nureg/ia-0186 'analysis of the relap5/mod3.2.2beta ... · contents 1 introduction 1 2 analysis...

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


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


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


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


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

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


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


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


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

vii

viii LIST OF FIGURES


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


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


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


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


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


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


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


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


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


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


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



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



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



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




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..


(BCM). CFT-11..


(BCM). CFT-15..


(BCM). CFT-17..


(BCM). CFT-21..


(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


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


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


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


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


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


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


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


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


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


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


J. CFT-15 .......... ................................ 113

xiv LIST OF FIGURES


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


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




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


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




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


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.


nozzle exit. Discharge coefficient adjustment, BCM-P.


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 FIGURESxiv

nt. nn,77.1p Pvif. Pt('.M-T


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

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

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


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


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


(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


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


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


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


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 ..................


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


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

1 Subroutine JCHOKE flow logic. ...

2 Subroutine JCHOKE flow logic (contir

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

BCM-

136

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 junction 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

5Chapter 2. Analysis of RELAP5/MOD3.2 Critical Flow Model

!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-5OR 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 Steam tables-uf<_um<Ug 240 • .-•/•.•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


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:

9Chapter 3. Sensitivity Analysis of RELAPS/MOD3 CFM

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

1.0e+07I-

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.


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


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


650.0

600.0

550.0 ,

500.0

450.0

400.0

350.0 0


-I

I

.0 100.0 200.0I )o.o

Time (s)



650.0

550.0

500.0 -

E

450.0

400.0

-J

E 9


X(



1

100.0 200.0 Time (s)

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


of the subcooled


8000

6000

4000

0

2000

0.0 0.0

1

100.0 200.0 300.0Time (s)

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


I I

14

15000

0

a.

10000

5000

0 L 0.0 300.0



15000.0 i

.2

V.

10000.0

5000.0

0.0 0.0

Time (s)


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


600.0

500.0

400.0

300.0 0.0 100.0 200.0 300.0

Time (s)


model, with decreasing temperature). CFM on.

.2

.a3

650.0

600.0

550.0

500.0

450.0

400.0

350.0 0.0


100.0 200.0 300.0Time (s)


model, with decreasing temperature). CFM off.

-_L - - t


Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CEM 17


100.0 200.0 300.0

Time (s)


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


model, with decreasing temperature). CFM off.

15000

10000

_o

5000 -

0.0 0.0

17Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM

ETSI Minas - Universidad Polittcnica de Madrid

15000.0


10000.0 -

0•

5000.0

0.0 L 0.0 100.0 200.0 300.0

Time (s)


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

18

- L


CRITICAL SUBCOOLED MODEL

700.0

650.0Steam

Non-choked subcooled model

0-0 Transition temperature &-e Saturated temperature,

5.0e+06 1.0e+07 1.5e+07Pressure (Pa)

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


40.0

0

o Subcooling Data 1 -- Quadratic Regression

5.0e+06 1.0e+07Pressure (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


CRITICAL SUBCOOLED MODEL Pressure Sensitivity

50.01

100.0 150.0Time (s)

Figure 3.16: Liquid temperature at the last node

subcooled model, with increasing pressure). CFM on.

700.0

(Pressure sensitivity of the


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



-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,


1.0e+07

5.0e+06 •

O.Oe+00 0.0 50.0 100.0 150.0Time (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



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,


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


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

23Chapter 3. Sensitivity Analysis of RELAP5/MOD3 CFM


2.0e+07

1.5e+07


1.0e+07U,

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.


1.0e+07 -

5.0e+06

0.Oe+00 -0.0 50.0 100.0 150.0

Time (s)


with decreasing pressure). CFM

node (Pressure sensitivity of the subcooled model,

off.



15000.0

Z

10000.0

5000.0


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

150.0Time (s)


with decreasing pressure). CFM on.

25



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,


50.0 100.0 150.0Time (s)


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


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


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 MODELMDC 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---

50.0 100.0 150.0Time (s)

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

subcooled model.

I I I

28

aj�

0

7500.0

5000.0

2500.0

0.0 U0.0

4500.0

4000.0

3500.0

3000.0

.2 .

2500.0

2000.0 0.0



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

150.0Time (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


- 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.

I I I

30ETSI Minas - Universidad Politecnica de Madrid3{}vv


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.

100.0 200.0Time (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 10.0


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 A0.0


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

1030.0 200.0 300.0Time (s)

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

model. Homogeneous model.

two-phase

I I I

32

3500.0

3000.0

2500.0

2000.0

1500.0

1000.0

500.0

0


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

3dU


CRITICAL TWO-PHASE MODEL Void-fraction Sensitivity. Non-homogeneous model

1.0 .

100.0 200.0 Time (s)

- P.150 bar SP.140 bar

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

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

0 ~-P30 bar

1000.0

500.0

300.0Time (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


8.05e+06

CRITICAL TWO-PHASE MODEL TDC Sensitivity

8.00e+06 LCu

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 MODELTDC Sensitivity

--- TDCO.6-0.7 I TDC=0.8-1.4 -

100.0 200.0 300.0Time (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

36ETSI Minas - Universidad Politkcnica de Madrid36

i


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-0.9Void=0.1

100.0 200.0 300.0Time (s)

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

4000.0

3000.0 -

2000.00

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.


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

38ETSI Minas - Universidad Politkcnica, de Madrid38


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_

3939

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).


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

ETSI Minas - Universidad PolitAnica de Madrid40


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)


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



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.


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.


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.


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


1.5e+07

1.0e+07 -


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).


-4

50.0 100.0 150.0

Time (s)

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

I I I


.=



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


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 Po1it�cnica de Madrid


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

I I I

ETSI Minas - Universidad Politknica de Madrid46


1.5e+07

1.0e+07

5.0e+06

/

O.Oe+00 0.0

CRITICAL STEAM MODEL SDC Sensitivity

50.0 100.01

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


CRITICAL STEAM MODEL

E C

.5

SDC Sensitivity675.0

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 MODELSDC 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

50.0 100.0Time (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



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


- Temperature.

- Pressure.


- 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.


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



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


Void-fraction.


I I I


2000

0 0.0


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.


0 i0.0 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 Henry-

0-- 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


CRITICAL SUBCOOLED MODELDisequilibrium 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

0.050.0 100.0

Time (s)150.0

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

subcooled Henry-Fauske model.


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

50.0 100.0 150.0Time (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


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 ".- - P= 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


CRITICAL TWO-PHASE MODEL Void-fraction Sensitivity

1.0

0.8

o 0.6

CuLL > 0.4

0.2

100.0 200.0 300.0Time (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

S30000X

S20000-

10000

0•


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

ETSI Minas - Universidad Politk•nica de Madrid *56

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


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.


Figure 4.2: Discharge pipe and test nozzle.

I I I

60


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


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?


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 '0.0 15.0

Pressure (MPa)

THYDE -P2 id Evaporaton Rate (kg/m3/s)

./.

0.0 5.0 10.0 (5.0 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


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 -1040s-

id

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.

io¾

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



* 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.

I 1 I

ETSI Minas - Universidad Politknica de Madrid72


- 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.


I III


- 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.

I I I



- 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).

I 1



* 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

I I I

ETSI Minas - Universidad Polit~cnica de Madrid80


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.

81

82

5.5e+06


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.


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



20.0 40.0 60.0 Time (s)

80.0 100.0

Figure 4.11: Static quality at bottom vessel. Test data. CFT-01.


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)


0.0020

0.0015 -

0.0010

.E

0.0005 L

0.0000 0..0

83


530.0

2

0�

2


520.0

510.0 -

500.0 0.0 20.0 40.0 60.0 80.0 100.0

Time (s)



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)


I I I

ETSI Minas - Universidad Politkcnica de Madrid84

1(


MARVIKEN CFT-11

6.0e+06Boundary 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)


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 60.0Time (s)


85

86 ES ia nvria oi~nc eMdi

MuRVIKEN CFT-11

0.80Boundary Conditions

0.60

0.40

05

0.20

A

0.0 20.0 40.0 60.0Time (s)



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)


I I I

0..

U,

0..

ETSI Minas - Universidad Politkcnica. de Madrid86



/ I

/1

�1

20.0 40.0 60.0Time (s)



0.40

0.30

0.20 . H

0.10 -

A flA0.0n 0.0 20.0 40.0 610.0Time (s)


530.0

2 520.0

E

E

> 500.0 -

490.0 0.0

>5

Cu

Cu

S =

87



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)


509.0


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)


I I I

88

x.)

2


MARVIKEN CFT-21

6.0e+06

5.0e+06

§ 4.0e+06

3.0e÷06

2.0e+06 0.0

Boundary Conditions

20.0 40.0Time (s)


60.0

89

i t I i


515.0

P

E

.7

E


510.0

505.0 -

T-VI

500.0

20.0 40.0 60.0495.0

0.0Time (s)



0.015

S0.010 0'

E

S0.005

0.000 0.0 20.0 40.0 60.0

Time (s)


I I



6.0e+06

2.0e+06

1.0e+06 0.0


20.0 40.0 60.0Time (s)


510.0

500.0 -


A

490.0 -

480.0 -

20.0 40.0 60.0Time (s)


5.0e+06

4.0e+06

3.0e+06

U,

E

E 0

470.0 0.0

91

i J t



0.80

0.60

CY

E

0.40

7I0.20 -

0.00 0.0 20.0 40.0 60.0

Time (s)


I I I

92 ETSI Minas - Universidad Politecnica de Madrid


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.

9393


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 80.0 100.0Time (s)


(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.

I I I

94ETSI Minas - Universidad Politkcnica, de Madrid94

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

100.0Time (s)

Figure 4.30: Mass flow at nozzle exit.

(BCM). CFT-06.

Comparison between CFM and non-CFM

5000.0

4000.0

3000.0

2000.00

Mo

1000.0

95Chapter 4.


MARVIKEN CFT-11

15000a--- 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 60.0Time (s)


(BCM). CFT-15.

I I I

96

10000

5000

0


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


(BCM). CFT-17.


MARVIKEN CFT-21

15000.0o-o CFM on. Junction non-smooth

- CFM off. Junction -Test data

i - CFM on. Pipe

!.i

20.0 40.0 60.0

Time (s)


(BCM). CFT-21.


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 60.0

97


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 60.0Time (s)


(BCM). CFT-24.

I I I

98


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


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

100.0Time (s)


06.

MARVIKEN CFT-11

- Junction model o--o Pipe model. Outlet nozzle

-Pipe model. Inlet nozzle

-I

A

20.0 40.0 60.0Time (s)


11.

I I I

100

0.30

0

.50.20

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 60.0Time (s)


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). CFT-

IL

.5

0.00 0 20.0

D 9 V e e eD

101

1I I i

0.0


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 60.0Time (s)


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

i0.0 a"

0.0 40.0 60.0Time (s)


24.

p .....


/16- rlý-/\,ý ý


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

0.010.0

220.0 40.0 60.0

Time (s)


homogeneous options. BCM-J. CFT-24.

,z,

.2

;L

10000.0

5000.0

0.0 40.0 60.0

00

4.2 Cu

0

103


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 k0.0 20.0 40.0

Time (s)60.0


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 60.0Time (s)


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

104

I I I


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.

I I 1



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 80.0 100.0Time (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


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)


CFT-06.

I I I


MARVIKEN CFT-06

0.08 ! I

0.06 -

20.0 40.0 60.0 80.0 Time (s)


CFT-06.

0

U 0.04 -

1

0.02

0.00 0.0 100.0

109

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)



I I I

110


MARVIKEN CFT-11

15000-- CFM on. mdc=0.85 bdc=0.95 -Test data

10000 -

00.0 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)


CFT-11.

:0

CO

5000

60.0

ill

4

I ! !

1


MARVIKEN CFT-11

E

540.0

530.0

520.0

510.0

-Saturation Temperature ____ Liquid Temperature

500.0

490.0 0 20.0 40.0 60.0.0

Time (s)



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 60.0Time (s)


CFT-15.

I II



MARVIKEN CFT-15

1.0Z

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


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)


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.


100.0

Discharge coefficient

I I I



MARVIKEN CFT-21

15000.0

I0

10000.0

5000.0

0.0 L0.0

-- CFM on. mdc=0.85 bdc=0.95 -Test data

20.0 40.0 Time (s)

60.0


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

60.0Time (s)

Figure 4.64:

CFT-21.


115


MARVIKEN CFT-21

-- Liquid Temperature

-Saturation TeTperature,

490.0 0.0 20.0 40.0 60.0

Time (s)



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)


CFT-24.

I I I

116

540.0

530.0

"- 520.0

S510.0

500.0


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)


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)



i q


MARVIKEN TESTS

1.0

0-0 cM o---octl 1 *--.cft15

0.8 -cft2l CRt24

M- Ct6

0.6

> 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.

I I I

118

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 80.0 100.0Time (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

0.00.0

Marviken Tests 119


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


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 60.0Time (s)


CFT-11.

I I I

Politkcnica de Madrid120

S-- -

ETSI Minas - Universidad


MARVIKEN CFT-15

15000.0

-Test data A-A Pipe mdc=1.0 '*e-o Pipe mdc=0.90

-1

40.0 60.0Time (s)


CFT-15.

MARVIKEN CFT-15

1.0

SPipe ndco.9o ,- Pipe mdc.1.0

20.0 40.0 Time (s)


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

121

ETSI Minas - Universidad Polit~cnica de Madrid

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)


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


CFT-17.

I I I

122

i


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 60.0Time (s)


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)


CFT-21.

123


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


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].



MARVIKEN CFT-06

- Test Data i *-- Nozzle as JUNCTION. MDC=-1.0 TDC=1 .i 5

1

20.0 40.0 60.0 80.0 100.0Time (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


(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


MARVIKEN CFT-21

0 L0.0

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)


(ICM). CFT-21.

MARVIKEN CFT-24RELAP5MQD3.2

_ 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


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

AAN0.0 20.0

129129 v

1U



____ 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


I I I

15.0

0o.o

0 a; 5.0

1

0.0 0.0

cc

130

I


15.0

,- 10.0

0

' 5.0

0.0


- 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


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


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



* 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.

I I I



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 60.0Time (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 60.0Time (s)


with dp = 0.14 and 0.01. CFT-21.

CE

0 n-

cc

LL

135


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 60.0Time (s)


with dp = 0.14 and 0.01. CFT-24.


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 40.0Time (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


J

I



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


with dp = 0.14 and 0.01. CFT-21.


1.0

0.8

50.6

0.2

0.0 0.0 20.0 40.0

Time (s)60.0


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.

I I I


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


"* 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 disequilibrium 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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[FOR-88] R. Pochard A. Forge, F. Steinhoff A. Porracchia (CEA). J. Miro,

H.G. Sonnenburg, and V. Teschendorff (GRS). Comparison of Thermal-Hydraulic Safety Codes for P WR Systems. Graham and

Trotman for the Commission of the European Communities, 1988.

[BAR-901 F. Barre and M. Bernard. The CATHARE code strategy and assessment. Nuclear Engineering and Design, 124:257-284, 1990.

[BES-90] D. Bestion. The physical closure laws in the CATHARE code.

Nuclear Engineering and Design, 124:229-245, 1990.

[TRA-97] B.E. Boyack. TRAC-PF1/MOD2 adequacy assessment closure

and special models. Technical Report LA-UR-97-232, LANL,

1997.

[SPI-901 M. Pellissier B. Spindler. Assessment of TRAC-PF1/MOD1 version 14.3 using separate effects critical flow and blowdown

experiments. Technical Report NUREG/IA-023, US-NRC, 1990.

[TBD-85b] B.L. Charboneau. Overview of TRAC-BD1/MOD1 assessment

studies. Technical Report NUREG/CR-4428, INEL, 1985.

[TRA-86] Safety Code Development Group. Energy Division. TRAC

PF1/MODI: An advanced best-estimate computer program for

pressurized water reactor thermal-hydraulic analysis. Technical

Report NUREG/CR-3858. LA-10157-MS, LANL, 1986.

tTRA-811 T.D. Knight et al. TRAC-PlA independent assessment

1979. Technical Report NUREG/CR-1652. LA-8477-MS, LASL

(LANL), 1981.

[TBD-85a] R.W. Shumway et al. TRAC-BD1/MOD1: An advanced best

estimate computer program for boiling water reactor transient

145

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analysis. volume 4: Developmental assessment. Technical Report

NUREG/CR-3633, INEL, 1985.

IREL-90] K.E. Carlson et al. RELAP5/MOD3.2 code manual. volume III:

Developmental assessment problems (draft). Technical Report

NUREG/CR-5535, INEL, 1990.

[TRA-931 J.W. Spore et al. TRAC-PF1/MOD2. volume I: Theory manual.

Technical Report LA-12031-M. NUREG/CR-5673, LANL, 1993.

[KAE-941 S.Y. Lee et al. Uncertainty quantification of RE

LAP5/MOD3/KAERI critical flow model using Marviken

experimental data. Technical Report KAERI/TR-437/94,

KAERI, 1994.

[KAE-95] T.S. Kwon et al. Quantification of realistic discharge coefficients

for the critical flow model of RELAP5/MOD3/KAERI. Journal

of Korean Nuclear Society, 27(5):701-709, 1995.

ICQS-97] C. Queral et al. Analysis and comparison of TRAC-BF1 and

RELAP5/MOD3.2 critical flow models (in spanish). In SNE,

editor, XXIII Reuni6n SNE, 1997.

[ELI-94] E. Elias and G. S. Lellouche. Two-phase critical flow. Int. J.

Multiphase Flow, 20:91-168, 1994.

[REL-98] The Thermal Hydraulics Group. RELAP5/MOD3 code manual.

volume VII: Summaries and reviews of independent code assess

ment reports. Technical Report NUREG/CR-5535 Volume VII.

Revision 1, SCIENTECH, Inc., 1998.

[JOH-96] Gary Johnsen. RELAP5 code development status. In CAMP

ESPANA, 1996.

[TRA-80] J.F. Jackson and J.C. Vigil. Comparison of TRAC calculations

with experimental data. Technical Report LA-UR-80-1267, LASL

(LANL), 1980.

[KIM-92] K. Kim and H.J.Kim. Assessment of RELAP5/MOD2 critical flow

with Marviken test 15 and 24. Technical Report NUREG/IA-086,

US-NRC, 1992.

[TRA-84] T.D. Knight. TRAC-PD2 independent assessment. Technical

Report NUREG/CR-3866. LA-10166-MS, LANL, 1984.

I I i

146

BIBLIOGRAPHY 147

[GOM-981

[MOR-981

[MAR-4-90]

[ROS-86J

ILAH-93]

[LEV-82]

[TRA-831

[TRA-961

ISTE-98]

ITRA-791

[REL-871

[WEA-89]

E. Valero M. G6mez and I.E. Parra. Analysis of the critical flow

model in TRAC-BF1. International agreement report, Depart

ment of Applied Mathematics and Statistics. Universidad Polit&c

nica de Madrid, 1998.

G.A. Mortensen. Critical flow model. RELAP5/MOD3.2.2Beta.

In CAMP. Idaho Falls, ID USA, 1998.

The Marviken Project. The Marviken Full-Scale Critical-Flow

Test, volume 4 of NUREG/CR-2671, chapter Description of the

Test Facility. EPRI-NP-2370, 1990.

0. Rosdahl and D. Caraher. Assessment of RELAP5/MOD2

against critical flow data from Marviken tests JIT-11 and CFT

21. Technical Report NUREG/IA-007. STUDSVIK/NP-86/99,

Swedish Nuclear Power Inspectorate, 1986.

Jr. R.T. Lahey and F.J. Moody. The Thermal-Hydraulics of a

Boiling Water Nuclear Reactor. American Nuclear Society, 1993.

Inc. S. Levy. Critical flow data review and analysis. Technical

Report EPRI-NP-2192, EPRI, 1982.

M.S. Sahota and J.F. Lime. TRAC-PF1 choked-flow model.

Technical Report LA-UR-82-1666, LANL, 1983.

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

rmd velocity 13,• .1_

Figure 2: Subromutie diwHOKEj fofi l 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


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

DI'>M -. SOR (MPrc +w on Ibroj 56

(SONIC2 a mi(SNL-P .PQL)j 6

SONIC .(SON1CI + SONIC2~ 63

Figue 6 Surouine GHO fowCompic (rontinued).

I I I

157

- FI ,oc'1.2"oRco--soKCI-" , '70 2-26 R S MATC H4 - 2"FICONS -SONs*C |

- .9g" Jc XA " "1) - "71

AT AT/tJCATS• '72

-j L NO !, F"/REVCýS 4


76

77

1990

MA)VO1G < ) 0. 10)- 7

Figre : SbrotinJCompue o Mlogc(otne)

I I I

158

159

00

1"~)

85

88

89


159

160

21236 CRSPUall BR=1 90a tbeswt

1990 820 'ý RF =JNadUA

,9

Var with T< > 93

NO 99DPDT = Cpd(T-'"sA) 94

cam table failure 1 10 junction vapor diens.cy 96

deriniuon ~1h and 10 NIL AvSrn tH 98

NO

Fiur 0:Sbruineins Jith K flow 10 gi (Icntinued).kE9

I I I


161

I P*

129

"132

] 133

134

135

136

137

138


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 (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


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


call sth2xl (fa(ndxstd),prop,err)


call std2xl (fa(ndxstd),properr)

$if def,nevvwtrp,3


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


call sth2x2 (fa(ndxstd).prop.err)


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


call sth2x6 (fa(ndxstd),prop,iq,err)


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)



$if def,nevvtrp,3


call stpu2p (fa(ndxstd),prop,36,1)

err = lptop(32)

else

call strpx (fa(ndxstd),prop,err)

endif

if (err) go to 1990

176


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


call sth2x2 (fa(ndxstd),prop,err)


call std2x2 (fa(ndxstd).prop,err)

Sif def,nevvtrp,3



err = lprop(32)

else


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




call std2x2 (fa(ndxstd),properr)

Sit def,nevvtrp,3

elseif (ntluid .eq. 12) then


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***


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


call sth2x2 (fa(ndxstd),properr)



$if defnenvtrp,3



err = lprop(32)

else


endif

if (err) go to 1990


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= TTTTTTT1 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.


call psatpd (tmaxl,pjun,dpdt,2,err)


call pstpd2 (tmaxl,pjun,dpdt,2,err)

Sif def,newvtrp,5


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.


call sth2xl (fa(ndxstd),properr)


call std2xl (fa(ndxstd),prop,err)

$if def,nevvtrp,3


call stpu2t (fa(ndxstd),prop,36.1)

err = lprop(32)

else

call strtx (fa(ndxstd),prop,err)

endif

if (err) go to 252


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




call std2x3 (fa(ndxstd),prop,iq,err)

$if def,newwtrp,4


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.


call sth2xO (tgpsatt,err)

else if (nfluid .eq. 2 ) then

call std2xO (tg,psatt,err)

$if def,newvtrp,4


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


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




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 NNNNBBM U NN NNBU NNENIEnWBNNNNNNNNNU -h

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 ±± i±±± I II I II II ±1L1 L ±TTTTTlrTT7TTTTTTT1TTTTTTTrTTTTTT1TTTTTTTTTTTT

I I I

185

c90 cqs call steam tables




call std2z6 (fa(ndxstd),prop,iq,err)

$if def,newvtrp,4


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


cIO0 cqs saturated liquid . call steam tables


call sth2xl (fa(ndxstd).prop,err)


call std2xl (fa(ndxstd)tproperr)

Sif def,newvtrp,3


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


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( 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', 2z.'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 iz I ITTTTTTTTTTTTTTTTTTTTTTTTTTTTTT

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( 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 (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( 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 v by 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


9. SPONSORING ORGANIZATION - NAP AND ADDRESS (NR, ta "Smee as e•bow o Ic,,,c, provide ARC Dvi, orf O •a.g•n U.SL -uw•- -=-E-"WY C4VIVSSII-

Division 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 i orpsiura w" ee& as eWierrewc In ioceIn ie repot) AvALAB mL sTAedNI

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