Post on 06-Mar-2018
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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.
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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
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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
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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
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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
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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
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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
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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
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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