On the mixture model for multiphase flow

VTT Publications

Volumn , Issue 288, 1996, Pages 3-67

[No Author Info available]

Author keywords

Computers; Dispersions; Equations; Flow; Flow control; Mathematical models; Mixtures; Models; Multiphase flow; Simulation

Indexed keywords

EID: 5644247447     PISSN: 12350621     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Article

References (75)

1. AEA Technology 1994. CFDS-FLOW3D user guide. AEA Technology, Harwell Laboratory.
2. Adeniji-Fashola, A. & Chen, C. P. 1990. Modeling of confined turbulent fluid-particle flows using Eulerian and Lagrangian schemes. Int. J. Heat Mass Transfer, Vol. 33, No. 4, pp. 691-701.
3. Ahmadi, G. & Ma, D. 1990. A thermodynamical formulation for dispersed multiphase turbulent flows - I. Basic theory. Int. J. Multiphase Flow, Vol. 16, No. 2, pp. 323 - 340.
4. Amberg, G. & Ungarish, M. 1993. Spin-up from rest of a mixture: numerical simulation and asymptotic theory. J. Fluid Mech., Vol. 246, pp. 443 - 464.
5. Bakker, A., Fasano, J. B. & Myers, K. J. 1994. Effects of Flow pattern on the solids distribution in a stirred tank. Mixing 8, Cambridge, UK, September 1994. ICheme Symposium series No. 136, pp. 1-8.
6. Bakker, W. A. M., van Can, H. J. L., Tramper, J. & de Gooijer, C. D. 1993. Hydrodynamics and mixing in a multiple air-lift loop reactor. Biotechnol. Bioeng., Vol. 42, pp. 994 - 1001.
7. Bottoni, M. & Lyczkowski, R. W. 1994. Modeling of bubbly and annular two-phase flow in subchannel geometries with BACCHUS-3D/TP. Nuclear Technology, Vol. 106, pp. 186-201.
8. Bowen, R. M. 1976. Theory of Mixtures, Part I. In: Eringen, A. C. (Ed.), Continuum Physics, Vol. III. New York: Academic Press.
9. Brockmeier, U., Schaffrath, A. & Unger, H. 1995. Verification of the two-phase stratified-flow model in ATHLET by separate effect tests. Nucl. Eng. & Des., Vol. 154, pp. 43 - 50.
10. CHAM 1991. The PHOENICS Reference Manual. London: Concentration, Heat and Momentum Ltd.
11. Clark, N. N., Van Egmond, J. W. & Nebiolo, E. P. 1990. The drift-flux model applied to bubble columns and low velocity flows. Int. J. Multiphase Flow, Vol. 16, No. 2, pp. 261 - 279.
12. Clift, R., Grace, J. R. & Weber, M. E. 1978. Bubbles, Drops, and Particles. London: Academic Press. 351 p.
13. Cook, T. L. & Harlow, F. H. 1986. Vortices in bubbly two-phase flow. Int. J. Multiphase Flow, Vol. 12, pp. 36 - 61.
14. Csanady, C. T. 1963. Turbulent Diffusion of Heavy Particles in the Atmosphere. J. Atm. Sci., Vol. 20, pp. 201 - 208.
15. Dahlkild, A. A. & Amberg, G. 1994. Rotating axial flow of a continuously separating mixture. J. Fluid Mech., Vol. 266, pp. 319 - 346.
16. Dalla Valle, J. M. 1948. Micromeritics. London: Pitman.
17. Ding, J. & Gidaspow, D. 1990. A bubbling fluidization model using kinetic theory of granular flow. AIChE Journal, Vol. 36, No. 4, pp. 523 - 538.
18. Drew, D. A. 1983. Mathematical modelling of two-phase flow. Ann. Rev. Fluid. Mech., Vol. 15, pp. 261 - 291.
19. Drew, D. A. & Lahey, R. T. 1979. Application of general constitutive principles to the derivation of multidimensional two-phase flow equations. Int. J. Multiphase Flow, Vol. 5, pp. 243 - 264.
20. Elghobashi, S. E. & Abou-Arab, T. W. 1983. A two-equation turbulence model for two-phase flows. The Physics of Fluids, Vol. 26, pp. 931 - 938.
21. Ergun, S. 1952. Fluid flow through packed columns. Chemical Engineering Progress, Vol. 48, No. 2, pp. 89 - 94.
22. Fluent Inc. 1995. FLUENT User's guide. Lebanon: Fluent Inc.
23. Franca, F. & Lahey, R. T. Jr. 1992. The use of drift-flux techniques for the analysis of horizontal two-phase flows, Int. J. Multiphase Flow, Vol. 18, pp. 787 - 801.
24. Garside, J. & Al-Dibouni, M. R. 1977. Velocity-voidage relationships for fluidization and sedimentation. I & EC Process Des. Dev., Vol. 16, pp. 206 -214.
25. Gidaspow, D. 1994. Multiphase flow and fluidization. Continuum and kinetic theory descriptions. San Diego: Academic Press.
26. Gore, R. A. & Crowe, C. T. 1989. Effect of particle size on modulating turbulent intensity. Int. J. Multiphase Flow, Vol. 15, No. 2, pp. 279 - 285.
27. Greenspan, H. P. & Ungarish, M. 1982. On hindered settling of particles of different sizes. Int. J. Multiphase Flow, Vol. 8, pp. 587 - 602.
28. Hallanger, A., Sveberg, K., Anfinsen, N., Sønstabø & Knutsen, T. 1995. A Simulation Model for Three-Phase Gravity Separators. Proceedings of the 2nd Colloquium on Process Simulation. 6-8 June, 1995. Espoo, Finland: Helsinki University of Technology. Pp. 199 - 213.
29. Hirsch, C. 1992. Numerical computation of internal and external flows. Volume 1: Fundamentals of numerical discretization. Chichester: John Wiley & Sons.
30. Hwang, G.-J. & Shen, H. H. 1989. Modeling the solid phase stress in a fluid-solid mixture, Int. J. Multiphase Flow, Vol. 15, No. 2, pp. 257 - 268.
31. Hwang, G.-J. & Shen, H. H. 1991. Modeling the phase interaction in the momentum equations of a fluid-solid mixture. Int. J. Multiphase Flow, Vol. 17, No. 1, pp. 45 - 57.
32. Hwang, G.-J. 1989. Modeling two-phase flows of fluid and solid mixture. PhD dissertation. Ann Arbor, MI: Clarkson University. 163 p.
33. Ihme, F., Schmidt-Traub, H. & Brauer, H. 1972. Theoretische Unter-suchungen über die Umströmung und den Stoffübergang an Kugeln. Chemie-ing.-Tech., Vol. 44, No. 5, pp. 306 - 313.
34. Ishii, M. 1975. Thermo-fluid Dynamic Theory of Two-phase Flow. Paris: Eyrolles.
35. Ishii, M. & Mishima, K. 1984. Two-fluid model and hydrodynamic constitutive relations. Nucl. Eng. & Des., Vol. 82, pp. 107 - 126.
36. Ishii, M. & Zuber, N. 1979. Drag coefficient and relative velocity in bubbly, droplet and particulate flow. AlChE J., Vol. 25, pp. 843 - 854.
37. Johansen, S. T., Anderson, N. M. & De Silva, S. R. 1990. A two-phase model for particle local equilibrium applied to air classification of powers. Power Technology, Vol. 63, pp. 121 - 132.
38. Joseph, D. D., Lundgren, T. S., Jackson, R. & Saville, D. A. 1990. Ensemble averaged and mixture theory equations for incompressible fluid-particle suspensions. Int. J. Multiphase Flow, Vol. 16, No. 1, pp. 35 - 42.
39. Johnson, G., Massoudi, M. & Rajagopal, K. R. 1991. Flow of a fluid-solid mixture between flat plates. Chem. Eng. Sci., Vol. 46, No. 7, pp. 1713 - 1723.
40. Kataoka, I. & Ishii, M. 1987. Drift flux model for large diameter pipe and new correlation for pool void fraction. Int. J. Mass Transfer, Vol. 30, pp. 1927 - 1939.
41. Kim, K., & Doster, J. M. 1991. Application of mixture drift flux equations to vertical separating flows. Nuclear Technology, Vol. 95, pp. 103 - 115.
42. Kocaefe, D., Bui, R. T. & Provencher, R. 1994. One-phase model for stirring solid-liquid mixtures: SiC-Al melt. Proceedings of the international symposium on recent developments in light metals, Toronto, Ontario, August 20-25, 1994. Montreal: Canadian Institute of Mining, Metallurgy and Petroleum. Pp. 49 - 60.
43. Landau, L. D. & Lifshitz 1982, E. M. Course of Theoretical Physics, Volume 6. Fluid Mechanics. Oxford: Pergamon Press.
44. Lo, S. 1994. Private communication.
45. Mostafa, A. A. & Mongia, H. C. 1988. On the interaction of particles and turbulent fluid flow. Int. J. Heat Mass Transfer, Vol. 31, No. 10, pp. 2063 - 2075.
46. Myers, K. J., Fasano, J. B. & Bakker, A. 1994. Gas dispersion using mixed high-efficiency/disc impeller systems. Mixing 8, Cambridge, UK, September 1994. ICheme Symposium Series No. 136, pp. 65 - 72.
47. Nigmatulin, R. I. 1979. Spatial averaging in the mechanics of heterogeneous and dispersed systems. Int. J. Multiphase Flow, Vol. 5, pp. 353 - 385.
48. O'Brien, T. J. & Syamlal, M. 1993. Particle Cluster effects in the numerical simulation of a circulating fluidized bed. 4th Int. Conf. on CFB, Somerset, USA, Preprint Volume. Pp. 430 - 435.
49. Passman, S. L., Nunziato, J. W. & Walsh, E. K. 1984. A theory of multiphase mixtures. Rational Thermodynamics. Second Edition (ed. by Truesdell, C.). New York: Springer-Verlag.
50. Pericleous, K. A. & Drake, S. N. 1986. An Algebraic Slip Model of PHOENICS for Multi-phase Applications. Numerical Simulation of Fluid Flow and Heat/Mass Transfer Processes. (Eds. Markatos, N. C., Tatchell, D. G., Cross, M. & Rhodes, N.) Lecture Notes in Engineering 18. Berlin: Springer-Verlag.
51. Pericleous, K. A & Patel, M. K. 1987. The modelling of tangential and axial agitators in chemical reactors. PhysicoChemical Hydrodynamics, Vol. 8, No. 2, pp. 105 - 123.
52. Picart, A., Berlemont, A. & Gouesbet, G. 1986. Modelling and predicting turbulence fields and the dispersion of discrete particles transported by turbulent flows. Int. J. Multiphase Flow, Vol. 12, No. 2, pp. 237 - 261.
53. Richardson, J. F. & Zaki, W. N. 1954. Sedimentation and fluidisation: Part I. Transactions of Institution of Chemical Engineers, Vol. 32, pp. 35-53.
54. Rutgers, I. R. 1962a. Relative viscosity of suspensions of rigid spheres in Newtonian liquids. Rheologica Acta, Band 2, Heft 3, pp. 202 - 210.
55. Rutgers, I. R. 1962b. Relative viscosity and concentration. Rheologica Acta, Band 2, Heft 4, pp. 305 - 348.
56. Sakaguchi, T., Minagawa, H., Sahara, K., Kato, Y., Kuroda, N. & Matsumoto, T. 1987. Estimation of volumetric fraction of each phase in gas-liquid-solid three-phase flow. Proceedings of the 1987 ASME-JSME Thermal Engineering Joint Conference. New York: ASME. Pp 373 - 380.
57. Simonin, O. 1990. Eulerian formulation for particle dispersion in turbulent two-phase flows. Proc. 5th Workshop on Two-Phase Flow Predictions, March 19 - 22, Erlangen, FRG. Jülich: Kernforschungsanlage Jülich. Pp. 156 - 166.
58. Singhal, A. K., Keeton, L. W. & Spalding, D. B. 1980. Predictions of thermal hydraulics of a PWR steam generator by using the homogeneous, the two-fluid, and the algebraic-slip model. AIChE Symposium Series No. 199, Vol. 76, pp. 45 - 55.
59. Soo, S. L. 1990. Multiphase fluid dynamics. Hong Kong: Science Press.
60. Soria, A. & de Lasa, H. 1992. Averaged kinematics of liquid fluidized beds. Fluidized processes: Theory and practice, AIChE Symposium Series No. 289, Vol. 88, pp. 51 - 60.
61. Syamlal, M. & O'Brien, T. J. 1988. Simulation of granular layer inversion in liquid fluidized beds. Int. J. Multiphase flow, Vol. 14, No. 4, pp. 473 - 481.
62. Tsuji, Y., Kawaguchi, T. & Tanaka, T. 1993. Discrete particle simulation of two-dimensional fluidized bed. Powder Technology, Vol. 77, pp. 79 - 87.
63. Tsuo, Y. P. & Gidaspow, D. 1990. Computation of flow patterns in circulating fluidized beds. AIChE J., Vol. 36, pp. 885 - 896.
64. Tu, J. Y. & Fletcher, C. A. J. 1994. An improved model for particulate turbulence modulation in confined two-phase flow. Int. Comm. in Heat and Mass Transfer, Vol 21, No. 6, pp. 775 - 783.
65. Ungarish, M. & Greenspan, H. P. 1984. On centrifugal separation of particles of two different sizes. Int. J. Multiphase Flow, Vol. 10, pp. 133 - 148.
66. Ungarish, M. 1990. Spin-up from rest of a mixture. Physics of Fluids A (Fluid Dynamics), Vol. 2, No. 2, pp. 160 - 166.
67. Ungarish, M. 1993. Hydrodynamics of suspensions: Fundamentals of centrifugal and gravity separation. Berlin: Springer.
68. Ungarish, M. 1995. On the modelling and investigation of polydispersed rotating suspensions. Int. J. Multiphase Flow, Vol. 21, pp. 267 - 284.
69. Verloop, W. C. 1995. The inertial coupling force. Int. J. Multiphase Flow, Vol. 21, pp. 929-933.
70. Wallis, G. B. 1969. One-dimensional two-phase flow. New York: McGrawHill.
71. Wehmeier, G., Westphal, F. & Friedel, L. 1994. Pressure relief system design for vapour or two-phase flow. Trans IChemE, Vol. 72, Part B, pp. 142 - 148.
72. White, F. M. 1974. Viscous fluid flow. New York: McGraw-Hill.
73. Yonemura, S., Tanaka, T. & Tsuji, Y. 1993. Cluster formation in gas-solid flow predicted by the DSMC method, In: Stock, D. E., Reeks, M. W., Tsuji, Y., Gautam, M., Michaelides, E. E. & Jurewicz, J. T. (Ed.), Gas-Solid Flows. ASME, FED-Vol. 166, Book No. H00806.
74. Zhou, Z. A. & Egiebor, N. O. 1993. A gas-liquid drift-flux model for flotation columns. Technical note. Minerals Engineering, Vol. 6. No. 2, pp. 199 - 205.
75. Zuber, N. & Findlay, J. A. 1965. Average Volumetric Concentration in Two-Phase Flow Systems. J. Heat Trans., Vol. 87, pp. 453 - 468.