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Thermal convection in gas–droplet mixtures with phase transition

Published online by Cambridge University Press:  29 March 2006

T. Kambe  and
R. Takaki
T. Kambe
Affiliation:
Institute of Space and Aeronautical Science, University of Tokyo, Komaba, Meguro-ku, Tokyo, Japan
R. Takaki
Affiliation:
Faculty of General Education, Tokyo University of Agriculture and Technology, Fuchu-shi, Tokyo, Japan
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Abstract

Thermal convection in a three-component fluid consisting of an inert carrier gas, a condensable vapour and small liquid droplets dispersed throughout the gaseous components has been investigated both theoretically and experimentally. The theoretical study is concerned with the stability of a horizontal fluid layer subject to gradients of both temperature and droplet density. The stability is characterized by four parameters: two material constants, that is, a modified Prandtl number P and a constant Q proportional to Dm − κ (Dm is the mutual mass diffusivity of the two gaseous constituents, κ the thermometric conductivity of the gas phase), a modified Rayleigh number R and a parameter S defined as the ratio of the droplet density gradient to the gas density gradient. It is shown for positive R that, irrespective of the value of R, the system is stable for S > S∞ (S∞ is a constant dependent on P and Q) and unstable for S < Q (Q is normally less than S∞) and that for the intermediate range Q < S < S∞ a transition from stability to instability occurs via an oscillatory state as R is increased through a critical value depending on S. It is shown that the stability is governed largely by both vapour diffusion through the inert gas and droplet growth or decay due to phase changes.

In the experiments, thermal convection in a three-component fluid consisting of air, water vapour and water droplets was investigated. The cloud of droplets was mainly formed by injecting cigarette smoke into a horizontal layer of air saturated with water vapour. After the injection several phases of motion were observed successively. Among them there were travelling waves and steady cellular convection. Measurements were made of the critical Rayleigh numbers for the onset of the phases, the scale of the steady convection cells and the speed of the travelling waves. It is found that all the qualitative features of the experiment are explained by the theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 70 , Issue 1 , 15 July 1975 , pp. 89 - 112
Copyright
© 1975 Cambridge University Press

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References

Agee, E. M. 1969 Weathermise, 22, 19.
Baines, P. G. & Gill, A. E. 1969 J. Fluid Mech. 37, 289.
Hadlock, R. K. & Hess, S. L. 1968 J. Atmos. Sci. 25, 161.
Marble, F. E. 1969 Astron. Acta, 14, 585.
Schechter, R. S., Prigogine, I. & Hamm, J. R. 1972 Phys. Fluids, 15, 379.
Schwiderski, E. W. & Schwab, H. J. A. 1971 J. Fluid Mech. 48, 703.
Sparrow, E. M., Goldstein, R. J. & Jonsson, V. K. 1964 J. Fluid Mech. 18, 513.
Spiegel, E. A. & Veronis, G. 1960 Astrophys. J. 131, 442.
Steen, M. E. 1960 Tellus, 12, 172.
Stommel, H., Arons, A. B. & Blanchard, D. 1956 Deep-Sea Res. 3, 152.
Teitton, D. J. & Zarraga, M. N. 1967 J. Fluid Mech. 30, 21.
Turner, J. S. 1963 Quart. J. Roy. Met. Soc. 89, 62.
Turner, J. S. 1973 Buoyancy Effects in Fluids, chap. 8. Cambridge University Press.
Turner, J. S. & Yang, I. K. 1963 J. Fluid Mech. 17, 212.
Veronis, G. 1965 J. Mar. Res. 23, 1.
Wollkind, D. J. & Frisch, H. L. 1971 Phys. Fluids, 14, 13.
Yang, I. K. 1968 Proc. Int. Conf. on Cloud Physics, Toronto, p. 529.