Hostname: page-component-6bf8c574d5-gr6zb Total loading time: 0 Render date: 2025-02-14T10:39:58.042Z Has data issue: false hasContentIssue false
  • English
  • Français

Convective instabilities in a closed vertical cylinder heated from below. Part 2. Binary gas mixtures

Published online by Cambridge University Press:  19 April 2006

J. M. Olson  and
F. Rosenberger
J. M. Olson
Affiliation:
Department of Physics, University of Utah, Salt Lake City, Utah 84112 Present address: Solar Energy Research Institute, Golden, CO 80401.
F. Rosenberger
Affiliation:
Department of Physics, University of Utah, Salt Lake City, Utah 84112
Get access Rights & Permissions [Opens in a new window]

Abstract

Non-reactive binary gas mixtures (Xe + He, SiCl4 + H2) have been investigated for convective instabilities in closed vertical cylinders with conductive walls heated from below. Critical Rayleigh numbers NiRa for the onset of various convective modes (including the onset of marginally stable and periodic flow) have been determined with a high resolution differential temperature sensing method. It is found that the second component can significantly alter the hydrodynamic state of the fluid compared to the monocomponent behaviour. Considerably lower critical thermal Rayleigh numbers for steady and time dependent convective modes are observed. The Xe : He system shows stable oscillatory modes similar to those observed in monocomponent gases (periodic disturbances of the mean flow, T0 ≈ 5 s) from NRa = 713 to 780, where a new mode with T0 = 15 s sets in. The frequency of these slower temperature oscillations can be fitted by an equation of the form f2 = k’(NRa − N0Ra) where k’ and N0Ra are constants, which supports the contention that these oscillations are the result of vertical vorticity. For SiCl4 : H2 the high frequency oscillations occur only as a transient mode eventually evolving into the low frequency mode characteristic of binary gas mixtures. This low frequency state is degenerate with a stable time-independent state over a considerable range of NRα. Finite amplitude perturbations can lead to (1) transient oscillatory phenomena accompanied by reorientations of the roll cells with mean periods of 3–5 min; and (2) stable oscillatory flow at NRa 's considerably below NoscRα. The unique behaviour of these binary fluids is tentatively assigned to thermal diffusion.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 92 , Issue 4 , 27 June 1979 , pp. 631 - 642
Copyright
© 1979 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Atkins, B. E., Bastick, R. E. & Ibbs, T. L. 1939 Thermal diffusion in mixtures of the inert gases. Proc. Roy Soc. A 172, 142.Google Scholar
Busse, F. H. 1972 The oscillatory instability of convection rolls in a low Prandtl number fluid. J. Fluid Mech. 52, 97.Google Scholar
Grew, K. E. & Ibbs, T. L. 1952 Thermal Diffusion in Gases, p. 7. Cambridge University Press.
Howard, L. N. 1964 Convection at high Rayleigh number. In Proc. Eleventh Intern. Congr. Appl. Mech. ed. H. Grötler), p. 1109. Springer.
Legros, J. C., Van Hook, W. A. & Thomaes, G. 1968a Convection and thermal diffusion in a solution heated from below. Chem. Phys. Lett. 1, 696.Google Scholar
Legros, J. C., Van Hook, W. A. & Thomaes, G. 1968b Convection and thermal diffusion in a solution heated from below. II. Chem. Phys. Lett. 2, 249.Google Scholar
Olson, J. M. & Rosenberger, F. 1979 Convective instabilities in a closed vertical cylinder heated from below. Part I. Monocomponent gases. J. Fluid Mech. 92, 609.Google Scholar
Platten, J. K. & Chavepeyer, G. 1973 Oscillatory motion in Bénard cell due to the Soret effect. J. Fluid Mech. 60, 305.Google Scholar
Platten, J. K. & Chavepeyer, G. 1975 A hysteresis loop in the two-component Bénard problem. Int. J. Heat Mass Transfer 18, 1071.Google Scholar
Platten J. K. & Chavepeyer, G. 1977 Nonlinear two dimensional Bénard convection with Soret effect: free boundaries. Int. J. Heat Mass Transfer 20, 113.Google Scholar
Schechter R. S., Velarde, M. G. & Platten, J. K. 1973 The two-component Bénard problem. Adv. Chem. Phys. 26, 266.Google Scholar
Touloukian, Y. S. 1970 Thermophysical Properties of Matter. New York: Plenum Publishing Company.
Ulybin, S. A. 1959 Temperature dependence of the viscosity of rarefied gas mixtures. Teplofiz. Vysok. Temp. 2, 583; English translation 1964; High Temp. 2, 526.Google Scholar
Ulybin, S. A., Burgrov, V. P. & Il'in, A. V. 1966 Temperature dependence of the thermal conductivity of chemically nonreacting rarefied gas mixtures. Teplofiz. Vysok. Temp. 4, 214.Google Scholar