NUREG/IA-0186

International 

Agreement Report 

Analysis of the 

RELAP5/MOD3.2.2beta 

Critical Flow Models and 

Assessment Against Critical Flow 

Data From the Marviken Tests 

Prepared by 

C. Queral, J. Mulas, C. G. de la Rfia 

Energy Systems Department 

School of Mining Engineering 

Polytechnic University of Madrid 

SPAIN 

Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission 

Washington, DC 20555-0001 

July 2000 

Prepared as part of 

The Agreement on Research Participation and Technical Exchange 

under the International Code Application and Maintenance Program (CAMP) 

Published by 

U.S. Nuclear Regulatory Commission
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I I ;Il
NUREG/IA-0186

International 

QU Agreement Report 

Analysis of the 

RELAP5/MOD3.2.2beta 

Critical Flow Models and 

Assessment Against Critical Flow 

Data From the Marviken Tests 

Prepared by 

C. Queral, J. Mulas, C. G. de la Rda 

Energy Systems Department 

School of Mining Engineering 

Polytechnic University of Madrid 

SPAIN 

Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission 

Washington, DC 20555-0001 

July 2000 

Prepared as part of 

The Agreement on Research Participation and Technical Exchange 

under the International Code Application and Maintenance Program (CAMP) 

Published by 

U.S. Nuclear Regulatory Commission
iii

Abstract 

In this report the critical flow models of RELAP5/MOD3.2.2beta have been 

analized. Firstly, an analysis of the implementation of the RELAP5/MOD3.2.2beta 

models have been performed in which it has been proved that the transition from the 

critical to the non-critical flow model is not well done for the Ransom-Trapp model. 

Secondly, a sensitivity analysis of both models (Ransom-Trapp and Henry-Fauske) 

in subcooled, two-phase and vapor conditions has been taken with respect to 

temperature, pressure, void-fraction, discharge coefficients, energy loss coefficient 

and disequilibrium parameter. Finally, seven Marviken tests have been simulated 

and compared with the experimental data in order to validate both models. As 

a part of this assessment, an adjustment of the discharge coefficients for the 

Ransom-Trapp model with different nodalizations has been done and also it has 

been checked which are the best values of the disequilibrium parameter for the 

Henry-Fauske model in subcooled and two-phase conditions. 

Conclusions indicate that the behaviour of the Henry-Fauske model is better than 

that of the Ransom-Trapp. In this sense, the new model is an improvement with 

respect to the Ransom-Trapp.
Contents 

1 Introduction 1 

2 Analysis of RELAP5/MOD3.2 Critical Flow Model 3 

2.1 Problems with the transition from CFM to Non-CFM. Logic of 

JCHOKE subroutine ........................... 4 

3 Sensitivity Analysis of RELAP5/MOD3 CFM 7 

3.1 Sensitivity Analysis of Ransom-Trapp Model .............. 7 

3.1.1 Sensitivity Analysis of Subcooled CFM to Temperature, Pres

sure, MDC and Forward Energy Loss Coefficient .......... 9 

3.1.2 Sensitivity Analysis of Two-phase CFM to Void-fraction and 

TDC ........ ................................ 30 

3.1.3 Sensitivity Analysis of Steam CFM to Temperature, Pressure 

and SDC ........ .............................. 38 

3.2 Sensitivity Analysis of Henry-Fauske Model ................... 47 

3.2.1 Sensitivity Analysis of Subcooled CFM to Temperature, Pres

sure, Disequilibrium Parameter and Forward Energy Loss Co

efficient ........ .............................. 49 

3.2.2 Sensitivity Analysis of Two-phase CFM to Void-fraction and 

Disequilibrium Parameter ...... .................... 50 

3.3 Discussion and Conclusions of the Sensitivity Results ............ 56 

4 Assessment of RELAP5/MOD3 CFM against Marviken Tests 57 

4.1 Facility and Test Description ............................. 58 

4.2 Models Description ........ ............................ 64 

4.3 Review of the Marviken Tests Simulation Bibliography ........... 67

v
vi CONTENTS 

4.4 Results and Discussion of Boundary Condition Model (BCM). 

Ransom-Trapp Model .................................. 81 

4.4.1 Comparison of Critical and Non-critical Flow Models ..... .. 93 

4.4.2 Selection of Model Options .......................... 99 

4.4.3 Discharge Coefficient Adjustment ..................... 106 

4.5 Results and Discussion of the Initial Condition Model (ICM). 

Ransom-Trapp Model .................................. 125 

4.5.1 Discharge Coefficient Adjustment ..................... 125 

4.5.2 Comparison between TRAC-BF1 and RELAP5/MOD3.2 Re

sults ........ ................................. 132 

4.6 Results and Discussion of Boundary Condition Model (BCM). Henry

Fauske Model ........ ............................... 132 

5 Conclusions 139 

Bibliography 145 

I Appendix: Subroutine JCHOKE flow logic 148 

II Appendix: Modified JCHOKE Subroutine 163

I I I
List of Figures 

2.1 Selection model block diagram. JCHOKE Subroutine ............ 5 

2.2 Transition from CFM to Non-CFM block diagram. JCHOKE sub

routine ......... ................................... 6 

3.1 Sensitivity nodalization model ............................ 8 

3.2 Pressure at the last node (Temperature sensitivity of the subcooled 

model, with increasing temperature). CFM on .................. 12 

3.3 Pressure at the last node (Temperature sensitivity of the subcooled 

model, with increasing temperature). CFM off ................. 12 

3.4 Temperature at the last node (Temperature sensitivity of the sub

cooled model, with increasing temperature). CFM on .......... .. 13 

3.5 Temperature at the last node (Temperature sensitivity of the sub

cooled model, with increasing temperature). CFM off .......... .13 

3.6 Mass flow at the last node (Temperature sensitivity of the subcooled 

model, with increasing temperature). CFM on .................. 14 

3.7 Mass flow at the last node (Temperature sensitivity of the subcooled 

model, with increasing temperature). CFM off ................. 14 

3.8 Mass flow at the last node (Temperature sensitivity of the subcooled 

model, with increasing temperature). Comparison of CFM on with 

CFM off ........................................... 15 

3.9 Temperature at the last node (Temperature sensitivity of the sub

cooled model, with decreasing temperature). CFM on ........... 16 

3.10 Temperature at the last node (Temperature sensitivity of the sub

cooled model, with decreasing temperature). CFM off ......... .. 16 

3.11 Mass flow at the last node (Temperature sensitivity of the subcooled 

model, with decreasing temperature). CFM on ................. 17

vii
viii LIST OF FIGURES 

3.12 Mass flow at the last node (Temperature sensitivity of the subcooled 

model, with decreasing temperature). CFM off ................. 17 

3.13 Mass flow at the last node (Temperature sensitivity of the subcooled 

model, with decreasing temperature). Comparison of CFM on with 

CFM off ........................................... 18 

3.14 Transition at temperature from CFM to Non-CFM. Subcooled region. 19 

3.15 Subcooling. Transition from CFM to Non-CFM. Subcooled region... 19 

3.16 Liquid temperature at the last node (Pressure sensitivity of the 

subcooled model, with increasing pressure). CFM on ............ 20 

3.17 Liquid temperature at the last node (Pressure sensitivity of the 

subcooled model, with increasing pressure). CFM off ............ 20 

3.18 Pressure at the last node (Pressure sensitivity of the subcooled model, 

with increasing pressure). CFM on .......................... 21 

3.19 Pressure at the last node (Pressure sensitivity of the subcooled model, 

with increasing pressure). CFM off. ....................... 21 

3.20 Mass flow at nozzle exit (Pressure sensitivity of the subcooled model, 

with increasing pressure). CFM on .......................... 22 

3.21 Mass flow at nozzle exit (Pressure sensitivity of the subcooled model, 

with increasing pressure). CFM off. ....................... 22 

3.22 Mass flow at nozzle exit (Pressure sensitivity of the subcooled model, 

with increasing pressure). Comparison of CFM on with CFM off. . 23 

3.23 Pressure at the last node (Pressure sensitivity of the subcooled model, 

with decreasing pressure). CFM on ......................... 24 

3.24 Pressure at the last node (Pressure sensitivity of the subcooled model, 

with decreasing pressure). CFM off. ....................... 24 

3.25 Mass flow at nozzle exit (Pressure sensitivity of the subcooled model, 

with decreasing pressure). CFM on ......................... 25 

3.26 Mass flow at nozzle exit (Pressure sensitivity of the subcooled model, 

with decreasing pressure). CFM off. ....................... 26 

3.27 Mass flow at nozzle exit (Pressure sensitivity of the subcooled model, 

with decreasing pressure). Comparison of CFM on with CFM off.. 26 

3.28 Pressure at the last node. MDC sensitivity of the subcooled model. 27 

3.29 Temperature at the last node. MDC sensitivity of the subcooled model. 27

I I I
LIST OF FIGURES ix 

3.30 Mass flow at nozzle exit. MDC sensitivity of the subcooled model.. 28 

3.31 Mass flow at nozzle exit. Energy loss coefficient sensitivity of the 

subcooled model ........ .............................. 28 

3.32 Pressure at the last node. Energy loss coefficient sensitivity of the 

subcooled model ........ .............................. 29 

3.33 Pressure at the last node. Void-fraction sensitivity of the two-phase 

model. Homogeneous and non-homogeneous models .............. 31 

3.34 Void-fraction at nozzle exit. Void-fraction sensitivity of the two-phase 

model. Homogeneous model .............................. 32 

3.35 Mass flow at nozzle exit. Void-fraction sensitivity of the two-phase 

model. Homogeneous model .............................. 32 

3.36 Critical mass flux. Ransom-Trapp model ..................... 33 

3.37 Critical mass flux. Homogeneous model (Taken from ILAH-93J pp 444). 34 

3.38 Void-fraction at nozzle exit. Void-fraction sensitivity of the two-phase 

model. Non-homogeneous model ........................... 35 

3.39 Mass flow at nozzle exit. Void-fraction sensitivity of the two-phase 

model. Non-homogeneous model ........................... 35 

3.40 Pressure at the last node. TDC sensitivity of the two-phase model. 36 

3.41 Void-fraction at nozzle exit. TDC sensitivity of the two-phase model. 36 

3.42 Mass flow at nozzle exit. TDC sensitivity of the two-phase model. .. 37 

3.43 Pressure at the last node (Temperature sensitivity of the steam 

model). CFM on ...................................... 40 

3.44 Pressure at the last node (Temperature sensitivity of the steam 

model). CFM off ..................................... 40 

3.45 Temperature at the last node (Temperature sensitivity of the steam 

model). CFM on ...................................... 41 

3.46 Temperature at the last node (Temperature sensitivity of the steam 

model). CFM off ..................................... 41 

3.47 Mass flow at nozzle exit (Temperature sensitivity of the steam model). 

CFM on ........................................... 42 

3.48 Mass flow at nozzle exit (Temperature sensitivity of the steam model). 

CFM off ........................................... 42
x LIST OF FIGURES 

3.49 Liquid temperature at the last node (Pressure sensitivity of the steam 

model). CFM on ..................................... 43 

3.50 Liquid temperature at the last node (Pressure sensitivity of the steam 

model). CFM off ..................................... 43 

3.51 Pressure at the last node (Pressure sensitivity of the steam model). 

CFM on ........................................... 44 

3.52 Pressure at the last node (Pressure sensitivity of the steam model). 

CFM off. .......................................... 44 

3.53 Mass flow at nozzle exit (Pressure sensitivity of the steam model). 

CFM on ........................................... 45 

3.54 Mass flow at nozzle exit (Pressure sensitivity of the steam model). 

CFM off ........................................... 45 

3.55 Mass flow at nozzle exit (Pressure sensitivity of the steam model). 

Comparison of CFM on and CFM off ....................... 46 

3.56 Pressure at the last node. SDC sensitivity of the steam model ..... .47 

3.57 Temperature at the last node. SDC sensitivity of the steam model. . 48 

3.58 Mass flow at nozzle exit. SDC sensitivity of the steam model ..... .48 

3.59 Mass flow at nozzle exit. Temperature sensitivity of the subcooled 

Henry-Fauske model, with increasing temperature .............. 50 

3.60 Mass flow at nozzle exit. Temperature sensitivity of the subcooled 

Henry-Fauske model, with decreasing temperature .............. 51 

3.61 Mass flow at nozzle exit. Pressure sensitivity of the subcooled Henry

Fauske model, with decreasing pressure ..................... 51 

3.62 Mass flow at nozzle exit. Disequilibrium parameter sensitivity of the 

subcooled Henry-Fauske model ............................ 52 

3.63 Mass flow at nozzle exit. Forward energy loss coefficient sensitivity 

of the subcooled Henry-Fauske model ....................... 52 

3.64 Mass flow at nozzle exit. Void-fraction sensitivity of the Henry-Fauske 

model ......... .................................... 53 

3.65 Void fraction at nozzle exit. Void-fraction sensitivity of the Henry

Fauske model ........................................ 54 

3.66 Critical mass flux. Henry-Fauske model ..................... 54
LIST OF FIG URES xi

3.67 Mass flow at nozzle exit. Disequilibrium parameter sensitivity of the 

Henry-Fauske model ................................. 

3.68 Void fraction at nozzle exit. Disequilibrium parameter sensitivity of 

the Henry-Fauske model ..............................

4.1 Pressure vessel diagram ............................ 

4.2 Discharge pipe and test nozzle ....................... 

4.3 Test nozzle used from Test 15 onwards .................. 

4.4 Locations of typical measurements in the pressure vessel..... 

4.5 MARVIKEN initial conditions models ................... 

4.6 MARVIKEN boundary conditions models. ............... 

4.7 Evaporation during flashing. CATHARE, DRUFAN, R 

LAP5/MOD2 and THYDE-P2 codes .................... 

4.8 Evaporation during flashing of TRAC-PF1 code and comparison 

the models .....................................

4.9 

4.10 

4.11 

4.12 

4.13 

4.14 

4.15 

4.16 

4.17 

4.18 

4.19 

4.20 

4.21 

4.22 

4.23

. . . 59 

.. . 60 

. . . 61 

.. . 63 

.. . 66 

.. . 67

E

of

68 

69

Pressure at bottom vessel. Test data. CFT-01 ................. 82 

Liquid temperature at bottom vessel. Test data. CFT-01 ........ .. 82 

Static quality at bottom vessel. Test data. CFT-01 .............. 83 

Pressure at bottom vessel. Test data. CFT-06 ................. 83 

Liquid temperature at bottom vessel. Test data. CFT-06 ........ .. 84 

Static quality at bottom vessel. Test data. CFT-06 ............. 84 

Pressure at bottom vessel. Test data. CFT-11 ................. 85 

Liquid temperature at bottom vessel. Test data. CFT-11 ........ .. 85 

Static quality at bottom vessel. Test data. CFT-11 .............. 86 

Pressure at bottom vessel. Test data. CFT-15 ................. 86 

Liquid temperature at bottom vessel. Test data. CFT-15 ........ .. 87 

Static quality at bottom vessel. Test data. CFT-15 ............. 87 

Pressure at bottom vessel. Test data. CFT-17 ................. 88 

Liquid temperature at bottom vessel. Test data. CFT-17 ........ .. 88 

Pressure at bottom vessel. Test data. CFT-21 ................. 89

4.24 Liquid temperature at bottom vessel. Test data. CFT-21 ....... .9

55 

55

LIST OF FIGURES xi

90
xii LIST OF FIGURES

Static quality at bottom vessel. Test data. CFT-21 .... 

Pressure at bottom vessel. Test data. CFT-24 ........ 

Liquid temperature at bottom vessel. Test data. CFT-24. 

Static quality at bottom vessel. Test data. CFT-24 ...

4.29 Mass flow at nozzle exit. Comparison between CFM and

(BCM). CFT-01.. 

4.30 Mass flow at nozzle 

(BCM). CFT-06.. 

4.31 Mass flow at nozzle 

(BCM). CFT-11.. 

4.32 Mass flow at nozzle 

(BCM). CFT-15.. 

4.33 Mass flow at nozzle 

(BCM). CFT-17.. 

4.34 Mass flow at nozzle 

(BCM). CFT-21.. 

4.35 Mass flow at nozzle 

(BCM). CFT-24..

exit. 

exit. 

exit. 

exit. 

exit. 

exit.

Comparison 

Comparison 

Comparison 

Comparison 

Comparison 

Comparison

between CFM 

between CFM 

between CFM 

between CFM 

between CFM

and 

and 

and 

and 

and

between CFM and

4.25 

4.26 

4.27 

4.28

90 

91 

91 

92 

94 

95 

96 

96 

97 

97 

98

4.36 Void fraction. 

CFT-01. ... 

4.37 Void fraction. 

CFT-06. ... 

4.38 Void fraction. 

CFT-11. .... 

4.39 Void fraction. 

CFT-15. .... 

4.40 Void fraction. 

CFT-17. .... 

4.41 Void fraction. 

CFT-21 ... 

4.42 Void fraction.

CFT-24.

Comparison 

Comparison 

Comparison 

Comparison 

Comparison 

Comparison 

Comparison

between 

between 

between 

between 

between 

between 

between

CFM and 

CFM and 

CFM and 

CFM and 

CFM and 

CFM and 

CFM and

non-CFM 

non-CFM 

non-CFM 

non-CFM 

non-CFM 

non-CFM 

non-CFM

(BCM). 

(BCM). 

(BCM). 

(BCM). 

(BCM). 

(BCM). 

(BCM).

• 9, 

•100 

.100 

•101 

.101 

. 102

S............................... 102

I I I

non-CFM 

non-CFM 

non-CFM 

non-CFM 

non-CFM 

non-CFM 

non-CFM
LIST OF FIGURES xiii 

4.43 Mass flow at nozzle exit. Comparison between Homogeneous and 

Non-homogeneous options. BCM-J. CFT-15 .................. 103 

4.44 Mass flow at nozzle exit. Comparison between Homogeneous and 

Non-homogeneous options. BCM-J. CFT-24 .................. 103 

4.45 Mass flow at nozzle exit. Comparison between Homogeneous and 

Non-homogeneous options. BCM-P. CFT-15 .................. 104 

4.46 Mass flow at nozzle exit. Comparison between Homogeneous and 

Non-homogeneous options. Nozzle modeled as PIPE (BCM). CFT-24. 104 

4.47 Comparison of Single junction, Trip-Valve and Motor-Valve Models. 

Subcooled CFM. MDC=1.0, 0.85 (BCM). CFT-21 ............. 105 

4.48 Comparison of Single junction, Trip-Valve and Motor-Valve Models. 

Subcooled and two-phase CFM (BCM). CFT-21 ............... 105 

4.49 Mass flow at nozzle exit. Discharge coefficient adjustment, BCM-J. 

CFT-01 ........................................... 107 

4.50 Void fraction at nozzle exit. Discharge coefficient adjustment, BCM

J. CFT-01 .......... ................................ 107 

4.51 Liquid and saturation temperatures at nozzle exit. Discharge coeffi

cient adjustment, BCM-J. CFT-01 .......................... 108 

4.52 Mass flow at nozzle exit. Discharge coefficient adjustment, BCM-J. 

CFT-06 ........................................... 108 

4.53 Void fraction at nozzle exit. Discharge coefficient adjustment, BCM

J. CFT-06 .......... ................................ 109 

4.54 Liquid and saturation temperatures at nozzle exit. Discharge coeffi

cient adjustment, BCM-J. CFT-06 ......................... 110 

4.55 Mass flow at nozzle exit. Discharge coefficient adjustment, BCM-J. 

CFT-11 ......................................... .. 111 

4.56 Void fraction at nozzle exit. Discharge coefficient adjustment, BCM

J. CFT-11 ......................................... 111 

4.57 Liquid and saturation temperatures at nozzle exit. Discharge coeffi

cient adjustment, BCM-J. CFT-11 .......................... 112 

4.58 Mass flow at nozzle exit. Discharge coefficient adjustment, BCM-J. 

CFT-15 ........................................... 112 

4.59 Void fraction at nozzle exit. Discharge coefficient adjustment, BCM

J. CFT-15 .......... ................................ 113
xiv LIST OF FIGURES

4.60 Liquid and saturation temperatures at nozzle exit. Discharge coeffi

cient adjustment, BCM-J. CFT-15 ....................... 

4.61 Mass flow at nozzle exit. Discharge coefficient adjustment, BCM-J. 

CFT-17 ........ .................................. 

4.62 Liquid and saturation temperatures at nozzle exit. Discharge coeffi

cient adjustment, BCM-J. CFT-17 ....................... 

4.63 Mass flow at nozzle exit. Discharge coefficient adjustment, BCM-J. 

CFT-21 ........ .................................. 

4.64 Void fraction at nozzle exit. Discharge coefficient adjustment, BCM

J. CFT-21 ........................................ 

4.65 Liquid and saturation temperatures at nozzle exit. Discharge coeffi

cient adjustment, BCM-J. CFT-21 ....................... 

4.66 Mass flow at nozzle exit. Discharge coefficient adjustment, BCM-J. 

CFT-24 ........ .................................. 

4.67 Void fraction at nozzle exit. Discharge coefficient adjustment, BCM

J. CFT-24 ....................................... 

4.68 Liquid and saturation temperatures at nozzle exit. Discharge coeffi

cient adjustment, BCM-J. CFT-24 .......................

4.69 

4.70

Void fraction 

Mass flow at 

CFT-01...

4.71 Void fraction 

P. CFT-01. 

4.72 Mass flow at 

CFT-11... 

4.73 Void fraction 

P. CFT-11. 

4.74 Mass flow at 

CFT-15... 

4.75 Void fraction 

P. CFT-15. 

4.76 Mass flow at 

CFT-17.. 

I

nozzle exit. Discharge coefficient adjustment, BGM-P. 

at nozzle exit. Discharge coefficient adjustment, BCM

nozzle exit. Discharge coefficient adjustment, BCM-P. 

at nozzle exit. Discharge coefficient adjustment, BCM

nozzle exit. Discharge coefficient adjustment, BCM-P. 

at nozzle exit. Discharge coefficient adjustment, BCM

nozzle exit. Discharge coefficient adjustment, BCM-P. ... ....... . . . . . . . . . . . . . . .

113 

114 

114 

115 

115 

116 

116 

117 

117

118 

119 

119 

120 

120 

121 

121 

122

I I

LIST OF FIGURES xiv

nt. nn,77.1p Pvif. Pt('.M-T
4.77 Void fraction at nozzle exit. Discharge coefficient adjustment, BCM

P. CFT-17 ........ ................................. 122 

4.78 Mass flow at nozzle exit. Discharge coefficient adjustment, BCM-P. 

CFT-21 ........................................... 123 

4.79 Void fraction at nozzle exit. Discharge coefficient adjustment, BCM

P. CFT-21 ........ ................................. 123 

4.80 Comparison of MDC and TDC adjustment for BCM-J and BCM-P. . 124 

4.81 MDC and TDC adjustment. Nozzle modeled as SINGLE JUNCTION 

(ICM). CFT-06 ...................................... 127 

4.82 MDC and TDC adjustment. Nozzle modeled as SINGLE JUNCTION 

(ICM). CFT-15 ...................................... 127 

4.83 MDC and TDC adjustment. Nozzle modeled as SINGLE JUNCTION 

(ICM). CFT-21 ...................................... 128 

4.84 TDC adjustment. Nozzle modeled as SINGLE JUNCTION (ICM). 

CFT-24 ........................................... 128 

4.85 MDC and TDC adjustment. Mass flow at nozzle exit. Nozzle modeled 

as PIPE (ICM). CFT-06 ................................ 129 

4.86 MDC adjustment. Mass flow at nozzle exit. Nozzle modeled as PIPE 

(ICM). CFT-15 ...................................... 129 

4.87 TDC adjustment. Mass flow at nozzle exit. Nozzle modeled as PIPE 

(ICM). CFT-15 ...................................... 130 

4.88 MDC and TDC adjustment. Mass flow at nozzle exit. Nozzle modeled 

as PIPE (ICM). CFT-21 ................................ 130 

4.89 MDC and TDC adjustment. Mass flow at nozzle exit. Nozzle modeled 

as PIPE (ICM). CFT-24 ................................ 131 

4.90 Mass flow at nozzle exit. Comparison between TRAC-BF1 and 

RELAP5/MOD3.2 results. Nozzle modeled as PIPE. CFT-24 ..... .132 

4.91 Mass flow at nozzle exit. Comparison between BCM-J and BCM-P 

with dp = 0.14 and 0.01. CFT-15 .......................... 135 

4.92 Mass flow at nozzle exit. Comparison between BCM-J and BCM-P 

with dp = 0.14 and 0.01. CFT-21 .......................... 135 

4.93 Mass flow at nozzle exit. Comparison between BCM-J and BCM-P 

with dp = 0.14 and 0.01. CFT-24 .......................... 136

LIST OF FIGURES XV
xvi LIST OF FIGURES

4.94 Void-fraction at nozzle exit. Comparison between BCM-J and 

P with dp = 0.14 and 0.01. CFT-15 .................. 

4.95 Void-fraction at nozzle exit. Comparison between BCM-J and 

P with dp = 0.14 and 0.01. CFT-21 .................. 

4.96 Void-fraction at nozzle exit. Comparison between BCM-J and

P with dp = 0.14 and 0.01. CFT-24. 

1 Subroutine JCHOKE flow logic. ... 

2 Subroutine JCHOKE flow logic (contir

Subroutine JCHOKE flow 

Subroutine JCHOKE flow 

Subroutine JCHOKE flow 

Subroutine JCHOKE flow 

Subroutine JCHOKE flow 

Subroutine JCHOKE flow 

Subroutine JCHOKE flow 

Subroutine JCHOKE flow 

Subroutine JCHOKE flow 

Subroutine JCHOKE flow

logic (contir 

logic (contir 

logic (conti 

logic (conti 

logic (contir 

logic (contir 

logic (contir 

logic (conti] 

logic (contii 

logic (contir

S.... . . . . . . . . . . . . . . 137 

S.... . . . . . . . . . . . . . . 151 

nued) ................... 152 

nued) ................... 153 

nued) ................... 154 

aued) ................... 155 

aued) ................... 156 

nued) ................... 157 

anued) ................... 158 

aued) ................... 159 

aued) ................... 160 

aued) ................... 161 

aued) ................... 162

BCM

BCM

BCM136 

137

3 

4 

5 

6 

7 

8 

9 

10 

11 

12

I I I

xvi LIST OF FIG URES
List of Tables 

4.1 Main characteristics of the Marviken Tests .................. 

4.2 Discharge coefficient adjustment. Comparison between BCM-J and 

BCM-P ........ ................................. 

4.3 Discharge coefficient adjustment. Comparison between ICM-J and 

ICM-P ........ .................................. 

4.4 Discharge coefficient adjustment. Comparison between ICM and 

BCM results (The values marked with * do not adjust with test data) .

xvii

* 65 

* 124 

* 126 

* 131
xix 

Executive Summary 

The analysis and assessment of the critical flow models of RELAP5/MOD3.2.2beta 

(Ransom-Trapp and Henry-Fauske) has been performed in three stages: 

Firstly, the implementation of the RELAP5/MOD3.2.2beta models has been 

checked. It was concluded that the transition from the critical to the non-critical 

flow model is not always adecuate in the Ransom-Trapp model because one of the 

conditions checked in the subroutine in order to determine whether the flow is crit

ical or non-critical (flow critical in the previous time step and pressures strictly 

decreasing in the flow direction) is only a neccesary but no sufficient condition to 

assure if the flow will unchoke. 

Secondly, a sensitivity analysis of both models in subcooled, two-phase and vapor 

conditions has been taken with respect to temperature, pressure, void-fraction, 

discharge coefficients, energy loss coefficient and disequilibrium parameter. In these 

analysis several anomalous behaviours of the Ransom-Trapp model are shown. In 

the other hand the Henry-Fauske model shows a good behaviour. 

Finally, RELAP5/MOD3.2.2beta simulations have been conducted to assess the 

critical flow models of the code. As a part of this assessment an adjustment of 

the discharge coefficients for the Ransom-Trapp model with different nodalizations 

has been done and also it has been checked which are the better values of the 

disequilibrium parameter for the Henry-Fauske model in subcooled and two-phase 

conditions. The main conclusions of this assessment are: 

From the simulation of the Marviken tests with the Ransom-Trapp model it is 

observed that the comparison between the Initial Condition Model (ICM) and the 

Boundary Condition Model (BCM) results and their discharge coefficients shows 

that the values used to adjust the mass flow for ICM are always greater than for 

BCM. This problem may be caused by experimental errors or some constitutive 

relations or correlations not compatibles with the critical flow model (e.g. the 

"Fflashing model and the interfacial friction model). 

From the simulation of the Marviken tests with the Henry-Fauske model it is 

concluded that, 

1. The best values of dp for adjusting the model are, 

"* dp = 0.14 for subcooled blowdown and LID < 1.5. 

"* dp = 0.01 for LID > 1.5.

o dp = 0.01 for saturated blowdown.
xx 

2. The best models for the different nozzles are, 

"* Short nozzles LID < 0.3 should be modeled as a junction. 

"* Long nozzles LID > 1.5 should be modeled as a pipe. 

"* This assessment does not give enough information about the which is the 

best model for intermediate nozzles 1.5 > LID > 0.3. 

3. At present, only one dp value can be used for subcooled and two-phase periods. 

So, two disequilibrium parameters should be implemented in order to include 

the values mentioned above (one of them for the subcooled period and another 

for the two-phase one), and also the transition between them. This solution 

generates a problem because it implies a new degree of freedom, and therefore 

a negative consequence for the user effect.
Chapter 1 

Introduction 

In a Loss of Coolant Accident (LOCA) analysis, the accurate prediction of the mass 

flow through a break during the blowdown phase is very important in evaluating the 

remaining coolant inventory and system pressure. In the RELAP5/MOD3.2 code, 

the break flow is calculated primarily by a critical flow model, consisting of the 

Lienard-Alamgir-Jones (LAJ) model for subcooled critical flow, and the Ransom

Trapp model for two-phase flow. 

As part of the Code Assessment and Maintenance Program (CAMP), the sensitiv

ity analysis and assessment of the RELAP5/MOD3.2 for the critical flow model has 

been carried out. The purpose of the sensitivity analysis is performing a qualitative 

and quantitative analysis of the model in comparison with data from the available 

bibliography, and its application to the uncertainty analysis of the plant models. 

The goal of this assessment is also to complete the previous Marviken critical flow 

tests analysis performed by other work teams (STUDSVIK, KAERI, INEL, ...). 

With this in mind, seven tests have been simulated using all the different models 

found in the bibliography, and compared with the test data. The discharge coeffi

cients for all the models have also been obtained. 

It is important to remark that new versions of the code (RELAP5/MOD3.2.2beta 

and RELAP5/MOD3.2.2gamma) have been developed during the realization of this 

report. These new versions include the Henry-Fauske model, which was not in 

RELAP5/MOD3.2. Therefore, a sensitivity analysis of this new model and also an 

assessment with Marviken tests has been performed.

1
Chapter 2 

Analysis of RELAP5/MOD3.2 

Critical Flow Model 

In order to deeply understand the Critical Flow Model (CFM) used by RE

LAP5/MOD3.2 and its implementation into the JCHOKE subroutine, the following 

tasks have been achieved: 

"* Analysis of the implementation of the model, relating the equations and the 

subroutine block diagram in volume 4 of the RELAP5/MOD3 manuals. 

"* Numbering of the subroutine block diagram, shown in Appendix I. 

"* Modification of the subroutine, including the comments and the previous 

numbering of the block diagram. The commented subroutine with the 

numbering of the block diagram is shown in Appendix IL. 

"* From the last two items, a simplified block diagram have been obtained, shown 

in Figure 2.1. 

In the simplified block diagram of the subroutine (Figure 2.1), the following points 

can be remarked: 

" Sound velocity selection (among subcooled, two-phase and steam) depending 

on the thermal-hydraulic conditions of the junction analyzed. The variable 

which represents the sound velocity is SONIC. 

" Interpolation and under relaxation of SONIC and JCAT variables. We 

performed a comparison between TRAC-BF1 and RELAP5/MOD3 critical 

flow models and its interpolations and under relaxations, to be found in 

[CQS-971.

3
* Logic of transition from critical flow to non-critical flow (TESTI and TEST2 

blocks). 

In order to understand the transition from critical to non-critical flow, a more 

detailed analysis has been performed in the next section. 

2.1 Problems with the transition from CFM to 

Non-CFM. Logic of JCHOKE subroutine 

In JCHOKE subroutine, a test is performed in order to check if the flow is critical 

or not, as is shown in Figure 2.2. So, in the subroutine, the flow is critical if one of 

the following conditions is verified: 

1. The mass flow calculated from the momentum solution is greater than the 

critical mass flow. 

2. The logical variable CHOKE is equal to TRUE. This condition is verified if 

the flow was critical in the previous time step and the pressures are strictly 

decreasing in the flow direction (two-fold pressure comparison). 

We must remark that the pressure condition is a poor test for determining if a junc

tion will unchoke (it is only a necessary but not sufficient condition), and so the 

logic of the subroutine could fail. Several examples of this problem are shown in the 

next chapter. 

In RELAP5/MOD3.2.2beta, the Henry-Fauske model has been also included. This 

new model has not been analyzed with the same level of detail in this work, but it 

has been checked that only the first condition is used. Therefore, the logic problem 

is not present in the new Henry-Fauske model. 

The solution of the problem is very easy, only it is necesary to remove the second 

condition (CHOKE=.TRUE.) from the second test. The problem has been reported 

to Scientech and they agreed with the previous statements.

4 ETSI Minas - Universidad Polit~cnica de Madrid
Chapter 2. Analysis of RELAP5/MOD3.2 Critical Flow Model 5

!BEGIN

Discharge coefficient 014 

calculation 

TEST-0 c22-C24 

C26 

- VOID>0.1... YES

TWO-PHASE 

OR 

STEAM

228 

TEST-1 c77-C79

AU Correlation C47-C62

C2ph(void=0.0) 

C64 

SVOID>1.0E-5

OR X>l.0e-9 

NO 

SUBCOOLED 

0 C66-04 

SONIC= 

max(ALJ,C2ph(void=0.0) 

SUBCOOLED C71-C72 

Underrelax JCAT

C63 

TRANSITION C75 v TRANSR- 3 Um C82-C8S 

YES 226 .TRUE. 2yU0

" YES Non-condesable 

C89 < .Xnc>1l.0e-63--- - model 

236 NO 

Um>Ug C90 

240 240 Steam tables-uf<_um<Ug • .-•/•.•248 

TWO-PHASE 

STEAM SAT. LIQUID 244 ' UmnOUf OR 

-- TRANSITION 

Steam tables x=O, TI=Tsat 

5o8 C93-C98 C102 107 C -C101 

SONIC=Csteam SONIC=C2ph • 

251 

251 0109-0110 YES 

o TRANSR-.TRUE. 258 S/~-/ 258 

257 NO C111-Cl15 TRANSIM 

TWO-PHASE v ,v 

OR Underrelax JCAT Interpolate SONIC, JCi 

STEAM Underrelax JCAT 

0 C116-Cl018 256 

v

C1191

C74 

TEST-2 

•.820

Underrelax SONIC

C122 TEST-2

Velocities calculation. VI, Vg

Underrelax VI, Vg

v •C126-C133

C138

1RETURNj

Figure 2.1: Selection model block diagram. JCHOKE Subroutine.

SUBCOOLED 

OR 

TRANSITION 

NO

TEST-1 C32-C37

251 v

TION 

AT'
6 ETSI Minas - Universidad Polit6cnica de Madrid

TEST-O NO 

Choked last dt? 1 CHOKE=.FALSE. 

YES 

CHOKE=.TRUE.

V

NO 

CHOKE=.FALSE.

TEST-i1 NO NON-CRmC 

Vm>0.5Vsound . r FLOWI

YES

CHOKE=.TRUE. 

OR 

-. Vm>Vsound .

YES

Figure 2.2: Transition from CFM to Non-CFM block diagram. JCHOKE subrou

tine.

I I

Pj>Pdown 

AND 

Pj<Pup

YES

NO NO• cRMC]II 

j--- FLOW

6 ETSI Minas - Universidad Polit~cnica de Madrid
Chapter 3 

Sensitivity Analysis of 

RELAP5/MOD3 CFM 

In RELAP5/MOD3.2.2beta, there are two critical flow models available: 

Ransom-Trapp and Henry-Fauske. A sensitivity analysis has been done for each 

model and a comparison of the results is presented at the end of the chapter. 

The model used for the sensitivity analysis is a vertical straight pipe, 0.441 m2 

of area, with an outlet single junction (abrupt area change option), 0.0707 m2 of 

area, and two time dependent volumes limiting the pipe, Figure 3.1. This model 

corresponds to the discharge pipe of Marviken critical flow test 06. The conditions 

for the analysis are given in the upper volume, while the atmospheric conditions are 

fixed in the lower one. 

The main applications of these results are: 

* Performing qualitative and quantitative analysis in comparison with the 

bibliography data. 

* Uncertainty analysis for plant models or experimental tests: If the uncertainty 

in the thermal hydraulic variables is known, one can estimate its impact in 

the associated critical mass flow uncertainty. 

3.1 Sensitivity Analysis of Ransom-Trapp Model 

A sensitivity analysis of the subcooled, two-phase and steam CFMs is presented in 

this section. The objective of this analysis is to obtain the dependence of the CFM 

with respect to the following variables:

7
ETSI Minas - Universidad Politkcnica de Madrid

INLETV 

TMDPVOL 

OUTLETJ SNGLJUN 

DISCHP PIPE 

DISCHP SGLJUN 

OUTLETV 

TMDPVOL 

Figure 3.1: Sensitivity nodalization model. 

- Temperature. 

- Pressure. 

- Void Fraction. 

- Discharge Coefficient. 

- Forward Energy Loss Coefficient 

In the same way, critical mass flow is compared with the non-critical mass flow in 

the same conditions in order to observe the differences between them. On the course 

of the analysis of the subcooled CFM, several problems associated with the logic of 

transition from critical to non-critical flow have appeared.

8
3.1.1 Sensitivity Analysis of Subcooled CFM to Tempera

ture, Pressure, MDC and Forward Energy Loss Coeffi

cient 

For the subcooled model, sensitivity analysis has been done with respect to the 

following variables: 

- Temperature. 

- Pressure. 

- Monophasic Discharge Coefficient (MDC). 

- Forward Energy Loss Coefficient 

The temperature sensitivity analysis was performed in the following way: The pipe 

inlet pressure (upper TMDPVOL) was fixed for each case and the temperature was 

ramped from 373 K to T8 ,r (increasing temperatures, 1 K/s). These calculations 

have been done for different pressures (from 10 bar to 150 bar). 

The same analysis have also been performed with temperatures decreasing from Tsat 

to 373 K, due to the non-expected results related to the transition from Non-CFM 

to CFM. 

The pressure sensitivity was performed in a similar way to the temperature sensi

tivity: 

The pipe inlet temperature (upper TMDPVOL) was fixed for each case and the pres

sure was varied from 10 bar to P,8a (increasing pressures). These calculations have 

been done for different temperatures (from 373 K to 613 K). For the same reason 

than in temperature analysis, a decreasing pressure analysis was also performed. 

For the MDC sensitivity analysis, a case from pressure sensitivity analysis was used 

as the base case, varying MDC from 0.6 to 1.4. In order to compare the CFM with 

the Non-CFM, temperature and pressure were checked values at the last node for 

assuring that they were similar. 

In the Forward Energy Loss Coefficient sensitivity analysis, the pipe inlet pressure 

was fixed to 40 bar and the temperature was varied from 373 K to 523 K. The mass 

flow is also compared for five different values of the forward energy loss coefficient 

(0, 25, 50, 75 and 100). 

The results obtained for the different sensitivity analysis are described below:

Chapter 3. Sensitivity Analysis of RELAPS/MOD3 CFM 9
Temperature Sensitivity. First, an increasing temperature sensitivity analysis 

was made for CFM and Non-CFM. In the results, it can observed that pressure, 

Figures 3.2 and 3.3, and temperature at the last node, Figures 3.4 and 3.5, are quite 

similar, so that the critical mass flow, Figure 3.6, and non-critical mass flow, Figure 

3.7, results can be compared. 

Two different behaviours are observed in Figure 3.6. These differences can be 

explained by comparison of CFM and Non-CFM, Figure 3.8, where a transition 

point is observed for each pressure. Also it is observed that critical mass flow is 

greater than non critical mass flow in a wide range of values. This is clearly a non

physical behaviour and also means that the transition from CFM to Non-CFM is 

not well implemented in the JCHOKE subroutine, as it was described in Section 

2.1. 

Second, a decreasing temperature sensitivity analysis was made for CFM and Non

CFM, Figures 3.9 and 3.10. Results of CFM-on and CFM-off are shown in Figures 

3.11 and 3.12, and a comparison between them in Figure 3.13. Results of CFM-on, 

Figure 3.11, show a different behaviour than in the increasing temperature analysis, 

Figure 3.6, with no transition for any pressure. 

This is in accordance with the explanation given in Section 2.1, because if a 

decreasing temperature transient begins with critical flow, the model selection logic 

could fail and then it could stay critical during all the transient. Moreover, if at 

beginning of the transient the JCHOKE subroutine selects the non-critical flow 

model, for increasing temperature transients with P < 50 bar, the model becomes 

non-critical while non-critical flow is smaller than critical one. The latter means 

that the selection of CFM or Non-CFM will depend on the history of the transient, 

and not only on the instantaneous physical conditions. 

Finally, for achieving a complete analysis of the problem, the transitions points 

for each pressure are obtained from Figure 3.8, and with these values the transition 

temperature and subcooling as a function of pressure are obtained, Figures 3.14 and 

3.15. The values of the transition subcoling point out that this transition problem 

is only important for large subcolings. 

Pressure Sensitivity. First, an increasing pressure sensitivity analysis was made 

for CFM and Non-CFM. In the results it can be observed that pressure, Figures 3.18 

and 3.19, and temperature, Figures 3.16 and 3.17, at the last node are quite similar, 

so that the critical mass flow, Figure 3.20, and non-critical mass flow, Figure 3.21, 

results can be compared, Figure 3.22. As in the temperature sensitivity analysis

10 ETSI Minas - Universidad Politkcnica de Madrid
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM

a non-physical behaviour is observed: the critical flow is sometimes greater than 

non-critical mass flow for a wide range of values. 

Second, a decreasing pressure sensitivity analysis was made for CFM and Non-CFM, 

Figures 3.23 and 3.24. The comparison between CFM-on and CFM-off, Figure 3.25 

shows a similar behaviour than in the increasing pressure analysis, Figure 3.22. 

MDC Sensitivity. For this analysis, a case from pressure sensitivity analysis was 

taken as a base case. Temperature is fixed at the pipe inlet, T= 553 K, and the 

pressure is varied from 160 to 65 bar. The results show that pressure, Figure 3.28, 

and temperature, Figure 3.29, are quite similar for all the discharge coefficients 

values. It is easy to check in Figure 3.30 that the variation of the mass flow with the 

discharge coefficient has the same value than the discharge coefficient, as expected. 

Forward Energy Loss Coefficient Sensitivity. The base case used here was 

taken from the temperature sensitivity analysis. Pressure is fixed to 40 bar and 

temperature is varied from 373 to 523 K at the pipe inlet. 

This case was chosen because in the first part of the transient the Non-CFM is 

selected by JCHOKE while in the second part the CFM is selected. The variation 

of both models with respect to the loss coefficient can thus be observed. In Figure 

3.31 it can be seen that Non-CFM varies with the loss coefficient, as expected, while 

the CFM does not. Thus, the CFM is independent of the loss coefficient. This 

shows that the energy loss coefficient must be used with care in junctions where 

critical mass flow is expected, because the CFM does not depend on it but non

CFM decreases with it.

11
12 ETSI Minas - Universidad Politknica de Madrid

2.0e+07

CRITICAL SUBCOOLED MODEL 

Temperature Sensitivity

1.5e+07 

I- 1.0e+07

5.0e+06 

O.Oe+00 

0.0 100.0 200.0 300.0 

Time (s) 

Figure 3.2: Pressure at the last node (Temperature sensitivity of the subcooled 

model, with increasing temperature). CFM on. 

CRITICAL SUBCOOLED MODEL 

Temperature Sensitivity

2.0e+07

1.5e+07

C 

U, 

U, 

C 1..

1.0e+07

5.0e+06

O.Oe+00 

0.0 100.0 200.0 

Time (s)

300.0

Figure 3.3: Pressure at the last node (Temperature sensitivity of the subcooled 

model, with increasing temperature). CFM off.

I I
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM 13

CRITICAL SUBCOOLED MODEL 

Temperature Sensitivity

600.0

- Liquid temperature 

Saturation temperature

350.0 -

0.0 100.0 200.0 300.0

Time (s) 

Figure 3.4: Temperature at the last node (Temperature sensitivity of the subcooled 

model, with increasing temperature). CFM on.

650.0 

600.0

550.0 ,

500.0

450.0 

400.0 

350.0 

0

CRITICAL SUBCOOLED MODEL 

Temperature Sensitivity

-I 

I

.0 100.0 200.0

I 

)o.o

Time (s)

Figure 3.5: Temperature at the last node (Temperature sensitivity of the subcooled 

model, with increasing temperature). CFM off.

650.0

550.0

500.0 -

E

450.0 

400.0

-J

E 

9

Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM 13

X(
ETSI Minas - Universidad Politkcnica de Madrid

CRITICAL SUBCOOLED MODEL 

Temperature Sensitivity

1

100.0 200.0 

Time (s)

Figure 3.6: Mass flow at the last node (Temperature sensitivity 

model, with increasing temperature). CFM on.

of the subcooled

CRITICAL SUBCOOLED MODEL 

Temperature Sensitivity

8000 

6000

4000

0

2000

0.0 0.0

1

100.0 200.0 300.0

Time (s) 

Figure 3.7: Mass flow at the last node (Temperature sensitivity of the subcooled 

model, with increasing temperature). CFM off.

I I

14

15000

0 

a.

10000 

5000

0 L 0.0 300.0
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM 15

CRITICAL SUBCOOLED MODEL 

Temperature Sensitivity 

15000.0 i

.2 

V.

10000.0 

5000.0

0.0 0.0

Time (s)

Figure 3.8: Mass flow at the last node (Temperature sensitivity of the subcooled 

model, with increasing temperature). Comparison of CFM on with CFM off.

Chapter 3. Sensitivity Analysis of RELAP51MOD3 CFM 15
16 ETSI Minas - Universidad PoliiAcnica de Madrid

700.0

E 

E 

0~ 

S 

.3

CRITICAL SUBCOOLED MODEL 

Temperature Sensitivity

600.0 

500.0 

400.0

300.0 

0.0 100.0 200.0 300.0

Time (s)

Figure 3.9: Temperature at the last node (Temperature sensitivity of the subcooled 

model, with decreasing temperature). CFM on.

.2 

.a3

650.0 

600.0 

550.0 

500.0 

450.0

400.0 

350.0 

0.0

CRITICAL SUBCOOLED MODEL 

Temperature Sensitivity

100.0 200.0 300.0

Time (s) 

Figure 3.10: Temperature at the last node (Temperature sensitivity of the subcooled 

model, with decreasing temperature). CFM off.

16 ETSI Minas - Universidad Polit~cnica de Madrid
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CEM 17

CRITICAL SUBCOOLED MODEL 

Temperature Sensitivity

100.0 200.0 300.0

Time (s)

Figure 3.11: Mass flow at the last node (Temperature sensitivity of the subcooled 

model, with decreasing temperature). CFM on.

CRITICAL SUBCOOLED 

Temperature Sensitivity

8000 

6000

00 

0

4000

2000 

0 

0.0 100.0 200.0 

Time (s)

MODEL

300.0

Figure 3.12: Mass flow at the last node (Temperature sensitivity of the subcooled 

model, with decreasing temperature). CFM off.

15000

10000

_o

5000 -

0.0 0.0

Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM 17
ETSI Minas - Universidad Polittcnica de Madrid

15000.0

CRITICAL SUBCOOLED MODEL 

Temperature Sensitivity

10000.0 -

0•

5000.0

0.0 L 

0.0 100.0 200.0 300.0

Time (s) 

Figure 3.13: Mass flow at the last node (Temperature sensitivity of the subcooled 

model, with decreasing temperature). Comparison of CFM on with CFM off.

18
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM

CRITICAL SUBCOOLED MODEL

700.0 

650.0

Steam

Non-choked subcooled model 

0-0 Transition temperature 

&-e Saturated temperature,

5.0e+06 1.0e+07 1.5e+07

Pressure (Pa) 

Figure 3.14: Transition at temperature from CFM to Non-CFM. Subcooled region.

CRITICAL SUBCOOLED MODEL

40.0

0

o Subcooling Data 1 -- Quadratic Regression

5.0e+06 1.0e+07

Pressure (Pa)

Figure 3.15: Subcooling. Transition from CFM to Non-CFM. Subcooled region.

19

2 

E

600.0 

550.0 

500.0

450.0 

400.0 

O.Oe+00

P 

=. 

a 

[-

30.0 

20.0 -

0

10.0 

0.Oe+00 1.5e+07

19
ETSI Minas - Universidad Politkcnica de Madrid

CRITICAL SUBCOOLED MODEL 

Pressure Sensitivity

50.0

1 

100.0 150.0

Time (s)

Figure 3.16: Liquid temperature at the last node 

subcooled model, with increasing pressure). CFM on.

700.0

(Pressure sensitivity of the

CRITICAL SUBCOOLED MODEL 

Pressure Sensitivity

600.0

500.0

400.0

300.0 

0.0 50.0 

Time (s)

100.0 150.0

Figure 3.17: Liquid temperature at the last node (Pressure sensitivity of the 

subcooled model, with increasing pressure). CFM off.

I I I

20

700.0 

600.0

2 

C.) 

Cu 

& 

S 

4.)

500.0

400.0

300.0 

0.0

4.)

I i 

I 

p 

"1
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM

CRITICAL SUBCOOLED MODEL 

Pressure Sensitivity

-l

50.0 100.0 

Time (s)

150.0

Figure 3.18: Pressure at the last node (Pressure 

with increasing pressure). CFM on.

2.0e+07 

1.5e+07

E 0..

sensitivity of the subcooled model,

CRITICAL SUBCOOLED MODEL 

Pressure Sensitivity

1.0e+07

5.0e+06 • 

O.Oe+00 0.0 50.0 100.0 150.0

Time (s)

Figure 3.19: Pressure at the last node (Pressure 

with increasing pressure). CFM off.

sensitivity of the subcooled model,

2 Oe÷07

1.5e+07

0.. 

a., 

a., 

0..

1.0e+07

5.0e+06

0.Oe+00 

0.0

21
ETSI Minas - Universidad Politkcnica de Madrid

CRITICAL SUBCOOLED MODEL 

Pressure Sensitivity

I

50.0 100.0 150.0 

Time (s)

Figure 3.20: Mass flow at nozzle exit 

with increasing pressure). CFM on.

10000.0 

8000.0

U, 

4.

(Pressure sensitivity of the subcooled model,

CRITICAL SUBCOOLED MODEL 

Pressure Sensitivity

6000.0

4000.0 

2000.0

0.0 L 

0.0 50.0 100.0 150.0

Time (s)

Figure 3.21: Mass flow at nozzle exit (Pressure sensitivity of the 

with increasing pressure). CFM off.

subcooled model,

22

15000

10000

C.2 

0Z

5000 -

0 L 

0.0

I I I

J
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 OEM 23

CRITICAL SUBCOOLED MODEL 

Pressure Sensitivity

50.0 100.0 

Time (s)

150.0

Figure 3.22: Mass flow at nozzle exit (Pressure sensitivity of the subcooled model, 

with increasing pressure). Comparison of CFM on with CFM off.

15000.0

10000.0 

5000.0

0

0.0 1 

0.0

Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM 23
24 ETSI Minas - Universidad Polit6cnica de Madrid

2.0e+07 

1.5e+07

CRITICAL SUBCOOLED MODEL 

Pressure Sensitivity

1.0e+07 U,

5.0e+06 

0.0e+00 

0.0 50.0 100.0

Time (s)

Figure 3.23: Pressure at the last 

with decreasing pressure). CFM

2.0e+07 

1.5e+07

.,

node (Pressure sensitivity of the subcooled model, 

on.

CRITICAL SUBCOOLED MODEL 

Pressure Sensitivity

1.0e+07 -

5.0e+06

0.Oe+00 -

0.0 50.0 100.0 150.0 

Time (s)

Figure 3.24: Pressure at the last 

with decreasing pressure). CFM

node (Pressure sensitivity of the subcooled model, 

off.

24 ETSI Minas - Universidad Politkcnica de Madrid
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM

15000.0

Z

10000.0 

5000.0

CRITICAL SUBCOOLED MODEL 

Pressure Sensitivity

o--o T=453 K 

T- "=473 K 

c-- T=493 K 

U-H T=513 K 

!o- T=533 K 

T-. "=553 K 

S T-"573 K 

A-- T=593 K 

<---< T=613 K

150.0

Time (s)

Figure 3.25: Mass flow at nozzle exit (Pressure sensitivity of the subcooled model, 

with decreasing pressure). CFM on.

25
26 ETSI Minas - Universidad Polit6cnica de Madrid

CRITICAL SUBCOOLED MODEL 

Pressure Sensitivity

50.0 100.0 

Time (s)

Figure 3.26: Mass flow at nozzle exit (Pressure sensitivity of the 

with decreasing pressure). CFM off.

15000.0

0

10000.0 

5000.0

0.01 

0.0

subcooled model,

CRITICAL SUBCOOLED MODEL 

Pressure Sensitivity

50.0 100.0 150.0

Time (s) 

Figure 3.27: Mass flow at nozzle exit (Pressure sensitivity of the subcooled model, 

with decreasing pressure). Comparison of CFM on with CFM off.

10000.0 

8000.0

6000.0 

4000.0

0•

2000.0 

0.0 L 

0.0 150.0

26 ETSI Minas - Universidad Politkcnica de Madrid

1
Chapter 3. Sensitivity Analysis of RELAP51MOD3 CFM

1.6e+07 

1.4e+07

CRITICAL SUBCOOLED MODEL 

MDC Sensitivity

8.0e+06 

6.0e+06 

0.0 20.0 

Figure 3.28: Pressure at the last

0. 

I

a 

_2 

0O 

V

553.10 

553.05 

553.00 

552.95 

552.90 

552.85 -

40.0 60.0 80.0 100.0 

Time (s) 

node. MDC sensitivity of the subcooled model.

CRITICAL SUBCOOLED MODEL 

MDC Sensitivity

-1

0.0 20.0 40.0 60.0 80.0 100.0 

Time (s) 

Figure 3.29: Temperature at the last node. MDC sensitivity of the subcooled model.

27

0 

z

1.2e+07 

1.0e+07
ETSI Minas - Universidad Po1itkcnica de Madrid

CRITICAL SUBCOOLED MODEL

MDC Sensitivity

12500.0 

MDC=O.7 

MDC=0.8 

- MDC=0.9 

10000.0 - MDC=1.0 

MDC=1.1 

MDC=1.2 

- MDC=1.3, 

MDC=1.4

25.0 50.0 75.0 100.0 

Time (s)

Figure 3.30: Mass flow at nozzle exit. MDC sensitivity of the subcooled model. 

CRITICAL SUBCOOLED MODEL 

Forward Energy Loss Coefficient Sensitivity

--o Forward energy loss coefficient=0.00 

a--* Forward energy loss coefiicient=25.0 

a-- Forward energy loss coefficlent-50.0 

H-. Forward energy loss coefficient=75.0 

- Forward energy loss coefficient-100.Oi

-9---

50.0 100.0 150.0

Time (s)

Figure 3.31: Mass flow at nozzle exit. Energy loss coefficient sensitivity of the 

subcooled model.

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28

aj

0

7500.0 

5000.0

2500.0

0.0 U

0.0

4500.0 

4000.0

3500.0 

3000.0

.2 

.

2500.0 

2000.0 

0.0
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM

CRITICAL SUBCOOLED MODEL 

Forward Energy Loss Coefficient Sensitivity

o-- Forward energy loss coefficient=0.0 

9-6 Forward energy loss coefficient=25.0 

SForward energy loss coefficient=50.0 

*--u Forward energy loss coefficient=75.0 

-- Forward energy loss coefficient=1 00.01

150.0

Time (s)

Figure 3.32: Pressure at the last node. 

subcooled model.

Energy loss coefficient sensitivity of the

4.04e+06

29
3.1.2 Sensitivity Analysis of Two-phase CFM to Void

fraction and TDC 

For the two-phase model, a sensitivity analysis has been done with respect to the 

following variables: 

- Void-fraction. 

- Two-phase Discharge Coefficient (TDC). 

A sensitivity analysis with respect to the pressure was not performed because if the 

quality is fixed and the pressure is varied at the pipe inlet, the void-fraction and 

quality are not fixed at the last node. So, it is not possible to make a pressure 

sensitivity analysis for the two-phase CFM. 

The void-fraction sensitivity analysis was performed in the following way: the pipe 

inlet pressure (upper TMDPVOL) was fixed for each case and the quality was 

varied from 0.001 to 0.9999 (increasing void-fractions). These calculations have 

been done for different pressures (from 10 bar to 150 bar). In order to compare the 

homogeneous and non-homogeneous options the analysis has been made for both 

models. 

In TDC sensitivity analysis, a case taken from the void-fraction sensitivity analysis 

was used, with P = 80 bar, varying TDC from 0.6 to 1.4. 

Void Fraction Sensitivity. An increasing void-fraction sensitivity analysis was 

made for CFM with the homogeneous and non-homogeneous options. In the results 

it can be observed that the last node pressure, Figure 3.33, remains constant during 

the transient and the void-fraction, Figures 3.34 and 3.38, grows from 0 to 1. The 

mass flow shows an unexpected behaviour for homogeneous and non-homogeneous 

options: 

- Homogeneous option, Figure 3.35. A maximum is observed for void-fractions 

near to 0.1 and pressures higher than 90 bar. In order to show the dependence 

of the critical mass flux upon the void fraction, the stationary states of the 

Figures 3.34 and 3.35, are represented in Figure 3.36. 

- Non-homogeneous option, Figure 3.39. One or two maxima are observed 

depending on pressure.

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30

3{} ETSI Minas - Universidad Politecnica de Madrid vv
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM 31

CRITICAL TWO-PHASE MODEL 

Void-fraction Sensitivity. Homogeneous model 

-P.150 bar 

-- PO1 bar

1.5e+07 

1.0e+07 

5.0e+06 

O.Oe+00 

0.0

Figure 3.33: Pressure at the last node. Void-fraction sensitivity 

model. Homogeneous and non-homogeneous models.

of the two-phase

Typical data of the homogeneous model, Figure 3.37, and experimental data do not 

show any maximum. 

For pressures below 50 bar, an oscillatory behaviour is observed, Figures 3.35 and 

3.39. This problem can not be removed with a smaller time step. Clearly, this is a 

numerical phenomenon, because for higher pressures a similar oscillatory behaviour 

was observed and removed diminishing the time step. 

Two-phase Discharge Coefficient Sensitivity. In this analysis the base case 

was taken from the void fraction sensitivity analysis. With fixed pressure at the 

pipe inlet, P = 80 bar, and quality varying from 0.001 to 0.999. The results show 

that pressure, Figure 3.40, and void-fraction, Figure 3.41, are quite similar for the 

different discharge coefficients. In Figure 3.42 is easy to check that for a void fraction 

between 0.1 and 0.9, the variation of the mass flow with the discharge coefficient 

has the same value than the discharge coefficient, as expected. For void fractions 

smaller than 0.1 the transition from MDC=1.0 to TDC can be observed. Also, 

for void fractions greater than 0.9 the transition from TDC to SDC=1.0 can be 

observed.

100.0 200.0

Time (s)

300.0

Chapter 3. Sensitivity Analysis of R/ELAP5/MOD3 CFM 31
ETSI Minas - Universidad Polit~cnica de Madrid

1.0 

0.8 

. 0.6 

> 0.4 

0.2 

0.0 1

0.0

CRITICAL TWO-PHASE MODEL 

Void-fraction Sensitivity. Homogeneous model

100.0 200.0 

Time (s)

300.0

Figure 3.34: Void-fraction at nozzle exit. Void-fraction sensitivity of the two-phase 

model. Homogeneous model.

0.0 A

0.0

CRITICAL TWO-PHASE MODEL 

Void-fraction Sensitivity. Homogeneous model 

P.1 50 bar 

S- P.140 bar 

PI130 bar "P:120 bar 

o-o P.110 bar 

6 P.100 bar 

P-90 bar 

P-80 bar t \I oi--' P,,70 bar 

N- P.50 bar 

. P-40 bar 

- P.10 bar

1030.0 200.0 300.0

Time (s)

Figure 3.35: Mass flow at nozzle exit. Void-fraction sensitivity of the 

model. Homogeneous model.

two-phase

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32

3500.0 

3000.0 

2500.0 

2000.0 

1500.0 

1000.0 

500.0

0
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM

Ransom-Trapp Model. Homogeneous option.

Figure 3.36: Critical mass flux. Ransom-Trapp model.

33

50000

C, c'J 

x 

E 

LO

33
ETSI Minas - Universidad Politcnica de Madrid

I.

U

STAGNATION ENTIALPY. hoaREF

Figure 3.37: Critical mass flux. Homogeneous model (Taken from ILAH-931 pp 444).

I I I

3d

U
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM

CRITICAL TWO-PHASE MODEL 

Void-fraction Sensitivity. Non-homogeneous model 

1.0 .

100.0 200.0 

Time (s)

- P.150 bar 

bar SP.140 

H P.130 bar 

Az-6 PN120 bar 

A P-110 bar 

P.100 bar 

*-H P.90 bar 

P-80 bar 

P.70 bar 

0--o P.60 bar 

- P-50 bar 

P=40 bar 

P-30 bar 

-P.20 bar 

P-10 bar

300.0

Figure 3.38: Void-fraction at nozzle exit. Void-fraction sensitivity of the two-phase 

model. Non-homogeneous model. 

CRITICAL TWO-PHASE MODEL 

Void-fraction sensitivity. Non-homogeneous model 

3500.0 - P150 bar 

P.140 bar 

-- P.130 bar 3000.0 - P.120 bar 

G, 0 P.1 10 bar .- P.100 bar 

2500.0 &---6P--- bar 

P-80 bar 

c ---- F P.70 bar 

4 2000.0 s--n P-60-ba P-O br 

0 ~-P30 bar 

1000.0

500.0

300.0

Time (s)

Figure 3.39: Mass flow at nozzle exit. 

model. Non-homogeneous model.

Void-fraction sensitivity of the two-phase

35

0.8

S0.6 

> 0.4 

0.2

0.0 0 

0.0
36 ETSI Minas - Universidad Polit6cnica de Madrid

8.05e+06

CRITICAL TWO-PHASE MODEL 

TDC Sensitivity

8.00e+06 L

Cu

7.95e+06

7.90e+06 

0.0 100.0 200.0 300.0

Time (s)

Figure 3.40: Pressure at the last node. TDC sensitivity of the two-phase model. 

CRITICAL TWO-PHASE MODEL

TDC Sensitivity

--- TDCO.6-0.7 I 

TDC=0.8-1.4 -

100.0 200.0 300.0

Time (s) 

Figure 3.41: Void-fraction at nozzle exit. TDC sensitivity of the two-phase model.

I I I

1.0 

0.8 

S0.6 

> 0.4 

0.2 

0.0 

0.0

3636 ETSI Minas - Universidad Politkcnica de Madrid

i
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM 37

CRITICAL TWO-PHASE MODEL 

TDC Sensitivity

'0-c TDC=0.6: 

TDC,0.71 

TDC=0.8i 

_ TDC=0.9i 

- TDC=1.0O -- TDC=1.1 1 

-TDC=1.2i 

_ TDC=1.3 

; T"FOMC=1.4

Void=0.1 Void-0.9

100.0 200.0 300.0

Time (s)

Figure 3.42: Mass flow at nozzle exit. TDC sensitivity of the two-phase model.

4000.0 

3000.0 -

0 2000.0

1000.0
3.1.3 Sensitivity Analysis of Steam CFM to Temperature, 

Pressure and SDC 

For the steam model, a similar study to the subcooled CFM (Section 3.1.1) has been 

performed. The sensitivity analysis has been done with respect to the following 

variables: 

- Temperature. 

- Pressure. 

- Steam Discharge Coefficient (SDC). 

The temperature sensitivity analysis was performed in the following way: fixed pipe 

inlet pressure (upper TMDPVOL) for each case and decreasing temperature from 

673 K to T, at. These calculations have been done for different pressures (from 10 

bar to 150 bar). 

The pressure sensitivity was performed in a similar way to temperature sensitivity: 

fixed pipe inlet temperature (TMDPVOL) each case and pressure varying from 10 

bar to P,,,t (increasing pressures). These calculations have been done for different 

temperatures (from 473 K to 673 K). 

For the SDC sensitivity analysis, a case from the pressure sensitivity analysis was 

taken, varying SDC from 0.6 to 1.4. In order to compare the CFM with the Non

CFM, both temperature and pressure were checked at the last node to make sure 

that they were similar. 

The results obtained for the different sensitivity analysis are described below: 

Temperature Sensitivity. An increasing temperature sensitivity analysis was 

made for CFM and Non-CFM. In the results the similarity between the pressure, 

Figures 3.43 and 3.44, and the temperature at the last node, Figures 3.45 and 3.46, 

can be seen, so that the critical mass flow, Figure 3.47, and non-critical mass flow 

results, Figure 3.48, can be compared: the mass flow with CFM-on is always lower 

than CFM-off. This implies that the transition logic from CFM to Non-CFM is 

correct. 

Pressure Sensitivity. An increasing pressure sensitivity analysis was made for 

CFM and Non-CFM. In the results it can be observed that pressure, Figures 3.51 

and 3.52, and temperature at the last node, Figures 3.49 and 3.50, are quite similar,

I I I

38

38 ETSI Minas - Universidad Politkcnica, de Madrid
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM

so critical mass flow, Figure 3.53, and non-critical mass flow results, Figure 3.54, 

can be compared. Mass flow of CFM-on is always lower than CFM-off, as is shown 

in Figure 3.55. Anyway, the user must be careful because if an energy loss coefficient 

is used, the non-critical mass flow could decrease and become lower than the critical 

mass flow. 

Steam Discharge Coefficient Sensitivity. In this analysis a case from pressure 

sensitivity analysis was used. The temperature is fixed at the pipe inlet, T= 673 K, 

and pressure is varied from 10 to 150 bar. The results show that pressure, Figure 

3.56, and temperature, Figure 3.57, are quite similar for the different discharge 

coefficients. In Figure 3.58 it is easy to check that the variation of the mass flow 

with the discharge coefficient has the same value than the discharge coefficient, as 

expected.

w_ 39

39
40 ES ia nvria oi~nc eMdi

CRITICAL STEAM MODEL 

Temperature Sensitivity

1.5e+07

1.0e+07 

t, 

W

5.0e+06

100.0 150.0 

Time (s)

200.0 250.0

Figure 3.43: 

CFM on.

Pressure at the last node (Temperature sensitivity of the steam model).

CRITICAL STEAM MODEL 

Temperature Sensitivity

1.5e+07 

1.0e+07 

5.0e+06

Figure 3.44: 

CFM off.

O.Oe+O0 

0.0 50.0 100.0 150.0 200.0 250.0 

Time (s) 

Pressure at the last node (Temperature sensitivity of the steam model).

O.Oe+00 0.0 50.0

I I I

40 ETSI Minas - Universidad PolitAnica de Madrid
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM

C]

700.0 

- 600.0 

E 

E 500.0 

.5 

400.0 

0.0 50

RITICAL STEAM MODEL 

Temperature Sensitivity

.0 100.0 150.0 200.0 250.0 

Time (s)

Figure 3.45: Temperature at the last node (Temperature sensitivity of the steam 

model). CFM on.

700.0 

600.0 

E 500.0 _2 

0 

U)

CRITICAL STEAM MODEL 

Temperature Sensitivity

4

100.0 150.0 

Time (s)

200.0 250.0

Figure 3.46: Temperature at the 

model). CFM off.

last node (Temperature sensitivity of the steam

400.0 

0.0 50.0

41

v_

I t 

1 

i
42 ETSI Minas - Universidad Politkcnica de Madrid 

CRITICAL STEAM MODEL 

Temperature Sensitivity 

2 0 0 0 .0 . . ..... . .. ... 

1500.0 -< 

S1000.0 

500.0 

0.0 50.0 100.0 150.0 200.0 250.0 

Time (s) 

Figure 3.47: Mass flow at nozzle exit (Temperature sensitivity of the steam model). 

CFM on. 

CRITICAL STEAM MODEL 

Temperature Sensitivity 

3000.0 

2000.0 

1000.0 

0.0 

0.0 50.0 100.0 150.0 200.0 250.0 

Time (s) 

Figure 3.48: Mass flow at nozzle exit (Temperature sensitivity of the steam model). 

CFM off.
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM

700.0

43

CRITICAL STEAM MODEL 

Pressure Sensitivity

600.0 _____

E 

E!!

500.0 -

400.0 

0.0 50.0 100.0 150.0

Time (s)

Figure 3.49: Liquid temperature at the last node (Pressure sensitivity of the steam 

model). CFM on.

CRITICAL STEAM MODEL 

Pressure Sensitivity

50.0 100.0 

Time (s)

Figure 3.50: Liquid 

model). CFM off.

temperature at the last node (Pressure sensitivity of the steam

700.0

E E.2

600.0 

500.0

400.0 

0.0 150.0
44 ETSI Minas - Universidad Polit6cnica de Madrid

1.5e+07 

1.0e+07 -

CRITICAL STEAM MODEL 

Pressure Sensitivity

5.0e+06

O.Oe+00 0.0 50.0 100.0 150.0

Time (s)

Figure 3.51: Pressure at 

CFM on. 

1.5e+07 

1.0e+07 

5.0e+06 

O.Oe+00 

0.0 

Figure 3.52: Pressure at 

CFM off.

the last node (Pressure sensitivity of the steam model). 

CRITICAL STEAM MODEL 

Pressure Sensitivity 

-4

50.0 100.0 150.0

Time (s)

the last node (Pressure sensitivity of the steam model).

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44

44 ETSI Minas - Universidad Politkcnica de Madrid

.=
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM

CRITICAL STEAM MODEL 

Pressure Sensitivity

1500.0

1000.0 - 0,

500.0

Figure 3.53: 

CFM on.

0.0 1 - - - - -

0.0 50.0 100.0 150.0 

Time (s) 

Mass flow at nozzle exit (Pressure sensitivity of the steam model).

3000.0

0

CRITICAL STEAM MODEL 

Pressure Sensitivity

2000.0 

1000.0 -

0.0 1 

0.0 50.0 100.0 150.0

Time (s) 

Figure 3.54: Mass flow at nozzle exit (Pressure sensitivity of the steam model). 

CFM off.

2000.0

45
46 ETSI Minas - Universidad Po1itcnica de Madrid

CRITICAL STEAM MODEL 

Pressure Sensitivity

50.0 100.0 

Time (s)

Figure 3.55: Mass flow at nozzle exit 

Comparison of CFM on and CFM off.

(Pressure sensitivity of the steam model).

3000.0

2000.0 

1000.0

0•

0.0 L 0.0 150.0

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46 ETSI Minas - Universidad Politknica de Madrid
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM

1.5e+07 

1.0e+07

5.0e+06 

/ 

O.Oe+00 

0.0

CRITICAL STEAM MODEL 

SDC Sensitivity

50.0 100.0

1 150.0

Time (s) 

Figure 3.56: Pressure at the last node. SDC sensitivity of the steam model. 

3.2 Sensitivity Analysis of Henry-Fauske Model 

In this section, the sensitivity analysis of the subcooled and two-phase CFMs is 

analyzed in a way similar to that done for the Ransom-Trapp model. The objective 

of this analysis is to obtain the dependence of the CFM with respect to the following 

variables: 

- Temperature. 

- Pressure. 

- Void Fraction. 

- Disequilibrium Parameter. 

- Forward Energy Loss Coefficient. 

The range of variation of the variables and the models used for the sensitivity 

analysis is the same than for the Ransom-Trapp model, see Section 3.1.

47

v
48 ETSI Minas - Universidad Polit6cnica de Madrid

CRITICAL STEAM MODEL

E 

C

.5

SDC Sensitivity

675.0 

674.0 

673.0 

672.0 

671.0 

670.0 

0.0 50.0 100.0 150.0

Time (s)

Figure 3.57: Temperature at the last node. SDC sensitivity of the steam model. 

CRITICAL STEAM MODEL

SDC Sensitivity

SDC-0.6 - SDC=0.7 

-SDC-0.8 

-- SDC-0.9 

-SDC-1.0 

-- SDCf1i.1 

2000.0 - -- SDC-1.2 

-- SDC=1.3 

SDC=1.4

50.0 100.0

Time (s)

Figure 3.58: Mass flow at nozzle exit. SDC sensitivity of the steam model.

I I

3000.0

00 

Z 

S0

1000.0 -

0.0 1 

0.0 150.0

48 ETSI Minas - Universidad Politkcnica de Madrid
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM

3.2.1 Sensitivity Analysis of Subcooled CFM to Tempera

ture, Pressure, Disequilibrium Parameter and Forward 

Energy Loss Coefficient 

For the subcooled model, sensitivity analyses have been done with respect to the 

following variables: 

- Temperature. 

- Pressure. 

- Disequilibrium Parameter. 

- Forward Energy Loss Coefficient. 

The temperature sensitivity analysis was performed in the following way: pipe inlet 

pressure (upper TMDPVOL) was fixed for each case and temperature was varied 

from 373 K to Tsat (increasing temperatures). These calculations have been done 

for different pressures (from 10 bar to 150 bar). 

The same analyses have also been performed for temperatures decreasing from Teat 

to 373 K, in order to compare with the results of the Ransom-Trapp model. 

The pressure sensitivity analysis was performed in the same way than for Ransom

Trapp model: pipe inlet temperature (upper TMDPVOL) was fixed for each case and 

pressure was varied from P,8 , to 10 bar (decreasing pressures). These calculations 

have been done for different temperatures (from 373 K to 613 K). 

For the disequilium parameter sensitivity analysis, the pipe inlet pressure was fixed 

to 80 bar and the temperature varied from 373 K to 523 K. The mass flow was 

calculated for several values of the disequilibrium parameter (0, 0.01, 0.05, 0.1, 

0.14, 0.3, 0.5, 1, 1000), using the abrupt area change option of the code. 

The results obtained for the different sensitivity analysis are described below: 

Temperature Sensitivity. In both cases (decreasing and increasing tempera

tures), Figures 3.60 and 3.59, the behaviour is the same, with no transition logic 

problems. This is in accordance with the analysis performed in Section 2.1. 

Pressure Sensitivity. The results in this case, Figure 3.61, do not show any 

transition problems. This is also in accordance with the analysis performed in 

Section 2.1.

49
50 ETSI Minas - Universidad Politkcnica de Madrid 

CRITICAL SUBCOOLED MODEL 

Temperature Sensitivity 

8000.0 

G-•-P=150 bar 

0--01P.140 bar 

6000.0 -A- -- -IP.130 bar 

IF--NIP=110 bar 

_A- _ 0- -0-1P.IO0 bar 

-A1- A----IP=80 bar 

A- -&.P-90 bar 

CD _<-- <P.70 bar 

S4 0 0 0 .0 -- - v -- -- \- - -P- 6 0 bar 

E V--ViP.50 bar 

"---V!P-40 bar 

>-->]P-30 bar 

IL-*IP.20 bar O----OP-IO bar 

2000.0 

0.01I6 

0.0 100.0 200.0 300.0 

Time (s) 

Figure 3.59: Mass flow at nozzle exit. Temperature sensitivity of the subcooled 

Henry-Fauske model, with increasing temperature. 

Disequilibrium Parameter Sensitivity. As is shown in Figure 3.62, the critical 

flow is strongly dependent on the disequilibrium parameter. This dependence is 

more important when the temperature approaches the saturation temperature. 

Forward Energy Loss Coefficient Sensitivity. The results and conclusions 

of this analysis, Figure 3.63, show the same behaviour than in the Ransom-Trapp 

model, Figure 3.31. 

3.2.2 Sensitivity Analysis of Two-phase CFM to Void

fraction and Disequilibrium Parameter 

For the two-phase model, a sensitivity analysis has been done with respect to the 

following variables: 

Void-fraction. 

- Disequilibrium Parameter.

I I I
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM

2000 

0 

0.0

CRITICAL SUBCOOLED MODEL 

Temperature Sensitivity

8000 

6000

100.0 200.0 

Time (s)

300.0

Figure 3.60: Mass flow at nozzle exit. Temperature sensitivity of the subcooled 

Henry-Fauske model, with decreasing temperature.

CRITICAL SUBCOOLED MODEL 

Pressure Sensitivity

0 i

0.0 50.0 100.0 

Time (s)

150.0

Figure 3.61: Mass flow at nozzle exit. Pressure 

Fauske model, with decreasing pressure.

sensitivity of the subcooled Henry0-- P= 150bar 

0-0 P=1 40bar 

* -_P=130bar 

*-N P=120bar 

o---- P= 11Obar 

--- P=lOObar 

A-A P=9Obar 

- P=8Obar 

•-X-) P=7Obar 

>-> P=6Obar 

A P=5Obar 

-- q P=4Obar 

S<-'< P=3Obar 

4 P---2Obar 

P--' P=lObar

LL

4000

8000 

6000 

U) 

m -- 4000 

0 

2000

51
ETSI Minas - Universidad Politcnica de Madrid

CRITICAL SUBCOOLED MODEL

Disequilibrium Parameter Sensitivity

6000.0

4000.0

.o-Odp=O.01 

.- •dp--0.05 

a dp=0.1 

0--odp=0.114 

2000.0 - -. dp--0.3 

i•- dp=0.5 

-A -dp=l1.0 

<--<dp= l000

0.0 50.0 100.0 

Time (s)

150.0

Figure 3.62: Mass flow at nozzle exit. Disequilibrium parameter sensitivity of the 

subcooled Henry-Fauske model. 

CRITICAL SUBCOOLED MODEL 

Forward Energy Loss Coefficient Sensitivity

U,

4000 

3000

2000

1000

0-0 Forward energy loss coefficient-C 

Forward energy loss coefficient-25 

- Forward energy loss coefficient=50 

V - -V Forward energy loss coefficient=75 

0----e Forward energy loss coefficient.1 00

50.0 100.0 150.0

Time (s)

Figure 3.63: Mass flow at nozzle exit. Forward energy loss coefficient sensitivity of 

the subcooled Henry-Fauske model.

I I I

52

U, 

0, 

C) 

a 0

2J 

200.0

52
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM

CRITICAL TWO-PHASE MODEL 

Void-fraction Sensitivit

5000 G-OP) ; 10 bar 

P- 20 bar 

- P-. 30 bar 

P- N40 bar 

PN 50 bar 

4000 - P. 60 bar 

P. 70 bar 

0-0 P. 80 bar 

P- 90 bar 

-- P=lOObar 

"PN 110 bar 

3000 ".- - P.= 120bar 130 bar 

-- P. 140 bar 

ca -L_•r.- : P. 150 bar 

.22000 

1000 

0 G 0.0 100.0 200.0 

Time (s) 

Figure 3.64: Mass flow at nozzle exit. Void-fraction sensitivity of the Henry-Fauske 

model. 

The void-fraction sensitivity analysis was performed in the following way: the pipe 

inlet pressure (upper TMDPVOL) was fixed for each case and the quality varied 

from 0.001 to 0.9999 (increasing void-fraction). These calculations have been done 

for different pressures (from 10 bar to 150 bar). 

For the sensitivity analysis of the disequilium parameter, the pipe inlet pressure 

was fixed to 80 bar and the void fraction was varied from 0 to 1. The mass flow 

was calculated for the same values of the disequilibrium parameter than for the 

subcooled analysis, using the abrupt area change option of the code. 

Void Fraction Sensitivity. The results of this analysis, Figure 3.64, do not show 

any maximum, nor oscillatory behaviours unlike in the Ransom-Trapp model. In 

order to show the dependence of critical mass flux with void fraction, the stationary 

states of the Figures 3.64 and 3.65, are represented in Figure 3.66. 

Disequilibrium Parameter Sensitivity. As is shown in Figure 3.67, critical 

flow is also strongly dependent on the disequilibrium parameter. This dependence 

is more important when the void fraction approaches zero, Figure 3.68.

53
ETSI Minas - Universidad Politkcnica de Madrid

CRITICAL TWO-PHASE MODEL 

Void-fraction Sensitivity

1.0 

0.8

o 0.6 

Cu

LL 

> 0.4 

0.2

100.0 200.0 300.0

Time (s)

Figure 3.65: Void fraction at nozzle exit. Void-fraction sensitivity of the Henry

Fauske model. 

Henry-Fauske Model

-10 bar 

_ 20 bar 

S30 bar 

-40 bar 

-50 bar 

-60 bar 

-70 bar 

-80 bar 

-90 bar 

100 bar 

-110 bar 

120 bar 

-130 bar 

140 bar 

-150 bar

0.0 0.1 0.2 0.3 0.4 0.5 

Void-fractio

0.6 0.7 0.8 0.9 1.0

Figure 3.66: Critical mass flux. Henry-Fauske model.

I I 1 I

54

o--o 150 bar 

__ 140 bar 

-- 130 bar 

120 bar - 110 bar 

-- 100 bar 

-- 90 bar 

0--- 80 bar 

-- 7 0 b a r 

-- 60 bar 

50 bar 

- 40 bar 

-- 30 bar 

-- 20 bar 

9-o 10 bar

60000

50000

CN 40000

S30000

X 

S20000-

10000

0•
Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM

CRITICAL TWO-PHASE MODEL 

Disequilibrium Parameter Sensitivity

6000 

4000 

2000 

0.0

Figure 3.67: Mass flow 

Henry-Fauske model.

1.0 

0.8

S0.6 

U5 

.-. 

0 0.4 

0.2-

0.0 ... 0.0

at nozzle exit. Disequilibrium parameter sensitivity of the

CRITICAL TWO-PHASE MODEL 

Disequilibrium Parameter Sensitivity

1 

]

100.0 200.0 

Time (s)

Figure 3.68: Void fraction at 

the Henry-Fauske model.

nozzle exit. Disequilibrium parameter sensitivity of

55

100.0 200.0 

Time (s)
3.3 Discussion and Conclusions of the Sensitivity 

Results 

The main conclusions for the Ransom-Trapp model are: 

" Subcooled. The behaviour is anomalous due to the transition logic from critical 

flow to non-critical flow. 

" Two-phase. The results show one or two maxima for the mass flow. This is not 

an expected behaviour and is not found in the literature. Oscillatory results 

below 60 bar are observed. 

" Energy loss coefficient. It must be used with care in junctions where critical 

mass flow is expected, because the CFM does not depend on it but non-CFM 

decreases with it. 

" Discharge coefficients. From the results it can be concluded that the variation 

of the mass flow with the discharge coefficient has the same value than the 

discharge coefficient. 

" There are several other known problems with this model, that makes it 

necessary changing the model or avoiding its use. 

The main conclusions for the Henry-Fauske model are: 

"* Subcooled. There are no problems with the transition logic from critical flow 

to non-critical flow. 

"* Two-phase. There is not any maxima for the mass flow, nor is here oscillatory 

behaviour unlike in the Ransom-Trapp model. 

"* Energy loss coefficient. It must be used with care in junctions where critical 

mass flow is expected, because the CFM does not depend on it, but non-CFM 

decreases with it. 

"* Disequilibrium parameter. Mass flow is strongly dependent on this parameter. 

In order to avoid the user effect, this value should be internally fixed or at least 

detailed user guidelines should be supplied. 

"* In general the model shows good behaviour, but user guidelines should be 

supplied for the discharge coefficient and the disequilibrium parameter.

I I1 1

56 ETSI Minas - Universidad Politk•nica de Madrid *
Chapter 4 

Assessment of RELAP5/MOD3 

CFM against Marviken Tests 

One of the main objetives of the Marviken tests was the assessment of critical-flow 

calculations at a scale and in a geometry important for large-break LOCAs. The 

Marviken full-scale critical-flow tests provide data to assess the ability of the CFM 

implemented in the computer codes to calculate large pressure-vessel blowdowns 

and critical flow in large-size pipes, in a critical-flow geometry that is reasonably 

typical of that assumed in the licensing design-basis, large-break LOCA. The tests 

cover both subcooled and two-phase critical flow. 

In this chapter, data from Marviken Tests CFT-01, 06, 11, 15, 17, 21 and 24 are 

used to assess the default critical flow model of RELAP5/MOD3.2, Ransom-Trapp 

model, and the new Henry-Fauske option. 

To achieve this goal, the following steps have been included: 

"* Description of the facility and of the test. 

"* Description of the RELAP5/MOD3.2 facility models used for the simulation. 

"* Review of the bibliography of the Marviken tests simulation. 

"* Comparison of critical and non-critical flow models with test data. 

"* Comparison and selection of the options for the different models. 

"* Discharge coefficient adjustment for subcooled and two-phase conditions with 

different nozzle models. 

"* Analysis of the results.

57
4.1 Facility and Test Description 

Marviken Power Station was originally built as a boiling heavy water direct cycle 

reactor with natural circulation and provisions for nuclear super-heating of the 

steam, but nuclear fuel was never charged. The reason was that the plant could 

not verify General Design Criterion 12 about stability. An oil fired boiler was built 

instead to provide steam for the turbine, leaving the nuclear steam supply system 

intact: reactor vessel and most of the auxiliary systems, pressure containment, 

reactor hall and fuel handling area. After testing the containment pressure

suppression systems, the nuclear island was modified to accommodate the Marviken 

series large scale critical flow experiments. 

Two full scale critical flow series of experiments were developed at the site: 

"* Critical Flow Test (CFT) project. The test phase was conducted between 

January 1978 and July 1979. The objective of this test program was to obtain 

full scale critical flow data for test nozzles as a function of pressure, subcooling, 

low inlet quality, length and nozzle diameter from two-phase mixtures from 

27 experiments. 

"* Jet Impingement Test (JIT) program. This test program, developed after the 

CFT program, was focused on measuring loads due to a fluid jet impinging 

upon a flat plate, and also generated full scale critical flow data. 

The aim at the CFT experiments was to collect critical flow data as a function of 

the nozzle geometries and the initial steam conditions at the upper plenum. The 

significance of this test program as a large scale experiment was to be the first one 

performed with nozzle diameters comparable to existing plant geometries - in order 

to avoid the use of estimations -, and also to provide a connection with the large 

amount of the small-scale critical flow data previously available. 

The major components of the facility are the pressure vessel, the discharge pipe, the 

test nozzles and rupture disk assemblies, and the containment and exhaust tubes. 

A complete description of the components and dimensions are amply described in 

[MAR-4-90]. 

Figure 4.1 shows the vessel, that includes part of the core superstructure and the 

moderator tank, plus three gratings installed to limit vortex formation. Figure 

4.2 shows the discharge-pipe. All elevations in both figures are measured relative 

to the vessel bottom. Pressure and temperature transducers are located along 

the vessel and the discharge pipe (see Figures 4.4 and 4.2). The signals from

I I

58 ETSI Minas - Universidad Politkcnica de Madrid
Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests 59

All aimensions are 

in meters

To discharge pipe

Figure 4.1: Pressure vessel diagram.
ETSI Minas - Universidad Politkcnica de Madrid

Figure 4.2: Discharge pipe and test nozzle.

I I I

60
Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests 61

Figure 4.3: Test nozzle used from Test 15 onwards.
the various transducers are processed through a signal-conditioning unit with its 

channels connected to a pulse-code modulation system and with a process computer. 

Before a test is run, the vessel is partially filled with deionized water and heated 

by removing water from the vessel bottom, passing it through an electric heater, 

and returning it to the steam dome at the vessel top. This procedure produces a 

complicated initial temperature distribution in the vessel. A saturated steam dome 

fills the vessel region above the initial water level and the water at the nozzle inlet 

is substantially subcooled (AT8 ub = -60 K). 

Most of the test fluid was contained in the pressure vessel. A test was initiated 

by breaking the disks contained in the rupture disk assembly and terminated by 

closing a ball valve in the discharge pipe when voiding is detected upstream of the 

test nozzle. Data obtained from the vessel, discharge pipe, and test nozzle provided 

measurements needed to meet the test objectives, whereas the vessel fluid, in the 

form of a steam-water mixture, was exhausted through the test nozzle into the 

containment. Most of the liquid discharge was retained in the containment, and the 

containment pressure was relieved by discharging a steam-water mixture through the 

ground level and upper exhaust tubes to the atmosphere. The main characteristics 

of the CFT program are resumed in Table 4.1. 

The purpose of the experiments was to get enough data so that the critical 

flow problem could be deeply undertaken, and analyze the dependence on nozzle 

geometries, and initial pressure and temperature conditions. For this goal, different 

subcoolings, upper plenum pressures and temperature profiles were used. 

Nozzles used had nominal diameters from 200 mm to 500 mm, and L/D ratios 

between 0.3 and 3.7. Nozzle diameters larger than 500 mm were not tested because 

of the restrictions of the equipment. LID range was selected to provide information 

just for short pipes (with L/D < 4). 

The behavior observed during each of the Marviken tests can be characterized as 

having three distinct periods: 

1. Following the opening of the break, the system experiences a pressure under

shoot, which is terminated by the incidence of flashing inside the vessel. As 

the vessel water begins to flash, the system pressure rapidly increases until a 

stable flashing rate is established, after which the vessel begins to depressurize 

again. 

2. The second period during MARVIKEN experiments is marked by a steadily 

decreasing flow rate and pressure with an established vessel-water flashing rate.

I I

62 ETSI Minas - Universidad Polit~cnica de Madrid
Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

-- 22

20 

18.--- Standpipe level 

16 

14

- 12

-- 10

6 

4 

2 

o

Figure 4.4: Locations of typical measurements in the pressure vessel.

63
The water entering the test nozzle during this period is subcooled, although 

a mixture of subcooled and saturated water was discharged from the nozzle 

near the end of the second and the beginning of the third period. 

3. The third period is characterized by a reduction in the discharge flow rate as 

a result of two phase water entering the test nozzle. 

4.2 Models Description 

When the Marviken tests simulation amply bibliography is analyzed, see Section 4.3, 

it is observed that several models have been used for simulating the experiments. 

The Marviken facility has been modeled in two different ways: 

"* Only the discharge pipe and the nozzle are modeled, and the boundary 

conditions at the inlet of the discharge pipe are specified. This model is 

referred to here as Boundary Condition Model (BCM). 

"* All the facility is modeled, and the initial conditions are specified. This model 

is referred to here as Initial Conditions Model (ICM). 

For both models, the nozzle has been modeled as a PIPE or as a SINGLE 

JUNCTION, in order to evaluate the importance of the nucleating time inside the 

nozzle. Therefore, there are four different models, shown in Figures, 4.5 and 4.6. 

The four models will be referred to as: 

"* BCM-P: Boundary Condition Model with the nozzle modeled as a PIPE. 

"• BCM-J: Boundary Condition Model with the nozzle modeled as a SINGLE 

JUNCTION. 

"* ICM-P: Initial Condition Model with the nozzle modeled as a PIPE. 

"* ICM-J: Initial Condition Model with the nozzle modeled as a SINGLE 

JUNCTION. 

In this report, the simulation of the Marviken Test has been done with the four 

models. The BCM allows the analysis of critical mass flow in an independent 

way from other physical phenomena. Furthermore, this kind of model gives 

the instantaneous error between experimental and simulated mass flow, as the

I I I

64 ETSI Minas - Universidad Politkcnica, de Madrid
Test No Diameter Length L/D Subcooling Steam Pressure Test Category rest Duration Saturation Temp. Initial Water Level 

S (mm) (m177) (C) (MPa) (s) (C) (m) 

13 200 590 3.0 < 5 5.09 I 148 265 17.52 

14 30 4.97 III 146 264 18.10 

6 300 290 1.0 30 4.95 I 87 263 17.81 

7 15 5.01 I 87 264 17.86 

25 511 1.7 < 5 4.92 III 88 263 19.73 

26 30 4.91 n1 147 263 19.31 

1 895 3.0 15 4.94 1 108 263 19.73 

2 30 4.98 I 93 264 17.41 

12 30 5.00 I 126 264 17.52 

17 1116 3.7 30 4.94 11 90 265 19.85 

18 30 5.02 I 87 264 17.30 

19 < 5 5.06 iii 87 265 16.99 

23 500 166 0.3 < 5 4.96 I11 69 263 19.85 

24 30 4.96 ii 54 263 19.88 

20 730 1.5 < 5 4.99 iii 58 264 16.65 

21 30 4.94 II 60 263 19.95 

22 50 4.93 ii 48 263 19.64 

27 30 4.91 nI 59 263 19.82 

15 1809 3.6 30 5.04 II 55 264 19.93 

16 30 5.00 I 49 264 17.60 

3 509 1589 3.1 15 5.02 I 42 264 17.06 

4 30 4.94 I 49 264 17.59 

5 30 4.06 1 52 251 17.44 

8 30 4.95 1 49 263 17.51 

9 < 5 5.02 III 66 264 18.15 

10 < 5 4.97 Ill 64 263.5 17.66 

11 30 4.97 I 48 264 17.63 

Table 4.1: Main characteristics of the Marviken Tests

p-I 

(Ci 

(Ci
VESSEL PIPE

OUrLETJ SNG.JUN OUTLETJ SNLI.UN 

DISCHP PIPE DISCHP PIPE 

DISCHP SNGIJUN 

NOZZLE PIPE DtSCHP SGLJUN 

OUTLETJ SNGLJUN 

OUTLE'rV OUTh.ETV 

TMDPVOL TMDPVOL 

a b 

Figure 4.5: MARVIKEN initial conditions models. 

experimental data are used as boundary conditions for the simulations. On the 

other side, the ICM mixes different physical phenomena: mass flow rate and steam 

generation rate due to flashing, rflashing9 . Errors related to the steam generation 

rate have an effect on depressurization rate (system pressure), avoiding critical mass 

flow phenomena from being isolated. This model has also another problem: Since 

only initial conditions are imposed, the simulations give an error integrated on time. 

The comparison of the different correlation for rflashing implemented in various 

thermal hydraulic codes shows great differences among them, [FOR-88] pp 360

364, Figures 4.7 and 4.8. With this in mind, it can not be ascertained it any of the 

flashing models (including RELAP5/MOD3 model) is right; so an error in the steam 

generation rate, that affects the system pressure, could be expected. This problem 

was detected in the assessment of the TRAC-PD2 code and several F!flashin. models 

were implemented in order to improve the critical flow calculation, [TRA-84], but 

none of the models gave good results. 

Due to these differences, simulations with all the models have been performed and 

compared.

I I I
INLETV INLErY 

TMDPVOL TMDPVOL 

OUTLETJ SNGLrUN OUTLETJ SNGLUUN 

DISCHP PIPE DISCHP PIPE 

DISC-P SNGLJUN 

NOZZLE PIPE DISCHP SGLIUN 

OUTLETJ SNGLUUN 

OunzErv OtJTLETV 

TMDPVOL TMDPVOL 

a b 

Figure 4.6: MARVIKEN boundary conditions models. 

4.3 Review of the Marviken Tests Simulation Bib

liography 

This section is a review of all the bibliography that was found related to the 

Marviken experiments and their application in the assessment of several codes 

(CATHARE, TRAC-PlA, TRAC-PD2, TRAC-PF1/MOD1, TRAC-PF1/MOD2, 

TRAC-BD1/MOD1, TRAC-BF1, RELAP5/MOD2, RELAP5/MOD3 and RE

LAP5/MOD3.2.2) and also in the comparison of critical flow models. We have 

analyzed several aspects of the simulations in these reports and papers: 

"* Which are the CFT simulated? 

"* Which is the model used for the simulation? 

"* Which are the different critical flow models tested? 

"* Which are deficiencies of the code in these simulations? 

"* Which are the discharge coefficients used for adjusting the simulated to the 

test data?
ETSI Minas - Universidad Politkcnica de Madrid

CATHARE 

10, Evaporation Rate (kg/ml3/s) 

10'. ° .... .. ..... .. . 

0.0 5 .0 10.0 1.0 

Pressure (AIPa) 

RELAP5 Mod2 

10' Evaporation Rate (k /m3/s) 

10, 

.•.. 

Id .................. .

10' . . , 

O0 S.0 10.0 *5.0 

Pressure (MPa)

DRUFAN 

Em. aration Rate 

-..

71U 

10" I . . . . , . . . . . 

0.0 5.0 15.0 '0.0 

Pressure (MPa)

THYDE -P2 

id Evaporaton Rate (kg/m3/s) 

./. 

0.0 5.0 (5.0 10.0 Pressure (MPa)

Dm=O5m. V. rromCode.TL- =K HowiPipe. a Oi. OZ,0.3..C10O3 -1 

Figure 4.7: Evaporation during flashing. CATHARE, DRUFAN, RELAP5/MOD2 

and THYDE-P2 codes.

I I I

68
Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

TRAC PF1 

Evaporation Rate (kg/m3/s) I I

Legend for all Codes

Void Firadion

-....... 

02 

0.0 5.0 10.0 15.0 

Pressre (M~to) 

Fig. 2.5 

DH- 05 m. Vr frmn Code- TL - Ts -1I K ho••z Pipe- a= 01. OZ•OC = 3 -1040sid

Code 

X CA"HARE 

+ DRIUAN/FLUT 

SREL.AP 

x TRYDE 

0 ?RAC

0.o 5.o 16.0 15.0 

Pressure (MPa) Fig. 2.6 

DH=05m.V.fromCode, a=O.1.TL-Ts=IK, horizPi:4. G=3.O'10'Jk 

Figure 4.8: Evaporation during flashing of TRAC-PF1 code and comparison of the

models.

io3⁄4

69
"* Which are the non-equilibrium constant values recommended for Henry-Fauske 

model? 

"* Which are the main conclusions of each report? 

The comments and conclusions on the references founded are described below. They 

are divided in two groups: In the first, the thermal hydraulic codes references are 

commented; and in the second, the reviews on critical flow data and models are also 

commented. 

"* CATHARE. 

Two Marviken tests (CFT-17 and CFT-24) were selected for the validation 

matrix of CATHARE code. The main conclusions were, [BAR-90] and 

[BES-90]: 

- The initial pressure undershoot is not well predicted. 

- The mass flow rate is overestimated because the multidimensional phe

nomena which occur in a steep convergent nozzle and cause a flow area . 

restriction cannot be taken into account by the CATHARE 1-dimensional 

model. 

"* TRAC-P1A. 

In the developmental assessment, the simulation of CFT-04 was performed, 

[TRA-791 and [TRA-80]. Later, several CFT (01, 02, 04, 07, 13, 22 and 24) 

were also simulated during the independent assessment, [TRA-811. The model 

used was the ICM-P. The conclusions were similar in all reports: 

- The constitutive relations in TRAC-PlA did not permit delayed nucle

ation; this problem prevents the code from calculating the initial dip in 

the pressure at the beginning of the tests and forced the critical flow 

calculation toward equilibrium, resulting in an under prediction of the 

flow. 

- The simulation results under predict the subcooled part of the blowdown 

(10 %) and agree very well with the saturated part of the blowdown. 

- The quality of the comparisons, between simulated and test data, de

graded with decreasing length to diameter ratio.

I 1 1

70 ETSI Minas - Universidad Polit~cnica de Madrid
Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

* TRAC-PD2. 

In the TRAC-PD2 independent assessment, five CFT were selected (04, 13, 20, 

22 and 24), [TRA-84]. The model used was the same than TRAC-PlA model. 

In this assessment several steam generation rate models were implemented. 

The main conclusions were: 

- The unrealistically large steam generation rate causes the code to expe

rience an early flow limitation caused by choking. 

- None of the steam generation rate models that were used in this analysis 

(Rivard and Travis, Jones, Hunt and RELAP5 models) adequately 

improve the critical flow calculation. 

- When the initial liquid temperature in the lower part of the vessel 

is artificially reduced, the flashing is avoided inside the nozzle during 

subcooled blowdown. In this case the comparison between simulated and 

experimental data is excellent. So, the flow through the nozzle seems 

to take place under highly non-equilibrium conditions. Such a high 

non-equilibrium is not calculated by any of the mass transfer models 

mentioned above. 

- An increase of the nozzle area does not increase the flow linearly because 

of the increased steam generation rate. 

- The constitutive relations in TRAC-PD2 did not permit delayed nucle

ation; this problem prevents the code from calculating the initial dip in 

the pressure at the beginning of the tests and forced the critical flow 

calculation toward equilibrium, resulting in an under prediction of the 

flow. 

- The simulation results under predict the subcooled part of the blowdown 

(10 %) and agree very well with the saturated part of the blowdown. 

* TRAC-PF1/MOD1. 

In the TRAC-PF1/MOD1 description report, [TRA-83] and [TRA-86], the 

simulations of two tests used for the assessment of the code, CFT-04 and 

CFT-24, are described. ICM-P was selected to make the simulations. The 

main results were: 

- For the test with long nozzle (CFT-04), the calculations during the 

subcooled blowdown phase with CFM-on gave almost identical results 

than those with CFM-off and fine mesh (30 cells for CFT-04 and 12 cells

71
for CFT-24). During the two phase blowdown period the results with 

CFM-off and fine mesh are a 10% higher than the results with CFM-on. 

Both models calculations under predict the experimental mass flow by 

an average of 10% during the subcooled blowdown period. During the 

two phase blowdown phase the mass flow results with CFM-on are quite 

similar to test data. 

- For the test with short nozzle (CFT-24), the agreement between both 

models is not as good as for CFT-04. This discrepancy is attributed to 

the predominance of non-equlibrium effects between the phases caused by 

the short nozzle length. These non-equilibrium effects are not modeled 

in the TRAC-PF1/MOD1 choking calculation. The comparison between 

choking model and test data shows that the simulation under predicts the 

experimental mass flow by 20% - 40% during the subcooled blowdown 

phase. During the two phase blowdown phase the mass flow results with 

CFM-on are quite similar to test data. 

- To investigate non-equilibrium effects in CFT-24, short nozzle, a sensi

tivity run with the frozen assumption was performed. Using the frozen 

model the mass flow is over predicted and the pressure under predicted. 

- The dip in the measured pressure during the first 3 seconds of the 

transient indicates a significantly more pronounced nucleation delay than 

predicted by the TRAC-PF1/MOD1 model. 

In the independent assessment of TRAC-PF1/MOD1 performed by the 

CEA in the frame of the ICAP program, [SPI-901, several blowdown 

tests were selected: MOBY-DICK, SUPERMOBY-DICK, CANON, SUPER

CANON, VERTICAL CANON, OMEGA-TUBE, OMEGA-BUNDLE and 

MARVIKEN. Three Marviken test were simulated (CFT-06, CFT-17 and 

CFT-24). ICM-P (the one with the nozzle modeled with two or three cells 

is called "the reference model") was selected to make the simulations. The 

main conclusions were: 

- The initial pressure undershoot is not predicted, due to the absence of a 

delayed boiling model. 

- The mass flow rate obtained with the reference model is under predicted 

with discrepancies of 20% for the test with long nozzles (CFT-17) and of 

25%-30% for the tests with short nozzles (CFT-24 and CFT-06). 

- The results obtained with a fine mesh (six or more cells) at the nozzle 

give similar results than the reference model with a reduced time step.

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72 ETSI Minas - Universidad Politknica de Madrid
Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

- The simulation performed with the reference mesh at the nozzle and 

natural choking (CFM-off) gives different results than CFM-on. 

- The results obtained with a fine mesh at the nozzle and natural choking 

give similar results for test with long nozzle (CFT-17) and a mass flow 

rate larger than the reference model (better agreement with test data) for 

test with short nozzle (CFT-24). The absence of thermal disequilibrium 

for CFT-17 leads to equivalent results, with and without the choked 

flow model. For CFT-24, a better agreement is found when the thermal 

disequilibrium is taken into account (CFM-off). 

- Simulations of the first period (subcooled liquid at the discharge pipe) 

with the BCM-P were performed. The results of this model differ from 

the reference model results. Some of the results with BCM-P are in better 

agreement with test data, but others have higher discrepancies. There 

are not important conclusions respect these differences. 

- The lack of virtual mass term in the natural choking model probably 

takes part in the poor agreement between simulation and test data in 

some of the tests simulations. 

- An improvement of the choked flow model is needed in order to take into 

account the inter phase thermal disequilibrium. 

- The inception of boiling is predicted too early, so a delayed boiling model 

is needed. 

* TRAC-PF1/MOD2. 

In the TRAC-PF1/MOD2 manual, [TRA-93] pp. 599 to 605, two tests used 

for the assessment of TRAC-PF1/MOD2, CFT-04 and CFT-24, are described 

(the input of CFT-04 is included in [TRA-96] appendix A-3, and a detailed 

description of the critical flow model can be found in [TRA-971). The ICM-P 

was selected to make the simulations. The main conclusions of the report 

were identical to TRAC-PF1/MOD1 assessment, [TRA-86], however a few 

differences could be observed between the graphics of both reports. The main 

conclusions about TRAC-PF1/MOD2 were: 

- For the test with long nozzle (CFT-04) the calculations during the 

subcooled blowdown phase with CFM-on give almost identical results to 

those for with CFM-off and fine mesh (30 cells for CFT-04 and 12 cells 

for CFT-24). During the two phase blowdown phase the results with

73
CFM-off and fine mesh are a 10% higher than the results with CFM

on. Both calculations under predict the experimental mass flow by an 

average of 5% (10% in the manual) during the subcooled blowdown phase. 

These results are better than those obtained in the TRAC-PF1/MOD1 

assessment, [TRA-86]. During the two phase blowdown period the mass 

flow results with CFM-on are quite similar to test data. 

- For the test with short nozzle (CFT-24) the agreement between both 

models is not as good as for CFT-04. This discrepancy is attributed to 

the predominance of non-equlibrium effects between the phases caused by 

the short nozzle length. These non-equilibrium effects are not modeled 

in the TRAC-PF1/MOD2 choking calculation. The comparison between 

choking model and test data shows that the simulation under predicts 

the experimental mass flow by 20%-40% during the subcooled blowdown 

period. During the two phase blowdown phase the mass flow results with 

CFM-on are quite similar to test data. 

- The dip in the measured pressure during the first 3 seconds of the 

transient indicates a significantly more pronounced nucleation delay than 

predicted by the TRAC-PF1/MOD2 model. 

During the update of the critical flow model subroutine of TRAC-P, FXCFM, 

several areas were corrected, [STE-98]. Knolls Atomic Power Laboratory, 

Marviken (CFT-04, CFT-13, CFT-20, CFT-22 and CFT-24), Edwards and 

Scientech critical flow tests were used for investigate the reported errors and 

further errors that were found and to verify their correction. The main 

conclusion about the Marviken tests was that better agreement with the 

experimental data probably requires making changes elsewhere in the choked 

flow model. Such changes may need to be made in the modeling assumptions 

rather than in searching for further corrections. 

* TRAC-BD1/MOD1. 

Three tests were simulated for the assessment of TRAC-BD1/MOD1, CFT

15, CFT-18 and CFT-24, ITBD-85a] pp 22-28 and [TBD-85b] pp 18-19, 41. 

ICM-P was selected to make the simulations. The main results were: 

The computed value is a 20-25% lower than test data during subcooled 

and low-quality period and 10-15% for high-quality period. The difference 

for high qualities may be due to some error in the extrapolated fluid 

properties used to calculate the sonic velocity or multidimensional effects 

not accounted for in the one-dimensional flow model.

74 ETSI Minas - Universidad Polit~cnica de Madrid

I III
Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

- Independent calculations suggest that substantial improvement may be 

achieved by appropriated correcting the numerical treatment of the mo

mentum equation to account for artificial pressure drop at flow restric

tions due to the backward (donnor cell) differencing used in the TRAC 

numerical scheme. 

- The subcooled CFM is very sensitive to the amount of fluid subcooling. 

A sensitivity study showed that a 5VC change in break flow subcooling 

can cause a 15% decrease in break mass flow. 

- An adjustment of the discharge coefficient, from 0.7 to 1.0, is required to 

correctly simulate the mass flow. 

"* TRAC-BF1/MOD1. 

Five tests (CFT-10, CFT-15, CFT-21, CFT-23 and CFT-24) were simulated 

to analyse de capacity of TRAC-BF1 to reproduce blowdowns under critical 

conditions, [GOM-981. The ICM-P was selected to make the simulations. The 

main results were: 

- TRAC-BF1 numerical scheme is unable to reproduce critical solutions 

with natural choking, so an externally imposed critical condition is 

needed. 

- TRAC-BF1 fails to reproduce the thermal disequilibrium arising in the 

transition from liquid to boiling mixture. Therefore, the critical flow rates 

are underestimated in subcooled conditions through very short nozzles. 

"* RELAP5/MOD2. 

In the developmental assessment of RELAP5/MOD2 two CFT were simulated, 

[REL-87] pp 21-25. ICM-J was used for the test with short nozzle (CFT-24, 

LID = 0.33) and ICM-P for the long one (CFT-22, L/D = 1.5). The sub

cooled period is well adjusted for both cases, but in the two-phase period the 

simulation underestimates the mass flow in 10%. 

In the independent assessment of RELAP5/MOD2 performed by the Swedish 

Nuclear Power Inspectorate, [ROS-861, in the framework of ICAP, two tests 

were analyzed (JIT-11 and CFT-21). The models used were BCM-J and BCM

P. The main conclusions were: 

- The subcooled critical mass flow rate for CFT-21 is over predicted with 

the BCM-J; a discharge coefficient of 0.85 is necessary to agree the 

calculated mass flow with the measured ones.

75
- When the nozzle geometry was explicitly modeled (BCM-P) mass flow 

rates for CFT-21 were under predicted. Application of discharge coeffi

cients greater than unity did not improve the computed results; on the 

contrary, doing so gave rise to a very numerically noisy solution. It is 

concluded that short discharge nozzles or pipes (L/D < 2) should not be 

modeled explicitly in RELAP5. 

- Other modeling deficiencies in the critical flow model were identified. 

These were the unrealistic spikes in the steam discharge choked flow of 

JIT-11, the unrealistic effects of discharge coefficients in the region of 

subcooled critical flow (non-linearity effect on the discharge coefficient), 

and the discontinuity of critical mass flow rate in the transition region. 

These deficiencies were modified in RELAP5/MOD3, and a new assess

ment was performed [WEA-89]. 

In the assessment of RELAP5/MOD2 and MOD3 performed by the Korea 

Institute of Nuclear Safety (KINS), two tests were analyzed (CFT-15 and 

CFT-24), [KIM-92]. In this report a sensitivity analysis of the nodalization of 

the discharge pipe and the nozzle are performed. The model used is the ICM. 

In the test with long nozzle (CFT-15, L/D=3.6), the nozzle is modeled as a 

PIPE (ICM-P). In the test with short nozzle (CFT-24), the nozzle is modeled 

as a PIPE (ICM-P) or SINGLE JUNCTION (ICM-J). The main conclusions 

are: 

- For the CFT-15 simulation (long nozzle), it may be recommended that a 

nozzle is modeled as PIPE. 

- For the CFT-24 simulation (short nozzle), ICM-J gives better results 

than ICM-P. 

- In RELAP5 the pressure drop due to friction loss in a PIPE is over 

predicted relative to actual data. 

- When the nozzle is modeled as a PIPE in CFT-24 the prediction 

with RELAP5/MOD2 of the inception of boiling at the nozzle inlet is 

somewhat faster and the calculated mass flow rate at the beginning of 

the two phase-region is very low due to the generation of high void

fraction. When the simulation is performed with RELAP5/MOD3 the 

inception of boiling appears at the beginning of the transient, which is 

not in accordance with experimental data.

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Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

- The critical flow model in RELAP5/MOD3 under predicts in about 

5% the mass flow rate and shows oscillations during two-phase region, 

although it predicts a smoothly transition region. 

* RELAP5/MOD3. 

In the developmental assessment of RELAP5/MOD3, [REL-90], the same 

analysis than RELAP5/MOD2, [REL-87J was performed. The conclusions 

were the same, but with one difference: The mass flow rate computed by 

RELAP5/MOD3 in the two-phase portion of the test lies slightly below the 

mass flow rate computed by RELAP5/MOD2. This is due to the change in the 

interfacial friction model for large-diameter pipes, which results in a higher slip 

ratio in RELAP5/MOD3 relative to MOD2 for the same set of fluid conditions. 

The slip ratio implied by the interfacial friction model is used to unfold the 

phasic velocities from the choking condition, and a higher slip ratio results in 

a lower liquid velocity and a higher vapor velocity. Since the void fraction at 

the choking plane remains relatively low (less than 0.3) throughout the test, 

the lower liquid velocity computed by RELAP5/MOD3 results in a slightly 

lower discharge flow rate. The results of this assessment demonstrate that 

changes to one code model (i.e. the interfacial friction model) can affect the 

performance of other, completely separate model (i.e. the critical flow model). 

The KAERI team has developed a new version of RELAP5/MOD3 called 

RELAP5/MOD3/KAERI. In this version the CFM is the same than in 

RELAP5/MOD3 (Ransom-Trapp model) and so, the conclusions are valid 

for both codes. They performed an uncertainty analysis of the CFM for 

its application in a best estimate methodology. Nine CFTs (03, 04, 08, 

11, 15,16, 21, 22 and 27) with LID > 1.5 were simulated with BCM

J and BCM-P, [KAE-94] and [KAE-951. They only simulated tests with 

LID > 1.5 for minimizing the effect of LID ratio (it must be remembered 

that in MARVIKEN tests the critical mass flow under subcooled conditions 

diminishes with L/D ratio if L/D < 1.5, and also that further increase in LID 

ratio does not reduce the mass flow appreciably). The main conclusions were: 

- The two-phase critical flow rates are nearly the same for all the discharge 

pipe nodalization (two to six cells), except the single cell case. So, the 

two-cell model was adopted. 

- The discharge coefficients and standard deviation (SD) for BCM-J are: 

0.82115 (SD= 7.5E - 2) for subcooled flow and 1.1485 (SD= 8.8E - 2) 

for two-phase flow.

77
- The discharge coefficients for the BCM-P are: 0.89 (SD= 3.5E - 2) for 

subcooled flow and 1.07 (SD= 1.2E - 1) for the two-phase flow. 

The evolution of RELAP5/MOD3.1 to MOD3.2 code version is described in 

IREL-98]. The changes performed in JCHOKE subroutine were: 

- Improvement to the calculation of sonic velocity for critical flow of 

subcooled liquid: During critical flow of subcooled liquid, the mass 

flow rate may be unaffected by a change of upstream pressure. This 

problem occurs because the equilibrium sound speed at the junction 

is calculated assuming the junction contains saturated liquid at the 

upstream temperature. The change performed in JCHOKE subroutine 

was: Use momentum and mechanical energy balances to calculate the 

pressure and internal energy at the junction and use the water property 

tables to obtain the thermodynamic properties of a saturated liquid-vapor 

mixture at this pressure and internal energy. 

- Improvement to the unchoking test used in the critical flow model: The 

unchoking test checked that the throat pressure was larger than the 

downstream pressure. Although this test was not plausible, it was left in 

the code because no problems were observed. Later, they saw that this 

test may cause oscillations in the flow rate. For this reason, an improved 

unchoking test was implemented. 

RELAP5/MOD3.2.2. 

CFT-22 (L/D = 1.5) was simulated in order to compare the default CFM of 

RELAP5/MOD3.2 (Ransom-Trapp model) and the new option of the Henry

Fauske CFM, [JOH-96] and [MOR-98]. This new model sets a single discharge 

coefficient and the non-equilibrium constant dp based on geometry and test 

data. ICM-P was selected to make the simulations. The main results were: 

- The comparison between test data, the Ransom-Trapp CFM and Henry

Fauske CFM show that the Henry-Fauske CFM gives better results than 

the Ransom-Trapp model. 

- A discharge coefficient of 0.95 is necessary for adjusting to MARVIKEN 

data (dp = 0.14). 

- The incorporation of the Henry-Fauske CFM overcomes the limitations 

of RELAP5/MOD3 CFM: multiple discharge coefficients, low two-phase 

critical flow at low pressures (P < 0.2MPa) or low quality (0.01 to 0.2).

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78 ETSI Minas - Universidad Politkcnica de Madrid
Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

* E. Elias and G.S. Lellouche. 

They made a detailed review in two phase critical flow problem, [ELI-94]. 

Several aspects of the problem are analyzed in this paper: Theoretical 

foundations, numerical considerations, critical flow models, experimental data 

sources and model evaluations. For the model evaluations, the inlet conditions 

at the start of the discharge pipe of several Marviken tests (CFT-04, CFT

06, CFT-09, CFT-13, CFT-14, CFT-18, CFT-19, CFT-23 and CFT-24) were 

used. Some of the conclusions of the report are: 

- Due to the errors in the initial period of the blowdown, the data of the 

first five seconds are no used. 

- The analytic and fitted models (Burnell, isenthalpic, Moody with slip, 

fit to the Moody model, Henry-Fauske, fit to Henry Fauske Model and 

HEM) do not provide good predictions, as required of a viable calculation 

tool. 

- Among the space-dependent models (Elias-Chambre model, complete 

drift flux model and Richter model), only the Richter model have been 

partly successful. It is surprising that these models fail in large diameter 

down flow situations if we take into account that all of them produce 

reasonable results for small diameter pipes. Perhaps it only shows that 

these correlations are based in data-based set for small diameter pipes 

and that the large extrapolation in diameter and mass flow rate that it 

is made when they are applied to Marviken tests is just too large. So, it 

is clear that much further work is needed at these conditions. 

- The TRAC-P code nearly always under predict the data. 

- In general, the calculated critical flow in a code (TRAC-P/B, RELAP5, 

RETRAN) may depend more on the constitutive relations and correla

tions than on the imposed critical flow model. 

- Best estimate calculations of large break situations are unreliable and can 

only be interpreted through an analysis which includes an uncertainty in 

the critical flow model. 

- The use of natural choking, the own critical flow condition of the system 

of equations (characteristic root null), presents several problems: 

• The existence of a spatial singularity in pressure cannot be resolved 

completely in discrete mesh. If we want to resolve the calculated 

critical flow rates to less than 1% of error, extremely fine meshes 

(3-10 mm) must be used.

79
"• In the explicit and semi-implicit numerical methods (semi-implicit 

in RELAP5, SETS in TRAC-P) there is a stability limit near to 

the Courant limit that makes it necessary to use very little time 

steps when applying the natural choking criterion, for two reasons: 

extremely fine mesh and high speeds (sound speed). This has led 

to the introduction of separate choking models in codes as RELAP5 

and TRAC-P. 

" A separate choking model is not necessary if fully implicit schemes 

are used, like in the CATHARE code, because this kind of numerical 

methods allows the use of very fine meshes near the break without 

affecting the time step. 

* Critical Flow Data Review and Analysis. 

MARVIKEN data were analyzed in [LEV-82] to evaluate critical flow models 

against the large scale critical flow data. Some of the conclusions were: 

- Comparison with more detailed models shows that non-equilibrium is 

important when the stagnation state is in the region of subcooled liquid 

or very low quality and LID < 1.5. The duration of meta-stability is 

important. 

- HEM results are in fair agreement for subcooled stagnation conditions 

and length-to-diameter ratios greater than 1.5. For two-phase conditions 

and long nozzles the predictions are close to experimental data, for short 

nozzles the mass flow is under predicted (20 %). 

- The Henry-Fauske model, which was developed for orifices and short 

tubes, over predicts most of the data except the subcooled portions of 

tests with LID < 1.5. If the non-equilibrium parameter of Henry-Fauske 

model is modified to be a function of stagnation conditions and nozzle 

geometry a good agreement with the experimental data is obtained. 

In the comparison of the test data of MARVIKEN CFT-04, 06, 10, 

14, 18, 19, 23, 24, 25 with the Henry-Fauske CFM several values of 

the disequilibrium parameter, N, are compared. The best results are 

obtained with, 

* N - 7.1Xe for subcooled blowdown and a < 1.5 

"* N= 100OXe for - > 1.5 D 

"* N = lOOXe for saturated blowdown

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Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

Where Xe is the equilibrium quality. The disequilibrium parameter 

used in RELAP5/MOD3.2.2beta (dp) is related with N through the 

expression, N = min(1, x-). Therefore the recommended values for dp 

are, 

"• dp = 0.14 for subcooled blowdown and L < 1.5 D 

"* dp = 0.01 for L > 1.5 D 

"* dp = 0.01 for saturated blowdown 

- The correlations included in best estimate codes that are used to represent 

phase interactions at conditions within the reactor primary system may 

not be appropriate to represent these phenomena at a choke plane. 

No attempt is made to summarize these conclusions, because we believe it is better 

for everybody to take their own conclusions. 

4.4 Results and Discussion of Boundary Condition 

Model (BCM). Ransom-Trapp Model 

The analysis of Marviken experiments with this model has the following objectives, 

"* Comparison of critical and non-critical flow models with test data. 

"* Comparison and selection of model options: 

- Homogeneous versus non-homogeneous flow. 

- Comparison of SINGLE JUNCTION, trip valve and motor valve models. 

- Comparison of discharge coefficient and nozzle area variations. 

"* Discharge coefficient adjustment for subcooled and two-phase conditions with 

different nozzle models: 

- Nozzle modeled as SINGLE JUNCTION. 

- Nozzle modeled as PIPE. 

For this analysis it is important to cover different thermo-hydraulic conditions at the 

nozzle, subcooled and two-phase, and also different L/D relations for the nozzles. For 

these reasons the experiments selected were: CFT-01, CFT-06, CFT-11, CFT-15, 

CFT-17, CFT-21 and CFT-24. In all these tests there are subcooled and two

phase periods, except in CFT-17, where only the subcooled period is observed. The 

boundary conditions used in this model are shown in Figures 4.9 to 4.28. The results 

and conclusions are described in next sections.

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5.5e+06

ETSI Minas - Universidad Politkcnica de Madrid

MARVIKEN CFT-01 

Boundary Conditions

5.0e+06 -

Cu

4.5e+06 -

4.0e+06

3.5e+06' 

0.0 20.0 40.0 60.0 

Time (s)

80.0 100.0

Figure 4.9: Pressure at bottom vessel. Test data. CFT-01. 

MARVIKEN CFT-01 

Boundary Conditions

530.0

N4 525.0 

E 

E2 520.0 

Er 

>2 

;0 515.0-

510.0 

0.0 20.0 40.0 

Time (s)

60.0 80.0 100.0

Figure 4.10: Liquid temperature at bottom vessel. Test data. CFT-01.

i 

i i 

I

i 

4

ýIýy
Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

MARVIKEN CFT-01 

Boundary Conditions

20.0 40.0 60.0 

Time (s)

80.0 100.0

Figure 4.11: Static quality at bottom vessel. Test data. CFT-01. 

MARVIKEN CFT-06 

Boundary Conditions

5.0e+06

,/

4.5e+06 -

I-.

4.0e+06 -

3.5e+06 -.. 0.0 20.0 40.0 60.0 80.0 100.0 

Time (s)

Figure 4.12: Pressure at bottom vessel. Test data. CFT-06.

0.0020

0.0015 -

0.0010

.E

0.0005 L

0.0000 

0..0

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84 ETSI Minas - Universidad Polit6cnica de Madrid

530.0

2 

0

2

MARVIKEN CFT-06 

Boundary Conditions

520.0 

510.0 -

500.0 

0.0 20.0 40.0 60.0 80.0 100.0

Time (s) 

Figure 4.13: Liquid temperature at bottom vessel. Test data. CFT-06.

MARVIKEN CFT-06 

Boundary Conditions

0.0020 

0.0015 -

E 

0

0.0010 -

0.0005 -

0.0000 0..0 20.0 40.0 60.0 80.0

0I 

)0.0

Time (s)

Figure 4.14: Static quality at bottom vessel. Test data. CFT-06.

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Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

MARVIKEN CFT-11

6.0e+06

Boundary Conditions

5.0e+06 L

"* 'I,

4.0e+06 -' IU 

WI)

3.0e+06

2.0e+06 

0.0 20.0 40.0 60.0

Time (s)

Figure 4.15: Pressure at bottom vessel. Test data. CFT-11. 

MARVIKEN CFT-11

E 

0.-) 

I

4.1 

E 

"Z 

E

530.0 

520.0 

510.0 

500.0 , 

490.0 . 

0.0

Boundary Conditions

j

20.0 40.0 60.0

Time (s)

Figure 4.16: Liquid temperature at bottom vessel. Test data. CFT-11.

85
86 ES ia nvria oi~nc eMdi

MuRVIKEN CFT-11

0.80

Boundary Conditions

0.60 

0.40 

05 

0.20

A

0.0 20.0 40.0 60.0

Time (s) 

Figure 4.17: Static quality at bottom vessel. Test data. CFT-11.

MARVIKEN CFT-15 

Boundary Conditions

6.0e+06 

5.0e+06 • 

4.0e+06 -

20.0 40.0 60.0

3.0e+06 

2.0e+06 

0.0

Time (s) 

Figure 4.18: Pressure at bottom vessel. Test data. CFT-15.

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U, 

0..

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Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

MARVIKEN CFT-15 

Boundary Conditions

/ 

I 

/1

1

20.0 40.0 60.0

Time (s)

Figure 4.19: Liquid temperature at bottom vessel. Test data. CFT-15. 

MARVIKEN CFT-15 

Boundary Conditions

0.40 

0.30

0.20 . H

0.10 -

A flA0.0n 0.0 20.0 40.0 610.0

Time (s)

Figure 4.20: Static quality at bottom vessel. Test data. CFT-15.

530.0

2 520.0

E 

E 

> 500.0 -

490.0 

0.0

>5 

Cu 

Cu 

S 

=

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ETSI Minas - Universidad Politkcnica de Madrid

MARVIKEN CFT-17 

Boundary Conditions

6.0e+06 

5.5e+06 

5.0e+06 

4.5e+06 

4.0e+06 

3.5e+06 

3.Oe+06-

0.0 20.0 40.0 60.0 80.0 100.0 

Time (s) 

Figure 4.21: Pressure at bottom vessel. Test data. CFT-17.

509.0

MARVIKEN CFT-17 

Boundary Conditions

508.0 -

E 

0

507.0

506.0 

505.0 

504.0 

0.0 20.0 40.0 60.0 80.0 100.0

Time (s) 

Figure 4.22: Liquid temperature at bottom vessel. Test data. CFT-17.

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Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

MARVIKEN CFT-21

6.0e+06 

5.0e+06 

§ 4.0e+06 

3.0e÷06 

2.0e+06 

0.0

Boundary Conditions

20.0 40.0

Time (s)

Figure 4.23: Pressure at bottom vessel. Test data. CFT-21.

60.0

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515.0

P 

E 

.7 

E

MARVIKEN CFT-21 

Boundary Conditions

510.0

505.0 -

T-V

I

500.0

20.0 40.0 60.0 495.0 

0.0

Time (s) 

Figure 4.24: Liquid temperature at bottom vessel. Test data. CFT-21.

MARVIKEN CFT-21 

Boundary Conditions

0.015 

S0.010 

0' 

E 

S0.005 

0.000 

0.0 20.0 40.0 60.0

Time (s) 

Figure 4.25: Static quality at bottom vessel. Test data. CFT-21.

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Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

6.0e+06

2.0e+06 

1.0e+06 

0.0

MARVIKEN CFT-24 

Boundary Conditions

20.0 40.0 60.0

Time (s) 

Figure 4.26: Pressure at bottom vessel. Test data. CFT-24.

510.0

500.0 -

MARVIKEN CFT-24 

Boundary Conditions

A

490.0 -

480.0 -

20.0 40.0 60.0

Time (s)

Figure 4.27: Liquid temperature at bottom vessel. Test data. CFT-24.

5.0e+06 

4.0e+06 

3.0e+06

U,

E 

E 

0

470.0 

0.0

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MARVIKEN CFT-24 

Boundary Conditions

0.80

0.60

CY 

E

0.40

7I

0.20 -

0.00 

0.0 20.0 40.0 60.0

Time (s) 

Figure 4.28: Static quality at bottom vessel. Test data. CFT-24.

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Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

4.4.1 Comparison of Critical and Non-critical Flow Models 

The models and options being compared are: 

"* CFM-off and nozzle modeled as a SINGLE JUNCTION. 

"* CFM-on and nozzle modeled as a PIPE. 

"* CFM-on and nozzle modeled as a SINGLE JUNCTION, smooth area change. 

"* CFM-on and nozzle modeled as a SINGLE JUNCTION, abrupt area change. 

The code options used for all the cases are: 

"* Homogeneous option, vg = v1 . 

"* Discharge coefficients equal to one. 

"* Null friction coefficient at the nozzle outlet. 

The following conclusions are obtained from Figures 4.29 to 4.42: 

"* In general, the mass flow simulated with CFM-off is always greater than with 

CFM-on, except at the beginning of CFT-01, CFT-06 and CFT-17 (see Section 

2.1, problems with the transition from CFM-on to CFM-off). Also, the CFM

off results do not fit the experimental data and so the critical flow model is 

necessary. 

"* When nozzle is modeled as a single junction, the results obtained with the 

abrupt area change option are better than with the smooth area option. 

However, the differences between them are small. 

"* The subcooled period is apparently better reproduced with the nozzle modeled 

as a pipe than as a single junction (except in CFT-24), Figures 4.36 to 4.42, 

but it must be taken into account that the void fraction at nozzle outlet is 

not null from the beginning of the transient with the nozzle modeled as a 

pipe, which is not in accordance with experimental data. This problem is also 

reported in [KIM-92]. So, the subcooled period is modeled with a two-phase 

critical flow model with a non null void fraction, which is wrong. This problem 

is not present when the nozzle is modeled as a single junction because it is 

equivalent to freezing the model.

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MARVIKEN CFT-01

00

5000.0 

4000.0 

3000.0 

2000.0 

1000.0

0.0 0.0

- Test data 

o-c CFM on. Junction non-smooth 

- CFM off. Junction 

o-- CFM on. Junction smooth 

;A-k- CFM on. Pipe

20.0 40.0 60.0 80.0 100.0

Time (s)

Figure 4.29: Mass flow 

(BCM). CFT-01.

at nozzle exit. Comparison between CFM and non-CFM

"* The results obtained with both models during the two-phase period are quite 

similar to experimental data, Figures 4.29 to 4.35. CFT-06 and CFT-24 are 

better reproduced with the nozzle modeled as a junction. 

"* As the subcooled period is better reproduced with the nozzle modeled as a 

junction and for the two phase period both models seem to give similar results, 

it should be better to choose the junction model for the nozzle.

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Assessment of RELAP5/MOD3 CFM against Marviken Tests

MARVIKEN CFT-06

-Test data 

0-- CFM on. Junction non-smooth[ 

L--: CFM off. Junction 

e-o CFM on. Junction smooth 

- CFM on. Pipe

100.0

Time (s)

Figure 4.30: Mass flow at nozzle exit. 

(BCM). CFT-06.

Comparison between CFM and non-CFM

5000.0 

4000.0

3000.0 

0 2000.0

Mo

1000.0

Chapter 4. 95
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MARVIKEN CFT-11

15000

a--- CFM off. Junction 

o-o CFM on. Non-smoothi 

-Test data 

a-- CFM on. Smooth 

A-- CFM on. Pipe

0 a 

0.0 20.0 40.0 

Time (s)

60.0

Figure 4.31: Mass flow at nozzle exit. Comparison between CFM and non-CFM 

(BCM). CFT-11.

MARVIKEN CFT-15

30000

0---o CFM on. Junction non smooth 

"a--o CFM off. Junction 

- Test data 

- CFM on. Pipe

20000-

00

10000

20.0 40.0 60.0

Time (s) 

Figure 4.32: Mass flow at nozzle exit. Comparison between CFM and non-CFM 

(BCM). CFT-15.

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Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

MARVIKEN CFT-17

-Test data 

G--c CFM on. Junction non-smooth 

- CFM off. Junction 

A-s CFM on. Pipe

40.0 60.0 

Time (s)

80.0

Figure 4.33: Mass flow 

(BCM). CFT-17.

at nozzle exit. Comparison between CFM and non-CFM

MARVIKEN CFT-21

15000.0

o-o CFM on. Junction non-smooth 

- CFM off. Junction 

-Test data 

i - CFM on. Pipe

!.i

20.0 40.0 60.0

Time (s)

Figure 4.34: Mass flow 

(BCM). CFT-21.

at nozzle exit. Comparison between CFM and non-CFM

5000.0 

4000.0 

3000.0 

2000.0

occ 

0€

1000.0-

1nf1 B- 0.0 0.0 20.0 100.0

10000.0 

5000.0

0

0.0 6

0.0

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0•

30000.0 

25000.0 t 

20000.0 

15000.0 

10000.0 

5000.0 

0.0 

0.0

MARVIKEN CFT-24 

0-0 CFM on. Junction smooth 

- CFM off. Junction 

-Test data 

SCFM on. Pipe

20.0 40.0 60.0

Time (s) 

Figure 4.35: Mass flow at nozzle exit. Comparison between CFM and non-CFM 

(BCM). CFT-24.

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Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

MARVIKEN CFT-01

0.50

- Junction model 

0-0 Pipe model. Outlet nozzle 

-- Pipe model. Inlet nozzle

0 

L. 

"0 

.5

0.40 

0.30 

0.20

0.10 

0.00 

0.0 20.0 40.0 60.0 80.0 100.0

Time (s)

Figure 4.36: Void fraction. Comparison between CFM and non-CFM (BCM). CFT

01. 

4.4.2 Selection of Model Options 

The following comparisons have been made in order to analyze the influence of the 

different code options and available models: 

*Comparison between Homogeneous and Non-homogeneous options. This 

option has only an effect on the two-phase period. CFT-15 and CFT-24 have 

been used for this analysis. The results obtained with the homogeneous option 

are closer to test data than those obtained with the non-homogeneous option, 

independently of the model used for the nozzle (pipe or junction), Figures 4.43 

to 4.46. 

e Comparison of SINGLE JUNCTION, trip-valve and motor-valve models. All 

the models give the same results for the CFT-21 simulation, Figures 4.47 and 

4.48, for subcooled and two-phase periods, and also for discharge coefficients 

different from one. 

From the previous analysis, the homogeneous option should be used with any of the 

three models above mentioned.

99
ETSI Minas - Universidad Politkcnica de Madrid

MARVIKEN CFT-06

0.40

- Junction model mdc=l 

o-O Pipe model mdc-1. Outlet nozzle -- Pipe model mdc=1. Inlet nozzle

).0 20.0 40.0 60.0 80.0

I

100.0

Time (s)

Figure 4.37: Void fraction. Comparison between CFM and non-CFM (BCM). CFT

06.

MARVIKEN CFT-11

- Junction model 

o--o Pipe model. Outlet nozzle 

-Pipe model. Inlet nozzle

-I 

A

20.0 40.0 60.0

Time (s)

Figure 4.38: Void fraction. Comparison between CFM and non-CFM (BCM). CFT

11.

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100

0.30

0 

.5

0.20

0.10

0.00 

0

1.0 

0.8 

0.6 

> 0.4 

0.2
Chapter 4. Assessment of RELAP5!MOD3 CFM against Marviken Tests

MARVIKEN CFT-15

1.0 

0.8-

-Junction model mdc-l SPipe model mdc=l. Outlet nozzle 

-- Pioe model mdc-l. Inlet nozzle

S0.6 

0 

> 0. 4

0.2 -

20.0 40.0 60.0

Time (s)

Figure 4.39: Void fraction. Comparison between CFM and non-CFM (BCM). CFT

15.

MARVIKEN CFT-17

0.20 -

- Pipe model. Outlet nozzle 

0-O Junction model and Pipe model. Inlet nozzlei

0.15

0.10

0.05

40.0 60.0 

Time (s)

80.0 100.0

Figure 4.40: 

17.

Void fraction. Comparison between CFM and non-CFM (BCM). CFTIL 

.5

0.00 0 20.0

D 9 e e eDV 

101

1I 

I 

i

0.0
102 ETSI Minas - Universidad Polit6cnica de Madrid

MARVIKEN CFT-21

0.8

- Junction model mdc=1 

o---- Pipe model mdc=1. Outlet model 

- Pipe model mdc=1. Intel model

0.6 -

0 

Z .4 

0 .4 

0

0.2

20.0 40.0 60.0

Time (s)

Figure 4.41: Void fraction. Comparison between CFM and non-CFM (BCM). CFT

21.

MARVIKEN CFT-24

1.0 

0.8

S0.6 

> 0.4

0.2

- Junction model mdc-1 o--- Pipe model mdc-i. Outlet model 

-- Pioe model mdc=1. Intel model

i

0.0 a" 0.0 40.0 60.0

Time (s)

Figure 4.42: Void fraction. Comparison between CFM and non-CFM (BCM). CFT

24.

p .....

102 ETSI Minas - Universidad Politkcnica de Madrid

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Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

MARVIKEN CFT-15

15000.0

0-0 CFM on. Junction homogeneous 

F-o Test data 

- CFM on. Junction non-homooeneous

20.0 40.0 

Time (s)

Figure 4.43: Mass flow at nozzle exit. Comparison between Homogeneous and Non

homogeneous options. BCM-J. CFT-15.

MARVIKEN CFT-24

15000.0 

- Junction. Non-homogeneous model 

-q - Junction. Homogeneous model 

, o----c Test data

10000.0 

5000.0

0.01

0.0

2

20.0 40.0 60.0

Time (s) 

Figure 4.44: Mass flow at nozzle exit. Comparison between Homogeneous and Non

homogeneous options. BCM-J. CFT-24.

,z, 

.2 

;L

10000.0 

5000.0

0.0 4

0.0 60.0

00 

4.2 

Cu 

0

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ETSI Minas - Universidad Politkcnica de Madrid

MARVIKEN CFT-15

15000.0

-- o Test data 

A-- Pipe. Homogeneous Model 

- Pipe. Non-homogeneous Model

0 

.2 

L1.

10000.0 

5000.0

0.0 k

0.0 20.0 40.0 

Time (s)

60.0

Figure 4.45: Mass flow at nozzle exit. Comparison between Homogeneous and Non

homogeneous options. BCM-P. CFT-15. 

MARVIKEN CFT-24

15000.0

- Pipe. Non-homogeneous model 

,--o Test data 

A-- Pioe. Homooeneous model

0

10000.0 

5000.0

!1

20.0 40.0 60.0

Time (s)

Figure 4.46: Mass flow at nozzle exit. Comparison between Homogeneous and Non

homogeneous options. Nozzle modeled as PIPE (BCM). CFT-24.

104

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Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

MARVIKEN CFT-21

15000

-- mflowj Trip-valve. MDC = 1.0. 

6-A mftowj Sngljun. MDC = 1.0 

SA- -A mflowj Motor-valve. MDC = 1.0. 

rmflowj Trip-valve. MDC = 0.85 

0 o o mflowj Sngljun. MDC = 0.85. 

0 - mflowi Motor-valve. MDC = 0.85:

10000 

5000

0S 

0.0 5.0 10.0 15.0 20.0 25.0 30.0 

Time (s)

Figure 4.47: Comparison of Single junction, Trip-Valve and Motor-Valve Models. 

Subcooled CFM. MDC=1.0, 0.85 (BCM). CFT-21. 

MARVIKEN CFT-21

15000

- mflowj Trip-valve. MDC = 0.85 & BDC = 1.0 

0-o mflowj Sngljun. MDC = 0.85 & BDC = 1.0. 

0-- mflowj Motor-valve. MDC - 0.85 & BDC = 1.0.

10000

0 

0

5000

0.

0.0 10.0 20.0 30.0 40.0 50.0 60.0 

Time (s)

Figure 4.48: Comparison of Single junction, Trip-Valve and Motor-Valve Models. 

Subcooled and two-phase CFM (BCM). CFT-21.

105

0 

0

105

i
4.4.3 Discharge Coefficient Adjustment 

For the adjustment of the discharge coefficients (subcooled and two-phase), mod

elling the nozzle as a PIPE and a SINGLE JUNCTION, data from CFT-01, 11, 15, 

17, 21 and 24 have been used. 

" Nozzle modeled as SINGLE JUNCTION. The comparison between test data 

and the results for the mass flow with the adjustment of the discharge coeffi

cients are shown in Figures 4.49, 4.52, 4.55, 4.58, 4.61, 4.63 and 4.66. A very 

good adjustment is achieved with the coefficients shown in table 4.2 The tran

sitions present in the critical flow model (for void fractions a = 10-5, a = 0.1, 

a = 0.9, and a = 0.99 ) are shown on the figures by means of vertical lines. 

Void fraction results, Figures 4.50, 4.53, 4.56, 4.59, 4.64 and 4.67, and liquid 

temperature with saturation temperature at the nozzle exit, Figures 4.51, 4.54, 

4.57, 4.60, 4.62, 4.65 and 4.68, allow observing the range of variation of the 

void fraction and the subcooling in the simulations. It is important to remark 

that the range of variation of the void fraction is approximately below 0.4 

in all the cases analyzed, Figure 4.69, and so, other experiments should be 

necessary in order to validate the model in all its range. 

" Nozzle modeled as PIPE. The comparison between test data and the results 

for the mass flow with the adjustment of the discharge coefficients, table 4.2, 

Figures 4.70, 4.72, 4.74, 4.76 and 4.78, shows that the adjustment in the sub

cooled period is not so good as in the previous case. The reason is that when 

the subcooled discharge coefficients are fitted, the beginning of the boiling 

process is delayed, Figures 4.71, 4.73, 4.75, 4.77 and 4.79. However, it can be 

observed that boiling is still beginning too early respect to the test data. 

In the other hand, a good adjustment for the mass flow is achieved for the 

two-phase period, but the void fraction values are higher than with the nozzle 

modeled as a SINGLE JUNCTION. 

" The comparison of the discharge coefficient adjustment for both models, Ta

ble 4.2 and Figure 4.80, shows that the discharge coefficients used with the 

BCM-P are higher than for BCM-J.

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Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

MARVIKEN CFT-01

5000.0 

4000.0

- Test data - CFM on. mdc.0.82 bdc=0.95

3000.0 

2000.0

1000.0 

0.0 

0.0

1

20.0 40.0 60.0 80.0 100.0

Time (s) 

Figure 4.49: Mass flow at nozzle exit. Discharge coefficient adjustment, BCM-J. 

CFT-01.

MARVIKEN CFT-01

0.08

20.0 40.0 60.0 80.0 

Time (s)

Figure 4.50: Void fraction at nozzle exit. Discharge coefficient adjustment, BCM-J. 

CFT-01.

0

0.06 -

.0.04 

0.02

2

0.00 

0.0 100.0

107
108 ETSI Minas - Universidad Politkcnica de Madrid 

MARVIKEN CFT-01 

540.0 

Liquid Temperature - Saturation Temperature 

530.0 

. 520.0 

E 

510.0 

500.0 

0.0 20.0 40.0 60.0 80.0 100.0 

Time (s) 

Figure 4.51: Liquid and saturation temperatures at nozzle exit. Discharge coefficient 

adjustment, BCM-J. CFT-01. 

MARVIKEN CFT-06 

5000.0 ... ...... 

CFM on. mdc- 0.95 bdc. 1 .05 

-Test data 

4000.0 

S3000.0 

.2 2000.0 

1000.0 

0 .0 -..... . . . . . .. .. . . . . . . . . . 

0.0 20.0 40.0 60.0 80.0 100.0 

Time (s) 

Figure 4.52: Mass flow at nozzle exit. Discharge coefficient adjustment, BCM-J. 

CFT-06.

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Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

MARVIKEN CFT-06

0.08 ! I

0.06 -

20.0 40.0 60.0 80.0 

Time (s)

Figure 4.53: Void fraction at nozzle exit. Discharge coefficient adjustment, BCM-J. 

CFT-06.

0 

U 0.04 -

1

0.02 

0.00 

0.0 100.0

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ETSI Minas - Universidad Polit6cnica de Madrid

MARVIKEN CFT-06

2 

E

540.0 

530.0 

520.0

- Liquid Temperature 

- Saturation Temperature

510.0 

500.0 -

490.0 

0.0 20.0 40.0 60.0 80.0 100.0

Time (s) 

Figure 4.54: Liquid and saturation temperatures at nozzle exit. Discharge coefficient 

adjustment, BCM-J. CFT-06.

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Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

MARVIKEN CFT-11

15000 -- CFM on. mdc=0.85 bdc=0.95 

-Test data

10000 -

0

0.0 20.0 40.0 

Time (s)

Figure 4.55: Mass 

CFT-11.

flow at nozzle exit. Discharge coefficient adjustment, BCM-J.

MARVIKEN CFT-11

1.0

0.8 -

.- 0.6 

.>; 0.4

0.2 

0.0 

0.0 20.0 40.0 60.0

Time (s)

Figure 4.56: Void fraction at nozzle exit. Discharge coefficient adjustment, BCM-J. 

CFT-11.

:0 

CO

5000

60.0

ill

4

I ! ! 

1
112 ETSI Minas - Universidad Po1itcnica de Madrid

MARVIKEN CFT-11

E

540.0 

530.0 

520.0 

510.0

-Saturation Temperature 

____ Liquid Temperature

500.0

490.0 

0.0 20.0 40.0 60.0

Time (s) 

Figure 4.57: Liquid and saturation temperatures at nozzle exit. Discharge coefficient

adjustment, BCM-J. CFT-11. 

MARVIKEN CFT-15 

15000

- Test data ___ CFM on. mdc-O.85 bdc*1.00

00 

S 

(U 

0

10000 

5000

0.0 0.0 20.0 40.0 60.0

Time (s) 

Figure 4.58: Mass flow at nozzle exit. Discharge coefficient adjustment, BCM-J. 

CFT-15.

I II

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Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

MARVIKEN CFT-15

1.0

Z

0.8 

g 0.6 

- . 4 :> 0.4-

0.2 

0.0 

0.0 20.0 40.0 60.0

Time (s)

Figure 4.59: 

CFT-15.

Void fraction at nozzle exit. Discharge coefficient adjustment, BCM-J.

MARVIKEN CFT-15

2

560.0 

550.0 

540.0 

530.0 

520.0 

510.0 

500.0 

490.0 

480.0 

0.0

_ Liquid Temperature 

- Saturation Temperature

20.0 40.0

6 

60.0

Time (s)

Figure 4.60: 

adjustment,

Liquid and saturation temperatures at nozzle exit. Discharge coefficient 

BCM-J. CFT-15.

113

t I 

i
114 ETSI Minas - Universidad Po1itcnica de Madrid

U, 

00 

(0 

0

4500.0 

4000.0 

3500.0 

3000.0 

2500.0 

2000.0 

1500.0 -

MARVIKEN CFT-17 

C---0 CFM on. Junction non-smooth. mdn-0.85 bdc-1.00 

0--- CFM on. Junction smooth. mdc=0.85 bdc= 1.00 

-Test data

1000.0 0.0 20.0 40.0 60.0 80.0 100.0 

Time (s) 

Figure 4.61: Mass flow at nozzle exit. Discharge coefficient adjustment, BCM-J. 

CFT-17. 

MARVIKEN CFT-17

540.0

-Saturation Temperature 

- Liquid Temperature

530.0 -

E 

2

520.0

510.0 -

-v

500.0 

0.0 20.0 40.0 60.0 80.0

Time (s) 

Figure 4.62: Liquid and saturation temperatures at nozzle exit. 

adjustment, BCM-J. CFT-17.

100.0 

Discharge coefficient

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Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

MARVIKEN CFT-21

15000.0

I0

10000.0 

5000.0

0.0 L

0.0

-- CFM on. mdc=0.85 bdc=0.95 

-Test data

20.0 40.0 

Time (s)

60.0

Figure 4.63: Mass flow at nozzle exit. Discharge coefficient adjustment, BCM-J. 

CFT-21. 

MARVIKEN CFT-21

0.50

0.40 

S0.30 

0 

> 0.20 

0.10

0.00 

0.0 20.0 40.0

-i

60.0

Time (s)

Figure 4.64: 

CFT-21.

Void fraction at nozzle exit. Discharge coefficient adjustment, BCM-J.

115
ETSI Minas - Universidad Politkcnica de Madrid

MARVIKEN CFT-21 

-- Liquid Temperature 

-Saturation TeTperature,

490.0 

0.0 20.0 40.0 60.0 

Time (s) 

Figure 4.65: Liquid and saturation temperatures at nozzle exit. Discharge coefficient 

adjustment, BCM-J. CFT-21. 

MARVIKEN CFT-24 

15000.0 

--- CFM on. mdc. 0.95 bdcW1.00 

- Test data 

v--- CFM on. mdc-1.00 bdc=1.00 K!*

Co 

4.) 

0

10000.0 

5000.0

11 

\J

0.04 

0.0 20.0 40.0 60.0 

Time (s) 

Figure 4.66: Mass flow at nozzle exit. Discharge coefficient adjustment, BCM-J. 

CFT-24.

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116

540.0

530.0 

"- 520.0 

S510.0 

500.0
Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests 117 

MARVIKEN CFT-24 

1.0 

0.8-

0.6 

"0 > 0.4

0.2

Figure 4.67: 

CFT-24.

0.0 __ _ 

0.0 20.0 40.0 60.0 

Time (s) 

Void fraction at nozzle exit. Discharge coefficient adjustment, BCM-J.

MARVIKEN CFT-24

540.0 

520.0 

E 500.0 

E 

480.0

-Saturation Temperature 

-- Liquid Temperature

LFDU.U .. .. 0.0 20.0 40.0 60.0 

Time (s) 

Figure 4.68: Liquid and saturation temperatures at nozzle exit. Discharge coefficient 

adjustment, BCM-J. CFT-24.

i 

q
ETSI Minas - Universidad Politkcnica de Madrid

MARVIKEN TESTS

1.0 

0-0 cM 

o---octl 1 

*--.cft15 

0.8 -cft2l 

CRt24 

Ct6M0.6 

> 0.4

0.2

0.0 

0.0 20.0 40.0 60.0 80.0 

Time (s)

100.0

Figure 4.69: Void fraction at nozzle exit, BCM-J.

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Chapter 4. Assessment of RELAP5/MOD3 CFM against

MARVIKEN CFT-01

- Test dala 

i,-A Pipe mdc=1.0 

0-C Pipe mdc=0.85

I

20.0 40.0 60.0 80.0 

Time (s)

100.0

Figure 4.70: Mass flow at nozzle exit. Discharge coefficient adjustment, BCM-P. 

CFT-01.

MARVIKEN CFT-01

0.50 

0.40

CO 

.5

- Pipe fdc=0.85 

-- Pipe mdc=1.0

0.30 

0.20 

0.10 -

r. U.UU ' 

0.0

-i

20.0 40.0 60.0 80.0 100.0

Time (s)

Figure 4.71: Void fraction at nozzle exit. Discharge coefficient adjustment, BCM-P. 

CFT-01.

4000.0 

3000.0

00 

CO

2000.0

1000.0

0.0

0.0

Marviken Tests 119
120 ETSI Minas - Universidad Polit6cnica de Madrid

MARVIKEN CFT-11

15000.0

-Test data 

S- Pipe mdc-1.0 

o-o Pipe mdc=0.85

., 

S 

0,.

10000.0 

5000.0

Ant0.0 0.0 20.0 40.0 

Time (s)

60.0

Figure 4.72: Mass flow at nozzle exit. Discharge coefficient adjustment, BCM-P. 

CFT-11.

MARVIKEN CFT-11

1.0

Pipe mdc=1.0

0.8 

g 0.6 

.2= 

"> 0.4 

0.2 

0.0 

0.0

1 

1

20.0 40.0 60.0

Time (s)

Figure 4.73: Void fraction at nozzle exit. Discharge coefficient adjustment, BCM-P. 

CFT-11.

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ETSI Minas - Universidad
Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

MARVIKEN CFT-15

15000.0

-Test data 

A-A Pipe mdc=1.0 

'*e-o Pipe mdc=0.90

-1

40.0 60.0

Time (s)

Figure 4.74: Mass flow at nozzle exit. Discharge coefficient adjustment, BCM-P. 

CFT-15.

MARVIKEN CFT-15

1.0

SPipe ndco.9o ,- Pipe mdc.1.0

20.0 40.0 

Time (s)

Figure 4.75: Void fraction at nozzle exit. Discharge coefficient adjustment, BCM-P. 

CFT-15.

10000.0 

5000.0

ZU 

02

20.0

0.8 

. 0.6 

> 0.4

0.2 

0.0 

0.0

j

60.0

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MARVIKEN CFT-17

5000.0

- Test data 

:A-&Pipe mdc=1.0 

0O- -0 Pipe rc0.90

4000.0 1

,0 

u.,

3000.0 

2000.0

1000.0 -

0.0 

0.0 20.0 40.0 60.0 80.0 100.0

Time (s)

Figure 4.76: Mass flow at nozzle exit. Discharge coefficient adjustment, BCM-P. 

CFT-17.

MARVIKEN CFT-17

0.20 

0.15 

S0.10 

"0 

0.05 

0.00 

0.0

-Pipe mdc-0.90 

-- Pipe mdc-1.0

20.0 40.0 60.0 80.0 

Time (s)

100.0

Figure 4.77: Void fraction at nozzle exit. Discharge coefficient adjustment, BCM-P. 

CFT-17.

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Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

MARVIKEN CFT-21

15000.0

- Test data 

A-k Pipe mdc=1.0 

G-O Pipe mdc=0.90

I2

10000.0 

5000.0

20.0 40.0 60.0

Time (s)

Figure 4.78: Mass flow at nozzle exit. Discharge coefficient adjustment, BCM-P. 

CFT-21.

MARVIKEN CFT-21

0.8

- Pipe mdc=1.90 

__" mfdc=1.0O

0.6 

0 

0.42 

0.4 

0.2

0.0 L= 

0.0 20.0 40.0 60.0

Time (s) 

Figure 4.79: Void fraction at nozzle exit. Discharge coefficient adjustment, BCM-P. 

CFT-21.

123
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SINGLE JUNCTION PIPE 

Test L/D MDC TDC MDC TDC 

24 0.3 0.95 1.00 - 1.05 

06 1.0 0.95 1.05 - 1.05 

21 1.5 0.85 0.95 0.90 1.00 

01 3.0 0.82 0.95 0.85 = 1.05 

11 3.1 0.85 0.95 0.85 1.00 

15 3.6 0.85 1.00 0.90 1.00 

17 3.7 0.85 - 0.90 

KAERI >1.5 0.82 1.14 0.89 1.07

Table 4.2: Discharge coefficient adjustment. 

BCM-P

Comparison between BCM-J and

MARVIKEN TESTS 

Discharge Coefficient Adjusment

0-0 Pipe model. MDC 

&-e Junction model. MDC 

* .-. Pipe model. TDC 

*,-.- Junction model. TDC

-I

2.0 3.0 

L/D

Figure 4.80: Comparison of MDC and TDC adjustment for BCM-J and BCM-P.

I I I

1.10 

' 1.00 

U 

S0.90 

0.80 

0.0 1.0 4.0

124
Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

4.5 Results and Discussion of the Initial Condition 

Model (ICM). Ransom-Trapp Model 

As it was pointed out in Section 4.2, ICM mixes different physical phenomena while 

BCM allows the analysis of critical mass flow in an independent way from other 

physical phenomena. In ICM the error related to steam generation rate has an 

effect on the depressurization rate (system pressure), avoiding critical mass flow 

phenomena to be isolated. 

With this in mind, four cases have been simulated with the ICM, CFT-06, 15, 21 and 

24, and the discharge coefficients have been adjusted for them. Then, comparing 

the results and the adjusted discharge coefficients of ICM and BCM, it is possible to 

analyze if the model of the steam generation rate due to flashing is the appropriate. 

At the end of this section a comparison between the simulations of CFT-24 with 

TRAC-BF1, RELAP5/MOD3.2 and the experimental data is presented. 

4.5.1 Discharge Coefficient Adjustment 

For the adjustment of the discharge coefficients (subcooled and two-phase), mod

elling the nozzle as a PIPE and a SINGLE JUNCTION, data from CFT-06, 15, 21 

and 24 have been used. 

" Nozzle modeled as SINGLE JUNCTION. The comparison between the test 

data and the results for the mass flow with the adjustment of the discharge 

coefficients are shown in Figures 4.81, 4.82, 4.83 and 4.84, In general, a good 

adjustment is achieved with the coefficients shown in table 4.3, except in the 

subcooled period of CFT-21. 

" Nozzle modeled as PIPE. The comparison between test data and the results 

for the mass flow with the adjustment of the discharge coefficients are shown 

in Figures 4.85, 4.86, 4.87, 4.88 and 4.89. The adjustment of the coefficients 

is shown in table 4.3. The fitting for the subcooled period for all cases is very 

poor, but on the other hand for the two-phase period the adjustment is good. 

"* The comparison of the adjusted discharge coefficients for both models is shown 

in table 4.3. The values are similar but taking in account that with the nozzle 

modeled as a PIPE the adjustment in the subcooled period is very poor, it 

seems to be better to model the nozzle as a SINGLE JUNCTION.

125
SINGLE JUNCTION PIPE 

Test L/D MDC TDC MDC TDC 

24 0.3 1.00 1.30 1.00* 1.15 

06 1.0 1.00 1.15 1.00* 1.15 

21 1.5 1.00* 1.00 1.00* 0.90 

15 3.6 0.90 1.10 0.92 1.10 

Table 4.3: Discharge coefficient adjustment. Comparison between ICM-J and ICM

P 

e The comparison between the ICM and BCM results and their discharge 

coefficients, table 4.4, show that the values used to adjust the mass flow 

for ICM are always greater than for BCM. This problem may be caused 

by experimental errors or some constitutive relations or correlations not 

compatibles with the critical flow model, [ELI-94]. For example, one of 

the critical flow models and the Fflashing model of CATHARE code, were 

simultaneously obtained from Moby Dyck experiments, [FOR-88].

126 ETSI Minas - Universidad Politkcnica, de Madrid
Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests 127

MARVIKEN CFT-06

- Test Data i 

*-- Nozzle as JUNCTION. MDC=-1.0 TDC=1 .i 5 

1

20.0 40.0 60.0 80.0 100.0

Time (s) 

Figure 4.81: MDC and TDC adjustment. Nozzle modeled as SINGLE JUNCTION 

(ICM). CFT-06.

MARVIKEN CFT-15

15.0

- Test data 

I -- Nozzle as JUNCTION MDC=0.92 + BDC=1ý1

10.0 20.0 30.0 

Time (s)

40.0 50.0 60.0

Figure 4.82: MDC and TDC adjustment. Nozzle modeled as SINGLE JUNCTION 

(ICM). CFT-15.

5000.0

4000.0 

3000.0 

2000.0 

1000.0

0.0 

0

p

).0

10.0 

0 

m 5.0

0.0 I 

0.0
ETSI Minas - Universidad Politkcnica de Madrid

MARVIKEN CFT-21

0 L

0.0

Nozzle as JUNCTION, MDC-1.0, TDC=1 .0 

Nozzle as JUNCTION, MDC=1.1, TDC=1.0

10.0 20.0 30.0 40.0 50.0 60.0 

Time (s)

Figure 4.83: MDC and TDC adjustment. Nozzle modeled as SINGLE JUNCTION 

(ICM). CFT-21.

MARVIKEN CFT-24

RELAP5MQD3.2

_ Test data 

1.- HEM + MDC-1.0 + BDC.1.0; 

s-- HEM + MDC=1.0 + BDC=1.3j

10.0 20.0 30.0 

Time (s)

40.0 50.0 60.0

Figure 4.84: TDC'adjustment. Nozzle modeled as SINGLE JUNCTION (ICM 

CFT-24.

I I i

15000

cc 

0

10000 

5000

15.0 

:1 10.0 

. 5.0

0.0 i--- 

0.0

128

J
Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

MARVIKEN CFT-06

I - Test Data i 

I1-0 Nozzle as PIPE. MDC=1.0. TDC=1.15

5000.0 

4000.0 

3000.0 

2000.0 

1000.0

40.0 60.0 

Time (s)

80.0 )0.0

Figure 4.85: MDC and TDC adjustment. Mass flow at nozzle 

as PIPE (ICM). CFT-06.

15.0

10.0 

E 5.0

exit. Nozzle modeled

MARVIKEN CFT-15 

RELAP5/MOD3.2

-- Test data 

.-. HEM + MDC=1.0 i 

!---3 HEM + MDC=0.92!

0.0. - -:--- _ ____ 

0.0 10.0 20.0 30.0 40.0 50.0 60.0 

Time (s)

Figure 4.86: MDC adjustment. Mass flow at nozzle exit. Nozzle modeled as PIPE 

(ICM). CFT-15.

i1

Z 

to

AAN

0.0 20.0

129

129 v

1U
ETSI Minas - Universidad Politkcnica de Madrid

MARVIKEN CFT-15 

RELAP5/MOD3.2

____ Test data 

HEM + MDC-0.92 

- HEM + MDC-0.92 + BDC-1 .1

10.0 20.0 30.0 

Time (s)

40.0 50.0 60.0

Figure 4.87: TDC adjustment. Mass flow at nozzle exit. Nozzle modeled as PIPE 

(ICM). CFT-15.

MARVIKEN CFT-21

15000

10000 

5000

- Test Data 

0-H Nozzle as PIPE, MDC-1.0, TDC-i.b 

o---o Nozzle as PIPE, MDC-i.3, TDC-i.D 

-Nozzle as PIPE. MDC-1.0. TDC-0.9

10.0 20.0 30.0 

Time (s)

40.0 50.0 60.0

Figure 4.88: MDC and TDC adjustment. Mass flow at nozzle exit. Nozzle modeled 

as PIPE (ICM). CFT-21.

I I I

15.0

0o.o 

0 

a; 5.0

1

0.0 0.0

cc

130

I
Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

15.0 

,- 10.0 

0 

' 5.0 

0.0

MARVIKEN CFT-24 

RELAP5/MOD3.2

- Test data 

i 2 cell nozzle + MDC=1.0 + BDC=1.0 

2 cell nozzle + MDC=1.2 + BDC=1.0 

I-i 4 a,2 cell nozzle + MDC=1.0 + BDC=1.15

10.0 20.0 30.0 40.0 50.0 60.0 

Time (s)

Figure 4.89: MDC and TDC adjustment. Mass flow at nozzle exit. Nozzle modeled 

as PIPE (ICM). CFT-24.

ICM BCM 

JUNCTION PIPE JUNCTION PIPE 

Test L/D MDC TDC MDC TDC MDC TDC MDC TDC 

24 0.3 1.00 1.30 1.00* 1.15 0.95 1.00 1.3* - 1.05 

06 1.0 1.00 1.15 1.00* 1.15 0.95 1.05 1.0* - 1.05 

21 1.5 1.00* 1.00 1.00* 0.90 0.85 0.95 0.90 1.00 

01 3.0 - - - - 0.82 0.95 0.85 t- 1.05 

11 3.1 - - - - 0.85 0.95 0.85 1.00 

15 3.6 0.90 1.10 0.92 1.10 0.85 1.00 0.90 1.00 

17 3.7 - - - 0.85 - 0.90 

KAERI >1.5 - 0.82 1.14 0.89 1.07 

Table 4.4: Discharge coefficient adjustment. Comparison between ICM and BCM 

results (The values marked with * do not adjust with test data)

131
132 ETSI Minas - Universidad Po1itcnica de Madrid

15.0

"z" 10.0 

0•.5.0 

0.0 

0.0

MARVIKEN CFT-24 

CRITICAL FLOW RATE

-Test data - RELAP5IMOD3.2 without nozzle 

A-- TRAC-BF1/MOD1 with two cell nozzle

20.0 40.0 

Time (s)

60.0

Figure 4.90: Mass flow at nozzle exit. Comparison between TRAC-BF1 and 

RELAP5/MOD3.2 results. Nozzle modeled as PIPE. CFT-24.

4.5.2 Comparison between 

RELAP5/MOD3.2 Results

TRAC-BF1

The comparison between the simulations of CFT-24 with TRAC-BF1, RE

LAP5/MOD3.2 and the experimental data, Figure 4.90, shows that both codes 

give similar results as it was expected, because both have quite similar critical flow 

models implemented, with just small differences. 

4.6 Results and Discussion of Boundary Condition 

Model (BCM). Henry-Fauske Model 

The Henry-Fauske CFM has different model options than the Ransom-Trapp model: 

"* Henry-Fauske CFM does not depend on smooth/abrupt area change option, 

"* the homogeneous condition, v9 = v1, is imposed in the model, 

"* there is only one discharge coefficient for all conditions (subcooled, two-phase 

and steam), and

I II

and

132 ETSI Minas - Universidad Politkcnica de Madrid
Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

* there is a new parameter in Henry-Fauske model, the disequilibrium parameter 

dp. 

Apart from this, the assessment of RELAP5/MOD3.2.2beta with the Henry-Fauske 

model has been performed with several experiments, but only one Marviken CFT 

has been included (CFT-22, LID = 1.5) among the selected experiments. Marviken 

CFT-22 does not cover all the different LID relations for the nozzles. With this 

mind, three experiments (CFT-15, CFT-21 and CFT-24) have beeen selected for 

this assessment, which cover different thermo-hydraulic conditions at nozzle, sub

cooled and two-phase, and also different LID relations for the nozzles (0.3, 1.5 and 

3.3). The boundary conditions used in this analysis are shown in Figures 4.9 to 

4.28. 

The simulations have been performed with the nozzle modeled as a pipe and 

as junction (BCM-J, BCM-P), because as we have shown in the assessment of 

Ransom-Trapp model, sometimes modelling the nozzle as a junction is better than 

as a pipe. 

The results show that the discharge flow rate, Figures 4.91 to 4.93, is better adjusted 

with: 

"* Subcooled conditions: 

- LID = 0.3. Nozzle as a junction and dp = 0.14 

- LID = 1.5. Nozzle as a pipe and dp = 0.14. The results with dp = 0.01 

are not so good than dp = 0.14 but they are acceptable. 

- LID = 3.6. Nozzle as a pipe and dp = 0.01 

"* Two-phase conditions: 

- LID = 0.3. Nozzle as a junction and dp = 0.01 

- LID = 1.5. Nozzle as a pipe and dp = 0.01. Similar results are obtained 

with dp = 0.14. 

- LID = 3.6. Nozzle as a pipe and dp = 0.01 

These results show that the advised dp value, dp = 0.14, in IMOR-98] is not adecu

ate for adjusting the simulated values to test data.

133
The inception of boiling is in accordance with the experimental data when the above 

dp values are used, see Figures 4.94 to 4.96. It must be remembered that when the 

simulation is performed with the Ransom-Trapp model and the nozzle is modeled 

as a pipe, the inception of boiling appears too early. So, the Henry-Fauske model 

gives better results, with respect to the inception of boiling, than the Ransom-Trapp 

model. 

Several conclusions can be obtained from the above results: 

"* The best values of dp for adjusting the model are (in accordance with the 

results obtained in [LEV-821), 

- dp = 0.14 for subcooled blowdown and L/D < 1.5 

- dp = 0.01 for L/D > 1.5 

- dp = 0.01 for saturated blowdown 

"* The best models for the different nozzles are: 

- Short nozzles LID < 0.3 should be modeled as a junction. 

- Long nozzles L/D > 1.5 should be modeled as a pipe. 

- This assessment does not give enough information about the which is the 

best model for intermediate nozzles 1.5 > LID > 0.3. 

"* The inception of boiling is in accordance with the experimental data when 

Henry-Fauske model is used. 

At present, only one dp value can be used for subcooled and two-phase periods. So, 

two disequilibrium parameters should be implemented in order to include the values 

mentioned above (one of them for the subcooled period and another for the two

phase one), and also the transition between them. This solution generates a problem 

because it implies a new degree of freedom, and therefore a negative consequence 

for the user effect.

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134 ETSI Minas - Universidad Politkcnica de Madrid
Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

1.5e+04

1.0e+04 

5.0e+03

MARVIKEN CFT-15 (LID=3.6) 

Henry-Fauske model

G-0 nozzle as junction. dp=0.14 

- nozzle as pipe. dp=0.14 

- test data 

-Enozzle as pipe. dp=0.01 

H- nozzle as junction. dp=0.01

j

20.0 40.0 60.0

Time (s)

Figure 4.91: Mass flow at nozzle exit. Comparison between BCM-J and BCM-P 

with dp = 0.14 and 0.01. CFT-15. 

MARVIKEN CFT-21 (LMD= 1.5) 

Henry-Fauske model

1.5e+04

1.0e+04 

5.0e+03

o-o nozzle as junction. dp=f0.14 

*-0 nozzle as pipe. dp=0.14 

- test data 

-- nozzle as pipe. dp=0.01 

i-. nozzle as junction. dp=0.01

20.0 40.0 60.0

Time (s)

Figure 4.92: Mass flow at nozzle exit. Comparison between BCM-J and BCM-P 

with dp = 0.14 and 0.01. CFT-21.

CE 

0 

ncc 

LL

135
136 ETSI Minas - Universidad Polit6cnica de Madrid

MARVIKEN CFT-24 (L/D=0.3) 

Henry-Fauske model

1.5e+04

1.0e+04 

0 

5.09+03

- junction dp=O.14 

- nozzle as pipe dp=O.14 

- Test data 

- nozzle as pipe dp=0.01 

n- nozzle as junction. dp=0.01

20.0 40.0 60.0

Time (s)

Figure 4.93: Mass flow at nozzle exit. Comparison between BCM-J and BCM-P 

with dp = 0.14 and 0.01. CFT-24. 

MARVIKEN CFT-15 (L/D=3.6) 

Henry-Fauske model

1.0

C 

0

nozzle as junction. dp=0.14 

- - - nozzle as pipe. dp=0. 14 

0.8 nozzle as junction. dp=0.01 

nozzle as pipe. dp=0.01 

0.6 

0.4 --. N 

0.2 

/I

0.0 0.0 20.0 40.0

Time (s)

Figure 4.94: Void-fraction at nozzle exit. Comparison between BCM-J and BCM-P 

with dp = 0.14 and 0.01. CFT-15.

I I

136 ETSI Minas - Universidad Politkcnica de Madrid

J

I
Chapter 4. Assessment of RELAP5/MOD3 CFM against Marviken Tests

MARVIKEN CFT-21 (L/D=1.5) 

Henry-Fauske model

nozzle as junction. dp=0.14 

nozzle as pipe. dp=0.14 

nozzle as junction. dp=-.01 

nozzle as pipe. dp=0.01

4

0.60 

o 

L 0.40

0 

0.20 

0.00 

0.0 60.0

Figure 4.95: Void-fraction at nozzle exit. Comparison between BCM-J and BCM-P 

with dp = 0.14 and 0.01. CFT-21. 

MARVIKEN CFT-24 (L/D=0.3) 

Henry-Fauske model

1.0 

0.8 

50.6 

0.2 

0.0 

0.0 20.0 40.0 

Time (s)

60.0

Figure 4.96: Void-fraction at nozzle exit. Comparison between BCM-J and BCM-P 

with dp = 0.14 and 0.01. CFT-24.

0.80

20.0 40.0 

Time (s)

137
Chapter 5 

Conclusions 

The conclusions of this report are as follows: 

1. The transition logic from CFM to Non-CFM for the default model 

(Ransom-Trapp) is not always adequate for changing from one model to the 

other correctly, as it is showed in Section 2.1. 

2. The main conclusions of the sensitivity analysis of the Ransom-Trapp model 

are: 

" Subcooled. The behaviour is anomalous due to the transition logic from 

critical flow to non-critical flow. This problem only is important for large 

subcoolings. 

" Two-phase. The results show one or two maxima for the mass flow with 

pressures greater than 90 bar. This is not an expected behaviour and is 

not found in the literature. Oscillatory behaviour appears below 60 bar. 

" Energy loss coefficient. It must be used with care in junctions where 

critical mass flow is expected, because CFM does not depend on it, but 

non-CFM decreases with it. 

"* Discharge Coefficients. From the results it can be concluded that the 

variation of the mass flow with the discharge coefficient has the same 

value than the discharge coefficient. 

"* There are several other known problems with this model, that makes it 

necessary improving the model or the avoidance of its use. 

3. The main conclusions of the sensitivity analysis of the Henry-Fauske model 

are:

139
"* Subcooled. No problems were found with the transition logic from critical 

to non-critical flow. 

"* Two-phase. There are neither maxima for the mass flow nor oscillatory 

behaviour unlike in the Ransom-Trapp model. 

"* Energy loss coefficient. It must be used with care in junctions where 

critical mass flow is expected, because CFM does not depend on it, but 

non-CFM decreases with it. 

"* Disequilibrium parameter. Mass flow is strongly dependant on this 

parameter. In order to avoid the user effect, the value should be internally 

fixed or at least detailed user guidelines should be supplied. 

"* In general the model shows a good behaviour, but user guidelines should 

be supplied for the discharge coefficient and the disequilibrium parameter. 

4. The following conclusions are obtained from the comparison of Ransom-Trapp 

model and Marviken tests: 

" In general, the mass flow simulated with CFM-off is always greater than 

with CFM on, except at the beginning of CFT-01, CFT-06 and CFT-17 

(see Section 2.1, problems with the transition from CFM to Non-CFM). 

Also, CFM-off results do not adjust to experimental data and therefore 

the critical flow model is necessary. 

" When the nozzle is modeled as a single junction, better results are 

obtained with the abrupt area change option than with the smooth 

option. However, the differences between them are small for the Marviken 

experiments. 

" The subcooled period is apparently better reproduced with the nozzle 

modeled as a pipe than as a single junction (except in CFT-24), but it 

must be taken into account that the void fraction at the nozzle outlet 

is not null from the beginning of the transient with the nozzle modeled 

as a pipe, which is not in accordance with experimental data. So, the 

subcooled period is modeled with a two-phase critical flow model with 

non-null void fraction, which is wrong. This problem is not present 

when the nozzle is modeled as a SINGLE JUNCTION because that is 

equivalent to freezing the model. 

"* The results obtained with both models during the two-phase period are 

quite similar to experimental data. CFT-06 and CFT-24 are better 

reproduced with the nozzle modeled as a junction.

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140 ETSI Minas - Universidad Polit~cnica de Madrid
Chaper 5 Coclusons141

" It should be better to choose the SINGLE JUNCTION model for the 

nozzle, since the subcooled period is better reproduced with the nozzle 

modeled as a SINGLE JUNCTION and for the two phase period both 

models seem to give similar results. 

" The homogeneous option gives better results than the non-homogeneous 

one. 

"* SINGLE JUNCTION, trip-valve and motor valve models give similar 

results. 

"* The following conclusions are obtained from the discharge coefficient 

adjustment for BCM: 

- Nozzle modeled as SINGLE JUNCTION. A very good adjustment is 

achieved with the coefficients shown in Table 4.2. 

- Nozzle modeled as PIPE. The adjustment in the subcooled period 

is not so good as in the previous case. The reason is that when 

the subcooled discharge coefficients are fitted, the beginning of the 

boiling process is delayed. However, it can be observed that boiling 

is still starting too early with respect to the test data. Probably a 

delayed boiling model is needed in order to model the nozzle as a 

pipe. 

On the other hand, a good adjustment for the mass flow is achieved 

for the two-phase period, but the void fraction values are higher than 

with the nozzle modeled as a SINGLE JUNCTION. 

- The comparison of the discharge coefficient adjustment for both mod

els, Table 4.2, shows that the discharge coefficients used with the 

nozzle modeled as a PIPE are higher than for SINGLE JUNCTION. 

"* The following conclusions are obtained from the discharge coefficient 

adjustment for the Initial Condition Model (ICM): 

- Nozzle modeled as SINGLE JUNCTION. In general, a good adjust

ment is achieved with the coefficients shown in Table 4.3, except in 

the subcooled period of CFT-21. 

- Nozzle modeled as PIPE. The fitting for the subcooled period for all 

cases is very poor, but on the other hand the adjustment is good for 

the two-phase period. 

- The comparison of the adjusted discharge coefficients for both models 

is shown in Table 4.3. The values are similar but, taking into account

Chapter 5. Conclusions 141
that with the nozzle modeled as a PIPE the adjustment in the 

subcooled period is very poor, it seems to be better to model the 

nozzle as a SINGLE JUNCTION. 

The comparison between ICM and BCM results and their discharge 

coefficients, Table 4.4, shows that the values used to adjust the mass 

flow for ICM are always greater than for BCM. This problem may 

be caused by experimental errors or some constitutive relations or 

correlations not compatibles with the critical flow model, [ELI-94J 

(e.g. the rflashing model and the interfacial friction model). 

5. The following conclusions are obtained from the comparison of Henry-Fauske 

model and Marviken tests: 

"* The best values of dp for adjusting the model are (in accordance with the 

results obtained in [LEV-82]), 

- dp = 0.14 for subcooled blowdown and LID < 1.5 

- dp = 0.01 for L/D > 1.5 

- dp = 0.01 for saturated blowdown 

"* These results show that the advised dp value, dp = 0.14, in [MOR-981 is 

not adecuate for adjusting the simulated values to test data. 

"* The best models for the different nozzles are: 

- Short nozzles L/D < 0.3 should be modeled as a junction. 

- Long nozzles L/D > 1.5 should be modeled as a pipe. 

- This assessment does not give enough information about the which 

is the best model for intermediate nozzles 1.5 > LID > 0.3. 

"* The inception of boiling is in accordance with the experimental data when 

the Henry-Fauske model is used. 

"* At present, only one dp value can be used for subcooled and two-phase 

periods. So, two disequilibrium parameters should be implemented 

in order to include the values mentioned above (one of them for the 

subcooled period and another for the two-phase one), and also the 

transition between them. This solution generates a problem because it 

implies a new degree of freedom, and therefore a negative consequence 

for the user effect. 

6. Final Conclusions:

I I I

142 ETSI Minas - Universidad Politkcnica de Madrid
"* The behaviour of the Henry-Fauske model is better than that of the 

Ransom-Trapp. In this sense, the new model is an improvement with 

respect to the Ransom-Trapp. On the other hand, the Henry-Fauske 

model is not a definitive solution for critical flow phenomena simulation, 

because it has several parameters (discharge coefficient and disequilib

rium parameter) that are geometry dependent (i.e. L/D). 

" It is necessary to have a critical flow model compatible with the consti

tutive relations and correlations of the code. 

" In general, it is possible that any of the one-dimensional models could 

not simulate the critical flow phenomena in all conditions, due to the 

existence of two-dimensional effects. Anyway, the critical flow problem 

is not still solved, and new theoretical studies and experiments should 

be performed, with special emphasis in geometries and sizes similar to 

nuclear power plants.

Chapter 5. Conclusions 143
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R.G. Steinke. A description of the test problems in the TRAC-P 

standard test matrix. Technical Report LA-UR-96-1475, LANL, 

1996. 

R.G. Steinke. Task completion report for update FXCFM. Tech

nical Report LA-UR-98-1397, LANL, 1998. 

J.C. Vigil and K.A. Williams (Editors). TRAC-PlA developmen

tal assessment. Technical Report NUREG/CR-1059. LA-8056-MS, 

LASL (LANL), 1979. 

R.J. Wagner V.H. Ransom and G.W. Johnsen. RELAP5/MOD2 

code manual. volume III: Developmental assessment problems. 

Technical Report EGG-TFM-7952, INEL, 1987. 

Walter L. Weaver. Improvements to the RELAP5/MOD3 choking 

model. International Agreement Report EGG-EAST-8822, EG&G 

Idaho, Inc., 1989.

BIBLIOGRAPHY 147
Part I

Appendix: Subroutine JCHOKE

flow logic

149
151 

Subroutine JCHOKE

Figure 1: Subroutine JCHOKE flow logic.
152

OIPL - C . sobok w: d •rit 

velocity 13,• rmd 

.1_ 

Figure 2: Subromutie diwHOKEj l fofi owlge(otne)

I I I
1990

17 

18 

19

22

26

28 

29 

30

Figure 3: Subroutine JCHOKE flow logic (continued).

153
154 

YES CHOKL I. MV 31 

NO 

jwI , .. ;,,•J 32 

1 

215 CtRM w -;ý 

SY.. Vs SC alef• m 34 

1990 (*4JPc vekPcity at 35 

YFuS 4EI ogic -(c..oWnt 'iued 

-2. I'm A~/f 

YeS IC<SNC.A 1 37I 

Ntbl 

215 Uocm , testror c•nF 38 

usul .Tr and QtAIL 39 

YES Stmtbefiue 40 

Figure 4: Subroutine JCHOKE flow logic (continued).

I I I
155 

Comnpute wall friction muluiplied by juncti~on 41 upwind volume arra raiio -C rAFRWAUI.) 4 

Fisrtimt throat selo,.ity squaredusn 

Bemauvilli equatkin with fricion tZipcoN) 42 

AT = AJU?4(l- ATHRcUr() junction gulw"ical ame 43 

YES SONIC > 0and 44 

SONIC. SON 1 45

Figure 5: Subroutine JOHOKE flow logic (continued).
156 

-. SOR (MPrc DI'>M +w on Ibroj 56 

(SONIC2 a mi(SNL-P .PQL)j 6 

SONIC .(SON1CI + SONIC2~ 63 

Figue Surouine 6 GHO fowCompic (rontinued).

I I I
157

2-26 - FI S ,oc'1.2"oRco--soKCI-" R MATC H4 - 2"FICONS -SONs*C , | '70 

- .9g" Jc XA " - "1) "71 

AT AT/tJCATS• '72 

-j L NO !, F"/REVCýS 4 

Figure 7: Subroutine JCHOKE flow logic (continued).
76 

77

1990 

MA)VO1G < 0. ) 10)- 7 

Figre : SbrotinJCompue o Mlogc(otne)

I I I

158
159

00

1"~)

85

88

89

Figure 9: Subroutine JCHOKE flow logic (continued).

159
160

21236 CRSPUall tbeswt BR=1 90a 

1990 820 'ý RF =JNadUA ,9 

T< > Var with 93 

NO 99DPDT = Cpd(T-'"sA) 94 

cam table failure 1 10 junction vapor diens.cy 96 

deriniuon ~1h 10 and NIL AvSrn tH 98 

NO 

Fiur 0:Sbruineins Jith K 10 flow gi (Icntinued).kE9

I I I
Figure 11: Subroutine JCHOKE flow logic (continued).

161

I P*

129
"132 

] 133 

134 

135 

136 

137 

138

Figure 12: Subroutine JCHOKE flow logic (continued).

I I I

162
Part II

Appendix: Modified JCHOKE

Subroutine

163
165

*deck jchoke 

subroutine jchoke 

*in32 iprop 

*in32 iprop 

*in32end 

c 

c $Id: jchoke.Fv 1.6.2.1 1995/09/15 16:23:35 rjv Exp $ 

c 

c Computation of choking theory. 

c These local variables had their names changed (4/12/95 gam) 

c all => cll 

c a12 => c12 

c a21 => c21 

c a22 => c22 

c avrf => avrff 

c avrg => avrgg 

c convf => convff 

c convg => convgg 

c diff => difff 

c diug => difgg 

c difold => difld 

c dx => ddx 

c f2 => 1f2 

c fricfj => frcfj 

c fricgj => frcgj 

c psld => psldd 

c psm- => psmlf 

c psg I> psmgg 

c sumf => sumfl 

c suing => sumgg 

c sumold -> sumld 

c vpgen => vpgenn 

c vpgnx *> vpgnxx 

c figj => figjj 

c fifj => fifjj 

C tt => ttt 

c beta => betaa 

c betaf => betff 

"c betag => betgg 

"c betags => betgs 

"c cp => cpp 

"c cpf => cppf 

"c cpg => cppg 

c ubar -> ubarr 

c qual => quall 

c hbar -> hbarr 

c kapa => kpa 

c kapaf => kpal 

c kapag -> kpag 

c kapags => kpags 

c pres => press 

c vbar => vbarr 

c vs => VsS 

c vsubf -> vsublf 

c vsubg => vsubgg 

c us => usS 

c usubf => usubhf
166

c usubg => usubgg 

c delpz => delpzz 

c 

c Cognizant engineer: w1v. 

C

$if defimpnonl 

implicit none 

*call comctl 

*call contrl 

*call fast 

*call jundat 

*call lpdat 

*call machas 

*call machns 

*call machos 

*call machss 

*call scrtch 

*call statec 

*call stcblk 

*call stcom 

*call trablp 

*call ufiles 

*call voldat 

c 

c Local variables.

real aOlaO2,clicl2,c2lc22,aheajarfgargfarsmatatin, 

" avkavoDtkavrffavrggavrhob*taabatfbetgbetgsconvff, 

" convficonvggconvgiepp.cppf.cppgcvaocvaqdcvadelptidelpzz, 

deltapdetdfidpsdfldtgdfldttdf2dpsdf2dtgdifffdifggdifld, 

dpdtdpfiocdprcondpsdsondpdtgdttdufdptdufdttdusdttddx,

ff2,ficonsfjfgfrcfjfrcgjfrvallhbarrhsubfhsubgkpakpaf, 

kpagkpagspapjunpllpressprop(36),psattpsldd.psnffpsagg, 

qaqairl.q-aqflqsquallraratiosrdetrhofgrhofinrhoinv, 

S(26),scrachsigniksignvcsonicsoniclsonic2,sonicssumff, 

sumgg, 

sumldtermtermztolerttttgt-vlvbarrvcvfvffVgvirmas, 

vpgennvpgnxxvssvsubffvsubgguaualuaoubarruffujunuss, 

usubff, 

usubgg, xe, zip, zipcon, cO, cl , figj j , f ifj j , dummy.xintrp, relax, j catsc, 

icattp.vgtpon.vgtpoxvgshmnvgscmxvoidjcavkxjdxkxjxisctp, 

xitpshjcatstchockjchockvvfsavevgsavejcsavequalty 

integer iidgikimpltininkiqis.isfiskipitix, 

kkkklkxkx2,kyky2,1,11,lxlx2,mnrodo 

logical errchokeredo

c State properties 

equivalence 

( prop( 3), vbarr 

( prop( 6), betaa 

( prop( 9), quall 

( prop(12). vsubgg), 

( prop(IS), hsubf 

( prop(18). betg 

( prop(21). cppf 

$if defnewvtrp,3 

integer iprop(36)

prop( 1), 

prop( 4), 

prop( 7), 

prop(10), 

prop(13), 

prop(16). 

prop(19), 

prop(22),

ttt 

ubarr 

kpa 

psatt 

usubff), 

hsubg 

kpaf 

cppg

( prop( 2). 

( prop( 5), 

( prop( 8), 

( prop(11), 

( prop(14), 

( prop(17), 

( prop(20),

press 

hbarr 

cpP 

vsubff), 

usubgg), 

betf 

kpag

I I I
167 

logical lprop(36) 

equivalence (prop(l),iprop(1),iprop(1)) 

C 

equivalence (rhofin,rhoinv),(ficons,fjfg),(ahe.aj) 

equivalence (frvall,vf),(pjunvg) 

equivalence (deltap.sonic2,virmas),(zip,vpgenn) 

equivalence (xe,rhofg),(sonici,dsondp) 

equivalence (avolkkdet,rdet,s(1l)),(vff,vf,s(12)), 

"* (delpfi,sumtf,uff,s(13)),(dpfiocsumgg,usss(14)), 

"* (dprconsumldvss.s(15)),(betgs,vpgnxx,zipcon,s(16)), 

"* (difff,cll,dfldps,s(17)),(difgg,c12,dfidtg,s(18)), (term,scrach), 

"* (difld,c21,df2dps,s(19)),(c22,df2dtg,s(20)),(aOl,fl,s(21)), 

"* (a02,ff2,s(22)),(dtg.s(25)),(dps,dtt,s(26)),(qss(7)),(qf,s(8)) 

c 

logical jstop,transr 

c 

c Data statements. 

data iq/O/, toler/O.0025/ 

*call machaf 

*call machnf 

*call machof 

*call machsf 

c 

c Set flag for standard semi-implicit or 2-step implicit. 

implt = 0 

if (iand(print,128) .ne. 0) implt = 1 

iskip = 0 

ix = ixjff 

is = ixsopr(issys) 

c Junction loop. 

i = lij(issys) 

do 2000 m = 1,lijn(issys) 

cl cqs choking calculation desired 

if (chngno(52)) then 

jc(i) = iand(jc(i),not(i)) 

go to 1990 

endif 

c2 cqs is junction connected to an accumulator? 

if (iand(jc(i),80) .ne. 0) go to 1990 

redo = .false. 

100 transr = .false. 

relax = 0.0 

c3 cqs junction choked last dt and vapor velocity in same direction 

choke = iand(jc(i),l).ne.0 and. velgj(i)*velgjo(i).gt.0.0 

jc(i) = iand(jc(i),not(1)) 

c4 cqs junction is timedependent junction or has countercurrent flow 

if (iand(jc(i),2).ne.0 .or. velfj(i)*velgj(i).le.0.0) 

& go to 1990
168 

cS cqs get the "from" and "to" volume indices 

k = ijlnx(i) 

kx = iand(ishftCjcex(i),-12),7) 

kx2 = k + kx 

kx = k + ishft(kx,-1) 

1 = ij2nx(i) 

lx = iand(ishft(jcex(i).-9),7) 

1x2 = 1 + lx 

lx = 1 + ishft(lx,-1) 

c Define flow direction. 

c6 cqs liquid velocity >0 < 0 

if (velfj(i) .ge. 0.0) then 

c7 cqs 

kk = k 

ky = kx 

ky2 = kx2 

A 1 

ik = 1 

iq = 8192 

kl= 0 

avk = avkx(ix) 

ddx = dxkx(ix)*avk*0.5 

else 

cS cqs 

kk= 1 

ky = lx 

ky2 = 1x2 

11 =k 

ik= 2 

iq = 4096 

kl= 2 

avk = avlx(ix) 

ddx = dxlx(ix)*avk*0.5 

endif 

signik = 1.0 

c9 cqs set signik for reverse connections 

if (iand(jc(i),ik*4) .ne. 0) signik = -signik 

c1O cqs reflood flag set? 

if (iand(imap(ky),ishft(1,29)) .ne. 0) go to 1990 

c 

"c If current donor volume contains a different fluid from the last one, 

"c call stcset. 

if (volmat(kk).ne.nfluid) call stcset (volmat(kk)) 

C 

c Set-up junction velocities for choke test. 

cli cqs compute arfgpargf

I I I
169 

arfg = voidfj(i)*rhogj(i) 

argf = voidgj(i)*rhofj(i) 

arsm = arfg + argf 

c12 cqs average rho<E-i0 

if (arsm .It. 1.0e-i0) go to 1990 

c13 cqs compute choking criteria vc 

vc = (arfg*velfj(i) + argf*velgj(i))/arsm 

signvc = sign(1.0,vc) 

vc = abs(vc) 

c14 cqs compute discharge cofficient from user input values 

c cqs *start of discharge coefficient calculation***s**ee**a 

c Discharge coefficient.***e**ee*e**eeeeee********e 

c Define upper and lower bounds of transition region in void. 

vgscmx = 1.0e-05 

vgtpun = 0.10 

xisctp = (voidgj(i) - vgscmx)/(vgtpmn - vgscmx) 

xisctp = max(O.O,min( 1.0,xisctp)) 

xisctp = xisctp*xisctp*(3.0 - 2.0*xisctp) 

at = jdissc(i) + xisctpe(jdistp(i) - jdissc(i)) 

vgtpmx = 0.90 

vgsbmn = 0.99 

xitpsh = (voidgj(i) - vgtpmx)/(vgshmn - vgtpmx) 

xitpsh = max(O.O,min(t.O,xitpsh)) 

xitpsh = zitpsh*xitpsh*(3.0 - 2.0*xitpsh) 

at = at + xitpsh*(jdissh(i) - jdistp(i)) 

c cqs *end of discharge coefficient calculatione****ee**e a 

c15 cqs 

at = at*athrot(i) 

c General values needed in the calculation. 

c16 cqs 

avolkk = ajun(i)/avk 

c17 cqs compute avrf, avrg ... 

avrff = voidfj(i)*rhofj(i) 

avrgg = voidgj(i)*rhogj(i) 

avrho = avrff+avrgg 

c18 cqs 

term = 1.0 

if (iand(jc(i),iq) .ne. 0) term = 0.0 

termz = term 

c19 cqs compute wall friction from cell upstream center to junction edge

c Wall frictions. 

frcfj = ddx*term*fvalf(ky)/(max(1.Oe-5,voidfj(i))*rhofj(i))
170 

frcgj = ddx*term*fwalg(ky)/(maxl(.Oe-5,voidgj(i))*rhogj(i)) 

c20 cqs compute convective terms. compute gravity terms 

c Convective terms. 

if (redo) then 

atin = signvc*jcatn(i)/at**2 

convfi = atin*velfj(i)**2 

convgi = atinevelgj(i)**2 

else 

atin = signvc*jcato(i)/at**2 

convfi = atin*velfjo(i)**2 

convgi = atin*velgjo(i)**2 

endif 

convff - 0.5*(convti - term*signvc*velf(ky)**2) 

convgg = 0.5*(convgi - term*signvc*velg(ky)**2) 

psmff = frcfj*avrff 

psmgg = frcgj*avrgg 

c Gravitational force. 

delpzz = gravcn*hydzc(ky2)*signik*term 

psldd = -(delpzz*avrho + avrff*convff + avrgg*convgg 

& - pmpph(ix)) 

c21 cqs compute junction pressure 

if (redo) then 

pjun = po(kk) + (psldd - psmff*velfj(i) 

& - psmgg*velgj(i))*signvc 

else 

pjun = po(kk) + (psldd - psmff*velfjo(i) 

& - psmgg*velgjo(i))*signvc 

endif 

c cqs *******CC************C**********d****S 

c cqs * start of test for knowing if the flow is still choked in the new time step 

c cqs **CCC*******CCC*****************C***CCC*C***************C**C**C******* 

c22 cqs choke on last time step?. See step 3 

if (choke) then 

c23 cqs Unchoking test. 

scrach = max(pjun.scvjck(ix)) 

pll = po(kk) + scvtur(ix)*(po(ll) - po(kk)) 

c24 cqs this is the test for knowing if the flow is still choked in the new time step 

if (chngno(42)) then 

if (pjun.gt.po(kk) .or. scvjck(ix).lt.pll) choke=.false. 

else 

if (scrach.lt.pll .or. pjun.gt.po(kk)) choke-.false. 

endif 

endif 

c cqs * 

c cqs * end of test for knowing if the flow is still choked in the new time step 

c cqs 

c

I I I
171 

c25 cqs set qual to the static quality at junction based on donor properties 

voidjc = min(vgscmx,voidgj(i)) 

quall = voidjc*rhogj(i) 

quall = quall/(quall + (1.0 - voidjc)*rhofj(i)) 

qualty = qualla 

c26 cqs donor gas void fraction >0.10? ("yes" go to 228, two-phase model, "no" continue with subcooled model) 

if (voidgj(i) .gt. vgtpmn) go to 228 

jcatsc = 1.0 

c27 cqs Subcooled choking criterion. This is only a comment of R5 

cSSSSSSSSS•••••S••S•SSSSSSSSSSSSSSSSSSSSSSSSsSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS 

c cqs here starts the model for subcooled fluid or two-phase with void<0.10 SSSSSSSSSSSSSSSSSSSSSSSSSSSS 

cS••••••••••S••S•SS•SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS 

ttt = tempf(kk) 

rhofin = 2.0/rhof(kk) 

c28,29 are missing 

c30 cqs calculate zip 

zip = (po(kk)+pmpph(ix)*signvc)*rhofin + 

& termz*velf(ky)**2 - delpzz*signvc*2.0 

c31 cqs choke = true. see at step c24. This is the first time (subcooled fluid) that the test is made 

c cqs if the flow was not-choked last time step. 

c cqs ***CCC*****C**e*****e***eeeeeeeeee 

c cqs start first test of choking. This test is made only if choke=.false.* 

c cqs*****************e**e**eeeeeee**ee* 

if (.not.choke) then 

c First test of choking. 

c32 cqs it is only a comment. The test is in c37 

c33 cqs get thermodynamic properties for subcooled liquid 

if (nfluid .eq. 1) then 

call sth2x0 (tttpsatterr) 

elseif (nfluid .eq. 2) then 

call std2x0 (ttt,psatt.err) 

$if def,nevwtrp,3 

elseif (nfluid .eq. 12) then 

call stpuOp (fa(ndxstd),prop,36,1) 

err = lprop(32) 

else 

call strsat (fa(ndxstd),l,ttt,psatt.dummy,err) 

endif 

c34 cqs steam table failure
172 

if (err) go to 228 

c35 cqs estimate sonic velocity at throat 

sonic = sqrt(max(O.O,zip - psatt*rhofin)) 

c36 cqs quale(kk) > 0.0 

if (quale(kk) .gt .0.0) sonic = max(sonicsounde(kk)) 

c37 cqs vc<sonic*at/2. First test for choking 

if (vc .lt. 0.5*at*sonic) go to 1990 

endif 

"c cqs ***********************CC**C C** **SC*****CCCCC******C 

"c cqs end first test of choking. Subcooled odel**********e*******b 

"c cqs ************ S*C****SC******CC**CC***S*********C***** 

c38 cqs this is only a comment 

c Second test of choking. The second test is at c74 

c39 cqs get thermodynamic properties 

if (nfluid .eq. 1) then 

call sth2xl (fa(ndxstd),prop,err) 

elseif (nfluid .eq. 2) then 

call std2xl (fa(ndxstd),properr) 

$if def,nevvwtrp,3 

elseif (nfluid .eq. 12) then 

call stpu2t (fa(ndrstd),prop,36,1) 

err = lprop(32) 

else 

call strtx (fa(ndxstd),properr) 

endif 

c40 cqs steam table failure? 

if (err) go to 1990 

c41 cqs compute wall friction 

frwall = frcfj*at 

c42 cqs estimate throat velocity 

zipcon = zip + frvall**2 - psatterhofin 

c43 cqs 

aj = ajun(i)eathrot(i) 

scrach = max(O.Ozipcon) 

sonicl = max(O.O,sqrt(scrach) - fruall) 

c44 cqs sonic>O and not a time dependent volume 

if (iand(vctrl(kk),1).ne.0 .or. sonicl.le.0.0) then

I I I
173 

c Time-dependent donor volume or negative Bernoulli extrapolated 

c velocity 

dpdt = (hsubg - hsubf)/(ttt*(vsubgg - vsubff)) 

if (sonicl .eq. 0.0) sonicl = vsubff*dpdt 

& *sqrt(ttt/(cppf - ttt* 

& vsubff*dpdt*(2.0*betf - kpaf*dpdt))) 

c45 cqs 

sonic = sonicl 

delpfi = 0.0 

go to 219 

endif 

c cqs********S******s*****ese*****e* 

c cqs start ALJ model****************************************** 

c Get saturated liquid properties. 

press = pjun 

quall = qualty 

if (nfluid .eq. 1) then 

call sth2x2 (fa(ndxstd).prop.err) 

elseif (nfluid .eq. 2) then 

call std2x2 (fa(ndxstd),prop,err) 

Sif def,nevvtrp,3 

elseif (ufluid .eq. 12) then 

call stpu2p (fa(ndxstd),prop,36.1) 

err = lprop(32) 

else 

call strpx (fa(ndxstd),prop.err) 

endif 

if (err) go to 1990 

c Constants for Jones-Alamgir-Lienhard correlation. 

c47 cqs setup coefficients dpfioc, avolkk 

dpfioc - (2.72958e9*(ttt*1.5448787e-3)**13.76)*sigma(kk)* 

& sqrt(sigma(kk))*vsubgg/(vsubgg - vsubff) 

avolkk = min(aj*50.0,avolkk) 

scrach - avolkk - aj 

if (iand(jc(i),256) .eq. 0) then 

c Smooth junction. 

if ((kk.eq.k .and. iand(jc(i),8192).ne.0) .or. 

& (kk.eq.1 .and. iand(jcMi),4096).ne.0)) then 

c Upstream volume is cross flow volume. 

avkxj = 3.141592*diamv(ky)**2/4. 

dxkxj - diamv(ky)*0.5 

scrach = (avkxj - aj)/(dxkxj*aj) 

else 

scrach = 2.0*scrach/(dl(ky)*aj) 

endif
174 

else 

scrach = O.1*scrach/(diamv(ky)*aj) 

endif 

c51 cqs compute constants for ALJ model 

dprcon = ((rhof(kk)*max(O.O,scrach))**0.8)*2.078e-8 

ficons = (rhof(kk)*(aj/avolkk)**2)*6.9984e-2 

c cqs the constant 6.9984e-2 is 7.2e-2 in TRAC-BF1 

c52 cqs start iteration loop. This is only a comment 

c Iteration solution for jones-alamgir-lienhard correlation. 

c53 cqs compute starting estimating for sonic2 

sonic2 = sqrt(zip + frvall**2) - frwall 

sonic2 = min(sonic2,sqrt(zipcon + dpfioc*rhofin*4.9) 

& frwall) 

c54 cqs 

do 218 it = 1,24 

c55 cqs 

sonic = (sonici + sonic2)*0.5 

scrach = sqrt(l.0 + dprcon*sonic**2.4) 

delpfi = dpfioc*scrach - ficons*sonic**2 

zip - zipcon 

c56 cqs compute throat velocity squared based on throat pressure calculated from ALJ equation ZIP 

if (delpfi.gt.O.O) zip - zip + delpfi*rhofin 

c57 cqs 

zip = sqrt(maz(zip,O.O)) 

c58,59,60 cqs 

if (sonic - maz(O.O.zip - frwall)) 216,219,217 

c61 cqs 

216 sonicl - sonic 

go to 218 

c62 cqs 

217 sonic2 = sonic 

218 continue 

c cqs ************************ *S***C*****C**CC*****C********* 

c cqs end AL.! modelS***S***************S*** 

c63 cqs subcooled speed of sound 

sonic = (sonicl + sonic2)*0.5

I I I
175 

c64 cqs 

"c cqs vgscmx= 1.0e-5. If void>1.Oe-5 or quality>1.Oe-9 then we are in TRANSITION REGION 

"c cqs the program go on in the two phase region (c75).--------- >>>>>TWO PHASE MODEL 

219 if (voidgj(i).gt.vgscmx .or. qualaj(i).gt.1.Oe-9) go to 226 

c cqs start HEM model for subcooled region (void<1.Oe-5) e********eeeeee**e****** 

c cqs We are in subcooled region. The -aiman of AL] and start of HEM(void=O.O) is used. 

c cqs it is necesary to calculate a.sound-HEM(void=O.O) 

jcatsf = avrho*(quall*vsubgg + (1.0 - quall)*vsubff) 

sonic2 = 0.0 

if (ttt .le. tcrit-7.0) then 

c Get saturated liquid-vapor properties of two-phase mixture. 

press = pjun 

quall = qualty 

ubarr = quall*ugj(i) + (1.0 - quall)*ufj(i) 

ubarr = ubarr + po(kk)*(quall*rhofj(i) 

& + (1.0 - quall)*rhogj(i))/ 

& (rhogj(i)*rhofj(i)) - press*(quall*vsubgg + 

& (1.0 - quall)*vsubff) 

& - (delpzz+quall*(convgg - convmf)+convff)*signvc 

c cqs ubarr= u-mixture for calling steam-tables 

if (nfluid .eq. 1) then 

call sth2x6 (fa(ndxstd),prop,iq,err) 

elseif (nfluid .eq. 2) then 

call std2x6 (fa(ndxstd),prop,iq,err) 

Sit def,newwtrp,4 

elseif (nfluid .eq. 12) then 

call stpu2pu (fa(ndxstd),prop,36,1) 

iq = iprop(36) 

err = lprop(32) 

else 

call strpul (fa(ndxstd).propiq,err) 

endif 

if (err) then 

press = pjun 

quall = qualty 

if (nfluid .eq. 1) then 

call sth2x2 (fa(ndxstd),prop,err) 

elseif (nfluid .eq. 2) then 

call std2x2 (fa(ndxstd),prop,err) 

$if def,nevvtrp,3 

elseif (nfluid .eq. 12) then 

call stpu2p (fa(ndxstd),prop,36,1) 

err = lptop(32) 

else 

call strpx (fa(ndxstd),prop,err) 

endif 

if (err) go to 1990
176

dpdt = (hsubg - hsubf)/(ttt*(vsubgg - vsubff)) 

sonicl = vsubff*dpdt*sqrt(ttt/(cppf - ttt*vsubff*dpdt* 

& (2.O*betf - kpaf*dpdt))) 

c cqs iq=2 two phase 

elseif (iq.eq.2) then 

dpdt - (hsubg - hsubf)/(ttt*(vsubgg - vsubff)) 

ahe = ttt/(quall*(cppg - ttt*vsubgg*dpdt* 

& (2.0*betg - kpag*dpdt)) 

& + (1.0 - quall)*(cppf - ttt*vsubff*dpdt* 

& (2.0*betf - kpaf*dpdt))) 

if (ahe .ge. 0.0) then 

sonici = vsubff*dpdt*sqrt(ahe) 

else 

press = pjun 

quall= qualty 

if (nfluid .eq. 1) then 

call sth2x2 (fa(ndxstd),prop,err) 

elseif (nfluid .eq. 2) then 

call std2x2 (fa(ndxstd).prop,err) 

Sif def,nevvtrp,3 

elseif (nfluid .eq. 12) then 

call stpu2p (fa(ndxstd),prop,36,1) 

err = lprop(32) 

else 

call strpx (fa(ndxstd),prop,err) 

endif 

if (err) go to 1990 

dpdt - (hsubg - hsubf)/(ttt*(vsubgg - vsubff)) 

sonicl = vsubff*dpdtesqrt(ttt/(cppf - ttt*vsubffedpdt* 

(2.0*betf - kpaf*dpdt))) 

endif 

c cqs iq=l liquid 

elscif (iq.eq.1) then 

press - pjun 

quall = qualty 

if (nfluid .eq. 1) then 

call sth2x2 (fa(ndxstd),prop,err) 

elseif (nfluid .eq. 2) then 

call std2x2 (fa(ndxstd),properr) 

Sit def,nevvtrp,3 

elseif (ntluid .eq. 12) then 

call stpu2p (fa(ndxstd),prop,36,1) 

err = lprop(32) 

else 

call strpx (ta(ndxstd),properr) 

endif 

if (err) go to 1990

I I I
177 

"C cqs ******************* 

"c cqs sound spped of HEM with void=0.0 

"c cqs this is the model that is normally used 

"c cqs in HEM model for subcooled liquid 

"C cqs ****************C***********C*** 

dpdt = (hsubg - hsubf)/(ttt*(vsubgg - vsubff)) 

sonicl = vsubff*dpdt*sqrt(ttt/(cppf - ttt*vsubff*dpdt* 

& (2.0*betf - kpaf*dpdt))) 

"c cqs iq=3 vapor 

elseif (iq.eq.3) then 

press = pjun 

quall = qualty 

if (nfluid .eq. 1) then 

call sth2x2 (fa(ndxstd),properr) 

elseif (nfluid .eq. 2) then 

call std2x2 (fa(ndxstd),prop,err) 

$if defnenvtrp,3 

elseif (nfluid .eq. 12) then 

call stpu2p (fa(ndxstd),prop,36,1) 

err = lprop(32) 

else 

call strpx (fa(ndxstd),prop,err) 

endif 

if (err) go to 1990 

dpdt = (hsubg - hsubf)/(ttt*(vsubgg - vsubff)) 

sonic1 = vsubff*dpdt*sqrt(ttt/(cppg - ttt*vsubgg*dpdt* 

(2.0*betg - kpag*dpdt))) 

endif 

ceee*eeeeeeeeeeeee*eee******eee***ee**e***e*eee*eee*ee*****e*eee*eeeeeeeeeeeee**eeeeeeee*ee 

c cqs end of HEM model for subcooled region ******************ee**eeeeeee**eeeeeeee 

"c Set sonic velocity to maximum of equilibrium sound speed 

"c and velocity needed to obtain required pressure drop. 

c66 cqs 

if (sonic .At. sonicl/jcatsf) then 

c68 cqs 

jcatsc = jcatsf 

c67 cqs 

sonic = sonicl 

else 

c69,70 cqs 

if (delpfi .gt. 0.0) sonic2 = dpfioc*1.2*dprcon* 

& sonic**l.4/scrach - 2.0*ficons*sonic 

endif 

endif
178 

c73 cqs 

dsondp = at/(sonic*rhof(kk) - sonic2) 

xej(i) = 0. 

sonicj(i) = sonic/jcatsc 

c cqs jcat is relaxed with the value in the last time step 

c71 cqs 

jcatn(i) = jcato(i) + 0.1*(jcatsc - jcato(i)) 

c72 cqs 

sonic = sonic/jcatsc 

dsondp = dsondp/jcatsc 

sonic = at*sonic 

c cqs ** start write output ****************************************** 

if (help .ne. 0) then 

if( iand(ihlppr(l),ishft(1.18)).ne.0 ) then 

if( iand(jcex(i),ishft(1,20)).ne.0 ) then 

if Ciskip .eq. 0) then 

iskip = 1 

call helphd ('jchoke',7) 

endif 

write (output,1909) junno(i),ncounttimehy 

1909 format ('OFrom jchoke ',2i1O,lpei3.5) 

write (output,1910) voidgj(i),signvc 

1910 format (' Junction void fraction' .2x,1p,e13.5,'flow direction', 

& 3x,e13.5) 

write (output,1908) psmff,psmgg,psldd,pjun,choke,press,psatt, 

& po(kk),po(ll) 

1908 format (' psmff',9x,'psmgg',gx,'psldd',9x,'pjun',9x,'choke', 

& 8x,'press',8x,'psatt',8x,'po-up',8x,'po-dn'/' ', 

& 1p,4e13.5,113,4e13.5) 

write (output,1911) sounde(kk),sonic,dsondpquale(kk), 

& quals(kk),velfj(i),velgj(i),vc 

1911 format C' sounde-up',4x,'sonic',8x,'dsondp',7x,'quale-up', 

& Sx,'qualso-up' ,4x,'velfj(i)',5x,'velgj(i)',Sx,'vc'/lp,8e13.5) 

endif 

endif 

endif 

c cqs ** end write output ****************S********************S 

c 

c74 cqs 

c cqs second choking criterion. Subcooled model 

if (choke .or. vc.ge.sonic) go to 820 

go to 1990 

c cqs end of subcooled region *************SSS************ S********S**S*********S 

c75 cqs 

c cqs the calculation in transition region (l.Oe-5<void<0.1) go on in this point. 

c cqs it comes from (c64) 

226 transr = .true.

I I I
179

sonics = sonic 

c76 cqs go to two-phase flow-model 

go to 232

cTTTTTTTTTT=ITTT7TTTTTTTTTTTTTTTTTTTTTTTTTTTTT TTTTTTTTTTTTTTT mTT=TTTTnrrrnTT 

c cqs start of two-phase modelTTTTTTTTTTT TTTTTTTTTTTTTTTTTTTTTTTTTTTTTrrTTT=tTTTTTT 

cTTTTTTTTTTTTTTTTTTTTTTTTTTiixiiiiziiiii j±±j±±±j± T= TTTTT= TTTTTTT 1 1 ±i± TTTTTT 

c77,78 cqs 

c cqsSS************eeeeee*eeeee**en*e.. 

c cqs start first test of choking. This test is made only if choke=.false.* 

c cqs *********e**.e**e~eeee*eeee*~e**.* 

c Two-phase sonic velocity check. 

228 if (.not.choke) then 

c79 cqs 

if (vc .At. 0.5*at*sounde(kk)) go to 1990 

endif 

c cqs ********************C**C**e*e*****eeeee* .eee*eee*eeee.*ee*.eeee 

c cqs end first test of choking. Two-phase region ****ee*e**ese***e**e 

c cqs ******************** e****************************** ******** 

c80 cqs 

232 press = pjun

c81 cqs

if (redo) then 

deltap = po(kk) 

else 

deltap = po(kk) 

endif

- presse*jcatn(i) 

- press*jcato(i)

c83 cqs vgtpmn= 0.10 

voidjc = -mx(voidgj(i),vgtpmn)

c84 cqs

scrach = voidjc*rhogj(i) 

zip = scrach/(scrach+(1.0 - voidjc)*rhofj(i))

c82 cqs compute donor specific internal energy based on junction static quality 

ubarr = zip*ugj(i) + (i.0 - zip)*ufj(i) 

c85 cqs compute junction specific internal energy 

ubarr = ubarr + deltap*(zip*rhofj(i) + (1.0 - zip)*rhogj(i))/ 

& (rhogj(i)*rhofj(i)) - (delpzz+zip*(convgg - convff)+convff)* 

& signvc
180

c86 cqs set RATIOS to 1 

ratios = 1.0 

c87 cqs 

if (choke) then 

if (redo) then 

ratios = sqrt(1.0 + max(zip*(velgj(i)/velfj(i) - 1.0),0.0)) 

else 

ratios = sqrt(1.0 + max(zip*(velgjo(i)/velfjo(i) - 1.0), 

0.0)) 

endif 

endif 

c88 cqs 

jcattp = 1.0 

c89 cqs noncondensable quality < 1.E-6 

if (qualaj(i).lt.i.Oe-6) go to 236

cNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNONNI NNNNNNNNNNNNK U 

c cqs start of noncondensable model NNHNINHMRNNNNRNNNNINNNNNNNNNNNNUNNNNNNNNNNNNWNNNNNNNN 

cNNNNNNNNNNNNNNNNNNNNNIMININ NOOUWNNN flODUDUINNNNNNNNNNNN

c Junction equilibrium sound speed calculation vhen air is present. 

c See subroutine state for details. 

cvao = 0.0 

uao = 0.0 

dcva = 0.0 

ra = 0.0 

do 63 in - i,lnoncn(issys) 

ink = kk + in -1 

cvao = cvaox(in)*qualan(ink) + cvao 

uao = uaox(in)*qualan(ink) + uao 

dcva = dcvax(in)*qualan(ink) + dcva 

ra = rax(in)*qualan(ink) + ra 

63 continue 

ujun = ubarr 

qa = qualaj(i)*zip 

if (qa .1t. 1.0e-5) go to 236 

qairl = 1.0 - qa 

qara = qacra 

if (qa. ge. 0.998) then 

c Pure air. 

ual = ujun - cvao*tao - uao 

if Cual .le. 0.0) then 

tg = (ujun - uao)/cvao 

else 

tg = tao + (sqrt(cvao**2 + 2.0*ual*dcva) - cvao)/dcva 

endif 

vbarr = ra*tg/pjun 

c Specific heat of air. 

cvaq = cvao+dcva*max(tg - tao,0.0)

I I I
181 

"c Sonic velocity. 

sonic = sqrt(vbarr*pjun*(cvaq + ra)/cvaq) 

jcattp = rhogj(i)*vbarr 

go to 251 

endif 

"c Calculation of equilibrium state. 

"c Find saturation temperature of pjun to set up the upper limit. 

if (nfluid .eq. 1) then 

call psatpd (tmaxl,pjun,dpdt,2,err) 

elseif (nfluid .eq. 2) then 

call pstpd2 (tmaxl,pjun,dpdt,2,err) 

Sif def,newvtrp,5 

elseif (nfluid .eq. 12) then 

prop(2) = pjun 

call stpuO0 (fa(ndxstd),prop,36,1,2) 

tmaxl = prop(1) 

dpdt = prop(3) 

else 

call strsat(fa(ndxstd),2,pjun,tmaxl,dpdt,err) 

endif 

if (err) tmaxl = tcrit 

tmaxl = tmaxl*0.9999 

c Initialize equilibrium temperature, ttt -- te. 

ttt = min(satt(kk),tmaxl) 

jstop = .false. 

do 260 it = 1,16 

c Get saturation vapor properties. 

if (nfluid .eq. 1) then 

call sth2xl (fa(ndxstd),properr) 

elseif (nfluid .eq. 2) then 

call std2xl (fa(ndxstd),prop,err) 

$if def,nevvtrp,3 

elseif (nfluid .eq. 12) then 

call stpu2t (fa(ndxstd),prop,36.1) 

err = lprop(32) 

else 

call strtx (fa(ndxstd),prop,err) 

endif 

if (err) go to 252 

dpdt = (hsubg - hsubf)/(ttt*(vsubgg - vsubff)) 

dusdtt - cppg - vsubgg*(betg*press - (press*kpag 

& ttt*betg)*dpdt) 

uss = usubgg 

vss = vsubgg 

kpags - kpag 

betgs = betg 

pa = pjun-press 

"c Call steam tables interpolation routine to get liquid properties from 

"c temperature and pressure. 

"c Note-liquid is subcooled. 

press = pjun 

if (nfluid .eq. 1) then 

call sth2x3 (fa(ndxstd),prop,iq,err) 

elseif (nfluid .eq. 2) then 

call std2x3 (fa(ndxstd),prop,iq,err) 

$if def,newwtrp,4 

elseif (nfluid .eq. 12) then
182 

call stputp (fa(ndxstd),prop,36,1) 

err = lprop(32) 

iq = 1 

else 

call strtp (fa(ndxstd) ,propiq,err) 

endif 

if (err or. iq.ne.1) go to 252 

dufdtt = cpp - betaa*pjun*vbarr 

c Internal energy and specific heat*quala of air. 

term = max(ttt - tao,0.O) 

ua = cvao*ttt + 0.5*dcva*term**2+uao 

cvaq = (cvao + dcva*term)*qa 

c Values needed for newton iteration. 

term = vss*(ujun - qa*ua - qairl*ubarr) 

fl = pa*term - qara*(uss - ubarr)*ttt 

dfldtt = term*(pa*(betgs - kpagsedpdt) - dpdt)- pa*vss* 

& (cvaq + qairl*dufdtt) - qara*((uss - ubarr) + ttt* 

& (dusdtt - dufdtt)) 

if (jstop) go to 262 

dtt = fl/dfldtt 

ttt = max(min(ttt - dtt,tmaxl),ttrip) 

if (abs(dtt) .lt. toler*ttt) jstop = .true. 

260 continue 

c No solution after 15 iterations. 

go to 252 

c End of iteration. 

262 vff = vbarr 

dufdpt = vff*(pjun*kpa - ttt*betaa) 

c Calculation of equilibrium quality,xe. 

xe = (ujun - ubarr - qa*(ua - uss))/(uss - ubarr) 

if(xe .1t. qa) go to 252 

if (xe .gt. 1.005) go to 263 

c Calculation of equilibrium sound speed. 

qs = xe - qa 

qf = 1.0 - xe 

term = vss*(betgs - kpags*dpdt) 

c Set up the equation: a* (ddx/dp)s,(dt/dp)s =aO. 

cli = uss-ubarr + pjun*(vss - vff) 

c12 = qf*(dufdtt + pjun*betaa*vff) + cvaq + qs*(dusdtt + 

& pjun*term) 

c21 - pa*vss 

c22 = qs*(pa*term - dpdt*vss) - qara 

aOl = -qf*(dufdpt - kpa*vft*pjun) 

a02 = -qs*vss 

c Solution for (ddx/dp)s -- dtt/det, (dt/dp)s -- dtg/det. 

c det = cll*c22-c12*c21 

dtt = aOlcc22 - a02*c12 

dtg = a02*cll - aOl*c21 

vbarr - qf*vff + qsovss 

jcattp = avrho*vbarr*ratios 

c ahe=-(dv/dp)s 

abe = kpa*vff*qf - ((qf*vff*betaa + qs*term)*dtg + 

& (vss - vff)*dtt)/(cll*c22 - c12*c21) 

if (abe .le. 0.0) go to 252 

sonic = vbarr/sqrt(ahe) 

go to 251 

c Single phase vapor.

I I I
183

"c Initialize press and tg. 

263 tg = ttt 

press = pjun - pa 

"c Newton iteration to find press,tg. 

jstop = false. 

do 283 it = 1,16 

"c Find psatt of tg. 

if (nfluid .eq. 1) then 

call sth2xO (tgpsatt,err) 

else if (nfluid .eq. 2 ) then 

call std2xO (tg,psatt,err) 

$if def,newvtrp,4 

elseif (nfluid .eq. 12) then 

prop(1) = tg 

call stpuOp (fa(ndxstd),prop,36,1) 

err = lprop(32) 

else 

call strsat (fa(ndxstd),l,tg,psatt,dummy,err) 

endif 

if (.not.err) then 

if (press .ge. psatt) go to 268 

endif 

c Superheated vapor. 

ttt = tg 

if (nfluid .eq. 1) then 

call sth2x3 (fa(ndxstd),propiq,err) 

elseif (afluid .eq. 2) then 

call std2x3 (fa(ndxstd),propiq,err) 

Sif def,nevvtrp,4 

elseif (nfluid .eq. 12) then 

call stputp (fa(ndxstd),prop,36,i) 

err = lprop(32) 

iq - 3 

else 

call strtp (fa(ndxstd),prop,iq,err) 

endif 

if (err) go to 252 

if (iq .eq. 3) then 

usubgg = ubarr 

vsubgg = vbarr 

cppg = CPP 

kpag - kpa 

betg = betas 

go to 270 

endif 

c Subcooled steam. 

c Extrapolation of vapor properties. 

268 if (nfluid .eq. 1) then 

call sth2x2 (fa(ndxstd),prop,err) 

elseif (nfluid .eq. 2) then 

call std2x2 (fa(ndxstd),prop,err) 

else 

call strpx (fa(ndxstd),properr) 

endif 

if (err) go to 252 

term = vsubgg 

vsubgg = term*(1.0 + betg*(tg - ttt))

183
184 

if (vsubgg .1e. 0.0) go to 252 

usubgg = usubgg + (cppg - term*betg*press)*(tg - ttt) 

betg = betg*term/vsubgg 

c Internal energy and specific heat*quala of ideal gas. 

270 term = max(tg - tao.0.0) 

ual = cvao*tg + 0.5*dcva*term**2+uao 

cvaq = (cvao + dcva*term)*qa 

c Iteration parameters. 

pa = pjun - press 

fl = pa *qairl*vsubgg - qara*tg 

ff2 = ujun - qa*ual - qairi*usubgg 

dfldps = -qairl*vsubgg*(1.0 ÷pa*kpag) 

dfldtg = pa*qairlsvsubgg*betg - qara 

df2dps = -qairl*vsubgg*(press*kpag - tg*betg) 

df2dtg = -cvaq - qairl*(cppg - press*vsubgg*betg) 

rdet = 1.0/(dfldps*df2dtg - df2dps*dfldtg) 

if (jstop) go to 286 

dps = rdet*(df2dtg*fl - dfidtg*ff2) 

dtg = rdet*(dfldps*ff2 - df2dps*fl) 

press = max(min(press - dps,pjun),pmin) 

tg = min(max(tg - dtg,ttrip),tcrit) 

if (max(abs(dps/press),abs(dtg/tg)) .lt. toler) 

& jstop=.true. 

283 continue 

c No solution after 15 iterations. 

go to 252 

286 vbarr - qairl*vsubgg 

jcattp = rhogj(i)*vbarr 

c Calculation of single phase sound speed. 

c Set up the equation: a* (dps/dp)s,(dtg/dp)s =a0. 

c Note -- c1l and c12 are defined through equivalence to. 

c dfldps and dfldtg 

c aOl = -vbarr 

c21 = -vbarr*(tg*betg + pa*kpag) 

c22 = cvaq + qairlscppg + pa*vbarr*betg 

c a02 = 0.0 

c Solution for (dps/dp)s -- dps/det, (dtg/dp)s -- dtg/det. 

c* det = c11*c22-c12*c21 

c* dps = aOl*c22 

c* dtg - -aOl*c21 

c 

c abe = aOl/-(dv/dp)s 

she = (c12*c21 - cll*c22)/(betg*c21 + kpag*c22) 

if (ahe.le.0.0) go to 252 

sonic = sqrt(ahe) 

go to 251 

c 

cNNNMNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN- N-- NNNNNNNNNUNNNNNNN1NNNNNNN NNNNNNNNN 

c cqs end of noncondensable model NNNNNNRNN IBNRNNNNNNN-NNNNNNNNNNNNNNNNNNNNN NNNNN 

cNNNNNNNNNNNNNNNNNNNNNNNN U NNNNBBM NN NNBU -h NNENIEnWBNNNNNNNNNU 

cTTTTTTTTTTTTTTTTTTTTT7TTTTTTTTTTTTTTTTTTTrTT=TI TTl rI Ir I I I IrI IrIiI±I±±II±I±I±I±I±I TTTT'TT 

c cqs continuation of two-phase model without noncondensable gas present 1,1Ii± I±I~i•]iTfl 

cTTTTTTTTfl711TTTTT7TTi LI III ±± II i±±± I II II ±1L1 L ±TTTTTlrTT7TTTTTTT1TTTTTTTrTTTTTT1TTTTTTTTTTTT

I I I
185 

c90 cqs call steam tables 

236 if (nfluid .eq. 1) then 

call sth2x6 (fa(ndxstd),prop,iq,err) 

elseif (nfluid .eq. 2) then 

call std2z6 (fa(ndxstd),prop,iq,err) 

$if def,newvtrp,4 

elseif (nfluid .eq. 12) then 

call stpu2pu (fa(ndxstd),prop,36,1) 

iq = iprop(36) 

err = lprop(32) 

else 

call strpul (fa(ndxstd),prop,iq,err) 

endif 

c91 cqs steam table failure or vapor with T>Tcrit 

if (err .or. iq.eq.4) go to 252 

c92 cqs 

c cqs iq is calculated in sth2x6 (for nfluid=l, water) 

c cqs selection of the model iq= 4 (T>Tcrit); 3 (vapor); 2 (two-phase); 1 (liquid) 

if (iq - 2) 244,248,240 

c cqs if vapor goto 240; two-phase 248; saturated liquid 244 

cVVV 

c cqs start vapor model vVVVVVV 

cVVVVVVVVVVVVVVVVVVVVVVVVVVWVVVVVVVVVVVV1J VVVVVVVVV VVVVVVV 

c93 cqs vapor with T<Tcrit 

c94 cqs compute dpdt 

240 dpdt = cpp/(tttevbarr*betaa) 

c95 cqs compute AHE 

abe = dpdt/(vbarr*(kpa*dpdt - betaa)) 

c96 cqs compute JCATTP using junction vapor density and v from steam tables 

jcattp = rhogj(i)evbarr 

c97 cqs AHE<0.0 

if (ahe .1t. 0.0) go to 252 

c98 cqs 

sonic = vbarr*sqrt(ahe)

go to 251

cVVVVvvvvvvvvvvvVVVVVVVVWVVVV 

c cqs end vapor model vvVVVVVVVVVVVV 

cVVVV yVVVVVVVVVWW
186

cSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS 

c cqs start saturated liquid model SSSSSSSSSSSSSSSSSSSSSSSSSSSSSS 

cSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS

cIO0 cqs saturated liquid . call steam tables 

244 if (nfluid .eq. 1) then 

call sth2xl (fa(ndxstd).prop,err) 

elseif (nfluid .eq. 2) then 

call std2xl (fa(ndxstd)tproperr) 

Sif def,newvtrp,3 

elseif (nfluid .eq. 12) then 

call stpu2t (fa(ndxstd) ,prop,36,1) 

err = lprop(32) 

else 

call strtx (fa(ndxstd),prop.err) 

endif

c101 cqs steam table failure 

if (err) go to 252

cTT TTT TTTTflTTTTTTTTTTTT7iji Iiii TTLTlTiTTlTlI T TIITIIIT IIIIIT 

c102 cqs start two phase model. Saturated liquid model go on TTTTTTTT 

cTTTTlTT=TTTTTTTTITT=TTTTTTTTTTTTTTTrTTTTTTTTfTTTTTTTTTTTT 

248 dpdt = (hsubg - hsubf)/(ttt*(vsubgg - vsubff)) 

c103 cqs compute AME using definitions with DPDT and thermodynamic properties

& 

&

abe = ttt(quall*(cppg - tttevsubggedpdt*(2.0*betg 

kpag*dpdt)) + (1.0 - quall)*(cppf - ttt*vsubff*dpdt*(2.0*betf 

kpa:f*dpdt)))

c104 cqs

c105 cqs 

c106 cqs 

c107 cqs

jcattp - avrho*vbarr*ratios 

if (ahe ge. 0.0) then

sonic - (quall*vsubgg + (1.0 - quall)*vsubff)*dpdt*sqrt(ahe)

if (iq .eq. 1) sounde(kk) - sonic

cTTTTTTTTTTTT 77TTTTfTTTTTTTTTTTTTTTTTTTThI •£II I I II I I I±II TTTITTTTTTT 

c cqs end of two phase and saturated liquid model I±±±z±±±ii 

cSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS 

go to 251 

endif 

c108 cqs we take sound- sounde(kk) if there is any problem 

C 

252 sonic = sounde(kk)

I I I
187 

ci09 cqs test the transition flag is set TRANS= TRUE? 

if (transr) go to 258 

go to 257 

ciiO cqs test the transition flag i.e. NOT TRANSR 

C 

251 if (.not.transr) go to 257 

c cqs TRANSITION ZONE. l.Oe-5<void<O.1 . Interpolate SONIC and JCAT 

clii cqs Interpolate ratio of sound spped and throat density ratio using interpolation factor XISCTP 

258 xintrp = xisctp 

c cqs transition between subcooled and two-phase models 

sonic = sonics/jcatsc + xintrpe(sonic/jcattp - sonics/ 

& jcatsc) 

c112 cqs interpolate the derivative of the sound speed with pressure DSONDP 

dsondp = xintrp*0.15/(sounde(kk)erho(kk)*jcattp) + 

& (1.0 - xintrp)/(sonics*rhof(kk)ijcatsc) 

c113 cqs interpolate throat density ratio 

jcatn(i) = jcatsc + xintrp*(jcattp - jcatsc) 

if (.not.redo) then 

c114 cqs underrelax density ratio JCATN 

jcatn(i) = jcato(i) + O.l*(jcatn(i) - jcato(i)) 

endif 

c11B cqs --------------- >>>>>>>> c119 

go to 256 

c cqs start two-phase ZONE. void>O.1. Underrelax JCAT 

cCeC* !*****CCCC*C C*CC* *** * C***CCCCC***CC *C***CC**C!*l**C* 

c116 cqs underrelax JCATTP with JCATO using variable relaxation factor RELAX 

c 

257 if (redo) then 

jcatn(i) = jcatn(i) + O.l*(jcattp - jcatn(i)) 

else 

jcatn(i) = jcato(i) + O.i*(jcattp - jcato(i)) 

endif 

"c In the two-phase region relax jcat. 

"c ramp the old time weighting factor to ninety percent at a void 

c fraction fifty percent greater than the upper bound of the 

c transition region between the subcooled and two-phase regions.
188 

c cqs vgtpmn=O.1 

xitpsh = (voidgj(i) - vgtpmn)/(O.5*vgtpmn) 

xitpsh = max(0.0,min(l.Oxitpsh)) 

xitpsh = xitpsh*xitpsh*(3.0 - 2.0*xitpsh) 

relax = 0.9*xitpsh 

if (redo) then 

jcattp = jcattp + relax*(jcatn(i) - jcattp) 

else 

jcattp = jcattp + relax*(jcato(i) - jcattp) 

endif 

c118 cqs calculate sound speed derivative DSONDP 

dsondp O.15/(sounde(kk)*rho(kk)*jcattp) 

c117 cqs 

sonic = sonic/jcattp 

c cqs end two-phase ZONE. void>0.1. Underrelax JCAT 

c cqs start two-phase and transition region. Underrelax sonic 

c119 cqs underrelax SONIC with old time value using variable relaxation factor RELAX 

c In the transition region relax sonic 

c Ramp the old time weighting factor to ten percent at a void fraction 

c fifty percent greater than the upper bound of the 

c transition region between the subcooled and two-phase regions. 

c cqs vgtpmns 0.1. If voidgj(i) > 0.1 then xisctp-0.O and relax=0.9 

256 xisctp = (voidgj(i) - vgtpann)/(O.5*vgtpmn) 

xisctp = max(O.0,min(1.0,xisctp)) 

xisctp = xisctp*xisctp*(3.0 - 2.0*xisctp) 

relax = 0.8*(1.eO - xisctp) + 0.10 

if (sonicj(i).ne.O.0e0) sonic = sonic + relax*(sonicj(i) 

k sonic) 

sonicj(i) = sonic 

xej(i) = quall 

c cqs end two-phase and transition region. Underrelax sonic 

c120 cqs 

sonic = at*sonic 

dsondp = atodsondp 

c cqs ** start write utt*************************************e******** 

C

I I I
189 

if (help .ne. 0) then 

if( iand(ihlppr(l),ishft(1,18)).ne.0 ) then 

if( iand(jcex(i),ishft(1,20)).ne.0 ) then 

if (iskip eq. 0) then 

iskip = 1 

call helphd ('jchoke',7) 

endif 

write (output,1909) junno(i),ncount,timehy 

write (output,1910) voidgj(i),signvc 

write (output,1908) psmff,psmgg,psldd,pjun,choke,press,psatt, 

& po(kk),po(ll) 

write (output,1912) iq,sounde(kk),sonicquale(kk), 

& quals(kk),velfj(i),velgj(i),vc 

1912 format(' iq', 2 z.'sounde-up',4z,'sonic',Sx,'quale-up',sx, 

& 'qualso-up',4z,'velfj(i)',Sx,'velgj(i)',sz,5 vc'/ 

& i6,1p,7e13.5) 

c 

endif 

endif 

endif 

c cqs ** end write o*tput *******eee************e**eeee*******eee 

c122 cqs NOT CHOKE and VC<SONIC?. number 963 is not used. 

c cqs second test of choking criterion. Two-phase zone 

953 if (.not.choke .and. vc.lt.sonic) go to 1990 

cTTTTTTTTTTTTTTTTTTTTTTTTTTT TTTTTTTTTTTTTT7TTTTTTTTTTTT YTTTrTrTTnTTn•Trrn-rrTTTTTT 

c cqs end of two-phase and transition model without noncondensable gas present TTTTTTTTTTTT 

cTTTTT TTTTTTTTTTT TTTTTTTrl= I Iii I II I I zIi I ITTTTTTTTTTTTTTTTTTTTTTTTTTTTTT iz 

c123 cqs test for time dependent volume 

"c Use regular momentum solution in the single phase limit unless the 

"c donor volume is a time dependent volume. 

820 if (iand(vctrl(kk),l) .ne. 0) then 

c124 cqs set up matrix terms for velocity solution 

difff = 1.0 

difgg = -difff 

difld = 0.0 

c125 cqs 

go to 839 

endif 

c cqs ** start the calculation of vapor and liquid velocities*********** 

c 

c By eliminating pressure from two momentum equations, 

c a velocity equation of the form 

c difff*(liquid vel.)+difgg*(vapor vel.)sdifld 

c is obtained.

c126 cqs set vapor generation rate, VAPGEN
190 

vpgenn = vapgno(kk)*ddx 

c12T cqs check sign on VAPGEN 

if (vpgenn .ge. 0.0) then 

c128 cqs 

vpgnxx = -vpgenn/mAx(l.0e-15,voidg(kk)) 

else 

c129 cqs 

vpgnxx - vpgenn/max(i.0e-15,voidf(kk)) 

endif 

c130 cqs set up matrix terms for velocity solution 

term = atin*(1.0 + jcatn(i)/jcato(i))*0.5 

fl term*velfjo(i) 

ff2 =termevelgjo(i) 

virmas =faaj(i)*avrho 

sungg =(rhog~kk) + virmas)*ddx 

sumff =(rhof(kk) + virmas)*ddx 

c Incorporate fij(i), fxj(i) and cOj(i) into interphase 

c friction terms of momentum difference equation. 

c (figjj and fifjj nov replace fjfg). 

co = coj(i) 

cC = min(l.33,mAY(i.0,c0)) 

if (voidg(kk) .gt. 0.0) cC min(cO.1.0/voidg(kk)) 

if (voidg(kk) Alt. 0.99999) then 

ci - (1.0 - cOevoidg(kk))/(1.0 - voidg(kk)) 

else 

ci = ((voidg(kk) - 0.99999)+(i.0 - voidg(kk))*(1.0 

& 0.99999*c0)*i.0e6)*l.0e5 

endif 

figjj -(dl(ky)*(fij(i)*(abs(cl*velgjo(i) - cO*velfjo(i))* 

& ci + 0.0l))*0.5 + fidxup(ix))/.ax(i.Oe-20,voidgj(i)* 

k voidfj(i)) 

fifjj - (dl(ky)*(fij(i)*(abs(ci*velgjo(i) - cO*velfjo(i))* 

& cC + 0.0i))*0.S + fidxup(ix))/max(i.0e-20,voidgj(i)* 

k voidfj(i)) 

frcgj = frcgj*(l.0 - fxj Ci)) 

frcfj - frcfj*(l.0 - fxj~i)) 

c Incorporate interphase friction terms fifjj and figjj into difff and 

c difgg. 

difgg - sumgg + (rhog(kk)*(frcgj + ff2) + figjj - vpgaxx)*dt 

difff - -sumff - (rhof(kk)*(frcfj + fi) + fifjj - vpgnxx)*dt 

difld -sumggevelgjo(i) - sum~ff*velfjo(i) - (Crhog(kk) 

k rhof(kk))*delpzz + rhog~kk)*(convgg - convgi) - rhof(kk)* 

kt (convff - convfi))*dt 

c131 cqs 

c Velocity solution. 

c132 cqs compute SUMOLD, DET terms needed for velocity solution 

839 sumjld - arsmosonic*sigflvc 

dot = 1.0/(difffea~rg~f - difggearfg)

I I i
191 

c133 cqs solve 2x2 matrix for vapor and liquid velocties 

vf = (difld*argf - difgg*sumld)edet 

vg = (difff*sumld - difld*arfg)*det 

if (err) relax = 0.9 

c cqs ** end the calculation of vapor and liquid velocities*********** 

c134 cqs check for cocurrent flow 

if (vg*vf .le. 0.0) then 

c135 cqs counter-current flow 

det = 1.O/(argf + arfg) 

vf = sumld*det 

vg = vf 

difff = 1.0 

difgg = -difff 

difld = 0.0 

endif 

c136 cqs co-current flow. Set matrix terms for final velocity equations. 

if Cimplt .eq. 0) then 

velfj(i) - vf 

velgj(i) = vg 

scrach = dsondp*arsm*det 

vfdpk(ix+kl) = -difgg*scrach 

vgdpk(ix+kl) = difff*scrach 

vfdpl(ix-kl) = 0.0 

vgdpl(ix-kl) = 0.0 

else 

isf = jcnxd(i) 

idg = jcnxd(i+l) 

coefv(isf) = arfg 

coefv(isf+l) = argf 

sourcv(is) = sumald 

coefv(idg-l) = difff 

coefv(idg) = difgg 

sourcv(is+l) = difld 

sourcv(is) - relax*(arfg*velfjo(i) + argf*velgjo(i)) + 

h (1.0 - relax)*sumld 

sourcv(is+l) = relax*(difff*velfjo(i) + difgg*velgjo(i)) + 

& (1.0 - relax)*difld 

sumdpk(ix+kl) = dsondp*arsm 

difdpk(ix+kl) = 0.0 

sumdpl(ix-kl) = 0.0 

difdpl(ix-kl) = 0.0 

endif 

c137 cqs set choking flag bit in jc

jc(i) = ior(jc(i),l)
192 

c cqs start write output****************************** 

if (help .ne. 0) then 

if( iand(ihlppr(l),ishft(1,18)).ne.0 ) then 

ifW iand(jcex(i),ishft(1,20)).ne.0 ) then 

write (output,1914) junno(i),ncount,timehy, 

* velfjo(i),velfj(i),velgjo(i),velgj(i) 

endif 

endif 

endif 

1914 format(' Final vel',2i10,ip,5e13.5) 

c cqs end write output ******************************* 

c Do calculations again if velocity or 

c density ratio have changed too much. 

if (chngno(43)) then 

if (redo) then 

checkj = abs((jcatn(i) - jcsave)/jcatn(i)) 

checkv = voidfj(i)*abs((velfj(i) - vfsave)/velfj(i)) 

+ voidgj(i)*abs((velgj(i) - vgsave)/velgj(i)) 

else 

checkj = abs((jcatn(i) - jcato(i))/jcatn(i)) 

checkv = voidfj(i)*abs((velfj(i) - velfjo(i))/velfj(i)) 

* voidgj(i)*abs((velgj(i) - velgjo(i))/velgj(i)) 

endif 

if (checkj.gt.0.01 .or. checkv.gt.0.01) then 

vfsave = velfj(i) 

vgsave = velgj(i) 

jcsave = jcatn(i) 

if (redo) then 

nredo = nredo - 1 

if (nredo.gt.0) go to 100 

else 

redo = true. 

nredo = 10 

go to 100 

endif 

endif 

endif 

c138 cqs under relaxation for velocities 

c Under-relaxation treatment for choking. 

if (implt .eq. 0) then 

velfj(i) - velfjo(i) + (1.0 - relax)*(velfj(i) 

& velfjo(i)) 

velgj(i) = velgjo(i) + (1.0 - relax)*(velgj(i) 

t velgjo(i)) 

c 

if (help .ne. 0) then 

if( iand(ihlppr(l),ishft(1.18)).ne.O ) then 

if( iand(jcex(i),ishft(1,20)).ne.O ) then 

write (output,1915) junno(i),ncount, 

& timehyrelax,velfj(i),velgj(i) 

endif 

endif 

endif 

1915 format (' Under relax vel',2i1O,lp,4e13.5)

I I I
193 

c 

endif 

1990 ix 

- ix + scskp 

is = is + 2 

i = i + ijskp 

2000 continue 

sif def,nanscr 

c Nan out scvtur, pmpph 

call nanscj(16,17) 

Sendif 

return 

end
NRC FORM 36 U.S. NUCLEAR REGULATORY COMMISSION 1. REPORT NLMkSER 

(A2lMfild by v NRC. Add Vol., &W. Rev.. 

NR.89 110Z AldfWum Numb$ V W Ny.) 

WMc. 3=• BIBLIOGRAPHIC DATA SHEET 

2. TrTLE AND SUBTITLE 

NUREG/IA-0186 

Analysis of the RELAP5/MOD3.2.2 Beta Critical Flow Models 3. DATE REPORT PUBLISHED 

and Assessment Against Critical Flow Data From the Marviken Tests 3. REA 

July 2000 

4. FIN OR GRANT NUIABER 

s. AUTHOR(S) 

6. TYPE OF REPORT 

C. Queral, J. Mulas, C. G. de la Rua Technical 

7. PERIODo COVERED pPiivOaAe) 

8. PERPOiNG ORGANIZATION - NAME AND ADDRESS (INRC p DkM~I fa or ftiO.- U.S. Nw;e-Rmg.i.-Y C n 'a and n-- a- ie I .-t-c

piWwS arn.and flv~dins

Energy Systems Department 

School of Mining Engineering 

Polytechnic University of Madrid 

SPAIN 

9. SPONSORING ORGANIZATION - NAP AND ADDRESS (NR, ta "Smee as e•bow Ic,,,c, o provide ARC Dvi, orf O •a.g•n U.SL -uw•- -=-E-"WY C4VIVSSIIDivision of Systems Analysis and Regulatory Effectiveness 

Office of Nudear Regulatory Research 

U.S. Nuclear Regulatory Commission 

Washingon, DC 20555-0001 

1O. SUPPLEMENTARY NOTES 

11. ABSTRACT (200o ws orAe) 

In this report the critical low models of RELAPSMOD3.2.2 beta have been analyzed. Fist, an analysis of the implementation of 

the RELAPS/MOD3.2.2bets models have been performed in which it has been proved that the transition from the ctical to the 

non-critical flow model is not well done for the Ransom-Trapp model. Second, a sensitivity analysis of both models 

(Ransom-Trapp and Henry-Fauske) im subcooled, two-phase and vapor conditions has been taken with respect to temperatre, 

pressure, void-raction, discharge coefficients, energy loss coefficient and disquilibrium parameter. Finally, Seven Marvken tests 

have been simulated and compared with the exprmental data in order to validate both models. As par of this assessment an 

adustment of the discharge coefficients for the Ransom-Trapp model with different nodaizations has been done and also it has 

been checked which are the best values of the disequbnum parameter for the Henry-Fauske model in subcooled and two-phase 

conditions. Conclusions indicate that the behavior of the Henry-Fauske model is better than that of the Ransom-Trapp. In this 

sense, the now model is an improvement with respect to the Ransom-Trapp. 

12. KEY WORD6JOESCRIPTORS (9.d a w orpsiura i w" as ee& eWierrewc ioceIn In ie repot) AvALAB sTAedNI mL 

RELAP5 

unlimited 

Critical Flow 

14. SECUP T CLASSh ATM 

unclassified 

unclassified 

1S. NUhMER OF PAGES 

16. PRICE

NRC FORM = (2-4)
Federal Recycling Program
UNITED STATES 

NUCLEAR REGULATORY COMMISSION 

WASHINGTON, D.C. 20555-0001

years