Master Thesis Report Projet de Fin d’Études (PFE)

Master Thesis Report

Projet de Fin d’Études (PFE)

Speciality : Nuclear Plant Design

School year : 2020/2021

Assessment of RELAP5-3D two phase flow models

for MYRRHA secondary cooling system conditions.

A thesis by : Krzysztof Otlik

Referent teacher ENSTA Paris Host organization tutor

Kim Pham Tewfik Hamidouche

Internship carried out from 05/04/2021 to 17/09/2021

SCK CEN

Boeretang 200, 2400 Mol, Belgium

Confidentiality statement This thesis is non confindential

Assessment of RELAP5-3D two phase flow models for MYRRHA secondary cooling system conditions

Krzysztof Otlik, SCK CEN

2

Acknowledgements

There are many people to whom I owe finishing this Master and who I am now. I

cannot list them all so please forgive me for not mentioning someone.

First and foremost I would like to thank SCK CEN for offering me a master thesis

internship in a subject I enjoy at one of the most well-known research centers in

Europe or even in the world. Because of the situation, it did not go as I expected,

but it is no one fault. I did my best and took the most out of the situation and this is

what matters. I am also grateful for the incredible work of my supervisor Mr.

Hamidouche, the knowledge and experience he shared with me are invaluable.

Thank you for your patience, positive approach and faith in achieving the goal,

which always cheered me up and helped me a lot with finishing this project.

Secondly, I have to thank all my teachers, mentors and coordinators that I had the

pleasure to meet and learn from during my studies. Thank you Jordi and Daniele

for being such an inspiration for me and for your amazing classes that I was always

excited about. Thank you, Lluis for always carrying about students, wanting the

best for us and doing everything you could to facilitate our lives (except these 10

hours classes online). Thank you, Kim, for being a wholesome person, we do not

know each other that well, but you were always there when I needed help, you

made my life as a foreign student in Paris much easier. Thank you Chirayu for all

the talks about a professional career that we had, for all the advice, they helped me

a lot with finding the right path.

Last but not least I cannot thank my family and friends enough for supporting me

and making my master studies fun. Thanks to my parents and my sister for the

motivation boosts, conversations and everything you did for me, I do not have words

for that. To all my friends together, thank you for sharing with me so many fun

moments live and online, for all the work we did together and for just being

yourselves. Thanks to Ana for the disco polo dance at 4 am; to Narcis for not dying

young; to Pau for the romantic date talking about bosons and quarks and for

knowing how old Laura was; to Mario for not choosing my shoes and for being so

good at singing polish songs; to Oscar for all the “dank” parties. Thanks to all my

other friends that are not mentioned here. I love you all and see you at the top guys!

It was quite an adventure…



3

Abstract

In this project, a numerical model is developed to assess the thermal-hydraulic

system code RELAP5-3D correlations’ used for two-phase flow in MYRRHA

secondary circuit conditions. The well-known drift-flux model is applicable to a wide

range of thermal-hydraulic problems in nuclear reactors. The selected correlations

for the model, based on the 4 equations drift-flux model, show better performance at

lower pressures due to its approach to interfacial interaction and it is suitable for a

wide range of thermal-hydraulic problems in nuclear reactors. All field and

constitutive equations were properly selected and derived to get as acceptable with

respect to the simplified approach. For the solution methodology, an iterative

scheme was chosen with convergence criteria on exit pressure. The results show

great compliance with experimental results and for some conditions are even better

than RELAP5-3D results.

Keywords:

Thermal-hydraulics, two-phase flow, drift-flux model, RELAP5-3D, MYRRHA

Résumé

Dans ce projet, un modèle numérique est développé afin d'évaluer les corrélations

utilisées par le code de calcul thermohydraulique RELAP5-3D pour l'écoulement

biphasique dans les conditions du circuit secondaire MYRRHA. Le modèle de la

dérive du flux est applicable à un large éventail de problèmes thermohydrauliques

dans les réacteurs nucléaires. Le choix de correlations appropriées, à l’aide modèle

de dérive de flux à à quatre equations, montre de meilleures performances du

modèle simplifié pour les basses pressions en raison de son approche de l'interaction

interfaciale et il est applicable à un large éventail de problèmes

thermohydrauliques dans les réacteurs nucléaires. Toutes les équations de champ et

constitutives ont été correctement sélectionnées, dérivées et nodalisées pour obtenir

des résultats acceptables au vu de l’approche simplifiée. Pour une méthodologie de

calul, un schéma itératif a été choisi avec un critère de convergence sur la pression

de sortie. Les résultats montrent une grande conformité avec les résultats

expérimentaux et pour certaines conditions meilleurs que les résultats RELAP5-3D.

Mots-clés:

Modèle thermohydraulique, écoulement diphasique, flux de dérive, RELAP5-3D,

MYRRHA



4

Table of content

Acknowledgements ...................................................................................................... 2

Abstract ........................................................................................................................ 3

Table of content ............................................................................................................ 4

Chapter 1 - Introduction ............................................................................................. 6

1.1 Motivation ................................................................................................................................. 6

1.2. MYRRHA reactor ................................................................................................................... 7

1.3 Objectives .................................................................................................................................. 9

Chapter 2 – Two-phase flow ..................................................................................... 10

2.1 Drift flux versus two fluid ...................................................................................................... 10

2.2 Flow regimes ........................................................................................................................... 10

2.3 Heat transfer ........................................................................................................................... 12

2.4 Flow instability ....................................................................................................................... 13

Chapter 3 – Numerical model .................................................................................. 14

3.1 Mixture field equations .......................................................................................................... 14

3.1.1 Two phase .......................................................................................................................... 14

3.1.2 Single phase....................................................................................................................... 14

3.2 Drift flux equation .................................................................................................................. 15

3.3 Constitutive equations ............................................................................................................ 15

3.3.1 Friction factor .................................................................................................................... 15

3.3.2 Heat transfer coefficient .................................................................................................... 16

3.3.3 Transition correlations ....................................................................................................... 17

3.3.4 Drift flux parameters ......................................................................................................... 17

3.3.5 Void fraction ...................................................................................................................... 17

3.4 Numerical scheme nad methodology .................................................................................... 18

Chapter 4 – Selection of experiment for validation process .................................. 21

Chapter 5 – Results ................................................................................................... 22



5

5.1 Pressure drops ........................................................................................................................ 22

5.1.1 Experiment FED15A ......................................................................................................... 22

5.1.2 Experiment FE712B .......................................................................................................... 23

5.1.3 Experiment FE714B .......................................................................................................... 25

5.1.4 Experiment FE715B .......................................................................................................... 26

5.2 Temperature evolution .......................................................................................................... 27

5.3 Drift velocity ........................................................................................................................... 28

Chapter 5 – Conclusion ............................................................................................. 30

Nomenclature ............................................................................................................. 31

Bibliography ............................................................................................................... 32



6

Chapter 1 - Introduction

1.1 Motivation

Nowadays humanity is facing an enormous challenge, global emissions were

roughly 52 GtCO2 in 2016 and are expected to reach 52-58 GtCO2 by 2030 [1]. We

are already seeing the consequences of 1°C of global warming through more

extreme weather, rising sea levels and diminishing Arctic sea ice, among other

changes. The United Nations Intergovernmental Panel on Climate Change

highlighted in a special report that these emissions have to be cut by half to limit

global warming to 1,5°C [1]. In the past, there have been examples of quick changes

in specific technologies or industries, but there is no case at the scale required for

limiting these emissions. The possibility of making this shift will require great

investments in low-carbon sources of energy. The report by IPCC explains four

various pathways and unsurprisingly each of them includes a noticeable increase in

nuclear energy [1].

The nuclear industry can satisfy the demand for free of CO2 energy sources in

mainly two ways; either by the construction of large advanced reactors or by small

modular reactors using 4th generation technology that are expected to start to be

deployed in the early 2030s. One can argue there is a third solution connected to

fusion reactors, but it is not foreseen to be happening in the nearest future by many

experts. However, to make any of the solutions possible a huge research and

development effort is required by all people in the industry and not only. Research

projects like MYRRHA might have a great impact on the development of 4th

generation of nuclear reactors. It is also hoped to help with one of the biggest

problems of the atomic industry nowadays – high-level wastes. The possibility of

using it to study the transmutation of nuclear wastes might be invaluable and

makes the project so crucial. The safety of such a state of art reactor is also a great

concern and should be investigated in-depth, including thermal-hydraulics and two-

phase flow considerations.

Two-phase flow is an essential phenomenon widely seen in various engineering

applications like renewable energy systems, different types of heat exchangers, but

it is the most important in nuclear applications. Therefore, knowledge of its

characteristic, proper modeling and simulation of two-phase flow is of great

importance to the design and safety. Only the joint effort of the entire industry can

ensure the safety of nuclear installations. This is a key aspect in gaining public

acceptance after nuclear accidents that had happened in the past. In the end, safe

and publicly accepted nuclear installations together with the solved nuclear waste

problem will result in a clean and sustainable future for current and next

generations.



7

1.2. MYRRHA reactor

MYRRHA (Multi-purpose HYbrid Research Reactor for High-tech Applications) is

conceived as a flexible fast spectrum irradiation facility for various applications, for

example, fuel research for innovative reactor systems, material development for

Generation-IV advanced reactor systems, a study of transmutation of high-level

nuclear waste and the production of radioisotopes for medical and industrial

applications. It is designed as an accelerator-driven system (ADS) to operate in sub-

critical mode, but it is also able to be run in a critical mode [2].

The MYRRHA reactor core power is released to the environment utilizing four

independent secondary and tertiary loops, which use saturated water and air

respectively. The loops can operate in forced circulation (normal operation mode) or

passive natural circulation (decay heat removal mode). The pressure in the

secondary circuit is maintained constant, at 16 bar, during all normal operation

conditions, which corresponds to a saturation temperature of around 200 °C.

Each loop is made up of one primary heat exchanger (PHX) where steam is

generated, a steam separator for the water/steam mixture coming from the PHX,

steam condensers that use air as a cold source (tertiary system), a circulation pump

and the interconnecting piping. In normal operation mode, slightly subcooled (-1°C)

water enters the PHX and leaves it as a steam-water mixture towards the

separator. Steam from the separator is guided to the air-cooled condensers from

which the condensate water flows back to the lower part of the separator where it is

mixed with the water to feed the pump, which forces it back to the PHX, thereby

closing the loop. In decay heat removal mode, the SCS works in natural circulation

mode. The driving force for the natural circulation is provided by the hydrostatic

head difference between the feedwater going from the separator to the PHX and the

vapor/water mixture going from the PHX to the separator. The loop is sketched in

Figure 1.



8

Figure 1: MYRRHA secondary circuit scheme

The MYRRHA PHX is based on a double-wall bayonet tube concept as shown in

Figure 2. For simplification, the model to develop will focus on the two-phase flow in

a single annulus of the PHX.

Figure 2: MYRRHA primary heat exchanger

Steam

Steam Drum/ Separator

Drum Feedwater

Feedwater

PHX

Riser

fan

Air

Pump



9

1.3 Objectives

For the safety demonstration of MYRRHA, the RELAP5-3D system code is used to

model the secondary circuit. The safety demonstration relies on safety analysis that

is performed with only adequately validated models.

RELAP5 is a thermal-hydraulic system code originally developed for the simulation

of pressurized light water reactors. It is used to analyze the behavior of thermal-

hydraulic systems in transient/accident conditions to determine the margin to

safety criteria. An extensive validation program has been launched around the

world to demonstrate the code capabilities concerning the nuclear power reactor

safety requirements. This program was sponsored by both US-NRC and US-DOE

and resulted in the wide acceptance and use of this code in the licensing processes

of many nuclear power plants in the world [3].

In the two-fluid model, each phase is considered separately; hence the model is

formulated in terms of two sets of conservation equations governing the balance of

mass, momentum, and energy of each phase. This model presents considerable

uncertainties in specifying interfacial interaction terms between two phases which

can cause numerical instabilities, not necessarily physical, because of an improper

choice of interfacial-interaction terms in the phase-momentum equations. Such

difficulties occur at low pressure and low flow conditions.

Careful studies on the interfacial constitutive equations are required in the

formulation of the two-fluid model. RELAP5-3D uses a partition wall model and a

look-up table concerning flow regime to select the closure relationships for the

interphase mass, momentum and heat exchange. The particular case of low-

pressure conditions applicability of the code models is to be investigated.

Therefore, the objective of this master thesis is to investigate the validity of the

selected closure relationships for some typical MYRRHA secondary circuit

conditions using a simplified numerical model. The model should be based on a

simplified drift flux model in contrast to RELAP5 two-fluid model. The particular

case of low-pressure conditions applicability of the code models is to be checked.



10

Chapter 2 – Two-phase flow

2.1 Drift flux versus two fluid

Two-phase flow involves the relative motion of one phase with respect to the other,

thus it has to be formulated in terms of fields of velocity. In general, a two-phase

flow transient problem can be formulated by using a drift flux model or a two-fluid

model. In the two-fluid model each phase is treated independently, thereby the

model uses two sets of conservation equations of mass, momentum and energy for

each phase. The introduction of two different momentum equations causes

significant complications that can induce numerical instabilities that may be also

physical, mainly because of the uncertainties related to interfacial interaction

models. It is a common issue in simulation results, therefore a careful choice of

constitutive correlations is required for two-fluid models [4].

The formulation of the motion of the whole mixture by the mixture momentum

equation and a kinematic constitutive equation that takes into account relative

motion of the two phases makes the drift flux model a simplified version of the two-

fluid model as it considers mixture rather as a whole. The use of this model is

acceptable when the two phases are solidly coupled [4]. Because of its simplicity, it

has a wide range of applicability to engineering problems. There are numerous

examples of such applications of drift flux models in simulations codes in the

nuclear industry: RETRAN-3D code, subchannel analysis of BWR fuel bundles,

TASS/SMR system analysis code, inclusion in the TRAC (Transient Reactor

Analysis Code) [5]. Therefore, a drift flux model has been chosen as the best option

for the subject of this project.

2.2 Flow regimes

Different transfer mechanisms between the two-phase mixture and the wall depend

on flow regimes, which results in the use of various correlations related to flow

regime criteria. Many works were undertaken to predict flow regimes based on flow

regime maps derived from experimental observations. Most of them are based on

dimensional liquid and gas superficial velocities. However, in practical applications,

it causes another problem for two-fluid models where the relative velocity is

unknown and void fraction cannot be derived uniquely from these superficial

velocities. This problem does not arise in the drift flux model, because a constitutive

equation to determine relative velocity is used there. The most common flow

regimes are presented in Figure 3 and explained below [6].

a) Bubbly flow - the gas phase of the flow is distributed in the form of bubbles

dispersed in the liquid which constitutes the continuous phase. The

dimensions of these bubbles are small compared to the diameter of the pipe.

This regime only appears for low superficial gas velocities.



11

b) Slug flow – the gas or vapor bubbles are on average almost the diameter of

the pipe. The top of the bubble has a distinguishing spherical cap. There is a

slowly descending film of fluid that separates the bubble from the wall. The

length of the slug can vary significantly and it can contain smaller entrained

gas bubbles inside.

c) Churn flow – continuity of the large slug is repeatedly destroyed which

results in the chaotic flow of vapor. Meanwhile, the fluid is mainly distributed

at the pipe wall. The character of the flow can greatly vary with time.

d) Annular flow – the fluid forms a film at the wall with an uninterrupted gas

flow in the middle of the channel. Waves occurring at the surface of the film

continuously break up and lead to droplet entrainment in different amounts.

e) Wispy-annular flow – The difference between this flow regime and annular

flow is a thicker liquid film on the channel wall and the liquid entrained is

agglomerated as large droplets rather than separated small bubbles.

Figure 3: Flow regimes



12

2.3 Heat transfer

Consider a tube heated uniformly with low heat flux and fed with subcooled liquid

at the inlet. Figure 4 shows an ideal form of the flow patterns, variation of surface

and liquid temperature and boiling regions.

In the first part of the tube, the temperature of the liquid and the temperature of

the wall increase, due to single-phase convective heat transfer to the liquid phase

(region A). At some point along the channel, the wall temperature reaches the

minimum required to trigger nucleation (onset of nucleate boiling). When

nucleation occurs at the wall, few bubbles (nucleation sites) are formed in the

presence of the undersaturated liquid. The bubble collapse as soon as they detach

from the wall. We are then in the region of subcooled boiling (region B in Figure 4).

In this zone, the temperature of the liquid has not yet reached saturation

temperature and wall temperature remains essentially constant, few degrees above

saturation. The difference between wall and saturation temperature is called the

degree of superheat and the amount by which saturation temperature exceeds local

liquid temperature is knowns as the degree of subcooling.

The liquid temperature increases until it reaches the detachment threshold

temperature, at this point bubbles detach but do not condensate within the liquid.

This new region is called the fully developed undersaturated boiling and this point

is named the onset of significant void (OSV). In this zone the temperature of the

liquid keeps rising until it reaches saturation temperature, then the saturated

boiling zone is entered (region C) [7].

Figure 4: Boiling zones



13

2.4 Flow instability

Flow instability is a crucial phenomenon in the design of a nuclear reactor as there

is a possibility of flow excursion during an accident. Flow instability in a heated

channel is divided into two groups: dynamic and static [8]. Static instability is

described as the occurrence of a minimum peak in the pressure demand curve. This

curve represents channel pressure drop as a function of velocity or mass flux. This

type of instability is often named Ledinegg or excursive instability. The point at

which pressure drop reaches a minimum is called the onset of flow instabilities

(OFI). This static instability occurs before the onset of significant void [8].

The pressure drop across a heated channel at uniform heat flux as a function of

mass flux can take one of the two different forms that are presented in Figure 5.

Line ΔPTpump shows stable flow conditions without minimum and maximum. The

flow instability may happen in the case of ΔPTline(actual) when the slope of the

pressure drop is lower than the slope of the internal characteristic. In this figure

the working point is unstable and even a small change of mass flux will lead to a

jump to the nearest stable working point. Stable points are placed at an intersection

of line ΔPTpump with line ΔPTline (all vapor) or ΔPTline (all liquid) [8].

Figure 5: Sketch ilustrating static flow instability



14

Chapter 3 – Numerical model

In this chapter, all equations used to develop four equations drift flux model are

presented. It includes three field equations for both mixture and liquid, an equation

for drift velocity and constitutive correlations for other required parameters.

3.1 Mixture field equations

The final forms of the four basic field equations for the drift flux model are

presented below. They were simplified assuming a one-dimensional approach as

well as steady-state conditions. In these forms, equations are practically applied to

solve the problem of the subject.

3.1.1 Two phase

Mixture continuity equation:

CstGVmm == (3.1)

Mixture momentum conservation equation:

gD

GfV

dz

d

dz

dG

dz

dPm

m

m

gm

ml

m

gl

gj

m

t

−−

−

−−

−=

2'

12

22

(3.2)

Mixture energy balance equation:

−

−

−

= gl

gl

ml

m

gl

gj

hm HVdz

d

GAG

pq

dz

dH

'

1

(3.3)

3.1.2 Single phase

Liquid continuity equation:

GVll = (3.4)

Liquid momentum conservation equation:

gdz

dG

D

Gf

dz

dPl

llh

ll

−

−−=

1

2

2

2

(3.5)



15

Liquid energy balance equation:

AG

pq

dz

dH hl

=

(3.6)

3.2 Drift flux equation

End form of the drift flux equation is shown below [7]

( )

JVV

g

gj

−=

(3.7)

where J, the superifical velocity equals

+

−=

gl

XXGj

1

(3.8)

3.3 Constitutive equations

In order to complete the drift-flux model, it is necessary to add several constitutive

correlations and laws for a mixture. The most important equations used in the

model are listed below with brief explanations and a range of applicability if

needed.

3.3.1 Friction factor

a) Single phase Faning friction factor [9]:

for laminar flow (Re < 2300):

1Re24

−= lf (3.9)

For transition flow regime (2300 ≤ Re < 4000):

( ) 4/3

Re83.234.5 lEEf −+−= (3.10)

And for turbulent flow, correlation by Kakac (Re ≥ 4000 ):

3.03 Re1143.01028.1−− += lf (3.11)

For subcooled region, after onset of nucleate boiling, the friction factor has to be

corrected, correlation by Owens et Schrock is used in this case [7]:

( ) 13.6exp28.097.04 += ff l (3.12)

where



16

( )( ))(

)(1

onblsat

lsat

zTT

zTT

−

−−=

(3.13)

b) Two phase

For two phase flow a Blasius relation is implemented [7]

for Retp < 10000:

25.0)(Re316.0 −= tpmf (3.14)

and for Retp ≥ 10000:

25.0)(Re079.0 −= tpmf (3.15)

where two phase Reynolds number is calculated using following equation:

TP

tp

GD

=Re

(3.16)

Viscosity of a mixture is obtained by Mac Adams correlation [7]:

lgtp

xx

)1(1 −+=

(3.17)

3.3.2 Heat transfer coefficient

There are two equations for heat transfer coefficient in this model, Dittus-Boetler

correlation for single phase [10]:

( ) ( ) 4.08.0PrRe023.0 ll

L

hsp

K

DhNu ==

(3.18)

thus temperature of the wall:

)()( zTh

qzT l

sp

w +

=

(3.19)

Chen correlation for two-phase flow [7]:

F

D

k

k

CpDXGh

h

l

l

ll

l

h

CF )()1(

023.0

4.08.0

−=

(3.20)

SPT

H

Cpkh satsat

vgll

lll

NCB

75.024.0

24.024.029.05.0

49.045.079.0

00122.0

=

(3.21)

Where F is two-phase multiplier and S is the nucleate boiling suppression factor



17

Then wall temperature equals:

)()(

)()()()()(

ihih

iTihiTihqiT

CFNCB

lCFsatNCB

w+

++=

(3.22)

3.3.3 Transition correlations

a) Onset of Nucleate Boiling (ONB)

The temperature at which the model transfers to subcooled boiling is obtained by

Bergles-Rohsenow correlation [11]:

16.2

158.1

0234.0

10829

5P

onbp

qT

=

(3.23)

Thus ONB occurs when:

onbsatw TTT + (3.24)

b) Onset of Significant Void (OSV)

The liquid temperature at which bubbles start to detach (OSV) is given by

correlation [12]:

For Pe ≤ 70000

l

h

satdlK

DqTzT

−= 002.0)(

(3.25)

And for Pe > 70000

l

h

satdlK

DqTzT

−= 002.0)(

(3.26)

3.3.4 Drift flux parameters

Drfit velocity is evaluated using Sun correlation, however plenty of other equations

can be found in the literature [13]: ( ) 4

1

2)(

)()()(41.1)(

−=

i

iigiiV

l

gl

gj

(3.27)

Mean drift velocity of gas phase is then given by following equation:

( ) )(1)()(' 0 iJCiViV gjgj −+= (3.28)

3.3.5 Void fraction

Evolution of void fraction between onset of nucleate boiling and onset of significant

void can be predicted using Griffith, Clark and Rohsenow correlation [7]:

A

Pzaz h)()( =

(3.29)



18

where

( ))()()(07.1

)()(Pr)(

2 zTzTzh

zKzqza

lsatCF

ll

−

=

(3.30)

After the point of OSV, void fraction is given by following equation [7]:

( )

g

l

inletl

gj

g

gl

V

VCzX

C

zXz

++

−

=

,

0

0)(

)()(

(3.31)

Where X’ is the equilibrium quality calculated by Levy correlation [7] :

−−= 1

)(

)(exp)()()(

d

dzX

zXzXzXzX

(3.32)

3.4 Numerical scheme nad methodology

The conservation and state equations, as well as the constitutive relations, are

solved under the following conditions:

• the temperature at the inlet of the channel is constant.

• a constant and uniform surface heat flux q is applied along the channel.

• constant outlet pressure.

• there is no pressure difference between the two phases.

• the enthalpy of the vapor phase is constant and equal to the saturation value.

The analysis of the steady-state problem involves space steps, which follow the

evolution of the physical properties and the parameters axially along the channel.

They are characterized initially by the starting conditions (boundary condition) of

the calculation and make it possible to determine the unknowns at the node (i + 1).

Later the values of the physical quantities obtained at the node (i + 1) are used as

initial conditions for the computation at the node (i + 2). The numerical diagram

corresponding to the variables (z) in space is represented geometrically by

Figure 6.

Figure 6: Nodalization scheme

The physical properties of the liquid are calculated at each node according to local

conditions (P, T) using thermodynamic tables.



19

The equations established previously are discretized in the direction of flow using

the finite difference method. They are obtained by replacing the differential

equations with elementary difference operators. An example of such a discretized

equation 3.2 is presented below:

ZgiZ

iD

Gif

iiGiPiP l

lh

l

ll

−−

−−−−= )(

)(2

)(

)1(

1

)(

1)1()( 2

(3.33)

A case of an upward flow in forced circulation in a vertical channel, subjected to a

constant and uniform heat flux is considered in this model. In particular, the model

focuses on studying pressure drop, which is a clear indicator of void fraction, void

fraction itself and influence of other correlations, mainly regarding drift flux

parameters.

The numerical model is divided into 4 main parts: single-phase, partial boiling zone,

developed boiling zone and saturated boiling zone. It is initialized with a provided

by user channel geometry, mass flux, heat flux, number of nodes, outlet pressure

and arbitrarily chosen value of inlet pressure. Given this data, the model evaluates

liquid and wall temperature, based on them and constitutive correlations it

transitions to an adequate region. Later fluid properties for subsequent nodes are

calculated until a condition of region transition is met or until the last node is

reached. The outlet pressure of the channel is calculated and compared to exit

pressure that is known and was given in the initialization.

Results are validated when the difference between the calculated pressure and the

external (known) pressure is less than the desired error, at this point code

terminates. However, if the difference is not lower than the chosen value of error

the code iterates using a new inlet pressure until the condition is satisfied or until

the maximum number of iterations is reached. The model is programmed using

Matlab R2019a. All the steps and the methodology can be seen on a flow chart

(Figure 7).



20

Figure 7: Flow chart of numerical model



21

Chapter 4 – Selection of experiment for

validation process

Pressure and geometry of the channel were the main criteria for selection of proper

experiment for validation of the code. As a result an experiment by Simon Tov et al.

was picked, because the pressure condition of it (17 bar) is very close to the

conditions of the MYRRHA secondary circuit (16 bar). The rectangular channel used

in the experiment is also similar to a narrow annulus of the MYRRHA primary heat

exchanger. The experiment is described below.

In order to determine the operating limits of a new type of nuclear reactor (ANSR:

Advanced Neutron Source Reactor), Simon-Tov and Al, researchers from the ORNL

laboratory (Oak Ridge National Laboratory (USA)) had to design a simulation

system for a hot region of the core of this nuclear reactor and the corresponding

cooling channel. This process consists of a thermo-hydraulic loop (THTL Thermal

Hydraulic Test Loop) in which the heat released during nuclear fission is replaced

by the provision of an electrical heat flow on the wall of a channel where a coolant

circulates. The aim was to determine the conditions that would induce the

occurrence of undesirable phenomena such as flow instability or flow excursion. The

rectangular test section was sized to reflect the operating conditions in a single

channel of the nuclear reactor, it can be seen in Figure 8 [14].

For this experiment only measurements of pressure drops are available. It is a

reason why validation outcomes are presented in the form of figures representing

the evolution of the pressure drop (DP) as a function of the mass flux (G).

Figure 8: Geometry of the channel used in the experiment of Simon-Tov



22

Chapter 5 – Results The results of the numerical simulation of the equations and their boundary

conditions are gathered and commented on in this chapter. The code is validated

against the results of the experiment described in chapter 4 and compared to

RELAP5-3D results.

5.1 Pressure drops

5.1.1 Experiment FED15A Conditions: q = 0 Mw/m2 , Tinlet = 45 oC , Pexit = 1,7 Mpa

For this experiment, there is no heat flux, which means there is no generation of

steam and no appearance of a void. The flow is in the single liquid phase alone,

along the whole channel. The maximum difference in the pressure drop between the

result obtained using the studied model and the experimental results is 0.131 MPa,

this difference occurs at a mass flux G = 30600 kg/m2/s and corresponds to an error

of 7,91%. The highest error equals 10% for mass flux G = 10250 kg/m2s. These

deviations are not dependent on the mass flux, however they do not exceed 10%.

Although it might be considered high, this value is acceptable because the error of

experimental results is not known and also each correlation includes uncertainty.

The results prove:

• the physical model established in this study reflects the experimental

process.

• the digital model is convergent.

• the friction factor used in the liquid monophasic equations, which is the most

recommended for this type of channel geometry, allows us to reduce the

differences between the experimental results and those of the simulation.

Table 1: Results for experiment FED15A

G

[kg/m2/s]

Experimental

DP[MPa]

Numerical

model DP[MPa]

Difference

[MPa]

Error

%

34800 2.03 1,925 0,105 5,19

33000 1.83 1,751 0,079 4,33

30600 1.66 1,531 0,131 7,91

28500 1.45 1,349 0,101 6,98

26500 1.28 1,185 0,095 7,39

24500 1.12 1,031 0,089 7,90

22500 0.97 0,887 0,083 8,53

20500 0.83 0,753 0,077 9,30

16250 0.55 0,500 0,046 8,36

14500 0.45 0,410 0,040 8,90

10250 0.25 0,225 0,025 10,0

8200 0.17 0,153 0,017 9,77

6200 0.10 0,096 0,004 4,10

Average error 7,60%



23

Figure 9: Results for experiment FED15A

5.1.2 Experiment FE712B Conditions: q = 2 Mw/m2 , Tinlet = 45 oC , Pexit = 1,7 MPa

This case shows that the discrepancies in the single-phase are preserved if

compared to experimental data and RELAP5-3D. As shown for the cold case, the

numerical model slightly underestimates the pressure drop. However, the error is

higher than what is observed for the cold case and it increases as the mass flux is

reduced. This error increase may occur due to the heat transfer correlation used

that is was derived from circular channels rather than annular or rectangular flow

sections.

At around 3000 kg/m2/s the pressure drop as a function of mass flux has its

minimum and starts to even increase, similar to what is observed in the

experiments. This phenomenon indicates the initiation of the unstable region and is

usually defined as the onset of flow instabilities, also referred to as the static

instability also called Ledinegg, mentioned in chapter 2.4. RELAP5-3D is also able

to determine the upturn of the pressure drops curve even though the flow is

considered in a single phase. RELAP5-3D has no defined subcooling flow regime.

There is no void fraction measurement during the experiment however a

comparison of the void fraction profile estimated by the present model and

RELAP5-3D is shown in Figure 11. For RELAP5-3D the void fraction suddenly

skyrockets in the last two nodes of the channel, while for the numerical simulation

the void fraction gradually increases starting from a point around 10 cm before

that. It is clear evidence RELAP5-3D performance in predicting the void before the

OSV is not ideal, it might make a significant difference at lower pressures.

0,00

0,50

1,00

1,50

2,00

2,50

0,0 5,0 10,0 15,0 20,0 25,0 30,0 35,0

Pre

ssu

re D

rop

, MP

a

Mass flux, t/m2/s

FED15A

RELAP5-3D

Experiment

Model



24

Table 2: Results for experiment FE712B

G

[kg/m2/s]

Experimental

DP[MPa]

Numerical

model DP[MPa]

Difference

[MPa]

Error

%

16300 0,53 0,487 0,043 8,05

14300 0,44 0,386 0,054 12,29

12300 0,33 0,295 0,035 10,52

6000 0,1 0,084 0,016 15,69

5200 0,08 0,066 0,014 17,25

4000 0,06 0,043 0,017 28,23

3200 0,04 0,031 0,009 21,71

2800 0,033 0,032 0,001 1,95

2100 0,044 0,063 0,019 43,40

Average error 17,68 %

Figure 10: Results for experiment FE712B

Figure 11: Comparison of void fraction across the channel between RELAP5-3D and numerical model

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

0,45

0,50

0,00 2,00 4,00 6,00 8,00 10,00 12,00 14,00

Pre

ssu

re D

rop

, MP

a

Mass flux, t/m2/s

FE712B

RELAP5-3D

Experiment

Model

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,3 0,3 0,4 0,4 0,5 0,5

Vo

id f

ract

ion

Channel length, m

RELAP5-3D

Model



25

5.1.3 Experiment FE714B Conditions : q = 5,3 Mw/m2 , Tinlet = 45 oC , Pexit = 1,7 Mpa

Results for this experiment are almost a copy of the previous one, the same trend

and phenomena are observed. In this case, the decrease of the discrepancies in

pressure drops for the single-phase is noticed. However, for this experiment, the

error of numerical results for higher mass flux is less than 5% which further

confirms its accurateness. When mass flux is reduced the flow instabilities start to

occur again, the pressure drop is overestimated and RELAP5-3D gives more correct

results. Table 3: Results for experiment FR714B

G

[kg/m2/s]

Experimental

DP[MPa]

Numerical

model DP[MPa]

Difference

[MPa]

Error

%

22500 0,89 0,85 0,044 4,92

20200 0,72 0,70 0,024 3,28

18200 0,6 0,58 0,023 3,83

16200 0,48 0,47 0,012 2,50

14100 0,37 0,36 0,005 1,37

12300 0,28 0,29 0,006 2,19

10300 0,22 0,21 0,011 4,91

8300 0,16 0,16 0,003 1,86

7700 0,14 0,17 0,030 21,74

7000 0,16 0,20 0,041 25,50

6800 0,18 0,21 0,033 18,31

6200 0,2 0,25 0,053 26,48

Average error 9,74%


0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

5,00 10,00 15,00 20,00

Pre

ssu

re D

rop

, MP

a

Mass flux, t/m2/s

FE714B

RELAP5-3D

Experiment

Model



26

5.1.4 Experiment FE715B Conditions : q = 12,15 Mw/m2 , Tinlet = 45 oC , Pexit = 1,7 Mpa

In this case, the same tendency is observed as in all previous graphs. For higher

mass flux, results with a low error are obtained and the error increases significantly

for a lower value of mass flux, same as described above. After the onset of flow

instability, the values start to diverge as has been seen before.

Table 4: Results for experiment FE715B:

G

[kg/m2/s]

Experimental

DP[MPa]

Numerical

model DP[MPa]

Difference

[MPa]

Error

%

33000 1,8 1,663 0,137 7,60

30800 1,6 1,468 0,132 8,27

29300 1,4 1,341 0,059 4,22

27000 1,2 1,157 0,043 3,57

24500 1,02 0,972 0,048 4,71

22800 0,9 0,855 0,045 5,02

20500 0,8 0,752 0,048 5,96

19000 0,72 0,732 0,012 1,65

18000 0,68 0,733 0,053 7,85

17370 0,67 0,753 0,083 12,45

16830 0,68 0,778 0,098 14,48

15800 0,75 0,836 0,086 11,49

33000 1,8 1,663 0,137 7,60

Average error 7,27 %


0,00

0,50

1,00

1,50

2,00

2,50

10,00 15,00 20,00 25,00 30,00 35,00 40,00

Pre

ssu

re D

rop

, Mp

a

Mass flux, t/m2/s

FE715B

RELAP5-3D

Experiment

Model



27

5.2 Temperature evolution

As an additional check of modeled physical phenomena, an evolution of liquid, wall

and saturation temperature is plotted below for two different cases. The heat flux

equals 2MW and 5,3 MW, the mass flux is 3200 kg/m2/s and 6200 kg/m2/s for the

first and second case respectively.

It is observed that the evolution of liquid, wall and saturation temperature for both

cases is consistent with theoretical considerations presented in chapter 2.3 which

further proves the correctness of the model.

Wall temperature in both situations is steadily increasing until it reaches a value

corresponding to the onset of nucleate boiling. At this point, the convection is

slightly enhancing which explains the drop of the local wall temperature, because of

the subcooled boiling process at the wall surface. Further downstream, the wall

temperature continues increasing up the exit of the heated channel.

Liquid temperature is gradually increasing until ONB, where a small discontinuity

can be observed due to a region transition (because of the use of the different

correlations as mentioned in chapter 3). The slopes of temperature trends are

consistent with theory and are confirmed in Figure 4.

Figure 14: Evolution of liquid, wall and saturation temperature along the channel for experiment FE712B

0,00

50,00

100,00

150,00

200,00

250,00

0,0 20,0 40,0 60,0 80,0 100,0

Tem

pe

ratu

re, °

C

Axial node number

Tl

Tw

Tsat



28

Figure 15: Evolution of liquid, wall and saturation temperature along the channel for experiment FE714B

5.3 Drift velocity

The drift velocity is an essential parameter in the drift flux model. There are many

correlations for this parameter in the literature and according to some authors, the

drift flux model is sensitive to the correlations used [4]. In this subsection more

recent correlations are considered for sensitivity analyses:

Wang correlation [15]:

𝐶0 =2

1 + (𝑅𝑒1000)

2+

1,2 − 0,2𝛼4

1 + (𝑅𝑒1000)

24.1

𝑉𝑔𝑗 = 1,53(𝑔𝜎(𝜌𝑓 − 𝜌𝑔)

𝜌𝑙2)0,25 + 0,35√

𝑔𝐷(𝜌𝑓 − 𝜌𝑔)

𝜌𝑓𝛼(1 − 𝛼)0,25 4.2

Correlation by Hibiki [16]:

𝐶0 = (1,2 − 0,2√𝜌𝑔

𝜌𝑓)(1 − exp(−18𝛼))

4.3

𝑉𝑔𝑗 = √2(𝑔𝜎(𝜌𝑓 − 𝜌𝑔)

𝜌𝑙2)0,25(1 − 𝛼)1,75 4.4

0,00

50,00

100,00

150,00

200,00

250,00

0,0 20,0 40,0 60,0 80,0 100,0

Tem

pe

ratu

re, °

C

Axial node number

Tl

Tw

Tsat



29

The impact of each correlation on the minimum pressure drop is assessed for the

FE714 case (5,3 MW).

In Figure 14 one can notice that the value of drift velocity calculated by 3 different

correlations is in the same order of magnitude at the exit of the channel (i.e. in the

fully developed boiling region). A small decrease can be spotted only for drift

velocity calculated using the Hibiki equation. The value of drift velocity is around

0,18 m/s, 0,20 m/s and 0,22 m/s for Hibiki, Sun and Wang correlation respectively.

The difference is not significant but not negligible. When looking at the difference of

pressure drops obtained using these three correlations they are very close to each

other with an average error of around 0,75%. The correlation by Sun is taken as a

reference value in this error calculation. It is concluded, the deviations observed in

the previous sections are not related to the drift flux correlations used.

Figure 16: Drift velocity for 3 different correlations

Table 5: Pressure drops for 3 different drift velocity correlations

G

[kg/m2/s]

Pressure

drop using

Sun [bar]

Pressure

drop using

Wang [bar]

Difference

[kPa]

Error

[%]

Pressure

drop using

Hibiki [bar]

Difference

[kPa]

Error

[%]

6000 2,54 2,53 13,67 0,54 2,53 13,83 0,54

5900 2,54 2,52 14,66 0,58 2,52 14,83 0,58

5800 2,53 2,52 15,68 0,62 2,52 15,86 0,63

5700 2,53 2,51 16,74 0,66 2,51 16,93 0,67

5600 2,52 2,50 17,84 0,71 2,50 18,03 0,72

5500 2,51 2,49 18,98 0,76 2,49 19,18 0,76

5400 2,48 2,46 19,99 0,81 2,46 20,20 0,81

5300 2,59 2,57 20,59 0,80 2,57 20,80 0,80

5200 2,55 2,53 21,70 0,85 2,53 21,91 0,86

5100 2,65 2,63 22,39 0,84 2,63 22,60 0,85

5000 2,46 2,44 23,77 0,97 2,44 24,04 0,98

0,00

0,05

0,10

0,15

0,20

0,25

93,0 94,0 95,0 96,0 97,0 98,0 99,0 100,0

Dri

ft v

elo

city

, m/s

Axial node number

Sun

Wang

Hibiki



30

Chapter 5 – Conclusion

This work is part of the assessment of the RELAP5-3D correlations at low pressure

operating conditions relevant to MYRRHA secondary circuit normal operating

conditions.

A numerical model based on the drift flux model with properly selected closure

correlations was developed to predict two-phase flow physical phenomena

happening in a uniformly heated rectangular channel. The study focused on heat

transfer and pressure drop at conditions very similar to MYRRHA heat exchanger

conditions (pressure equal to 17 bar and inlet temperature equal to 200°C).

Considerable attention was paid to the selection of drift flux parameters and their

applicability to different flow regimes to model the studied phenomena. An iterative

scheme with exit pressure convergence criteria is selected to solve the system of

equations.

The model was validated against experiments related to the determination of the

onset of flow instabilities at very similar conditions to the ones of interest. In this

validation process, a pressure drop as a function of mass flux for four different

values of heat flux was examined. Overall the results are quite satisfactory and

encourage the future usage of drift flux models for low-pressure conditions. The

simplified drift flux model is shown in good agreement with the more sophisticated

thermal-hydraulic system code RELAP5-3D and shows that RELAP5-3D does not

detect any onset of nucleate boiling which can be more important at very low

pressures which will be the scope of the future work.

While the results are acceptable for a five-month project timeline for such a complex

problem, there is still plenty of room for further improvement and future work. An

energy partition model was already derived to increase the applicability range of

the model to other pressure conditions, however, because of the complexity of the

subject and so far, non-identified problems (either the numerical method or the

vapor generation models selected), further investigations will be undertaken in the

future.



31

Nomenclature

Nomenclature (all the variables are in SI units):

• A – cross section of the channel

• C0 – drift flux distribution parameter

• Cp – specific heat

• 𝐷ℎ - hydraulic diameter

• 𝑓 – friction factor

• 𝐺 – mass flux

• g - gravity

• H – enthalpy

• h - heat transfer coefficient

• i – indicator of node number

• j – superficial velocity

• K - thermal conductivity

• Nu – Nusselt number

• Nz – number of nodes

• P - pressure

• Ph – hydraulic perimeter

• Pr – Prandtl number

• q’’ - heat flux

• Re – Reynolds number

• T – temperature

• 𝑉 – velocity

• 𝑉𝑔𝑗 – drift velocity

• 𝑉′𝑔𝑗 - mean drift velocity of gas phase

• X – thermodynamic quality

• 𝑧 – axial distance

• 𝛼 - void fraction

• 𝜇 - viscosity

• 𝜌 - density

• 𝜎 – surface tension

Subscripts:

• m - mixture

• l - liquid

• g - gas

• sat – saturation

• sp – single phase

• tp – two phase

• d – detachment



32

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Master Thesis Report Projet de Fin d’Études (PFE)

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