Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-19T10:25:15.519Z Has data issue: false hasContentIssue false
  • English
  • Français

One-field equations for two-phase flows

Published online by Cambridge University Press:  17 February 2009

Murray Rudman
Murray Rudman
Affiliation:
Commonwealth Scientific and Industrial Research Organisation, Division of Building, Construction and Engineering, PO Box 56, Highett, Victoria 3190, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A new derivation of the averaged heat and mass transport equations for two-phase flows is presented. A volume averaging technique is used in which averaging is perform over both phases simultaneously in order to derive equations that describe transport the mixture, rather than transport in each phase. The derivation is particularly applicable to incompressible liquid/solid systems in which the two phases are tightly coupled. An example of the numerical solution of the equations is then presented in which a thermally convecting suspension is modelled. It is seen that large-scale instability can result from the interaction of thermal and compositional density gradients.

Type
Research Article
Information
The ANZIAM Journal , Volume 39 , Issue 2 , October 1997 , pp. 149 - 170
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Batchelor, G. K., “Sedimentation in a dilute dispersion of spheres”, J. Fluid Mech. 52 (1972) 245–268.Google Scholar
[2]Cook, T. L. and Harlow, F. H., “VORT - A Computer Code for Bubbly Two-phase Flow”, Los Alamos National Laboratory Report No. LA-10021-MS, (1978).Google Scholar
[3]Drew, D. A. “Two-phase flows: Constitutive equations for lift and Brownian motion and some basic flows”, Arch. Rat. Mech. Analysis 62 (1976) 149–163.Google Scholar
[4]Drew, D. A., “Mathematical modelling of two-phase flow”, Ann. Rev. Fluid Mech. 15 (1983) 261–291.Google Scholar
[5]Drew, D. A. and Segel, L. A., “Averaged equations for two-phase flows”, Studies in Appl. Math. 50 (1971) 205–231.CrossRefGoogle Scholar
[6]Drew, D. A. and Segel, L. A., “Analysis of fluidized beds and foams using averaged equations”, Studies in Appl. Math. 50 (1971) 233–257.Google Scholar
[7]Einstein, A., “Eine neue Bestimmung der Moleküldimensionen”, Annalen der Physik 19, (1908) 289–307.Google Scholar
[8]Gray, W. G. and Lee, P. C. Y., “On the theorems for local volume averaging of multiphase systems, Int. J. Multiphase Flow 3 (1977) 333–340.Google Scholar
[9]Hwang, G. J. and Shen, H. H., “Modelling the solid phase stress in a fluid-solid mixture”, Int. J. Multiphase Flow. 15 (1989) 257–268.CrossRefGoogle Scholar
[10]Ishii, M., Thermo-fluid Dynamic Theory of Two-phase Flow (Eyrolles, Paris, 1975).Google Scholar
[11]Lamb, H., Hydrodynamics, Sixth edition, § 337 (Dover, New York, 1945).Google Scholar
[12]Lundgren, T. S., “Slow flow through stationary random beds and suspensions of spheres”, J. Fluid Mech. 51 (1972) 273–299.Google Scholar
[13]Murray, J. D., “On the mathematics of fluidization”, J. Fluid Mech. 21 (1965) 465–493.Google Scholar
[14]Prosperetti, A. and Jones, A. V., “Pressure forces in disperse two-phase flow”, Int. J. Multiphase Flow 10 (1984) 425–440.Google Scholar
[15]Rudman, M., “Low Reynolds number two-phase flows”, Ph.D. thesis, Monash University, 1990.Google Scholar
[16]Rudman, M., “Two-phase thermal convection: Implications for crystal settling in magma chambers”, Phy. Earth Plan. Int. 72 (1992) 153–172.Google Scholar
[17]Taylor, G. I., “The viscosity of a fluid containing small drops of another fluid”, Proc. Roy. Soc. London, A, 138 (1932) 41–48.Google Scholar
[18]Thomas, D. G., “Transport characteristics of suspensions: VIII A note on the viscosity of Newtonian suspensions of uniform spherical particles”, J. Coll. Sci. 20 (1965) 267–277.CrossRefGoogle Scholar
[19]Travis, J. R., Harlow, F. H. and Amsden, A. A., “Numerical Calculation of Two-Phase Flows’, Los Alamos Scientific Laboratory Report No. LA-5942-MS (1975).Google Scholar
[20]Whitaker, S., “The transport equations for multi-phase systems”, Chem. Eng. Sci. 28 (1973) 139–147.Google Scholar