The two fluid model is used to simulate upward gas-liquid bubbly flow through a vertical conduit. Coalescence and breakup of bubbles have been accounted for by embedding the population balance technique in the two fluid model. The simulation enables one to track the axial development of the voidage pattern and the distribution of the bubbles. Thereby it has been possible to propose a new criterion for the transition from bubbly to slug flow regime. The transition criteria depend on (i) the breakage and coalescence frequency, (ii) the bubble volume count below and above the bubble size introduced at the inlet, and (iii) the bubble count histogram. The prediction based on the present criteria exhibits excellent agreement with the experimental data. It has also been possible to simulate the transition from bubbly to dispersed bubbly flow at a high liquid flow rate using the same model.
Issue Section:
Multiphase Flows
1.
Zuber
, N.
, and Findlay
, J. A.
, 1965, “Average Volumetric Concentration in Two Phase Flow Systems
,” ASME J. Heat Transfer
0022-1481, 87
, pp. 453
–468
.2.
Ishii
, M.
, and Zuber
, N.
, 1970, “Thermally Induced Flow Instabilities in Two-Phase Mixtures
,” Proceedings of the Fourth International Heat Transfer Conference
, Paris, France.3.
Saha
, P.
, and Zuber
, N.
, 1978, “An Analytical Study of the Thermally Induced Two Phase Flow Instabilities Including the Effects of Thermal Non-Equilibrium
,” Int. J. Heat Mass Transfer
0017-9310, 21
, pp. 415
–426
.4.
Kim
, C.
, and Roy
, R. P.
, 1981, “Two Phase Flow Dynamics by a Five Equation Drift Flux Model
,” Lett. Heat Mass Transfer
0094-4548, 8
, pp. 57
–68
.5.
Hibiki
, T.
, and Ishii
, M.
, 2000, “Two-Group Interfacial Area Transport Equations at Bubbly-to-Slug Flow Transition
,” Nucl. Eng. Des.
0029-5493, 202
, pp. 39
–76
.6.
Rakhmatulin
, K. A.
, 1956, “Fundamentals of Gas Dynamics of Interpenetrating Motions of Compressible Media
,” Prikl. Mat. Mekh.
0032-8235, 20
(2
), pp. 184
–195
.7.
Ishii
, M.
, 1977, “One Dimensional Drift Flux Model and Constitutive Equations for Relative Motion Between Phases in Various Two-Phase Flow Regimes
,” Argonne National Laboratory, Technical Report No. ANL-77-47.8.
Wu
, Q.
, Ishii
, M.
, and Uhle
, J.
, 1998, “Frame Work of Two-Group Model for Interfacial Area Transport in Vertical Two-Phase Flows
,” Trans. Am. Nucl. Soc.
0003-018X, 79
, pp. 351
–352
.9.
Fu
, X. Y.
, and Ishii
, M.
, 2003, “Two-Group Interfacial Area Transport in Vertical Air-Water Flow I. Mechanistic Model
,” Nucl. Eng. Des.
0029-5493, 219
, pp. 143
–168
.10.
Kumar
, S.
, and Ramkrishna
, D.
, 1996, “On the Solution of Population Balance Equations by Discretization—I. A Fixed Pivot Technique
,” Chem. Eng. Sci.
0009-2509, 51
(8
), pp. 1311
–1332
.11.
Marchisio
, D. L.
, Vigil
, R. D.
, and Fox
, R. O.
, 2003, “Quadrature Method of Moments for Aggregation-Breakage Processes
,” J. Colloid Interface Sci.
0021-9797, 258
, pp. 322
–334
.12.
Dorao
, C. A.
, and Jakobsen
, H. A.
, 2006, “A Least Squares Method for the Solution of Population Balance Problems
,” Comput. Chem. Eng.
0098-1354, 30
, pp. 535
–547
.13.
Yao
, W.
, and Morel
, C.
, 2004, “Volumetric Interfacial Area Prediction in Upwards Bubbly Two-Phase Flow
,” Int. J. Heat Mass Transfer
0017-9310, 47
, pp. 307
–328
.14.
Chen
, P.
, Sanyal
, J.
, and Duduković
, M. P.
, 2005, “Numerical Simulation of Bubble Columns Flows: Effect of Different Breakup and Coalescence Closures
,” Chem. Eng. Sci.
0009-2509, 60
(4
), pp. 1085
–1101
.15.
Yeoh
, G. H.
, and Tu
, J. Y.
, 2006, “Two-Fluid and Population Balance Models for Subcooled Boiling Flow
,” Appl. Math. Model.
0307-904X, 30
, pp. 1370
–1391
.16.
Cheung
, S. C. P.
, Yeoh
, G. H.
, and Tu
, J. Y.
, 2007, “On the Modelling of Population Balance in Isothermal Vertical Bubbly Flows—Average Bubble Number Density Approach
,” Chem. Eng. Process.
0255-2701, 46
, pp. 742
–756
.17.
Jakobsen
, H. A.
, Lindborg
, H.
, and Dorao
, C. A.
, 2005, “Modeling of Bubble Column Reactors: Progress and Limitations
,” Ind. Eng. Chem. Res.
0888-5885, 44
, pp. 5107
–5151
.18.
Krepper
, E.
, Lucas
, D.
, and Prasser
, H. M.
, 2005, “On the Modelling of Bubbly Flow in Vertical Pipes
,” Nucl. Eng. Des.
0029-5493, 235
, pp. 597
–611
.19.
Lo
, S.
, 1996, “Application of the MUSIG Model to Bubbly Flows
,” AEA Technology, Technical Report No. AEAT-1096.20.
Lucas
, D.
, Krepper
, E.
, and Prasser
, H. M.
, 2001, “Prediction of Radial Gas Profiles in Vertical Pipe Flow on Basis of the Bubble Size Distribution
,” Int. J. Therm. Sci.
1290-0729, 40
, pp. 217
–225
.21.
Esmaeeli
, A.
, and Tryggvason
, G.
, 1998, “Direct Numerical Simulations of Bubbly Flows. Part 1—Low Reynolds Number Arrays
,” J. Fluid Mech.
0022-1120, 377
, pp. 313
–345
.22.
Bunner
, B.
, and Tryggvason
, G.
, 2002, “Dynamics of Homogeneous Bubbly Flows: Part 1. Rise Velocity and Microstructure of the Bubbles
,” J. Fluid Mech.
0022-1120, 466
, pp. 17
–52
.23.
Bunner
, B.
, and Tryggvason
, G.
, 2002, “Dynamics of Homogeneous Bubbly Flows: Part 2. Velocity Fluctuations
,” J. Fluid Mech.
0022-1120, 466
, pp. 53
–84
.24.
Bunner
, B.
, and Tryggvason
, G.
, 2003, “Effect of Bubble Deformation on the Properties of Bubbly Flows
,” J. Fluid Mech.
0022-1120, 495
, pp. 77
–118
.25.
Biswas
, S.
, Esmaeeli
, A.
, and Tryggvason
, G.
, 2005, “Comparison of Results From DNS of Bubbly Flows With a Two Fluid Model for the Two-Dimensional Laminar Flows
,” Int. J. Multiphase Flow
0301-9322, 31
, pp. 1036
–1048
.26.
Shnip
, A. I.
, Kolhatkar
, R. V.
, Swamy
, D.
, and Joshi
, J. B.
, 1992, “Criteria for Transition From the Homogeneous to Heterogeneous Regime in Two-Dimensional Bubble Column Reactors
,” Int. J. Multiphase Flow
0301-9322, 18
(5
), pp. 705
–726
.27.
Olmos
, E.
, Gentric
, C.
, Vial
, C.
, Wild
, G.
, and Midoux
, N.
, 2001, “Numerical Simulation of Multiphase Flow in Bubble Column Reactors. Influence of Bubble Coalescence and Break-Up
,” Chem. Eng. Sci.
0009-2509, 56
, pp. 6359
–6365
.28.
Olmos
, E.
, Gentric
, C.
, Ponsin
, S.
, and Midoux
, N.
, 2003, “Description of Flow Regime Transitions in Bubble Columns Via Laser Doppler Anemometry Signal Processing
,” Chem. Eng. Sci.
0009-2509, 58
, pp. 1731
–1742
.29.
Sankaranarayanan
, K.
, and Sundaresan
, S.
, 2002, “Lift Force in Bubbly Suspensions
,” Chem. Eng. Sci.
0009-2509, 57
, pp. 3521
–3542
.30.
Taitel
, Y.
, Bornea
, D.
, and Dukler
, A. E.
, 1980, “Modelling Flow Pattern Transitions for Steady Upward Gas-Liquid Flow in Vertical Tubes
,” AIChE J.
0001-1541, 26
(3
), pp. 345
–354
.31.
Dukler
, A. E.
, and Taitel
, Y.
, 1977, “Flow Regime Transitions for Vertical Upward Gas Liquid Flow
,” Houston University, Progress Report No. 2, NUREG-0163.32.
Mishima
, K.
, and Ishii
, M.
, 1984, “Flow Regime Transition Criteria for Upward Two-Phase Flow in Vertical Tubes
,” Int. J. Heat Mass Transfer
0017-9310, 27
, pp. 723
–737
.33.
Anderson
, T. B.
, and Jackson
, R.
, 1967, “A Fluid Mechanical Description of Fluidized Beds: Equations of Motion
,” Ind. Eng. Chem. Fundam.
0196-4313, 6
, pp. 527
–539
.34.
Richter
, H. J.
, 1983, “Separated Two-Phase Flow Model: Application to Critical Two Phase Flow
,” Int. J. Multiphase Flow
0301-9322, 9
(5
), pp. 511
–530
.35.
Chisholm
, D.
, 1973, “Pressure Gradient Due to Friction During the Flow of Evaporating Two Phase Mixtures in Smooth Tubes and Channel
,” Int. J. Heat Mass Transfer
0017-9310, 16
, pp. 347
–358
.36.
Burns
, A. D.
, Frank
, T.
, Hamill
, I.
, and Shi
, J.
, 2004, “The Farve Averaged Drag Model for Turbulent Dispersion in Eulerian Multi-Phase Flows
,” Proceedings of the Fifth International Conference on Multiphase Flow
, Yokohama, Japan.37.
Ramkrishna
, D.
, 2000, Population Balances—Theory and Applications to Particulate Systems in Engineering
, Academic
, San Diego, CA
.38.
Wang
, T.
, Wang
, J.
, and Jin
, J.
, 2003, “A Novel Theoretical Breakup Kernel Function for Bubbles/Droplets in a Turbulent Flow
,” Chem. Eng. Sci.
0009-2509, 58
, pp. 4629
–4637
.39.
Luo
, H.
, and Svendsen
, H. F.
, 1996, “Theoretical Model for Drop and Bubble Breakup in Turbulent Dispersions
,” AIChE J.
0001-1541, 42
, pp. 1225
–1233
.40.
Kostoglou
, M.
, and Karabelas
, A. J.
, 2005, “Towards a Unified Framework for the Derivation of Breakage Functions Based on the Statistical Theory of Turbulence
,” Chem. Eng. Sci.
0009-2509, 60
, pp. 6584
–6595
.41.
Ioannou
, K.
, Hu
, B.
, Matar
, O. K.
, Hewitt
, G. F.
, and Angeli
, P.
, 2004, “Phase Inversion in Dispersed Liquid–Liquid Pipe Flows
,” Proceedings of the Fifth International Conference on Multiphase Flow
, Yokohama, Japan.42.
Tsouris
, C.
, and Tavlarides
, L. L.
, 1994, “Breakage and Coalescence Models for Drops in Turbulent Dispersions
,” AIChE J.
0001-1541, 40
, pp. 395
–406
.43.
Troshko
, A. A.
, and Zdravistch
, F.
, 2009, “CFD Modeling of Slurry Bubble Column Reactors for Fisher–Tropsch Synthesis
,” Chem. Eng. Sci.
0009-2509, 64
, pp. 892
–903
.44.
Carrica
, P. M.
, and Clausse
, A. A.
, 1993, “Mathematical Description of the Critical Heat Flux as Nonlinear Dynamic Instability
,” Instabilities in Multiphase Flow
, G.
Gouesbet
and A.
Berlemont
, eds., Plenum
, New York
.45.
Kostoglou
, M.
, and Karabelas
, A. J.
, 1998, “Theoretical Analysis of Steady State Particle Size Distribution in Limited Breakage Process
,” J. Phys. A
0305-4470, 31
, pp. 8905
–8921
.46.
Tomiyama
, A.
, Nakahara
, Y.
, Adachi
, Y.
, and Hosokawa
, S.
, 2003, “Shapes and Rising Velocities of Single Bubbles Rising Through an Inner Subchannel
,” J. Nucl. Sci. Technol.
0022-3131, 40
, pp. 136
–142
.47.
Coulaloglou
, C. A.
, and Tavlarides
, L. L.
, 1977, “Description of Interaction Processes in Agitated Liquid-Liquid Dispersions
,” Chem. Eng. Sci.
0009-2509, 32
, pp. 1289
–1297
.48.
Chesters
, A. K.
, 1991, “The Modelling of Coalescence Processes in Fluid-Liquid Dispersions: A Review of Current Understanding
,” Trans. Inst. Chem. Eng.
0371-7496, 69
, pp. 259
–270
.49.
Lovick
, J.
, 2004, “Horizontal Oil-Water Flows in the Dual Continuous Flow Regime
,” Ph.D. thesis, University College London, England.50.
Hu
, H. G.
, and Zhang
, C.
, 2007, “A Modified k−ε Turbulence Model for the Simulation of Two-Phase Flow and Heat Transfer in Condensers
,” Int. J. Heat Mass Transfer
0017-9310, 50
, pp. 1641
–1648
.51.
Ekambara
, K.
, Sanders
, R. S.
, Nandakumar
, K.
, and Masliyah
, J. H.
, 2008, “CFD Simulation of Bubbly Two-Phase Flow in Horizontal Pipes
,” Chem. Eng. J.
0300-9467, 144
, pp. 277
–288
.52.
Prosperetti
, A.
, and Tryggvason
, G.
, 2007, “Introduction: A Computational Approach to Multiphase Flow
,” A.
Prosperetti
and G.
Tryggvason
, eds., Computational Methods for Multiphase Flow
, Cambridge University Press
, Cambridge, England
.53.
Tomiyama
, A.
, and Shimada
, N.
, 2001, “A Numerical Method for Bubbly Flow Simulation Based on a Multi-Fluid Model
,” ASME J. Pressure Vessel Technol.
0094-9930, 123
, pp. 510
–516
.54.
Schumann
, U.
, 1975, “Subgrid Scale Model for Finite Difference Simulations of Turbulent Flows in Plane Channels and Annuli
,” J. Comput. Phys.
0021-9991, 18
, pp. 376
–404
.55.
Serizawa
, A.
, Kataoka
, I.
, and Michiyoshi
, I.
, 1975, “Turbulence Structure of Air-Water Bubbly Flow—II. Local Properties
,” Int. J. Multiphase Flow
0301-9322, 2
, pp. 235
–246
.56.
Ohnuki
, A.
, and Akimoto
, H.
, 2000, “Experimental Study on Transition of Flow Pattern and Phase Distribution in Upward Air-Water Two-Phase Flow Along a Large Vertical Pipe
,” Int. J. Multiphase Flow
0301-9322, 26
(3
), pp. 367
–386
.57.
Shen
, X.
, Mishima
, K.
, and Nakamura
, H.
, 2005, “Two-Phase Phase Distribution in a Vertical Large Diameter Pipe
,” Int. J. Heat Mass Transfer
0017-9310, 48
(1
), pp. 211
–225
.58.
Nakoryakov
, V. E.
, Kashinsky
, O. N.
, Randin
, V. V.
, and Timkin
, L. S.
, 1996, “Gas Liquid Bubbly Flow in Vertical Pipes. Data Bank Contribution
,” ASME J. Fluids Eng.
0098-2202, 118
, pp. 377
–382
.59.
Lucas
, D.
, Krepper
, E.
, and Prasser
, H. M.
, 2005, “Development of Co-Current Air-Water Flow in a Vertical Pipe
,” Int. J. Multiphase Flow
0301-9322, 31
, pp. 1304
–1328
.60.
Radovicich
, N. A.
, and Moissis
, R.
, 1962, “The Transition From Twophase Bubble Flow to Slug Flow
,” MIT Technical Report No. 7-7633-22.61.
Bilicki
, Z.
, and Kestin
, J.
, 1987, “Transition Criteria for Two Phase Flow Patterns in Vertical Upward Flow
,” Int. J. Multiphase Flow
0301-9322, 13
, pp. 283
–294
.62.
Mercadier
, Y.
, 1981, “Contribution al'etude des propagations de perturbations de taux de vide dans les ecoulements diphasiques eau-air a’ bulles
,” Ph.D. thesis, Institut National Polytechnique de Grenoble, Universite’ Scientifique et Me’dicale, France.63.
Matuszkiewicz
, A.
, Flamand
, J. C.
, and Boure
, J. A.
, 1987, “The Bubble Slug Flow Pattern Transition and Instabilities of Void Fraction Waves
,” Int. J. Multiphase Flow
0301-9322, 13
, pp. 199
–217
.64.
Sun
, B.
, Wang
, R.
, Zhao
, X.
, and Yan
, D.
, 2002, “The Mechanism for the Formation of Slug Flow in Vertical Gas-Liquid Two Phase Flow
,” Solid-State Electron.
0038-1101, 46
, pp. 2323
–2329
.65.
Krussenberg
, A. K.
, Prasser
, H. M.
, and Schaffrath
, A.
, 1999, “A New Criterion for the Bubble Slug Transition in Vertical Tubes
,” Proceedings of the Ninth International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-9)
, San Francisco, CA.66.
Hinze
, J.
, 1955, Turbulence
, McGraw-Hill
, New York
.67.
Brauner
, N.
, 2001, “The Prediction of Dispersed Flows Boundaries in Liquid-Liquid and Gas-Liquid Systems
,” Int. J. Multiphase Flow
0301-9322, 27
, pp. 885
–910
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