Multiphase flow dynamics: Theory and numerics

VTT Publications

Volumn , Issue 722, 2009, Pages 1-117

  Hiltunen, Kai ^a   Jäsberg, Ari ^a   Kallio, Sirpa ^a   Karema, Hannu ^a   Kataja, Markku ^a   Koponen, Antti ^a   Manninen, Mikko ^a   Taivassalo, Veikko ^a  

^a VTT TECHNICAL RESEARCH CENTRE OF FINLAND   (Finland)

Author keywords

Ensemble averaging; Mixture models; Multifluid finite element method; Multifluid finite volume method; Multiphase flows; Particle tracking; The lattice BGK model; Volume averaging

Indexed keywords

ENSEMBLE AVERAGING; LATTICE BGK MODEL; MIXTURE MODELS; MULTI-FLUIDS; PARTICLE TRACKING; VOLUME-AVERAGING;

FINITE ELEMENT METHOD; FINITE VOLUME METHOD; LIQUIDS; MULTIPHASE FLOW; NUMERICAL METHODS; POROUS MATERIALS;

SUSPENSIONS (FLUIDS);

EID: 78651094989     PISSN: 12350621     EISSN: 14550849     Source Type: Book Series    
DOI: None     Document Type: Article

References (123)

1. Auton, T. R. The dynamics of bubbles, drops and particles in motion in liquids. PhD thesis, University of Cambridge, 1983.
2. Basset, A. B. Treatise on hydrodynamics. Pp. 285-297. Deighton Bell, London, 1888.
3. Batchelor, G. K. The theory of homogeneous turbulence. Cambridge University Press, London, 1953.
4. Batchelor, G. K. The effect of brownian motion on the bulk stress in a suspension of spherical particles. Journal of Fluid Mechanics, 83:97-117, 1977.
5. Burry, D. and Bergeles, G. Dispersion of particles in anisotropic turbulent flows. Int. J. Multiphase Flow, 19:651-664, 1993.
6. Boëlle, A., Balzer, G., and Simonin, O. Second order prediction of the particle phase stress tensor of inelastic spheres in simple shear dense suspensions. Gas-Solid Flows, ASME FED, 228:9-18, 1995.
7. Berlemont, A., Desjonqueres, P., and Gousbet, G. Particle lagrangian simulation in turbulent flows. Int. J. Multiphase Flow, 16:19-34, 1990.
8. Bear, J. Dynamics of Fluids in Porous Media. American Elsevier, New York, 1972.
9. 2. Journal of Fluid Mechanics, 56:401-427, 1972.
10. Brown, D. J. and Hutchinson, P. The interaction of solid or liquid particles and turbulent fluid flow fields - a numerical simulation. Journal of Fluids Engineering, 101:265-269, 1979.
11. Burnage, H. and Moon, S. Predetermination de la dispersion de particules materielles dans un ecoulement turbulent. C. R. Acad. Sci. Paris, 310:1595-1600, 1990.
12. Boemer, A. Euler/Euler-Simulation der Fluiddynamik Blasenbildender Wirbelschichten. PhD thesis, Aachen, 1997.
13. Boussinesq, J. Theorie analytique de la chaleur. L'école Polytechnique, Paris, 1903.
14. Baliga, B. R. and Patankar, S. V. A new finite-element formulation for convection-diffusion problems. Numerical Heat Transfer, 3:393-409, 1980.
15. Buyevich, Y. A. and Shchelchkova, I. N. Flow of dense suspensions. Prog. Aerospace Sci., 18:121-150, 1978.
16. Benzi, R., Succi, S., and Vergassola, M. Phys. Rap., 222:145, 1992.
17. Burgers, J. M. 2nd report on viscosity and plasticity. Kön. Ned. Akad. Wet., Verhand, 1938.
18. Buyevich, Y. A. Motion resistance of a particle suspended in a turbulent medium. Izv. AN SSSR. Mechanika Zhidkosti i Gaza, 1:182-183, 1966. English translation in Fluid Dynamics.
19. Buyevich, Y. A. Statistical hydromechanics of disperse systems. Part 1. Physical background and general equations. J. Fluid Mech., 49(3):489-507, 1971.
20. Buyevich, Y. A. Heat and mass transfer in disperse media - I. Averaged field equations. Int. J. Heat Mass Transfer, 35(10):2445-2452, 1992.
21. Buyevich, Y. A. Heat and mass transfer in disperse media - II. Constitutive equations. Int. J. Heat Mass Transfer, 35(10):2453-2463, 1992.
22. Burns, A. D. and Wilkes, N. S. A finite difference method for the computation of fluid flows in complex three dimensional geometries. Technical Report AERE-R 12342, Harwell Laboratory, 1987.
23. Chapman, S. and Cowling, T. G. The mathematical theory of non-uniform gases. Cambridge Mathematical Library, Cambridge, 1970.
24. Choquet, R. and Erhel, J. Some convergence results for the Newton-GMRES algorithm. Internal publication 755, IRISA, September 1993.
25. Chao, B. T. Turbulent transport behavior of small particles in dilute suspension. österreichisches Ingenieur Archiev, 18(7):7-21, 1964.
26. Computational fluid dynamics services, Oxfordshire. CFDS-FLOW3D; User Manual, Release 3.3.
27. Crowe, C. T. Modeling turbulence in multiphase flows. In W., Rodi and F., Martelli (editors), Engineering Turbulence Modelling and Experiments 2. Pp. 899-913. 1993.
28. Csanady, G. T. An atmospheric dust fall experiment. J. Atm. Sci., 21:222-225, 1963.
29. Csanady, G. T. Turbulent diffusion of heavy particles in the atmosphere. J. Atm. Sci., 20:201-208, 1963.
30. Crowe, C. T., Sharma, M. P., and Stock, D. E. The particle Source-in-Cell Method for gas-droplet flows. J. Fluid Eng., 99:325-332, 1977.
31. Crowe, C. T., Troutt, T. R., and Chung, J. N. Numerical models for two-phase turbulent flows. Annu. Rev. Fluid. Mech., 28:11-43, 1996.
32. Drew, D. A., Arnold, G. S., and Lahey Jr., R. T. Relation of microstructure to constitutive equations. In Joseph, D. D. and Schaeffer, D. G. (editors), Two phase flows and waves. Pp. 45-56, 1990.
33. Ding, J. and Gidaspow, D. A bubbling fluidization model using kinetic theory of granular flow. AIChE Journal, 36(4):523-538, 1990.
34. Drew, D. A. and Lahey Jr., R. T. Application of general constitutive principles to the derivation of multidimensional twophase flow equations. Int. J. Multiphase Flow, 5:243-264, 1979.
35. Drew, D. A. and Lahey Jr., R. T. Chapter 16: Analytical modeling of multiphase flow. In Roco, M. (editor), Particulate Two-Phase Flows. Butterworth-Heinemann, 1992.
36. Drew, D. A. Averaged field equations for two-phase media. Studies in Applied Mathematics, 50:133-166, 1971.
37. Drew, D. A. Two-phase flows: Constitutive equations for lift and Brownian motion and some basic flows. Arch. Rat. Mech. Anal., 62(117), 1976.
38. Drew, D. A. Mathematical modeling of two-phase flow. Ann. Rev. Fluid Mech., 15:261-291, 1983.
39. Drew, D. A. and Segel, L. A. Averaged equations for two-phase flows. Studies in Applied Mathematics, 50(3):205-231, 1971.
40. Eaton, J. K. and Fessler, J. R. Preferential concentration of particles by turbulence. Int. J. Multiphase Flow, 20 Suppl.: 169-209, 1994.
41. Einstein, A. Ann. Phys., 19:289, 1906.
42. Einstein, A. Ann. Phys., 34:591, 1911.
43. Ergun, S. Fluid flow through packed columns. Chemical Engineering Progress, 48(2):89-94, 1952.
44. Faeth, G. M. Recent advances in modeling particle transport properties and dispersion in turbulent flow. In Proc. ASME-JSME Thermal Engineering Conference, Vol. 2. Pp. 517-534, 1983.
45. Faxen, H. Die Bewegung einer starren Kugel lνgs der Achse eines mit zäher Flüssigkeit gefüllten Rohres. Ark. Mat., Astron. Fys., 17:1-28, 1922.
46. Frisch, U., d'Humiéres, D., Hasslacher, B., Lallemand, P., Pomeau, Y., and Rivet, J.-P. Complex Syst., 1:649, 1987.
47. Franca, L. P. and Frey, S. L. Stabilized finite element methods: II. The incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering, 99:209-233, 1992.
48. Franca, L. P., Frey, S. L., and Hughes, T. J. R. Stabilized finite element methods: I. Application to the advective-diffusive model. Computer Methods in Applied Mechanics and Engineering, 95:253-276, 1992.
49. Filippova, O. and Haenel, D. Computers in Fluids, 26:697, 1997.
50. Franca, L. P., Hughes, T. J. R., and Stenberg, R. Stabilized finite element methods. In Gunzburger, M. D. and Nicolaides, R. A. (editors), Incompressible Computational Fluid Dynamics Trends and Advances. Pp. 87-107. Cambridge University Press, 1992.
51. Gidaspow, D., Bezburual, R., and Ding, J. Hydrodynamics of circulating fluidized beds, kinetic theory approach. In Fluidization VII, Proceedings of the 7th Engineering foundation conference on fluidization. Pp. 75-82, 1992.
52. Govan, A. H., Hewitt, G. F., and Ngan, C. F. Particle motion in a turbulent pipe flow. Int. J. Multiphase Flow, 15:471-481, 1989.
53. Gosman, A. D. and Ioannides, E. Aspects of computer simulation of liquid-fuelled combustors. In AIAA 19th Aerospace Sciences Meeting, Paper AIAA-81-0323. 1981.
54. Gosman, A. D. and Ioannides, E. Aspects of computer simulation of liquid-fuelled combustors. Paper AIAA-81-0323, presented at AIAA 19th Aerospace Science Meeting, St Louis, MO, 1981.
55. Gidaspow, D. Multiphase flow and fluidization. Continuum and kinetic theory descriptions. Academic Press, San Diego, 1994.
56. Graham, D. I. and James, P. W. Turbulent dispersion of particles using eddy interaction models. Int. J. Multiphase Flow, 22(1):157-175, 1996.
57. Hutchinson, P., Hewitt, G. F., and Dukler, A. E. Deposition of liquid or solid dispersions from turbulent gas streams: a stochastic model. Chem. Engineering Sci., 26:419-439, 1971.
58. Hiltunen, K. A stabilized finite element method for particulate two-phase flow equations: Laminar isothermal flow. Computer Methods in Applied Mechanics and Engineering, 147:387-399, 1997.
59. Hinze, J. O. Turbulence. McGraw-Hill, New York, 1975.
60. Hansbo, P. and Johnson, C. Adaptive streamline diffusion methods for compressible flow using conservation variables. Computer Methods in Applied Mechanics and Engineering, 87:267-280, 1991.
61. Hughes, T. J. R. and Jansen, K. A stabilized finite element formulation for the Reynolds-averaged Navier-Stokes equations. Surveys on Mathematics for Industry, 4(4):279-317, 1995.
62. Hwang, G.-J. and Shen, H. H. Modeling the solid phase stress in a fluid-solid mixture. Int. J. Multiphase Flow, 15(2):257-268, 1989.
63. Hwang, G.-J. and Shen, H. H. Modeling the phase interaction in the momentum equations of a fluid-solid mixture. Int. J. Multiphase Flow, 17(1):45-57, 1991.
64. Hwang, G.-J. Modeling two-phase flows of a fluid and solid mixture. PhD thesis, Clarkson University, 1989.
65. Ishii, M. and Mishima, K. Two-fluid model and hydrodynamic constitutive relations. Nucl. Eng. & Des., 82:107-126, 1984.
66. Ishii, M. Thermo-fluid dynamic theory of two-phase flow. Eyrolles, 1975.
67. Ishii, M. and Zuber, N. Drag coefficient and relative velocity in bubbly, droplet or particulate flows. AIChE Journal, 25(5):843-855, September 1979.
68. James, P. W., Hewitt, G. F., and Whalley, P. B. Droplet motion in two-phase flow. In Proc. ANS/ASME/NRC International Topical Meeting on Nuclear Reactor Thermal-Hydraulics. Pp. 1484-1503, 1980.
69. Joseph, D. D. and Lundgren, T. S. Ensemble averaged and mixture theory equations for incompressible fluid-particle suspensions. Int. J. Multiphase Flow, 16:35-42, 1990.
70. Jenkins, J. T. and Richman, M. W. Grad's 13 moment system for a dense gas of inelastic spheres. Arch. Ratio. Mech. Anal., 87:355-377, 1985.
71. Jenkins, J. T. and Savage, S. B. A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J. Fluid Mech., 130:187-202, 1983.
72. Karema, H. Application of pressure correction method to multipressure systems of dispersed flows. PhD thesis, Tampere University of Technology, 2002.
73. Krieger, I. M. and Dougherty, T. J. Trans. Soc. Rheol., 3:2817, 1959.
74. Koponen, A., Kandhai, D., Hellén, E., and Alava, M. Phys. Rev. Lett., 80:716, 1998.
75. Karema, H. and Lo, S. Efficiency of interphase coupling algorithms in fluidized bed conditions. Computers & Fluids, 28:323-360, 1999.
76. Krizek, M. and Neittaanmäki, P. Finite Element Approximation of Variational Problems and Applications. Longman Scientific & Technical, 1990.
77. Koponen, A. Simulations of fluid flow in porous media by lattice gas and lattice-Boltzmann methods. PhD thesis, University of Jyväskylä, 1998.
78. Kalio, G. A. and Reeks, M. W. A numerical simulation of particle deposition in turbulent boundary layers. Int. J. Multiphase Flow, 15:433-446, 1989.
79. Kandhai, D., Vidal, D., Hoekstra, A., Hoefsloot, H., Iedema, P., and Sloot, P. Int. J. Num. Meth. Fluids, 31:1019, 1999.
80. Ladd, A. J. C. J. Fluid. Mech., 271:285, 1994.
81. Ladd, A. J. C. J. Fluid. Mech., 271:311, 1994.
82. Lu, Q. Q., Fontaine, J. R., and Aubertin, G. A lagrangian model for solid particles in turbulent flows. Int. J. Multiphase Flow, 19:347-367, 1993.
83. Lesoinne, M., Farhat, C., and Franca, L. P. Unusual stabilized finite element methods for second order linear differential equations. In Cecchi, M. M., Morgan, K., Periaux, J., Schrefler, B. A., and Zienkiewicz, O. C. (editors), Finite elements in fluids, New trends and applications. Pp. 377-386. IACM, October 1995.
84. Lien, F. S. and Leschziner, M. A. A general non-orthogonal collocated finite volume algorithm for turbulent flow at all speeds incorporating second-moment turbulence-transport closure, part 1: Computational implementation. Computer Methods in Applied Mechanics and Engineering, 114:149-167, 1994.
85. Lo, S. M. Mathematical basis of a multi-phase flow model. Technical Report AERE R 13432, Harwell Laboratory, Oxfordshire, 1989.
86. Lo, S. M. Multiphase flow model in the Harwell-Flow3D computer code. unclassified AEA-InTec-0062, Harwell Laboratory, Computational fluid dynamics section, Thermal hydraulics division, Oxfordshire, June 1990.
87. Lun, C. K. K., Savage, F. B., Jeffrey, D. J., and Chepurniy, N. Kinetic theories for granular flow: Inelastic particles in couette flow and slightly inelastic particles in a general flowfield. Journal of Fluid Mechanics, 140(4):223-256, 1984.
88. Lumley, J. L. Some problems connected with the motion of small particles suspended in turbulent fluid. PhD thesis, the Johns Hopkins University, 1957.
89. Masson, C. and Baliga, B. R. A control-volume finite-element method for dilute gas-solid particle flows. Computers & Fluids, 23(8):1073-1096, 1994.
90. Marsh, C., Backs, G., and Ernst, M. Phys. Rev. E, 56:1676, 1997.
91. Martys, N. and Chen, H. Phys. Rev. E, 53:743, 1996.
92. Mathur, S. R. and Murthy, J. Y. A pressure-based method for unstructured meshes. Numerical Heat Transfer, part B, 31:195-215, 1997.
93. Maxey, M. R. and Riley, J. J. Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids, 26:883-889, 1983.
94. Manninen, M., Taivassalo, V., and Kallio, S. On the mixture model for multiphase flow. Research report 288, VTT Technical Research Centre of Finland, Espoo, 1996.
95. Nigmatulin, R. I. Spatial averaging in the mechanics of heterogeneous and dispersed systems. Int. J. Multiphase Flow, 5:353-385, 1979.
96. Oseen, C. W. Hydrodynamik. Akademische Verlagsgesellschaft M. B. H., Leipzig, 1927.
97. Picart, A., Berlemont, A., and Gouesbet, G. Modelling and predicting turbulence fields and the dispersion of discrete particles transported by turbulent flows. Int. J. Multiphase Flow, 12:237-261, 1986.
98. Peirano, E. Modelling and simulation of turbulent gas-solid flows applied to fluidization. PhD thesis, Chalmers University of Technology, 1998.
99. Patankar, S. V. and Spalding, D. B. A calculation procedure for heat, mass and momentum transfer in parabolic flows. Int. J. Heat Mass Transfer, 15:1787-1806, 1972.
100. Qian, Y. H., d'Humiéres, D., and Lallemand, P. Europhys. Lett., 17:479, 1992.
101. Rhie, C. M. and Chow, W. L. Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA Journal, 21(11):1525-1532, 1983.
102. Riley, J. J. PhD thesis, The Johns Hopkins University, 1971.
103. Raiskinmäki, P., Shakib-Manesh, A., Koponen, A., Jäsberg, A., Kataja, M., and Timonen, J. Simulations of non-spherical particles suspended in a shear flow, to be published in. Comput. Phys. Comm., 2000.
104. Rutgers, I. R. Relative viscosity and concentration. Rheologica Acta, Band 2, Heft 4:305-348, 1962.
105. Richardson, J. F. and Zaki, W. N. Sedimentation and Fluidisation: Part I. Transactions of the Institution of Chemical Engineers, 32(1):35-53, 1954.
106. Rothman, D. H. and Zaleski, S. Lattice-gas cellular automata. Cambridge University Press, Cambridge, 1997.
107. Sommerfeld, M., Ando, A., and Wennerberg, D. Swirling, particle-laden flows through a pipe expansion. ASME J. Fluids Engineering, 114:648-655, 1992.
108. Shirolkar, J. S., Coimbra, C. F. M., and Queiroz McQuay, M. Fundamental aspects of modeling turbulent particle dispersion in dilute flows. Progr. Energy Combust. Sci., 22:363-399, 1996.
109. Soo, S. L. Multiphase Fluid Dynamics. Science Press, Beijing, 1990.
110. Spalding, B. D. The calculation of free-convection phenomena in gas-liquid mixtures. In Spalding B. D., Afgan N. (editor), Heat transfer and turbulent buoyant convection studies and application. Pp. 569-586. Hemisphere, 1977.
111. Spalding, D. B. Numerical computation of multi-phase fluid flow and heat transfer. In Taylor, C. and Morgan, K. (editors), Recent Advances In Numerical Methods In Fluids. Pp. 139-168. Pineridge Press, Swansea U. K., 1980.
112. Spalding, D. B. Developments in the IPSA procedure for numerical computation of multiphase-flow phenomena with interphase slip, unequal temperatures, etc. In Shih, T. M. (editor), Numerical Methodologies in Heat Transfer. Pp. 421-436. Second National Symposium, Hemisphere, 1983.
113. Syamlal, M., Rogers, W., and O'Brien, T. J. MFIX Documentation, Theory Guide, Technical Note DOE/METC-94/1004. DOE, Morgatown, 1993.
114. Saad, Y. and Schultz, M. H. GMRES: A generalized minimum residual algorithm for solving nonsymmetric linear systems. Technical Report Research report 254, Department of computer science, Yale University, 1983.
115. Sonneveld, P., Wesseling, P., and de Zeeuw, P. M. Multigrid and conjugate gradient methods as convergence acceleration techniques. In Paddon, D. J. and Holstein, H. (editors), Multigrid methods for integral and differential equations. Clarendon Press, Oxford, 1985.
116. Taylor, G. I. Diffusion by continuous movements. Proceedings of the London Mathematical Society, Series 2, 20:196, 1921.
117. Tchen, C. M. Mean value and correlation problems connected with the motion of small particles suspended in a Turbulent fluid. Martinus Nijhoff, The Hague, 1947.
118. Tennekes, H. and Lumley, J. L. A first course in turbulence. The MIT Press, Cambridge, 1972.
119. Ungarish, M. Hydrodynamics of suspensions: Fundamentals of centrifugal and gravity separation. Springer-Verlag, Berlin, 1993.
120. Van Doormal, J. P. and Raithby, G. D. Enhancements of the SIMPLE method for predicting incompressible fluid flows. Numerical Heat Transfer, 7:147-163, 1984.
121. Wilkes, N. S., Azzopardi, B. J., and Willets, I. Drop motion and deposition in annular two-phase flow. Research report HTFS RS425 AERE R10571, AERE Engineering Sciences Division, Harwell, 1982.
122. Weber, R., Boysan, F., Ayers, W. H., and Swithenbank, J. Simulation of dispersion of heavy particles in confined turbulent flows. AICHE J., 30:490-493, 1984.
123. Wang, L-P. and Stck, D. E. Stochastic trajectory models for turbulent diffusion: Monte carlo process versus markov chains. Atmospher. Envir., 26 A: 1599-1607, 1992.