Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-19T06:22:09.244Z Has data issue: false hasContentIssue false
  • English
  • Français

Convective instabilities in a closed vertical cylinder heated from below. Part 1. Monocomponent gases

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

Kr, Xe and SiCI4 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. Flow patterns were deduced from a multiple sensor arrangement. For the three lowest modes (i = 1, 2, 3) good quantitative agreement with linear stability theory is found. Stable oscillatory modes (periodic fluctuations of the mean flow) with a period of approximately 5 s are found for a relatively narrow range of NRa. The critical Rayleigh number NoscRa for the onset of oscillatory temperature fluctuations is 1348 ± 50 for an aspect ratio (height/radius) of 6.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 92 , Issue 4 , 27 June 1979 , pp. 609 - 629
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

Ahlers, G. 1975 The Rayleigh-Bénard instability at helium temperatures. In Fluctuations, Instabilities and Phase Transitions (ed. T. Riste). New York: Plenum.
Batchelor, G. K. 1954 Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures. Quart. Appl. Math. 12, 209.Google Scholar
Behringer, R. & Ahlers, G. 1978 Evolution of turbulence form the Rayleigh-Bénard instability. Phys. Rev. Lett. 40, 712.Google Scholar
Carruthers, J. R. 1976 Origins of convective temperature oscillations in crystal growth melts. J. Cryst. Growth 32, 13.Google Scholar
Catton, I. 1966 The effect of lateral boundaries on natural convection between horizontal surfaces. Ph.D. dissertation, UCLA.
Charlson, G. S. & Sani, R. L. 1971 On thermoconvective instability in a bounded cylindrical fluid layer. Int. J. Heat Mass Transfer 14, 2157.Google Scholar
Graham, R. 1973 Generalized thermodynamic potential for the convection instability. Phys. Rev. Lett. 31, 1479.Google Scholar
Hales, A. L. 1937 Convection currents in geysers. Roy. Astro. Soc. Geophys. Suppl. 4, 122.Google Scholar
Heitz, W. L. & Westwater, J. W. 1971 Critical Rayleigh numbers for natural convection of water confined in square cells with L/D from 05 to 8. Trans. A.S.M.E. J. Heat Transfer 93, 188.Google Scholar
Koschmieder, E. L. 1974 Bénard convection. Adv. Chem. Phys. 26, 177.Google Scholar
Krishnamurti, R. 1970 On the transition to turbulent convection. Part 2. The transition to time-dependent flow. J. Fluid Mech. 42, 309.Google Scholar
Malkus, W. V. R. 1954 Discrete transitions in turbulent convection. Proc. Roy. Soc. A 225, 185.Google Scholar
Mitchell, W. T. & Quinn, J. A. 1966 Thermal convection in a completely confined fluid layer. A.I.Ch.E. J. 12, 1116.Google Scholar
Olson, J. M. & Rosenberger, F. 1979 Convective instabilities in a closed vertical cylinder. Part 2. Binary gas mixtures. J. Fluid Mech. 92, 631–642.Google Scholar
Ostroumov, G. A. 1952 Free convection under the conditions of the internal problems. Tech. Theor. Lit. Moscow-Leningrad: State Publishing House. [Engl. trans. N.A.C.A.-TM-1407 (1958).]
Slavnova, E. I. 1961 On the cellular structure of the convective flow of a fluid in a vertical cylinder of circular cross section. Inzh. Fiz. Zh. 4, 80.Google Scholar
Smith, W. A. 1974 Temporal correlations near the convective-instability threshold. Phys. Rev. Lett. 32, 1164.Google Scholar
Svehla, R. A. 1962 Estimated viscosities and thermal conductivities of gases at high temperatures. Estimated viscosities and thermal conductivities of gases at high temperatures.Rep. R-132.
Touloukian, Y. S. 1970 Thermophysical Properties of Matter. New York: Plenum.
Verhoeven, J. D. 1969 Experimental study of thermal convection in a vertical cylinder of mercury heated from below. Phys. Fluids 12, 1733.Google Scholar
Whitehead, J. A. 1975 A Survey of Hydrodynamic Instabilities. In Fluctuations, Instabilities, and Phase Transitions (ed. T. Riste). New York: Plenum.
Willis, G. E. & Deardorff, J. W. 1967 Confirmation and renumbering of the discrete heat flux transitions of Malkus. Phys. Fluids 10, 1861.Google Scholar
Willis, G. E. & Deardorff, J. W. 1970 The oscillatory motions of Rayleigh convection. J. Fluid Mech. 44, 661.Google Scholar
Yih, C. S. 1959 Thermal instability of viscous fluids. Quart. Appl. Math. 17, 25.Google Scholar