iii

Abstract This work describes in detail the assessment of the CFD code CFX to predict adiabatic

liquid-gas two-phase bubbly flow. All the state of the art approaches for the simulation

of the flow have been tested and all the theoretical models studied and analyzed.

When using the monodispersed or mono-size approach, the simulations have been

performed with constant bubble diameter assuming no bubble interactions and the effect

of drag force, lift force, wall lubrication force and the turbulent dispersion force have

been assessed using experimental data obtained at the PUMA facility in Valencia

[Santos Méndez (2008)] for air-water upward bubbly flows through a pipe. Different

approaches for modeling the bubble induced turbulence (BIT) were studied, namely

Sato [Sato et al. (1981)] and Morel [Yao and Morel (2004)]. This exercise resulted in

selection of the most appropriate closure form and closure coefficients for the above

mentioned forces for the range of flow conditions chosen. The homogeneous Multi-size

approach (MUSIG) was also tested. The capabilities of this model are discussed via the

example of adiabatic bubbly flow through a vertical pipe.

In the last exercise, the One-Group Interfacial Area Transport equation was introduced

in the two-fluid model of CFX. The interfacial area density plays important role in the

correct prediction of interfacial mass, momentum and energy transfer and is affected by

bubble breakup and coalescence processes in adiabatic flows. The One-Group

Interfacial Area Transport Equation (IATE) has been developed and implemented for

one-dimensional models and validated using cross-sectional area averaged experimental

data over the last decade by various researchers. Different models for the breakup and

coalescence mechanisms were studied, namely Yao and Morel (2004), Hibiki and Ishii

(1999), Ishii and Kim (2000), Wu (1997) and Wang (2010). The original one-

dimensional models were implemented in their original form without changing any

closure coefficients and, the results are presented in this thesis. Although the results are

far from exact, reasonable predictions were obtained in the simulations for

multidimensional case, being the general structure of the flow well reproduced. This

study demonstrates the complicated interplay between size dependent bubble migration

and the effects of bubble coalescence and breakup on real flows. The closure models

that characterize the bubble forces responsible for the simulation of bubble migration

show agreement with the experimental observations. However, clear deviations occur

for bubble coalescence and breakup. The models applied here, which describe bubble

breakup and coalescence could be proved as a weakness in the validity of numerous

CFD analyses of vertical upward two-phase pipe flow. The thesis also discusses

constraints posed by the commercial CFD code Ansys CFX and the solutions worked

out to obtain the most accurate implementation of the model. For all those reason this

work allows laying the ground for new formulations of source and sink terms for IATE

(Interfacial area transport equation), as well as for a future implementation of this

approach in the code Ansys CFX.

iv

v

Contents

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

Contents ........................................................................................................................... v

List of Figures ................................................................................................................ ix

List of Tables ................................................................................................................ xiii

List of Acronyms .......................................................................................................... xiv

Chapter 1: Motivation and objectives .......................................................................... 1

1.1 Background and Motivation ................................................................................... 1

1.2 Objectives and Aims of the work ........................................................................... 4

1.3 Outline of the work ................................................................................................. 5

Chapter 2: Introduction ................................................................................................. 7

2.1 Multiphase flow. ..................................................................................................... 7

2.1.1Flow patterns ..................................................................................................... 9

2.1.2Bubbly flow development ............................................................................... 12

2.2 Main useful parameters definition ........................................................................ 14

2.2.1 Basic parameters: ........................................................................................... 14

2.2.2 Dimensionless numbers: ................................................................................ 15

2.3 General conservation equations: ........................................................................... 17

2.4 Turbulence: ........................................................................................................... 18

2.5 Contamination effect: ........................................................................................... 19

Chapter 3: State of the art, simulation approaches. .................................................. 21

3.1 Introduction: .......................................................................................................... 21

3.2 Two Fluids Model: ................................................................................................ 23

3.3 Monodispersed approach. ..................................................................................... 24

3.4 Multi-Size Group approach .................................................................................. 25

3.4.1 Homogeneous MUSIG ................................................................................... 25

3.4.2 Inhomogeneous MUSIG: ............................................................................... 27

3.5 Interfacial area transport equation: ....................................................................... 29

3.6 Present Forces and closure relations for the momentum exchange: ..................... 31

3.6.1 Surface tension and viscous force : ................................................................ 31

3.6.2 Modeling of the forces acting on a bubble: .................................................... 32

vi

3.7 Two phase flow turbulence Modeling. ................................................................. 53

3.7.1 Bubbly flow turbulence Modeling: ................................................................ 54

3.7.2 BIT Additional Source Terms Models ........................................................... 56

Chapter 4: One group interfacial area transport equation ...................................... 59

4.1. Introduction .......................................................................................................... 59

4.2 Interaction mechanisms and their modeling: ........................................................ 61

4.3 Analysis of the considered Models ....................................................................... 64

4.3.1 General ideas .................................................................................................. 64

4.3.2 Differences among models: ............................................................................ 65

4.3.3 Yao and Morel [Yao and Morel (2004)]: ....................................................... 66

4.3.4 Hibiki and Ishii [Hibiki and Ishii (1999)]: ..................................................... 73

4.3.5 Wu et al. [Wu et al.(1997)] : .......................................................................... 75

4.3.6 Ishii and Kim [Ishii and Kim(2000)]: ............................................................ 77

4.3.7 Wang [Wang (2010)]: .................................................................................... 77

Chapter 5: CFD Theory and Models .......................................................................... 79

5.1 The commercial software ANSYS CFX ............................................................... 79

5.2 Mesh generation in ICEM CFD ............................................................................ 80

5.2.1 Geometry Tools .............................................................................................. 80

5.2.2 Mesh Tools ..................................................................................................... 80

5.2.3 Mesh Quality .................................................................................................. 81

5.3 Fundamental equations of fluid dynamics ............................................................ 82

5.4 Turbulence models ................................................................................................ 83

5.4.1 Continuous or liquid phase ............................................................................. 83

5.4.2 Disperse or Gas phase .................................................................................... 86

5.5 Near Wall Treatment ............................................................................................ 86

5.6. Closure models for bubble coalescence and breakup , .................................. 87

5.6.1 The breakup kernel function .......................................................................... 87

5.6.2 The coalescence kernel function .................................................................... 88

5.7 Implementing one group Interfacial area transport equation in Ansys CFX ........ 89

5.7.1 Eliminating the diffusive term........................................................................ 89

5.7.2 The Transformed Source Term ...................................................................... 90

Chapter 6: Upward turbulent adiabatic bubbly flow experimental data ............... 91

6.1 Experimental Facility ............................................................................................ 91

vii

6.2 Experimental results ............................................................................................. 92

Chapter 7: Simulations: ............................................................................................... 93

7.1 Set up of the simulation ........................................................................................ 93

7.1.1 Boundary conditions ...................................................................................... 93

7.1.2 General Considerations and closure relations. ............................................... 94

7.1.3 Fluid definition ............................................................................................... 96

7.1.4 Simulation numerics ....................................................................................... 96

7.2. Mesh size sensitivity Analysis for the case F02G02: .......................................... 96

7.3 Monodispersed approach. ................................................................................... 105

7.3.1 Complete mesh sensitivity analysis.............................................................. 105

7.3.2 Force models analysis .................................................................................. 110

7.3.3 Bubble induced Turbulence models: ............................................................ 114

7.4 Homogeneous Multi-Size Group approach. ....................................................... 119

7.5 Interfacial area transport equation: ..................................................................... 122

7.5.1 Yao and Morel [Yao and Morel (2004)] and Hibiki and Ishii[Hibiki and

Ishii(1999)]: ........................................................................................................... 122

7.5.2 Wang [Wang (2010)], Ishii and Kim [Ishii and Kim(2000)], and Wu [Wu et

al(1997)]: ............................................................................................................... 130

7.5.3 Effect of increasing the superficial velocity of each phase: ......................... 134

Chapter 8: Conclusions and future work ................................................................. 141

8.1 Conclusions: ........................................................................................................ 141

8.2 Future Work ........................................................................................................ 143

Appendix A: Experimental Results Profiles ............................................................ 145

Bibliography ................................................................................................................ 149

viii

ix

List of Figures

Fig.2. 1: Two phase flow classification by Ishii (1976) ................................................... 8

Fig.2. 2: Engineering data book III (2007). [John R. Thome (2007)] .............................. 9

Fig.2.3 Flow regimes in a vertical evaporator tube. [Collier and Thome (1994)].......... 10

Fig.2. 4 Typical air-water flow images in a 25.4 mm diameter pipe (above) compared to

typical images in a 50.8 mm pipe (bottom). [Ishii and Hibiki (2006)] .......................... 11

Fig.2. 5: Taitel’s flow map for bubbly-slug flow. [Taitel (1980)].................................. 13

Fig.3. 1: Scheme of the standard MUSIG model: all size fractions representing different

bubble sizes move with the same velocity field. ............................................................ 26

Fig.3. 2: Scheme for the Inhomogeneous MUSIG Approach. ....................................... 28

Fig.3. 3:Elliptical distorted bubble ................................................................................. 36

Fig.3. 4: Influence of the lift force depending on the bubble size. ................................. 38

Fig.3. 5: Lift Coefficient dependency with the bubble diameter, and critical bubble

diameter dependency with the saturation pressure ......................................................... 40

Fig.3. 6: Dimensions and coordinates of a distorted oblate sphereoidal bubble.

[Tomiyama (2002)]......................................................................................................... 40

Fig.3. 7: Aspect ratio-Eötvös number possible correlation ............................................ 41

Fig.3. 8: Possible new Tomiyama´s Lift coefficient for air-water pure systems............ 42

Fig.3. 9: Shape regimes for gas bubbles and liquid drops in unhindered gravitational

motion through liquids. Grace (1967) ............................................................................ 43

Fig.3. 10: Evolution of the Wall lubrication coefficient provided by different models. 48

Fig.3. 11: Turbulent dispersion force effect. .................................................................. 49

Fig.3. 12: Bubble moving with a relative velocity U ..................................................... 51

Fig.3. 13 DNS calculations of different closure laws for the bubble-induced turbulence

[Wörner et al. (2004)] ..................................................................................................... 57

Fig.4. 1: From left to right, coalescence and breakup example images. ........................ 61

Fig.4. 2: Coalescence due to wake entrainment. ............................................................ 62

Fig.4.3:Breakup Mechanisms ......................................................................................... 63

Fig.6. 1: Setup of the PUMA experiment ...................................................................... 91

Fig.6. 2 :Positions of the measuring ports (left), scheme of the measuring principle in

the flow (center), a particular of the four-sensor probe (right) ....................................... 92

Fig.6. 3: Maps of phase distribution patterns at z/D=5 ................................................. 92

Fig.7. 1: Nearly 2D grid used for the definition of the computational domain; View

downstream the main flow direction ............................................................................. 96

x

Fig.7. 2: Effect of incrementing the nodes in the flow direction .................................... 99

Fig.7. 3: Effect of incrementing the number of nodes in the radial direction ................ 99

Fig.7. 4: Effect of incrementing the number of nodes in both directions, on the

computational time ....................................................................................................... 100

Fig.7. 5: Sensitivity analysis results rising the number of nodes in the axial direction 100

Fig.7. 6: Some sensitivity analysis results .................................................................... 101

Fig.7. 7: Effect of the first node-wall distance. ............................................................ 102

Fig.7. 8: Original mesh facing some other alternatives. ............................................... 103

Fig.7. 9: Effect of the first node-Wall distance on the calculation time ....................... 104

Fig.7. 10 : Results complete sensitivity analysis F01 ................................................... 106

Fig.7. 11: Results complete sensitivity analysis F02 .................................................... 107

Fig.7. 12: Results complete sensitivity analysis F03 .................................................... 109

Fig.7. 13: Turbulent dispersion force Influence, Monodispersed, BIT Sato ................ 111

Fig.7. 14: Wall lubrication force influence, Monodispersed, BIT Sato ....................... 112

Fig.7. 15: Lift force influence, Monodispersed, BIT Sato ........................................... 113

Fig.7. 16: Drag force influence, Monodispersed, BIT Sato ......................................... 113

Fig.7. 17: Comparison with original coefficients of BIT Sato and Morel for F02G02, on

the left side, IAC, on the right one the void fraction is shown. .................................... 114

Fig.7. 18: Comparison between the main variables of the turbulence for Morel and Sato

BIT for Jf (m/s) =2.036 ................................................................................................ 116

Fig.7. 19: Dimensionless wall distance for Sato and Morel BIT ................................. 117

Fig.7. 20: BIT Morel, small sensitivity analysis for F02G02, IAC (left side) and void

fraction (right side) ....................................................................................................... 117

Fig.7. 21: BIT Morel, General results for the cases F02G02, F03G02, F03G03, from left

to right, IAC, gas volume fraction, and gas velocity. ................................................... 118

Fig.7. 22: Typical results of IAC and gas volume fraction for the cases F01G03,

F02G02, F03G02 and F03G03 with the MUSIG approach and comparing with the

monodispersed approach results. .................................................................................. 121

Fig.7. 23: General results for F02G02, Yao and Hibiki source/sink terms. From left to

right, 1) BIT Sato with original coefficients, 2) BIT Morel with lift coefficient 0.288

and wall lubrication force Antal (-0.01,0.05), 3) BIT Morel with lift coefficient 0.1, and

4) BIT Sato with lift coefficient 0.1 ............................................................................. 124

Fig.7. 24: Results with BIT Morel, Lift coefficient 0.288, Lopez de Bertodano 1 and

0.75, Antal (-0.01, 0.05). For the cases F02G02 (IAC, top left, void fraction, top right)

and F03G03. ................................................................................................................. 125

Fig.7. 25: Influence of the interfacial forces, for Morel BIT, taking a low lift coefficient

(0.1) as a basis, IAC(left) and void fraction(right) from top to bottom: the influence of

setting a lower FAD coefficient, influence of setting an even lower lift coefficient, and

influence of setting a stronger wall lubrication force when using a low lift. ............... 127

Fig.7. 26: Gas velocity (left) and Sauter mean diameter(right), for lift coefficient 0.1,

comparison between Morel and Sato BIT Models, for Yao and Hibiki proposals for one

group IATE. .................................................................................................................. 128

xi

Fig.7. 27: IAC change due to turbulent impact (bottom) and random collision(top), for

Yao and Hibiki models, the influence of the lift coefficient with Sato BIT (left) and the

influence of the BIT model with lift coefficient 0.1(right) can be seen. ...................... 129

Fig.7. 28: General results for F02G02, Wu, Ishii-Kim and Wang source/sink terms.

From left to right, 1) BIT Sato with original coefficients, 2) BIT Morel with lift

coefficient 0.288 and wall lubrication force Antal (-0.01,0.05), 3) BIT Morel with lift

coefficient 0.1, 4) BIT Sato with lift coefficient 0.1 .................................................... 131

Fig.7. 29: Velocity (top left), TI (top right) comparison between Morel and Sato BIT.

RC dependence on the lift coefficient (middle left) and the BIT model (middle right).

On the bottom, the same for the wake entrainment is shown. ...................................... 132

Fig.7. 30 : Results for the case F03G02, with BIT Sato and original coefficients (top)

and BIT Morel and lift coeff. 0.1 (below). From left to right, interfacial area

concentration, gas volume fraction, mean gas velocity and mean Sauter diameter ..... 135

Fig.7. 31 : F03G02 results with BIT Sato and original coefficients (above) and BIT

Morel and lift coeff. 0.1 (below). From left to right: Gas expansion term, random

collision, wake entrainment and turbulent impact. ....................................................... 136

Fig.7. 32 : Results for the case F03G03, with BIT Sato and original coefficients (top)

and BIT Morel and lift coeff. 0.1 (bottom). From left to right, interfacial area

concentration, gas volume fraction, mean gas velocity and mean Sauter diameter ..... 138

Fig.7. 33: F03G03 results with BIT Sato and original coefficients (top) and BIT Morel

and lift coeff. 0.1 (bottom). From left to right: Gas expansion term, random collision,

wake entrainment and turbulent impact........................................................................ 139

xii

xiii

List of Tables

Table 7. 1: Summary of the superficial velocities of both phases for our cases ............ 94

Table 7. 2:”Original coefficients” proposed by Krepper and Lucas [Krepper, Lucas et al.

(2005)] ............................................................................................................................ 95

Table 7. 3: Overview of the possibilities considered in the mesh sensitivity analysis

when changing the number of nodes .............................................................................. 98

Table 7. 4: Overview of the considered possibilities for the mesh sensitivity analysis

when changing the first node distance to the wall. ....................................................... 102

Table 7. 5: Computational time and possibilities for the case F01, monodispersed

approach........................................................................................................................ 105

Table 7. 6: Computational time and possibilities for the case F02, monodispersed

approach........................................................................................................................ 107

Table 7. 7: Computational time and possibilities for the case F03, monodispersed

approach........................................................................................................................ 108

Table 7. 8: Real computational time for all cases with the best considered meshes. ... 109

Table 7. 9: Force models sensitivity analysis possibilities ........................................... 111

Table 7. 10: Diameter and size fraction for the distributions of the homogeneous

MUSIG approach .......................................................................................................... 119

Table 7. 11: Comparison among the computational times for the MUSIG approach and

the monodispersed one. ................................................................................................ 120

Table A. 1:Void fraction experimental measures profiles in the upper and lower port of

the PUMA facility. ....................................................................................................... 145

Table A. 2: Interfacial area concentration experimental measures profiles in the upper

and lower port of the PUMA facility. ........................................................................... 146

Table A. 3: Gas velocity experimental measures profiles in the upper and lower port of

the PUMA facility. ....................................................................................................... 147

Table A. 4: Sauter mean diameter experimental measures profiles in the upper and

lower port of the PUMA facility................................................................................... 148

xiv

List of Acronyms

CFD Computational Fluid Dynamics

PWR Pressurized Water Reactor

BWR Boiling Water Reactor

LOCA Loss Of Coolant Accident

CHF Critical Heat Flux

ECCS Emergency Core Cooling System

IATE Interfacial Area Transport Equation

MUSIG Multi-Size Group Approach

DNS Direct Numerical Simulation

VOF Volume Of Fluid

LS Level Set Method

FT Front Tracking Method

E-L Euler-Lagrange or dispersed bubble approach

E-E Euler-Euler or continuous approach

IAC Interfacial Area Concentration

BIT Bubble Induced Turbulence

TED Turbulence eddy dissipation rate

RC Coalescence due to Random Collision

WE Coalescence due to Wake Entrainment

TI Breakup due to Turbulent Impact

RANS Reynolds Averaged Navier-Stokes equation