Thermal-fluid simulation investigation of the reactor cavity cooling system standpipes design for the pebble bed modular reactor

THERMAL-FLUID SIMULATION

INVESTIGATION OF THE REACTOR CAVITY

COOLING SYSTEM STANDPIPES DESIGN

FOR THE PEBBLE BED MODULAR

REACTOR

P.R. Oosthuizen, B Eng.

Dissertation submitted in partial fulfillment of the degree Masters of Engineering in the

School of Mechanical and Materials Engineering Faculty of Engineering

at the

Potchefstroom University for Christian Higher Education

Promotor: Prof. P.G. Rousseau Potchefstroom

ACKNOWLEDGEMENTS

"Douglas Adarns"

I may not have gone where I intended to go, but I think I have ended up where I intended to be.

I thank God for the strength and courage he bestowed upon me over the past two years. His might cannot be comprehended.

I want to thank Prof. P.G Rousseau for his guidance and motivation.

Many thanks to my parents for their love and support.

I also want to thank my colleagues for creating the illusion of stability.

Pebble Bed Modular Reactors are advanced nuclear reactors and are being developed to possess inherent safety and reliability. This is achieved by utilizing a sequence of passive thermal storage and heat transfer mechanisms, to perform long term decay heat removal. The Reactor Cavity Cooling System (RCCS) facilitates this long term decay heat removal. The purpose of this study was to develop a one-dimensional, homogeneous twephase flow model in order to perform investigative thermal-fluid studies on the concept designs of the standpipes of a typical RCCS system, such as that proposed for PBMR .

An extensive literature survey was conducted and revealed that numerous research projects have been done in the field of passive heat removal systems. It was found that the twephase homogeneous model was used by many authors to investigate the characteristics of natural circulation systems; however, discrepancies were found in the implementation strategy of the twephase friction multiplier. Research proved that the theoretically derived, homogeneous multiplier were applicable to this study.

A simulation model was developed to perform investigative studies on the standpipes of the RCCS. This model is capable of simulating various fundamental phenomena, found in natural convective boilers, including heat transfer in the sub-cooled and nucleate boiling regions. The model was verified with experimental data obtained from Kyung and Lee (1996). The simulation results were in good agreement with the experimental data, even though deviations were observed in the mid heat flux region. These deviations occur due to flow oscillations that were not modelled in this study.

The two concepts (UTube and Annulus) of typical RCCS stand pipes were compared with each other, subjected to a heat load of 23 MW. The effect of the heater and riser diameter, as well as the effect of different reactor power profiles (constant and axial varying) on the flow characteristics w r e investigated. It was found that the annulus concept performed better, compared to the UTube, due to lower wall temperatures and higher flow rates.

"Pebble Bed Modular Reactors" is gevorderde kemkrag reaktors wat ontwerp word vir beter veiligheid en betroubaarheid. Die doel word bereik deur gebruik te maak van 'n geintegreerde reeks passiewe hitte-storing en hitte-oorgrag meganismes. Die reaktorholte verkoelingstelsel (RCCS) verseker die langtermyn wegvoering van vewal hitte. Die doel van die studie is om ondersoek in te stel na verskillende konsepte vir 'n tipiese RCCS stelsel om sy eienskappe te karakteriseer. Daar is besluit om 'n een- dimensionele, homogene, Wee-fase vloei model te ontwikkel vir hierdie doel.

'n Uitgebreide literatuurstudie is ondemeem en daar is gevind dat baie navorsing al gedoen is in die veld van passiewe verkoelingstelsels. Daar is gemerk dat die twee- fase, homogene model deur baie outeurs gebruik word om die karakteristieke eienskappe van natruurlike sirkulasie sisteme te ondersoek. Die implimenteeringstrategie van die twee-fase wrywingsverrnenigvuldiger word baie vaag

gestel in die literatuur. Verdere ondersoek het bewys dat die teoreties afgeleide homogene vermenigvuldiger toepaslik is in die studie.

'n Simulasie model is ontwikkel om navorsing studies op die staanpype van 'n RCCS stelsel te doen. Die model is in staat om verskeie fundamentele verskynsels wat teenwoordig is in natuurlike konveksie ketels te voorspel, insluitend hitte-oordrag in die ondewerkoelde- (sub-cooled) en kernkook (nucleate boiling) gebied. Die model is geverifieer met eksperimentele data van Kyung en Lee (1996). Die simulasie resulate vergelyk goed met die eksperimentele data, maar afwykings opgernerk. Hierdie afwykings word toegeskryf aan vloei-ossilasies, wat nie ingesluit is in die numeriese model nie.

Die Ubuis en annulus konsepte vir die RCCS is vergelyk in parametriese studies met 'n hitte inset van 23 MW. Die effek van die verhitter en stygleiding (riser), sowel as verskillende reaktor hitte profiele is getoets. Daar is gevind dat die annulus konsep beter is as die u-buis konsep, omdat laer wand temperature en hoer massa vloeie verkry is.

NOMENCLATURE

A C C~

D

f

F g G H h h, htc J

L

m

Nu

P

P

PI

q*

Q

R

Re

S

C

K T

v

Cross Sectional Area Martinelli Constant Specific Heat Diameter Friction factor

T w ~ P h a s e Reynolds number factor Gravitational acceleration

Mass Flux Height Enthalpy

Latent heat of vaporization heat transfer coefficient Relative velocity

Length

Mass flow rate Nusselt number Pressure Perimeter Brandt Number Heat flux Heat input Thermal resistance Reynolds Number Suppression factor Form loss factor Temperature Velodty

"C

x Quality

XC

Martinelli factor

z Elevation

-

vii

-

SUBSCRIPTS

e f 9 G H i L I lo m nb 0

oe

oi P S sat tot TP vo W WP WS Exit Fluid Gas Gas Homogeneous Inlet Liquid Liquid Liquid only Mean Nucleate boiling Total Total outlet Total inlet Primary Secondary Saturation Total TwePhase Vapor only wall Wall primary Wall secondary

.

viii

-

SUPERSCRIPTS

-

Average

+

Dynamic Rate TP Twophase

GREEK

SYMBOLS

a

Void fraction E Surface rougness Y Viscosity rP Fluid property P Density

o

Surface Tension

z

Shear Stress m k g l m .s k g l m 3 N l m N l m

Table of

Content

Acknowledgements Abstract Opsomming Nomenclature Subscripts Superscripts Greek Symbols List of figures List of tables ii iii iv v vii viii

ix

xiv xvii

C!HAPTER

1:

INTRODUCTION

1 1.1 PREFA 1.2 BACKGROUND 1.2.1 ThePBMR 1.2.2 TheRCC

1.2.3 Natural Circulation Systems ... 4

1.2.4 Two-Phase Flow ... 5

1.3 PROBLEM SATEMENT ... 8

1.4 AIM AND OUTLINE OF SITJDY ... 10

2.1 INTRODUCnO 2.2 TWSPHASE MODELLING APPROACHE 2.2.1 Correlations 2.2.2 AnalyticalModel 2.2.3 DifferentialAnalysi 2.3 HOMOGENEOUS TWO-PHASE FLOW MOD ... 15

2.3.1 FluidProperties for Homogeneous Flo 2.3.2 Two-Phase Frictional Pressure Dr

2.3.3 Two-Phase Heat Transfer ... 20

2 . 4 NATURAL CIRCULATI

2.4.1 Natural Circulation Characteristic 2.4.2 Flow Instabilitie

2.4.3 Heat Transfer

2 . 5 CONCLUSlON

...

CHAPTER

3: THEORETICAL

BACICGROUNR

33

3 . 1 INTCUDUCTIO 3 . 2 MODELLING APPROACHES 3 . 3 CONSERVA 3.3.1 Conservation ofMas 3.3.2 Conservation of Momentu 3.3.3 Conservation ofEner 3 . 4 COMPONENT ~ C T E R I S T I C EQUATION 3.4.1 Void Fraction 3.4.2 Pressure Dr 3 . 5 HEAT TRANSFE

3.5.1 One Dimensional Conduction 3.5.2 Flow Boilin

3 . 6 CONCLUSION

CHAPTER

4:

SIMULATION MODEL

4 . 1 INlXODUCI10 4 . 2 SIMULATION SOFTW 4 . 3 SIMULATION MODEL 4.3.1 Boundary 4.3.2 Model Inpu 4.3.3 Simulation Routine ... 60 4.3.4 Model Output 4.4 MODEL VERmCATlO ... 70 4.4.1 Experimental Set-up 4.4.2 Model Set-

4.4.3 Verification ofModel Calculatio

...

.

xii

-

CHAPTER 5:

INVESTIGATIVE

SZMUTIONS

79

5.1 INTRODUCTIO

5 . 2 HEAT INPUT CALCULATIONS 5.3 U-TUBE MODE 5.3.1 Parametric Stu 5.3.2 Loop Characteristic 5 . 4 ANNULUSMODE 5.4.1 Parametric Stu 5.4.2 Loop Characteristic 5 . 5 CONCEPT COMPARISON 5.5.1 Constant Heat Profil 5.5.2 Axial Varying Hear Profile 5 . 6 CONCLUSION

6.1 I ~ O D U C T T O N . 03

6 . 2 CHneTER SUMMARY 0 3

6 . 3 STUDY CONCLUS~ON 0 4

6.4 RECOMMENDATIONS FOR FURTHERRES 05

REFERENCES

106

k 1 NOMENCLAW AND UNIT

A.2 EES CODE ...

APPENDIX B1: U-TUBE- SIMULATION MQD

B 1.1 NOMENCLATURE AND UNIT

B 1 . 2 EESCODE ... 136

B 2 . 2 NOMENCLATURE AND UNITS ...

.

.

... 15 1

C. 1 NOMENCLATURE AND UNITS ,... 170

C.2 EESCODE 170

.

xiv

.

List of

figures

Page

Figure 1 . 1. Heat transfer mechanisms to the RCCS

...

2

Figure 1.2. Detail section of the reactor

...

3

Figure 1.3. Schematic Natural Circulation Loop ... 4

Figure 1.4. Flow patterns in the vertical direction ... 6

Figure 1.5. Schematic drawing of the nucleation sites

...

7

Figure 1.6. Adiabatic and Diabatic Flow

...

8

Figure 1.7. Information needs of twephase flow analysis ... 10

Figure 2.1. Flow pattern map for vertical flow (Hewitt and Roberts)

...

14

Figure 2.2. Different circulation modes (Kyung and Lee) ... 26

Figure 2.3. Typical instability map (Kyung and Lee)

...

27

Figure 2.4: Illustration of flow excursion in natural circulation systems (Jiang et a1 (2000))

...

29

Figure 3.1 : Variation of void fraction with quality

...

39

Figure 3.2. Moody friction factor chart ... 39

Figure 3.3. Comparison of various multipliers, evaluated at atmospheric pressure

...

44

Figure 3.4. Schematic of the heat transfer trough a wall

...

46

Figure 3.5. Regions of heat transfer in a flow boiling system ... 50

Figure 3.6. Reynolds number factor (F)

...

52

Figure 3.7. Temperature profile for flow boiling (Chen 1963)

...

53

Figure 4.1. Schematic layout of the UTube concept ... 57

Figure 4.2. Schematic layout of the annulus concept

...

58

Figure 4.3. Corresponding flow areas of the two concepts ... 60

Figure 4.4. Equation rank

...

61

Figure 4.5. Basic structure of the fluid property function ... 62

Figure 4.6. Structure of the quality function

...

63

Figure 4.7: Moody friction chart with interpolation between laminar and turbulent region

...

64

Figure 4.8. One dimensional heat conduction to the pipe

...

65

Figure 4.9. Algorithm to calculate the heat transfer coefficient ... 66

Figure 4.10. Algorithm to evaluate the frictional multiplier

...

67

...

Figure 4.12. Heat transfer to the annulus 69

...

Figure 4.1 3: Experimental Set-up [Kyung and Lee (1 996)] 71 Figure 4.14: Variations of the heater inlet velocity with inlet sub-cooling

[Kyung et a1 (1 996)]

...

73

Figure 4.15. Comparison at an inlet sub-cooling of 5°C

...

74

Figure 4.16: Comparison between analytical and experimental data obtained by

...

Kyung et a1

.

(1996) for an inlet sub-cooling of 5°C 75 Figure 4.17. Comparison at an inlet sub-cooling of 20°C

...

76

Figure 4.18. Comparison at an inlet sub-cooling of 35°C

...

77

Figure 4.19: Comparison between analytical and experimental data obtained by Kyung and Lee (1996) for an inlet sub-cooling of 35"CError! Bookmark not defined

.

Figure 5.1 : Typical Decay heat profile

...

80

Figure 5.2. Axial varying heat profile

...

81

Figure 5.3. Mass flow rate vs . diameter (UTube)

...

81

Figure 5.4. Exit velocity vs

.

diameter (U-Tube)

...

82

Figure 5.5. Exit quality vs

.

diameter (U-Tube)

...

83

Figure 5.6. Maximum wall temperature vs

.

diameter (UTube)

...

84

Figure 5.7. Pressure distribution (UTube)

...

85

Figure 5.8. Density distribution (UTube)

...

85

Figure 5.9. Velocity distribution (UTube)

...

86

Figure 5.10. Heater wall temperature (UTube)

...

87

Figure 5.1 1: Heat transfer coefficient (Utube)

...

88

Figure 5.12. Bulk fluid temperature (Utube)

...

88

Figure 5.13. Mass flow rate vs

.

diameter (Annulus)

...

89

Figure 5.1 4: Exit velocity vs

.

diameter (Annulus)

...

90

Figure 5.1 5: Exit quality vs . diameter (Annulus: constant heat rate)

...

91

Figure 5.16. Maximum wall temperature vs . diameter (Annulus)

...

91

Figure 5.1 7: Pressure distribution (Annulus)

...

92

Figure 5.18. Density distribution (Annulus)

...

93

Figure 5.1 9: Velocity profile (Annulus)

...

94

Figure 5.20. Wall temperatures (Annulus)

...

95

Figure 5.21. Heat transfer coefficient (Annulus)

...

95

.

xvi .

Figure 5.23. Comparison of mass flow rate (constant heat profile)

...

97

...

Figure 5.24. Comparison of the exit velocity (constant heat profile) 97 Figure 5.25. Comparison of the exit quality (constant heat profile)

...

98 Figure 5.26. Comparison of the maximum wall temperature (constant heat profile) ... 99 Figure 5.27. Comparison of mass flow rate (varying heat profile)

...

100

...

Figure 5.28. Comparison of the exit velocity (varying heat profile) 100 Figure 5.29. Comparison of the exit quality (varying heat profile)

...

101 Figure 5.30. Comparison of the maximum wall temperature (varying heat profile)

...

102

...

Figure C.1. Unit Curve 172

.

xvii .

List of tables

Page

Table 4-1: General fixed inputs

...

59 Table 4-2: Model outputs ... 70 Table 4-3: Parameters of the experimental loop

... 72

1.1 Preface

Hight Temperature Gas Reactors tereafler refered to HTGR) such as the PBMR

6

advanced reactors and are being developed to possess inherent safety, reliability and economic performance. The design approach to safety of such nuclear reactors is to provide a plant that limits the potential for upset events that may have adverse consequences. This is achieved by limiting component temperatures, pressures, stresses and chemical reactions that the plant may experience during such events.

1.2 Background

1.2.1 The PBMR

Typical PBMR designs achieve inherent reactor safety by utilising an integrated sequence of completely passive thermal storage and heat transfer mechanisms. These mechanisms reject decay heat in the event that all the active cooling systems of the plant fail to operate. During such an event, the initial heat up transient in the core is followed by a cool down process, which, if uninterrupted could continue for several days.

A catastrophic event involving the failure of both the main and standby "active" core cooling systems is called Depressurised Loss of Forced Cooling (DLOFC). This event is initiated by a primary system leak which ensures helium depletion, which leads to the depressurization of the reactor. If such an event is initiated by a loss of offsite power followed by a turbine trip, the reactor remains in a pressurised state. This event is called Pressurised Loss of Forces Cooling (PLOFC).

Cooling of typical PBMR designs during a conduction cooldown is achieved via passive heat transfer mechanisms (i.e. thermal radiation, conduction and natural convection). Figure 1.1 shows the ,heat transfer mechanism schematically. A buoyancydriven cooling, called the Reactor Cavity Cooling System (hereafter referred to as the RCCS) facilitates this function.

THERMPL-FLUID S1WLATK)N INVESTlGATlON OF THE REACTOR C A W COOLING SYSTEM STIIEIPIPfS DESIGN FOR THE PEBBLE BED MODUUR R W T O R

Reactor Cavity

Reactor Vessel

r

ZCCS Standpipe

Heat Transfer Modes

Radiation

a

Free Convection

-

Conduction L

Core Radiation

Figure 1.1: Heat transfer mechanisms to the RCCS

1.2.2 The RCCS

The RCCS is a continuously operational, safety-related system, which provides adequate heat removal without dependence on active components. The passive RCCS design incorporates a substantial performance margin and a high degree of redundancy to achieve extremely high reliability and thus ensures reactor safety. The RCCS is not dependent on operator action and its performance is insensitive to operator error.

Owing to the large thermal capacitance, the reactor core heats up very slowly following boiling in the standpipes over a period of many hours. As the active core temperature increases, heat is conducted through graphite blocks, primarily in the radial direction. Heat is transferred across the core annulus from the outside of the core barrel to the vessel wall via thermal radiation and natural convection. Heat is rejected from the uninsulated reactor vessel primarily by means of thermal radiation to an array of stand THERMPL-FLUID SIMULATION INKSTKiATION OF THE REACTOR CAVITY COOLING SYSTEM STANPWS DESIGN FOR THE PEBBLE BED M O W M REKTOR

pipes situated around the perimeter of the reactor cavity. Figure 1.2 shows a more detailed section of the reactor and the RCCS.

RCCS standpipes

lmpigement plate

Core barrel

Reactor pressure

Figure 1.2: Detail section of the reactor

The RCCS concept employs water boiling and steam condensation for transport of heat from the stand pipes to the environment. Boiling is only used if the RCCS water supply fails.

- - --

THERMMFCUID SlMlLATIQN INKSTIGATIQN OF THE REACTOR CAVITY COOLING SYSTEM STMPPES DEW24 FOR THE PEBBLE BED W U I R REACTOR

CHAPTER1: INTRQDUCTION

-4-1.2.3 Natural Circulation Systems

There are many applications for natural convection (also known as natural circulation or free convection). systems. Natural convection strongly influences heat transfer from pipes and transmission lines, as well as from various electronic devices. It is also relevant to the environmental sciences, where it is responsible for oceanic and atmospheric motion. The accident at the Three Mile Island reactor in 1979 proved the importance of the concept of inherent reactor safety. This led to the development of passive residual heat removal systems, Su Guanhui (2001) et al. A number of organisations world-wide have proposed natural circulation as the operation mode for the latest generation reactors, under both normal and abnormal operating conditions.

Natural circulation is an important heat removal mechanism in modem reactors, owing to its simplicity and passivity. Flow in a natural circulation or gravity-driven system is induced by a density gradient between the cold side and the heated side of the system, such a basic system can be seen in Figure 1.3. This density gradient generates a body force that acts on the fluid, which in turn induces fluid flow. The density gradient is caused by heat addition in the heater part of the system. This heat addition (reactor core power) is the most important parameter in a natural circulation system since it drives the flow.

CONDENSER

Figure 1.3: Schematic Natural Circulation Loop

THERMAl.-FlUID SIMULATIONIN'JESTIGATtONOF THE REN;TOR CAVITY COOLING SYSTEM STANPIPESDESIGNFORTHE PEBBLEeED MOCULM REACTOR

SCHOOLOF MECHANICAlAND MATERiAlSENGINEERING.PO FOR CHE

-1.2.4 Two-Phase Flow

The importance of fluid flow and heat transfer with a change in phase arises from the fact that many industrial processes rely on these phenomena for materials processing, or for energy transfer; e.g. petroleum processing, paper-pulping and power plants. According to classical thermodynamics a phase is a macroscopic state of matter that is homogeneous in chemical composition and physical structure. These phases of matter are:

Solid state Liquid state Gas state

Twophase flow is the simplest case of multiphase flow in which two phases are present for a pure substance. Sometimes the term "multi-component" is used to describe flows in which the phases consist of materials of different substances, for example, the flow of steam and water is twephase flow with a single component.

1.2.4.1 Flow Patterns

In single-phase flow it is important to know whether the flow is laminar or turbulent, or whether flow separation or secondary flow exists. These characteristics help in modelling specific phenomena because it indicates the flow character for a particular geometry. The key towards understanding multi-phase flow phenomena is the ability to identify the internal geometry of the flow; i.e., the relative location of interfaces between the phases, how they are affected by pressure, flow, heat flux and channel geometry and how transition between the flow patterns occur.

Two fundamental types of flow pattems can be identified, stratified and dispersed. In a stratified flow pattern the two phases are separated by a continuous interface at a length scale compared to the external scale of the flow; e.g. a liquid film on a wall with a gas or other immiscible fluid at the centre of the channel. The separation of the two phases usually occurs due to density differences combined with a relatively low mass flow rate of the phase near the wall compared to the phase in the centre of the channel. These separated flow pattems can occur when the phases flow in the same direction ( c o current flow) or in opposite directions (counter-current flow). The balance between buoyancy and inertial forces governs the transition between these two types of stratified flow.

MERMPL-FLUID SIMULATION IN'ESTK;ATK)N OF M E REXTOR CAVITY COOLING S W M

STANP~PES DEW FOR

mE

PEBBLE BED MODUCPR RWTOR

CHAPTER 1: INTRODUCTION

A dispersed

flow

patternis one in which one or more phasesare uniformlydispersed within a continuum of another phase with a length scale, much smaller than the external scale; e.g. gas bubbles or solid particles in a liquid, or liquid droplets in a gas or another immiscible liquid. In this case the dispersed phase forms into nearly regular shaped particles with their size governed by a balance of buoyancy, inertial and surface tension forces. The transitional flow regimes between these two fundamental types of flow patterns can take on many different kinds of geometries. Some of the more common transitional flow patterns are chum-turbulent and slug flow. Figure 1.4 shows the general flow patterns for vertical fluid flow.

Bubble flow Slug or plug flow Vertical Direction Chum flow Annular flow . 0"' ..' . ,. . .. . .... I.... ,.. ,'., . - . .' .' . ,. . ~, Dispersed flow Figure 1.4: Flow patterns in the vertical direction

1.2.4.2 Pool Boiling

Boiling is the process in which a liquid evaporates and forms vapour pockets or regions within the continuous liquid phase. Boiling can take many forms. When a stagnant pool of liquid is heated and boiling occurs in the bulk liquid pool, it is called pool boiling. To form the vapour phase within the continuous liquid phase one must heat the liquid to a

temperatureabove its saturationtemperature,Tsat' The saturationtemperatureis that

temperature at which the liquid exerts a vapour pressure equal to the ambient pressure.

If the temperatureof the fluid increasesa substantialamountabove Tsat' vapourwill be

formed (nucleate) as bubbles within the bulk of the liquid, causing "bulk" pool boiling.

THERMAl.FlUIDSIMULATIONINVESTIGATIONOF THE REACTORCAVITYCOOliNG S'YSTEM

STANPIPESDESIGNFORTHEPEBBLEBEDMODULARREACTOR

__ * _ _** U. _ _** *_.* u. * -* - --- - -- - .*

CHAPTER1: INTRODUCTION

~7-This type of nucleation is termed "homogeneous nucleation" and is rarely observed in most common boiling situations. If one takes a look at the heated surface, one will notice that vapour bubbles nucleate at the surface. In this case the temperature of the

liquiddoes not need to be far aboveTsar' This nucleationoccursat crevices(nucleation

sites) inside the reated surface, aided by trapped vapour and gas and is termed "heterogeneous nucleation". Figure 1.5 shows the nucleation sites schematically. This type of pool boiling is quite common in many industrial applications.

. L.iquid

. Liquid_

Heated surface

Heatedsurf'ace

Figure 1.5: Schematic drawing of the nucleation sites

1.2.4.3Flow Boiling

Flow boiling occurs when all the phases are in bulk flow together in a channel; e.g. vapour and liquid flow in a pipe. The multi-phase flow might be classified an adiabatic or diabatic Le. without or with heat addition at the channel wall. An example of adiabatic flow would be oil/gas flow in a pipeline, or air/w9ter flow. The difference between adiabatic and diabatic flow is shown in Figure 1.6. In these cases the flow patterns would change as the inlet mass flow rates of the gas or liquid are altered, or as the velocity and void distributions develop along the channel. An example of diabatic flow is to be found in the riser tubes of steam generators and boiler tubes in power plants, or in the cooling channels of nuclear power plants. Boiling occurs on the walls of the channels and flow patterns change due to vapour production as one observes the flow downstream in the channel. This is an important difference between pool boiling and flow boiling, Le. that the forced flow of the multi-phase system causes flow pattern transition at a given wall heat flux (or temperature).

THERWL-FLUID SIMULATIONIN\,/ESTIGATIONOF THE REACTOR CAVITY COOLING S'tSTEM STANPIPESDESIGNFORTHE PEBBLEBED MODULARREACTOR

--CHAPTER1: INTRODUCTION ~8-Bubbly Slug Chum AD/ABA TICFLOW Annular Single phase Vapour

tl....

AnnularI~ Flow -x=1 '" Bubbly Flow 1 I~ Slngl;;i:e Liquid

-x.o

D/ABA TICFLOW Figure 1.6: Adiabatic and Diabatic Flow

1.3

Problem Statement

The function of the RCCS is to actively remove heat from the reactor cavity in order to ensure t~at the various structures and equipment attached to the reactor are not damaged due to overheating.

The RCCS must satisfy the following requirements:

· To protect the reactor cavity concrete from excessive temperatures and to prevent the concrete from heating up to critical temperatures during upset events such as PLOFC and DLOFC.

THERMAl..fLUID SIMULATIONIN'JESTIGATIONOF THE REACTOR CAVITY COOLING SYSTEM

STANPIPES DESIGN FOR THE PEBBLE BED MODULAR REACTOR SCHOOL OF MECHANICAL AND MATERIALS ENGINEERING, PU FOR CHE

CHAPTER 1: INTRODUCTION

.9-·

The RGGS should have sufficient heat capacity to provide a three to four day boil-off period during which the water in the stand pipes will be allowed to evaporate, thus utilising the latent heat of evaporation as an additional heat sink.

·

Part of the function of the RGGS is also to ensure that the reactor pressure vessel support structure is cooled sufficiently during upset events so that the concrete is not damaged due to excess heat that is conducted through the reactor pressure vessel supports to the concrete.

·

Must have a mechanical robust structure that will not fail under vibrations generated by the boiling action of the water.

A comprehensive performance analysis of the RGGS is essential to confirm that the PBMR design satisfies the component temperature safety criteria described above. It is appropriate to start the process of analysing two-phase flow systems by asking the following questions.

1. What are the number of flow dimensions that need to be presented?

2. What is the expected degree of mechanical equilibrium between the phases? 3. What is the expected degree of thermal non-equilibrium in the flow?

Once these questions are answered, an appropriate two-phase flow model can be selected. The information needed to solve a two-phase flow problem is depicted in Figure 1.7.

THERMAl-FlUID SIMULATION IN'JESTIGATION OF THE REACTOR CAVITY COOLING S'tSTEM

STANPIPES DESIGN FOR THE PEBBLE BeD MODUlAR REACTOR SCHOOl OF MECHANIC;\L AND MATERIM..5ENGINEERING, PU FOR CHE

---CHAPTER 1: INTRODUCTION .10

-Figure 1.7: Information needs of two-phase flow analysis.

1.4

Aim and Outline of Study

As pointed out in the previous section, the PBMR design philosophy places emphasis on inherent safety. This is achieved by the simplification of the plant structure and use of passive safety systems. These passive safety systems must be independent ci external power as well as operator action to perform long-term decay heat removal.

The performance of the ReeS is being verified in an analytical way. The analytical work consists of building a two-phase model of the standpipes of the ReeS so that thermal-fluid simulations can be conducted. The computer codes that are being developed for the analysis of the stand pipes must be able to accurately model various

THERWL-FlUID SIMULATIONIN\JESTIGATIONOF THE REACTOR CAVITY COOLING S'tSTEM

STANPIPESDESIGNFORTHEPEBBLEBED MOOULARREACTOR

SCHOOl OF MECHANICAlAND MATERiAlSENGINEERING.PU FORCHE

GEOMETRY

-

MODEL _{TYPE OF}

1D...1.2DL3.D _HEM

I

SLIPI?D

TRANSIENT

.TRANSIENT INTERFACE_JUMP

EQUATIONS _CONDITIONS WALL _INTERFACE RELATIONS RELATIONS IEQUATIONSSTATE BOUNDARY INITIAL CONDITIONS CONDITIONS SOLUTION

physical phenomena found in twephase flow. These phenomena include fluid dynamics, heat conduction, convection and convective boiling.

The geometry of the stand pipes has a direct effect on the heat transfer characteristics of the RCCS. Changes in the stand pipe geometry are being investigated to determine the optimum RCCS geometry to dissipate heat from the reactor core and structures.

MERMPL-RUID SlWLATlQFl INKSTIGATKN OF W E REKTOR CAVITY COOCWG SYSTEM

STPNPtPES DESIGN FOR THE PEBBLE BED MOOULPR REPCTW

SCHOOC OF AlECHPNlCM PND MATERIMS ENGElEERlNG

W

FOR CHE

G W E R 2: LITERATURE SURKY

-

12

-

2

LKERATURE SURVEY

2.1

Introduction

The previous chapter described the basic concepts of passive heat removal systems in nuclear power plants and the conditions under which they operate. The fundamentals of twephase flow have also been discussed.

In this chapter an extensive literature survey is presented on the field of single component, twephase flow. The focuses is placed on ways to build a twephase flow model in order to investigate the characteristics of an emergency backup cooling system, operating under natural convection conditions.

Some aspects of twephase flow and natural circulation systems that fall outside the scope of this study will also be discussed, as it is of great importance for the detailed analysis of such systems.

2.2

Two-Phase Modelling Approaches

All the basic laws of fluid mechanics can be applied to twephase flow. The equations are merely more numerous and complicated than those of single-phase flow. Wallis (1969) stated that several techniques could be used to analyse one-dimensional flow. These techniques will be discussed in ascending order of sophistication.

2.2.1 Correlations

Correlations of experimental data in terms of chosen variables are a convenient way of obtaining design equations. The crudest correlations are merely mathematical exercises performed by a computer. More advanced techniques use dimensional analysis or a grouping of several variables together on a logical basis.

The advantage of correlations is that they are easy to use. They can give quite satisfactory results, if they are applied to situations similar to those that were used to obtain the uiginal data (Collier (1972)). The statistical limits of the correlations are

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usually known. Conversely, they can be quite misleading if used unsystematically in a variety of applications. Little insight into the basic phenomena is achieved by data correlations; no indication is given of ways in which performance or accuracy could be increased. In general, correlations will be avoided in this study unless they possess a viable claim to generality.

2.2.2 Analytical Models

Very simple analytical models, which take no account of the details of the flow, can be quite successful. They can be used for both organising experimental results and for predicting design parameters. For example, in the homogeneous model approach, the components are treated as a pseudo fluid with average properties, as explained by Todreas etal. (1993). This means that a suspension of droplets in a gas, foam or the stratified flow of a gas over a liquid are all treated exactly alike.

Whalley (1987) stated that in the separated-flow I twefluid model the phases are assumed to flow side by side. Each phase has its own set of equations and the interaction between the phases is also considered. These models are being used widely in complex computer codes because they can permit different gas and liquid velocities and flow directions as well as different liquid and gas temperatures. These models still rely on one-dimensional formulations and require closure laws to deal with the interfaces as well as boundary conditions. Because these closure laws are known to depend on flow patters, flow regime maps must also be specified. Figure 2.1 shows an example of a typical flow pattern map for vertical flow.

The drift-flux model is essentially a separated flow model in which attention is focused on the relative motion of the individual phases (Todreas et a/. (1993)). The convenience of this model is that the relative motion is determined by a few key parameters, which is independent of the flow rate of each phase. The drift-flux model is useful for low pressure andlor low flow conditions such as found in PBMR systems.

Wen etal. (2003) and Xu et

d.

(2003) stated that the homogeneous model can be used satisfactory for investigative purposes. The accuracy of this model can be improved with the use of appropriate correlations for the heat transfer coefficient and twephase

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pressure drop. The separated-flow model is very complex and in most cases can only be solved with the use of advanced simulation programs.

Annular 70"

Figure 2.1: Flow pattern map for vertical flow (Hewitt and Roberts) / I I I _WSPY I Annular I I \ \

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2.2.3 Differential Analysis

Wallis (1969) stated that in differential analysis the velocity and concentration fields are deduced from suitable differential equations. The equations are written for time- averaged quantities, following the one-dimensional flow idealisation, as in single-phase theories of turbulence. Temporal variations might even be considered in more sophisticated versions of the heory. Usually the more complex theories lead to the inclusion of additional effects and the prediction of numerical values of correction factors. These correction factors can be applied to simpler theories in order to increase their accuracy. These complex theories may also lead to an analytical rather than an empirical relation between the important variables.

1

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2.3 Homogeneous Two-Phase Flow Model

The simplest technique used for analysing twephase (or multi-phase) flow is through the use of homogeneous flow theories. Suitable average properties are calculated and the mixture is treated as a pseudo fluid that obeys the usual laws of single-component flow. All the standard methods of fluid mechanics could then be applied. The homogeneous model is most suitable for investigative studies due to its simplicity and is used throughout the literature to investigate the characteristics of natural circulation systems due to the stability of the model. The model proves to give good results when (Whalley (1987));

the liquid to gas density ratio is smaller than 10 or, the mass flux is higher than 2000 kglm s'

.

If the mass flux of the system is higher than 2000 kglm 's, it could be assumed that the two phases are evenly (homogeneously) mixed over the flow area,

The average properties that are required by the model are velocity, thermodynamic properties (e.g. temperature, density and enthalpy), and transport properties (e.g. viscosity). These properties are the weighted mass averages of the liquid and gas properties, as will be seen in section 2.3.1.

Differences in velocity, temperature and chemical potential between the phases will promote mutual momentum, heat and mass transfer. When one phase is finely dispersed in the other, these processes proceed very rapidly and it can be assumed that equilibrium is reached. In this case the average values of velocity, temperature, and chemical potential are the same as the value for each component, hence homogeneous equilibrium flow.

In some cases the use of homogeneous models are not advised. For example, a suitable average velocity cannot describe counter current vertical flow.

2.3.1 Fluid Properties for Homogeneous Flow

Levy (1999) and Wallis (1969) defined homogeneous flow as one where the fluid properties of the twephases are constant and the liquid and gas velocities and MERMAL-FCUID SIMJLATION INWSTIGATION OF M E REPCTOR CAVITY COOLING SYSTEM STPNPfPES DESIGN FOR THE PEBBLE BED M O B U M R W T O R

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temperatures are equal over the flow cross-sectional area. It is assumed that all fluid properties are constant across the flow area. Wallis (1969) defined the effective fluid properties in terms of the weighted average liquid and gas properties and are calculated as follows:

with fp representing any fluid property such as density, conductivity, viscosity, etc.,

q L

represents the saturated liquid properties and plG the saturated gas properties with x the fluid quality. The subscript H represents the homogeneous twephase state.

Various methods exist to calculate the average twephase viscosity. This is an important fluid property, as it is used to determine twephase flow patterns and Reynolds numbers. The flow patterns are dependant on the viscosity, density and surface tension of the fluid. The expressions available for calculating the twephase viscosity are of an empirical nature for no theoretical models exist.

Various methods exist to calculate the two-phase viscosity in terms of saturation properties. Some of these correlations are summarised by Levy (1999). Bankoff (1960) and others defined

pH

in terms of the average gas volume fraction

a .

Jaspari et a/. (1964) preferred to weigh the liquid and gas viscosity according to the liquid and gas weight-rate fraction. Wallis (1969) relates the viscosity, friction factor and frictional pressure drop in two-phase flow to the equivalent values for single-phase flow of one of the phases alone. Other methods to calculate the twephase viscosity does exist, but it falls outside the scope of this study, as it applies only to solid-fluid flow.

2.3.2 Two-Phase Frictional Pressure Drop

Several methods to predict the two-phase pressure dop have been developed. It should be noted that a large degree of empiricism is involved in calculating the pressure drop, as the flow is inherently chaotic.

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The earliest proposed single-phase model assumed that all the fluid properties (including the density and volume fraction) were constant and uniform across the flow area. This led to direct applications of single-phase correlations to twephase tlow. The most frequently used analysis methods for evaluating the friction component in the momentum conservation equation are based on the concept of twephase multipliers. These multipliers are used as a correction factor when the single phase friction factor is used to evaluate the friction component of the pressure drop. Correlations for the twephase wall friction factor exist, but few correlations are to be found 'in the literature. Many correlations have been developed over the last decade to calculate the twephase multipliers instead. It is important to note that these multipliers were correlated at different reference flow-patterns. Thus when designing a boiling system, the dominant flow pattern must be known to ensure that the most appropriate multiplier correlation is chosen. These multipliers have the form:

PL

A - P

$2

:=

-P m - 6 0

,

where liquid is the reverence single-phase

2

PC

f T P $ =--

"0

,

where vapour is the reverence single-phase

Thus the frictional pressure drop component can be calculated as follows:

The subscript R in equation (2.3) donates the reference single-phase flow.

Holland et a/. (1995) proposed that there are four possible reference single-phase flow conditions that might exist for a gas-liquid twephase flow problem:

Liquid overall, denoted by the subscript lo Vapour overall, denoted by the subscript vo

Only the liquid in the twephase mixture, denoted by the subscript 1

Only the gas in the twephase mixture, denoted by the subscript g

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The assumption where only the liquid or gas phase in the twephase mixture is considered could only be applied to the separate twephase flow models. When using this assumption t must be noted that the relevant phase velocity (not the total flow

velocity) should be used to calculate the pressure drop. However, Todreas et a/. (1993) proposed an equation to convert the multiplier to

4:.

Lockhart and Martinelli (1949) calculated the twephase pressure drop from the pressure drop that would occur in one of the phases, if it were flowing alone in a duct. They suggested that

h2

or

4;

could be calculated uniquely as a function of

X,

, where

X,

is a function of the frictional pressure drop of only-liquid and only-vapour flow, given by equation (2.4).

1

(L@pT(g'

--

-

x,,

1 - x

Their results were obtained from horizontal flow of twecomponent systems at low pressures. Many works showed that the Lockhart-Martinelli method could give first estimations of data over a wide range of experimental conditions.

The frictional multipliers used by Chisholm (1 973) correlated the twephase pressure drop to that which would occur in single-phase flow if the total mass flux was liquid or vapour only. This method was mainly developed for pressure drop in turbulent flow. Wen et a/. (2003) compared various correlations and found that the Chisholm correlation

over estimated the data by 300% for small channels.

Wallis (1969) developed a homogeneous twephase flow pressure drop model, which uses twephase friction factors. The assumptions he made was that the twephase friction factor is equal to that of liquid single-phase flow at the same mass flux as the total twephase mass flux and that it has the same Reynolds number dependence as the single-phase friction factor. This model predicted the experimental data with an accuracy of 50%.

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Yu et a1 (2002) studied twephase pressure drop in small diameter channels. They found that the twephase pressure drop data of the small channel was consistently lower than would be expected in larger channels with the same mass fluxes. They made a modification to the Chisholm correlation to predict the pressure drop better for small channels. Their modification predicted the experimental data with a root mean square error of 7%.

Martinelli et al. (1948) dealt with steam-water data. The basic assumption they made was that the twephase multiplier could be related to the flow quality at any given pressure. They also assumed that thermodynamic equilibrium and flow patterns exist. Their correlation used the X , (turbulent-turbulent) factor from Lockhart-Martinelli's work to establish values for the twephase multiplier. This approach assumes, as with the homogeneous approach, that the flow rate does not affect the twephase multiplier. This correlation still seems to be applicable with an uncertainty of 35%.

Sumith et a/. (2003) studied the characteristics of saturated flow boiling and used a correlation for the twephase wall friction factor; this led to the exclusion of the t w e phase multiplier. They found that this correlation could be used for calculating the single and twephase friction factor in small diameter pipes. However, the range of the correlations was not clearly stated.

Holland et a1 (1995) stated that the frictional component during natural circulation is less dominant than the gravity component in the momentum conservation law thus one should not use the frictional multiplier. Three approaches to estimate the twephase wall friction factor were given.

These approaches are:

The use of a constant friction factor with a value of 0.007, irrespective of the fluid conditions.

Calculating the friction factor in the same way as for single-phase flow, but the Reynolds number must be evaluated using the mean mixture viscosity.

Using a friction factor for a corresponding single-phase flow. This corresponding single-phase depends on the quality of the mixture, e.g. for a twephase flow with

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a high quality, for example in the spray regime, use gas flow as the reference single-phase flow.

2.3.3 Two-Phase Heat Transfer

Heat exchangers are used extensively in various fields. Some of these heat exchangers work under twmphase boiling conditions. Boiling heat transfer is present in steam generators and steam equipment of practically all nuclear power plants. It is therefore a common technique for cooling high power thermal systems. As discussed in Chapter 1, two main types of boiling exists i.e. pool boiling and flow boiling. Because the RCCS operates under flow conditions, the focus of this section will fall on flow boiling mechanisms. Flow boiling has been an active field of research in the past decades due to its many practical applications.

In this section an extensive literature survey has is presented twmphase heat transfer coefficients and critical heat flux correlations. The margin between the anticipated heat flux and the critical heat flux (hereafter referred to as CHF) is a major factor in the design of boiler systems, as the avoidance of CHF is extremely important.

2.3.3.1 Two-Phase HeatTransfer Coefficients

Barbosa eta/. (2002) stated that of all the possible flow regimes, annular flow is the most important one, occurring over qualities ranging from a few percent up to values close to unity. They conducted boiling experiments in a vertical annulus in which heat was applied to the inner surface of the channel. In this experiment they tested several heat transfer coefficient correlations and found that Bennett's correlation was the most accurate.

A popular composite correlation to cover the entire range of saturated boiling is that of Chen (1963). His correlation, which is widely used, is expressed in the form of a convective part and nucleation boiling part as can be seen in equation

(2.5)

-- - -

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where F is the twophase Reynolds number factor and S is the boiling suppression factor. The terms htc,, htc, and htc,, are the twophase heat transfer coefficient, the well known Dittus-Boelter heat transfer coefficient and the Forster-Zuber heat transfer coefficient, respectively. These terms will be discussed in more detail in the next chapter.

Yu et a1 (2002) studied boiling heat transfer and CHF applicable to water in small

diameter tubes. They found that the heat transfer coefficient were heat flux dependent, but mass flux independent They found that in large diameter channels the nucleation heat transfer dominated over the convective and that it persisted to qualities above 0.5.

Collier (1982) discussed the possibility of using the Chen (1963) correlation in the sub- cooled boiling region by adding a temperature difference weighting to each of its components:

For subcooled boiling, F can be set equal to unity and S can be calculated with the quality x being set to zero. He found that this method gave acceptable results against experimental data of water and ammonia.

Kang (1998) studied the effect of a vertically installed tube length on the nucleate boiling heat transfer coefficient under atmospheric pressure. His experimental results showed that a shorter tube is more efficient to increase the heat transfer rate due to smaller bubble slug formations on the tube surface. The study showed that the effect of tube length is negligible for a length to diameter ration of less than 50. After that the heat flux decreases linearly with an increase of H. He found that the heat transfer in natural circulation systems can be calculated with reasonable accuracy, using appropriate pool boiling correlations.

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2.3.3.2 Critical Heat Flux

During pool or flow boiling the heat transfer coefficient could fall rapidly and the wall temperature increases rapidly at some point along the channel. At this point there is not enough fluid to wet the surface of the heated channel due to rapid forming vapour, thus dryout occurs. This phenomenon is known by names of; Burnout, Dryout, Critical Heat flux (CHF) or Boiling Crisis.

Sang Jun Ha et a/. (2000) developed a phenomenological model of CHF, applicable to

both pool and sub-cooled forced convective boiling. They used the dryspot model proposed recently, existing correlations for active site density, bubble departure diameter and heat transfer coefficient in nucleate boiling. They made some modifications to the suppression factor to enhance the accuracy of the model.

Schoesse et a/. (1997) studied the characteristics of CHF under low flow conditions. The CHF measurements were conducted in a vertical upward annulus channel with a heated inner wall. They found that the CHF at low pressures and low velocities could be classified into a low and high mass flux and transition region. The influence of sub- cooling on the CHF was remarkable only in the transition region and high mass flux region. This behaviour is affected by the flow pattern, which is developed for given inlet conditions. They also found that the most probable point of CHF occurrence is related to the region of the most unstable flow conditions. They developed correlations for that and predicted the CHF with reasonable accuracy for stable flow under low pressures and flow velocities.

Celata et a/. (2001) presented an analytical model to predict the CHF for water in saturated flow boiling in a round vertical and uniform heated pipe. The CHF is assumed to occur in annular flow when the liquid film vanishes at the exit section of the heated channel. They found that the CHF occurred when the vapour quality was higher than 0.3. Their model predicted the data points within an error range of k30% and a root mean square error of 28%. Yu eta/. (2002) found that the CHF quality decreased with a decrease in mass flux and this trend is opposite to that found in large diameter tubes.

Many studies of CHF in flow boiling systems are reported in the literature. These studies however focus on the boiling process in small diameter tubes, flat plates and in the fuel THERMPL-FLUID SIMJLATKN INKSTGATKN OF THE REACTOR CAVITY COOClNG SYSTEM STlVJPlPES DESK34 FOR THE PEBBLE BED MCDULPR R W T O R

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rods. No research has been done on CHF for large diameter tubes under natural circulation conditions.

2.4

Natural Circulation

Natural circulation is an important mechanism in passive heat removal systems for both existing and new generation reactors. This section considers situations for which there is no forced mass flow, yet convective currents exist in the fluid. Such situations are referred to as free or natural convection, also known as natural circulation. A buoyancy force within the fluid, which is created by a density gradient, induces natural circulation. There are several ways in which a mass density gradient may arise; the most common of these are due to temperature gradients.

An important flow feature is the degree to which the pressure field is influenced by density variations in the channel, Todreas et a/. (1993). For forced flow conditions, the flow is mildly affected by the density change along the length of the channel. Hence buoyancy force effects may be neglected. The pressure gradient during natural circulation is governed by density changes; thus the buoyancy head should be described accurately. The dependence of the density gradient on the enthalpy change makes the heat addition to the system a very important parameter, for it drives the flow in natural circulation systems. The relationship between the heat added to the system and the loop flow rate is the key parameter when analysing the steady state or transient characteristics of a natural circulation system. Chatoorgoon et a/. (2002) showed that the loop flow rate in a single-phase natural circulation system is proportional to one third of the power input.

It will be seen in the next section that the loop flow rate vs heater power curve is multi- valued for certain operating conditions in a natural circulation loop. In other words, one can find more than one steady-state solution for a given heater power. According to Prof. Niyazi Sokmen (2003), this multi-valued characteristic is an important phenomenon and should be studied carefully. It may lead the loop flow rate to bifurcate for certain values of the heater power that causes a steep reduction of the flow rate of the simulation. This phenomenon is called "Static Bifurcation".

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During natural circulation, the buoyancy head governs the momentum conservation equation. Thus the frictional component does not govern the pressure gradient. Holland et a/. (1995) stated that when the frictional component of the pressure drop does not dominate the pressure gradient, the use of frictional multipliers should be avoided.

When considering a system, three possible assumptions can be made for the boundary conditions to solve the conservations equations for the fluid mass and momentum equations.

1. Specified inlet and outlet pressure 2. Specified inlet flow and exit pressure 3. Specified inlet pressure and outlet velocity

For the boundary conditions of case (2) and (3), the unspecified boundary pressure can be uniquely obtained. These boundary conditions are usually applied to forced convection problems. However, for the boundary conditions of case (A), more than one inlet flow rate may satisfy the equations. This is physically possible, for density changes in the heated channel may create several flow pattems at which the integrated pressure drops are identical, particularly if boiling occurs within the channel. These boundary conditions of case (1) are usually applied to natural circulation problems. Numerous researchers have reported on studies of the characteristics of natural circulation and the multiple flow rate phenomena.

Jeng and Pan (1999) investigated the steady-state characteristics of a twephase natural circulation loop based on the drift-flux model. They took into consideration the effect of flow pattems and sub-cooled boiling. The studied characteristics were; the one-third- power dependence of the single-phase mass flow rate on the heating power, the incipient power of twephase flow, the maximum flow rate and the existence of multiple solutions under certain conditions. They have tested the validity of the homogeneous model and the drift-flux model. The results generated by their models showed that the drift-flux model predicted the loop flow rate much more accurately than the homogeneous model. This is due to the fad that the drifl-flux model Bkes twephase flow patterns into account, which significantly affects the flow rate of the loop. They also found that a region of multiple steadystate solutions exist for a natural circulation THERMAL-FLUID SIMJLATION INVESTIGATKM OF THE RESTOR C A W Y COOLING SYSTEM STPNPlPES D E S W FOR THE PEBBLE BED MDDUUR REPCTW

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system with high inlet sub-axding. Such a region coincides with multi mode instabilities that were observed experimentally. Increasing the inlet loss coefficient can eliminate this unstable region.

Xinian etal. (2001) developed a program, which could be used in the system design of a passive heat removal system. They used the one-dimensional drift flux model to analyse the steam water loop. They analysed the effect of riser height, heated area and height difference between the hot and cold leg on the heat removal capacity. The author plans to verify the computer code with experimental data in the future.

It is not clear in the literature which frictional multiplier should be used in natural circulation systems. It was seen previously that Holland et a/. (1995) avoided the use of the multiplier, and Todreas et a/. (1993) also proposed the avoidance of a frictional multiplier in a natural circulation system. Communication with Kuran, S. (2003) revealed that the multiplier should be used, but care must be taken for specialised correlations exist for the frictional multiplier in natural circulation systems. However no correlations were found. Dr. T.H.J.J van der Hagen (2003) pointed out that the frictional multiplier should be used to compensate for the extra pressure losses found in twephase flow but no insight was given into which correlation to use. He also stated that discrepancies between measured and estimated data are not uncommon in the literature.

Manera, A. (2003) explained that one should always use a twephase frictional multiplier when evaluating the pressure drop in a boiling channel, and that the work of Todreas et a/. (1993) is a bit misleading for they refer to the distributed pressure drop. She proposed the use of the homogeneous frictional multiplier in a low pressure, natural circulation loop, for it agrees well with experimental data.

2.4.2 Flow Instabilities

Chatwrgoon et a/. (2002) studied advanced reactor designs where natural circulation is an important design feature in heat removal processes. They studied the feasibility of flashing driven and natural circulation driven systems to remove heat from the reactor. It was found through experiments and code simulations that a flashing driven system is feasible at normal operating conditions, but flow instabiliCes may occur at low power

THERMM-FLUID SlMJLATlON INWSTRXTION OF THE RESTOR C A W COOLING S % E M

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inputs. Their studies also showed that with a natural circulation system, large variations in fluid properties near the critical point might heighten the potential for flow instabilities. Kyung and Lee (1996) studied flow excursion instabilities in an open twephase natural circulation loop, both experimentally and analytically. They found that at high values of the inlet sub-cooling temperature, stable steady-state conditions (continuous circulation) do not exist. Instead, three different circulation modes such as periodic circulation A, multi mode circulation and periodic circulation B appears at different heat flux conditions. Figure 2.2 shows four circulation modes that were identified throughout a series of experiments, these modes are:

(a) Periodic circulation (A) _{PC (A)} (b) Continuous circulation CC (c) Periodic circulation (B) _{PC (B)} (d) Multimode circulation MC

Figure 2.2: Different circulation modes (Kyung and Lee).

The PC (A) mode [Figure 2.2 (a)] appears at low heat flux conditions where it is characterised by the periodic flow oscillations with incubation (neboiling) periods. This mode is considered as the geysering instability, because forceful ejections of fluid from the heater occur (owing to the boiling), followed by incubation periods. These incubation periods can be seen on the void fraction charts in Figure 2.2. The second mode is the CC mode Figure 2.2 (b)]. This mode can only occur at very low inlet sub-cooling conditions. The mass flow and void fraction remain almost constant without any M E R W - F L U I D SIWLATtON INKSTK;ATY)N OF THE REACTOR CAVITY COOLING SYSrrM STANPIPES O E S W FOR THE PEBBLE BED H O O U M REPCTOR

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significant flow oscillations. It is considered to be the stable mode in twephase natural circulation. The third mode is the PC (B) mode, which occurs at a higher heat flux [Figure 2.2 (c)]. Here the liquid boils continuously without any incubation period. The void fraction oscillates slightly within the high value range and the flow rate also fluctuates regularly with temporal flow reversal, which is higher than that o b s e ~ e d in PC (A) mode. Many researchers described this as the density wave oscillation due to its self-excited nature. The last mode is the MC mode Figure 2.2 (d)]. This exhibits a modulated shape of PC (A) mode; for example the void fraction variation of the MC mode exhibits a combined shape of PC (A) and PC (B) oscillations with double peaks in on cycle. Thus the MC mode retains the main frequencies of both PC (A) and PC (B) modes.

These instability boundaries can be seen in Figure 2.3. It can be seen that the CC mode region becomes smaller as the inlet subcooling is increased. The PC (A) and PC (B) modes are present at low and high heat fluxes, respectively. The MC mode region becomes wider as the inlet sub-cooling increases. Thus at high inlet sub-cooling, the circulation mode is always unstable and varies from PC (A) to PC (B) mode (via MC mode) with increasing heat flux,

Heat Flux ~ w l r n ~ ]

Figure 2.3: Typical instability map (Kyung and Lee)

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