NUREG/IA-0401 

International 

Agreement Report

Assessment of Two-Phase Critical Flow Models 

Performance in RELAP5 and TRACE Against 

Marviken Critical Flow Tests

 

Prepared by:

Lukasz Sokolowski

 Tomasz Kozlowski

 

A. Calvo, NRC Project Manager

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

Manuscript Completed: June 2011

Date Published: February 2012

Prepared as part of 

The Agreement on Research Participation and Technical Exchange

Under the Thermal-Hydraulic Code Applications and Maintenance Program (CAMP)

Published by

U.S. Nuclear Regulatory Commission
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NUREG/IA-0401 

International 

Agreement Report

Assessment of Two-Phase Critical Flow Models 

Performance in RELAP5 and TRACE Against 

Marviken Critical Flow Tests

 

Prepared by:

Lukasz Sokolowski

 Tomasz Kozlowski

 

A. Calvo, NRC Project Manager

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

Manuscript Completed: June 2011

Date Published: February 2012

Prepared as part of 

The Agreement on Research Participation and Technical Exchange

Under the Thermal-Hydraulic Code Applications and Maintenance Program (CAMP)

Published by

U.S. Nuclear Regulatory Commission

iii

Abstract

The project aims to (1) conduct the validation of thermal-hydraulics codes RELAP5

Mod 3.3 Patch 03 and TRACE v5.0 Patch 2 on the critical flow experiment giving 

comprehensive knowledge about the codes’ behavior; (2) provide information 

about sensitivity impact of user-defined variables of critical two-phase models 

implemented into the codes; (3) and to obtain statistical data for variety of lengthto-diameter L/D ratios of pipe. The experimental set-up consisted of vessel, 

discharge pipe and the group of test nozzles. The vessel was 24.5 m high, with 

internal average diameter of 5.2 m. The discharge pipe was 6.308 m long with 

internal diameter of 0.72 m. A total number of nine nozzles was used in the 

experiment and is characterized by L/D ratios of 0.3, 1.0, 1.5, 1.7, 3.0, 3.1, 3.6 and 

3.7. The main conclusions of the studies are that for Marviken Critical Flow Test 

(CFT) (i) RELAP5 Henry-Fauske model gives more accurate results than RELAP5 

Ransom-Trapp (R-T) model; (ii) TRACE R-T gives better results than RELAP5 R-T; 

and (iii) the dependence between length-to-diameter L/D ratio of the nozzle and the 

calculation’s accuracy has not been observed.

v

Table of Contents

Abstract................................................................................................................... iii

Table of Contents.....................................................................................................v

List of Figures......................................................................................................... vii

Executive Summary ................................................................................................ix

Introduction ............................................................................................................. 1

1. Two-Phase Critical Models .............................................................................. 3

1.1. Critical Flow .............................................................................................. 3

1.2. Two-Phase Critical Models ....................................................................... 6

1.3. Henry-Fauske Theoretical Background..................................................... 9

1.4. Ransom-Trapp Theoretical Background ................................................. 11

2. Marviken CFT Description.............................................................................. 13

2.1. Historical Background............................................................................. 13

2.2. Description of the Test Facility................................................................ 13

2.2.1. Vessel.............................................................................................. 16

2.2.2. Discharge Pipe ................................................................................ 17

2.2.3. Nozzles............................................................................................ 18

2.3. Experiment.............................................................................................. 20

2.4. Measurement System............................................................................. 20

3. Modeling & Simulation ................................................................................... 23

3.1. Modeling Approach................................................................................. 23

3.2. Nodalization ............................................................................................ 23

3.3. Initial Conditions ..................................................................................... 27

3.4. Numerical Solution Accuracy Quantification ........................................... 29
vi

4. Validation and Results ................................................................................... 31

4.1. Background............................................................................................. 31

4.2. Sensitivity Studies................................................................................... 31

4.2.1. Initial Conditions (RELAP5) ............................................................. 31

4.2.2. Discharge Pipe Length .................................................................... 32

4.2.3. Junction Control Flag....................................................................... 33

4.2.4. Loss Coefficient ............................................................................... 34

4.2.5. Time Dependent Volume (RELAP5)................................................ 34

4.3. Henry-Fauske and Ransom-Trapp Performance .................................... 35

4.3.1. Code Accuracy ................................................................................ 35

4.3.2. Quantitative Code Assessment........................................................ 39

5. Discussion and Conclusions .......................................................................... 43

6. References..................................................................................................... 44

7. Appendix A: Summary of the Initial and Final Conditions .............................A-1

8. Appendix B: Data Channel Outputs Used in the Computational Model ........B-1

9. Appendix C: Flow Rate Comparisons ...........................................................C-1
vii

List of Figures

Figure 1.1 Critical pressure and mass flow velocity behaviors [1]........................... 4

Figure 1.2 Classification of two-phase critical models............................................. 8

Figure 1.3 Henry-Fauske and Ransom-Trapp models’ basic equations.................. 9

Figure 2.1 Outline diagram of the Marviken facility ............................................... 15

Figure 2.2 Vessel outline....................................................................................... 16

Figure 2.3 Discharge pipe ..................................................................................... 17

Figure 2.4 Dimensions of the test nozzle used for tests 1-12 [12]......................... 19

Figure 2.5 Dimensions of the test nozzle used for tests 13-14 [12]....................... 19

Figure 2.6 Dimensions of the test nozzle used for tests 15-27 [12]....................... 20

Figure 2.7 Locations of temperature measurements in the pressure vessel [11] .. 21

Figure 2.8 Locations of measurements in the discharge pipe [15] ........................ 22

Figure 3.1 Visualization of the final nodalization used in the calculations; RELAP5 

(left) and TRACE (right) ........................................................................................ 24

Figure 3.2 Nodalization approaches: fine model (left) and coarse model (right) ... 25

Figure 3.3 Comparison of the different approaches’ performance ........................ 26

Figure 3.4 Nodalization of nozzles used in the computational model.................... 27

Figure 3.5 Vessel zones denotation and arrangement.......................................... 28

Figure 3.6 Vessel matrixes.................................................................................... 29

Figure 4.1 Distinctions in usage of different initial condition types ........................ 32

Figure 4.2 Different approaches of the discharge pipe modeling .......................... 33

Figure 4.3 Different choking options...................................................................... 34

Figure 4.4 Code accuracy, RELAP5 Henry-Fauske.............................................. 36

Figure 4.5 Code accuracy, RELAP5 Ransom-Trapp............................................. 37
viii

Figure 4.6 Code accuracy, TRACE Ransom-Trapp .............................................. 38

Figure 4.7 Relative L1 norm versus Marviken CFT Test no .................................. 40

Figure 4.8 Relative L1 norm versus Marviken CFT L/D ratio ................................ 40

Figure 4.9 Relative L2 norm versus Marviken CFT Test no .................................. 41

Figure 4.10 Relative L2 norm versus Marviken CFT L/D ratio .............................. 41
ix

Executive Summary

The up-to-date thermal-hydraulics models and correlations are of the great 

importance in computational code environment. Thus, the validation of the systems 

codes is an important issue. The purpose of the project was to perform a 

comprehensive Marviken CFT investigation by a comparison between RELAP5

Mod 3.3 Patch 03 and TRACE v5.0 Patch 2 model data and experimental data. 

The main conclusions of the studies are that for Marviken CFT experiment: 

• RELAP5 Henry-Fauske (RELAP H-F) model gives more accurate results than 

RELAP5 Ransom-Trapp (RELAP5 R-T) model; 

• TRACE R-T gives better results than RELAP5 R-T;

• The dependence between length-to-diameter L/D ratio of the nozzle and the 

calculation’s accuracy has not been observed.

1

Introduction

The aspects of safety are important in nuclear power plant maintenance and 

employ significant resources of engineer activity and wide varieties of tools. The 

thermal-hydraulics simulation codes play significant role in this work. They are 

basic tools for evaluation of safety aspects of nuclear reactors. It is crucial to 

ensure code’s computational engine uses up-to-date correlations, definitions, and 

models. Thus, the RELAP5 Mod 3.3 Patch 03 and TRACE v5.0 Patch 2 validation

on the Marviken Critical Flow Tests (CFT) experiment has been conducted.

The project aims to (1) conduct the validation of thermal-hydraulics codes RELAP5 

and TRACE on the critical flow experiment giving comprehensive knowledge about 

the codes’ behavior; (2) provide information about sensitivity impact of user-defined 

variables of critical two-phase models implemented into the codes; (3) and to 

obtain statistical data for variety of length-to-diameter L/D ratios of pipe.

The Marviken CFT experiment has been one of the biggest facilities in the world 

intended to test blowdown phenomena. It has been conducted in Sweden by an 

international project with participation from the Netherlands, Germany, France, 

USA, Denmark, Finland, Norway and Sweden. The experiment investigated the 

critical flow phenomena as a dependence on the discharge nozzle length-todiameter ratio. The experimental set-up consisted of vessel, discharge pipe and 

the group of test nozzles. The vessel was 24.55 m high, with internal average 

diameter of 5.2 m. The discharge pipe was 6.3 m long with internal diameter of 

0.72 m. The total number of nine nozzles was used in the experiment and is 

characterized by L/D ratios of 0.3, 1.0, 1.5, 1.7, 3.0, 3.1, 3.6 and 3.7. 

The experiment was initiated when the pressure in the vessel was exceeding the 

rupture disc bursting pressure and the rupture disc was released. The bursting 

pressure was generally about 5 MPa but about 4 MPa for Test 5. The single test 

was finished when the steam reached the discharge pipe inlet or when the ball 

valve was closed. The data used to obtain a computational model, such as initial 

level of water, pressure, temperature, steam qualities, were obtained from the 

experimental data collected by measurement devices. Within the Marviken CFT

experiment the total numbers of 27 experiments were conducted for different initial 

conditions and discharge nozzles.

As a part of a computational model development the following steps were 

undertaken. The components geometries were nodalized in order to match the 

RELAP5 and TRACE nodalization requirements with simplifying assumptions. The 

initial conditions were collected from the measurement data and implemented into 

the model input. Finally, the model’s settings were adjusted.

The computational model provides the same information as the measurement data 

from the experiment. Moreover, the combination of models and assumptions can 
2

be examined, e.g. comparison of critical flow models of Henry-Fauske and 

Ransom-Trapp. The sensitivity studies of these two models have been conducted.

The results have shown that the code’s critical two-phase flow calculations’ 

accuracy depends primarily on nodalization approximation and the type of a 

choking model. It can be stated that for Marviken CFT the Henry-Fauske model 

gives more accurate results compare to Ransom-Trapp model (both implemented 

in RELAP5 and TRACE) within the whole range of examined nozzles. The project 

results provide essential knowledge about the code behavior modeling blowdown 

phenomena, which is important in evaluation of the Loss of Coolant Accidents 

(LOCA).

The work was performed in the framework of power uprate project supported by 

the Swedish Radiation Safety Authority (SSM). The ultimate goal of this project is 

to perform independent analyses of some limiting transients associated to the 

power uprates. The present validation study is a Swedish contribution to the 

international Code Assessment and Maintenance Program (CAMP).
3

1. Two-Phase Critical Models

1.1.

The knowledge about the phenomenon of critical flow is important in evaluation of 

Loss of Coolant Accident (LOCA). Thus, it is important to know basic properties of 

a flow as a function of time, i.e. density, velocity of vapor and liquid, type of a flow.

Critical Flow

The critical flow occurs when speed of flow equals speed of sound and is defined 

in terms of Mach number:

c

U M = , (1.1)

where 

U is the local speed of medium, 

c is local speed of sound. 

For different nature of the flow one will get:

 M > 1 supersonic flow,

 M = 1 critical flow,

 M < 1 subcritical flow.

The critical flow is also called as a choking flow. The fundamental reason that 

choking occurs is that acoustic signal can no longer propagate upstream. Simply 

put, the speed of sound is the maximum speed of the compressible fluid when it 

flows from the region of higher pressure to region of lower pressure.

The phenomenon of critical flow can be visualized in the following graphs. The 

discharge from the tank is presented where the po and pR are the pressures inside 

the tank and at the end of the pipe, respectively.
4

Figure 1.1 Critical pressure and mass flow velocity behaviors [1]

The critical mass flow rate depends only on stagnation parameters. As can be 

seen from the picture above, when downstream pressure pR decreases the 

medium velocity w increases. However, the changes take place up to a point when 

the increasing in downstream pressure does not affect the process behavior. It can 

be seen in Fig. 1.1 that the downstream pressures pR,3, pR,4, and pR,5 have identical 

impact on velocity of medium. This situation occurs since the choking occurs above 

pressure pR,3.

The formula for single-phase critical mass flow rate can be derived from 

combination of the following equations [2]:

o i i U

+ = 2

2

(energy equation), (1.2)

κ ρ

κ

κ

κ p i RT

1 − 1 = − = (1.3)

(gas enthalpy assuming isentropic transition),
5

1 1

2

− = κ − ρ κ

κ c RT p (assuming that RT p p c κ

ρ

κ

ρ

κ = = ∂

∂ = ), (1.4)

where:

U – local velocity of medium, 

i – downstream enthalpy, 

io – stagnation enthalpy, 

κ – Poisson’s ratio, 

p – pressure, 

ρ – density, 

R – gas constant, 

T – temperature, 

c – speed of sound.

In Eq. (1.2) symbol “0” refers to condition inside a tank or stagnation conditions. By

combining Eqs. (1.2), (1.3) and (1.4) and assuming that the stagnation velocity is

negligible and Mach number is 1 one will get:

The symbol of “*” refers to critical conditions. Assuming an isentropic process:

const

T

p =

−

κ

κ 1

, (1.6)

const

T = κ −1 ρ

(1.7)

and employing ideal gas relations

1

0 1

2 −





 





+ = κ

κ

p κ

p* , (1.8)

1

2

0

+ = κ

c c * . (1.5)
6

1

1

0 1

2 −





 





+ = κ

ρ κ

ρ * , (1.9)

the critical flow rate will be as follows:

1

1

0

0

1

2 −

+





 





+ = = κ

κ

κ

κ

ρ T R

p W* *

U*A* A* , (1.10)

where:

W – mass flow,

A – nozzle area,

To – stagnation temperature.

To state whether the single phase flow is at critical condition is an obvious task. To 

do the same with two-phase flow is much more complicated. The main reasons of 

that state are [1]:

 Two-phase (t-p) critical flow cannot be uniquely determined: there are two 

existing phases so that means there might be two speeds of sound – for 

liquid and for vapor,

 The complicated character of t-p flow, e.g. different flow regimes exhibited 

make the calculations complicated and time-consuming.

To overcome mentioned obstacles some modeling approximations need to be 

employed.

1.2.

Starting from the 1947 (the first t-p critical model, proposed by J. G. Burnell) 

dozens of models describing critical t-p flow have been published. Critical flow 

models can be divided and classified with respect to:

Two-Phase Critical Models

 Model derivation technique,

 Model formulation,

 Undertaken assumptions,

 Output.

The first classification takes into account model’s derivation:
7

 Theoretical background – employ thermodynamic equations of mass, 

momentum, and energy for both phase (liquid and vapor) separately or for 

homogeneous mixture,

 No theoretical background – semi-empirical formulas, linking critical flow 

rate to thermodynamic variables; dimensionless empirical coefficients 

adopted in order to fit the experimental data.

The last subcategory is of the interest for this project since the state-of-the-art in 

critical flow modeling is represented by models with no theoretical background as 

Henry-Fauske and Ransom-Trapp model. These two are the most widespread twophase critical models.

To state that H-F and R-T do not have any theoretical background would be an 

oversimplification, see for instance the theory manuals of RELAP5 and TRACE, 

also paragraphs 1.3 and 1.4 below. So consider to reformulate.

The model formulation gives information about, e.g. number of conservation 

equation, i.e. of mass, momentum, energy, about number of state and/or 

transformation equations, constitutive equations, number of analytical conditions, 

and necessary semi-empirical parameters. 

Undertaken assumptions provide information about transient phenomena, 

multidimensional-effect, non-homogeneity in pressure vessel, heat exchange with 

surrounding, pipes, orifices, etc.

Output subcategory is related to model applicability. Depends on parameters of 

interest, the different diagrams, thermodynamic variables, or correlations might be 

needed.

The main classification of two-phase critical flow models is presented in Fig. 1.2 (is 

this a novel figure or does it come from any reference, in the latter case please 

provide actual reference). The main divisions are models which assume 

thermodynamic equilibrium through the expansion line and models which assume 

non-thermodynamic equilibrium. The first mentioned category can be divided into 

homogeneous and non-homogeneous models. The non-equilibrium theory can be 

divided into “frozen” theories and non-homogeneous models.

“Frozen” models employ so called slip ratio. Slip ratio k provides information about 

the relative velocity between vapor and liquid. The k might have value of zero, 

constant, and non-constant through the expansion. 

Homogeneous models assume that the liquid and vapor are mixed together and 

can be treated as a mixture. In this category there are Homogeneous Equilibrium 

Model (HEM) and Babitsky model. Non-homogeneous models assume that the 

vapor and liquid exist as separated phases. In this subcategory the value of k

changes throughout the expansion line. Moody, Fauske and Levy models are given 

as examples. 
8

Figure 1.2 Classification of two-phase critical models

The non-equilibrium models assumed that between two-phases, vapor and liquid, 

there are no presence of:

 Thermal equilibrium,

 Dynamic (mechanical) equilibrium,

 Chemical equilibrium.

Thermal equilibrium means that both phases coexist at the same saturation 

conditions.

The dynamic equilibrium means that both phases are well-mixed, with equal 

velocity.

The chemical equilibrium means that both phases’ densities do not change 

throughout the expansion.

The first category in non-equilibrium models are frozen theories with constant 

values k. Frozen means that there is no heat or mass transfer between the faces. 

Constant k denotes that there are no velocity changes through the expansion line. 

In this category there are models as e.g. Burnell, Zaloudek and D’Arcy.

The second subcategory of non-equilibrium models are non-homogeneous models

with slip ratio different than 1. These models are the most complicated than all 

mentioned models. Within the last decades many models have been derived. 

However, the most important ones are the two models, Henry-Fauske and Ransom 

Trapp. It is worth to note that these two can be formulated as the simplest 

subcategory, in frozen models. The visualization of this classification is presented 

in the Fig. 1.3.
9

The first derivation of Henry-Fauske model is from 1970. This a non-homogeneous 

type that means there is no thermal, dynamic, or chemical equilibrium between 

phases. According to [4] this model type is suitable for length-to-diameter ratio 

L/D ≤ 3 to 12.

After developing this model, Henry and Fauske decided to release modified version 

of it. The frozen model was developed. The aim of the work was to provide ability 

of predicting two-phase critical flow sharing the knowledge only about the 

stagnation conditions and accounting for the non-equilibrium nature of the flow [4]. 

Another reason was that this model is simpler than full non-equilibrium one. The 

advantages of the simpler version is less calculations’ time-consuming and 

computer storage. It is applicable only to long pipes, with L/D > 12.

The first Ransom-Trapp frozen model was released in 1978. The second version 

was the full non-equilibrium model published in 1982. The main goal of the work 

was to create a model having ability to predict critical flow rates with less sensitivity

to the time step and the correct chocked flow velocity [5].

Figure 1.3 Henry-Fauske and Ransom-Trapp models’ basic equations

The graph shows that to formulate the model, different equations and assumptions

have been used. 

1.3.

By combination of one-dimensional momentum equation (1.11) and the mass flux 

for high velocities (1.12), [6],

Henry-Fauske Theoretical Background
10

− AdP = d(mvuv + ml

ul) + dF , (1.11)

[ ( ) ]

t

v l

dP

d xu x u G 









 + − = − 1 , (1.12)

the choking criterion will be obtained as

( ) t s

v l

v l

c

P

x

v v

P

v

x

P

v

x

G













∂

∂

+ − ∂

∂

+ − ∂

∂

− =

(1 )

2 1

(1.13)

where 

G – mass flow rate, 

x – quality, 

vv – vapor velocity, 

vl – liquid velocity, 

P – pressure, 

A – cross section, 

mv,l – mass of vapor and liquid, 

u – velocity of vapor and liquid, 

F – wall shear stress.

Assuming that:

 Polytrophic expansion process affects the critical flow rate less than 1%,

 dvg/dp determined from saturation properties (n ~ 1) [4],

equation (1.13) simplifies into

e

g E

cHE

c

dP

dN

v x

G

N G

























−

=2 1 , (1.14)
11

where GcHE is the critical flow rate resulting from homogeneous equilibrium theory 

and N is a non-equilibrium parameter given by

( ) E g

f

x v

v

N − α = 1 , (1.15)

where α is the void fraction.

As can be seen in Eq. (1.14), the total two-phase critical mass flow rate definition is 

based on equilibrium theory.

1.4.

Ransom-Trapp’s two-fluid field under thermal equilibrium is described by the:

Ransom-Trapp Theoretical Background

 Mixture continuity equation,

( ) = 0

∂

∂

+

∂

∂ V

t x m

m ρ ρ , (1.16)

 Two-phase momentum equations,

1 = 0 



 





∂

∂ − ∂

∂ − ∂

∂

+

∂

∂

+ − ∂

∂  +



 





∂

∂

+

∂

∂

x

V

V

t

V

x

V

V

t

V

C

x x

V

V

t

V

g

g l

l

g

m

g

g

g

g α α ρ ρ αρ α ( ) , (1.17)

1 0

1 1

 =



 





∂

∂ − ∂∂ − ∂

∂

+

∂

∂

+ −

∂

∂  + −



 





∂

∂

+

∂

∂ −

x

V

V

t

V

x

V

V

t

V

C

x

p

x

V

V

t

V

g

l

l g

g

l

m

l

l l

α α ρ

α ρ α

( )

( ) ( ) (1.18)

 Mixture energy equation,

( ) [ + 1− ] = 0

∂

∂

+

∂

∂ m m g g g l l l V s V s

x

s

t

ρ αρ ( α)ρ , (1.19)

 Inert gas continuity equation,

( ) ( ) = 0

∂

∂

+

∂

∂ a aVg t x

αρ αρ , (1.20)

where:

ρ – density,

t – time,
12

V – velocity,

α – gas volume fraction,

C – virtual mass coefficient,

s – entropy;

subscripts:

m – mixture,

g – gas,

l – liquid,

α – noncondensable gas.

The Dalton’s law is assumed (total pressure equals sum of partial pressures). The 

matrix representation of these equations is:

( ) ( ) = 0

∂

∂

+

∂

∂

x

U B U

t

U A U , (1.21)

where U consists of pv, α, Vg, Vl, and pa. To solve the equation (1.21) the roots of 

the fifth-order polynomial needs to be obtained:

determinant(Aλ − B) = 0 . (1.22) 

Critical flow takes place if the maximum value of a characteristic root λi,re,max is zero.
13

2. Marviken CFT Description

2.1.

Marviken Critical Flow Tests experiment was conducted in 1978-1979 at the

Marviken Power Station facility located around 100 km south-west of Stockholm.

Historical Background

It was supposed to be the fourth Swedish reactor and was called R4 or Eva. It was 

designed as a heavy water moderated reactor and intended to have power of 

130 MWe. However, due to technical and economic reasons it has been never 

used. The total cost of installation was 500 mln SEK. Today the installation works 

as an oil-fired power station.

It was decided that Marviken facility would be an experimental facility. Since 1972 

to 1982 four series of experiment at Marviken facility was performed:

 Series I (green reports): The study of the pressure and temperature 

conditions during blowdown in pressure suppression containment. Following 

issues were investigated (16 experiments): 

o The effect of the energy content in the reactor and the steam in the 

reactor pressure vessel,

o The location and size of the depth of vent pump submergence in the 

condensation pool,

 Series II (blue reports): The study of the dynamic process in the blowdown 

lines and the condensation pool (9 experiments),

 Series III (Critical Flow Test, yellow reports): The aim of this series was to 

determine the critical mass flow rate of a two-phase mixture of steam and 

hot water from large diameter pipe (27 experiments),

 Series IV (Jet Impingement Test, grey reports): The investigation of the 

effect of large-scale two-face phenomena in the containment (12 

experiments).

The validation of RELAP5 code was performed based on Critical Flow Test (Series 

III). The Marviken Critical Flow Test (CFT) was conducted between January 1978 

and May 1979. The experiment was performed by the international team from the 

Netherlands, Germany, France, USA, Denmark, Finland, Norway, and Sweden.

2.2.

The facility consisted of several components which are [11]:

Description of the Test Facility
14

 The pressure vessel with net volume 425 m3, maximum design pressure 

5.75 MPa and maximum design temperature 272°C,

 The discharge pipe consisting of the ball valve and pipe spools which house 

the test nozzle upstream instrumentation,

 The nozzles and rupture disc assemblies: a set of nozzles of specified 

lengths and diameters to which the rupture disc assemblies were attached,

 The containment and exhaust pipes consisting of the drywell with net 

volume 1934 m3

, the wetwell with net volume 2144 m3, the fuel element 

transport hall with net volume 303 m3, the ground level 3.2 m diameter and 

the upper 0.4 m diameter exhaust pipe.

The outline of the facility is presented in Fig. 2.1. 

In order to satisfy the experiment criteria some components inside the reactor 

vessel were removed while the other components were installed, e.g. 

measurement devices. Many components were removed from the vessel so that 

the flow rate was uninterrupted and the measurement of vessel net volume was

simplified. However, some components were left but only if it was judged that they 

did not affect the experiment results significantly.
15

Figure 2.1 Outline diagram of the Marviken facility
16

2.2.1. Vessel

The pressure vessel was fastened and fully insulated using glass wool so that 

minimal heat transfer loss occurred. The vessel was of 24.55 m high and about

5.2 m inner diameter. The vessel was characterized by the elevation parameter

which was 0 for the lowest point of the vessel and 24.55 m for the highest point. At 

the top of the vessel the cupola neck was located.

The vessel was made of low alloy steel, Swedish standard: DE-631A with a 76 mm 

wall thickness in the cylindrical part and a wall thickness of 40 and 65 mm in the 

domes.

Although most of the vessel internals were removed some components remained 

because of the difficulties in removing it. Some components were installed 

deliberately and had special function. Among these components are vortex 

mitigators, the primary pipes and instrumentation lines.

The vessel is visualized in the Fig. 2.2.

Figure 2.2 Vessel outline
17

2.2.2. Discharge Pipe

The discharge pipe connected the vessel and the nozzle. The total length of 

discharge pipe was 6308 mm including part in the vessel. The average inlet 

diameter was 752 mm. The discharge pipe can be seen in Fig. 2.3.

Figure 2.3 Discharge pipe

The discharge pipe was supported during the tests so that the oscillations did not 

exceed critical value. Inside the discharge pipe three instrumentation rings were 

placed. The measurement devices responsible for collecting information about 

pressure and temperature were located in the instrumentation ring.

The pipe was made of stainless steel, SIS 1330, Swedish Standard. The inlet had

a wall thickness of 4 mm.
18

The ball valve was located in the discharge pipe. It could be closed within 10 

seconds during the test. 

2.2.3. Nozzles

The total numbers of nine nozzles were used in the experiment. Table 2.1 presents 

basic dimensions of the nozzles.

The nozzles’ parameters and dimensions were chosen to provide full critical flow 

data in a wide spectrum of length-to-diameter ratio L/D. The maximum nozzle 

diameter was 509 mm and bigger diameter was not possible to test due to 

equipment constraint.

Table 2.1 Test nozzles – basic dimensions and conditions

Nozzle 

type

D L L/D L1 L2 L3 L4 R Used in 

tests

no mm mm mm mm mm mm mm no

1 200 590 3,0 0 100 100 100 100 13, 14

2 300 290 1,0 55 150 150 150 150 6, 7

3 300 511 1.7 0 150 150 150 150 25, 26

4 300 895 3,0 55 150 150 150 150 1, 2, 12

5 300 111

6

3.7 0 150 150 150 150 17, 18, 19

6 500 166 0.3 0 225 225 250 250 23, 24

7 500 730 1.5 0 225 225 250 250 20, 21, 22,

27

8 500 180

9

3.6 0 181 156 241 250 15, 16

9 509 158

9

3.1 55 156 225 241 250 3, 4, 5, 8, 

9, 10, 11

For the first 12 tests the nozzle with flared outlet were used, as shown in Fig. 2.4.

Later it was decided to that the nozzles should have constant diameter test section 

which would exhaust a free expansion jet into the containment [12].

Nozzle used for test 13 and 14 is presented in Fig. 2.5. Nozzle geometry used for 

tests 15 onwards is visualized in Fig. 2.6.
19

Figure 2.4 Dimensions of the test nozzle used for tests 1-12 [12]

Figure 2.5 Dimensions of the test nozzle used for tests 13-14 [12]
20

Figure 2.6 Dimensions of the test nozzle used for tests 15-27 [12]

2.3.

Within the Marviken CFT the total number of 27 tests was performed during which 

the nozzles with different length-to-diameter L/D ratio were examining. Tests were 

conducted under different conditions in the vessel. Appendix A presents summary 

of initial and final conditions in the vessel.

Experiment

The average pressure in the vessel was about 5 MPa, only Test 5 was performed 

at 4 MPa. The water level varied from 16.5 to about 20 m.

The test period varied from 42 sec for Test 3 and to around 148 sec for Test 

13.The test was finished when the steam reached the discharge pipe or the ball 

valve was closed.

2.4.

Fig. 2.7 and 2.8 show locations of measurement devices used during the 

experiment. 

Measurement System

For the modeling purposes, the vessel, data channel number of 101 and 104 were 

for pressure measurement, and 401, 402, 501 to 520 were used for temperature 

measurement.

In the discharge pipe, data channel numbers from 107 to 109 were used for 

pressure measurement and 31, 37 to 39 for temperature measurement.
21

Figure 2.7 Locations of temperature measurements in the pressure vessel [11]
22

Figure 2.8 Locations of measurements in the discharge pipe [15]
23

3. Modeling & Simulation

3.1.

Modeling of Marviken CFT experiment was conducted in the following steps: 

nodalization, adjusting the initial conditions and formulating the code input files.

Modeling Approach

The RELAP5 Mod 3.3 Patch 03 and TRACE v.50 Patch2 computational model was 

created based on the Marviken facility description [11], [12], [16]. The model 

nodalization was adjusted to satisfy the condition that the calculation should not be 

time-consuming and should be possibility to run the calculations on commonly 

available personal computers. The guides provided by the code’s developer were 

followed [9], [20], [21].

The default values (1.0) of choking model input parameters were used for all 

choking models: subcooled, two-phase, and superheated discharge coefficients for 

R-T and discharge coefficient and thermal nonequilibrium constant for H-F, are 

treated as important model characteristics.

3.2.

The RELAP5 computational model was created based on the Marviken facility 

description. TRACE model was based on the RELAP5 model to make both models 

consistent with each other. The RELAP5 computational model consisted of two 

pipe components, two single junctions, and time dependent volume. The TRACE 

computational model consisted of two pipe components and a brake. The first pipe 

component modeled the vessel. It consisted of 21 volumes. The first two volumes 

simulate the cupola, cupola neck, and the vessel top. The next 18 volumes are the 

same and have the length of 967 mm and diameter of 5.2 m. The last volume is 

simulates the vessel bottom.

Nodalization

The second pipe component was a model of discharge pipe and nozzle. This 

component consisted of 15 volumes. The first 13 volumes correspond to the 

discharge pipe and the last 2 volumes correspond to the nozzle. The discharge 

pipe and nozzle nodalization was constant for all simulations. The nodalization of 

the computational model is shown in Fig. 3.1.
24

Figure 3.1 Visualization of the final nodalization used in the calculations; RELAP5 (left) and TRACE 

(right)

The RELAP5 time dependent volume and TRACE break component is 1 m long 

and the flow area was equal to the area of the nozzle.

The nodalization process is a complex task in which user experience is very 

essential. The example approaches that were tested are shown in Fig. 3.2.
25

Figure 3.2 Nodalization approaches: fine model (left) and coarse model (right)

The first nodalization was an ideal geometry taken from the Marviken facility 

description [12]. It was divided into six zones, which were then subjected to 

simplification. During this process the length and the volume of the vessel was 

conserved. The final nodalization is the final one which was used for calculations.

The number of cells can be reduced without significantly changing the performance 

of the model and simulation. The advantage is that the calculation time is much 

lower for models with smaller cell number. However, it should be kept in mind that 

sometimes when the number of cells is too low, the model’s accuracy becomes 

unacceptable. The example of the fine and coarse model performance is shown in 

Fig. 3.3.
26

Figure 3.3 Comparison of the different approaches’ performance

Fine course model gives quantitatively the same result, therefore course model 

was deemed acceptable.

The discharge pipe nozzle component consists of 15 cells. The two last cells are 

intended to simulate the nozzle. The discharge pipe was the same for the all 

experiments. The full abrupt area change model was applied on junction no. 7 and 

10 in discharge pipe, to take into account the abrupt in the location of 

instrumentation ring II and abrupt in the location of ball valve, respectively. No 

further nodalization studies were done for the discharge pipe.

The visualization of the discharge pipe and nozzle components nodalization is 

shown in Fig. 3.4.
27

Figure 3.4 Nodalization of nozzles used in the computational model

3.3.

Data necessary to determine initial conditions in the model was obtained from 

measurement. Appendix B presents data channels used in the computational 

model initial conditions.

Initial Conditions

The negative value of elevation level denotes that the measurement device was 

located in the discharge pipe.

As can be seen in the Appendix A, the different initial conditions were used for 

each experiment. The saturated zone, transition zone and subcooled zone in the 

vessel can be identified.

Fig. 3.5 shows vessel zones denotation and arrangement.
28

Figure 3.5 Vessel zones denotation and arrangement

The shape and the range of different zones were different for each experiment. 

Thus, the experiments were categorized in three categories depend on the type of 

initial conditions in the vessel.

Initial conditions category I test denotes that the test was conducted with water 

initially subcooled 15 °C or more.

Initial condition category II test denotes that the test was conducted with water 

initially subcooled 30 °C or more.

Initial condition category III test denotes that the test was conducted with water 

initially subcooled less than 5 °C. Fig. 3.6 shows the test matrix for sample tests.
29

-8,00

-6,00

-4,00

-2,00

0,00

2,00

4,00

6,00

8,00

10,00

12,00

14,00

16,00

18,00

20,00

22,00

24,00

220 240 260

Temperature, deg C

Level, m

-8,00

-6,00

-4,00

-2,00

0,00

2,00

4,00

6,00

8,00

10,00

12,00

14,00

16,00

18,00

20,00

22,00

24,00

220 240 260

Temperature, deg C

Level, m

-8,00

-6,00

-4,00

-2,00

0,00

2,00

4,00

6,00

8,00

10,00

12,00

14,00

16,00

18,00

20,00

22,00

24,00

220 240 260

Temperature, deg C

Level, m

Figure 3.6 Vessel matrixes (from left: Category I Marviken Test 13, Category II Marviken Test 15, 

Category III Marviken 14)

For statistical purposes it is worth to connect initial condition category with different 

nozzle types what is shown in Table 3.1.

Table 3.1 Vessel categories and nozzle types

Initial condition 

category type Test no Nozzle no

I 14

, 24, 39, 49, 59, 62, 72, 89, 119, 124, 131, 168, 

185

II 158, 175, 217, 227, 246, 263, 277, 227

III 99, 109, 141, 195, 207, 236, 253

3.4.

Quantification of systems code accuracy is important in the validation process. 

Numerical Solution Accuracy Quantification

The L1 and L2 norm method have been employed in this work:
30

∑=

− =

N

i i

i i

rel

e

c e

N

L

1

1

1 , , (4.1)

∑= 













 − =

N

i i

i i

rel

e

c e

N

L

1

2

2

1 , , (4.2)

where:

L1,rel – L1 norm, relative,

L2,rel – L2 norm, relative,

N – number of data points,

c – calculated data,

e – experimental data,

and standard deviation:

∑( ) =

= −

N

i

i e e

N 1

1 2

σ , (4.3)

where

σ – standard deviation,

e – mean value of N data.
31

4. Validation and Results

4.1.

The results from the comparison between two-phase critical models of HenryFauske and Ransom-Trapp are presented in this Chapter. In the next subsections 

the sensitivity studies of the computational model are presented.

Background

It is not intended to present the predicted flow rate results from every single 

experiment in this Chapter. These can be found in Appendix C. However, some 

selected results will be presented in order to show essential information about the 

code’s behavior, simulation technique or particular solution feature.

4.2.

The models sensitivity was investigated. The magnitude of influence of parameters 

having significant contribution to the simulation results were determined by 

examining following parameters.

Sensitivity Studies

4.2.1. Initial Conditions (RELAP5)

Fig. 3.6 in Chapter 3 shows three types of initial conditions in the vessel. The 

descriptions of each single vessel zones were provided in the mentioned Chapter.

In the RELAP5 model the saturated and transition zone was described by 

pressure-quality [p,x] initial condition type. The subcooled zone was described by 

pressure-temperature [p,T] initial condition type.

However, for category III initial condition tests and for some tests from category II, 

it was hard to determine single zone. Thus, it was decided that in such a situation 

the initial conditions in the vessel were described by [p,x] conditions. This is 

because for this type of condition it is easier to determine whether the medium is 

liquid [x = 1] or vapor [x = 0]. For [p,T] initial condition such a determination is more 

difficult since it depends on RELAP5 water properties tables.

Distinctions in usage of different initial condition types are shown in Fig. 4.1.
32

Figure 4.1 Distinctions in usage of different initial condition types

The essential difference in results can be observed between the case when all 

vessel zones were determined by [p,x] condition and condition were the transition 

zone is determined by [p,T].

If the water is at saturation state it is recommended to use [p,x] initial condition type 

instead of [p,T] initial condition type.

4.2.2. Discharge Pipe Length

For the modeling purposes it was assumed that the discharge pipe length is 5568 

mm. The 740 mm of the discharge pipe inside the vessel was neglected. However, 

the investigation whether such an approach influence much the simulation was 

conducted. 

Fig 4.2 shows different approaches of the discharge pipe modeling.
33

Figure 4.2 Different approaches of the discharge pipe modeling

As can be seen from the figure the differences between the two approaches are 

negligible thus it is recommended to use the simplified geometry of the discharge 

pipe.

4.2.3. Junction Control Flag

Junction control flags are next to nodalization, one of the most important 

parameters in RELAP5 modeling. 

In the computational the models of abrupt and chocking were in use:

• choking option specifies, whether (1) choking model is applied or (2) 

choking model is not applied,

• abrupt option specifies whether (1) the smooth option is applied, or (2) 

abrupt option is applied but without code’s calculations of forward and 

reverse coefficient Kloss, or (3) abrupt option is not applied.

Some tests were characterized by occurrence of characteristics dip after above 10 

seconds, as shown in Fig. 4.3. This phenomenon occurs in simulation because 

chocking flow is predicted in the last 2 junctions. Such a behavior can be avoided 

by applying the choking model only at the last junction.
34

Figure 4.3 Different choking options

4.2.4. Loss Coefficient

Loss coefficient is important parameter in thermal-hydraulics calculations. It 

provides information about the pressure losses. Although the information about the 

loss coefficient was not provided in the facility description, the sensitivity studies 

with using forward loss coefficient model were performed.

For forward loss coefficient K = 0.04 the calculations was performed for Test 24, 

the smallest length-to-diameter L/D ratio experiment. Such a loss coefficient does 

not affect appreciably the mass flow rate.

4.2.5. Time Dependent Volume (RELAP5)

Time dependent volume is the component which is used as an outlet pressure 

boundary condition. The sensitivity calculations were conducted using following 

parameters:

• Case 1: A = 0.1964 m2

, L = 1.0 m,

• Case 2: A = 0.1964 m2, L = 0.5 m,

• Case 3: A = 0.400 m2, L = 1.0 m.

The area for case 1 and 2 is equal to nozzle area for Test 24.
35

It was observed that the length of an area the time dependent volume do not affect 

appreciably the mass flow rate.

4.3.

The performance of two-phase critical models, Henry-Fauske (RELAP5) and 

Ransom-Trapp (RELAP5 and TRACE), is presented in this subsection. 

Henry-Fauske and Ransom-Trapp Performance

The first part shows the plots where the measured vs. calculated data are shown. 

This is necessary to determine whether code tends to under or over-predict. The 

straight line shows the perfect code prediction. The left bottom part of the plot is 

the region where the test ends. The right upper part of the plot is the region where 

the test starts. The data from all Marviken experiment (except Test no. 10: no 

available data) have been shown to these plots.

The second subsection is focused on models’ performance with respect to the 

length-to-diameter ratio (L/D).

4.3.1. Code Accuracy

The convenient but approximate way to compare measured and calculated data is 

to plot these two in the same graph. In this subsection such a comparison was 

done for two models implemented in RELAP5 and one model in TRACE.
36

Marviken Critical Flow Test (CFT)

RELAP5, Henry-Fauske model (default)

0

2000

4000

6000

8000

10000

12000

14000

0 2000 4000 6000 8000 10000 12000 14000

Measured Flow (kg/s)

Calculated Flow (kg/s)

Figure 4.4 Code accuracy, RELAP5 Henry-Fauske
37

Marviken Critical Flow Test (CFT)

RELAP5, Ransom-Trapp model (user-defined)

0

2000

4000

6000

8000

10000

12000

14000

0 2000 4000 6000 8000 10000 12000 14000

Measured Flow (kg/s)

Calculated Flow (kg/s)

Figure 4.5 Code accuracy, RELAP5 Ransom-Trapp
38

Marviken Critical Flow Test (CFT)

TRACE, Ransom-Trapp model

0

2000

4000

6000

8000

10000

12000

14000

0 2000 4000 6000 8000 10000 12000 14000

Measured Flow (kg/s)

Calculated Flow (kg/s)

Figure 4.6 Code accuracy, TRACE Ransom-Trapp
39

4.3.2. Quantitative Code Assessment

The following graphs show relative L1 and L2 norms with respect to Test no and 

L/D ratio. The special lines indicate the mean value and standard deviation of the 

computed results for both norms.

Table 5.1 shows values of standard deviation and mean value of two-phase critical 

models implemented in RELAP5 (R5 H-F and R5 R-T) and TRACE (TR R-T).

Table 4.1 Values of standard deviation and mean value of two-phase critical models implemented in 

RELAP5 (R5 H-F and R5 R-T) and TRACE (TR R-T)

R5 H-F R5 R-T TR R-T

L1 relative

Standard 

deviation 0.061 0.068 0.049

Mean value 0.154 0.183 0.156

L2 relative

Standard 

deviation 0.082 0.066 0.057

Mean value 0.190 0.205 0.189

Equations with definitions of L1 and L2 are shown in subsection 3.4.
40

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Marviken CFT Test no.

L1 Norm, relative

RELAP5 H-F

RELAP5 R-T

TRACE

σ□

σ□

σ+

σ+

σ

σ

Figure 4.7 Relative L1 norm versus Marviken CFT Test no

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,0 1,0 2,0 3,0 4,0 5,0

L/D

L1 Norm, relative

RELAP5 H-F

RELAP5 R-T

TRACE

σ□

σ□

σ+

σ+

σ

σ

Figure 4.8 Relative L1 norm versus Marviken CFT L/D ratio
41

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Marviken CFT Test no.

L2 Norm, relative

RELAP5 H-F

RELAP5 R-T

TRACE

σ□

σ□

σ+

σ+ σ

σ

Figure 4.9 Relative L2 norm versus Marviken CFT Test no

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,0 1,0 2,0 3,0 4,0 5,0

L/D

L2 Norm, relative

RELAP5 H-F

RELAP5 R-T

TRACE

σ□

σ□

σ+

σ+

σ

σ

Figure 4.10 Relative L2 norm versus Marviken CFT L/D ratio
42

The ratio between the number of tests in which Ransom-Trapp gives best results to 

the number of tests in which the same model gives the worst results is higher for 

R-T model in TRACE. Table 5.2 provides information about the number of 

experiments in which certain model gave the best and the worst result.

Table 4.2 Information about the number of experiments in which certain model gave the best and 

the worst result

L1 norm L2 norm

R5 H-F R5 R-T TR R-T R5 H-F R5 R-T TR R-T

Best 11 7 8 11 9 6

Worst 5 17 4 10 13 3

* Total number of simulations is 26 (Test 10 is missed due to lack of experimental 

data in [13]).
43

5. Discussion and Conclusions

The up-to-date thermal-hydraulics models and correlations are of the great 

importance in computational code environment. Thus, the validation of the systems 

codes is an important issue. Knowing the behavior of the code under different 

assumptions and conditions, the more reliable results can be obtained.

The intention of the project was to perform the comprehensive Marviken CFT 

investigation. This is to build computational models of all tests and conduct a 

comparison between RELAP5 and TRACE model data and experimental data.

The main conclusions of the study concerns two-phase critical flow models. It was 

shown that for Marviken CFT experiments RELAP5 Henry-Fauske model gives 

more accurate results than Ransom-Trapp model.

Additionally, it was found out that Ransom-Trapp implementation in TRACE is 

better than in RELAP5.

The calculations were performed for a variety of nozzles used in CFT experiment. 

However, the dependence between length-to-diameter L/D ratio of the nozzle and 

the calculation’s accuracy has not been observed.
44

6. References

[1] W. Ambrosini, “Critical flow, Flooding and boiling channel instabilities”, Lecture 

notes on for the course on single and two-phase thermal-hydraulics, University of 

Pisa, Italy, 2006.

[2] H. Anglart, “Thermo-hydraulics in nuclear energy engineering”, Compendium for 

students, KTH, Stockholm, 2008.

[3] R.F. Kunz, G.F. Kasmala, J.H. Mahaffy, C.J. Murray, “An Automated Code 

Assessment Program for Determining System Code Accuracy”, OECD/CSNI 

Workshop on Advanced Thermal-Hydraulic and Neutronic Codes: Current and 

Future Applications, Barcelona, Spain, April 10-13, 2000.

[4] F. D’Auria, P. Vigni, “Two-phase critical flow models”, A technical addendum to 

the CSNI state of the art report on critical flow modeling, Roma, May 1980.

[5] J.A. Trapp, V.H. Ransom, “A chocked-flow calculation criterion for 

nonhomogeneous, nonequilibrium, two-phase flows”, Idaho National Engineering 

Laboratory, April 27, 1982.

[6] I. Parzer, “Break model comparison in different RELAP5 versions”, International 

Conference Nuclear Energy for New Europe 2003, Portoroz, Slovenia, September 

8-11, 2003.

[7] RELAP5/MOD3.3 Code Manual, “Volume VII: Summaries and review of 

independent code assessment reports”, March 2006.

[8] G.A. Mortensen, et al, “RELAP5 status and user problem report”, Fall 2006 

CAMP Meeting, Idaho Falls, Idaho, USA, October 2006.

[9] RELAP5/MOD3.3 Code Manual, “Volume II: User’s guide and input 

requirements”, March 2006.

[10] The Marviken Full Scale Critical Flow Tests report, “Conclusions. MXC-402”,

December 1979.

[11] The Marviken Full Scale Critical Flow Tests report, “Summary report. MXC301”, December 1979.

[12] The Marviken Full Scale Critical Flow Tests report, “Description of the test 

facility. MXC-101”, December 1979.

[13] CSNI1001 MARVIKEN-CFT. The Nuclear Energy Agency NEA. November 4, 

1998.
45

[14] Marviken CFT data description. The Nuclear Energy Agency NEA.

[15] The Marviken Full Scale Critical Flow Tests report, “Measurement system. 

MXC-102”, December 1979.

[16] M. Lazor, “Recommended preliminary approach for quantitative code 

assessment”, Pennsylvania State University, Applied Research Laboratory, 

December 2004.

[17] R.F. Kunz, G.F. Kasmala, J.H. Mahaffy, “Automated Code Assessment 

Program: Technique selection and mathematical prescription”, Pennsylvania State 

University, Applied Research Laboratory, April 1998.

[18] Ö. Rosdahl, D. Caraher, “Assessment of RELAP/MOD2 against Critical Flow 

Data from Marviken Tests JIT 11 and CFT 21”, NUREG/IA-0007, US Nuclear 

Regulatory Commission, September, 1986.

[19] A. Ylönen, “Large break blowdown test facility study”, Master thesis, 

Lappeenranta University of Technology, Lappeenranta, Finland, March 3, 2008.

[20] TRACE v5.0 User’s Manual, 2008-10-07.

[21] TRAC-PF1/MOD2 Volume I. Theory manual, 1993-07-21.

A-1

7. Appendix A: Summary of the Initial and Final Conditions

1 Test No. 1 2 3 4 5

2 Data of test performance 1978

01-19

1978

02-02

1978

02-24

1978

03-09

1978

03-21

3 Steam dome pressure ~ MPa 4.94 4.98 5.02 4.94 4.06

4 Saturation temperature ~°C 263 264 264 264 251

5 Degree of nominal subcooling 

in the lower vessel (relative to 

steam dome saturation 

temperature)~°C

17-23 38 15-22 37 33

6 Min. fluid temperature in the 

vessel ~°C

238 226 243 224 218

7 Initial temperature at nozzle 

inlet ~°C

226 213 223 201 205

8 Mass of water and steam ~°C 

(incl the water in the 

discharge pipe)

287 284 274 286 286

9 Mass of steam ~ Mg 1.7 2.0 2.2 1.9 1.6

10 Mass of saturated water ~ Mg 114 104 100.5 109 110

11 Initial level in the vessel ~ m 17.84 17.41 17.06 17.59 17.44

12 Final level in the vessel ~ m 3.58 3.35 2.8 <0.74 <1.1

13 Nominal elevation of 

transition zone* = m ± 0.5

9-11 8-11 7-9.5 8-10.5 8-10.5

14 Test period** ~ s 108 93 42 49 52

1 Test No 6 7 8 9 10

2 Data of test performance 1978

04-13

1978

04-27

1978

05-18

1978

06-01

1978

06-20

3 Steam dome pressure ~ MPa 4.95 5.01 4.95 5.02 4.97

4 Saturation temperature ~°C 263 264 263 264 163.5

5 Degree of nominal subcooling 

in the lower vessel (relative to 

steam dome saturation 

temperature)~°C

31 18 35 2 3

6 Min. fluid temperature in the 

vessel ~°C

231 246 225 262 260

7 Initial temperature at nozzle 

inlet ~°C

219 229 200 243 242

8 Mass of water and steam ~°C 

(incl the water in the 

discharge pipe)

289 286 285 286 279

9 Mass of steam ~ Mg 1.7 1.7 1.9 1.6 1.8

10 Mass of saturated water ~ Mg 113 125 108 256 208

11 Initial level in the vessel ~ m 17.81 17.86 17.51 18.15 17.66
A-2

12 Final level in the vessel ~ m 3.39 4.36 <0.74 <0.74 <0.74

13 Nominal elevation of 

transition zone* = m ± 0.5

7.5-

10.5

8-9.5 8-10 III III

14 Test period** ~ s 87 87 49 66 64

1 Test No 11 12 13 14 15

2 Data of test performance 1978

08-17

1978

08-29

1978

09-12

1978

09-21

1978

11-01

3 Steam dome pressure ~ MPa 4.97 5.00 5.09 4.97 5.04

4 Saturation temperature ~°C 264 264 265 264 264

5 Degree of nominal subcooling 

in the lower vessel (relative to 

steam dome saturation 

temperature)~°C

35 33 31 3 31

6 Min. fluid temperature in the 

vessel ~°C

228 231 232 260 233

7 Initial temperature at nozzle 

inlet ~°C

202 215 170 170 177

8 Mass of water and steam ~°C 

(incl the water in the 

discharge pipe)

287 285 282 286 327

9 Mass of steam ~ Mg 1.8 1.9 1.9 1.6 0.6

10 Mass of saturated water ~ Mg 110 108 132 167 73.1

11 Initial level in the vessel ~ m 17.63 17.52 17.52 18.10 19.93

12 Final level in the vessel ~ m <0.74 <0.74 5.33 8.70 <0.74

13 Nominal elevation of 

transition zone* = m ± 0.5

7.5-10 7.5-

10.5

7-10 III 12.5-

14

14 Test period** ~ s 48 126 148 146 55

1 Test No 16 17 18 19 20

2 Data of test performance 1978

11-16

1978

11-30

1978

12-12

1979

01-09

1979

01-25

3 Steam dome pressure ~ MPa 5.00 4.94 5.02 5.06 4.99

4 Saturation temperature ~°C 264 263 264 265 264

5 Degree of nominal subcooling 

in the lower vessel (relative to 

steam dome saturation 

temperature)~°C

33 31 32 4 7

6 Min. fluid temperature in the 

vessel ~°C

231 232 232 261 257

7 Initial temperature at nozzle 

inlet ~°C

180 174 174 167 187

8 Mass of water and steam ~°C 

(incl the water in the 

discharge pipe)

286 329 281 267 262

9 Mass of steam ~ Mg 1.9 0.7 2.0 2.23 2.40

10 Mass of saturated water ~ Mg 102 38.8 97.3 262.6 257.3

11 Initial level in the vessel ~ m 17.60 19.85 17.30 16.99 16.65
A-3

12 Final level in the vessel ~ m <0.74 6.2 3.8 6.5 <0.74

13 Nominal elevation of 

transition zone* = m ± 0.5

7.5-

11.5

15.5-

16.5

8-11 III III

14 Test period** ~ s 49 90 87 87 58

1 Test No 21 22 23 24 25

2 Data of test performance 1979

02-08

1979

02-27

1979

03-13

1979

03-29

1979

04-19

3 Steam dome pressure ~ MPa 4.94 4.93 4.96 4.96 4.92

4 Saturation temperature ~°C 263 263 263 263 263

5 Degree of nominal subcooling 

in the lower vessel (relative to 

steam dome saturation 

temperature)~°C

33 52 3 33 6

6 Min. fluid temperature in the 

vessel ~°C

230 211 260 230 257

7 Initial temperature at nozzle 

inlet ~°C

184 168 19 27 189

8 Mass of water and steam ~°C 

(incl the water in the 

discharge pipe)

330 334 314 330 313

9 Mass of steam ~ Mg 0.60 0.75 0.65 0.63 0.70

10 Mass of saturated water ~ Mg 48.9 35.7 310.7 39.4 309.8

11 Initial level in the vessel ~ m 19.95 19.64 19.85 19.88 19.73

12 Final level in the vessel ~ m <0.74 <0.74 <0.74 <0.74 <0.74

13 Nominal elevation of 

transition zone* = m ± 0.5

15.5-

17

15.5-

17

III 15.5-

17

III

14 Test period** ~ s 60 48 69 54 88

1 Test No 26 27

2 Data of test performance 1979

05-03

1979

05-22

3 Steam dome pressure ~ MPa 4.91 4.91

4 Saturation temperature ~°C 263 263

5 Degree of nominal subcooling 

in the lower vessel (relative to 

steam dome saturation 

temperature)~°C

34 33

6 Min. fluid temperature in the 

vessel ~°C

229 230

7 Initial temperature at nozzle 

inlet ~°C

135 167

8 Mass of water and steam ~°C 

(incl the water in the 

discharge pipe)

320 329

9 Mass of steam ~ Mg 0.92 0.66

10 Mass of saturated water ~ Mg 38.8 46.9

11 Initial level in the vessel ~ m 19.31 19.82
A-4

12 Final level in the vessel ~ m <0.74 <0.74

13 Nominal elevation of 

transition zone* = m ± 0.5

15.5-

17

15.5-

17

14 Test period** ~ s 147 59

* III indicates that little or no transition zone was present; ** Test period is the time 

from test initiation to when steam enters the discharge pipe (or the ball valve 

begins to close).
B-1

8. Appendix B: Data Channel Outputs Used in the Computational 

Model

Data channel Type Elevation level, m

001M101 Pressure 23.13

001M104 Pressure 0.53

001M401 Temperature 20.54

001M501 Temperature 19.56

001M502 Temperature 18.59

001M503 Temperature 17.64

001M504 Temperature 16.67

001M505 Temperature 15.69

001M506 Temperature 14.71

001M507 Temperature 13.75

001M508 Temperature 12.78

001M509 Temperature 11.81

001M510 Temperature 10.84

001M511 Temperature 9.86

001M512 Temperature 8.88

001M514 Temperature 6.94

001M515 Temperature 5.97

001M516 Temperature 5.00

001M517 Temperature 4.03

001M419 Temperature 3.94

001M518 Temperature 3.040
B-2

001M519 Temperature 2.08

001M520 Temperature 1.11

001M402 Temperature 0.74

002M107 Pressure -0.630

003M108 Pressure -2.730

004M109 Pressure -4.868

002M403 Temperature -0.630

003M404 Temperature -2.730

004M405 Temperature -4.868

004M532 Temperature -5.543
C-1

9. Appendix C: Flow Rate Comparisons
C-2
C-3
C-4
C-5
C-6
C-7
C-8
C-9
C-10
C-11
C-12
C-13






UNITED STATES 

NUCLEAR REGULATORY COMMISSION

WASHINGTON, DC 20555-0001

--------------------

OFFICIAL BUSINESS
NUREG/IA-0401 Assessment of Two-Phase Critical Flow Models Performance in RELAP5

and TRACE Against Marviken Critical Flow Tests