and writes as 

follows 

f(x) = {

P(X = x), {x ∈ Z| − ∞ ≤ x ≤ ∞}

P(x − dx < X < x + dx), {x ∈ R| − ∞ ≤ x ≤ ∞} (29)

The PDF is the derivative of the cumulative distribution function which is the probability that a 

random variable (X) is less or equal to any integer or real number (x) and is given by the following 

equation 

F(x) = P(X ≤ x) =

{

 

 

 

 ∑f(t)

t≤x

{t ∈ Z| − ∞ ≤ t ≤ x}

∫ f(t)dt

x

−∞

{t ∈ R| − ∞ ≤ t ≤ x}

(30)

Input 

sample of

size N 

Input 

multivariate k

stochastic 

input variables 

Output sample of size N 

Input 

variables for 

N code 

executions N code executions 

Output 

multivariate m 

stochastic output 

variables 
4-12

Furthermore, the expected value or the population mean (μ), the population variance (σ2) and the 

standard deviation (σ) can be expressed by means of the PDF. 

μ = E(X) =

{

 

 ∑x ∙ f(x)

x

{x ∈ Z| − ∞ ≤ x ≤ ∞}

∫ x ∙ f(x)dx

∞

−∞

{x ∈ R| − ∞ ≤ x ≤ ∞}

(31)

σ

2 = E[(X − μ)2

]

{

 

 ∑(x − μ)

2

∙ f(x)

t

{x ∈ Z| − ∞ ≤ x ≤ ∞}

∫ (x − μ)

2

∙ f(x)dx

∞

−∞

{x ∈ R| − ∞ ≤ x ≤ ∞}

(32)

σ = √σ

2 = √E[(X − μ)2] =

{

 

 

√∑x ∙ f(x)

x

{x ∈ Z| − ∞ ≤ x ≤ ∞}

√∫ (x − μ)

2 ∙ f(x)dx

∞

−∞

{x ∈ R| − ∞ ≤ x ≤ ∞}

(33)

The above given formulas express statistical parameters of the input parameters with infinite 

boundary conditions but are identical for the analysis of output parameter with limited variation. 

The mean of the output parameter with limited numbers of samplings is expressed as y̅, and the 

sample variance, s2, can be written: 

y̅ =

1

N

∙ ∑ yi

i=1,N

(34)

s

2 =

1

N − 1

∙ ∑ (yi − y̅)

2

i=1,N

(35)

The equations above are valid for the scalar case meaning that the output parameter has no 

special or temporal dependency (index dependent) which is not part of the actual uncertainty 

analysis. In case the output parameter is a function of time (like the peak cladding temperature 

during LOCA transients) the mean and the sample variance can be calculated according to the 

hereafter given equations 

y̅(t) =

1

N

∙ ∑ [y(t)]i

i=1,N

(36)
4-13

[s(t)]

2 =

1

N − 1 ∙ ∑ {[y(t)]i − y̅(t)}

2

i=1,N (37) 

The standard deviation can be calculated by 

s = {

√s

2

√[s(t)]

2 (38) 

After the number of samples is defined, the distribution type must be specified. Based on the 

information known, e.g., the minimum and maximum, quantiles, the expected value, the 

standard deviation or the parameters of the untruncated distribution, distribution types such as 

the normal, log-normal, uniform, log-uniform, triangular, etc. can be selected. The normal 

distribution type will be chosen for a random number to demonstrate how known information can 

influence the distribution trend and subsequent the values which will be generated. For the 

normal distribution, given in Eq. (39), the reference value (= 3.0), the minimum (= 1.0), the 

maximum (= 5.0) and two quantiles are known. The quantiles are 2.0 with a probability of 10 % 

and 4.5 with a probability of 90%

F(x) = P(a ≤ X ≤ b) = ∫ 1

√2 ∙ π ∙ σ

∙ e

−

1

2

∙(x−μ

σ

)

2

dx

b

a

(39) 

The density function for the above given example is plotted in Figure 22. 

Figure 22 Normal Distribution with 2 Known Quantiles 

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00

Parameter Density Function

10 % quantile = 2.0

90 % quantile = 4.5

Reference value 
4-14

4.2.3 Number of Samples 

As shown in Eq. (27) each selected input and source code parameter will be sampled according 

to the statistical fidelity which is required (e.g. 95 %/95 %) and N values for each parameter will 

be generated. Afterwards, these N values will be written in N inputs and the N inputs will be 

executed yielding N outputs. Before the parameter sampling is performed, the size of N, the 

distribution of the N values between the minimum and maximum must be known and the type of 

sampling needs to be specified. Unfortunately, the distribution (PDF) is usually unknown. 

Sometimes only information about maximum and minimum are known. But information about 

PDF’s can be obtained from empirical distribution functions and estimators. Quantiles are useful 

estimators. A quantile of a random variable is a point in the sample space of the distribution of 

the random variable. 

P ≤ {

p {X < xp}

1 − p {X > xp} (40)

With that definition the tolerance interval can be introduced. The tolerance interval, with L as lower 

and U as upper interval limit is an estimate of a random variable which contains a fraction of the 

variable probability, p, with a specified level of confidence, β, which expresses that p is 

overestimated conservatively with a certain probability (e.g. 95 %) by the (p, β) tolerance limit. 

That means that the probability of having a sample of the random variable between the lower and 

upper interval is exactly p and β expresses how sure one is about this, see Figure 23. The 

confidence level accounts for the limited number of samples (or experimental data). 

For practical reasons one can write for the first one-sided tolerance limit 

P(xp ≤ X

N+1−l

) ≥ β

(41)

P(xp ≤ X

N+1−l

) ≥ ∑ (

N

i

) ∙ p

i

N−m

i=0

∙ (1 − p)

N−i

(42)

Rewriting the left side of Eq. (42), which is possible since the sum of the binomial probabilities 

yield unity, and changing the index, j = N – i, will result to the following equation. 

∑(

N

i

) ∙ p

i

N−l

i=0

∙ (1 − p)

N−i = 1 − ∑ (

N

i

) ∙ p

i

N

i=N−l+1

∙ (1 − p)

N−i

(43)

∑(

N

i

) ∙ p

i

N−l

i=0

∙ (1 − p)

N−i = 1 −∑(

N

j

) ∙ p

N−j

l−1

j=0

∙ (1 − p)

j

(44)

which yields 
4-15

1 −∑(

N

j

) ∙ p

N−j

l−1

j=0

∙ (1 − p)

j ≥ β

(45)

The second one-sided tolerance limit can be written as follows: 

1 − ∑(

N

i

) ∙ p

N−i

u−1

i=0

∙ (1 − p)

i ≥ β

(46)

After the aid of the calculus the two-sided tolerance limit can be written: 

1 − ∑ (

N

i

) ∙ p

N−i

l+u−1

i=0

∙ (1 − p)

i ≥ β

(47)

Figure 23 Definition of the Tolerance Interval 

In case the sum of the integers l + u = 1, the one-sided tolerance limit is used. If l + u = 2, the 

two-sided tolerance limit is used. Solving the binomial Eq. (47) it yield the following two 

equations which is known as the Wilk’s formula [16] for one-side tolerance limit, Eq. (48) and 

two-sided tolerance limit, Eq. (49). 

β = 1 − p

N

(48)

β = 1 − p

N − N ∙ (1 − p) ∙ pN−1

(49)

As it can be seen from Eq. (48) and Eq. (49), the number of samples depends only on the 

probability content and on the level of confidence but not on the number of input and source 

code parameters. Values of N are tabulated in Table 5 and Table 6 for various p and β 

combinations. The highlighted numbers correspond to a confidence level of 95 % and a 

probability content of 95 %. These numbers are accepted in (nuclear) engineering as being 

satisfactory in terms of statistical fidelity, see part 50, paragraph 46 of [17]. 
4-16

Table 5 Minimum Sample Size (N) for the One-sided Tolerance Limit (l + u = 1) 

β

p

0.500 0.700 0.750 0.800 0.850 0.900 0.950 0.975 0.980 0.990

0.500 1 2 3 4 5 7 14 28 35 69

0.700 2 4 5 6 8 12 24 48 60 120

0.750 2 4 5 7 9 14 28 55 69 138

0.800 3 5 6 8 10 16 32 64 80 161

0.850 3 6 7 9 12 19 37 75 94 189

0.900 4 7 9 11 15 22 45 91 144 230

0.950 5 9 11 14 19 29 59 119 149 299

0.975 6 11 13 17 23 36 72 146 183 368

0.980 6 11 14 18 25 38 77 155 194 390

0.990 7 13 17 21 29 44 90 182 228 459

Table 6 Minimum Sample Size (N) for the Two-sided Tolerance Limit (l + u = 2) 

β

p

0.500 0.700 0.750 0.800 0.850 0.900 0.950 0.975 0.980 0.990

0.500 3 6 7 9 11 17 34 67 84 168

0.700 5 8 10 12 16 24 49 97 122 244

0.750 5 9 10 13 18 27 53 107 134 269

0.800 5 9 11 14 19 29 59 119 149 299

0.850 6 10 13 16 22 33 67 134 168 337

0.900 7 12 15 18 25 38 77 155 194 388

0.950 8 14 18 22 30 46 93 188 236 473

0.975 9 17 20 26 35 54 110 221 277 555

0.980 9 17 21 27 37 56 115 231 290 581

0.990 11 20 24 31 42 64 130 263 330 662

4.2.4 Sampling 

After the probability density function has been characterized for each uncertain parameter and 

the number of code calculations has been calculated the sampling process can be performed. In 

the present case 93 numbers (or any other number) will be generated following the trend of the 

probability density function. In SUSA, two different ways of sampling are available. The first one 

is the simple random sampling, the second one is the Latin hypercube sampling. 

Random sampling is the simplest approach of sampling numbers of a particular subset. Each 

sample value is generated independently of the other sample values (rolling a die) by means of 

Monte-Carlo algorithm. Therefore, it is possible that a sample value is not going to be generated 

from a subset which might be of interest for the analysis. The sensitivity studies point out which 

of the parameter must be evaluated with special care. 

It is furthermore possible that sample values with a low probability but high consequences (like 

peak power or minimal mass flow rate) are missed. Considering a normal distribution and a limited 

number of 93 samples per parameter it is rather unlikely that, e.g., the highest power, the lowest 

mass flow rate and the lowest gas gap conductivity will be sampled at the same time. The 
4-17

combination of these, and other extreme cases, would be of high interest if analyzing the peak 

cladding temperature during different scenarios. 

In order to avoid the missing of extreme cases or more precisely the combination of extreme 

cases a different sampling technique is available in SUSA. For the present investigation, the Latin 

Hypercube Sampling (LHS) method is not applied. Therefore, only a brief introduction will be given 

here. Detailed information about Latin hypercube sampling can be found in [18] and [19]. 

In LHS n values of k parameters (X1, X2, ..., Xk) are selected. The range of variation is split into n

intervals which are non-overlapping and are of equal probability. One value from each interval is 

selected at random with respect to the probability density in the interval. The n values for X1 are 

paired randomly with the n values for X2. The n pairs are combined with the n values for X3, 

continuing in this manner until nk tuplets are formed [20]. In a matrix of (n x k) dimensions it will 

guarantee that in each column (n) and each row (k) only one sample can be found. In random 

sampling the distribution of the samples is independent of the previous sample. That means that 

some columns, which represent an interval on the parameter range, will remain empty. With the 

above given explanations the sampling can be performed and a pre-selected number of samples 

will be generated according to the chosen PDF. 

The so generated values for each parameter must be implemented in an existing code calculation 

strategy. The way such incorporation of n samples per k input parameters is done is given in subsection 5.2. Following the execution of the code(s) selected results will be transferred to SUSA to 

evaluate the uncertainty and the sensitivity. 

4.2.5 Statistical Measures 

During the sensitivity study with SUSA input and output parameters are checked if they are 

correlating in a linear manner. This can be expressed by the covariance between parameter x

(input variable) and parameter y (output variable). The covariance is defined as follows. 

Cov(x, y) =

∑(xi − μx) ∙ (yi − μy)

N (50)

In case the covariance is calculated to be zero no linear dependence exists between the two 

selected parameters. However, a correlation following a different function, e.g. polynomial, 

exponential, might be existing. The calculated value might be large but it is not possible to find 

out whether the relation between the parameters is strong or not [21]. In order to remove the 

dependency of the scale from the covariance it is divided by the standard deviation of the selected 

parameters. 

n1 n2 n3 n4 n1 n2 n3 n4

k1 X k1 X

k2 X k2 X

k3 X k3 X

k4 X k4 X

Figure 24 Comparison of Latin Hypercube Sampling (left side) and Random Sampling

(right side) Regarding the Sampling Distribution 
4-18

This approach is working if both parameters can be expressed in quantitative units, meaning 

physical values. In that case one is referring to parametric correlations. An example is the 

Pearson’s product momentum correlation coefficient. If at least one of the parameters is 

expressed in form of a ranking system non-parametric (monotonic) correlations will be used. If 

one parameter is a numerical value and the second one is based on ranks, the numerical values 

will be converted to ranks. Spearman’s rank correlation coefficient, Kendall’s tau and Blomqvist’s 

medial correlation coefficient are non-parametric correlation measures. The four named 

correlation measures are available in SUSA and will be shortly described in the following. 

One of the most used sensitivity measure is the product momentum correlation coefficient of 

Pearson (r) which is defined as: 

r =

∑ (xi − μx) ∙ (yi − μy)

N

i=1

[∑ (xi − μx

)

2 ∙ ∑ (yi − μy)

2

∙

N

i=1

N

i=1

]

1

2 (51)

The rank correlation coefficient of Spearman, denoted as ρ is writes as follows: 

ρ =

∑ R(xi) ∙ R(yi)

N

i=1 − N ∙ (

N + 1

2

)

2

[∑ R(xi

)

N 2

i=1 − N ∙ (

N + 1

2

)

2

]

1

2

∙ [∑ R(yi

)

N 2

i=1 − N ∙ (

N + 1

2

)

2

]

1

2 (52)

where R denotes the rank of the selected parameter. A simplified form can be used if no ties exist 

ρ =

6 ∙ ∑ [R(xi

) − R(yi)]

N 2

i=1

N ∙ (N2 − 1) (53)

A different approach is used by Kendall for his non-parametric correlation measure called tau [22]. 

In this measure, simulation results are grouped in concordant (nc) and discordant (nd) pairs. A pair 

is concordant if the values of one calculation are greater than the respective values of a second 

calculation. τ is defined as follows: 

τ =

2 ∙ (nc − nd

)

N ∙ (N − 1) (54)

For the sake of clarity, a small example will be used to illustrate the underlying methodology of 

Kendall’s tau. Assume that two persons have to rank the n = 4 parameters [a, b, c, d] in a certain 

way. Person number one ranks the parameters as follows [a, b, c, d] = [1, 2, 3, 4] while the second 

person ranks it in the following order [a, b, c, d] = [1, 3, 2, 4]. Based on that ranking six ordered 

pairs can be derived. For person number one {[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]} are the pairs 

and the six pairs for person number two are {[1, 3], [1, 2], [1, 4], [3, 2], [3, 4], [2, 4]}. 5 of the 

ordered pairs appear for both persons {[1, 2], [1, 3], [1, 4], [2, 4] and [3, 4]. These pairs are the 

concordant pairs (nc = 5). One pair per person is not represented in the sequence of the other 
4-19

person, [2, 3] for person 1 and [3, 2] for person 2. Therefore, the number of discordant pairs is 

1 (nd = 1). With these numbers Kendall’s tau can be rewritten as. 

τ =

2 ∙ (5 − 1)

4 ∙ (4 − 1)

=

8

12 = 0.667 (55) 

The last sensitivity measure is the medial correlation coefficient of Blomqvist, commonly referred 

to beta [23]. Let (x1, y1) ... (xn, yn) be a sample of a 2D population and mx, my the medians of the 

sample. The 2D plane spanned by x and y will be divided into four regions by introducing the lines 

x = mx and y = my. With the number of sample points in the different sectors a correlation between 

x and y can be obtained. The following formula shows Blomqvist’s β with two sample numbers 

where each number represents the sample numbers of two sectors. 

β =

N1 − N2

N1 + N2

=

2 ∙ N1

N1 + N2

− 1 (56) 

These four coefficients have in common that the result will be between -1.0 and +1.0. Based on 

the number and its algebraic sign the strength and the direction of the correlation are indicated. 

The strength is determined by the value. Values close to -1.0 or +1.0 indicate a very strong 

correlation while values close to zero indicate low or no correlation. The direction is indicated by 

the algebraic sign. A positive value means that with increasing X (input) value the Y (output) value 

is increasing, too. A negative sign means that if X is increasing Y is decreasing. Table 7 gives a 

qualitative overview whether the correlation is strong or not and Figure 25 illustrates the meaning 

of the calculated coefficient. 

The plots in the diagonal represent a coefficient of +1.0. The values on the abscissa are increasing 

and the ordinate is following. The number 0.025 in the upper right corner indicates a very low 

dependency which can be already called independent. The corresponding plot in the lower left 

corner shows that the points are scattered across the whole plot and no correlation can be 

deduced. 

Table 7 Dependency of Correlation as Function of the Sensitivity Coefficient 

Correlation Positive Negative 

Independent 0.0 

Weak + 0.29 ... + 0.10 - 0.29 ... - 0.10 

Medium + 0.49 ... + 0.30 - 0.49 ... - 0.30 

Strong + 1.00 ... + 0.50 - 1.00 ... - 0.50 
4-20

Figure 25 Meaning of Statistical Correlation [14] 

Besides the ordinary correlation coefficients, two other coefficients can be calculated. These are 

the partial correlation coefficient (PCC) and the standardized regression coefficient (SRC). The 

presented measures correlate the linear relationship between two random variables. In cases 

several random variables are involved these variables can influence each other in a way that the 

influence of one random variable on a second random variable might bias the results. With the 

PCC that perturbation is eliminated so that only the influence of variable 1 on variable 2 is 

evaluated. This can also be a disadvantage because it is possible that a parameter with an actual 

low correlation compared to another parameter can obtain a high sensitivity coefficient, meaning 

that its importance is over estimated. 

For the Pearson product momentum correlation the PCC is denoted as follows (if N = 3), 

r12.3 =

r12 − r13 ∙ r23

√(1 − r13

2

) ∙ (1 − r23

2

) (57)

where rij is the regular Pearson product moment correlation coefficient evaluated between Xi and 

Xj. In the same way the PCC of e.g. Kendall’s tau can be calculated 
4-21

τ12.3 =

τ12 − τ13 ∙ τ23

√(1 − τ13

2

) ∙ (1 − τ23

2

) (58)

The SRC is similar to the PCC since the influence of non-selected random variables will be 

eliminated. But in the SRC the linear influence of the other parameters will be erased. In addition, 

SUSA also offers importance measures like correlation ratios and correlation ratios on ranks. 

A figure of merit for the significance of the analysis (or how well fits a model the data) can be the 

coefficient of determination, R2 which is determined as follows: 

R

2 = 1 −

RSSmodel

RSS0−model (59)

It is the comparison of the residual sums of squares for the model and the 0-model which is the 

reference of comparison. This model describes a horizontal line at the level of the mean of the y 

values, which is the simplest possible model that could be fitted to any set of data [21]. 

To avoid confusion about the terminology “being of importance” or “being sensitive to” it must be 

clarified that the coefficients calculated consider the parameter variation and not only the 

parameter. During an uncertainty and sensitivity analysis the most important parameters for the 

peak cladding temperature might be the mass flow rate or the coolant inlet temperature while the 

power is evaluated to be of low or no importance. That is somehow violating the general 

understanding that the power is a dominant factor for the evaluation of the peak cladding 

temperature. The calculated values, however, are only valid for the selected case within the 

applied parameter range. If the power is changed only marginal but the mass flow rate and the 

inlet temperature show a high variation their variation has a bigger impact on the results than the 

small variation of the power. 

4.3 DAKOTA 

DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) is under development 

by the Sandia National Laboratories. It is intended to be a multilevel parallel object-oriented 

framework for design optimization, parameter estimation, uncertainty quantification, and 

sensitivity analysis [24]. DAKOTA has been implemented into the Symbolic Nuclear Analysis 

Package (SNAP) which is the graphical interface for using NRC codes such as TRACE (refer to 

section 4.4).

The general theory behind DAKOTA concerning the sampling, the uncertainty quantification and 

the sensitivity analysis is identical to SUSA. In addition, DAKOTA employs also the formula of 

Wilk. The data flow between TRACE and DAKOTA is similar to the one of TRACE and SUSA as 

depicted in Figure 26 with the exception that the data extracted is automatized and no actions 

from the user are required. Since everything is done in SNAP, the user does not need to write 

scripts for the data transfer. One only needs to select the input parameters, the uncertainty band 

with the corresponding distribution, the number of samples, the type of sampling and the desired 

output parameters. The disadvantage of this process is that only parameters can be selected 

which are made available to DAKOTA in SNAP. 
4-22

Figure 26 Coupling Scheme between DAKOTA and a Simulation Code 

Currently, not all parameters of the input deck are available for uncertainty analysis, see the 

following section. Moreover, the parameters which can be selected are limited to the input deck. 

Physical model parameters cannot be selected yet even if all necessary uncertain parameters are 

known. 

4.4 SNAP 

SNAP, the Symbolic Nuclear Analysis Package, is a graphical user interface which is under 

development by Applied Programing Technology, Inc [25]. The main purpose of SNAP is to 

simplify the analysis process related to engineering orientated simulations and modeling. By 

means of the Common Application Framework for Engineering Analysis (CAFEAN), a very flexible 

framework for creating, editing and processing input decks of several engineering codes is 

utilized. The major U.S. NRC codes for the evaluation and simulation of LWRs are incorporated 

into SNAP via java based plugins, among them TRACE, COBRA, RELAP5, MELCOR, PARCS 

and CONTAIN. The architecture, see Figure 27, is divided in client and server applications where 

a client application is the one which is performed on a local machine and provides a graphical 

user interface while the server application runs in the background and on a different machine [25]. 

Besides the main analysis tools, other programs can be used like DAKOTA to perform the 

uncertainty analysis or AptPlot to allow the graphical representation of results. 

Moreover, SNAP consists of a suite of integrated applications including the Model Editor, the 

Configuration Tool and the Job Status. 
4-23

Figure 27 SNAP Architecture [25] 

The Model Editor is the actual graphical user interface used for client applications. It is used for 

the development and modification of the input deck of the considered code(s). Within the model 

editor the components of the different codes can be presented and arranged to improve the 

modeling process. In addition, the modeled components/loops/plants can be animated to visualize 

the results. A screenshot of the Model Editor is given in Figure 28. The Model Editor itself is 

divided into five components or windows. At the Toolbar the main operations (safe, load, etc.) can 

be performed. It can also be used to create a new component. In the navigator window the 

different components and model options can be selected. These components will then appear in 

the Property View window where the modification of selected parameters can be done. The 

view/Dock view visualizes the component. In that window, the components can be connected to 

each other and arranged in loops to allow a better understanding on the behavior. The Message 

window keeps the user informed about the last actions performed. 

The Configuration Tool is used to define the global settings of the client application. With it, new 

applications, e.g., a new TRACE or DAKOTA model, can be created. It is also used to connect 

the executables of the involved programs (TRACE, JAVA, AptPlot, etc.) with the applications, 

Figure 29. 
4-24

Figure 28 Model Editor 
4-25

Figure 29 Configuration Tool 

The last integrated application is the Job Status which monitors the progress and status of each 

simulation. Besides that, local files can be imported as new jobs, Figure 30. 

Figure 30 Job Status

5-1

5 APPLIED UNCERTAINTY AND SENSITIVITY METHODOLOGY 

5.1 General Remarks 

To select parameters for the uncertainty and sensitivity study, the input and boundary conditions 

and the physical models need to be evaluated with respect to their impact on the output parameter 

of interest. 

The following sub sections are aimed to provide the reader the information necessary to perform 

similar investigations with TRACE-SUSA and TRACE-DAKOTA and can be used as a guideline. 

In case only the results of these investigations are of interest, this section can be skipped. 

To perform U+S studies two codes/programs are needed. The first code is to perform the analyses 

of interest, in the present case thermal-hydraulic evaluation of the BFPT benchmark. The tool of 

choice is TRACE. In order to evaluate the results regarding uncertainty and sensitivity constrains, 

a different code must be applied. In the first case it is SUSA (sub section 5.2) and in the second 

case it is DAKOTA (sub section 5.3).

5.2 Uncertainty and Sensitivity Study with TRACE-SUSA 

5.2.1 General Procedure 

A flow chart of the information processing is given in Figure 31. It consists of two separate SUSA 

applications and of one TRACE application. The presented steps are not done automatically but 

scripts have to be written to connect the different files. That is one of the main disadvantages of 

the TRACE and DAKOTA approach; everything has to be done manually. But it can also be 

considered as an advantage since every parameter, variable, number in the TRACE input file can 

be altered and with general scripts future investigations can be performed time and resources 

efficient. 

At the beginning of any U+S analysis stays the reference input of TRACE, or any other code 

which is designed to do thermal-hydraulic, mechanical, chemical, etc. analysis. It is evaluated 

regarding potential parameters, variables, input and boundary conditions which might be afflicted 

with uncertainty. In certain cases, physical models can also be afflicted with uncertainties. These 

parameters can be included in the analysis if access to the source code is possible. As mentioned 

in section 4.2, the number of runs is independent of the number of uncertain parameters. 

Therefore, it does not matter whether 10 or 20 parameters will be selected for the uncertainty and 

sensitivity analysis. Hence, in case it is not clear if an input parameter will influence an output 

parameter, it is reasonable to include it anyway. 

After the uncertain parameters have been selected the range of uncertainty must be known or 

should at least be estimable. The information can be taken out of measurements of the 

experiments which is subject of the investigation. In case the documentation of the experiment 

does not include measurement uncertainties, similar experiments have to be taken and their 

uncertainty ranges can be adopted. Also, in some cases, manufacturer of components provide 

this kind of information. In case no information is known or available engineering judgment based 
5-2

on best practice guidelines and experience has to be considered to define the uncertainty range 

of the parameters. 

The next information which is required is the distribution of the uncertainty parameter between 

the uncertainty ranges. Usually, that information is the most difficult to obtain. Again, 

measurements or manufacturer can provide the distribution. In the case the distribution is 

unknown it is advisable to use a uniform distribution. The uniform distribution has the advantage 

of treating the uncertain parameter in an unbiased way since every value, no matter whether it is 

an extreme case (minimum or maximum) or it is the reference case, has the same frequency of 

occurrences (conservative value). 

The three, aforementioned information, 1) uncertain parameter, 2) uncertainty range, and 3) 

uncertainty distribution will be entered into SUSA. In addition, the statistical fidelity needs to 

defined in SUSA in order to calculate the number of runs and hence the number of values per 

uncertain parameter (please refer to section 4.2). SUSA than generates a file which contains the 

information of the uncertain parameter, e.g. reference value, distribution type and the values for 

each uncertain parameter. That file is the base for the next step. In case of 95 % confidence level 

and 95 % probability content, 93 (two-sided) values per uncertain parameter will be generated. 

That means that 93 TRACE inputs must be generated and subsequently executed. Afterwards, 

selected output parameters will be extracted from the 93 TRACE output files and stored into a file 

which will be used to perform the actual uncertainty and sensitivity study with SUSA. 

Figure 31 Flow Chart of the TRACE-SUSA Interface [26]
5-3

In the uncertainty evaluation, statistical parameters will be calculated for each output parameter, 

namely mean, median, maximum, minimum and standard deviation. These values should be 

compared to the result of the reference input and to the measurements of the experiment or the 

plant. Besides that information, the underlying distribution type of the output parameter can be 

evaluated. During the statistical evaluation, sensitivity coefficients will be calculated and the most 

important parameters can be identified. 

In the following subsections, each step will be explained in detail how to get from the reference 

input to information regarding the uncertainty of output parameters and the sensitivity to input 

parameter changes. 

5.2.2 How to Run SUSA: The Sampling 

A detailed description of the capabilities of SUSA can be found in sub-section 4.2. Here, the path 

to generate the sampling for the single-phase pressure drop will be shown. SUSA will be launched 

and a new application will be opened. The uncertain parameters along with their range and 

distribution will be entered. As reported in sub section 6.2, all uncertain parameter ranges except 

for the inlet temperature are reported as percental variations. Therefore, an uncertainty factor was 

introduced which will be multiplied by the uncertain parameter in order to get the values for the 

uncertainty study. In case the variation is ± 1.0 % an uncertain parameter with a reference value 

of 1.0, a minimum of 0.99 and a maximum of 1.01 is generated. Hence, the uncertain parameter 

is multiplied by values between 0.99 and 1.01 which is identical to a percental variation of 1.0 %. 

For the inlet temperature an uncertain factor with a reference value of 0.0 is generated. That 

uncertain factor can range from -1.5 K to 1.5 K as reported in the benchmark specification. The 

uncertain factor will be added to the uncertain parameter to get the values for the study. A 

summary of the information, described in sub section 6.2, is given in 

Figure 32. That data sheet contains information with respect to the single-phase pressure drop 

analysis. For the other analyses (two-phase pressure drop, void fraction, etc.) a 10th parameter, 

the power will be introduced. 

After all information has been entered into SUSA, the sampling can be performed. For the present 

investigation the simple random sampling was applied. 

After the SUSA sampling, a file called medusa.prn is generated containing the uncertainty 

information of the selected input and source code variables/parameters. A copy of the 

medusa.prn file which is generated for the single-phase pressure drop analysis is given in the 

Appendix A. 

With the creation of the medusa.prn file the first step is finished and the information processing 

via scripts has to be performed. 
5-4

5.2.3 How to Generate n TRACE Input Files 

5.2.3.1 Auxiliary input files 

The file medusa.prn must now be converted into a file called Sample.dat. In general, arbitrary 

names can be given to the files but for the sake of clearness default names will be introduced. 

The format of the Sample.dat file must be of the following. 

n m 

A11 A21 A31 ... An1

A12 A22 A32 ... An2

A1m A2m A3m ... Anm

where: n is the number of uncertain parameters 

m is the number of values per uncertain parameter 

An example of Sample.dat is given in the Appendix D. A second file needs to be generated in 

order to connect the information of the Sample.dat file with the reference input. That file is called 

UncMod.dat. An example and a description of that file is given below. 

9 

S Single Variables

0 

T Trip Variables

0 

B Block Variables

0 

C Components

28

2 fill 100 flowin 1 3 1

1 fill 100 pin 1 1 1

3 fill 100 tlin 1 5 3

3 fill 100 tvin 1 5 3

Figure 32 SUSA Main Data Sheet for the Single-Phase Pressure Drop Analysis
5-5

4 chan 200 epsw 1 5 1

3 chan 200 toutl 1 5 3

3 chan 200 toutv 1 1 3

7 chan 200 vol 1 2 1 . 

7 chan 200 fa 1 2 1

5 chan 200 kfac 1 4 1

5 chan 200 kfac 2 3 1

5 chan 200 kfac 3 3 1

5 chan 200 kfac 4 2 1

5 chan 200 kfac 5 1 1

5 chan 200 kfac 6 1 1

5 chan 200 kfac 6 4 1

6 chan 200 hd 1 2 1

3 chan 200 tl 1 2 3

3 chan 200 tv 1 2 3

1 chan 200 p 1 2 1

3 chan 200 tw 1 2 3

3 chan 200 rftn 1 2 3

3 chan 200 rftn 2 2 3

3 chan 200 rftn 3 2 3

3 chan 200 rftn 4 2 3

3 chan 200 matwr 2 2 3

3 break 300 tin 1 4 3

1 break 300 pin 1 5 1

M Model Variables

2 

1 1

9 1

2 1

8 1

The number at the top of the file is the number of uncertain parameters. It must be the same 

number as in the Sample.dat file (n). That number is followed by information regarding how much 

signal, trip, block and component variables will be changed. These numbers or their sum must 

not be identical to the number of uncertain parameters. It is the number of locations where 

changes will take place. In the present case only component variables will be changed and 

changes will be performed at 28 positions in the TRACE input. 

Then, 28 entries follow to describe which value will be replaced with which value from the 

Sample.dat file. The first number corresponds to the columns in sample.dat, in that case column 

no. 2. The second entry on that line is the component name and the third is the component 

number, meaning that FILL component 100 is subject of changes. The next word defines the 

parameter in the component which will be changed which is flowin (the inlet mass flow rate). The 

last three numbers define the position of the parameter in the component array. The first digit 

specifies the line of the variable. In case of pipe, chan, or htstr components several lines with 

same parameters are present (as a result of multiple cells). In case of FILL and BREAK

components it happens that time dependent mass flow or pressure tables are defined. In the 

present case the flowin parameter appears only one time, therefore, the digit is 1. The second 

digit specifies the location in the line. The value for flowin appears in the third position, see below. 

The last digit is the flag which defines how the parameter will be changed. The user can chose 

between four ways of changing a variable 

1: In order to replace the value with the value of the columns in Sample.dat a 0 must be 

entered, If 0 Then Variable_new = uncertain value. 
5-6

2: 

3:

4:

To multiply the value with the value of the Sample.dat columns a 1 must be entered, If 1 

Then Variable_new = Variable_old x uncertain value. 

A fractional variation can be done to change the variable, indicated by a 2, If 2 Then 

Variable_new = Variable_old x (1.0 + uncertain value). 

The uncertain value can be add or subtracted from the variable by placing a 3, If 3 Then 

Variable_new = Variable_old + uncertain value 

As mentioned above all parameters except the temperature are multiplied by an uncertainty factor 

which is in the reference case 1.0. In the present case the highlighted value of the FILL component 

will be changed by multiplying it with the uncertain value. 

******* type num userid component name

fill 100 0 Inlet

* jun1 ifty ioff

10 2 0

* twtold rfmx concin felv

0.0 1.0E20 0.0 0.0

* dxin volin alpin vlin tlin

0.1545 1.462034E-3 0.0 0.0 307.550000

* pin pain flowin vvin tvin

2.0000E+05 0.0 2.750000 0.0 307.550000

From the TRACE.inp one gets 2.750000 and from Sample.dat one gets 9.9578E-01 and from 

UncMod.dat one gets 1 which means multiplication. 

2.750000 x 0.99578 = 2.738395 

2.738395 is the new value which will be written in the new TRACE input. The complete input 

for the single-phase pressure drop analysis (reference input for test scenario 1) is given in 

Appendix A as example. 

The last part of the of the UncMod.dat files is dedicated to the uncertain parameters in the 

source code. In the present case two parameters of the source code, the coolant density and 

the friction factor, will be considered in the uncertainty and sensitivity study. The first number is 

the number of locations in the TRACE source code where changes will take place (again, that is 

not the number of parameters which will be changed). For each value which will be changed 

two lines with two numbers must be entered. The first number in the first line is the identifier in 

the TRACE source code. The second number is the flag to determine how the parameter will be 

changed in TRACE. Unfortunately, these flags are different to the ones used to change the 

TRACE input file. For the source code, the following definitions are valid. 

If 1 Then Variable_new = uncertain value |replace 

If 2 Then Variable_new = Variable_old x (1.0 + uncertain value) |fractional variation 

If 3 Then Variable_new = Variable_old + uncertain value |summation 

If 4 Then Variable_new = Variable_old x uncertain value |multiplication 

The first number on the second line defines the column number in the Sample.dat file and the last 

number is identical to the second number on the first line. 
5-7

5.2.3.2 How to change the TRACE input file 

In this step, the reference TRACE input Trace.inp will be altered and 93 new inputs called 

Trace_1.inp – Trace_93.inp will be created. Thanks to R. Macian, Professor at the Technical 

University of Munich, a FORTRAN program is available to do the altering of the TRACE input 

file. 

The FORTRAN program, TRACEInpProc, contains six modules: 

IntrTypeM.f90

ProcessTraceFileM.f90

ReadArgM.f90 

ReadFilesM.f90

StringProcessM.f90

TraceInpProcM.f90

That file contains the information about the general structure of the 

UncMod.dat file. The maximum number of single, trip, block, etc 

variables are defined here. 

Reads the uncertainty data stored in the UncMod.dat file 

An auxiliary module for data processing 

This module reads the TRACE input and the sample.dat file 

An auxiliary module for data processing 

The master module which calls all other moduls, sub routines and 

functions to generate the new TRACE inputs. 

Besides the new TRACE inputs an additional file called TRACE_Unc_Models.dat will be 

created. The information regarding the TRACE source code changes are stored in that file. The 

meaning of that file will be explained in the following subsection. 

The arguments for the command lines to execute TRACEInpProc.exe are the following: 

-n # <# is the sample number to get processes> 

-i <UncMod.dat> 

-t <Trace.inp> 

-s <Sample.dat> 

-m <TRACE_Unc_Models.dat> 

5.2.3.3 How to change the TRACE source code parameters 

To change parameters in the TRACE source code, two additional modules must be introduced to 

the TRACE workspace (with Compaq Visual Fortran) and some minor changes must be done in 

some existing TRACE source files. 

Include the modules ModUncInfoM.f90 and ModUncVarM.f90 in the source folder of the TRACE 

code. 

Add them in the TRACE workspace by Projects → Add to Project → Files 

Change the module trac.f90 by introducing 

USE ModUncInfo

at the top of the file and 

IF (uncInf) THEN

CALL ReadUncInfo

ENDIF 
5-8

Change the module CmdLineArgsM.f90 by introducing 

USE ModUncVar

at the top of the file and 

CASE (‘—unc’)

UncInF = .TRUE.

Below the line containing runStats = .TRUE. 

Safe the changes and build trace.exe

The module ModUncVarM.f90 contains information on how much parameters can be changed 

and the module ModUncInfoM.f90 is reading the uncertainty information stored in the 

TRACE_Unc_Models.dat file. This file contains the information of the UncMod.dat file along with 

the values stored in the Sample.dat file. 

An example for TRACE_Unc_Models.dat is given below. 

 2 

* 

 1 1

 1 0.9618600

* 

 2 1

 1 0.9969400 

TRACE_Unc_Models.dat is generated automatically and the user has to do nothing. In case the 

uncertainty and sensitivity analysis is limited to the TRACE input file an empty 

TRACE_Unc_Models.dat file will be generated and the TRACE executable will not consider the 

changes in the code. 

With the changes and actions described in the previous paragraph the TRACE source code is 

ready to read uncertainty information. But in order to perform uncertainty investigations source 

code parameters need to be selected and changed as well. An example of the manipulation of a 

source code parameter is given below. In the present case the friction factor is selected and the 

altered TRACE routine is as follows. Yellow highlighted variables or comments have been added 

to do the uncertainty analysis. 

REAL(sdk) FUNCTION getfChurchill(re, epswOverhd)

!

!Uncertainty.Beginning

USE ModUncInfo

!Uncertainty.End

! 

REAL(sdk) :: a, b, re, epswOverhd, X1

! 

!Uncertainty.Beginning

INTEGER(sik) :: nuncMod = 1_sik

!Uncertainty.End 

!

!

X1 = 1.0_sdk

Right after the line containing CALL ProcessArgs 
5-9

IF(UncInf)THEN

X1 = MAX(ModUncval (nUncMod,1,X1),0.0_sdk)

END IF

!Uncertainty.End

! 

re = MAX(10.d0, re)

a = (2.457_sdk*LOG(1._sdk/((7._sdk/re)**0.9_sdk+0.27-

sdk*epswOverhad)))**16_sik

b = (37530._sdk/re)**16.0_sdk

GetfChurchill = (2.0_sdk*((8.0d0/re)**12_sik+1.d0/(a+b)*1.5_sdk)

**(1.0_sdk/12.0_sdk))*X1

RETURN

END FUNCTION GetfChurchill

5.2.3.4 How to execute all of it

The execution is done with batch files containing all the steps explained in the previous subsections. The lines of the batch file performing the analysis for the single-phase pressure drop 

is given as example below. 

In order to guarantee a proper execution and performance all commands must be in one line 

or line breaks have to be introduced since it is done in two loops. The outer loop is generating 

the “i” different reference files (depending on the different experimental scenarios which will be 

investigated). The second, the inner loop generates and performs “j” inputs per “i” reference 

cases. 

Step 1: a FOR loop to generate i inputs based on one basic input, in the following called 

RAW.inp, is initialized. For the single-phase pressure drop analysis 36 cases will be 

investigated. The variable is indicated by %%i and the dimensions are given in the 

parenthesis; (1 = Start point, 1 = Increment, 36 = End point) meaning that the FOR loop starts 

at 1 and counts i+1 all the way up to 36. The “do” indicates the actual command to perform. In 

the present case the program TRACEInpProc.exe is called with the arguments –t –s –i and –n 

(U:\WORK\NUPEC\ must be replaced according to the location of the executable). The files 

Cases.dat and CasesMod.dat correspond to the files Sample.dat and UncMod.dat, 

respectively described in sub-section 5.2.3.2, and are given at the end of this sub section. 

:FOR /L %%i IN (1,1,36) do "U:\WORK\NUPEC\TRACEInpProc.exe" -t RAW.inp -s

Cases.dat -i CasesMod.dat -n %%i

Step 2: Since the following commands are about to be executed within the FOR loop one new 

reference file is generated. The name of the file is RAW_MOD.inp which will be renamed to 

P7000%%i.inp (which is P70001.inp if i = 1). That new file is execute with TRACE. In the 

present case the command line argument –p is used which means that the suffix of the files 

(.inp) must not be given with the file name. 

& REN RAW_MOD.inp P7000%%i.inp & "U:\WORK\NUPEC\trace.exe" -p P7000%%i 

!Uncertainty.Beginning 
5-10

& FOR /L %%j IN (1,1,93) do "U:\WORK\NUPEC\TRACEInpProc.exe" -t P7000%%i.inp 

-s Sample.dat -i UncMod.dat -m TRACE_Unc_Models.dat -n %%j 

Step 4: The new generated file P7000%%i_MOD.inp is renamed to P7000%%i_%%j.inp (for i = 

1 and j = 1: P70001_MOD.inp will be renamed to P70001_1.inp) and afterwards executed with 

TRACE. This time the command argument –unc must be added in order to activate the usage 

of the TRACE uncertainty modules and routines (see sub-section 5.2.3.3). 

& REN P7000%%1_MOD.inp P7000%%i_%%j.inp & "U:\WORK\NUPEC\trace.exe" –unc -p 

P7000%%i_%%j

The file Cases.dat is given below. There are three parameters (first number on first line) which 

will be changed according to the 36 different experimental set-ups (second number on the first 

line). These parameters are the pressure (first column) the Inlet temperature (second column) 

and the mass flow rate (third column). 

3 36

0.2000E6 307.55 2.7500 

0.2000E6 311.65 4.0278 

0.2000E6 312.95 5.5278 

0.2000E6 311.55 6.9167 

0.2000E6 309.05 8.2778 

0.2000E6 309.35 9.6667 

0.2000E6 309.35 11.0278

0.2000E6 311.25 12.4444

0.2000E6 312.35 15.1667

0.2000E6 314.55 16.6111

0.2000E6 315.55 17.8333

0.2000E6 317.55 19.2222

1.0000E6 449.65 2.7500 

0.9900E6 449.65 4.1389 

0.9900E6 449.45 5.6389 

0.9800E6 449.35 6.8889 

0.9800E6 449.55 8.3056 

0.9900E6 449.35 9.6389 

0.9900E6 449.15 11.0556

0.9900E6 448.75 12.5833

1.0000E6 449.45 15.2222

0.9800E6 448.45 16.6111

0.9800E6 448.15 18.0000

0.9800E6 448.25 19.3889

7.1700E6 558.75 2.7500 

7.1500E6 558.65 4.2778 

7.1500E6 558.05 5.6389 

7.1600E6 558.25 6.9167 

7.1600E6 558.25 8.2778 

7.1600E6 558.85 9.6389 

7.1600E6 558.75 11.0278

7.1600E6 558.45 12.3889

7.1500E6 557.85 15.2778

7.1500E6 557.95 16.5833

7.1600E6 557.75 18.0000

7.1500E6 557.95 19.4167

Step 3: The inner loop, which handles the generation and execution of the actual uncertainty 

study will be started. The general concept is the same as in step 1. This time 93 files will be 

generated in total for all 36 selected scenarios. 
5-11

File CasesMod.dat starts also with a three as the indicator of the number of parameters which 

will be changed. Since these parameters appear at several positions in the TRACE input file, 

more than thee fields will be manipulated. For instance the pressure appears in the FILL, the 

BREAK and in the CHAN component. Also, the temperature is changed in FILL, BREAK and 

CHAN component. In total, 17 values are changed to generate an input for a new experimental 

scenario. 

3 

S Single Variables

0

T Trip Variables

0

B Block Variables

0

C Components

17

1 fill 100 pin 1 1 0

2 fill 100 tlin 1 5 0

2 fill 100 tvin 1 5 0

3 fill 100 flowin 1 3 0

2 chan 200 toutl 1 5 0

2 chan 200 toutv 1 1 0

2 chan 200 tl 1 2 0

2 chan 200 tv 1 2 0

1 chan 200 p 1 2 0

2 chan 200 tw 1 2 0

2 chan 200 rftn 1 2 0

2 chan 200 rftn 2 2 0

2 chan 200 rftn 3 2 0

2 chan 200 rftn 4 2 0

2 chan 200 matwr 2 2 0

2 break 300 tin 1 4 0

1 break 300 pin 1 5 0

M Model Variables

5.2.3.5 How to extract information out of n TRACE inputs 

The extraction of the relevant information is done with FORTRAN programs but can be also done 

with other programs like PERL or PHYTON. The information has to be stored in a file which can 

be read by SUSA. The formats for scalar and index dependent analysis are given below: 

R11 R12 ... R1m 

R21 R22 ... R2m 

 ⁞ ⁞ ⁞ 

Rn1 Rn2 ... Rnm 

where n is the total number of model runs 

m is the total number of model results per run 

Rij is the value of model result no. j, j = 1... m, in run no. i, i=1... n 
5-12

T11 R11-1 R11-2 ... R11-m 

T12 R12-1 R12-2 ... R12-m 

 ⁞ ⁞ ⁞ ⁞ 

T1L1 R1L1-1 R1L1-2 ... R1L1-m 

L2

T21 R21-1 R21-2 ... R21-m 

T22 R22-1 R22-2 ... R22-m 

 ⁞ ⁞ ⁞ ⁞ 

T2L1 R2L1-1 R2L1-2 ... R2L1-m 

 ⁞ 

Ln

Tn1 Rn1-1 Rn1-2 ... Rn1-m 

Tn2 Rn2-1 Rn2-2 ... Rn2-m 

 ⁞ ⁞ ⁞ ⁞ 

TnL1 RnL1-1 RnL1-2 ... RnL1-m

where Li is the number of time steps in run no. i, i =1 ... n 

n is the total number of model runs 

m is the total number of model results per run 

Tik is the time value of time step no. k, k = 1 ... Li in run no. i, i = 1 ... n 

Rik-j is the value of the model result no. j, j = 1 ... m at time step no. k, k = 1 ... Li 

in run no. i, i = 1 ... n 

For the single-phase pressure drop analysis the scalar format is required since only the 

pressure drop at steady state condition is needed. That means that n is 93 and m is 36. Due to 

that size (36 columns with 93 rows) a presentation is waived. For the void fraction in axial 

direction or the void fraction as a function of time during pump and turbine trip, the index 

dependent format will be used. Since TRACE does not provide the pressure drop as a general 

output variable a control block is defined in the TRACE input. That control block calculates the 

difference between the first (inlet) and last (outlet) cell of the CHAN component and subtracts 

the geodetic term (ρ·g·h). In the TRACE.inp file (Appendix A this control block has the id -300 

(highlighted in yellow) and can be found right above the FILL component. Appendix B shows a 

piece of the corresponding output, TRACE.out. The last line shows a -300, which is the control 

block id to calculate the pressure drop and 1.119079E+03 which is the calculated pressure drop 

in Pa. In order to evaluate the results of all 93 uncertainty cases per each experimental 

scenario this last number will be read out of the TRACE.out file and will be stored in a new file 

according to the specification given above. The FORTRAN code performing the extraction is 

given in Appendix E. 

5.2.4 How to Run SUSA: The Analysis 

That new file, called scalar.lst, must be copied into the corresponding SUSA directory. Based on 

the general SUSA window via the menu Uncertainty+Sensitivity one can chose between scalar 

and index dependent analysis and between uncertainty and sensitivity analysis. In the present 

L1
5-13

case the first option, scalar uncertainty analysis, is chosen. After selecting the results to be 

analyzed (36) and activating different statistical options (comparison with normal or uniform 

distribution, tolerance limits, etc.) a file is generated named EQUUS.prn. That file contains the 

statistical information like the minimum, the maximum, the mean, the standard deviation and the 

quantiles of each selected consequence. Consequence is identical to result which is in fact 

identical to the 36 different pressure drop sets. In addition, several graphs are generated 

showing the normalized distribution of the results together with fitted distribution types (e.g., 

normal, triangular). That procedure finishes the uncertainty analysis. 

The next step is the evaluation of the sensitivities. Therefore, the second option in the 

Uncertainty+Sensitivity menu is selected, scalar sensitivity analysis. Again, the result(s) to be 

analyzed must be selected and the sensitivity measure (Pearson, Spearman, etc.) must be 

chosen. Furthermore, the input parameters can be selected to be displayed. In case more than 

10 parameters are selected, it is recommended not to display of all of them in one graph. The 

new generated file, SAMOS.prn, contains the sensitivity coefficients and the ranking of each 

selected parameter calculated for the ordinary, the partial correlation and the standardized 

regression option of the selected sensitivity measure. The coefficient of determination as a figure 

of merit for the quality of the analysis is given as well. Together with the SAMOS.prn file plots are 

generated showing the sensitivity coefficients in a graphical way. 

5.3 Uncertainty and Sensitivity Study with TRACE-DAKOTA 

In order to perform uncertainty analysis with TRACE code, the ISE laboratories has implemented 

a new tool in the latest SNAP version (V2.0). This tool is based on the use of the uncertainty 

code DAKOTA which is described above. In this section, the main steps the user should follow 

to perform this kind of analysis will be described since a particular SNAP-DAKOTA user guide 

line is presently not available. The general implementation of DAKOTA is given in Figure 33. The 

report compiled by DAKOTA with respect to a single-phase flow pressure drop analysis is given 

in Appendix H 

5.3.1 Assignment of Uncertain Parameters 

Once the TRACE model is created or imported, the reference input will be executed in order to 

obtain the reference case. After the uncertainty analysis is performed, the reference case must 

be located between the minimum and maximum value. After the reference case has been 

obtained, the following steps must be performed. 

Create a new Job Stream and choose Dakota Uncertainty and Single Step TRACE stream

(Figure 34). To avoid confusion, the new created Single_Step_2 should be renamed to 

Uncertainty analysis. 

In order to plot the variable which is going to be analyzed (e.g. peak cladding temperature) the 

step described above would be sufficient. For a complete uncertainty analysis, however, 

additional steps are required, too. 

Click on Stream steps inside of Single_step_2 (or the renamed Uncertainty analysis) and select 

new, then click on Extract Data. Click again in Stream steps and select DAKOTA as new.
5-14

Figure 33 DAKOTA Reference Implementation Process Diagram1

1 Presented during the 2011 TRACE User Workshop. Potomac, Maryland, USA, March 2011.

This step is needed in order to extract data from the output files generated by TRACE and to 

send the information to DAKOTA (it is helpful to rename the tasks timestepsize step and 

step_4 as properly i.e. aptplot, extracdata and Dakota, Figure 36. Later, in the job status 

window it will be easier to distinguish between the different streams and cases, 
5-15

Figure 34 Adding Uncertainty Stream to Existing TRACE Job Stream 

Figure 35 Single Step TRACE Stream 
5-16

Figure 36 Job Stream Window with Added Uncertainty Step 

After the uncertainty stream step is added to the job stream menu the different parameters will be 

assigned. To enter the parameters the Numerics bullet in the SNAP selection window must be 

selected and by a right click on Reals new parameters can be entered. Figure 37 shows two 

parameters under the Reals item, the mass flow rate and the pressure. 

Figure 37 Unfolded Numerics Item in SNAP with Two New Parameters 
5-17

In the first real, mass flow rate, the physical unit will be defined by Available units mass flow

(kg/s) with a value of 2.5. For the second real NO units is selected with a given value of 1.0. 

Now, the real values will be assigned to a component. For the mass flow rate, go to: 

Hydraulic Components  Fills  Initial coolant Mass Flow and select select a shared real

(the two arrows heads pointing in opposite directions). The corresponding value must be selected. 

Figure 38 Fill with Initial Coolant Mass Flow Rate Assigned as an Uncertain Parameter 
5-18

The NO units factor is useful when it is necessary to assign a PDF to a set of values (i.e. pressure 

table of a BREAK component). In this case, the best option is to create a control block in which 

the inlet table will be multiply for a factor. This factor will be the uncertain value of the pressure. 

The mean is equal to 1.0, meaning that during normal operation (uncertainty analysis not used) 

the pressure table will not be changed. A scheme of such a control block is displayed in Figure 

39. 

The Real value (No Units) is assigned to a constant. The multiply control block is the pressure 

table of the BREAK component. This option can be used for different tables in a same component 

(e.g., FILL components general tables for temperature, mass flow). It must be taken into account 

that for a successful uncertainty analysis one value must be created for each variable in order to 

assign a different PDF to each variable. 

5.3.2 PDF and Monte Carlo Sampling 

This sub-section deals with the assignment of the PDF to each variable. By clicking on Job

Streams  Uncertainty  Parametric Properties  Variables  Select new variable 

reference, the window depicted in Figure 40 will open and the two previously defined variables, 

mass flow rate and pressure, should appear. By selecting Mass flow  Next  Scalar and 

Pressure  Next  Factor a distribution will be assigned which needs to be filled with 

information, see Figure 41. Under the Distributions register the distribution type can be chosen 

and known parameters can be entered. The information for mass flow and pressure are given in 

Table 8 and Figure 42. 

Table 8 PDF Characteristics for Mass Flow and Pressure 

Parameter Mass flow Pressure 

Distribution type Normal Normal 

μ (Mean) 2.5 1.0 

σ (STDV = Standard deviation) 0.025 0.01 

Min 2.475 0.99 

Max 2.525 1.01 

Figure 39 Control Block for the System Pressure with Assigned Shared Real (uncertain)

Value 
5-19

Figure 40 New Variable Reference to Assign PDF's 

Figure 41 Assigned Distribution Type for Mass Flow Rate and Pressure 
5-20

Figure 42 Parameters of the PDF's 

In the Report window (Figure 43) all the available options for the report compiled by SNAP after 

the TRACE and DAKOTA calculations, can be selected such as formats, distributions, MC 

samples etc. For the final step the DAKOTA Properties register must be selected. In this window 

the sampling method will be selected. For a complete DAKOTA analysis at least one figure of 

merit must be entered (e.g. PCT or maximum void). In the new ASV1 the lower or/and upper limit 

can be specified. Then, choosing the level of probability and confidence (typically 95/95 for safety 

analysis) the number of samples will be calculated with the formula of Wilk (for 95/95 and order 0 

the result will be 59 samples = 1-sided). The options for the sampling method are Monte Carlo 

and Latin Hypercube. 

5.3.3 Data Extraction 

Once the PDFs are ready, all the applications must be connected as depicted in Figure 44. In 

Extract Data the variable which is going to be analyzed must be entered. Right click on Extract

Data then Properties  AptPlot Script and the desired commandos can be entered into the 

AptPlot script such as shown in Figure 45. This action will extract all the values for all the cases 

from TRACE output files and they will be sent to DAKOTA. A last step for the setup is to click on 

TRACE model and then on Parametric  True. Now the job stream must look like in Figure 46. 

The difference to Figure 44 is that the icon for the TRACE input changed in a way that it is 

indicating several inputs. 
5-21

Figure 43 Definition of the Sampling Method and Size 

Figure 44 Job Stream with DAKOTA Uncertainty and a Single TRACE Input File 
5-22

Figure 45 AptPlot Data Extraction Scripting Window 

Figure 46 Job Stream with Multiple TRACE Input Files 

Before the uncertainty calculation can be started the whole SNAP model should be checked for 

errors and saved. If errors are evident the execution can be launched by either clicking on Tools

 Submit stream to local or by clicking on the Submit button displayed in the job stream 

window. 

The given example is only one of many possibilities of doing uncertainty analysis by means of 

DAKOTA-SNAP. In this example, a transient case was considered and the first 150 seconds were 

pre-transient (steady state conditions). If two different inputs are available, steady state and 
5-23

transient (restart), the model should look like Figure 47. If the uncertainty is considered in both, 

initial conditions and transient conditions, e.g., initial pressure and temperature uncertainty for 

the steady state and mass flow safety injection uncertainty for the transient, the two models 

must be set as parametric. In the AptPlot Step the variables can be chosen in order to show 

the desired variable for all cases (e.g. 93 cases for void fraction at certain axial location), see 

Figure 48. 

Figure 47 Job Stream Window with Steady State and Transient Uncertainty Models 

Figure 48 Example of an Uncertainty Analysis of a Specific Variable 

6-1

6 RESULTS OF THE UNCERTAINTY AND SENSITIVITY ANALYSES 

6.1 Modeling 

Figure 49 shows the TRACE representation of the assembly types 4 and C2A. The axial 

nodalization is shown on the right side. In total, 25 axial levels are modeled using the CHAN 

component (no. 200) whereas each cell has a length of 15.45 cm. The mass flow rate boundary 

conditions are stored in the FILL component, bottom right side (no. 100) while the pressure 

boundary condition is defined in the BREAK component (no. 300). The pins with the different 

power are modeled according to the distribution given in Figure 9 (see sub section 3.2). Five 

different pins are considered. Pins one till four represent the actual fuel pins while rod type five is 

dedicated to the water rod (1 = 1.30, 2 = 1.15; 3 = 0.89; 4 = 0.45 and 5 = water rod). Four water 

rods are present in the model since the real water rod is taking the place of four regular rods. 

Figure 49 TRACE Model of the BFBT Assembly 
6-2

6.2 Uncertain Parameters 

For the present investigations the output parameters of interest are the pressure drop (single and 

two-phase), the void fraction (steady state and transient) and the critical power. Most of the 

uncertain parameters which are selected are identical for all three applications. The selected 

parameters are listed in Table 9 and 

Table 10 for TRACE-SUSA and TRACE-DAKOTA, respectively, along with information about the 

uncertainty range. All uncertainty parameters have in common that the probability density function 

will follow a normal distribution except for the inlet temperature which is flat (uniform). The range 

of the uncertainties is taken from the NUPEC specification [27]. Besides the inlet temperature all 

uncertainty ranges are given as percental variation. For the temperature absolute values are 

reported. The inlet temperature varies by ± 1.5 K meaning that the mean value is 0.0 K. In order 

to include the temperature in the transient analysis with DAKOTA, a multiplication factor was used 

instead. That multiplication factor is 0.997 – 1.003 (meaning that a temperature of 500 K will be 

multiplied with a factor which varies between 0.997 and 1.003) and is almost identical to ± 1.5 K. 

However, the rather small difference will have several consequences in the analysis later on. 

In addition to the reported uncertainties, physical models of the TRACE code are also affected by 

uncertainties. Therefore, the friction factor and the density of the water have been selected. These 

parameters can only be incorporated during the TRACE-SUSA analysis since for the TRACEDAKOTA analysis, SNAP has no access to the source code and therefore only input parameters 

can be included. 

Table 9 Uncertain Parameters, Range and Distribution for TRACE-SUSA 

No. Parameter Range Distribution 

1 Outlet pressure ± 1.0 % Normal 

2 Mass flow rate ± 1.0 % Normal 

3 Inlet temperature ± 1.5 K Uniform 

4 Wall roughness ± 5.0 % Normal 

5 K-spacer ± 5.0 % Normal 

6 Hydraulic diameter ± 1.0 % Normal 

7 Flow area ± 1.0 % Normal 

8 Density ± 1.0 % Normal 

9 Friction Factor ± 5.0 % Normal 

10 Power ± 1.5 % Normal 

Table 10 Uncertain Parameters, Range and Distribution for TRACE-DAKOTA 

No. Parameter Range Distribution 

1 Outlet pressure ± 1.0 % Normal 

2 Mass flow rate ± 1.0 % Normal 

3 Inlet temperature ± 1.5 K (± 0.3 %) Uniform 

4 Wall roughness ± 5.0 % Normal 

5 K-spacer ± 5.0 % Normal 

6 Power ± 1.5 % Normal 
6-3

6.3 Pressure Drop Analyses 

The results presented in this sub section are for the pressure drop across the whole test section 

only. 

6.3.1 Single Phase Flow Pressure Drop 

The pressure drop is calculated between the first and the last cell of the TRACE model based on 

the following correlation. 

∆p = (pinlet − poutlet) − ρoutlet ∙ g ∙ ∆h (60) 

Figure 50 and Table 11 show the input and boundary conditions of each of the 36 experimental 

scenarios. These 36 scenarios can be divided into three groups, low, medium and high 

pressure/inlet temperature. The mass flow rate in each of these groups is linearly increased in 12 

steps. The pressure covers 0.2, 1.0 and 7.2 MPa, the temperature 310, 450 and 560 K while the 

mass flow rate ranges from 10 to 70 t/h. 

Figure 50 Input and Boundary Conditions for the Single-Phase Flow Pressure Drop

Cases 

300

325

350

375

400

425

450

475

500

525

550

575

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

Inlet temperature

Pressure & Mass flow rate

Case (P700xx)

Pressure [bar] Mass flow rate [t/h] Inlet temperature [K]
6-4

Table 11 Input and Boundary Conditions for the Single-Phase Flow Pressure Drop Cases

Case Outlet pressure [bar] Mass flow rate [t/h] Inlet temperature [K]

P70001 2.00 9.90 307.55

P70002 2.00 14.50 311.65

P70003 2.00 19.90 312.95

P70004 2.00 24.90 311.55

P70005 2.00 29.80 309.05

P70006 2.00 34.80 309.35

P70007 2.00 39.70 309.35

P70008 2.00 44.80 311.25

P70009 2.00 54.60 312.35

P70010 2.00 59.80 314.55

P70011 2.00 64.20 315.55

P70012 2.00 69.20 317.55

P70013 10.00 9.90 449.65

P70014 9.90 14.90 449.65

P70015 9.90 20.30 449.45

P70016 9.80 24.80 449.35

P70017 9.80 29.90 449.55

P70018 9.90 34.70 449.35

P70019 9.90 39.80 449.15

P70020 9.90 45.30 448.75

P70021 10.00 54.80 449.45

P70022 9.80 59.80 448.45

P70023 9.80 64.80 448.15

P70024 9.80 69.80 448.25

P70025 71.70 9.90 558.75

P70026 71.50 15.40 558.65

P70027 71.50 20.30 558.05

P70028 71.60 24.90 558.25

P70029 71.60 29.80 558.25

P70030 71.60 34.70 558.85

P70031 71.60 39.70 558.75

P70032 71.60 44.60 558.45

P70033 71.50 55.00 557.85

P70034 71.50 59.70 557.95

P70035 71.60 64.80 557.75

P70036 71.50 69.90 557.95

The single-phase pressure drop measurements at different elevations and the percental deviation 

of the predictions are given in Table 12 and Table 13, respectively. The data are limited to the 

cases P70027 till P70036. 
6-5

Table 12 Local Single-Phase Flow Pressure Drop Measurements 

Case dPT1 dPT2 dPT3 dPT4 dPT5 dPT6 dPT7 dPT8 dPT9

[kPa]

P70027 0.30 0.35 0.39 0.45 0.47 0.46 1.33 0.52 3.12

P70028 0.46 0.51 0.58 0.65 0.64 0.68 1.98 0.75 4.59

P70029 0.64 0.72 0.81 0.91 0.93 0.94 2.79 1.03 6.46

P70030 0.79 0.95 1.05 1.19 1.26 1.25 3.73 1.36 8.57

P70031 1.11 1.25 1.41 1.58 1.60 1.63 4.87 1.77 11.23

P70032 1.37 1.54 1.73 1.93 1.95 1.99 5.96 2.17 13.76

P70033 2.06 2.30 2.55 2.87 2.91 2.96 8.85 3.22 20.43

P70034 2.41 2.69 2.99 3.35 3.39 3.46 10.36 3.76 23.87

P70035 2.81 3.14 3.46 3.90 3.95 4.03 12.05 4.37 27.77

P70036 3.25 3.63 3.99 4.50 4.55 4.65 13.89 5.04 32.03

Table 13 Percental Error of the Predicted Local Single-Phase Flow Compared to

 the Measurements 

Case dPT1 dPT2 dPT3 dPT4 dPT5 dPT6 dPT7 dPT8 dPT9

[kPa]

P70027 -19.99 0.67 -15.15 -2.06 -6.23 -4.19 -0.34 -3.04 7.35

P70028 -21.46 2.59 -14.78 0.89 2.53 -3.51 -0.62 -0.24 5.45

P70029 -19.56 5.49 -15.54 2.79 0.19 -1.20 -0.16 2.38 4.34

P70030 -12.42 7.25 -11.48 4.80 -0.73 0.20 0.60 3.04 4.73

P70031 -18.77 6.00 -14.88 2.92 1.39 -0.06 0.28 2.71 3.08

P70032 -17.58 8.39 -13.43 5.58 4.71 2.27 2.50 5.34 4.93

P70033 -17.48 9.46 -11.95 6.85 5.23 3.43 3.84 6.45 5.52

P70034 -17.25 9.73 -11.89 7.27 5.95 3.83 4.03 6.78 5.83

P70035 -16.46 10.63 -10.56 8.12 6.84 4.77 5.07 7.76 6.55

P70036 -16.08 11.29 -10.09 8.74 7.62 5.37 5.76 8.62 7.06

These percental deviations are plotted in Figure 51 and one can see that the largest differences 

appear at the top positions. The comparison of the calculated and measured total single-phase 

pressure drop is given in Figure 52 for all 36 reference cases. The additional lines to indicate 

the ± 10 % bands show that the predictions are in good agreement with the experiment. In order 

to see the deviation of each run, Figure 53 is given. The relative error with respect to the 

experiment ranges from 2 to 36 %. Three sections are visible corresponding to the three 

different input and boundary condition sets.
6-6

Figure 51 Relative Error of the Local Single-Phase Flow Pressure Drop for Selected

Cases
6-7

Figure 52 Calculated versus Measured Pressure Drop for the Single-Phase Flow

Reference Cases 

Figure 53 Percental Error of the Reference Values Compared to the Experimental Data

for Single-Phase Flow Cases 
6-8

In that figure, it is visible that TRACE tends to over predict the single-phase pressure drop no 

matter the pressure drop is high or low, especially at medium and higher pressures and inlet 

temperatures. That figure also reveals that some of the predictions are far off the measured 

values. Case 13 (35.7 %) and case 25 (24.6 %) show a big deviation. Investigating Figure 55 

and Table 14 shows that the pressure drop is really small. The experimental value for case 13 is 

740 Pa while the calculated one is 1000 Pa which means that the deviation is only 260 Pa. Due 

to the low pressure drop an absolute deviation of only 260 Pa results is a relative large error. In 

addition, the lower the pressure drop the more difficult it gets to measure it. The average error 

over all 36 cases is 6.83 %. If the cases with an experimental pressure drop of less than 1000 

Pa are excluded, the average error is reduced to 5.46 %. The error as a function of pressure 

drop is given in Figure 54. 

Figure 55 shows the absolute pressure drop for each case together with the minimum and 

maximum value of the uncertainty analysis compared to the experimental value. Due to the 

mentioned handling inconveniences only six out of 36 cases are calculated with TRACEDAKOTA In general, the three sections characterized by the input and boundary conditions are 

also visible here. A clear parabolic trend is visible due to the quadratic influence of the mass flow 

rate (more precisely the velocity) on the pressure drop. The uncertainty band based on TRACEDAKOTA is narrower than the one of TRACE-SUSA since less parameter is involved. The mean 

values, however, are almost identical. In Figure 56, the relative pressure drop is given in order to 

highlight the deviations of the mean values and the uncertainty band from the experimental data. 

Figure 54 Error as Function of the Single-Phase Flow Pressure Drop 

0

5

10

15

20

25

30

35

40

0 5000 10000 15000 20000 25000 30000 35000

Erro [%]

Pressure drop [Pa]
6-9

Figure 55 Comparison of the Experimental and Predicted Pressure Drops for the

Single-Phase Flow Cases in Absolute Values 

Figure 56 Comparison of the Experimental and Predicted Pressure Drops for the

Single-Phase Flow Cases in Relative Values 

0

5000

10000

15000

20000

25000

30000

35000

40000

00 02 04 06 08 10 12 14 16 18 20 22 24 26 28 30 32 34 36

Pressure drop [Pa]

Case (P700xx)

Experiment Mean (SUSA)

Maximum (SUSA) Minimum (SUSA)

Mean (DAKOTA) Maximum (DAKOTA)

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

00 02 04 06 08 10 12 14 16 18 20 22 24 26 28 30 32 34 36

Relative pressure drop [-]

Case (P700xx)

Mean (SUSA)

Maximum (SUSA)

Minimum (SUSA)

Mean (DAKOTA)

Maximum (DAKOTA)

Minimum (DAKOTA)
6-10

Only in 6 out of 36 cases the maximum and minimum does not envelop the experimental data. 

These cases are: Case 13; 14; 15; 25; 26 and 27. The characteristic of these cases are the low 

pressure drop, the low mass flow rate and medium/high system pressure and inlet temperatures. 

The results for the: mean, minimum, maximum, standard deviation and error, for each scenario, 

are summarized in Table 14 and Table 15 for the TRACE-SUSA calculations and the TRACEDAKOTA predictions, respectively. The almost perfect agreement for the mean values and the 

smaller uncertainty band, best seen by the standard deviation, is verifiable. 

Table 14 Results of the Uncertainty Analysis for the Single-Phase Flow Pressure Drops

with TRACE-SUSA 

Case Ex [Pa] Mean [Pa] Max [Pa] Min [Pa] SD [Pa] Error [%] 

P70001 1090 1118 1187 1062 29 2.53 

P70002 1920 1872 2010 1762 57 -2.49 

P70003 3270 3075 3323 2879 101 -5.95 

P70004 4800 4501 4878 4203 155 -6.23 

P70005 6650 6190 6720 5772 218 -6.92 

P70006 8740 8158 8868 7602 291 -6.65 

P70007 10990 10356 11266 9647 372 -5.77 

P70008 13580 12877 14017 11994 466 -5.18 

P70009 19440 18539 20196 17267 675 -4.63 

P70010 22630 21901 23866 20402 799 -3.22 

P70011 25680 24985 27233 23277 914 -2.71 

P70012 29290 28700 31289 26743 1051 -2.01 

P70013 740 1004 1068 958 25 35.70 

P70014 1620 1806 1944 1705 54 11.46 

P70015 2790 3000 3250 2819 98 7.52 

P70016 4060 4252 4618 3988 144 4.73 

P70017 5710 5953 6476 5575 206 4.25 

P70018 7590 7821 8518 7321 275 3.05 

P70019 9810 10092 10999 9442 358 2.87 

P70020 12470 12865 14030 12033 460 3.17 

P70021 17490 18469 20154 17271 666 5.60 

P70022 20600 21803 23797 20387 789 5.84 

P70023 23900 25423 27752 23771 922 6.37 

P70024 27450 29328 32019 27422 1066 6.84 

P70025 840 1046 1120 994 28 24.57 

P70026 1810 2081 2252 1959 66 14.98 

P70027 3120 3349 3639 3140 112 7.35 

P70028 4590 4840 5269 4530 167 5.45 

P70029 6460 6740 7348 6301 236 4.34 

P70030 8570 8975 9793 8385 318 4.73 

P70031 11230 11576 12637 10809 413 3.08 
6-11

Case Ex [Pa] Mean [Pa] Max [Pa] Min [Pa] SD [Pa] Error [%]

P70032 13760 14438 15768 13478 518 4.93

P70033 20430 21557 23554 20116 778 5.52

P70034 23870 25261 27605 23569 914 5.83

P70035 27770 29588 32337 27604 1072 6.55

P70036 32030 34291 37481 31989 1245 7.06

Table 15 Results of the Uncertainty Analysis for the Single-Phase Flow Pressure Drops

with TRACE-DAKOTA 

Case Ex [Pa] Mean [Pa] Max [Pa] Min [Pa] SD [Pa] Error [%]

P70002 1920 1881 1928 1831 24 -2.05

P70007 10990 10371 10732 10009 181 -5.63

P70013 740 1010 1053 961 22 36.43

P70016 4060 4293 4427 4079 97 5.74

P70030 8570 9011 9366 8625 159 5.15

P70035 27770 29657 30887 28221 605 6.80

After showing the impact of the input parameters in the previous graphs, the corresponding 

sensitivity coefficients are plotted in Figure 57 (TRACE-SUSA) and Figure 58 (TRACEDAKOTA). It is clearly visible that parameters like the hydraulic diameter, the spacer form loss 

coefficient and the friction factor are the most influential parameters. The hydraulic diameter, as 

the dominating one has negative values for the sensitivity coefficient which indicates that an 

increase of the hydraulic diameter would provoke a reduction of the pressure drop and vice 

versa. The K factor for the spacer grid and the friction factor have positive values indicating a 

direct proportional relationship. As expected, the outlet pressure and the inlet temperature 

variations have no influence on the result since the pressure drop has only a weak dependence 

on them due to the pressure and temperature dependent properties. But also parameters like 

the density and the mass flow rate show a negligible impact even though the pressure drop is 

directly dependent on them. That can be explained with the presence of the other parameters 

where their variations have bigger influence. 

Regarding the TRACE-DAKOTA investigation, the most important parameter is the form loss 

coefficient of the spacer grid and the mass flow rate. The values for them are higher than they are 

for the TRACE-SUSA analysis. That is due to the presence of the hydraulic diameter and the 

friction factor in the TRACE-SUSA analysis which lowers the values of K-spacer and mass flow 

rate compared to them during TRACE-DAKOTA investigation. Outlet pressure, wall roughness 

and inlet temperature show a similar behavior indicating that their variation will have no or only 

little effect on the pressure drop. 

The ranking of the uncertain parameters with respect to their significance on the pressure drop 

is given in Figure 59 and Figure 60 for TRACE-SUSA and TRACE-DAKOTA, respectively. As 

indicated by the sensitivity coefficients, hydraulic diameter is ranked 1st, and friction factor and 

K factor for the spacer are ranked 2nd and 3rd (with changing positions after case 7). 
6-12

Figure 57 Sensitivity Coefficients for the Single-Phase Flow Pressure Drop Analysis

with TRACE-SUSA 

Figure 58 Sensitivity Coefficients for the Single-Phase Flow Pressure Drop Analysis

with TRACE-DAKOTA

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

00 02 04 06 08 10 12 14 16 18 20 22 24 26 28 30 32 34 36

Sensitivity coefficient

Case (P700xx)

Outlet pressure Mass flow rate Inlet temperature

Wall roughness K-spacer Hydraulic diameter

Density Friction factor

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

00 02 04 06 08 10 12 14 16 18 20 22 24 26 28 30 32 34 36

Sensitivity coefficient

Case (P700xx)

Outlet pressure Mass flow rate Inlet temperature

K-spacer Wall roughness
6-13

Figure 59 Ranking of the Uncertain Parameters for the Single-Phase Flow Pressure

Drop Analysis with TRACE-SUSA 

Figure 60 Ranking of the Uncertain Parameters for the Single-Phase Flow Pressure

Drop Analysis with TRACE-DAKOTA

0

1

2

3

4

5

6

7

8

9

00 02 04 06 08 10 12 14 16 18 20 22 24 26 28 30 32 34 36

Rank

Case (P700xx)

Outlet pressure Mass flow rate Inlet temperature

Wall roughness K-spacer Hydraulic diameter

Density Friction factor

0

1

2

3

4

5

6

00 02 04 06 08 10 12 14 16 18 20 22 24 26 28 30 32 34 36

Rank

Case (P700xx)

Outlet pressure Mass flow rate Inlet temperature

K-spacer Wall roughness
6-14

With TRACE and DAKOTA the parameter ranked no. one is the form loss coefficient for the 

spacer. The second rank is, during the most cases, the mass flow rate. In case 13 the spacer 

form loss coefficient and the mass flow rate change positions. In case 16 the outlet pressure 

gained importance and is positioned between form factor and mass flow rate. 

The sensitivity coefficients based on Pearson’s momentum correlation coefficient are listed in 

Table 16 and Table 17 for TRACE-SUSA and TRACE-DAKOTA, respectively. 

Table 16 Pearson's Momentum Correlation Coefficients for the Single-Phase Flow

Pressure Drop Cases with TRACE-SUSA Outlet pressure Mass flow rate Inlet temperature Wall roughness

K-spacer

Hydraulic 

diameter

Density

Friction 

factor

P70001 0.1370 0.2810 -0.2517 -0.0839 0.5233 -0.7488 -0.0800 0.6207

P70002 0.1431 0.2812 -0.2396 -0.1055 0.5388 -0.7492 -0.0815 0.6041

P70003 0.1464 0.2818 -0.2337 -0.1175 0.5501 -0.7489 -0.0801 0.5916

P70004 0.1484 0.2819 -0.2323 -0.1243 0.5564 -0.7483 -0.0796 0.5845

P70005 0.1498 0.2821 -0.2327 -0.1295 0.5603 -0.7476 -0.0793 0.5798

P70006 0.1508 0.2825 -0.2305 -0.1306 0.5656 -0.7473 -0.0789 0.5744

P70007 0.1516 0.2828 -0.2289 -0.1313 0.5699 -0.7471 -0.0786 0.5700

P70008 0.1522 0.2833 -0.2255 -0.1299 0.5750 -0.7471 -0.0782 0.5648

P70009 0.1531 0.2838 -0.2223 -0.1294 0.5817 -0.7468 -0.0775 0.5578

P70010 0.1535 0.2841 -0.2193 -0.1277 0.5857 -0.7468 -0.0770 0.5537

P70011 0.1538 0.2843 -0.2178 -0.1270 0.5883 -0.7467 -0.0767 0.5510

P70012 0.1541 0.2846 -0.2154 -0.1257 0.5915 -0.7466 -0.0762 0.5477

P70013 0.1376 0.2867 -0.1837 -0.0805 0.5845 -0.7542 -0.0318 0.5661

P70014 0.1449 0.2852 -0.1770 -0.0760 0.5921 -0.7533 -0.0707 0.5530

P70015 0.1480 0.2850 -0.1752 -0.0863 0.5987 -0.7515 -0.0738 0.5437

P70016 0.1495 0.2849 -0.1741 -0.0928 0.6028 -0.7507 -0.0724 0.5378

P70017 0.1508 0.2849 -0.1730 -0.0973 0.6066 -0.7498 -0.0712 0.5326

P70018 0.1517 0.2850 -0.1726 -0.0999 0.6096 -0.7491 -0.0702 0.5286

P70019 0.1524 0.2851 -0.1720 -0.1019 0.6122 -0.7485 -0.0693 0.5250

P70020 0.1531 0.2852 -0.1715 -0.1036 0.6145 -0.7480 -0.0684 0.5218

P70021 0.1539 0.2854 -0.1706 -0.1056 0.6178 -0.7473 -0.0669 0.5172

P70022 0.1543 0.2854 -0.1706 -0.1063 0.6192 -0.7470 -0.0663 0.5153

P70023 0.1546 0.2855 -0.1704 -0.1070 0.6204 -0.7467 -0.0657 0.5135

P70024 0.1548 0.2856 -0.1701 -0.1076 0.6215 -0.7464 -0.0651 0.5119

P70025 0.1463 0.2853 -0.1588 -0.0743 0.5945 -0.7547 -0.0609 0.5484

P70026 0.1525 0.2849 -0.1464 -0.0907 0.5989 -0.7530 -0.0636 0.5356

P70027 0.1477 0.2821 -0.1368 -0.0980 0.6066 -0.7512 -0.0660 0.5281

P70028 0.1489 0.2819 -0.1348 -0.1027 0.6100 -0.7503 -0.0642 0.5228

P70029 0.1497 0.2818 -0.1332 -0.1055 0.6130 -0.7495 -0.0627 0.5183

P70030 0.1536 0.2838 -0.1348 -0.1084 0.6138 -0.7492 -0.0597 0.5145

P70031 0.1510 0.2821 -0.1312 -0.1088 0.6173 -0.7485 -0.0599 0.5115

P70032 0.1509 0.2820 -0.1304 -0.1096 0.6192 -0.7481 -0.0592 0.5090

P70033 0.1516 0.2822 -0.1298 -0.1110 0.6220 -0.7473 -0.0575 0.5048
6-15

Outlet 

pressure

Mass 

flow rate

Inlet 

temperature

Wall 

roughness

K-spacer

Hydraulic 

diameter

Density

Friction 

factor

P70034 0.1518 0.2823 -0.1294 -0.1115 0.6230 -0.7471 -0.0568 0.5032

P70035 0.1520 0.2824 -0.1292 -0.1119 0.6240 -0.7468 -0.0561 0.5017

P70036 0.1522 0.2824 -0.1288 -0.1123 0.6249 -0.7466 -0.0554 0.5003

Table 17 Pearson's Momentum Correlation Coefficients for the Single-Phase Flow 

Pressure Drop Cases with TRACE-DAKOTA Outlet pressure Mass flow rate Inlet temperature Wall roughness

K-spacer

Hydraulic 

diameter

Density

Friction factor

P70002 0.0297 0.5496 0.0449 0.0758 0.8363

not included

P70007 0.0072 0.5064 0.0028 -0.0075 0.8587

P70013 0.0451 0.6360 -0.1133 -0.0294 0.7640

P70016 0.0438 0.8513 -0.2003 -0.0215 0.4764

P70030 -0.0215 0.5095 -0.0621 0.0238 0.8485

P70035 0.4335 0.3926 -0.2404 -0.0007 0.6451

6.3.2 Two-Phase Flow Pressure Difference 

For the two phase flow the pressure drop is rather a pressure difference since only the difference 

of the absolute pressures between inlet and outlet is considered, according to 

∆p = pinlet − poutlet (61)

The boundary and input conditions for the two-phase flow analysis of the pressure drop is shown 

in Figure 61 and Table 18 for the 33 cases. Besides pressure and mass flow rate, the inlet subcooling and the power are subject of variations throughout the experimental scenarios. It can be 

seen that the pressure is now in typical BWR regions, varying between 72 and 86 bar. The inlet 

sub-cooling is always around 50 kJ/kg. The power and the mass flow rate show several levels of 

variation making the overall distribution of the input and boundary conditions more diverse than 

for the single-phase flow cases. 
6-16

Figure 61 Input and Boundary for the Two-Phase Flow Pressure Drop Cases

Table 18 Input and Boundary Conditions for the Two-Phase Flow Pressure Drop Cases

Case Outlet pressure 

[bar]

Mass flow rate 

[t/h]

Inlet sub-cooling 

[kJ/kg]

Power

[MW]

P60001 71.6 20.2 53.3 0.863

P60002 71.6 20.1 51.8 1.117

P60003 71.6 20.1 50.8 1.521

P60004 71.6 20.2 51.3 1.951

P60005 71.6 20.0 51.1 2.357

P60006 71.6 20.1 50.8 2.366

P60007 71.7 55.0 51.1 2.375

P60008 71.7 55.0 49.0 3.057

P60009 71.7 55.0 51.1 4.197

P60010 71.7 54.9 47.3 5.311

P60011 71.7 54.9 50.6 6.478

P60012 71.7 55.0 49.7 6.483

P60013 71.6 69.9 47.2 3.022

P60014 71.6 70.1 50.6 3.884

P60015 71.7 70.0 49.5 5.340

P60016 71.8 70.1 50.3 6.795

P60017 71.6 45.1 51.0 1.919

P60018 71.7 44.9 50.8 2.495

P60019 71.7 45.0 49.4 3.437

P60020 71.6 45.1 51.8 4.363

P60021 71.6 45.1 50.8 5.312

0

1

2

3

4

5

6

7

8

10

20

30

40

50

60

70

80

90

01 03 05 07 09 11 13 15 17 19 21 23 25 27 29 31 33

Power

Pressure, Sub-cooling & Mass flow rate

Case (600xx)

Pressure [bar] Inlet sub-cooling [kJ/kg] Mass flow rate [t/h] Power [MW]
6-17

Case Outlet pressure 

[bar]

Mass flow rate 

[t/h]

Inlet sub-cooling 

[kJ/kg]

Power

[MW]

P60022 86.4 20.2 50.7 0.837

P60023 86.3 20.2 52.3 1.464

P60024 86.3 20.2 52.9 2.252

P60025 86.4 55.0 51.3 2.271

P60026 86.4 55.1 53.0 3.975

P60027 86.4 55.1 51.5 6.137

P60028 86.3 55.1 51.3 6.132

P60029 86.4 70.1 51.5 2.888

P60030 86.4 70.2 51.4 5.076

P60031 86.4 45.1 53.0 1.869

P60032 86.3 45.2 51.3 3.262

P60033 86.3 45.1 51.6 5.021

The local two-phase flow pressure drop measurements according to the locations of Figure 12

are summarized in Table 19. The percental deviations of the predictions are given in Table 20. 

Table 19 Local Two-Phase Flow Pressure Drop Measurements 

Case dPT1 dPT2 dPT3 dPT4 dPT5 dPT6 dPT7 dPT8 dPT9

[kPa]

P60001 1.15 1.96 2.53 3.48 3.66 3.93 12.27 5.50 27.40

P60003 1.54 2.22 2.81 3.61 3.63 3.69 11.72 5.50 27.22

P60005 2.10 2.81 3.43 4.26 4.11 3.97 11.84 5.47 29.16

P60007 5.59 6.70 8.11 9.55 9.06 8.40 22.84 8.25 57.89

P60009 9.24 10.91 12.39 14.26 13.54 11.83 29.30 8.48 78.59

P60011 13.56 16.05 17.81 20.04 19.39 16.73 39.14 8.93 106.72

P60013 8.92 10.24 12.15 13.58 12.98 11.65 30.31 10.07 79.71

P60015 14.93 17.00 19.33 20.96 20.33 17.40 41.22 10.48 113.97

P60017 3.93 4.91 6.08 7.23 7.03 6.73 18.92 7.24 46.54

P60019 6.43 7.73 8.94 10.54 9.98 8.90 22.97 7.44 60.11

P60021 9.30 11.24 12.51 14.42 13.98 12.17 29.32 7.72 78.76

P60022 1.11 1.94 2.49 3.44 3.48 3.88 11.99 5.36 26.83

P60023 1.39 2.08 2.62 3.44 3.49 3.63 11.54 5.36 26.38

P60024 1.82 2.49 3.03 3.88 3.55 3.75 11.47 5.33 27.55

P60025 4.96 6.08 7.29 8.74 8.15 7.96 22.05 8.17 54.66

P60026 7.75 9.23 10.47 12.61 11.43 10.50 26.89 8.36 70.06

P60027 11.18 13.30 14.69 17.40 16.10 14.40 34.79 8.79 92.41

P60029 7.60 8.96 10.54 12.32 11.43 10.70 28.79 10.08 73.55

P60030 12.39 14.28 16.19 18.14 17.16 15.33 37.62 10.40 100.77

P60031 3.49 4.50 5.50 6.78 6.36 6.42 18.29 7.09 44.32

P60032 5.42 6.62 7.63 9.34 8.47 8.02 21.35 7.28 54.32

P60033 7.61 9.31 10.28 12.62 11.50 10.49 26.21 7.54 68.44
6-18

Table 20 Percental Error of the Predicted Local Two-Phase Flow Compared to the

Measurements 

Case dPT1 dPT2 dPT3 dPT4 dPT5 dPT6 dPT7 dPT8 dPT9 

[%] 

P60001 9.41 -10.24 4.07 -10.17 -10.19 -8.78 -4.75 -10.06 -3.74 

P60003 -13.15 -16.55 -5.07 -14.26 -15.36 -14.67 -10.97 -11.09 -8.77 

P60005 -23.19 -21.42 -8.49 -16.47 -17.89 -19.15 -16.25 -13.05 -12.49 

P60007 -21.25 -7.11 -0.57 -3.42 -4.33 -6.07 -3.97 -6.50 -0.68 

P60009 -28.04 -16.32 -0.75 -4.31 -9.06 -10.91 -9.89 -8.93 -4.35 

P60011 -29.24 -18.46 -0.26 -1.63 -10.13 -14.11 -14.25 -11.72 -5.86 

P60013 -24.26 -7.00 -0.05 1.37 -2.19 -4.15 -2.61 -4.20 1.07 

P60015 -29.74 -15.44 -0.41 1.27 -6.88 -9.00 -8.20 -7.14 -2.33 

P60017 -18.77 -8.16 -1.89 -4.97 -6.18 -7.26 -4.75 -7.84 -2.10 

P60019 -27.59 -17.05 -2.77 -7.97 -11.06 -12.55 -11.00 -10.60 -6.24 

P60021 -28.82 -19.77 -1.42 -5.12 -12.87 -16.11 -15.58 -12.96 -7.86 

P60022 13.84 -9.08 6.15 -8.74 -5.56 -8.55 -4.55 -10.61 -3.06 

P60023 -7.20 -13.81 -1.06 -12.00 -12.87 -12.73 -9.52 -11.13 -7.04 

P60024 -17.77 -17.26 -3.53 -14.01 -9.21 -16.28 -13.77 -12.44 -10.16 

P60025 -16.55 -2.92 2.95 -0.62 1.25 -4.11 -2.19 -6.17 1.40 

P60026 -23.58 -10.69 3.29 -3.62 -2.96 -7.60 -6.91 -7.97 -1.23 

P60027 -24.74 -13.16 4.99 -1.15 -4.81 -10.74 -11.22 -10.95 -2.40 

P60029 -18.29 -1.31 4.30 2.57 3.21 -1.83 -0.28 -3.78 3.79 

P60030 -24.87 -9.73 3.88 3.35 -1.62 -6.05 -5.68 -6.10 0.62 

P60031 -13.13 -4.06 2.43 -3.21 -0.19 -5.37 -3.09 -6.97 -0.24 

P60032 -22.55 -11.71 1.67 -6.29 -4.29 -9.27 -8.13 -9.41 -3.19 

P60033 -23.77 -14.52 4.18 -5.23 -6.53 -12.34 -12.35 -12.03 -4.28 

Apparently, not for all 33 cases values have been reported. A graphical interpretation of the 

percental deviation of the predictions is given in the following figures. It is visible that the error is 

large for dPT1 and dPT2 which measured the pressure drop over the two highest spacers. These 

are the positions with the highest void fractions and even small variations of it will result in rather 

large differences of the pressure drop. Further down the bundle the error is relatively small. 
6-19

dPT1 dPT2 dPT3 dPT4 dPT5 dPT6 dPT7 dPT8 dPT9

Figure 62 Relative Error of the Local Two-Phase Flow Pressure Drop for Selected

Cases (1)

-25

-20

-15

-10

-5

0

5

10

dPT1 dPT2 dPT3 dPT4 dPT5 dPT6 dPT7 dPT8 dPT9

Relative error [%]

P60001 P60003 P60005 P60007

-30

-25

-20

-15

-10

-5

0

5

dPT1 dPT2 dPT3 dPT4 dPT5 dPT6 dPT7 dPT8 dPT9

Relative error [%]

P60009 P60011 P60013 P60015

-30

-25

-20

-15

-10

-5

0

5

10

15

Relative error [%]

P60017 P60019 P60021 P60022
6-20

dPT1 dPT2 dPT3 dPT4 dPT5 dPT6 dPT7 dPT8 dPT9

Figure 63 Relative Error of the Local Two-Phase Flow Pressure Drop for Selected 

Cases (2)

-25

-20

-15

-10

-5

0

5

dPT1 dPT2 dPT3 dPT4 dPT5 dPT6 dPT7 dPT8 dPT9

Relative error [%]

P60023 P60024 P60025 P60026

-25

-20

-15

-10

-5

0

5

dPT1 dPT2 dPT3 dPT4 dPT5 dPT6 dPT7 dPT8 dPT9

Relative error [%]

P60027 P60029 P60030 P60031

-25

-20

-15

-10

-5

0

5

Relative error [%]

P60032 P60033
6-21

The calculated total reference pressure difference (dPT9) compared to the measured ones for 

the 33 cases is depicted in Figure 64. That graph shows on the one side a good agreement 

between the calculated and the measured data and on the other side that the predictions are 

mostly underestimating the experiment. This can be even better seen in Figure 65 where the 

percental error of the calculations based on the experimental is shown. In fact, only for four 

cases the prediction gives higher values than the experiment. The error as a function of the 

pressure difference is shown in Figure 66. As for the single-phase flow cases, the error is higher 

at lower pressure differences. But in the two-phase flow cases that difference is not that 

pronounced. 

Figure 67 shows the results of the uncertainty study. The average error is 4.66 %.The mean 

values of TRACE-SUSA and TRACE-DAKOTA are depicted as squares with minimal and 

maximal values indicated by horizontal lines. The experimental values are shown as circles. Due 

to the wide pressure drop range of the experimental cases, a graph with relative pressure drops 

helps for the understanding. 

Figure 64 Calculated versus Measured Pressure Drop for the Two-Phase Flow

Reference Cases 

20000

40000

60000

80000

100000

120000

140000

20000 40000 60000 80000 100000 120000 140000

Pressure drop - calculated [Pa]

Pressure drop - measured [Pa]

+ 10 %

- 10 %
6-22

Figure 65 Percental Error of the Reference Values Compared to the Experimental Data

for the Two-Phase Flow Cases 

Figure 66 Error as Function of the Two-Phase Flow Pressure Difference 

-14

-12

-10

-8

-6

-4

-2

0

2

4

01 03 05 07 09 11 13 15 17 19 21 23 25 27 29 31 33

Error [%]

Case (600xx)

0

2

4

6

8

10

12

14

20000 40000 60000 80000 100000 120000 140000

Error [%]

Pressure difference [Pa]
6-23

Figure 67 Comparison of the Experimental and Predicted Pressure Drops for the

Two-Phase Flow Cases in Absolute Values 

Figure 68 shows again that most of the predicted values are below the experimental values 

(indicated by the vertical line intersecting with y = 1.0). Furthermore, it is visible that the 

uncertainty band of the TRACE-DAKOTA analysis is narrower than for the TRACE-SUSA 

calculations as expected since less uncertainty parameters are taken into account in the first case. 

In addition, the lower band/value being almost similar, the upper values show larger differences 

between TRACE-SUSA and TRACE-DAKOTA. The results for the two phase flow pressure drop 

cases are summarized in Table 21 and Table 22 for TRACE-SUSA and TRACE-DAKOTA, 

respectively. 

As mentioned above the average error is 4.66 % which is lower than for the single-phase case. 

Considering the complexity of two phase flow and the connected challenge in measuring 

pressures, the opposite would be expected. A reason for the lower average error in two phase 

flow can be the definition of the pressure drop. In single-phase flow the pressure drop is defined 

as the difference of the absolute pressures minus the difference of the geodetic pressure term, 

which involves the density. Therefore, considering the pure formalism and definition of the 

pressure drop it is more complex in single-phase flow than in two phase flow where only the 

difference of the absolute pressures is considered. In addition, the single-phase pressure drop is 

between 1000 and 30000 Pa. Especially at low pressure drop values the error is large which is 

connected to, on the one hand, the insensitivity of measurement devises at very low quantities 

and on the other hand the pronounced impact of a mismatch between measurement position and 

position of calculation. Due to the rather coarse nodalization in TRACE the pressure drop can 

only be calculated in approx. 15 cm increments. 

20000

40000

60000

80000

100000

120000

140000

160000

01 03 05 07 09 11 13 15 17 19 21 23 25 27 29 31 33

Pressure drop [Pa]

Case (P600xx)

Experiment

Mean (SUSA)

Maximum (SUSA)

Minimum (SUSA)

Mean (DAKOTA)

Maximum (DAKOTA)

Minimum (DAKOTA)
6-24

Figure 68 Comparison of the Experimental and Predicted Pressure Drops for the

Two-Phase Flow Cases in Relative Values 

Table 21 Results of the Uncertainty Analysis for the Two-Phase flow Pressure Drops with

TRACE-SUSA 

Case Ex [Pa] Mean [Pa] Max [Pa] Min [Pa] SD [Pa] Error [%]

P60001 27400 26376 26955 25788 264 -3.74

P60002 27020 25368 25892 24741 254 -6.12

P60003 27220 24833 25385 24122 283 -8.77

P60004 28100 25104 25852 24293 340 -10.66

P60005 29160 25518 26419 24551 398 -12.49

P60006 29260 25626 26538 24648 402 -12.42

P60007 57890 57494 61313 54877 1413 -0.68

P60008 65720 64000 68566 60755 1732 -2.62

P60009 78590 75174 80735 70791 2195 -4.35

P60010 93230 88199 94808 82549 2680 -5.40

P60011 106720 100465 107939 93651 3084 -5.86

P60012 107560 100824 108334 93981 3097 -6.26

P60013 79710 80561 87004 76017 2404 1.07

P60014 91270 90818 98174 85491 2817 -0.50

P60015 113970 111316 120364 104329 3596 -2.33

P60016 136510 131850 142309 122993 4271 -3.41

P60017 46540 45562 48022 43815 908 -2.10

P60018 51050 48982 51934 46781 1116 -4.05

P60019 60110 56361 60109 53328 1471 -6.24

P60020 68830 64003 68386 60185 1777 -7.01

0.8

0.9

1.0

1.1

1.2

01 03 05 07 09 11 13 15 17 19 21 23 25 27 29 31 33

Relative pressure drop [-]

Case (P700xx)

Mean (SUSA) Maximum (SUSA)

Minimum (SUSA) Mean (DAKOTA)

Maximum (DAKOTA) Minimum (DAKOTA)
6-25

Case Ex [Pa] Mean [Pa] Max [Pa] Min [Pa] SD [Pa] Error [%]

P60021 78760 72566 77622 67899 2092 -7.86

P60022 26830 26008 26587 25435 262 -3.06

P60023 26380 24523 25037 23853 265 -7.04

P60024 27550 24751 25548 23905 354 -10.16

P60025 54660 55427 59016 52968 1311 1.40

P60026 70060 69198 74237 65362 1952 -1.23

P60027 92410 90190 96885 84328 2734 -2.40

P60028 92460 90276 96984 84407 2738 -2.36

P60029 73550 76341 82295 72269 2187 3.79

P60030 100770 101399 109640 95273 3216 0.62

P60031 44320 44214 46496 42579 840 -0.24

P60032 54320 52585 55971 49930 1306 -3.19

P60033 68440 65509 70025 61503 1838 -4.28

Table 22 Results of the Uncertainty Analysis for the Two-Phase Flow Pressure Drops

 with TRACE-DAKOTA 

Case Ex [Pa] Mean [Pa] Max [Pa] Min [Pa] SD [Pa] Error [%]

P60001 27400 26369 26840 25915 196 -3.76

P60008 65720 63774 66553 61297 1098 -2.96

P60014 91270 90257 93822 86191 1835 -1.11

P60020 68830 63712 65725 61955 960 -7.44

P60022 26830 25934 26492 25377 236 -3.34

P60030 100770 100810 105480 95578 2086 0.04

The sensitivity coefficients are plotted in Figure 69 (TRACE-SUSA) and Figure 70 (TRACEDAKOTA). In general, for the SUSA cases, the sensitivity coefficients for the different parameters 

are almost at similar values for all 33 cases. The fluctuations between the cases are related to 

the varying input and boundary conditions. The only exception is the inlet temperature which has 

(relative high) negative values for cases 1 - 6 and 22 - 24 but for the rest of the cases positive 

values of approximately 0.3 - 0.4. For the named cases, the plot of the boundary conditions shows 

that they are characterized by a low mass flow rate and low power. Therefore, the impact of their 

variation is losing against the impact of the inlet sub cooling (inlet temperature) which is almost 

constant for all cases. The highest values are calculated again for the hydraulic diameter and the 

friction factor, followed by the inlet temperature and the K-factor for the spacer grid. 

The sensitivity coefficients of the TRACE-DAKOTA analysis indicate a slightly different relation 

between the parameters. For the inlet temperature exclusively high positive values, > 0.6, are 

calculated, even for case 1 for which the TRACE-SUSA analysis predicted a value of – 0.64. That 

means that for the TRACE-SUSA analysis the pressure drop would increase with decreasing inlet 

temperature. For TRACE-DAKOTA the influence of the inlet temperature would be in the opposite 

direction; increasing inlet temperature yield higher pressure drop. One explanation could be the 

absence of the friction factor and the hydraulic diameter in the TRACE-DAKOTA analysis, which 

amplifies the influence of the inlet temperature compared to the TRACE-SUSA analysis. The 

ranks of the uncertain parameters are plotted in Figure 71 and Figure 72 for TRACE-SUSA and 

TRACE-DAKOTA, respectively. 
6-26

Figure 69 Sensitivity Coefficients for the Two-Phase Flow Pressure Drop Analysis

with TRACE-SUSA 

Figure 70 Sensitivity Coefficients for the Two-Phase Flow Pressure Drop Analysis

with TRACE-DAKOTA 

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

01 03 05 07 09 11 13 15 17 19 21 23 25 27 29 31 33

Sensitivity coefficient

Case (P600xx)

Outlet pressure (S) Mass flow rate (S) Inlet temperature (S)

Wall roughness (S) K-spacer (S) Hydraulic diameter (S)

Density (S) Friction factor (S) Power (S)

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

01 03 05 07 09 11 13 15 17 19 21 23 25 27 29 31 33

Sensitivity coefficient

Case (P600xx)

Outlet pressure (D) Mass flow rate (D) Inlet temperature (D)

K-spacer (D) Wall roughness (D) Power (D)
6-27

Figure 71 Ranking of the Uncertain Parameters for the Two-Phase Flow Pressure

Drop Analysis with TRACE-SUSA 

Figure 72 Ranking of the Uncertain Parameters for the Two-Phase Flow Pressure

Drop Analysis with TRACE-DAKOTA

0

1

2

3

4

5

6

7

8

9

10

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33

Rank

Case (P600xx)

Outlet pressure Mass flow rate Inlet temperature

Wall roughness K-spacer Hydraulic diameter

Density Friction factor Power

0

1

2

3

4

5

6

7

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33

Rank

Case (P600xx)

Outlet pressure Mass flow rate Inlet temperature

Wall roughness K-spacer Power
6-28

Table 23 Pearson's Momentum Correlation Coefficients for the Two-Phase Flow Pressure

 Drop Cases with TRACE-SUSA Outlet pressure Mass flow rate Inlet temperature Wall

roughnessK-spacerHydraulicdiameterDensityFrictionfactorPower

P60001 0.189 0.212 -0.645 -0.013 0.387 -0.486 0.129 0.237 -0.040 

P60002 0.131 0.268 -0.485 0.002 0.427 -0.627 0.102 0.348 -0.012 

P60003 0.044 0.300 -0.248 0.019 0.434 -0.751 0.057 0.455 0.047 

P60004 -0.013 0.297 -0.094 0.025 0.412 -0.794 0.022 0.494 0.098 

P60005 -0.042 0.286 -0.020 0.025 0.393 -0.806 -0.000 0.505 0.131 

P60006 -0.044 0.286 -0.017 0.025 0.393 -0.806 -0.002 0.506 0.132 

P60007 -0.181 0.277 0.411 0.057 0.366 -0.693 -0.022 0.438 0.099 

P60008 -0.184 0.263 0.406 0.055 0.342 -0.700 -0.024 0.452 0.126 

P60009 -0.177 0.247 0.374 0.051 0.327 -0.720 -0.030 0.466 0.162 

P60010 -0.167 0.241 0.335 0.048 0.323 -0.739 -0.038 0.477 0.183 

P60011 -0.155 0.241 0.289 0.045 0.331 -0.756 -0.050 0.486 0.194 

P60012 -0.155 0.241 0.289 0.045 0.331 -0.756 -0.050 0.486 0.194 

P60013 -0.200 0.263 0.470 0.061 0.339 -0.662 -0.029 0.423 0.102 

P60014 -0.197 0.252 0.447 0.058 0.328 -0.678 -0.030 0.439 0.131 

P60015 -0.186 0.240 0.404 0.054 0.316 -0.706 -0.033 0.457 0.165 

P60016 -0.173 0.235 0.353 0.050 0.312 -0.731 -0.041 0.470 0.187 

P60017 -0.153 0.294 0.325 0.052 0.398 -0.728 -0.011 0.453 0.090 

P60018 -0.163 0.276 0.344 0.051 0.365 -0.727 -0.017 0.465 0.121 

P60019 -0.164 0.256 0.336 0.048 0.338 -0.737 -0.026 0.476 0.156

P60020 -0.158 0.245 0.308 0.044 0.331 -0.750 -0.034 0.483 0.181 

P60021 -0.149 0.243 0.273 0.042 0.333 -0.763 -0.045 0.489 0.194 

P60022 0.202 0.203 -0.653 -0.017 0.390 -0.479 0.124 0.225 -0.033 

P60023 0.071 0.300 -0.309 0.015 0.447 -0.726 0.064 0.424 0.024 

P60024 -0.027 0.298 -0.061 0.026 0.415 -0.799 0.008 0.494 0.105 

P60025 -0.177 0.291 0.376 0.058 0.398 -0.701 -0.034 0.433 0.083 

P60026 -0.182 0.259 0.365 0.053 0.351 -0.716 -0.035 0.460 0.144 

P60027 -0.167 0.244 0.302 0.048 0.342 -0.747 -0.045 0.478 0.185 

P60028 -0.167 0.245 0.302 0.048 0.342 -0.747 -0.045 0.478 0.184 

P60029 -0.198 0.278 0.438 0.062 0.374 -0.670 -0.044 0.418 0.087 

P60030 -0.193 0.250 0.400 0.056 0.338 -0.701 -0.039 0.450 0.149 

P60031 -0.145 0.306 0.279 0.052 0.432 -0.736 -0.021 0.447 0.077 

P60032 -0.167 0.269 0.322 0.051 0.365 -0.734 -0.030 0.471 0.138 

P60033 -0.159 0.250 0.279 0.045 0.347 -0.756 -0.041 0.483 0.181 
6-29

Table 24 Pearson's Momentum Correlation Coefficients for the Two-Phase Flow

 Pressure Drop Cases with TRACE-DAKOTA Outlet pressure Mass flow rate Inlet temperature Wall roughness

K-spacerHydraulicdiameterDensityFrictionfactorPower

P60001 -0.391 0.322 0.802 0.314 0.002

not included

0.029

P60008 -0.396 0.287 0.672 0.087 0.509 0.013

P60014 -0.394 0.272 0.730 0.061 0.408 0.232

P60020 -0.413 0.284 0.641 0.086 0.485 0.334

P60022 -0.280 0.250 0.865 0.030 0.263 0.098

P60030 -0.445 0.269 0.646 0.070 0.502 0.294

6.4 Void Fraction Analyses 

The third parameter which is subject of the presented investigation is the void fraction 

measurements. As mentioned in sub section 3.5 the void fraction has been measured at four 

different positions. At the first three positions (Z1 = 0.682 m; Z2 = 1.706 m; Z3 = 2.730 m) X-ray 

densitometers where used while at the fourth and highest position (Z4 = 3.758 m) an X-ray CT 

scanner was used. 

In an investigation performed by Glück [28], the reliability of the X-ray densitometer void fraction 

measurements have been discussed. Due to the used measurement technique, only a limited 

volume/layer of the bundle cross section was scanned. That yield to an under prediction of the 

void fraction during bubbly flow since the void is concentrated near the wall. With slug flow, the 

void is gathered in the center of the sub channel and the measurement gives higher values than 

expected. Glück proposed correlations to correct the void fraction measurements’ depending 

which assembly type is used. Since only assembly type four/C2A is used only the respective 

correlation will be depicted (void fraction in %). 

αcorrected =

αmeasured

−0.001 ∙ αmeasured + 1.167 (62)

Due to the different measurement procedure with the CT scanner, a correction was not necessary. 

The scanners employ 512 detectors with the scanner rotation around the tube. Compared to the 

rather simple design of the X-ray densitometers, a high spatial resolution was achieved with a 

pixel size of 0.3 x 0.3 mm. 

The input and boundary combination of 86 considered cases are depicted in Figure 73. In addition, 

Table 25 shows the input and boundary conditions for each case. 
6-30

Figure 73 Input and Boundary Conditions for the Steady State Void

Fraction Measurements 

Table 25 Input and Boundary Conditions for the Steady State Void Fraction

 Measurements 

Case Outlet pressure 

[bar]

Inlet sub-cooling 

[kJ/kg]

Mass flow rate 

[t/h]

Power

[0.1 x MW]

4101-01 9.95 54.1 10.12 2.20

4101-02 9.94 53.3 10.12 3.20

4101-03 9.78 50.7 10.12 4.30

4101-04 9.73 43.9 10.20 8.20

4101-05 10.02 55.4 30.00 6.00

4101-06 10.08 56.4 30.01 9.30

4101-07 10.06 55.0 30.00 12.60

4101-08 10.42 62.5 30.02 24.30

4101-09 9.84 50.6 54.99 10.80

4101-10 10.21 58.6 54.95 17.00

4101-11 10.96 71.1 54.85 23.10

4101-12 10.79 67.9 54.80 23.10

4101-13 12.24 92.5 55.01 44.60

4101-14 39.37 53.6 10.11 2.60

4101-15 39.32 52.0 10.10 3.90

4101-16 39.36 53.1 10.13 5.30

4101-17 39.25 51.4 10.14 7.20

4101-18 39.19 51.5 10.14 10.00

4101-19 39.36 52.5 10.12 13.40

0

10

20

30

40

50

60

70

80

90

100

01 06 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86

Pressure, Inlet sub-cooling, Mass flow 

rate & Power

Case (4101-xx)

Pressure [bar] Inlet sub-cooling [kJ/kg] Mass flow rate [t/h] Power [0.1 x MW]
6-31

Case Outlet pressure 

[bar]

Inlet sub-cooling 

[kJ/kg]

Mass flow rate 

[t/h]

Power

[0.1 x MW]

4101-20 39.40 52.2 29.98 7.20

4101-21 39.42 52.2 29.99 11.40

4101-22 39.31 50.8 29.97 15.70

4101-23 39.37 51.5 29.97 21.40

4101-24 39.43 51.7 29.93 30.00

4101-25 39.43 50.9 29.92 40.10

4101-26 39.55 52.5 54.78 13.00

4101-27 39.82 54.6 54.73 20.90

4101-28 39.18 50.6 54.71 28.80

4101-29 39.17 50.3 54.68 39.20

4101-30 39.61 52.7 54.71 55.00

4101-31 39.91 54.8 54.75 73.30

4101-32 39.88 54.6 54.77 73.30

4101-33 71.52 52.6 10.12 2.50

4101-34 71.55 53.4 10.12 3.60

4101-35 71.50 51.8 10.12 4.80

4101-36 71.45 51.7 10.10 6.50

4101-37 71.46 51.6 10.12 8.90

4101-38 71.50 51.6 10.12 11.90

4101-39 71.47 51.5 20.05 4.50

4101-40 71.44 52.0 20.03 7.00

4101-41 71.34 50.5 20.03 9.60

4101-42 71.38 52.0 20.03 12.90

4101-43 71.38 50.5 20.06 17.90

4101-44 71.41 50.6 20.09 23.60

4101-45 71.67 52.2 29.94 6.90

4101-46 71.63 51.2 29.93 10.60

4101-47 71.32 50.6 29.94 14.30

4101-48 71.65 51.2 29.91 19.30

4101-49 71.68 51.2 29.94 26.70

4101-50 71.76 50.3 29.91 35.50

4101-51 71.62 22.4 54.52 14.60

4101-52 72.09 24.8 54.52 30.70

4101-53 71.81 52.8 54.65 12.40

4101-54 71.86 52.7 54.63 12.30

4101-55 71.95 52.9 54.59 19.20

4101-56 71.75 51.8 54.62 25.90

4101-57 71.74 52.4 54.58 26.00

4101-58 71.52 50.6 54.58 35.20

4101-59 71.90 52.1 54.57 48.80

4101-60 71.78 50.5 54.62 48.90

4101-61 71.80 52.5 54.65 64.80

4101-62 71.90 127.0 54.84 30.00

4101-63 72.17 128.0 54.80 46.00

4101-64 71.59 53.6 69.53 15.70

4101-65 71.60 52.8 69.53 24.40

4101-66 72.02 52.9 69.69 33.20

4101-67 72.48 54.6 69.58 44.80
6-32

Case Outlet pressure 

[bar]

Inlet sub-cooling 

[kJ/kg]

Mass flow rate 

[t/h]

Power

[0.1 x MW]

4101-68 72.75 56.0 69.56 62.20

4101-69 86.38 52.5 10.08 2.30

4101-70 86.28 51.0 10.08 3.40

4101-71 86.28 51.2 10.09 4.50

4101-72 86.17 52.4 10.08 6.20

4101-73 86.11 52.4 10.10 8.60

4101-74 86.06 51.9 10.10 11.10

4101-75 86.41 53.8 29.88 6.70

4101-76 86.44 53.6 29.93 10.10

4101-77 86.33 53.4 29.93 13.70

4101-78 86.38 53.6 29.93 18.30

4101-79 86.14 51.1 29.89 25.20

4101-80 86.31 51.8 29.88 33.40

4101-81 86.36 51.5 54.60 12.00

4101-82 86.35 52.9 54.54 18.50

4101-83 86.66 53.2 54.62 24.90

4101-84 86.80 53.2 54.66 33.50

4101-85 87.00 53.8 54.61 46.20

4101-86 87.05 54.2 54.59 46.20

As Figure 73 indicates, a scheme can be identified for the parameter combinations. The inlet 

sub-cooling is around 50 kJ/kg in the most cases. Only a few cases show an inlet sub-cooling of 

more than 100 kJ/kg. The pressure is divided into four sections, section 1 around 10 bar; section 

2 around 40 bar; section 3 around 71 bar and section 4 around 86 bar. The mass flow rate is 

between 10 and 70 kg/s while the power ranges, without showing a pattern or routine, between 

0.2 and 7.4 MW. 

The calculated void fractions at the exit for each of the 86 cases are compared to the experimental 

values in Figure 74. It can be seen that the agreement is very good no matter it is in the low or 

high void fraction range. The relative error is plotted in Figure 75 for each case. A tendency to 

over predict the measured data can be seen with an average error of 3.72 %. Also, the errors 

based on the reference calculations, see Figure 76 are lower at higher void fractions. 

As for the previous cases, the uncertainty and sensitivity analysis was performed with TRACE 

and SUSA for all cases while for TRACE and DAKOTA only six of them were performed. The 

results in terms of absolute values are shown in Figure 77. One clear tendency can be deduced 

from that graph; the higher the void fraction the lower the uncertainty. At lower void fractions the 

results are spread over a wider range than at higher void fractions. That might be related to the 

flow regime which is present at the different void fractions. At lower void fractions the regime is 

bubbly slug flow while at higher void fractions annular mist flow is present. The differences in 

calculating the interfacial friction and their sensitivity to the parameters which are varied are most 

likely the reason for the observed behavior. 
6-33

Figure 74 Calculated versus Measured Outlet Void Fractions 

Figure 75 Percental Error of the Reference Values Compared to the Experimental Data

for the Outlet Void Fraction 

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Void fraction - calculated [Pa]

Void fraction - measured [Pa]

+ 10 %

- 10 %

-10

-8

-6

-4

-2

0

2

4

6

8

10

01 06 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86

Error [%]

Case (4101-xx)
6-34

Figure 76 Error as a Function of the Void Fraction 

Due to the complexity of the models for wall and interfacial drag it is challenging to determine 

which input and boundary parameter is influencing parameters related to the two different flow 

regimes a priori. A plausible explanation could be that at low void fractions the system is more 

sensitive to variations than at higher void fractions. A more quantitative explanation of the 

behavior can be given after the sensitivity analysis. 

The relative void fractions along with the uncertainty band for TRACE-SUSA and TRACEDAKOTA is given in Figure 78. The tendency to over predict the outlet void fraction can be seen 

here very clearly. One can also see that the uncertainty band is wider for the TRACE-DAKOTA 

cases. This is rather unexpected since less parameters are used in the uncertainty analysis. 

The results of the uncertainty analysis by means of mean, maximal and minimal value together 

with the standard deviation and the relative error are also given in Table 26 and in Table 27 for 

TRACE-SUSA and TRACE-DAKOTA, respectively. 

0

1

2

3

4

5

6

7

8

9

10

11

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Error [%]

Void fraction [-]
6-35

Figure 77 Comparison of the Experimental and Outlet Void Fractions in Absolute Values 

Figure 78 Comparison of the Experimental and Predicted Outlet Void Fractions

in Relative Values 

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

01 06 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86

Outlet void fraction [-]

Case (4101-xx)

Experiment Mean (SUSA) Maximum (SUSA)

Minimum (SUSA) Mean (DAKOTA) Maximum (DAKOTA)

Minimum (DAKOTA)

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

01 06 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86

Relative outlet void fraction [-]

Case (4101-xx)

Mean (SUSA) Maximum (SUSA) Minimum (SUSA)

Mean (DAKOTA) Maximum (DAKOTA) Minimum (DAKOTA)
6-36

Table 26 Results of the Uncertainty Analysis for the Outlet Void Fraction with

 TRACE-SUSA 

Case Ex [-] Mean [-] Max [-] Min [-] SD [-] Error [%]

4101-01 0.383 0.385 0.453 0.307 0.036 0.41

4101-02 0.571 0.603 0.634 0.572 0.015 5.62

4101-03 0.714 0.714 0.731 0.699 0.007 0.02

4101-04 0.840 0.843 0.847 0.838 0.002 0.31

4101-05 0.418 0.448 0.536 0.328 0.052 7.28

4101-06 0.668 0.687 0.709 0.662 0.011 2.90

4101-07 0.768 0.766 0.776 0.754 0.005 -0.26

4101-08 0.863 0.855 0.860 0.850 0.002 -0.88

4101-09 0.531 0.527 0.592 0.435 0.039 -0.81

4101-10 0.701 0.691 0.712 0.665 0.011 -1.43

4101-11 0.766 0.742 0.755 0.727 0.007 -3.10

4101-12 0.770 0.749 0.761 0.734 0.006 -2.75

4101-13 0.868 0.840 0.847 0.832 0.003 -3.21

4101-14 0.304 0.302 0.348 0.255 0.023 -0.59

4101-15 0.473 0.497 0.524 0.470 0.013 5.02

4101-16 0.586 0.607 0.626 0.590 0.008 3.65

4101-17 0.674 0.701 0.713 0.690 0.005 3.97

4101-18 0.755 0.778 0.785 0.770 0.003 2.98

4101-19 0.810 0.830 0.835 0.824 0.002 2.46

4101-20 0.366 0.372 0.427 0.310 0.029 1.68

4101-21 0.562 0.591 0.614 0.564 0.011 5.06

4101-22 0.662 0.691 0.703 0.676 0.006 4.31

4101-23 0.745 0.758 0.765 0.749 0.004 1.70

4101-24 0.803 0.814 0.819 0.808 0.002 1.39

4101-25 0.847 0.857 0.862 0.852 0.002 1.19

4101-26 0.369 0.392 0.447 0.327 0.030 6.29

4101-27 0.577 0.604 0.625 0.578 0.011 4.63

4101-28 0.679 0.704 0.715 0.690 0.006 3.61

4101-29 0.757 0.766 0.773 0.758 0.004 1.17

4101-30 0.821 0.819 0.825 0.813 0.003 -0.22

4101-31 0.861 0.875 0.883 0.866 0.004 1.60

4101-32 0.858 0.875 0.883 0.866 0.004 1.97

4101-33 0.212 0.216 0.259 0.172 0.022 1.97

4101-34 0.356 0.369 0.401 0.337 0.015 3.66

4101-35 0.469 0.488 0.511 0.464 0.011 4.01

4101-36 0.569 0.595 0.612 0.579 0.007 4.63

4101-37 0.664 0.689 0.701 0.678 0.005 3.78

4101-38 0.739 0.762 0.771 0.754 0.003 3.16

4101-39 0.230 0.218 0.271 0.162 0.028 -5.10

4101-40 0.410 0.424 0.457 0.389 0.016 3.43

4101-41 0.528 0.554 0.575 0.531 0.010 4.87

4101-42 0.622 0.648 0.662 0.632 0.007 4.12

4101-43 0.702 0.734 0.743 0.724 0.004 4.58

4101-44 0.769 0.792 0.798 0.784 0.003 2.95

4101-45 0.241 0.244 0.298 0.184 0.029 1.11

4101-46 0.421 0.455 0.487 0.421 0.016 8.17

4101-47 0.536 0.573 0.594 0.551 0.010 6.97
6-37

Case Ex [-] Mean [-] Max [-] Min [-] SD [-] Error [%]

4101-48 0.633 0.665 0.678 0.650 0.006 4.99

4101-49 0.720 0.743 0.752 0.734 0.004 3.25

4101-50 0.783 0.800 0.805 0.793 0.003 2.11

4101-51 0.437 0.471 0.501 0.439 0.016 7.85

4101-52 0.645 0.671 0.684 0.658 0.006 4.10

4101-53 0.250 0.250 0.309 0.184 0.033 -0.12

4101-54 0.242 0.246 0.305 0.180 0.033 1.59

4101-55 0.438 0.468 0.499 0.433 0.016 6.90

4101-56 0.544 0.584 0.604 0.562 0.010 7.40

4101-57 0.550 0.585 0.604 0.562 0.01 6.29

4101-58 0.645 0.676 0.688 0.662 0.006 4.87

4101-59 0.737 0.750 0.757 0.740 0.004 1.71

4101-60 0.740 0.751 0.759 0.742 0.004 1.49

4101-61 0.807 0.802 0.809 0.795 0.003 -0.61

4101-62 0.435 0.451 0.487 0.408 0.017 3.73

4101-63 0.645 0.666 0.679 0.649 0.006 3.23

4101-64 0.263 0.254 0.312 0.186 0.033 -3.38

4101-65 0.451 0.474 0.504 0.440 0.016 5.15

4101-66 0.571 0.586 0.605 0.564 0.010 2.66

4101-67 0.668 0.672 0.684 0.657 0.006 0.55

4101-68 0.751 0.748 0.755 0.738 0.004 -0.46

4101-69 0.182 0.166 0.210 0.120 0.024 -9.05

4101-70 0.316 0.329 0.362 0.296 0.016 4.06

4101-71 0.420 0.438 0.463 0.412 0.012 4.17

4101-72 0.523 0.553 0.571 0.534 0.008 5.66

4101-73 0.627 0.657 0.670 0.644 0.006 4.82

4101-74 0.695 0.728 0.738 0.718 0.004 4.78

4101-75 0.201 0.193 0.248 0.134 0.030 -3.81

4101-76 0.365 0.389 0.425 0.351 0.018 6.67

4101-77 0.470 0.517 0.541 0.490 0.012 9.92

4101-78 0.567 0.617 0.633 0.599 0.008 8.81

4101-79 0.679 0.710 0.720 0.698 0.005 4.52

4101-80 0.750 0.773 0.780 0.764 0.003 3.01

4101-81 0.226 0.213 0.270 0.150 0.032 -5.98

4101-82 0.376 0.416 0.450 0.377 0.018 10.54

4101-83 0.499 0.533 0.556 0.507 0.012 6.76

4101-84 0.602 0.630 0.645 0.613 0.007 4.70

4101-85 0.697 0.716 0.725 0.704 0.005 2.67

4101-86 0.698 0.715 0.725 0.704 0.005 2.48

Table 27 Results of the Uncertainty Analysis for the Outlet Void Fraction with

 TRACE DAKOTA 

Case Ex [-] Mean [-] Max [-] Min [-] SD [-] Error [%]

4101-04 0.840 0.842 0.846 0.838 0.002 0.25

4101-18 0.755 0.779 0.785 0.770 0.003 3.14

4101-29 0.757 0.765 0.774 0.757 0.004 1.11

4101-47 0.536 0.573 0.599 0.552 0.010 6.91

4101-64 0.263 0.254 0.327 0.181 0.033 -3.56

4101-82 0.376 0.415 0.456 0.375 0.020 10.31
6-38

The sensitivity coefficients according to Pearson’s momentum correlation coefficient are plotted 

in Figure 79 for TRACE-SUSA and in Figure 80 for TRACE-DAKOTA. For the TRACE-SUSA plot, 

a repeating pattern can be seen which is related to combination of the input and boundary 

condition parameters. It is clearly visible, also for the TRACE-DAKOTA, that the inlet temperature, 

which represents the inlet sub-cooling, is the input parameter of highest importance. Besides the 

inlet temperature, the power is also of importance but sensitivity coefficients range from almost 

zero to values up to 0.6. At low void fractions the values for the mass flow rate are close to zero 

while for high void fractions the values are close to -0.4, meaning that an increase of the mass 

flow rate always results in a decrease of the void fraction. Parameters like the friction factor, 

hydraulic diameter or K factor have almost no impact on the outlet void fraction. 

In order to evaluate the reason why at low void fractions the uncertainty band is wider than at 

higher values, the sensitivity coefficients for the inlet temperature and the power are plotted as a 

function of the void fraction, see Figure 81. It can be seen that at low void fractions the sensitivity 

coefficient for the inlet temperature is very high, around 0.9 while the power coefficient is very 

low. With increasing void fraction the sensitivity coefficient for the inlet temperature decrease to 

values of around 0.5 at a void fraction of > 0.8. The coefficient for the power is increasing linearly 

with increasing void fractions, going from < 0.1 at a void fraction of 0.15 to values of around 0.6 

at void fractions of around 0.9. Since the variation is almost constant, ± 1.5 K for the inlet 

temperature and ± 1 % for the power, the change of the absolute values is getting more 

pronounced with higher temperatures and powers. With increasing assembly power the outlet 

void fraction is increased. That means that a variation of 1% of an already high assembly power 

will result in much more additional energy which is released in the systems as 1 % at a low 

assembly power. 

At low void fractions, the variation of the inlet sub-cooling (inlet temperature) has more influence 

on the resulting void fraction compared to higher void fractions because the inlet sub-cooling is 

the only parameter which affects the results according to the sensitivity study. 

The ranks of the input and boundary condition parameters are given in Figure 82 and Figure 83

for TRACE-SUSA and TRACE-DAKOTA, respectively. 

For the sake of completeness the individual sensitivity coefficients for each parameter are listed 

in Table 28. 
6-39

Figure 79 Sensitivity Coefficients for the Outlet Void Fraction Analysis with TRACE-SUSA 

Figure 80 Sensitivity Coefficients for the Outlet Void Fraction Analysis with

TRACE-DAKOTA 

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

01 06 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86

Sensitivity coefficient

Case (4101-xx)

Outlet pressure Mass flow rate Inlet temperature

Wall roughness K-spacer Hydraulic diameter

Density Friction factor Power

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

01 06 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86

Sensitivity coefficient

Case (4101-xx)

Outlet pressure Mass flow rate Inlet temperature

Wall roughness K-spacer Power
6-40

Figure 81 Sensitivity Coefficients for Inlet Temperature and Power versus the Outlet

Void Fraction 

Figure 82 Ranking of the Uncertain Parameters for the Outlet Void Fraction with

TRACE-SUSA

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Sensitivity coefficient

Outlet void fraction [-]

Inlet temperature

Power

0

1

2

3

4

5

6

7

8

9

10

01 06 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86

Rank

Case (4101-xx)

Outlet pressure Mass flow rate Inlet temperature

Wall roughness K-spacer Hydraulic diameter

Density Friction factor Power
6-41

Figure 83 Ranking of the Uncertain Parameters for the Outlet Void Fraction with

TRACE-DAKOTA 

Table 28 Pearson's Momentum Correlation Coefficients for the Outlet Void Fraction

 Cases with TRACE-SUSA Outlet pressure Mass flow rate Inlet temperature 

Wall roughness K-spacer Hydraulic diameter Density Friction factor Power 

4101-01 -0.151 -0.036 0.945 0.036 -0.158 -0.068 0.177 0.089 0.089

4101-02 -0.159 -0.050 0.916 0.016 -0.148 -0.150 0.174 0.081 0.169

4101-03 -0.163 -0.073 0.875 -0.010 -0.142 -0.213 0.174 0.036 0.247

4101-04 -0.159 -0.216 0.721 -0.072 -0.150 -0.205 0.218 -0.090 0.461

4101-05 -0.140 -0.054 0.947 0.042 -0.162 -0.013 0.183 0.078 0.072

4101-06 -0.160 -0.099 0.918 0.010 -0.184 -0.028 0.218 -0.004 0.154

4101-07 -0.163 -0.154 0.868 -0.025 -0.203 -0.015 0.246 -0.118 0.226

4101-08 -0.161 -0.278 0.714 -0.080 -0.200 -0.039 0.285 -0.126 0.455

4101-09 -0.139 -0.061 0.947 0.041 -0.171 0.007 0.193 0.056 0.065

4101-10 -0.157 -0.117 0.915 0.006 -0.197 0.012 0.231 -0.027 0.150

4101-11 -0.159 -0.174 0.869 -0.023 -0.208 0.025 0.251 -0.092 0.227

4101-12 -0.159 -0.175 0.866 -0.024 -0.210 0.027 0.254 -0.105 0.227

4101-13 -0.151 -0.294 0.698 -0.090 -0.210 -0.002 0.291 -0.191 0.443

4101-14 -0.253 -0.031 0.910 0.043 -0.155 -0.064 0.188 0.092 0.103

4101-15 -0.259 -0.058 0.872 0.022 -0.143 -0.140 0.196 0.095 0.197

0

1

2

3

4

5

6

7

01 06 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86

Rank

Case (510xx)

Outlet pressure Mass flow rate Inlet temperature

Wall roughness K-spacer Power
6-42

Outlet pressure Mass flow rate Inlet temperature Wall roughness K-spacer Hydraulic diameter Density Friction factor Power 

4101-16 -0.258 -0.091 0.825 -0.001 -0.132 -0.200 0.202 0.083 0.286

4101-17 -0.249 -0.134 0.754 -0.031 -0.124 -0.256 0.211 0.041 0.388

4101-18 -0.225 -0.205 0.651 -0.071 -0.120 -0.275 0.226 -0.053 0.500

4101-19 -0.191 -0.293 0.546 -0.098 -0.118 -0.238 0.251 -0.087 0.602

4101-20 -0.255 -0.042 0.912 0.048 -0.162 -0.016 0.205 0.079 0.086

4101-21 -0.269 -0.099 0.872 0.021 -0.172 -0.033 0.244 0.033 0.183

4101-22 -0.270 -0.160 0.818 -0.011 -0.185 -0.029 0.280 -0.046 0.269

4101-23 -0.255 -0.233 0.734 -0.050 -0.194 -0.013 0.309 -0.148 0.362

4101-24 -0.222 -0.313 0.617 -0.090 -0.193 0.005 0.330 -0.224 0.469

4101-25 -0.193 -0.358 0.542 -0.103 -0.174 -0.050 0.332 -0.114 0.591

4101-26 -0.254 -0.049 0.912 0.047 -0.167 0.004 0.209 0.064 0.082

4101-27 -0.269 -0.117 0.867 0.016 -0.186 0.010 0.259 0.000 0.180

4101-28 -0.268 -0.181 0.807 -0.020 -0.202 0.024 0.299 -0.089 0.263

4101-29 -0.250 -0.252 0.718 -0.060 -0.210 0.043 0.325 -0.190 0.352

4101-30 -0.217 -0.321 0.608 -0.099 -0.205 0.035 0.337 -0.250 0.462

4101-31 -0.191 -0.336 0.545 -0.107 -0.198 -0.074 0.337 -0.144 0.582

4101-32 -0.191 -0.336 0.546 -0.107 -0.199 -0.074 0.338 -0.144 0.582

4101-33 -0.309 -0.015 0.895 0.054 -0.155 -0.033 0.192 0.090 0.074

4101-34 -0.314 -0.044 0.870 0.039 -0.148 -0.078 0.204 0.095 0.147

4101-35 -0.315 -0.073 0.838 0.023 -0.141 -0.125 0.215 0.096 0.221

4101-36 -0.309 -0.114 0.786 -0.001 -0.131 -0.179 0.226 0.086 0.316

4101-37 -0.290 -0.168 0.710 -0.031 -0.121 -0.227 0.236 0.053 0.425

4101-38 -0.254 -0.235 0.619 -0.065 -0.115 -0.245 0.244 -0.009 0.529

4101-39 -0.310 -0.016 0.898 0.059 -0.158 -0.007 0.197 0.085 0.056

4101-40 -0.322 -0.058 0.869 0.042 -0.157 -0.038 0.224 0.083 0.140

4101-41 -0.327 -0.100 0.833 0.023 -0.157 -0.061 0.249 0.064 0.218

4101-42 -0.323 -0.156 0.782 -0.002 -0.159 -0.073 0.275 0.023 0.307

4101-43 -0.300 -0.233 0.698 -0.039 -0.164 -0.070 0.304 -0.060 0.414

4101-44 -0.257 -0.309 0.603 -0.076 -0.164 -0.050 0.317 -0.149 0.501

4101-45 -0.312 -0.021 0.896 0.059 -0.159 0.000 0.201 0.083 0.060

4101-46 -0.326 -0.067 0.865 0.041 -0.162 -0.018 0.234 0.069 0.140

4101-47 -0.331 -0.114 0.830 0.021 -0.167 -0.024 0.264 0.038 0.213

4101-48 -0.326 -0.175 0.775 -0.006 -0.175 -0.021 0.296 -0.017 0.300

4101-49 -0.299 -0.256 0.688 -0.046 -0.180 -0.008 0.324 -0.104 0.403

4101-50 -0.253 -0.330 0.587 -0.083 -0.178 0.010 0.334 -0.190 0.491

4101-51 -0.330 -0.033 0.881 0.049 -0.173 0.010 0.240 0.037 0.074

4101-52 -0.333 -0.157 0.793 -0.003 -0.193 0.027 0.312 -0.056 0.241

4101-53 -0.311 -0.023 0.897 0.059 -0.161 0.009 0.201 0.074 0.056

4101-54 -0.311 -0.022 0.897 0.059 -0.161 0.009 0.200 0.074 0.055

4101-55 -0.327 -0.075 0.864 0.038 -0.171 0.010 0.242 0.043 0.134

4101-56 -0.332 -0.127 0.825 0.017 -0.181 0.017 0.278 0.003 0.205

4101-57 -0.332 -0.128 0.825 0.017 -0.181 0.017 0.278 0.003 0.207

4101-58 -0.325 -0.192 0.766 -0.014 -0.190 0.027 0.312 -0.058 0.293

4101-59 -0.294 -0.269 0.678 -0.054 -0.193 0.033 0.335 -0.138 0.395
6-43

Outletpressure Mass flow rate Inlet temperature Wall roughness K-spacer Hydraulic diameter Density Friction factor Power 

4101-60 -0.293 -0.269 0.678 -0.054 -0.193 0.033 0.336 -0.140 0.395

4101-61 -0.249 -0.338 0.581 -0.084 -0.192 0.046 0.344 -0.225 0.474

4101-62 -0.307 -0.172 0.810 0.011 -0.162 0.008 0.239 0.058 0.275

4101-63 -0.300 -0.271 0.698 -0.034 -0.175 0.023 0.300 -0.037 0.408

4101-64 -0.304 -0.018 0.899 0.053 -0.162 0.004 0.190 0.041 0.053

4101-65 -0.326 -0.077 0.864 0.035 -0.176 0.020 0.245 0.026 0.132

4101-66 -0.332 -0.132 0.823 0.014 -0.185 0.029 0.281 -0.008 0.205

4101-67 -0.324 -0.195 0.766 -0.014 -0.192 0.035 0.313 -0.059 0.291

4101-68 -0.294 -0.274 0.675 -0.056 -0.195 0.044 0.337 -0.142 0.394

4101-69 -0.326 -0.004 0.893 0.061 -0.155 -0.018 0.189 0.088 0.051

4101-70 -0.332 -0.032 0.871 0.047 -0.150 -0.060 0.205 0.094 0.121

4101-71 -0.333 -0.061 0.845 0.032 -0.145 -0.096 0.217 0.096 0.188

4101-72 -0.328 -0.104 0.799 0.010 -0.136 -0.146 0.230 0.092 0.283

4101-73 -0.308 -0.159 0.729 -0.019 -0.126 -0.196 0.242 0.070 0.394

4101-74 -0.278 -0.214 0.658 -0.047 -0.118 -0.223 0.249 0.031 0.488

4101-75 -0.328 -0.012 0.891 0.063 -0.158 0.006 0.197 0.083 0.047

4101-76 -0.341 -0.053 0.866 0.049 -0.160 -0.009 0.227 0.077 0.118

4101-77 -0.347 -0.096 0.835 0.032 -0.163 -0.017 0.256 0.058 0.188

4101-78 -0.345 -0.151 0.790 0.009 -0.168 -0.019 0.286 0.019 0.268

4101-79 -0.323 -0.227 0.717 -0.026 -0.175 -0.012 0.318 -0.053 0.369

4101-80 -0.280 -0.303 0.630 -0.063 -0.176 0.002 0.332 -0.129 0.462

4101-81 -0.328 -0.011 0.892 0.063 -0.160 0.011 0.198 0.075 0.042

4101-82 -0.343 -0.059 0.864 0.045 -0.167 0.011 0.234 0.052 0.115

4101-83 -0.349 -0.107 0.831 0.027 -0.175 0.016 0.267 0.024 0.181

4101-84 -0.345 -0.166 0.783 0.002 -0.182 0.023 0.301 -0.019 0.262

4101-85 -0.318 -0.240 0.710 -0.034 -0.187 0.025 0.328 -0.082 0.364

4101-86 -0.318 -0.241 0.710 -0.034 -0.186 0.024 0.328 -0.082 0.364

Table 29 Pearson's Momentum Correlation Coefficients for Outlet Void Fraction Cases

 with TRACE-DAKOTA Outlet pressure Mass flow rate Inlet

temperatureWall roughnessK-spacerHydraulic diameterDensityFriction factorPower

4101-04 -0.474 -0.239 0.640 -0.052 -0.012 

not included 

0.500 

4101-18 -0.415 -0.246 0.656 0.029 0.012 0.567 

4101-29 -0.476 -0.236 0.698 -0.039 0.005 0.459 

4101-47 -0.425 -0.185 0.828 0.010 0.014 0.284 

4101-64 -0.450 -0.080 0.884 -0.006 0.001 0.098

4101-82 -0.502 -0.130 0.862 -0.016 0.022 0.180 
6-44

Since the void fraction has been measured at four axial elevations the predictions along the BWR 

fuel assembly mock-up can be compared to them, Figure 84 to Figure 94. In addition to the 

corrected results, the original measured data points are plotted. It can be seen that the correction 

is more pronounced at higher void fractions. The agreement of the experimental values and the 

calculated ones is very good in the most cases. In these graphs it is also visible that the 

uncertainty range (indicated by the two red lines) is wider at low void fractions and getting smaller 

at higher elevations with higher void fractions. 

For two selected cases, case 4101-04 and 4101-18, the results of TRACE-SUSA are compared 

to the ones of TRACE-DAKOTA in Figure 95 and Figure 96. In both cases the results of TRACESUSA and TRACE-DAKOTA overlap each other. Even though in the TRACE-DAKOTA 

investigation less parameters are used the results are identical. The reason for that is that the 

parameters which are considered in the TRACE-SUSA study but not in the TRACE-DAKOTA 

study are of no importance for the void fraction. 
6-45

Figure 84 Axial Void Fraction for Cases 4101-01 - 4101-08 (x-axes = Axial Location [m];

y-axes = Void Fraction; Black Circles = Original Experimental Data; Red 

Diamonds = Corrected Experimental Data; Red Line = Uncertainty Range;

Black Line = Mean Value of the Calculations) 

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-01

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-02

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-03

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-04

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-05

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-06

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-07

-0.1

0.1

0.3

0.5

0.7

0.9

1.1

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-08
6-46

Figure 85 Axial Void Fraction for Cases 4101-09 - 4101-16 (x-axes = Axial Location [m];

y-axes = Void Fraction; Black Circles = Original Experimental Data; Red

Diamonds = Corrected Experimental Data; Red Line = Uncertainty Range;

Black Line = Mean Value of the Calculations) 

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-09

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-10

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-11

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-12

-0.1

0.1

0.3

0.5

0.7

0.9

1.1

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-13

-0.1

0.0

0.1

0.2

0.3

0.4

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-14

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-15

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-16
6-47

Figure 86 Axial Void Fraction for Cases 4101-17 - 4101-24 (x-axes = Axial Location [m];

y-axes = Void Fraction; Black Circles = Original Experimental Data; Red

Diamonds = Corrected Experimental Data; Red Line = Uncertainty Range;

Black Line = Mean Value of the Calculations) 

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-17

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-18

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-19

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-20

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-21

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-22

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-23

-0.1

0.1

0.3

0.5

0.7

0.9

1.1

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-24
6-48

Figure 87 Axial Void Fraction for Cases 4101-25 - 4101-32 (x-axes = Axial Location [m];

y-axes = Void Fraction; Black Circles = Original Experimental Data; Red

Diamonds = Corrected Experimental Data; Red Line = Uncertainty Range;

Black Line = Mean Value of the Calculations) 

-0.1

0.1

0.3

0.5

0.7

0.9

1.1

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-25

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-26

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-27

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-28

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-29

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-30

-0.1

0.1

0.3

0.5

0.7

0.9

1.1

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-31

-0.1

0.1

0.3

0.5

0.7

0.9

1.1

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-32
6-49

Figure 88 Axial Void Fraction for Cases 4101-33 - 4101-40 (x-axes = Axial Location [m];

y-axes = Void Fraction; Black Circles = Original Experimental Data; Red

Diamonds = Corrected Experimental Data; Red Line = Uncertainty Range;

Black Line = Mean Value of the Calculations) 

-0.1

0.0

0.1

0.2

0.3

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-33

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-34

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-35

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-36

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-37

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-38

-0.1

-0.1

0.0

0.1

0.1

0.2

0.2

0.3

0.3

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-39

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-40
6-50

Figure 89 Axial Void Fraction for Cases 4101-41 - 4101-48 (x-axes = Axial Location [m];

y-axes = Void Fraction; Black Circles = Original Experimental Data; Red

Diamonds = Corrected Experimental Data; Red Line = Uncertainty Range;

Black Line = Mean Value of the Calculations) 

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-41

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-42

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-43

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-44

-0.1

0.0

0.1

0.2

0.3

0.4

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-45

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-46

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-47

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-48
6-51

Figure 90 Axial Void Fraction for Cases 4101-49 - 4101-56 (x-axes = Axial Location [m];

y-axes = Void Fraction; Black Circles = Original Experimental Data; Red

Diamonds = Corrected Experimental Data; Red Line = Uncertainty Range;

Black Line = Mean Value of the Calculations) 

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-49

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-50

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-51

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-52

-0.1

0.0

0.1

0.2

0.3

0.4

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-53

-0.1

0.0

0.1

0.2

0.3

0.4

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-54

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-55

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-56
6-52

Figure 91 Axial Void Fraction for Cases 4101-57 - 4101-64 (x-axes = Axial Location [m];

y-axes = Void Fraction; Black Circles = Original Experimental Data; Red

Diamonds = Corrected Experimental Data; Red Line = Uncertainty Range;

Black Line = Mean Value of the Calculations) 

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-57

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-58

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-59

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-60

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-61

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-62

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-63

-0.1

0.0

0.1

0.2

0.3

0.4

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-64
6-53

Figure 92 Axial Void Fraction for Cases 4101-65 - 4101-72 (x-axes = Axial Location [m];

y-axes = Void Fraction; Black Circles = Original Experimental Data; Red

Diamonds = Corrected Experimental Data; Red Line = Uncertainty Range;

Black Line = Mean Value of the Calculations) 

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-65

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-66

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-67

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-68

-0.1

-0.1

0.0

0.1

0.1

0.2

0.2

0.3

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-69

-0.1

0.0

0.1

0.2

0.3

0.4

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-70

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-71

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-72
6-54

Figure 93 Axial Void Fraction for Cases 4101-73 - 4101-80 (x-axes = Axial Location [m];

y-axes = Void Fraction; Black Circles = Original Experimental Data; Red

Diamonds = Corrected Experimental Data; Red Line = Uncertainty Range;

Black Line = Mean Value of the Calculations) 

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-73

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-74

-0.1

-0.1

0.0

0.1

0.1

0.2

0.2

0.3

0.3

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-75

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-76

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-77

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-78

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-79

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-80
6-55

Figure 94 Axial Void Fraction for Cases 4101-81 - 4101-86 (x-axes = Axial Location [m];

y-axes = Void Fraction; Black Circles = Original Experimental Data; Red

Diamonds = Corrected Experimental Data; Red Line = Uncertainty Range;

Black Line = Mean Value of the Calculations) 

-0.1

-0.1

0.0

0.1

0.1

0.2

0.2

0.3

0.3

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-81

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-82

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-83

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-84

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-85

-0.1

0.1

0.3

0.5

0.7

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4101-86
6-56

Figure 95 Comparison of the Axial Void Fraction Predicted with TRACE-SUSA

and TRACE-DAKOTA for Case 4101-04

Figure 96 Comparison of the Axial Void Fraction Predicted with TRACE-SUSA

and TRACE-DAKOTA for Case 4101-18 

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Void fraction [-]

Axial location [m]

Experiment (orig.) Experiment (corr.)

Mean-SUSA Mean-DAKOTA

Minimum-SUSA Minimum-DAKOTA

Maximum-SUSA Maximum-DAKOTA

4101-04

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Void fraction [-]

Axial location [m]

Experiment (orig.) Experiment (corr.)

Mean-SUSA Mean-DAKOTA

Minimum-SUSA Minimum-DAKOTA

Maximum-SUSA Maximum-DAKOTA

4101-18
6-57

6.5 Critical Power Analyses

The critical power is not directly calculated in TRACE. What TRACE calculates is the critical power 

ratio based on a predefined input power. Therefore, the experimental results of the critical power 

serve as input values for the TRACE calculations. The obtained critical power ratio is than 

multiplied by the initial power input, where the result is the critical power based on TRACE 

simulations. 

The combination of pressure, inlet sub-cooling and mass flow rate is given in Figure 97 and Table 

30. As one can see, the spread of the inlet sub-cooling does not follow a pattern and is rather

chaotically distributed between values of 20 and 140 kJ/kg. The mass flow rate shows also a wide 

spread ranging from 10 to 65 kg/s. The pressure, on the contrary, ranges between three distinct 

areas. Pressures of around 55, 72 and 86 bar were realized. In total, 79 combinations of pressure, 

inlet sub-cooling and mass flow rate were investigated. 

Figure 97 Input and Boundary Conditions for the Critical Power Cases 

Table 30 Input and Boundary Conditions for the Critical Power Cases 

Case Outlet pressure [bar] Inlet sub-cooling [kJ/kg] Mass flow rate [t/h]

51001 54.90 50.95 20.16

51002 54.90 51.35 20.10

51003 55.10 84.79 20.12

51004 55.00 129.38 20.19

51005 54.90 26.04 20.14

51006 54.80 56.41 55.06

51007 55.10 62.48 55.11

10

20

30

40

50

60

70

80

90

100

110

120

130

140

010407101316192225283134374043464952555861646770737679

Pressure, Inlet sub-cooling, Mass flow 

rate & Power

Case (510xx)

Pressure [bar] Inlet sub-cooling [kJ/kg] Mass flow rate [t/h]
6-58

Case Outlet pressure [bar] Inlet sub-cooling [kJ/kg] Mass flow rate [t/h]

51008 55.10 96.16 54.70

51009 55.20 96.79 55.34

51010 55.10 134.97 54.81

51011 55.20 35.33 54.70

51012 55.10 35.02 55.05

51013 55.40 64.36 65.48

51014 55.10 99.60 64.97

51015 55.00 133.75 65.52

51016 55.20 40.30 65.12

51017 55.10 55.98 44.85

51018 55.20 91.83 45.03

51019 55.00 132.07 45.28

51020 55.20 35.66 45.13

51021 71.80 51.85 10.07

51022 71.60 86.12 10.07

51023 71.70 106.75 10.00

51024 71.60 122.79 10.00

51025 71.80 25.82 10.01

51026 71.60 50.55 20.09

51027 71.70 51.44 20.07

51028 71.70 83.57 20.19

51029 71.70 106.22 20.24

51030 71.60 127.20 20.21

51031 71.60 22.61 20.21

51032 71.30 48.35 30.02

51033 71.50 82.55 30.23

51034 71.60 106.63 30.00

51035 71.80 126.80 30.12

51036 71.50 23.42 30.23

51037 71.70 59.39 55.20

51038 71.70 58.09 55.47

51039 71.80 89.53 55.05

51040 71.30 107.61 55.20

51041 72.10 113.28 54.88

51042 72.40 137.26 55.30

51043 72.70 37.73 55.10

51044 71.80 32.94 55.42

51045 71.30 54.89 60.23

51046 71.20 89.39 60.18

51047 72.30 114.29 60.10

51048 71.50 131.68 60.07

51049 71.60 33.18 60.30

51050 71.60 55.66 65.36

51051 71.70 91.82 64.99

51052 71.70 107.82 65.19

51053 71.80 132.81 65.01

51054 71.60 32.31 65.72

51055 71.30 54.21 45.17

51056 71.90 88.72 45.01
6-59

Case Outlet pressure [bar] Inlet sub-cooling [kJ/kg] Mass flow rate [t/h]

51057 72.30 110.60 45.13

51058 71.50 128.01 45.07

51059 71.40 30.59 45.35

51060 86.30 51.00 20.30

51061 86.40 50.28 20.30

51062 86.20 82.58 20.26

51063 86.00 125.79 20.31

51064 86.30 27.84 20.13

51065 86.20 54.89 55.15

51066 86.40 55.12 55.16

51067 85.60 83.85 55.00

51068 86.40 88.54 55.21

51069 86.40 130.30 55.28

51070 86.60 30.97 55.38

51071 86.00 27.55 55.15

51072 86.40 58.08 65.25

51073 86.40 91.08 64.95

51074 86.70 135.52 65.27

51075 86.50 29.55 65.22

51076 86.10 52.22 45.24

51077 86.70 88.65 45.52

51078 86.00 128.18 45.23

51079 86.50 27.81 45.24

The comparison of the experimental critical power points and the ones predicted for the 

reference scenarios are shown in Figure 98. The resulting critical power can be classified in 

three groups. The first group is between 3.0 and 3.5 MW, the second group between 5.0 and 

6.5 MW, and the last group, with the biggest range, from 7.0 to 11.0 MW. For the values below 

7.0 MW the TRACE predictions are always below the experimental values. For critical power 

values higher than 7.0 MW TRACE over- and underestimates the critical power in the same 

way. The error in percent is given in Figure 99. The average error considering all 79 cases is 

4.70 %. The error as a function of the critical power is given in Figure 100. It is visible that at 

values below 7 MW the error is always higher than 6 % while at higher critical power values 

the error can range from almost 0 to 8 %. The calculated critical power values along with 

maximal and minimal values from the uncertainty study are compared to the experimental 

values in Figure 101 for absolute values and Figure 102 for relative values. 
6-60

Figure 98 Calculated versus Measured Critical Power 

Figure 99 Percental Error of the Reference Values Compared to the Experimental Data

for the Critical Power Cases 

2

3

4

5

6

7

8

9

10

11

12

2 3 4 5 6 7 8 9 10 11 12

Critical power - calculated [MW]

Critical power - measured [MW]

+ 10 %

- 10 %

-14

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

01 04 07 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79

Error [%]

Case (510xx)
6-61

Figure 100 Error as Function of the Critical Power 

Figure 101 Comparison of the Experimental and Predicted Critical Power in

Absolute Values 

0

2

4

6

8

10

12

14

3 4 5 6 7 8 9 10 11

Error [%]

Critical power [MW]

2

3

4

5

6

7

8

9

10

11

12

01 04 07 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79

Critical power [W]

Case (510xx)

Experiment

Mean

Minimum

Maximum
6-62

Figure 102 Comparison of the Experimental and Predicted Pressure Drops for

Critical Power in Relative Values 

As Figure 101 and Figure 102 indicate, no results are obtained for cases 51021 till 51025. As a 

matter of fact, during the execution of the 93 input decks for the uncertainty analysis not all 

execution delivered results. In some cases, the critical power ratio was not calculated by TRACE 

and hence the critical power could not be evaluated. Therefore, the affected critical power cases 

have been omitted from the analysis. Only the cases with an experimental value for the critical 

power of < 3.5 caused problems. These cases are also the ones where the lowest mass flow rate 

was considered. 

Moreover, no results are given for TRACE-DAKOTA because the critical power ratio cannot be 

extracted with DAKOTA. As mentioned in sub section 5.3.3, the variable which is the subject of 

the investigation must be selected in DAKOTA. Unfortunately, that variable is not present and can 

therefore not be included in the analysis. 

The results of the critical power investigation are also gathered in Table 31. 

Table 31 Results of the Uncertainty Analysis for the Critical Power with TRACE-SUSA 

Case Ex [MW] Mean [MW] Max [MW] Min [MW] SD [MW] Error [%]

51001 6.13 5.57 5.67 5.44 0.043 -9.21

51002 6.13 5.56 5.73 5.43 0.042 -9.37

51003 6.23 5.71 5.82 5.63 0.041 -8.34

51004 6.39 5.94 6.05 5.85 0.045 -7.06

51005 5.98 5.45 5.56 5.33 0.050 -8.82

51006 9.72 9.20 9.40 9.03 0.076 -5.32

0.85

0.90

0.95

1.00

1.05

1.10

1.15

010407101316192225283134374043464952555861646770737679

Relative critical power [-]

Case (510xx)

Mean (SUSA)

Maximum

Minimum
6-63

Case Ex [MW] Mean [MW] Max [MW] Min [MW] SD [MW] Error [%]

51007 9.81 9.23 9.48 8.98 0.106 -5.93

51008 10.09 9.59 9.93 9.32 0.135 -4.97

51009 10.19 9.63 9.99 9.31 0.126 -5.46

51010 10.20 10.09 10.31 9.77 0.114 -1.09

51011 9.56 8.92 9.11 8.72 0.078 -6.74

51012 9.66 8.92 9.10 8.71 0.083 -7.69

51013 10.41 9.94 10.24 9.64 0.139 -4.55

51014 10.75 10.38 10.61 10.05 0.120 -3.47

51015 11.09 11.01 11.37 10.70 0.130 -0.74

51016 10.26 9.62 9.90 9.38 0.110 -6.27

51017 9.15 8.48 8.68 8.28 0.092 -7.30

51018 9.40 8.79 9.01 8.61 0.085 -6.45

51019 9.58 9.15 9.43 8.91 0.106 -4.44

51020 8.92 8.33 8.55 8.05 0.093 -6.61

51021 3.25

51022 3.39

51023 3.39

51024 3.46

51025 3.20

51026 5.77 5.18 5.37 5.05 0.052 -10.18

51027 5.73 5.18 5.27 5.03 0.043 -9.65

51028 5.88 5.35 5.51 5.26 0.044 -8.95

51029 5.98 5.46 5.57 5.39 0.039 -8.71

51030 6.09 5.57 5.66 5.47 0.045 -8.61

51031 5.62 5.07 5.19 4.91 0.057 -9.73

51032 7.04 6.75 6.92 6.65 0.056 -4.16

51033 7.24 6.97 7.10 6.88 0.048 -3.69

51034 7.37 7.10 7.21 6.96 0.056 -3.70

51035 7.51 7.21 7.37 7.05 0.065 -4.02

51036 6.87 6.63 6.78 6.44 0.070 -3.56

51037 8.85 8.95 9.18 8.65 0.089 1.15

51038 8.91 8.95 9.11 8.68 0.085 0.41

51039 9.20 9.17 9.40 8.92 0.098 -0.32

51040 9.37 9.40 9.73 9.18 0.115 0.27

51041 9.38 9.38 9.79 9.15 0.133 0.02

51042 9.52 9.70 10.21 9.42 0.152 1.94

51043 8.66 8.71 8.89 8.46 0.079 0.54

51044 8.69 8.74 9.01 8.50 0.085 0.55

51045 9.10 9.18 9.45 8.96 0.095 0.85

51046 9.34 9.54 10.04 9.27 0.152 2.18

51047 9.57 9.69 10.12 9.38 0.124 1.25

51048 9.72 9.95 10.46 9.55 0.169 2.32

51049 8.75 9.00 9.23 8.76 0.095 2.81

51050 9.29 9.38 9.64 9.12 0.104 0.97

51051 9.61 9.71 10.08 9.40 0.132 1.05

51052 9.72 9.89 10.18 9.58 0.129 1.72

51053 10.00 10.10 10.39 9.83 0.129 0.97

51054 9.12 9.19 9.48 8.95 0.105 0.80

51055 8.30 8.15 8.34 7.98 0.074 -1.86
6-64

Case Ex [MW] Mean [MW] Max [MW] Min [MW] SD [MW] Error [%]

51056 8.50 8.44 8.66 8.22 0.085 -0.75

51057 8.65 8.65 8.87 8.41 0.110 0.04

51058 8.89 8.76 8.92 8.54 0.089 -1.47

51059 8.15 7.97 8.14 7.80 0.087 -2.21

51060 5.29 4.85 4.99 4.75 0.047 -8.25

51061 5.29 4.85 4.99 4.72 0.052 -8.40

51062 5.40 4.99 5.11 4.89 0.044 -7.58

51063 5.62 5.21 5.31 5.07 0.048 -7.38

51064 5.17 4.72 4.84 4.58 0.066 -8.66

51065 7.84 8.17 8.38 7.90 0.087 4.22

51066 7.88 8.16 8.43 7.79 0.099 3.61

51067 8.17 8.43 8.69 8.15 0.102 3.16

51068 7.94 8.45 8.66 8.23 0.102 6.40

51069 8.49 8.85 9.31 8.51 0.140 4.18

51070 7.52 7.98 8.19 7.77 0.099 6.18

51071 7.62 7.98 8.17 7.76 0.096 4.76

51072 8.23 8.48 8.79 8.15 0.126 3.02

51073 8.53 8.72 9.12 8.52 0.119 2.29

51074 8.90 9.18 9.63 8.85 0.141 3.14

51075 7.86 8.28 8.56 7.85 0.105 5.31

51076 7.27 7.63 7.87 7.42 0.084 4.94

51077 7.61 7.87 8.12 7.69 0.079 3.46

51078 7.71 8.24 8.60 8.04 0.133 6.90

51079 6.95 7.42 7.62 7.16 0.111 6.76

The sensitivity coefficients for the TRACE-SUSA analysis, except cases 51021 and 51025, are 

shown in Figure 103 and Table 32. The ranking is given in Figure 104. Based on the sensitivity 

coefficients, the inlet temperature (inlet sub-cooling) is the most important parameter. One can 

see that a reduction of the inlet temperature results in an increase of the critical power. This is 

because with a lower inlet temperature, more heat is needed to reach critical heat flux. In addition, 

all other parameters, besides inlet temperature, mass flow rate and hydraulic diameter, are of no 

or only low importance. 

Besides the difficulties to calculate the critical power at certain parameter combinations, the U+S 

analysis provides also the coefficient of determination. For all previous investigations, that 

coefficient is close to unity indicating a well performed analysis. Unfortunately, that coefficient is 

here in the range of 0.15 to 0.8, indicating a sometimes rather poor performance, even though 

the qualitative and quantitative comparison of the reference results shows a good agreement, 

room for improvement is given. 
6-65

Figure 103 Sensitivity Coefficients for the Critical Power Analysis with TRACE-SUSA 

Figure 104 Ranking of the Uncertain Parameters for the Critical Power Analysis

with TRACE-SUSA 

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

01 0407 1013 16 1922 2528 31 3437 4043 46 4952 5558 61 6467 7073 76 79

Sensitivity coefficient

Case (510xx)

Outlet pressure Mass flow rate Inlet temperature

Wall roughness K-spacer Hydraulic diameter

Density Friction factor

0

1

2

3

4

5

6

7

8

9

01 04 07 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79

Rank

Case (510xx)

Outlet pressure Mass flow rate Inlet temperature

Wall roughness K-spacer Hydraulic diameter

Density Friction factor
6-66

Table 32 Pearson's Momentum Correlation Coefficients for the Critical Power Cases with

 TRACE-SUSA Outlet pressure Mass 

flow rate Inlet temperature Wall roughness K-spacer Hydraulic diameter Density Friction factor 

51001 0.069 0.590 -0.625 -0.067 0.021 0.231 -0.130 -0.097

51002 0.072 0.663 -0.583 -0.030 -0.071 0.184 -0.106 -0.053

51003 0.107 0.640 -0.651 -0.007 -0.009 0.143 -0.006 -0.012

51004 0.191 0.618 -0.624 -0.072 0.168 0.088 0.019 0.068

51005 0.111 0.468 -0.489 -0.105 -0.061 0.051 -0.002 -0.141

51006 0.178 0.262 -0.178 0.137 -0.050 0.525 -0.019 0.167

51007 0.101 0.207 -0.618 -0.051 -0.231 0.304 -0.208 -0.074

51008 0.258 0.332 -0.688 0.112 0.075 0.155 -0.003 0.155

51009 0.281 0.212 -0.594 -0.170 0.000 0.317 -0.153 -0.019

51010 0.086 0.203 -0.508 -0.063 -0.172 0.187 -0.037 0.106

51011 0.108 0.429 -0.362 -0.017 -0.216 0.327 -0.183 0.031

51012 0.113 0.479 -0.417 0.030 -0.254 0.365 -0.175 0.068

51013 0.134 0.426 -0.492 0.005 -0.051 0.400 -0.121 0.144

51014 0.002 0.394 -0.582 0.018 0.057 0.124 -0.171 0.308

51015 -0.013 0.444 -0.341 0.010 -0.107 0.092 -0.100 0.038

51016 0.099 0.314 -0.694 -0.068 -0.102 0.350 -0.132 0.133

51017 0.254 0.345 -0.706 -0.074 -0.145 0.391 -0.107 -0.054

51018 -0.071 0.341 -0.032 0.037 -0.345 0.507 0.015 -0.132

51019 -0.015 0.185 -0.271 -0.006 -0.092 0.359 0.084 -0.015

51020 0.004 0.385 -0.550 0.006 -0.249 0.448 -0.087 0.036

51021

51022

51023

51024

51025

51026 0.014 0.579 -0.477 -0.025 0.043 0.187 0.069 -0.087

51027 0.072 0.563 -0.663 -0.005 0.011 0.209 -0.081 -0.045

51028 0.071 0.627 -0.629 -0.148 0.042 0.051 0.008 0.117

51029 0.014 0.563 -0.476 -0.139 0.026 0.218 0.088 -0.010

51030 -0.012 0.602 -0.606 -0.188 0.021 0.143 0.010 0.069

51031 0.124 0.298 -0.420 -0.093 -0.039 0.185 0.166 -0.075

51032 -0.050 0.285 -0.558 -0.042 -0.136 0.277 -0.018 -0.032

51033 -0.048 0.351 -0.226 0.143 -0.120 0.455 0.107 -0.204

51034 -0.030 0.457 -0.587 0.099 -0.072 0.267 0.096 -0.177

51035 -0.111 0.485 -0.534 -0.045 -0.090 0.274 -0.033 0.019

51036 0.057 0.423 -0.517 -0.036 -0.021 0.311 0.044 0.047

51037 -0.178 0.152 -0.245 0.163 -0.234 0.410 -0.175 0.105

51038 -0.179 0.268 -0.215 0.060 -0.182 0.340 -0.154 0.076

51039 0.127 0.265 -0.683 -0.132 0.005 0.317 -0.078 0.005

51040 -0.150 0.134 -0.055 -0.122 -0.166 0.411 -0.068 0.090

51041 0.118 0.222 -0.384 0.111 -0.028 0.307 -0.094 0.066

51042 -0.029 0.179 -0.185 -0.084 -0.129 0.406 0.037 -0.064
6-67

Outlet pressure Mass flow rate Inlet temperature Wall roughness K-spacer Hydraulic diameter Density Friction factor 

51043 -0.187 0.171 -0.369 0.055 -0.163 0.397 -0.155 0.044

51044 -0.015 0.453 -0.216 -0.033 -0.087 0.476 0.134 0.024

51045 -0.049 -0.029 -0.276 0.080 -0.292 0.455 -0.253 -0.112

51046 0.218 0.216 -0.558 -0.040 -0.019 0.155 -0.177 0.171

51047 0.233 0.218 -0.686 0.047 0.076 0.270 0.034 0.150

51048 -0.093 0.118 -0.036 0.075 -0.215 0.356 -0.057 -0.210

51049 -0.149 0.183 -0.167 0.107 -0.160 0.399 -0.159 0.171

51050 -0.085 0.205 -0.581 -0.020 -0.044 0.419 -0.037 0.146

51051 -0.231 0.099 0.098 0.178 -0.122 0.399 -0.036 -0.017

51052 0.022 0.264 -0.709 -0.106 0.038 0.169 -0.236 0.045

51053 -0.062 -0.052 -0.404 -0.101 -0.092 0.389 -0.026 0.107

51054 -0.066 0.109 -0.286 0.066 -0.160 0.223 -0.240 0.106

51055 0.141 0.363 -0.770 -0.069 -0.020 0.253 -0.108 0.002

51056 -0.062 0.387 -0.354 0.048 -0.092 0.522 -0.119 0.111

51057 0.109 0.393 -0.738 -0.071 -0.030 0.275 -0.089 0.119

51058 -0.034 0.309 -0.427 0.090 0.063 0.359 0.136 0.126

51059 0.130 0.323 -0.626 -0.124 -0.047 0.319 -0.183 0.056

51060 -0.052 0.440 -0.610 -0.094 0.017 0.186 0.041 0.022

51061 0.054 0.478 -0.619 -0.029 -0.028 0.127 -0.080 -0.074

51062 -0.028 0.567 -0.701 -0.053 0.038 0.076 -0.003 0.138

51063 -0.005 0.523 -0.418 0.049 -0.041 0.094 0.046 0.044

51064 -0.103 0.495 -0.236 0.023 -0.167 0.041 0.014 0.077

51065 -0.197 0.116 -0.225 0.044 -0.105 0.401 0.012 0.020

51066 -0.229 0.083 -0.245 0.210 -0.071 0.367 -0.211 0.001

51067 -0.015 0.095 -0.612 -0.039 0.144 0.344 -0.077 0.205

51068 -0.162 -0.030 -0.490 -0.003 -0.143 0.455 0.100 -0.053

51069 -0.327 0.130 -0.003 -0.093 -0.062 0.245 0.062 -0.024

51070 -0.139 0.135 -0.327 0.022 -0.042 0.471 0.062 -0.036

51071 -0.194 0.197 -0.470 -0.135 -0.004 0.250 -0.050 0.135

51072 -0.247 0.143 -0.002 0.126 -0.228 0.365 0.206 0.034

51073 -0.182 0.195 -0.326 0.107 0.112 0.037 0.033 0.115

51074 -0.152 -0.147 0.077 -0.089 -0.219 0.184 0.104 0.004

51075 -0.278 0.014 -0.108 -0.123 0.002 0.413 -0.113 0.083

51076 0.071 0.361 -0.731 -0.093 0.072 0.246 -0.033 0.071

51077 -0.310 0.179 -0.090 0.104 -0.312 0.448 -0.103 -0.055

51078 0.137 0.217 -0.546 -0.089 -0.218 0.231 -0.140 0.013

6.6 Transient Analyses

For the present analysis two transients, based on phase 1, exercise 3 of the NUPEC BFBT 

benchmark, are selected. The first transient is a turbine trip without bypass and the second one 

is a re-circulation pump trip. Information regarding the time depended trends of the inlet 

temperature, the bundle mass flow rate, the outlet pressure and the assembly power are provided. 

These time trends will be used as input and boundary conditions for the uncertainty and sensitivity 
6-68

study. These time-dependent trends are given in Figure 105 till Figure 108. Both transients start 

from steady state conditions, first 10 seconds of the plots. 

At 10 seconds the turbine is isolated. The outlet pressure changes due to the fast closure of the 

turbine isolation valve. That causes a pressure wave which is propagating from the main steam 

line through the core. As a consequence, the water level collapses and a better moderation takes 

place since the density is higher. That improved moderation leads then an increase of the power. 

In order to stabilize the system and to reduce the power, the pumps are throttled. The whole 

procedure takes place within 35 to 40 seconds (starting at second 10). Later on, the mass flow 

rate is increased to nominal condition. 

During the pump trip the mass flow rate is reduced resulting in a higher void fraction. With 

increased void fraction the moderation is deteriorated and the power is decreasing. The impact 

on the outlet pressure is not as pronounced as during the turbine trip. For the next 30 seconds 

the mass flow rate is stable at 1/3 of the nominal value. At second 40 the pump(s) are back online 

and the mass flow rate increases as the power does. 

Figure 105 Inlet Temperature Evolution During the Transients 

553.5

554.0

554.5

555.0

555.5

556.0

0 10 20 30 40 50 60

Inlet temperature [K]

Time [s]

Turbine trip

Re-circulation pump trip
6-69

Figure 106 Bundle Mass Flow Rate Evolution During the Transients 

Figure 107 Outlet Pressure Evolution During the Transients 

4

5

6

7

8

9

10

11

12

13

14

15

16

0 10 20 30 40 50 60

Bundle mass flow rate [kg/s]

Time [s]

Turbine trip

Re-circulation pump trip

6.8

7.0

7.2

7.4

7.6

7.8

8.0

8.2

0 10 20 30 40 50 60

Outlet pressure [MPa]

Time [s]

Turbine trip

Re-circulation pump trip
6-70

Figure 108 Assembly Power Evolution During the Transients 

6.6.1 Results for the Pressure Drop 

The transient pressure drop for the turbine trip and the re-circulation pump trip are plotted in 

Figure 109 and Figure 110, respectively. The plots contain the experimental data (yellow dots), 

the mean value of the uncertainty calculations for TRACE-SUSA (black line) and TRACEDAKOTA (grey line) as well as their uncertainty band; red for TRACE-SUSA and blue for TRACEDAKOTA. 

The experimental data show a rather large spread which seems to be to high keeping in mind a 

reported uncertainty of the pressure of just 1 %. The reason is related to the used pressure 

sensors. As mentioned in sub section 3.4, the differential pressure taps have only been used for 

the steady state scenarios (e.g. dpt9 for the total pressure drop). During the transients, the 

absolute pressure sensors PTN010 and PTN007 were used. The specification does not 

distinguish between the different sensors when assigning a general pressure (drop) uncertainty 

of 1 %. But if one takes the difference of two absolute pressure sensors and the difference is 

rather small even a small uncertainty will yield to a large spread of the resulting pressure 

difference. As example, for the turbine trip the inlet pressure at second 0 is 7.241 MPa and the 

outlet pressure is 7.141 MPa. An uncertainty of 1 % would be 0.07 MPa or 70000 Pa. The 

difference between outlet and inlet is at the beginning of the transient only 100000 Pa. With that 

in mind, the large spread of the experimental data is comprehensible but sobering. An explanation 

why the absolute pressure taps instead of the differential pressure taps dpT9 was used cannot 

be found in the specification. An explanation could be a faster sampling time of the absolute 

sensors compared to the differential ones. 

0

1

2

3

4

5

6

7

0 10 20 30 40 50 60

Assembly power [MW]

Time [s]

Turbine trip

Re-circulation pump trip
6-71

Figure 109 Pressure Drop During the Turbine Trip Transient 

Figure 110 Pressure Drop During the Re-Circulation Pump Trip 

0.0E+00

2.0E+04

4.0E+04

6.0E+04

8.0E+04

1.0E+05

1.2E+05

0 5 10 15 20 25 30 35 40 45 50 55 60

Pressure difference [Pa]

Time [s]

Experiment

Mean-SUSA

Minimum-SUSA

Maximum-SUSA

Mean-DAKOTA

Minimum-DAKOTA

Maximum-DAKOTA

0.0E+00

2.0E+04

4.0E+04

6.0E+04

8.0E+04

1.0E+05

1.2E+05

0 5 10 15 20 25 30 35 40 45 50 55 60

Pressure difference [Pa]

Time [s]

Experiment

Mean-SUSA

Minimum-SUSA

Maximum-SUSA

Mean-DAKOTA

Minimum-DAKOTA

Maximum-DAKOTA
6-72

As the initial and boundary conditions show, the variations, as a function of time, are not limited 

to the mass flow rate. As explained above, the initiating event (closure of the turbine valve and 

shut down of a re-circulation pump) will also affect the power and the pressure with different 

magnitudes. The change of the power will change the void fraction in the bundle and therefore 

the pressure drop is not only a function of the mass flow rate since density and velocity will change 

in axial direction. 

The TRACE predictions show an underestimation during the beginning (second 0 – 10) and at 

the end (second 45 – 60) of the transient. As mentioned above, at the beginning of the transient 

the experimental pressure difference was around 1 bar. TRACE predicts a value of around 0.825 

bar. Between second 10 and 40 the TRACE predictions are much closer to the average 

experimental value. For the turbine trip, the TRACE predictions are almost identical to the average 

experimental data. In both cases, a pressure drop of about 0.4 bar can be read from the plots. 

For the re-circulation transient, the TRACE predictions with around 0.2 bar are twice as high as 

the average experimental value, 0.1 bar. A check of the transient boundary conditions shows that 

for the turbine trip the reduction of the mass flow rate is from 100 % to around 66 %. The resulting 

experimental pressure drop reduction is therefore reasonable. For the re-circulation pump trip, 

the mass flow rate is reduced from 100 % to around 33 %. Again, the resulting reduction of the 

experimental pressure drop is understandable. 

One result of the present uncertainty study is that during normal operation (100 % mass flow rate) 

the pressure drop is subject of a variation of ± 0.04 bar while for the transient part (reduced mass 

flow rate) the error band is ± 0.02 bar and ± 0.01 bar for the turbine trip and the re-circulation 

pump trip, respectively. 

It is also visible that the uncertainty band is wider for DAKOTA than for SUSA even though less 

parameters are considered in the TRACE-DAKOTA study. That is due to the different treatment 

of the inlet temperature during the uncertainty study; please refer to sub section 6.2. 

The results of the sensitivity analysis with SUSA for the pressure drop are given in Figure 111. 

As one can see, the sensitivity coefficients of inlet temperature, hydraulic diameter and form loss 

coefficient (the three most important ones in terms of influence of their variation) change with 

time. The changes are rather small but observable. The hydraulic diameter, as parameter with 

the highest importance, is gaining importance for the time the mass flow rate is reduced. That 

behavior is more pronounced during the re-circulation pump trip since the mass flow rate 

reduction is considerably larger. 

The importance of the inlet temperature is reduced during the reduced mass flow rate period. It 

drops from values of 0.4 to about 0.2 for the turbine trip and 0.1 for the re-circulation pump trip. 

The form loss coefficient, on the contrary, is slightly gaining importance. For both transients the 

sensitivity coefficients are similar. 

6.6.2 Results for the Void Fraction 

The void fraction for the three X-ray densitometer positions, 682, 1706 and 2730 mm during the 

turbine trip are plotted in Figure 112, Figure 113 and Figure 114, respectively. Even though the 

X-ray CT scanner has been used during the transient void fraction measurements, only the first 

couple of seconds have been reported. Therefore, the comparisons of predictions to X-ray CT 

scanner results are not shown in this report. 
6-73

Figure 111 Sensitivity Coefficients for the Transient Pressure Drop Analysis with SUSA 

Each of the mentioned plots shows the original reported measured void fraction and the corrected 

one in order to see the improvement and the behavior over time. The mean values for TRACESUSA and TRACE-DAKOTA are plotted along with their corresponding maximum and minimum 

values. What is plotted there are the mean, maximum and minimum values based on the 93 runs 

for each interval. In SUSA, the 60 seconds transient time are split into 100 equidistant intervals. 

For each interval the mean is calculated and the minimum and maximum are derived. In theory, 

each maximum and minimum can originate from different runs since it is not taking the one which 

has the overall minimum or maximum and a given time. 

The impact of changing input and boundary conditions can clearly be seen. During the turbine 

trip, the power is increased for a short period of time resulting in a sharp increase of the void 

fraction. This is followed by a very pronounced drop of the void fraction due to the mass flow rate 

reduction. Afterwards, the void fraction rises continuously due to the slowly decreasing pressure, 

which results in a reduced saturation temperature and therefore a higher void generation. After 

the power, pressure and mass flow rate are reestablished to nominal condition the void fraction 

at the end of the transient (60 sec.) is almost identical to the one at the beginning (0 sec.). 

The diagrams also show that the correction is most effective at higher void fractions. Especially 

at the lowest densitometer one can see a clear difference between the beginning of the transient 

(high void) and the void at second 15. There, the difference between original and corrected is 

barely visible. The qualitative comparison of the mean values of TRACE-SUSA and TRACEDAKOTA show a good agreement for all three positions. Especially, for the second level (1706 

mm), the prediction and the experimental data are almost identical. For the lower and the upper 

level one can see a trend to overestimate the experiment. 

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0 5 10 15 20 25 30 35 40 45 50 55 60

Sensitivity coefficient [-]

Time [s]

Inlet temperature (turbine trip)

Inlet temperature (pump trip)

Hydraulic diameter (turbine trip)

Hydraulic diameter (pump trip)

K spacer (turbine trip)

K spacer (pump trip)
6-74

Figure 112 Void Fraction Predictions with Uncertainty Band Compared to Original

and Corrected Turbine Trip Measurements for the First Densitometer

at 682 mm 

Figure 113 Void Fraction Predictions with Uncertainty Band Compared to Original

and Corrected Turbine Trip Measurements for the Second Densitometer 

at 1706 mm 

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 5 10 15 20 25 30 35 40 45 50 55 60

Void fraction [-]

Time [s]

Experiment (orig.)

Experiment (corr.)

Mean-SUSA

Minimum-SUSA

Maximum-SUSA

Mean-DAKOTA

Minimum-DAKOTA

Maximum-DAKOTA

Densitometer 1 @ 682 mm

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0 5 10 15 20 25 30 35 40 45 50 55 60

Void fraction [-]

Time [s]

Experiment (orig.)

Experiment (corr.)

Mean-SUSA

Minimum-SUSA

Maximum-SUSA

Mean-DAKOTA

Minimum-DAKOTA

Maximum-DAKOTA

Densitometer 2 @ 1706 mm
6-75

Figure 114 Void Fraction Predictions with Uncertainty Band Compared to Original

and Corrected Turbine Trip Measurements for the Third Densitometer

at 2730 mm 

The quantitative comparison, given in Figure 115, shows the deviation of the calculated value 

from the corrected experimental one in percent. Even though the qualitative comparison seems 

to be good for the lower level a deviation of more than 100 % can be seen directly following the 

power peak (around second 15). Steadily, the deviation reduces with a progressing transient until 

second 45. A closer look to Figure 112 shows that at second 15 the experimental void fraction is 

around 0.01 while the prediction gives 0.02. This means a factor of 2 (100 % deviation) in relative 

words but the absolute deviation is marginal, and from the practical point of view it can be 

neglected. In general, TRACE and other system codes have problems at low void fractions where 

a transition from sub cooled boiling to nucleate boiling takes place. 

For the other two axial positions, the deviations are within ± 10 %. In general, there is an 

underestimation at the beginning and at the end of the transient (0 – 10 and 55 – 60 sec.) and an 

overestimating during the transient (10 – 55 sec.). 

One reason for the deviations, besides the applicability of the physical models used in TRACE, is 

the nodalization. As mentioned, the axial locations of the sensors are at 682, 1706 and 2730 mm. 

With the rather coarse nodalization of TRACE it is impossible to extract the void fraction at exactly 

682 mm. In order to calculate them at the three given positions, a much finer nodalization would 

be necessary including different axial cell lengths. From practical point of view TRACE models 

are not intended to have cell lengths of just a few mm. In addition, the corrective measure might 

not represent the reality but a possible one. 

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0 5 10 15 20 25 30 35 40 45 50 55 60

Void fraction [-]

Time [s]

Experiment (orig.)

Experiment (corr.)

Mean-SUSA

Minimum-SUSA

Maximum-SUSA

Mean-DAKOTA

Minimum-DAKOTA

Maximum-DAKOTA

Densitometer 3 @ 2730 mm
6-76

Figure 115 Deviation of the Fredictions from the Corrected Turbine Trip

Measurements for all Three Densitometer Positions 

The plots show also that the uncertainty band is getting smaller with increasing void fractions. 

That phenomenon has been seen during the steady state scenarios for the void fraction post-test 

simulations. 

Besides that, one can see that the uncertainty band of TRACE-SUSA is enveloped by the one of 

TRACE-DAKOTA. That seems to be unrealistic since with TRACE-SUSA more parameters have 

been considered and hence the uncertainty band of TRACE-SUSA should envelop the one of 

TRACE-DAKOTA. As the steady state investigations of the void fraction showed, the hydraulic 

diameter, e.g., is not of importance for the void. Therefore, both uncertainty bands should be 

identical. The reason for that situation is, most likely, the treatment of the inlet temperature. In sub 

section 6.2, the problems have been mentioned which arose with the transient temperature 

treatment. Since the ± 1.5 K could not be considered a multiplier was used instead. Ranging from 

0.997 to 1.003, the resulting temperatures for e.g. 554 K would be 555.62 K (554 x 1.003), which 

is slightly higher than the 555.5 which would be obtained with the ± 1.5 K (554 + 1.5) procedure. 

The steady state void fraction results showed also that the inlet temperature (inlet sub-cooling) is 

the parameter where a change of it has the biggest impact. 

The void fraction recorded and predicted for the re-circulation pump trip are given in Figure 116, 

Figure 117 and Figure 118 for 682, 1706 and 2730 mm, respectively. During this transient, only 

power and mass flow rate change. After 10-15 seconds, the mass flow rate is reduced which 

automatically provokes a rise in the void fraction. That rise would be even more pronounced since 

the mass flow rate reduces to 33 % of the nominal values if the power is reduced. Therefore, a 

stable void fraction is established between second 15 and 40. 

-10

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30 35 40 45 50 55 60

Error [%]

Time [s]

Densitometer 1 @ 682 mm

Densitometer 2 @ 1706 mm

Densitometer 3 @ 2730 mm
6-77

Figure 116 Void Fraction Predictions with Uncertainty Band Compared to Original and

Corrected Re-Circulation Pump Trip Measurements for the First

Densitometer at 682 mm 

Figure 117 Void Fraction Predictions with Uncertainty Band Compared to Original and

 Corrected Re-Circulation Pump Trip Measurements for the Second

Densitometer at 1706 mm 

0.05

0.15

0.25

0.35

0.45

0.55

0.65

0 5 10 15 20 25 30 35 40 45 50 55 60

Void fraction [-]

Time [s]

Experiment (orig.)

Experiment (corr.)

Mean-SUSA

Minimum-SUSA

Maximum-SUSA

Mean-DAKOTA

Minimum-DAKOTA

Maximum-DAKOTA

Densitometer 1 @ 682 mm

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0 5 10 15 20 25 30 35 40 45 50 55 60

Void fraction [-]

Time [s]

Experiment (orig.)

Experiment (corr.)

Mean-SUSA

Minimum-SUSA

Maximum-SUSA

Mean-DAKOTA

Minimum-DAKOTA

Maximum-DAKOTA

Densitometer 2 @ 1706 mm
6-78

Figure 118 Void Fraction Predictions with Uncertainty Band Compared to Original

and Corrected Re-Circulation Pump Trip Measurements for the Third

Densitometer at 2730 mm 

Afterwards, the mass flow rate and the bundle power are increased again to nominal values. 

Hence, the void fraction at the end of the transient is similar to the initial one. 

The same general trends and behaviors as during the turbine trip can be seen here. The 

difference between original and corrected void fraction is more pronounced at higher void 

fractions, uncertainty band of TRACE-DAKOTA envelopes the one of TRACE-SUSA, the 

uncertainty band is getting smaller with higher void fractions. The main difference, between the 

actual trend, is that a general under prediction is evident in this case. 

The quantitative comparison for the re-circulation pump trip is depicted in Figure 119. The highest 

deviations can be found for the lowest densitometer position, as for the turbine trip. That trend 

has been also confirmed during the steady state scenarios: the lower the void fraction, the higher 

the deviation to the experiment. The error is less than 15 % for the first 40 seconds and less than 

25 % for the last 15 seconds. At second 11, the time of the initiation of the mass flow rate and 

power reduction, the error is in the range of 30 % for just a few seconds. The deviation for the 

highest densitometer is less than 10 % while for the one in the middle an error of 5 % or less is 

computed. 

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

0 5 10 15 20 25 30 35 40 45 50 55 60

Void fraction [-]

Time [s]

Experiment (orig.)

Experiment (corr.)

Mean-SUSA

Minimum-SUSA

Maximum-SUSA

Mean-DAKOTA

Minimum-DAKOTA

Maximum-DAKOTA

Densitometer 3 @ 2730 mm
6-79

Figure 119 Deviation of the Predictions from the corrected Re-Circulation Pump

 Trip Measurements for all Three Densitometer Positions 

As for the pressure drop, a sensitivity study has been performed with SUSA to identify the most 

important parameters and to evaluate their behavior as function of time (void fraction). The 

resulting sensitivity coefficients for inlet temperature and power are plotted in Figure 120 and 

Figure 121 for the turbine trip and the re-circulation pump trip, respectively. 

As mentioned above, the TRACE-DAKOTA uncertainty band envelopes the one of TRACESUSA. Even though the differences between TRACE-SUSA and TRACE-DAKOTA with respect 

to the treatment of the inlet temperature are marginal, the differences in the uncertainty band are 

clearly visible. The inlet temperature has been identified as the parameter with the highest 

importance, as for the steady state void fraction investigation. The values are in the range of 0.8 

– 0.9 at the beginning and at the end of the transient. They indicate a very strong relation between

inlet temperature and void fraction. It can be seen that at lower void fractions (densitometer one) 

the sensitivity is at its maximum. In addition, the lower the void fraction, the lower the impact of 

the power. Values less than 0.3 are computed for the beginning and the end of the transient. This 

means actually a very weak or even no correlation between power and void fraction. However, 

this behavior changes with time. After the mass flow rate and the power has been reduced in both 

transients, the sensitivity coefficients for the inlet temperature are decreasing while the one for 

the power is increasing. During the re-circulation pump trip this behavior is more pronounced 

since the void fractions are larger. The changes are the most visible at densitometer 1. The 

sensitivity coefficients for power and inlet temperature are almost identical at that position. 

-30

-25

-20

-15

-10

-5

0

0 5 10 15 20 25 30 35 40 45 50 55 60

Error [%]

Time [s]

Densitometer 1 @ 682 mm

Densitometer 2 @ 1706 mm

Densitometer 3 @ 2730 mm
6-80

Figure 120 Sensitivity Coefficients for the Void Fraction Related to the Turbine Trip

with SUSA

Figure 121 Sensitivity Coefficients for the Void Fraction Related to the Re-Circulation

Pump Trip with SUSA

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 5 10 15 20 25 30 35 40 45 50 55 60

Sensitivity coefficient [-]

Time [s]

Inlet temperature (densitometer 1)

Power (densitometer 1)

Inlet temperature (densitometer 2)

Power (densitometer 2)

Inlet temperature (densitometer 3)

Power (densitometer 3)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 5 10 15 20 25 30 35 40 45 50 55 60

Sensitivity coefficient [-]

Time [s]

Inlet temperature (densitometer 1) Power (densitometer 1)

Inlet temperature (densitometer 2) Power (densitometer 2)

Inlet temperature (densitometer 3) Power (densitometer 3)
7-1

7 SUMMARY AND CONCLUSION 

7.1 Summary 

The present report contains a guideline for the performance of thermal hydraulic investigations 

with the best estimate system code TRACE in combination with U+S. For two U+S tools, SUSA 

and DAKOTA, the working methodology is presented in a way that the reader/user is possible to 

reproduce the presented results or to conduct a new investigation. 

Results are shown for steady state single and two phase flow pressure drop scenarios, void 

fraction and critical power tests. Each test scenarioss has been investigated with TRACE. Due to 

the structure of the TRACE-SUSA interface it was possible that for each of these cases a U+S 

was be performed. Unfortunately, such a comprehensive analysis was not possible with TRACEDAKOTA. Instead, six representative cases were selected for each variable. 

The comparison of the reference values with the experiments showed a good agreement in 

general. Just for a limited number of scenarios an agreement was not given. The reasons for 

these discrepancies have been pointed out and only in the minority of these cases, shortcomings 

or flaws of the TRACE code are responsible. The average errors are listed in Table 33. During 

the uncertainty study, it was possible for most scenarios that the calculated uncertainty band is 

enveloping the experimental value. The sensitivity study provided a qualitative and quantitative 

way of evaluating how sensitive an output parameter is to an input parameter variation. These 

parameters are listed also in Table 33. One figure of merit to evaluate the quality of a U+S study 

is the coefficient of determination. In general a high number has been calculated for the pressure 

drop and the void fraction cases. Only for the critical power cases low numbers are computed. A 

possible explanation is that these simulations are characterized by a poor quality. These values 

are only available for SUSA but not for DAKOTA. 

Transient scenarios have been investigated as well. Two representative transients were selected. 

The first one was a turbine trip and the second one was a re-circulation pump trip. Both transients 

are characterized by variation of the pressure, the mass flow rate and the bundle power over time. 

A quantitative comparison of the void fraction at different axial levels is given in order to show the 

agreement to the measurement. Additional sensitivity studies were performed to identify the 

variation of the sensitivity coefficients as a function of time. 

Table 33 Summary of the Uncertainty and Sensitivity Investigations 

Δp (single-phase) Δp (two phase) void fraction critical power 

Error 6.83 % 4.66 % 4.46 % 3.72 % 

SUSA

R1 Hyd. diameter Hyd. diameter Inlet temperature Inlet temperature 

R2 K-spacer K-spacer Power Mass flow rate 

R3 Friction factor Friction factor - Hyd. diameter 

R2 >0.95 > 0.95 > 0.95 0.15 – 0.80 

DAKOTA 

R1 K-spacer Inlet temperature Inlet temperature - 

R2 Mass flow rate K-spacer Outlet pressure - 

R3 Inlet temperature Outlet pressure - - 

R2 NA NA NA - 
7-2

7.2 Discussion 

The mathematical theory behind SUSA and DAKOTA is similar, almost identical. Therefore, the 

results are almost identical, too. The major difference between the two programs is the way they 

are utilized. The exchange between TRACE and SUSA is based on self-written scripts, requiring 

certain programming knowledge. That allows the user to manipulate every parameter of interest. 

Since a SNAP plugin of DAKOTA exists, the user can utilize the graphical user interface of SNAP 

to assign a U+S to any TRACE calculation. This is done automatically with predefined user 

functions which mean that no additional tools or programming skills are required. The 

disadvantage of it is that the number of input and output parameters to be manipulated is limited. 

Hence, the U+S might not be as comprehensive as with SUSA due to missing input and output 

parameters in the predefined list of variables. Another major drawback of DAKOTA is that in the 

current SNAP-DAKOTA interface access to the TRACE source code parameters is not available. 

Thus, the influence of physical models on the results cannot be analyzed. With SUSA it is not a 

problem. If the source code is available, an additional TRACE module is needed which reads in 

a second input file. This second input file contains information about selected TRACE models. 

Inside the TRACE source code, flags are inserted at the selected models to manipulate them 

(usually a simple multiplier in order to change the result of the model by ± X %). This is not in 

particular a SUSA task. But since TRACE and SUSA are used as a standalone tool independent 

of the framework of SNAP the user has more freedom during the application. 

As mentioned, the results of TRACE-SUSA and TRACE-DAKOTA are close together. The only 

difference occurred during the transient void fraction investigations. Despite the fact that TRACEDAKOTA employs less parameters than TRACE-SUSA, the uncertainty band is enveloping the 

one of TRACE-SUSA. A good explanation to that is the way the transient inlet temperature is 

treated in DAKOTA. As the sensitivity study revealed, the inlet temperature is one major 

parameter for the void fraction evaluation. Even (very) small changes of the temperature will 

provoke very pronounced changes in the void. 

As shown in sub section 6.5 some critical power cases (low mass flow rate, low critical power) 

could not have been simulated. It was also shown that the sensitivity study revealed a somehow 

poor analysis. The reason why especially these cases could not be performed is unclear and must 

be identified in further efforts. 

Besides the physical and engineering part of the sub section, it should be mentioned that at the 

time of the analysis no user manual was existing for DAKOTA and SNAP-DAKOTA. That could 

be a possible reason why some results are not satisfying 

7.3 Fields of Improvement 

The investigations showed some fields where investigations should be done in order to improve 

the results. The first is related to TRACE. As shown in sub section 6.5 problems occured during 

the critical power simulations. At low mass flow rate it was not possible to extract the critical power 

or to be more precise the critical power ratio. TRACE simply did not print these numbers in the 

output file. It needs to be checked whether that problem is related to the applied correlation 

(validation) or to the way the correlation is called/used inside TRACE (verification). 

A second field for TRACE improvements is the sub cooled boiling model. As shown during the 

transient void fraction investigation related to the turbine trip the predictions of TRACE differ 
7-3

considerably from the experiment. The review of the implemented sub cooled boiling models will 

be done in the aftermath of the present investigation. The sub cooled boiling process is 

characterized by its complex nature due to involvement of several phenomena like evaporation 

and condensation. The present TRACE model is based on the work of Lahey, Zuber & Saha and 

originates from the 1970’s (1). An improvement would require the analysis of recent experiments. 

DAKOTA, to be more precise its implementation in SNAP, has also the potential for 

improvements, especially the access to TRACE source code parameters would be preferable. As 

shown in the previous sections, not all TRACE input deck parameters can be used for the U+S 

study. Either the parameters cannot be selected or it is too time consuming to change every 

parameter (e.g. each volume or flow area of the cells) by hand. Furthermore, an option to correlate 

two or more parameters to each other was not found. This is especially necessary if the change 

of one parameter requires the change of another one, such as the change of diameter, flow area 

and volume at the same time. Besides the missing input parameter in the DAKOTA environment, 

some output parameters are not listed. That is the reason why no U+S study was performed for 

the critical power scenarios. In addition, in the present implementation status of DAKOTA only 

one sensitivity measure is available, Pearson’s product moment coefficient. SUSA offers four 

measures; Pearson’s product momentum correlation coefficient, Spearman’s rank correlation 

coefficient, Kendall’s tau and Blomqvist’s medial correlation coefficient. Furthermore, SUSA can 

compute the ordinary coefficient, the partial correlation coefficient and the standardized 

regression coefficient for each of the four sensitivity measures. For reasons of comparability it 

would be reasonable if more than one sensitivity measure is available in DAKOTA. 

7.4 Conclusion 

The investigation showed that TRACE is able to reproduce the experimental results with a high 

magnitude of agreement. The existing discrepancies between the experimental data and the 

predictions can be explained. By means of the U+S study, the investigation showed that even 

small variations of input parameters sometimes have a huge influence on selected output 

parameters. The general conclusion of this work and this report is that TRACE in combination 

with SUSA or DAKOTA is ready to be applied for further applications like large scale integral 

experimental facilities or even real plants. 

7.5 Outlook 

The next step is the application of these tools/programs to bigger problems like real plants in order 

to evaluate the design. Furthermore, valuable insights can be gained during the investigation of 

transients or accident scenarios such as LOCA’s. 

Besides the application of TRACE in combination with SUSA or DAKOTA, the validation of 

TRACE is not finished and my not be finished at all. The INR is strongly involved in two major 

fields of TRACE application, among others. The first application is the validation regarding LWR, 

especially BWR applications. The successful simulation of BFBT experiments is a prerequisite for 

the application to BWRs. The focus on the BWR application is the simulation of operational 

transients where a feedback between thermal hydraulic and neutron kinetic is present. In order to 

describe the phenomena taking place in a BWR it is necessary to improve the models of TRACE 

but also of the neutronic counterpart. 
7-4

The second field of application is related to liquid metals. Thereby, the implementation of new 

models is necessary to describe coolants like sodium, lead and lead-bismuth eutectics. For LWRs 

in general and BWRs in particular routines are available to describe the heat transfer or the wall 

drag. These models have been validated over the last decade by many members of the CAMP 

project. Concerning liquid metals, the validating process has just started. 

In both cases, the application of U+S is helpful to determine whether or not the design withstand 

the operational or transient conditions. 
8-1

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[23] N. Blomqvist, "On a measure of dependence between two random variables," The Annals of 

mathematical Statistics, no. 21, pp. 593-600, 1950. 

[24] B. Adams, K. Dalbey, M. Eldred, D. Gay, L. Swiler, W. Bohnhoff, J. Eddy, K. Haskell, P. 

Hough and S. Lefantzi, "DAKOTA, A Multilevel Parallel Object-Oriented Framework for 

Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity 

Analysis Version 5.1 User’s Manual," Sandia National Laboratories, Livermore, California, 

USA, 2011.

[25] APT1, "Symbolic Nuclear Analysis Package (SNAP) - User's Manual," Applied 

Programming Technology, Inc., 2011.

[26] W. Jäger, V. Sánchez and R. Macián-Juan, "On the uncertainty and sensitivity analysis of 

experiments with supercritical water with TRACE and SUSA," in 18th International 

Conference on Nuclear Enginnering (ICONE-18), Xi'an, China, 2010. 

[27] B. Neykov, L. Hochreiter, K. Ivanov, H. Utsuno, E. Sartori and M. Martin, "NUPEC BWR 

Full-Size Fine-Mesh Bundle Test (BFBT Benchmark) Volume II: Uncertainty and sensitivity 

analyses of void distribution and critical power - specification," 2007. 

[28] M. Glück, "Validation of the sub-channel code F-COBRA-TF Part II: Recalculation of void 

measurements," Nuclear Engineering and Design, no. 238, pp. 2317-2327, 2008b. 
A-1

APPENDIX A TRACE.INP 

free format

*

*************

* main data *

*************

*

* numtcr ieos inopt nmat id2o

1 0 1 0 0

* 

*****************

* namelist data *

*****************

* 

&inopts

dtstrt=-1.0,

iadded=0,

idiag=4,

ikfac=1,

inlab=3,

iogrf=0,

ioinp=0,

iolab=0,

ipowr=1,

isscvt=1,

nosets=0,

nsdl=0,

nsdu=0,

usesjc=3,

xtvres=4,

npower=1

&end

* 

***************

* Model Flags *

***************

*

* dstep timet

0 0.0

* stdyst transi ncomp njun ipak

1 0 4 2 1

* epso epss

1.0E-4 1.0E-4

* oitmax sitmax isolut ncontr nccfl

25 25 0 0 0 

* ntsv ntcb ntcf ntrp ntcp

5 6 6 0 0

* 

*************************

* component-number data *

*************************
A-2

* 

* Component input order (IORDER)

*-- type ---- num ----- name ---------------- + jun1 jun2 jun3

* FILL * 100 s * Inlet + 10

* CHAN * 200 s * Bundle + 10 20

* POWER * 201 s * Power + 

* BREAK * 300 e * Outlet + 20

* 

**************************************************

* Starting Signal Variable Section of Model *

**************************************************

* 

* idsv isvn ilcn icn1 icn2

1 0 0 0 0

*n: pressure

* 

* idsv isvn ilcn icn1 icn2

106 21 200 1 0 

* 

* idsv isvn ilcn icn1 icn2

206 75 200 25 0

*n: pressure

* 

* idsv isvn ilcn icn1 icn2

210 21 200 25 0

*n: pressure

* 

* idsv isvn ilcn icn1 icn2

211 21 300 1 0

**************************************************

* Finished Signal Variable Section of Model *

**************************************************

* 

*********************************************

* Starting Control System Section of Model *

*********************************************

* 

****** Control Blocks ******

* 

* idcb icbn icb1 icb2 icb3

-206 59 210 211 0

* cbgain cbxmin cbmax cbcon1 cbcon2

1.0 -1.0E20 1.0E20 0.5 0.5

* 

* 

* idcb icbn icb1 icb2 icb3

-207 9 0 0 0

* cbgain cbxmin cbmax cbcon1 cbcon2

1.0 -1.0E20 1.0E20 3.708 0.0

* 

* 

* idcb icbn icb1 icb2 icb3

-208 9 0 0 0

* cbgain cbxmin cbmax cbcon1 cbcon2

1.0 -1.0E20 1.0E20 9.806 0.0
A-3

* 

*n: geodatic

* 

* idcb icbn icb1 icb2 icb3

-209 104 3 0 0

* cbgain cbxmin cbmax cbcon1 cbcon2

1.0 -1.0E20 1.0E20 0.0 0.0

* ids * 206 -207 -208e

* 

*n: Outlet

* 

* idcb icbn icb1 icb2 icb3

-211 3 -206 -209 0

* cbgain cbxmin cbmax cbcon1 cbcon2

1.0 -1.0E20 1.0E20 0.0 0.0

* 

* 

* idcb icbn icb1 icb2 icb3

-300 54 106 -211 0

* cbgain cbxmin cbmax cbcon1 cbcon2

1.0 -1.0E20 1.0E20 0.0 0.0

* 

*********************************************

* Finished Control System Section of Model *

*********************************************

* 

******* type num userid component name

fill 100 0 Inlet

* jun1 ifty ioff

10 2 0

* twtold rfmx concin felv

0.0 1.0E20 0.0 0.0

* dxin volin alpin vlin tlin

0.1545 1.462034E-3 0.0 0.0 307.550000

* pin pain flowin vvin tvin

2.0000E+05 0.0 2.750000 0.0 307.550000

* 

* 

******* type num userid component name

chan 200 0 Heizstabbuendel

* ncell nodes jun1 jun2 epsw

25 3 10 20 2.5000E-6

* nsides

2 

* Water Rod inlet junction

* nclk junlk ncmpto nclkto nlevto

1 210 0 0 0

* theta

0.0

* Water Rod outlet junction

* nclk junlk ncmpto nclkto nlevto

24 220 0 0 0

* theta

0.0

* ichf iconc iaxcnd liqlev nhcom
A-4

2 0 0 0 0

* width th houtl houtv toutl

0.516265 3.0E-3 0.0 0.0 307.550000

* toutv advbwrf quadsym numwrods nvfrays

307.550000 1 2 1 0

* ngrp nchans nodesr nrow ncrz

5 1 22 8 24

* icrnk icrlh nmwrx nfci nfcil

0 0 0 0 0

* fmon reflood nzmax nzmaxw ibeam

0 0 100 100 0

* dznht dznhtw dtxht1 dtxht2

1.0E-3 1.0E-3 2.0 10.0

* hgapo pdrat pldr fucrac norad

6300.0 1.3170732 0.0 1.0 1

* emcif1 emcif2 emcif3 noani

0.0 0.0 0.0 0

* emcof1 emcof2 emcof3

0.0 0.0 0.0

* dx * 0.1545 0.1545 0.1545 0.1545s

* dx * 0.1545 0.1545 0.1545 0.1545s

* dx * 0.1545 0.1545 0.1545 0.1545s

* dx * 0.1545 0.1545 0.1545 0.1545s

* dx * 0.1545 0.1545 0.1545 0.1545s

* dx * 0.1545 0.1545 0.1545 0.1545s

* dx * 0.1e

* vol * f 1.5112E-3 e

* fa * f 9.7810E-3 e

* kfac * 0.0 0.0 0.0 1.2 s

* kfac * 0.0 0.0 1.2 0.0 s

* kfac * 0.0 0.0 1.2 0.0 s

* kfac * 0.0 1.2 0.0 0.0 s

* kfac * 1.2 0.0 0.0 0.0 s

* kfac * 1.2 0.0 0.0 1.2 s

* kfac * 0.0 0.0e

* grav * f 1.0 e

* hd * f 0.01295 e

* nff * f 1 e

* alp * f 0.0 e

* vl * f 0.0 e

* vv * f 0.0 e

* tl * f 307.55000 e

* tv * f 307.55000 e

* p * f 2.0000E+05 e

* pa * f 0.0 e

* qppp * f 0.0 e

* mat * 12 12 e

* tw * f 307.55000 e

* rdx * 12.0 19.0 22.0 7.0 1.0e

* radrd * 0.0 4.41667E-4 8.83333E-4 1.325E-3 1.76667E-3s

* radrd * 2.20833E-3 2.65E-3 2.81667E-3 2.98333E-3 3.15E-3s

* radrd * 3.31667E-3 3.48333E-3 3.65E-3 3.85E-3 4.05E-3s

* radrd * 4.25E-3 4.45E-3 4.65E-3 4.85E-3 5.28333E-3s

* radrd * 5.71667E-3 6.15E-3e

* matrd * 4 4 4 4s
A-5

* matrd * 4 4 5 5s

* matrd * 5 5 5 5s

* matrd * 4 4 4 4s

* matrd * 4 4 12 12s

* matrd * 12e

* nfax * f 3 e

* rftn * f 307.55000 e

* rftn * f 307.55000 e

* rftn * f 307.55000 e

* rftn * f 307.55000 e

* rdpwr * 0.0 0.0 0.0 0.0 0.0s

* rdpwr * 0.0 1.0 1.0 1.0 1.0s

* rdpwr * 1.0 1.0 1.0 0.0 0.0s

* rdpwr * 0.0 0.0 0.0 0.0 0.0s

* rdpwr * 0.0 0.0e

* cpowr * 1.3 1.15 0.89 0.45e

* radpw * f 1.0 e

* fpuo2 * 0.0 0.0 0.0 0.0e

* ftd * 1.0 1.0 1.0 1.0e

* gmix * f 0.0e

* pgapt * 0.0 0.0 0.0 0.0e

* burn * f 0.0 e

* burn * f 0.0 e

* burn * f 0.0 e

* burn * f 0.0 e

* mrod * 2 1 2 1 1s

* mrod * 2 1 2 1 4s

* mrod * 3 3 3 4 2s

* mrod * 1 2 3 3 3s

* mrod * 3 3 4 2 1s

* mrod * 3 3 5 5 3s

* mrod * 3 2 1 3 3s

* mrod * 5 5 3 3 2s

* mrod * 2 4 3 3 3s

* mrod * 3 4 2 1 2s

* mrod * 4 3 3 4 2s

* mrod * 1 2 1 2 2s

* mrod * 2 2 1 2 6e

* partial length rods

* i j levrod

-1 

* 

* water rod locations *

* i j flag xloc yloc

4 4 1 0.06625 -0.06625

4 5 1 0.0 0.0

5 4 1 0.0 0.0

5 5 1 0.0 0.0

-1 

* water rod data sets

* 

* igeom wrnodes

1 3

* wrinlet wroutlet dia sidea sideb

1 24 0.034 0.0 0.0
A-6

* th rcorner flowarea flwareai flwareao

1.0E-3 0.0 9.079203E-4 9.079203E-4 9.079203E-4 

* hd hdri hdro thrmdiai thrmdiao

0.032 0.032 0.032 0.032 0.032

* wrflossi wrflosso wrrlossi wrrlosso

1.0E20 1.0E20 1.0E20 1.0E20

* matwr * f 12 e

* tw * f 307.55000 e

* 

* 

******* type num userid component name

break 300 0 Outlet

* jun1 ibty isat ioff adjpress

20 0 0 1 0

* dxin volin alpin tin pin

0.1545 1.462034E-3 0.0 307.550000 2.0000E+05

* pain concin rbmx poff belv

0.0 0.0 1.0E20 0.0 0.0

* 

*

*****************************************

* Starting Power Components *

*****************************************

* 

******* type num userid component name

power 201 1 Power

* numpwr chanpow

1 1

* htnum * 200e

* irpwty ndgx ndhx nrts nhist

6 0 0 100 0

* irpwtr irpwsv nrpwtb nrpwsv nrpwrf

0 1 2 0 0

* izpwtr izpwsv nzpwtb nzpwsv nzpwrf

0 1 4 0 0

* ipwrad ipwdep promheat decaheat wtbypass

0 0 0.0 0.0 0.0

* nzpwz nzpwi nfbpwt nrpwr nrpwi

0 0 0 1 0

* react tneut rpwoff rrpwmx rpwscl

0.0 0.0 0.0 1.0E20 1.0

* rpowri zpwin zpwoff rzpwmx

0.1 0.0 -1.0E19 1.0E20

* extsou pldr pdrat fucrac

0.0 0.0 1.0 1.0

* zpwtb1* 0.0s

* zpwtb1* 0.46 0.58 0.69 0.79 0.88s

* zpwtb1* 0.99 1.09 1.22 1.22 1.34s

* zpwtb1* 1.34 1.40 1.40 1.34 1.34s

* zpwtb1* 1.22 1.22 1.09 0.99 0.88s

* zpwtb1* 0.79 0.69 0.58 0.46s

* zpwtb2* 1.0s

* zpwtb2* 0.46 0.58 0.69 0.79 0.88s

* zpwtb2* 0.99 1.09 1.22 1.22 1.34s

* zpwtb2* 1.34 1.40 1.40 1.34 1.34s
A-7

* zpwtb2* 1.22 1.22 1.09 0.99 0.88s

* zpwtb2* 0.79 0.69 0.58 0.46s

* zpwtb3* 2.0s

* zpwtb3* 0.46 0.58 0.69 0.79 0.88s

* zpwtb3* 0.99 1.09 1.22 1.22 1.34s

* zpwtb3* 1.34 1.40 1.40 1.34 1.34s

* zpwtb3* 1.22 1.22 1.09 0.99 0.88s

* zpwtb3* 0.79 0.69 0.58 0.46s

* zpwtb4* 1.0E6s

* zpwtb4* 0.46 0.58 0.69 0.79 0.88s

* zpwtb4* 0.99 1.09 1.22 1.22 1.34s

* zpwtb4* 1.34 1.40 1.40 1.34 1.34s

* zpwtb4* 1.22 1.22 1.09 0.99 0.88s

* zpwtb4* 0.79 0.69 0.58 0.46e

* rpwtbr* 0.0 0.1s

* rpwtbr* 100.0 0.1e

*****************************************

* Finished Power Components *

*****************************************

* 

end

* 

*****************

* Timestep Data *

*****************

* dtmin dtmax tend rtwfp

1.0E-6 0.01 100.0 10.0

* edint gfint dmpint sedint

100.0 0.1 100.0 100.0

* 

* endflag

-1.0

B-1

APPENDIX B TRACE.OUT 

===========================================================================================================

trac large edit

problem time is 0.000000E+00 s, time-step size is 3.9724E-03 s, time-step number is 455, outer-iteration number 

is 1

maximum convective power differance has been 0.0000000E+00 w in component 200002 at time-1.0000000E+00 s

time-step size was limited by component 0 at cell 26 to 4.5025E-01 s

average outer-iteration count over the last 456 time steps was 3.068

last minimum number of outer iterations was 1 at time step 454

(limited by component 200 with fr.error of 2.7052E-07)

last maximum number of outer iterations was 12 at time step 292

(limited by component 200 with fr.error of 9.9715E-07)

total number of times that each component (id#) was the last to converge since the last short edit

4( 200001) 451( 200) 0( 100) 0( 300)

current maximum time-step sizes and limitation counts since the last short edit

delamx delcmx deldmx delemx delpmx delrmx delvmx delxmx 

 1.0000E+08 s 1.0000E+08 s 1.0000E+08 s 1.0000E+08 s 1.0000E+08 s 1.0000E+08 s 4.5025E+02 s 

1.0000E+08 s

0 50 0 0 0 0 0 0 

further limitation counts on what controls delcmx

dtlmx dtvmx dprmx dtsms dtrmx delt/2

0 0 49 0 0 1

cpu execution time of this run is 3.603623E+00 s

total time steps since time 0.0 s is 455

total cpu time since time 0.0 s is 3.603623E+00 s

********************************** signal-variable values at time -0.00397 s 

*************************************

id sig.var. id sig.var. id sig.var. id sig.var. id sig.var. 

1 9.219819E-02 106 2.379322E+05 206 9.948135E+02 210 2.012821E+05 211 

2.000000E+05

time (s) pressure (pa) lq den (kg/m3) pressure (pa) pressure 

(pa)

******************************** control-block output values at time -0.00397 s 

***********************************

id con.blk. id con.blk. id con.blk. id con.blk. id con.blk.

 -206 2.006411E+05 -207 3.708000E+00 -208 9.806000E+00 -209 3.617206E+04 -211 

2.368131E+05

* * * * * 

 -300 1.119079E+03

*

C-1

APPENDIX C MEDUSA.PRN 

Uncertainty and Sensitivity Analysis

DATUM: 2012/02/02

TIME: 10:00

TYPE OF DESIGN: SIMPLE RANDOM

NUMBER OF PARAMETERS = 9

NUMBER OF FULLY DEPENDENT PARAMETERS = 1

NUMBER OF FREE PARAMETERS = 8

SAMPLE SIZE = 93

INITIAL DSEED = 123457.0

===============================================================

DISTRIBUTIONS OF THE PARAMETERS

=================================

PARAMETER NO. 1 : N O R M A L DISTRIBUTION

WITH MY= 1.0000E+00, SIGMA= 1.0000E-02

TRUNCATED AT ITS

1.59E+01 %- AND 8.41E+01 %-QUANTILES

---------------------------------------------------------------

PARAMETER NO. 2 : N O R M A L DISTRIBUTION

WITH MY= 1.0000E+00, SIGMA= 1.0000E-02

TRUNCATED AT ITS

1.59E+01 %- AND 8.41E+01 %-QUANTILES

---------------------------------------------------------------

PARAMETER NO. 3 : N O R M A L DISTRIBUTION

WITH MY= 0.0000E+00, SIGMA= 1.5000E+00

TRUNCATED AT ITS

1.59E+01 %- AND 8.41E+01 %-QUANTILES

---------------------------------------------------------------

PARAMETER NO. 4 : N O R M A L DISTRIBUTION

WITH MY= 1.0000E+00, SIGMA= 5.0000E-02

TRUNCATED AT ITS

1.59E+01 %- AND 8.41E+01 %-QUANTILES

---------------------------------------------------------------

PARAMETER NO. 5 : N O R M A L DISTRIBUTION

WITH MY= 1.0000E+00, SIGMA= 5.0000E-02

TRUNCATED AT ITS

1.59E+01 %- AND 8.41E+01 %-QUANTILES

---------------------------------------------------------------

PARAMETER NO. 6 : N O R M A L DISTRIBUTION

WITH MY= 1.0000E+00, SIGMA= 1.0000E-02

TRUNCATED AT ITS

1.59E+01 %- AND 8.41E+01 %-QUANTILES

---------------------------------------------------------------

PARAMETER NO. 7 : N O R M A L DISTRIBUTION

WITH MY= 1.0000E+00, SIGMA= 1.9900E-02
C-2

TRUNCATED AT ITS

1.59E+01 %- AND 8.44E+01 %-QUANTILES

---------------------------------------------------------------

PARAMETER NO. 8 : N O R M A L DISTRIBUTION

WITH MY= 1.0000E+00, SIGMA= 1.0000E-02

TRUNCATED AT ITS

1.59E+01 %- AND 8.41E+01 %-QUANTILES

---------------------------------------------------------------

PARAMETER NO. 9 : N O R M A L DISTRIBUTION

WITH MY= 1.0000E+00, SIGMA= 5.0000E-02

TRUNCATED AT ITS

1.59E+01 %- AND 8.41E+01 %-QUANTILES

---------------------------------------------------------------

===============================================================

FULLY DEPENDENT PARAMETERS

============================

DEPENDENT CORRESPONDING GRADE- 

# PARAMETER FREE PARAMETER CORRELATION

1 7 6 1.0

--------------------------------------------------------------

FREE PARAMETERS AND THE CORRESPONDING

COMPLETELY DEPENDENT PARAMETERS

INDEX OF +/- INDICES OF THE CORRESPONDING

# FREE PARAM. COMPLETELY DEPENDENT PARAMETERS

1 1

2 2

3 3

4 4 

5 5

6 6 7

7 8

8 9

REQUIRED MEASURES OF ASSOCIATION BETWEEN FREE PARAMETERS

========================================================

PAR.1 PAR.2 MEASURE TYPE

---------------------------------------------------------------

CONTROL OF THE COMPUTATION OF THE CORRELATION

OF THE TRANSFORMED NORMAL BY NUMERICAL INTEGRATION

( IF NECESSARY ) :

MAXIMUM NUMBER OF ITERATIONS = 20

DESIRED ACCURACY OF ITERATION PROCEDURE= 2.5000E-02

P A R A M E T E R V A L U E S O F T H E D E S I G N

RUN INDEX OF PARAMETER

1 2 3 4

1 1.0091E+00 9.9578E-01 7.0899E-01 1.0059E+00

2 1.0074E+00 9.9795E-01 -1.4338E+00 1.0075E+00
C-3

3 9.9227E-01 9.9819E-01 -4.0000E-01 9.6716E-01

4 9.9512E-01 9.9123E-01 5.4987E-01 1.0345E+00

5 1.0028E+00 1.0059E+00 -9.9602E-02 1.0282E+00

6 1.0031E+00 1.0037E+00 -3.8254E-02 9.5678E-01

7 1.0088E+00 9.9115E-01 -9.7341E-01 9.8529E-01

8 1.0094E+00 1.0087E+00 -1.1079E+00 9.6143E-01

9 1.0069E+00 1.0070E+00 -2.5163E-01 1.0096E+00

10 1.0033E+00 9.9381E-01 -1.4017E+00 9.6120E-01

11 1.0062E+00 9.9526E-01 1.4128E+00 1.0109E+00

12 9.9184E-01 9.9931E-01 1.0303E-01 1.0064E+00

13 9.9569E-01 9.9791E-01 -1.1151E+00 9.8905E-01

14 1.0055E+00 1.0051E+00 2.6796E-01 1.0190E+00

15 9.9574E-01 1.0049E+00 -1.4218E+00 1.0161E+00

16 9.9818E-01 1.0060E+00 -4.6491E-01 9.9170E-01

17 1.0067E+00 9.9963E-01 -7.8914E-01 9.7399E-01

18 1.0005E+00 1.0095E+00 -5.2672E-01 9.7641E-01

19 1.0074E+00 9.9273E-01 3.7218E-01 1.0171E+00

20 9.9802E-01 9.9871E-01 2.7618E-01 1.0159E+00

21 1.0054E+00 1.0062E+00 1.5286E-01 1.0153E+00

22 1.0069E+00 9.9045E-01 -9.8377E-01 9.9923E-01

23 1.0035E+00 9.9456E-01 6.3658E-01 1.0343E+00

24 9.9590E-01 1.0079E+00 -1.6739E-01 1.0239E+00

25 1.0056E+00 1.0033E+00 -8.8277E-01 9.8952E-01

26 1.0003E+00 9.9698E-01 -1.4097E+00 9.7315E-01

27 1.0025E+00 1.0038E+00 5.4078E-01 9.7047E-01

28 1.0005E+00 1.0044E+00 -1.4193E+00 9.6151E-01

29 1.0094E+00 9.9924E-01 4.0093E-01 1.0210E+00

30 9.9513E-01 1.0017E+00 1.1163E-01 1.0199E+00

31 1.0065E+00 9.9459E-01 -1.2241E+00 1.0068E+00

32 9.9442E-01 1.0047E+00 -9.7198E-02 1.0016E+00

33 1.0033E+00 9.9341E-01 -1.4340E+00 1.0362E+00

34 1.0044E+00 9.9133E-01 1.2405E-01 1.0317E+00

35 9.9369E-01 9.9905E-01 -1.1043E+00 9.6407E-01

36 1.0025E+00 9.9175E-01 1.4810E+00 9.8630E-01

37 1.0076E+00 9.9295E-01 -8.4229E-01 9.5251E-01

38 1.0050E+00 9.9671E-01 1.3930E+00 1.0371E+00

39 1.0099E+00 9.9085E-01 5.0285E-01 9.8797E-01

40 9.9526E-01 9.9736E-01 3.1890E-01 1.0451E+00

41 9.9732E-01 9.9605E-01 -5.1195E-01 9.8416E-01

42 9.9121E-01 9.9413E-01 1.3027E+00 9.5346E-01

43 1.0032E+00 9.9341E-01 -6.9382E-01 9.9855E-01

44 1.0060E+00 9.9739E-01 -4.9315E-01 1.0191E+00

45 9.9217E-01 9.9933E-01 4.1669E-01 9.7092E-01

46 9.9692E-01 1.0045E+00 -1.0865E+00 9.7738E-01

47 1.0083E+00 1.0029E+00 -1.1937E+00 1.0198E+00

48 9.9277E-01 9.9188E-01 1.3539E+00 1.0345E+00

49 9.9534E-01 9.9415E-01 8.5235E-02 9.8243E-01

50 1.0055E+00 1.0081E+00 -1.2160E+00 1.0260E+00

51 1.0084E+00 9.9870E-01 6.5411E-01 1.0000E+00

52 9.9131E-01 1.0005E+00 -1.4297E+00 1.0001E+00

53 9.9774E-01 1.0084E+00 5.2083E-01 9.9646E-01

54 9.9584E-01 9.9031E-01 2.2974E-01 1.0369E+00

55 1.0039E+00 1.0019E+00 -7.1682E-01 1.0103E+00

56 1.0015E+00 1.0022E+00 -4.8233E-01 1.0359E+00

57 1.0046E+00 9.9238E-01 1.0862E+00 9.8143E-01
C-4

58 9.9597E-01 9.9285E-01 9.3704E-01 9.7640E-01

59 1.0072E+00 9.9456E-01 7.0515E-01 9.5786E-01

60 1.0007E+00 9.9566E-01 -1.1160E+00 9.6265E-01

61 1.0075E+00 9.9832E-01 4.8105E-01 9.6804E-01

62 9.9608E-01 1.0002E+00 1.4391E+00 9.8761E-01

63 1.0037E+00 9.9797E-01 -9.2556E-01 1.0216E+00

64 1.0065E+00 1.0079E+00 1.0424E+00 9.7370E-01

65 9.9944E-01 9.9882E-01 7.5662E-01 9.8936E-01

66 1.0024E+00 1.0048E+00 1.1548E+00 1.0164E+00

67 9.9388E-01 9.9780E-01 8.7341E-01 1.0471E+00

68 9.9782E-01 1.0099E+00 -1.1552E+00 9.9027E-01

69 9.9552E-01 1.0006E+00 -4.8103E-01 9.5240E-01

70 9.9478E-01 9.9301E-01 1.0377E+00 1.0229E+00

71 1.0002E+00 1.0061E+00 2.8691E-01 1.0173E+00

72 1.0009E+00 1.0043E+00 4.7711E-01 1.0096E+00

73 9.9154E-01 1.0063E+00 6.4357E-01 1.0100E+00

74 1.0055E+00 9.9182E-01 1.3089E+00 1.0294E+00

75 9.9504E-01 1.0070E+00 -5.2694E-01 1.0401E+00

76 1.0022E+00 1.0025E+00 8.7840E-01 1.0039E+00

77 1.0039E+00 1.0047E+00 6.6405E-01 1.0077E+00

78 1.0092E+00 9.9101E-01 -1.0129E+00 1.0347E+00

79 9.9628E-01 9.9082E-01 1.9146E-01 1.0179E+00

80 1.0065E+00 1.0077E+00 -9.5867E-01 1.0235E+00

81 1.0005E+00 1.0022E+00 -1.1187E+00 9.9107E-01

82 9.9730E-01 1.0047E+00 -2.7360E-01 1.0411E+00

83 9.9446E-01 9.9154E-01 -1.1386E+00 9.8745E-01

84 1.0047E+00 1.0042E+00 9.4720E-02 9.8136E-01

85 1.0055E+00 1.0044E+00 1.2541E+00 1.0288E+00

86 9.9231E-01 1.0060E+00 5.1777E-01 1.0062E+00

87 1.0031E+00 1.0043E+00 7.9292E-01 9.8762E-01

88 1.0074E+00 1.0076E+00 6.0472E-01 9.8573E-01

89 9.9742E-01 9.9473E-01 7.5922E-01 9.8535E-01

90 1.0006E+00 9.9726E-01 9.4857E-02 9.7161E-01

91 9.9731E-01 1.0008E+00 7.2897E-01 9.7259E-01

92 1.0009E+00 9.9090E-01 1.6013E-01 9.5061E-01

93 9.9074E-01 9.9281E-01 6.8196E-01 1.0106E+00

P A R A M E T E R V A L U E S O F T H E D E S I G N

RUN INDEX OF PARAMETER

5 6 7 8

1 1.0315E+00 9.9118E-01 9.8245E-01 1.0096E+00

2 9.9904E-01 9.9399E-01 9.8807E-01 9.9487E-01

3 1.0057E+00 1.0075E+00 1.0150E+00 9.9631E-01

4 9.5441E-01 1.0072E+00 1.0145E+00 9.9964E-01

5 1.0138E+00 9.9400E-01 9.8809E-01 1.0000E+00

6 1.0025E+00 1.0014E+00 1.0028E+00 1.0040E+00

7 1.0396E+00 9.9409E-01 9.8827E-01 1.0049E+00

8 1.0227E+00 1.0071E+00 1.0143E+00 1.0065E+00

9 9.6598E-01 1.0062E+00 1.0124E+00 1.0053E+00

10 1.0053E+00 9.9498E-01 9.9003E-01 9.9589E-01

11 9.7171E-01 1.0007E+00 1.0015E+00 9.9181E-01

12 9.8158E-01 9.9523E-01 9.9054E-01 9.9272E-01

13 1.0418E+00 1.0030E+00 1.0061E+00 9.9789E-01

14 1.0064E+00 1.0066E+00 1.0133E+00 1.0093E+00

15 9.9305E-01 1.0028E+00 1.0057E+00 1.0086E+00
C-5

16 9.5861E-01 9.9457E-01 9.8922E-01 1.0096E+00

17 1.0392E+00 1.0089E+00 1.0179E+00 1.0004E+00

18 9.5519E-01 1.0077E+00 1.0154E+00 9.9326E-01

19 1.0240E+00 1.0007E+00 1.0015E+00 1.0057E+00

20 1.0003E+00 1.0061E+00 1.0122E+00 9.9186E-01

21 9.6420E-01 1.0076E+00 1.0153E+00 9.9231E-01

22 9.9827E-01 1.0008E+00 1.0017E+00 9.9641E-01

23 9.7332E-01 1.0021E+00 1.0043E+00 1.0069E+00

24 1.0226E+00 9.9407E-01 9.8822E-01 1.0023E+00

25 1.0461E+00 9.9059E-01 9.8129E-01 9.9834E-01

26 9.7303E-01 9.9275E-01 9.8558E-01 1.0092E+00

27 1.0323E+00 9.9930E-01 9.9867E-01 1.0034E+00

28 1.0215E+00 9.9776E-01 9.9559E-01 9.9888E-01

29 9.9403E-01 1.0068E+00 1.0138E+00 9.9608E-01

30 1.0412E+00 1.0038E+00 1.0076E+00 9.9787E-01

31 9.8423E-01 9.9993E-01 9.9992E-01 1.0085E+00

32 1.0193E+00 1.0016E+00 1.0034E+00 1.0036E+00

33 9.7425E-01 1.0053E+00 1.0107E+00 1.0037E+00

34 1.0020E+00 1.0087E+00 1.0175E+00 1.0049E+00

35 1.0020E+00 1.0025E+00 1.0051E+00 1.0021E+00

36 9.7359E-01 1.0081E+00 1.0162E+00 9.9682E-01

37 1.0210E+00 9.9597E-01 9.9202E-01 9.9924E-01

38 9.5647E-01 1.0047E+00 1.0094E+00 9.9028E-01

39 9.9662E-01 9.9848E-01 9.9703E-01 1.0034E+00

40 1.0420E+00 9.9965E-01 9.9936E-01 1.0052E+00

41 1.0183E+00 1.0095E+00 1.0192E+00 1.0072E+00

42 1.0244E+00 1.0040E+00 1.0081E+00 1.0039E+00

43 9.9623E-01 9.9425E-01 9.8858E-01 9.9114E-01

44 1.0314E+00 1.0058E+00 1.0117E+00 9.9480E-01

45 9.8598E-01 1.0032E+00 1.0065E+00 1.0078E+00

46 9.9021E-01 1.0040E+00 1.0080E+00 9.9616E-01

47 1.0351E+00 9.9806E-01 9.9619E-01 1.0013E+00

48 1.0169E+00 9.9933E-01 9.9873E-01 1.0032E+00

49 9.9982E-01 1.0065E+00 1.0130E+00 1.0063E+00

50 9.5925E-01 9.9849E-01 9.9704E-01 9.9183E-01

51 1.0006E+00 1.0022E+00 1.0045E+00 1.0006E+00

52 9.6979E-01 1.0066E+00 1.0132E+00 9.9309E-01

53 9.7739E-01 9.9628E-01 9.9264E-01 1.0061E+00

54 9.8312E-01 9.9985E-01 9.9976E-01 1.0004E+00

55 1.0462E+00 9.9338E-01 9.8684E-01 9.9540E-01

56 1.0044E+00 9.9711E-01 9.9429E-01 1.0012E+00

57 1.0176E+00 9.9993E-01 9.9992E-01 1.0072E+00

58 9.9728E-01 1.0053E+00 1.0107E+00 1.0071E+00

59 1.0010E+00 1.0083E+00 1.0166E+00 9.9150E-01

60 9.5138E-01 9.9318E-01 9.8646E-01 1.0027E+00

61 1.0445E+00 9.9881E-01 9.9768E-01 1.0017E+00

62 9.7179E-01 9.9849E-01 9.9705E-01 1.0013E+00

63 1.0345E+00 9.9124E-01 9.8258E-01 9.9616E-01

64 9.8425E-01 1.0041E+00 1.0083E+00 9.9694E-01

65 9.8846E-01 9.9266E-01 9.8540E-01 1.0004E+00

66 1.0057E+00 1.0042E+00 1.0084E+00 1.0086E+00

67 9.7036E-01 1.0031E+00 1.0063E+00 1.0024E+00

68 1.0068E+00 1.0055E+00 1.0110E+00 9.9921E-01

69 9.7420E-01 1.0044E+00 1.0088E+00 1.0066E+00

70 1.0111E+00 1.0069E+00 1.0138E+00 1.0037E+00
C-6

71 9.7063E-01 9.9802E-01 9.9610E-01 1.0057E+00

72 9.5459E-01 1.0098E+00 1.0198E+00 1.0035E+00

73 9.8005E-01 9.9981E-01 9.9969E-01 1.0057E+00

74 9.8359E-01 9.9256E-01 9.8521E-01 9.9011E-01

75 9.9894E-01 1.0092E+00 1.0184E+00 1.0081E+00

76 9.7017E-01 1.0020E+00 1.0041E+00 9.9121E-01

77 1.0129E+00 9.9812E-01 9.9630E-01 9.9922E-01

78 1.0101E+00 1.0078E+00 1.0156E+00 9.9020E-01

79 1.0137E+00 1.0058E+00 1.0116E+00 1.0029E+00

80 1.0439E+00 1.0036E+00 1.0072E+00 1.0062E+00

81 1.0189E+00 1.0030E+00 1.0061E+00 9.9545E-01

82 1.0456E+00 9.9960E-01 9.9926E-01 1.0029E+00

83 1.0402E+00 1.0054E+00 1.0108E+00 9.9830E-01

84 1.0498E+00 1.0034E+00 1.0068E+00 9.9831E-01

85 9.9130E-01 1.0033E+00 1.0066E+00 1.0032E+00

86 9.9917E-01 9.9775E-01 9.9556E-01 9.9328E-01

87 9.8252E-01 1.0053E+00 1.0107E+00 1.0047E+00

88 1.0310E+00 9.9025E-01 9.8061E-01 1.0033E+00

89 1.0476E+00 9.9506E-01 9.9020E-01 9.9905E-01

90 9.6736E-01 9.9473E-01 9.8953E-01 1.0023E+00

91 1.0290E+00 9.9011E-01 9.8033E-01 9.9806E-01

92 1.0405E+00 1.0047E+00 1.0095E+00 1.0071E+00

93 9.6470E-01 1.0017E+00 1.0034E+00 1.0064E+00

P A R A M E T E R V A L U E S O F T H E D E S I G N

RUN INDEX OF PARAMETER

9

1 1.0087E+00

2 9.7277E-01

3 1.0373E+00

4 1.0160E+00

5 1.0100E+00

6 9.8144E-01

7 9.9824E-01

8 1.0320E+00

9 9.5500E-01

10 9.6723E-01

11 9.7200E-01

12 9.8662E-01

13 1.0272E+00

14 1.0454E+00

15 9.6888E-01

16 1.0146E+00

17 9.9200E-01

18 9.8679E-01

19 1.0401E+00

20 1.0476E+00

21 9.9919E-01

22 1.0139E+00

23 1.0199E+00

24 1.0264E+00

25 1.0143E+00

26 1.0052E+00

27 9.5733E-01

28 1.0121E+00
C-7

29 9.5486E-01

30 9.8369E-01

31 1.0041E+00

32 1.0394E+00

33 9.6025E-01

34 9.5914E-01

35 9.6469E-01

36 1.0108E+00

37 1.0316E+00

38 9.8755E-01

39 1.0087E+00

40 1.0356E+00

41 9.9334E-01

42 9.9818E-01

43 1.0272E+00

44 1.0454E+00

45 9.7996E-01

46 1.0487E+00

47 1.0398E+00

48 1.0115E+00

49 1.0237E+00

50 9.7477E-01

51 1.0324E+00

52 1.0046E+00

53 9.7490E-01

54 1.0338E+00

55 1.0410E+00

56 1.0453E+00

57 1.0012E+00

58 1.0025E+00

59 1.0344E+00

60 1.0046E+00

61 9.9308E-01

62 1.0307E+00

63 1.0321E+00

64 9.6186E-01

65 1.0432E+00

66 9.8065E-01

67 9.8120E-01

68 1.0065E+00

69 9.6369E-01

70 9.5784E-01

71 9.5637E-01

72 1.0412E+00

73 1.0292E+00

74 9.8061E-01

75 1.0085E+00

76 9.7171E-01

77 1.0441E+00

78 1.0043E+00

79 9.7012E-01

80 1.0304E+00

81 1.0466E+00

82 9.8486E-01

83 1.0286E+00
C-8

84 9.5555E-01

85 9.7585E-01

86 9.8951E-01

87 9.9310E-01

88 1.0346E+00

89 9.9045E-01

90 1.0349E+00

91 1.0473E+00

92 1.0131E+00

93 9.6139E-01

NUMBER OF DESIGN REPETITIONS DUE TO PAR. RESTRICT.= 0

LAST DSEED= 192915327.0

DESIGN HAS BEEN GENERATED

AND WRITTEN ON OUTPUT FILE

LAST DSEED= 192915327.0
D-1 

APPENDIX D SAMPLE.DAT 

9 93

1.0091E+00 9.9578E-01 7.0899E-01 1.0059E+00 1.0315E+00 9.9118E-01 

9.8245E-01 1.0096E+00 1.0087E+00

1.0074E+00 9.9795E-01 -1.4338E+00 1.0075E+00 9.9904E-01 9.9399E-01 

9.8807E-01 9.9487E-01 9.7277E-01

9.9227E-01 9.9819E-01 -4.0000E-01 9.6716E-01 1.0057E+00 1.0075E+00 

1.0150E+00 9.9631E-01 1.0373E+00

9.9512E-01 9.9123E-01 5.4987E-01 1.0345E+00 9.5441E-01 1.0072E+00 

1.0145E+00 9.9964E-01 1.0160E+00

1.0028E+00 1.0059E+00 -9.9602E-02 1.0282E+00 1.0138E+00 9.9400E-01 

9.8809E-01 1.0000E+00 1.0100E+00

1.0031E+00 1.0037E+00 -3.8254E-02 9.5678E-01 1.0025E+00 1.0014E+00 

1.0028E+00 1.0040E+00 9.8144E-01

1.0088E+00 9.9115E-01 -9.7341E-01 9.8529E-01 1.0396E+00 9.9409E-01 

9.8827E-01 1.0049E+00 9.9824E-01

1.0094E+00 1.0087E+00 -1.1079E+00 9.6143E-01 1.0227E+00 1.0071E+00 

1.0143E+00 1.0065E+00 1.0320E+00

1.0069E+00 1.0070E+00 -2.5163E-01 1.0096E+00 9.6598E-01 1.0062E+00 

1.0124E+00 1.0053E+00 9.5500E-01

1.0033E+00 9.9381E-01 -1.4017E+00 9.6120E-01 1.0053E+00 9.9498E-01 

9.9003E-01 9.9589E-01 9.6723E-01

1.0062E+00 9.9526E-01 1.4128E+00 1.0109E+00 9.7171E-01 1.0007E+00 

1.0015E+00 9.9181E-01 9.7200E-01

9.9184E-01 9.9931E-01 1.0303E-01 1.0064E+00 9.8158E-01 9.9523E-01 

9.9054E-01 9.9272E-01 9.8662E-01

9.9569E-01 9.9791E-01 -1.1151E+00 9.8905E-01 1.0418E+00 1.0030E+00 

1.0061E+00 9.9789E-01 1.0272E+00

1.0055E+00 1.0051E+00 2.6796E-01 1.0190E+00 1.0064E+00 1.0066E+00 

1.0133E+00 1.0093E+00 1.0454E+00

9.9574E-01 1.0049E+00 -1.4218E+00 1.0161E+00 9.9305E-01 1.0028E+00 

1.0057E+00 1.0086E+00 9.6888E-01

9.9818E-01 1.0060E+00 -4.6491E-01 9.9170E-01 9.5861E-01 9.9457E-01 

9.8922E-01 1.0096E+00 1.0146E+00

1.0067E+00 9.9963E-01 -7.8914E-01 9.7399E-01 1.0392E+00 1.0089E+00 

1.0179E+00 1.0004E+00 9.9200E-01

1.0005E+00 1.0095E+00 -5.2672E-01 9.7641E-01 9.5519E-01 1.0077E+00 

1.0154E+00 9.9326E-01 9.8679E-01

1.0074E+00 9.9273E-01 3.7218E-01 1.0171E+00 1.0240E+00 1.0007E+00 

1.0015E+00 1.0057E+00 1.0401E+00

9.9802E-01 9.9871E-01 2.7618E-01 1.0159E+00 1.0003E+00 1.0061E+00 

1.0122E+00 9.9186E-01 1.0476E+00

1.0054E+00 1.0062E+00 1.5286E-01 1.0153E+00 9.6420E-01 1.0076E+00 

1.0153E+00 9.9231E-01 9.9919E-01

1.0069E+00 9.9045E-01 -9.8377E-01 9.9923E-01 9.9827E-01 1.0008E+00 

1.0017E+00 9.9641E-01 1.0139E+00

1.0035E+00 9.9456E-01 6.3658E-01 1.0343E+00 9.7332E-01 1.0021E+00 

1.0043E+00 1.0069E+00 1.0199E+00

9.9590E-01 1.0079E+00 -1.6739E-01 1.0239E+00 1.0226E+00 9.9407E-01 

9.8822E-01 1.0023E+00 1.0264E+00

1.0056E+00 1.0033E+00 -8.8277E-01 9.8952E-01 1.0461E+00 9.9059E-01 

9.8129E-01 9.9834E-01 1.0143E+00
D-2

1.0003E+00 9.9698E-01 -1.4097E+00 9.7315E-01 9.7303E-01 9.9275E-01 

9.8558E-01 1.0092E+00 1.0052E+00

1.0025E+00 1.0038E+00 5.4078E-01 9.7047E-01 1.0323E+00 9.9930E-01 

9.9867E-01 1.0034E+00 9.5733E-01

1.0005E+00 1.0044E+00 -1.4193E+00 9.6151E-01 1.0215E+00 9.9776E-01 

9.9559E-01 9.9888E-01 1.0121E+00

1.0094E+00 9.9924E-01 4.0093E-01 1.0210E+00 9.9403E-01 1.0068E+00 

1.0138E+00 9.9608E-01 9.5486E-01

9.9513E-01 1.0017E+00 1.1163E-01 1.0199E+00 1.0412E+00 1.0038E+00 

1.0076E+00 9.9787E-01 9.8369E-01

1.0065E+00 9.9459E-01 -1.2241E+00 1.0068E+00 9.8423E-01 9.9993E-01 

9.9992E-01 1.0085E+00 1.0041E+00

9.9442E-01 1.0047E+00 -9.7198E-02 1.0016E+00 1.0193E+00 1.0016E+00 

1.0034E+00 1.0036E+00 1.0394E+00

1.0033E+00 9.9341E-01 -1.4340E+00 1.0362E+00 9.7425E-01 1.0053E+00 

1.0107E+00 1.0037E+00 9.6025E-01

1.0044E+00 9.9133E-01 1.2405E-01 1.0317E+00 1.0020E+00 1.0087E+00 

1.0175E+00 1.0049E+00 9.5914E-01

9.9369E-01 9.9905E-01 -1.1043E+00 9.6407E-01 1.0020E+00 1.0025E+00 

1.0051E+00 1.0021E+00 9.6469E-01

1.0025E+00 9.9175E-01 1.4810E+00 9.8630E-01 9.7359E-01 1.0081E+00 

1.0162E+00 9.9682E-01 1.0108E+00

1.0076E+00 9.9295E-01 -8.4229E-01 9.5251E-01 1.0210E+00 9.9597E-01 

9.9202E-01 9.9924E-01 1.0316E+00

1.0050E+00 9.9671E-01 1.3930E+00 1.0371E+00 9.5647E-01 1.0047E+00 

1.0094E+00 9.9028E-01 9.8755E-01

1.0099E+00 9.9085E-01 5.0285E-01 9.8797E-01 9.9662E-01 9.9848E-01 

9.9703E-01 1.0034E+00 1.0087E+00

9.9526E-01 9.9736E-01 3.1890E-01 1.0451E+00 1.0420E+00 9.9965E-01 

9.9936E-01 1.0052E+00 1.0356E+00

9.9732E-01 9.9605E-01 -5.1195E-01 9.8416E-01 1.0183E+00 1.0095E+00 

1.0192E+00 1.0072E+00 9.9334E-01

9.9121E-01 9.9413E-01 1.3027E+00 9.5346E-01 1.0244E+00 1.0040E+00 

1.0081E+00 1.0039E+00 9.9818E-01

1.0032E+00 9.9341E-01 -6.9382E-01 9.9855E-01 9.9623E-01 9.9425E-01 

9.8858E-01 9.9114E-01 1.0272E+00

1.0060E+00 9.9739E-01 -4.9315E-01 1.0191E+00 1.0314E+00 1.0058E+00 

1.0117E+00 9.9480E-01 1.0454E+00

9.9217E-01 9.9933E-01 4.1669E-01 9.7092E-01 9.8598E-01 1.0032E+00 

1.0065E+00 1.0078E+00 9.7996E-01

9.9692E-01 1.0045E+00 -1.0865E+00 9.7738E-01 9.9021E-01 1.0040E+00 

1.0080E+00 9.9616E-01 1.0487E+00

1.0083E+00 1.0029E+00 -1.1937E+00 1.0198E+00 1.0351E+00 9.9806E-01 

9.9619E-01 1.0013E+00 1.0398E+00

9.9277E-01 9.9188E-01 1.3539E+00 1.0345E+00 1.0169E+00 9.9933E-01 

9.9873E-01 1.0032E+00 1.0115E+00

9.9534E-01 9.9415E-01 8.5235E-02 9.8243E-01 9.9982E-01 1.0065E+00 

1.0130E+00 1.0063E+00 1.0237E+00

1.0055E+00 1.0081E+00 -1.2160E+00 1.0260E+00 9.5925E-01 9.9849E-01 

9.9704E-01 9.9183E-01 9.7477E-01

1.0084E+00 9.9870E-01 6.5411E-01 1.0000E+00 1.0006E+00 1.0022E+00 

1.0045E+00 1.0006E+00 1.0324E+00

9.9131E-01 1.0005E+00 -1.4297E+00 1.0001E+00 9.6979E-01 1.0066E+00 

1.0132E+00 9.9309E-01 1.0046E+00
D-3

9.9774E-01 1.0084E+00 5.2083E-01 9.9646E-01 9.7739E-01 9.9628E-01 

9.9264E-01 1.0061E+00 9.7490E-01

9.9584E-01 9.9031E-01 2.2974E-01 1.0369E+00 9.8312E-01 9.9985E-01 

9.9976E-01 1.0004E+00 1.0338E+00

1.0039E+00 1.0019E+00 -7.1682E-01 1.0103E+00 1.0462E+00 9.9338E-01 

9.8684E-01 9.9540E-01 1.0410E+00

1.0015E+00 1.0022E+00 -4.8233E-01 1.0359E+00 1.0044E+00 9.9711E-01 

9.9429E-01 1.0012E+00 1.0453E+00

1.0046E+00 9.9238E-01 1.0862E+00 9.8143E-01 1.0176E+00 9.9993E-01 

9.9992E-01 1.0072E+00 1.0012E+00

9.9597E-01 9.9285E-01 9.3704E-01 9.7640E-01 9.9728E-01 1.0053E+00 

1.0107E+00 1.0071E+00 1.0025E+00

1.0072E+00 9.9456E-01 7.0515E-01 9.5786E-01 1.0010E+00 1.0083E+00 

1.0166E+00 9.9150E-01 1.0344E+00

1.0007E+00 9.9566E-01 -1.1160E+00 9.6265E-01 9.5138E-01 9.9318E-01 

9.8646E-01 1.0027E+00 1.0046E+00

1.0075E+00 9.9832E-01 4.8105E-01 9.6804E-01 1.0445E+00 9.9881E-01 

9.9768E-01 1.0017E+00 9.9308E-01

9.9608E-01 1.0002E+00 1.4391E+00 9.8761E-01 9.7179E-01 9.9849E-01 

9.9705E-01 1.0013E+00 1.0307E+00

1.0037E+00 9.9797E-01 -9.2556E-01 1.0216E+00 1.0345E+00 9.9124E-01 

9.8258E-01 9.9616E-01 1.0321E+00

1.0065E+00 1.0079E+00 1.0424E+00 9.7370E-01 9.8425E-01 1.0041E+00 

1.0083E+00 9.9694E-01 9.6186E-01

9.9944E-01 9.9882E-01 7.5662E-01 9.8936E-01 9.8846E-01 9.9266E-01 

9.8540E-01 1.0004E+00 1.0432E+00

1.0024E+00 1.0048E+00 1.1548E+00 1.0164E+00 1.0057E+00 1.0042E+00 

1.0084E+00 1.0086E+00 9.8065E-01

9.9388E-01 9.9780E-01 8.7341E-01 1.0471E+00 9.7036E-01 1.0031E+00 

1.0063E+00 1.0024E+00 9.8120E-01

9.9782E-01 1.0099E+00 -1.1552E+00 9.9027E-01 1.0068E+00 1.0055E+00 

1.0110E+00 9.9921E-01 1.0065E+00

9.9552E-01 1.0006E+00 -4.8103E-01 9.5240E-01 9.7420E-01 1.0044E+00 

1.0088E+00 1.0066E+00 9.6369E-01

9.9478E-01 9.9301E-01 1.0377E+00 1.0229E+00 1.0111E+00 1.0069E+00 

1.0138E+00 1.0037E+00 9.5784E-01

1.0002E+00 1.0061E+00 2.8691E-01 1.0173E+00 9.7063E-01 9.9802E-01 

9.9610E-01 1.0057E+00 9.5637E-01

1.0009E+00 1.0043E+00 4.7711E-01 1.0096E+00 9.5459E-01 1.0098E+00 

1.0198E+00 1.0035E+00 1.0412E+00

9.9154E-01 1.0063E+00 6.4357E-01 1.0100E+00 9.8005E-01 9.9981E-01 

9.9969E-01 1.0057E+00 1.0292E+00

1.0055E+00 9.9182E-01 1.3089E+00 1.0294E+00 9.8359E-01 9.9256E-01 

9.8521E-01 9.9011E-01 9.8061E-01

9.9504E-01 1.0070E+00 -5.2694E-01 1.0401E+00 9.9894E-01 1.0092E+00 

1.0184E+00 1.0081E+00 1.0085E+00

1.0022E+00 1.0025E+00 8.7840E-01 1.0039E+00 9.7017E-01 1.0020E+00 

1.0041E+00 9.9121E-01 9.7171E-01

1.0039E+00 1.0047E+00 6.6405E-01 1.0077E+00 1.0129E+00 9.9812E-01 

9.9630E-01 9.9922E-01 1.0441E+00

1.0092E+00 9.9101E-01 -1.0129E+00 1.0347E+00 1.0101E+00 1.0078E+00 

1.0156E+00 9.9020E-01 1.0043E+00

9.9628E-01 9.9082E-01 1.9146E-01 1.0179E+00 1.0137E+00 1.0058E+00 

1.0116E+00 1.0029E+00 9.7012E-01
D-4

1.0065E+00 1.0077E+00 -9.5867E-01 1.0235E+00 1.0439E+00 1.0036E+00 

1.0072E+00 1.0062E+00 1.0304E+00

1.0005E+00 1.0022E+00 -1.1187E+00 9.9107E-01 1.0189E+00 1.0030E+00 

1.0061E+00 9.9545E-01 1.0466E+00

9.9730E-01 1.0047E+00 -2.7360E-01 1.0411E+00 1.0456E+00 9.9960E-01 

9.9926E-01 1.0029E+00 9.8486E-01

9.9446E-01 9.9154E-01 -1.1386E+00 9.8745E-01 1.0402E+00 1.0054E+00 

1.0108E+00 9.9830E-01 1.0286E+00

1.0047E+00 1.0042E+00 9.4720E-02 9.8136E-01 1.0498E+00 1.0034E+00 

1.0068E+00 9.9831E-01 9.5555E-01

1.0055E+00 1.0044E+00 1.2541E+00 1.0288E+00 9.9130E-01 1.0033E+00 

1.0066E+00 1.0032E+00 9.7585E-01

9.9231E-01 1.0060E+00 5.1777E-01 1.0062E+00 9.9917E-01 9.9775E-01 

9.9556E-01 9.9328E-01 9.8951E-01

1.0031E+00 1.0043E+00 7.9292E-01 9.8762E-01 9.8252E-01 1.0053E+00 

1.0107E+00 1.0047E+00 9.9310E-01

1.0074E+00 1.0076E+00 6.0472E-01 9.8573E-01 1.0310E+00 9.9025E-01 

9.8061E-01 1.0033E+00 1.0346E+00

9.9742E-01 9.9473E-01 7.5922E-01 9.8535E-01 1.0476E+00 9.9506E-01 

9.9020E-01 9.9905E-01 9.9045E-01

1.0006E+00 9.9726E-01 9.4857E-02 9.7161E-01 9.6736E-01 9.9473E-01 

9.8953E-01 1.0023E+00 1.0349E+00

9.9731E-01 1.0008E+00 7.2897E-01 9.7259E-01 1.0290E+00 9.9011E-01 

9.8033E-01 9.9806E-01 1.0473E+00

1.0009E+00 9.9090E-01 1.6013E-01 9.5061E-01 1.0405E+00 1.0047E+00 

1.0095E+00 1.0071E+00 1.0131E+00

9.9074E-01 9.9281E-01 6.8196E-01 1.0106E+00 9.6470E-01 1.0017E+00 

1.0034E+00 1.0064E+00 9.6139E-01
E-1

APPENDIX E DATA EXTRACTION

PROGRAM DataExtraction

 IMPLICIT double PRECISION(a-h)

 IMPLICIT INTEGER (i-z)

 PARAMETER (nmax = 93)

 CHARACTER*11 eingabedatei

 CHARACTER*14 eingabedatei2

 CHARACTER*121 zeileA

 CHARACTER*121 zeileB

 CHARACTER*121 zeileC

 INTEGER :: count1, count2

 REAL*8 ::A1, A2, B1, B2

 REAL, DIMENSION(1:36) :: PressureDropRef

 REAL, DIMENSION(1:1,1:36) :: ReferencePD

 REAL, ALLOCATABLE, DIMENSION(:,:) :: scalar

 INTEGER :: NF = 36, NJ = 93

!--------------------------------------------------------------------------

!==== REFERENCE OUTPUTS DATA EXTRACTION SECTION - START ===================

!--------------------------------------------------------------------------

! 

 OPEN(201,file='reference.dat',form='formatted',status='replace',err=9001)

 DO i=1,NF

 IF (i .le. 9) THEN

WRITE(eingabedatei(6:6), '(I1)')i

 eingabedatei(1:5) = 'P7000'

eingabedatei(7:11) = '.out '

 ELSE IF (i .gt. 9 .AND. i .lt. 100) THEN

WRITE(eingabedatei(6:7), '(I2)')i

 eingabedatei(1:5) = 'P7000'

eingabedatei(8:11) = '.out'

 END IF

 OPEN(101,file=eingabedatei,form='formatted',status='old',err=9000)

 WRITE(*,*)eingabedatei,' has been opened succesfuly.'

 count1 = 0

 DO

READ(101, '(a121)',END=300) zeileA

 IF(zeileA(37:71) .eq. 'control-block output values at time')THEN

 count1 = count1 + 1

END IF

 END DO

300 CONTINUE

 REWIND(101)

 count2 = 0

 DO

READ(101, '(a121)',END=301) zeileB
E-2

IF(zeileB(37:71) .eq. 'control-block output values at time')THEN

count2 = count2 + 1

IF(count1 .eq. count2) THEN

 GO TO 234

END IF

END IF

 END DO

301 CONTINUE

234 CONTINUE

 !read useless information and dump them

 DO j=1,5

READ(101,'(a121)',END=9000) zeileC 

 END DO

 !read pressure drop data out of control-block output

 READ(101,*,END=499) A1, A2

499 CONTINUE

 PressureDropRef(i) = A2

 !scalar information stored in variable

 ReferencePD(1,i) = PressureDropRef(i)

 WRITE(201,'(f11.2)') ReferencePD(1,i)

 GO TO 500

500 CONTINUE

 END DO

 CLOSE(101)

 CLOSE(201)

! 

!-------------------------------------------------------------------------

!==== UNCERTAINTY OUTPUTS DATA EXTRACTION SECTION - START ================

!-------------------------------------------------------------------------

! OPEN(202,file='scalar.lst',form='formatted',status='replace',err=9001)

ALLOCATE (scalar(NF,NJ))

 DO k=1,NF

DO l=1,NJ

IF (k .le. 9 .AND. l .le. 9) THEN

WRITE(eingabedatei2,101) k,l

101 FORMAT("P7000",i1,"_",i1,".out")

ELSE IF (k .le. 9 .AND. l .gt. 9) THEN

WRITE(eingabedatei2,102) k,l

102 FORMAT("P7000",i1,"_",i2,".out")

ELSE IF (k .gt. 9 .AND. l .le. 9) THEN

WRITE(eingabedatei2,103) k,l
E-3

103 FORMAT("P7000",i2,"_",i1,".out")

ELSE IF (k .gt. 9 .AND. l .gt. 9) THEN

WRITE(eingabedatei2,104) k,l

104 FORMAT("P7000",i2,"_",i2,".out")

END IF

OPEN(102,file=eingabedatei2,form='formatted',status='old',err=9000)

WRITE(*,*)eingabedatei2,' has been opened succesfully.'

 count1 = 0

 DO

READ(102, '(a121)',END=302) zeileA

 IF(zeileA(37:71) .eq. 'control-block output values at time')THEN

count1 = count1 + 1

END IF

 END DO

302 CONTINUE

 REWIND(102)

 count2 = 0

 DO

READ(102, '(a121)',END=303) zeileB

IF(zeileB(37:71) .eq. 'control-block output values at time')THEN

count2 = count2 + 1

IF(count1 .eq. count2) THEN

GO TO 235

END IF

END IF

 END DO

303 CONTINUE

235 CONTINUE

 !read useless information and dump them

 DO m=1,5

READ(102,'(a121)',END=9000) zeileC 

 END DO

 !read pressure drop data out of control-block output

 READ(102,*,END=498) B1, B2

498 CONTINUE

 scalar(k,l) = B2

 END DO

 END DO

 DO l=1,NJ

WRITE(202,'(100f11.2)') (scalar(k,l) , k=1,NF)

 END DO
E-4

 CLOSE(102)

 CLOSE(202)

 GO TO 9999

9000 CONTINUE

 WRITE(*,*) '* ** ERROR: Could not open file on unit 101'

 GO TO 9998

9001 CONTINUE

 WRITE(*,*) '*** ERROR: Could not open file on unit',eingabedatei

 GO TO 9998

9998 CONTINUE

 WRITE(*,*)'Program termination due to errors'

 GO TO 9999

9999 CONTINUE

 WRITE(*,*)'finished'

END
F-1

APPENDIX F EQUUS.PRN 

Uncertainty and Sensitivity Analysis

DATE: 2012/03/30

TIME: 09:51

CURRENT SAMPLE SIZE = 93

CURRENT NUMBER OF CONSEQUENCES = 36

NUMBER OF SELECTED CONSEQUENCES : 

 1 

INDICES OF SELECTED CONSEQUENCES : 

 1 

NUMBER OF SELECTED DISTRIBUTIONS TO BE FITTED

 4 

INDICES OF SELECTED DISTRIBUTIONS : 

 3 : NORMAL

 4 : LOGNORMAL 

 5 : UNIFORM

 8 : LOG-TRIANGULAR 

EMPIRICAL QUANTILES OF CONSEQUENCE NO. 1

*******************************************

 CURRENT SAMPLE SIZE = 93

MINIMUM = 1.0617E+03

 # INDEX 

 1 1 1.00 %-QUANTILE = 1.0617E+03

 2 2 2.00 %-QUANTILE = 1.0698E+03

 3 3 3.00 %-QUANTILE = 1.0700E+03

 4 4 4.00 %-QUANTILE = 1.0719E+03

 5 5 5.00 %-QUANTILE = 1.0754E+03

 6 6 6.00 %-QUANTILE = 1.0754E+03

 7 7 7.00 %-QUANTILE = 1.0760E+03

 8 8 8.00 %-QUANTILE = 1.0769E+03

 9 9 9.00 %-QUANTILE = 1.0783E+03

 10 10 10.00 %-QUANTILE = 1.0802E+03

 11 11 11.00 %-QUANTILE = 1.0805E+03

 12 12 12.00 %-QUANTILE = 1.0852E+03

 13 13 13.00 %-QUANTILE = 1.0853E+03

 14 14 14.00 %-QUANTILE = 1.0876E+03

 15 14 15.00 %-QUANTILE = 1.0876E+03

 16 15 16.00 %-QUANTILE = 1.0884E+03

 17 16 17.00 %-QUANTILE = 1.0907E+03

 18 17 18.00 %-QUANTILE = 1.0908E+03

 19 18 19.00 %-QUANTILE = 1.0935E+03

 20 19 20.00 %-QUANTILE = 1.0935E+03

 21 20 21.00 %-QUANTILE = 1.0936E+03

 22 21 22.00 %-QUANTILE = 1.0937E+03

 23 22 23.00 %-QUANTILE = 1.0948E+03
F-2

 24 23 24.00 %-QUANTILE = 1.0953E+03

 25 24 25.00 %-QUANTILE = 1.0968E+03

 26 25 26.00 %-QUANTILE = 1.0970E+03

 27 26 27.00 %-QUANTILE = 1.0970E+03

 28 27 28.00 %-QUANTILE = 1.0978E+03

 29 27 29.00 %-QUANTILE = 1.0978E+03

 30 28 30.00 %-QUANTILE = 1.1000E+03

 31 29 31.00 %-QUANTILE = 1.1003E+03

 32 30 32.00 %-QUANTILE = 1.1005E+03

 33 31 33.00 %-QUANTILE = 1.1008E+03

 34 32 34.00 %-QUANTILE = 1.1008E+03

 35 33 35.00 %-QUANTILE = 1.1009E+03

 36 34 36.00 %-QUANTILE = 1.1014E+03

 37 35 37.00 %-QUANTILE = 1.1021E+03

 38 36 38.00 %-QUANTILE = 1.1068E+03

 39 37 39.00 %-QUANTILE = 1.1082E+03

 40 38 40.00 %-QUANTILE = 1.1095E+03

 41 39 41.00 %-QUANTILE = 1.1107E+03

 42 40 42.00 %-QUANTILE = 1.1113E+03

 43 40 43.00 %-QUANTILE = 1.1113E+03

 44 41 44.00 %-QUANTILE = 1.1116E+03

 45 42 45.00 %-QUANTILE = 1.1124E+03

 46 43 46.00 %-QUANTILE = 1.1126E+03

 47 44 47.00 %-QUANTILE = 1.1143E+03

 48 45 48.00 %-QUANTILE = 1.1159E+03

 49 46 49.00 %-QUANTILE = 1.1161E+03

 50 47 50.00 %-QUANTILE = 1.1164E+03

 51 48 51.00 %-QUANTILE = 1.1169E+03

 52 49 52.00 %-QUANTILE = 1.1188E+03

 53 50 53.00 %-QUANTILE = 1.1191E+03

 54 51 54.00 %-QUANTILE = 1.1194E+03

 55 52 55.00 %-QUANTILE = 1.1205E+03

 56 53 56.00 %-QUANTILE = 1.1208E+03

 57 54 57.00 %-QUANTILE = 1.1219E+03

 58 54 58.00 %-QUANTILE = 1.1219E+03

 59 55 59.00 %-QUANTILE = 1.1223E+03

 60 56 60.00 %-QUANTILE = 1.1229E+03

 61 57 61.00 %-QUANTILE = 1.1233E+03

 62 58 62.00 %-QUANTILE = 1.1242E+03

 63 59 63.00 %-QUANTILE = 1.1242E+03

 64 60 64.00 %-QUANTILE = 1.1285E+03

 65 61 65.00 %-QUANTILE = 1.1295E+03

 66 62 66.00 %-QUANTILE = 1.1296E+03

 67 63 67.00 %-QUANTILE = 1.1296E+03

 68 64 68.00 %-QUANTILE = 1.1306E+03

 69 65 69.00 %-QUANTILE = 1.1307E+03

 70 66 70.00 %-QUANTILE = 1.1316E+03

 71 67 71.00 %-QUANTILE = 1.1318E+03

 72 67 72.00 %-QUANTILE = 1.1318E+03

 73 68 73.00 %-QUANTILE = 1.1347E+03

 74 69 74.00 %-QUANTILE = 1.1353E+03

 75 70 75.00 %-QUANTILE = 1.1354E+03

 76 71 76.00 %-QUANTILE = 1.1355E+03

 77 72 77.00 %-QUANTILE = 1.1359E+03

 78 73 78.00 %-QUANTILE = 1.1381E+03
F-3

 79 74 79.00 %-QUANTILE = 1.1392E+03

 80 75 80.00 %-QUANTILE = 1.1427E+03

 81 76 81.00 %-QUANTILE = 1.1429E+03

 82 77 82.00 %-QUANTILE = 1.1437E+03

 83 78 83.00 %-QUANTILE = 1.1453E+03

 84 79 84.00 %-QUANTILE = 1.1457E+03

 85 80 85.00 %-QUANTILE = 1.1457E+03

 86 80 86.00 %-QUANTILE = 1.1457E+03

 87 81 87.00 %-QUANTILE = 1.1495E+03

 88 82 88.00 %-QUANTILE = 1.1513E+03

 89 83 89.00 %-QUANTILE = 1.1542E+03

 90 84 90.00 %-QUANTILE = 1.1544E+03

 91 85 91.00 %-QUANTILE = 1.1554E+03

 92 86 92.00 %-QUANTILE = 1.1572E+03

 93 87 93.00 %-QUANTILE = 1.1619E+03

 94 88 94.00 %-QUANTILE = 1.1697E+03

 95 89 95.00 %-QUANTILE = 1.1762E+03

 96 90 96.00 %-QUANTILE = 1.1812E+03

 97 91 97.00 %-QUANTILE = 1.1828E+03

 98 92 98.00 %-QUANTILE = 1.1843E+03

 99 93 99.00 %-QUANTILE = 1.1869E+03

MAXIMUM = 1.1869E+03

SAMPLE MEAN = 1.1175E+03

SAMPLE STANDARD DEVIATION = 2.8699E+01

FITTED DISTRIBUTION TO DATA OF CONSEQUENCE NO. 1

*****************************************************

N O R M A L DISTRIBUTION 

WITH MY = 1.1175E+03, SIGMA = 2.8699E+01

( NOT TRUNCATED )

RESULTS OF THE KOLMOGOROV-SMIRNOV-TEST FOR GOODNESS-OF-FIT

----------------------------------------------------------

(PARAMETERS ESTIMATED FROM THE SAME SAMPLE !!!)

KOLMOGOROV-SMIRNOV-D-STATISTICS = 8.1345E-02

CORRESPONDING LEVEL OF SIGNIFICANCE = 5.6962E-01

SELECTED QUANTILES OF THE FITTED DISTRIBUTION

-----------------------------------------------

 1.00 %-QUANTILE = 1.0508E+03

 5.00 %-QUANTILE = 1.0703E+03

10.00 %-QUANTILE = 1.0808E+03

20.00 %-QUANTILE = 1.0934E+03

30.00 %-QUANTILE = 1.1025E+03

40.00 %-QUANTILE = 1.1103E+03

50.00 %-QUANTILE = 1.1175E+03

60.00 %-QUANTILE = 1.1248E+03

70.00 %-QUANTILE = 1.1326E+03

80.00 %-QUANTILE = 1.1417E+03

90.00 %-QUANTILE = 1.1543E+03

95.00 %-QUANTILE = 1.1647E+03

99.00 %-QUANTILE = 1.1843E+03

FITTED DISTRIBUTION TO DATA OF CONSEQUENCE NO. 1
F-4

*****************************************************

L O G N O R M A L DISTRIBUTION 

WITH MY = 7.0186E+00, SIGMA = 2.5574E-02

( NOT TRUNCATED )

RESULTS OF THE KOLMOGOROV-SMIRNOV-TEST FOR GOODNESS-OF-FIT

----------------------------------------------------------

(PARAMETERS ESTIMATED FROM THE SAME SAMPLE !!!)

KOLMOGOROV-SMIRNOV-D-STATISTICS = 7.9045E-02

CORRESPONDING LEVEL OF SIGNIFICANCE = 6.0653E-01

SELECTED QUANTILES OF THE FITTED DISTRIBUTION

-----------------------------------------------

 1.00 %-QUANTILE = 1.0526E+03

 5.00 %-QUANTILE = 1.0712E+03

10.00 %-QUANTILE = 1.0812E+03

20.00 %-QUANTILE = 1.0934E+03

30.00 %-QUANTILE = 1.1023E+03

40.00 %-QUANTILE = 1.1100E+03

50.00 %-QUANTILE = 1.1172E+03

60.00 %-QUANTILE = 1.1244E+03

70.00 %-QUANTILE = 1.1323E+03

80.00 %-QUANTILE = 1.1415E+03

90.00 %-QUANTILE = 1.1544E+03

95.00 %-QUANTILE = 1.1652E+03

99.00 %-QUANTILE = 1.1857E+03

FITTED DISTRIBUTION TO DATA OF CONSEQUENCE NO. 1

*****************************************************

U N I F O R M DISTRIBUTION

BETWEEN 1.0603E+03 AND 1.1883E+03

RESULTS OF THE KOLMOGOROV-SMIRNOV-TEST FOR GOODNESS-OF-FIT

----------------------------------------------------------

(PARAMETERS ESTIMATED FROM THE SAME SAMPLE !!!)

KOLMOGOROV-SMIRNOV-D-STATISTICS = 1.9308E-01

CORRESPONDING LEVEL OF SIGNIFICANCE = 1.9475E-03

SELECTED QUANTILES OF THE FITTED DISTRIBUTION

-----------------------------------------------

 1.00 %-QUANTILE = 1.0616E+03

 5.00 %-QUANTILE = 1.0667E+03

10.00 %-QUANTILE = 1.0731E+03

20.00 %-QUANTILE = 1.0859E+03

30.00 %-QUANTILE = 1.0987E+03

40.00 %-QUANTILE = 1.1115E+03

50.00 %-QUANTILE = 1.1243E+03

60.00 %-QUANTILE = 1.1371E+03

70.00 %-QUANTILE = 1.1499E+03

80.00 %-QUANTILE = 1.1627E+03

90.00 %-QUANTILE = 1.1755E+03

95.00 %-QUANTILE = 1.1819E+03

99.00 %-QUANTILE = 1.1870E+03

FITTED DISTRIBUTION TO DATA OF CONSEQUENCE NO. 1
F-5

*****************************************************

L O G - T R I A N G U L A R DISTRIBUTION

BETWEEN 1.0617E+03 AND 1.1869E+03 WITH EXP(LOG-PEAK) AT 1.1065E+03

RESULTS OF THE KOLMOGOROV-SMIRNOV-TEST FOR GOODNESS-OF-FIT

----------------------------------------------------------

(PARAMETERS ESTIMATED FROM THE SAME SAMPLE !!!)

KOLMOGOROV-SMIRNOV-D-STATISTICS = 7.3853E-02

CORRESPONDING LEVEL OF SIGNIFICANCE = 6.9082E-01

SELECTED QUANTILES OF THE FITTED DISTRIBUTION

-----------------------------------------------

 1.00 %-QUANTILE = 1.0689E+03

 5.00 %-QUANTILE = 1.0779E+03

10.00 %-QUANTILE = 1.0847E+03

20.00 %-QUANTILE = 1.0944E+03

30.00 %-QUANTILE = 1.1019E+03

40.00 %-QUANTILE = 1.1083E+03

50.00 %-QUANTILE = 1.1150E+03

60.00 %-QUANTILE = 1.1223E+03

70.00 %-QUANTILE = 1.1308E+03

80.00 %-QUANTILE = 1.1409E+03

90.00 %-QUANTILE = 1.1542E+03

95.00 %-QUANTILE = 1.1637E+03

99.00 %-QUANTILE = 1.1765E+03

G-1

APPENDIX G SAMOS.PRN 

Uncertainty and Sensitivity Analysis

DATE: 2012/03/30

TIME: 09:59

CURRENT NUMBER OF PARAMETERS = 9

CURRENT SAMPLE SIZE = 93

CURRENT NUMBER OF CONSEQUENCES = 36

NUMBER OF ADMITTED CONSEQUENCES : 

 1 

INDICES OF ADMITTED CONSEQUENCES : 

 1 

INDEX OF TRANSFORMATION OF ADMITTED CONSEQUENCES : 

 0 

NUMBER OF ADMITTED PARAMETERS : 

 8 

INDICES OF ADMITTED PARAMETERS : 

 1 2 3 4 5 6 8 9

NUMBER OF SENSITIVITY MEASURES TO BE PLOTTED :

 0 

TRANSFORM.-TYPE= 0 , CONSEQUENCE NO.= 1

ORDERED SENSITIVITY MEASURES FROM ORDINARY CORRELATIONS

----------------------------------------------------------

CURRENT NUMBER OF PARAMETERS = 8

CURRENT SAMPLE SIZE = 93

 ORDINARY PARTIAL STD.REGR.

 # CC PAR.NO CC PAR.NO FROM CC PAR.NO

 1 -7.4877E-01 6 -9.9920E-01 6 -6.1222E-01 6

 2 6.2070E-01 9 9.9838E-01 9 4.3565E-01 9

 3 5.2325E-01 5 9.9688E-01 5 3.2136E-01 5

 4 2.8104E-01 2 9.9627E-01 2 2.7800E-01 2

 5 -2.5170E-01 3 -9.5269E-01 8 -7.6084E-02 8

 6 1.3701E-01 1 -9.4883E-01 3 -7.4161E-02 3

 7 -8.3884E-02 4 2.0496E-01 4 5.0635E-03 4

 8 -8.0042E-02 8 1.4600E-03 1 3.5640E-05 1

R**2 OF THE CORRELATION-MATRIX = 9.9944E-01

H-1

APPENDIX H DAKOTA REPORT

General

Error Handling Ignore model check errors

Total Tasks 93

Successful Tasks 93

Random Seed 666674 (system-generated)

Sampling Method Monte-Carlo

Order 1 

Probability 95.0%

Confidence 95.0%

Results Matrix

ASV1

1833.249267578125

1930.962158203125

1.1 Response Function: ASVI1 

Mean 1880.6939645

Standard Deviation 23.930941073

Coefficient of Variance 0.01272452697

95% Confidence Intervals

Mean 1875.7654456 1885.6224833

Standard Deviation 20.916625043 27.968357118

Cumulative Distribution Function
H-2

Response Correlations

Simple Partial Simple Rank Partial Rank

d1 0.763973 0.995819 0.759661 0.968054

d2 -0.0294279 0.144264 -0.00532661 0.0893693

d3 -0.113314 -0.79554 -0.11641 -0.369488

d4 0.636032 0.994048 0.630793 0.95478

d5 0.0450883 0.00679033 0.01125 -0.147751

Variable Nominal Distribution Type Adjustment Parameters

spacer k loss factor 1.2 d1 Normal Scalar μ:1.2, σ:0.06, [1.14, 

1.26]

wall rougness 2.5E-6 d2 Normal Scalar μ:2.5E-6, σ:1.25E-7, 

[2.38E-6, 2.53E-6]

inlet temperature 311.65 d3 Normal Scalar μ:311.65, σ:1.5, 

[310.15, 313.15]

mass flow 4.0277 d4 Normal Scalar μ:4.0277, σ:0.040277, 

[3.9875, 4.068]

outlet Pressure 2.0E5 d5 Normal Scalar μ:2.0E5, σ:2000.0, 

[1.98E5, 2.02E5]

Variate Data 1

Task d1 d2 d3 d4 d5

1 1.159147282 2.41350726e-006 311.6157123 4.01805752 199679.2688

2 1.140580281 2.440686607e-006 310.5791366 4.01042388 198311.7162

3 1.183774516 2.467981742e-006 311.66213 4.008888063 200753.8198
H-3

Task d1 d2 d3 d4 d5

4 1.254567857 2.397312291e-006 312.9951083 4.05421478 200725.8836

5 1.179015528 2.498942033e-006 310.8305097 4.014652344 201374.4395

6 1.217183749 2.381640664e-006 312.2962954 3.999774429 200646.8523

7 1.244098294 2.433406079e-006 310.419832 4.047694926 199748.4991

8 1.249676058 2.400160633e-006 311.7279177 4.056662259 201110.3817

9 1.191915532 2.428348731e-006 311.018016 4.008243881 199420.4141

10 1.196343206 2.447372578e-006 311.450467 4.031451431 201926.9268

11 1.210231613 2.419942869e-006 310.2469775 4.022415989 200012.6859

12 1.207410841 2.445885685e-006 310.4539735 4.042560128 198041.8542

13 1.169521818 2.381265429e-006 311.7022163 4.005767541 199470.6716

14 1.196277034 2.442382506e-006 310.70055 4.009077772 199672.0975

15 1.228678798 2.480529445e-006 310.5757818 4.013589268 199266.5988

16 1.158642504 2.464062971e-006 312.6503333 4.053142891 201365.2021

17 1.226548821 2.516986142e-006 311.652484 4.025791021 198765.1706

18 1.231635709 2.437499846e-006 312.5422494 4.019450335 199916.9608

19 1.225497991 2.516020578e-006 310.7045158 4.016074893 198823.5882

20 1.17228859 2.457294839e-006 311.1941262 3.997157162 201609.272

21 1.23947838 2.450469555e-006 310.5512761 4.062337962 200542.7174

22 1.210998283 2.490109423e-006 311.872142 4.051785577 198310.4498

23 1.254310581 2.482112245e-006 311.7417967 4.01077094 200003.3182

24 1.232111576 2.457043241e-006 310.7696093 4.037061209 199824.8352

25 1.202083796 2.522679596e-006 311.8212604 4.024132226 199330.8478

26 1.202299707 2.502838457e-006 311.7050961 3.996853469 199124.615

27 1.240500989 2.488351494e-006 310.4896208 4.031020564 200741.5426

28 1.161956351 2.463548047e-006 312.2665848 4.002305522 198809.0911

29 1.15002278 2.414515161e-006 310.5565587 4.051105899 201010.664

30 1.228788002 2.462730946e-006 311.9759123 4.002465142 198048.4394

31 1.172507784 2.439979243e-006 310.3445121 4.045835455 200929.8451

32 1.16274216 2.436677945e-006 310.8495717 4.052950386 198641.8908

33 1.163404786 2.448952579e-006 312.5822833 4.055311234 200710.9627

34 1.19363736 2.4407332e-006 310.7386866 4.04440186 201337.7593

35 1.156385116 2.443376736e-006 311.8955817 4.002870577 201142.5775

36 1.229423861 2.484883852e-006 311.3271903 4.000504766 198420.624

37 1.230494371 2.439937582e-006 311.7844628 4.03095448 199689.6207

38 1.249186462 2.526691404e-006 312.5467961 4.028011815 200876.8773

39 1.1673434 2.486111064e-006 312.7224697 4.020497728 198988.6399

40 1.16423133 2.522221303e-006 312.4896303 4.049045499 199894.4426

41 1.178605923 2.470474519e-006 310.3619594 4.007358948 198846.1086
H-4

Task d1 d2 d3 d4 d5

42 1.204764185 2.521025227e-006 310.2319293 4.056213847 200053.1158

43 1.23830385 2.493262945e-006 311.7110348 4.04915204 201195.4523

44 1.218549784 2.416811688e-006 310.5333318 4.014152869 199978.6343

45 1.200021797 2.450077201e-006 312.3524759 4.050320317 199519.9327

46 1.221765269 2.499322638e-006 312.8781127 4.03964463 201312.8011

47 1.211701304 2.518066864e-006 311.3942794 4.022256282 198041.8849

48 1.252444682 2.448642923e-006 311.7656376 4.048493204 200997.5058

49 1.174019596 2.420912562e-006 311.5015568 4.027505964 199923.8011

50 1.220077612 2.486782123e-006 311.3040702 4.026990518 200591.0934

51 1.180490223 2.395853495e-006 311.8770006 4.000823229 199240.1799

52 1.208376032 2.524637061e-006 310.6062005 4.005596217 201133.0435

53 1.225807226 2.515448503e-006 312.9513124 3.995255399 198552.7244

54 1.199700711 2.410784885e-006 310.3280243 4.026027434 199924.0856

55 1.151178144 2.431500469e-006 312.9397554 4.053789588 199530.9724

56 1.221949562 2.393842915e-006 311.5173876 4.012490291 200774.8046

57 1.194827188 2.443084275e-006 312.1149313 4.024035773 201431.4216

58 1.216611366 2.44225905e-006 312.5725676 4.065433359 198700.887

59 1.178958521 2.480195941e-006 310.3771229 4.066184681 199449.9095

60 1.254198012 2.395136977e-006 313.0961165 4.038898077 199720.0463

61 1.212774039 2.384986595e-006 311.6093553 4.01914102 198464.9359

62 1.245112926 2.383704995e-006 311.7856871 4.005556055 200890.4162

63 1.196573187 2.382105708e-006 310.6735401 4.006064372 200280.7129

64 1.177365087 2.467890752e-006 311.784395 4.001455371 201508.6504

65 1.195789659 2.392392496e-006 312.7900573 4.047265836 200137.1734

66 1.221721993 2.474430903e-006 311.8934408 4.021992312 200460.6741

67 1.236427478 2.474353577e-006 311.5493739 3.988591843 200465.2532

68 1.242977798 2.435275776e-006 311.1100819 4.023985526 198295.216

69 1.188578191 2.49716266e-006 311.6175088 4.009136206 200986.7938

70 1.200070251 2.512374927e-006 312.6671969 4.011062819 200670.4871

71 1.171520062 2.450486078e-006 313.0965151 4.063208392 200204.9271

72 1.252990503 2.381264575e-006 311.3799446 4.048431681 198725.0763

73 1.245641287 2.441558862e-006 311.2924641 4.038497292 198598.6882

74 1.220183188 2.435540174e-006 311.4759517 3.993550924 200084.7291

75 1.207060719 2.393156398e-006 311.155557 4.040436454 199941.8642

76 1.225528296 2.503549564e-006 312.2459477 4.017101359 198853.6507

77 1.168121787 2.514209322e-006 312.7066144 3.995907751 199403.9034

78 1.173906934 2.435796224e-006 311.43329 4.013397955 198180.3021

79 1.204945456 2.509581228e-006 312.7614165 4.031807069 199016.9069
H-5

Task d1 d2 d3 d4 d5

80 1.140466754 2.455592014e-006 310.9456994 4.049376788 200571.6432

81 1.185470414 2.3873701e-006 311.9450572 4.043927376 200100.6533

82 1.166923317 2.44067852e-006 311.6792041 4.02554793 198372.2961

83 1.241680803 2.429272926e-006 310.3971516 4.032208829 201432.7699

84 1.232028194 2.523661735e-006 310.1836821 4.06106545 200855.7882

85 1.177913604 2.473537202e-006 312.0595841 4.013136751 198408.4456

86 1.18142858 2.450264936e-006 311.9427259 4.063318637 198664.0121

87 1.203976444 2.484549815e-006 310.6574562 3.994142626 200297.2561

88 1.21735519 2.504901872e-006 311.8075461 4.014718318 201785.7967

89 1.173233238 2.433296083e-006 312.5010559 4.011062844 201055.5127

90 1.246597486 2.416417399e-006 312.7670575 4.009882403 199281.5335

91 1.20733848 2.458149972e-006 310.5739985 4.041158782 198261.7171

92 1.244646178 2.425144579e-006 311.070924 4.009238202 200815.2835

93 1.184760093 2.476395829e-006 312.3601637 4.064502643 199616.7621

DAKOTA Input File

The input file used in a -pre_run DAKOTA invocation to generate the random variates.

strategy, 

 single_method 

method, 

 nond_sampling, 

 samples = 93 

 # stub response levels 

 response_levels = 0.0 1.0 

 sample_type random 

 distribution cumulative 

variables, 

 normal_uncertain = 5 

 descriptors = 'd1' 'd2' 'd3' 'd4' 'd5' 

 means = 1.2 2.5E-6 311.65 4.0277 2.0E5 

 std_deviations = 0.06 1.25E-7 1.5 0.040277 2000.0 

 lower_bounds = 1.14 2.38E-6 310.15 3.9875 1.98E5 

 upper_bounds = 1.26 2.53E-6 313.15 4.068 2.02E5 

interface, 

 system 

 analysis_driver = '<not used>' 

responses, 

 num_response_functions = 1 

 no_gradients 

 no_hessians 







NUREG/IA-0462 August 2017 Uncertainty and Sensitivity Invetigations with TRACE-SUSA and TRACE-DAKOTA

by Means of Post-test Calculations of NUPEC BFBT Experiments