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Oscillatory motion in a side-heated cavity

Published online by Cambridge University Press:  26 April 2006

S. G. Schladow
S. G. Schladow
Affiliation:
Environmental Fluid Mechanics Laboratory, Department of Civil Engineering, Stanford University, Stanford, CA 94305-4020, USA Present address: Centre for Limnological Modelling, Department of Civil and Environmental Engineering, University of Western Australia, Nedlands, Western Australia, 6009.
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Abstract

Direct numerical simulations of the transient flow in a side-heated cavity have been conducted for a Rayleigh Number of 2 × 109, an aspect ratio of 1 and a Prandtl Number of 7.1. The results show the presence of both long-period and short-period oscillations. The long-period oscillation is a cavity-scale mode produced by the tilting of the isotherms. The short-period oscillations are shown to be the result of two distinct boundary-layer instabilities. Whereas the latter oscillations can produce large deviations in the observed temperature records, they are relatively shortlived and have only a minor influence on the evolution of the flow towards steady state. The suggestion of the existence of an internal hydraulic jump in such flows has been investigated and found to be incorrect.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 213 , April 1990 , pp. 589 - 610
Copyright
© 1990 Cambridge University Press

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References

Brown, S. N. & Riley, N. 1973 Flow past a suddenly heated vertical plate. J. Fluid Mech. 59, 225–237.Google Scholar
Ede, A. J. 1967 Advances in free convection. Adv. Heat Transfer 4, 1–64.Google Scholar
Gebhart, B. 1969 Natural convection flow, instability, and transition. Trans. ASME C: J. Heat Transfer 91, 293–309.Google Scholar
Gebhart, B. 1973 Instability transition and turbulence in buoyancy induced flows. Ann. Rev. Fluid Mech. 5, 213–246.Google Scholar
Gebhart, B. & Mahajan, R. L. 1982 Instability and transition in buoyancy-induced flows. Adv. Appl. Mech. 22, 231–315.Google Scholar
Gill, A. E. 1966 The boundary layer regime for convection in a rectangular cavity. J. Fluid Mech. 26, 515–536.Google Scholar
Gill, A. E. 1974 A theory of thermal oscillations in liquid metals. J. Fluid Mech. 64, 577–588.Google Scholar
Goldstein, R. J. & Briggs, D. G. 1964 Transient free convection about vertical plates and circular cylinders. Trans. ASME C: J. Heat Transfer 86, 490–500.Google Scholar
Gresho, P. M., Lee, R. L., Chan, S. T. & Sani, R. L. 1980 Solution of the time-dependent incompressible Navier–Stokes and Boussinesq equations using the Galerkin finite difference method In Approximation Methods for Navier–Stokes Problems, Lecture Notes in Mathematics, vol. 771, pp. 203–222 Springer.
Hirt, C. W. 1968 Heuristic stability theory for finite-difference equations. J. Comput. Phys. 2, 339–355.Google Scholar
Hurle, D. T. J., Jakeman, E. & Johnson, C. P. 1974 Convective temperature oscillations in molten gallium. J. Fluid Mech. 64, 565–576.Google Scholar
Ingham, D. B. 1978 Numerical results for flow past a suddenly heated vertical plate. Phys. Fluids 21, 1891–1895.Google Scholar
Ingham, D. B. 1985 Flow past a suddenly heated vertical plate. Proc. R. Soc. Lond. A 402, 109–134.Google Scholar
Ivey, G. N. 1984 Experiments on transient natural convection in a cavity. J. Fluid Mech. 144, 389–401.Google Scholar
Jaluria, Y. & Gebhart, B. 1973 An experimental study of non-linear disturbance behaviour in natural convection. J. Fluid Mech. 61, 337–365.Google Scholar
Joshi, Y. & Gebhart, B. 1987 Transition of transient vertical natural-convection flows in water. J. Fluid Mech. 179, 407–438.Google Scholar
Leonard, B. P. 1979 A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Computer Meth. Appl. Mech. Engng 19, 59–98.Google Scholar
Mollendorf, J. C. & Gebhart, B. 1970 An experimental study of vigorous transient natural convection. Trans. ASME C: J. Heat Transfer 92, 628–634.Google Scholar
Ostrach, S. 1952 An analysis of laminar free-convection flow and heat transfer about a flat plate parallel to the direction of the generating body force. NACA TN 2635, 47 pp.Google Scholar
Paolucci, S. & Chenoweth, D. R. 1989 Transition to chaos in a differentially heated vertical cavity. J. Fluid Mech. 201, 379–410.Google Scholar
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. Hemisphere. 197 pp.
Patterson, J. C. 1984 On the existence of an oscillatory approach to steady natural convection in cavities. Trans. ASME C: J. Heat Transfer 106, 104–108.Google Scholar
Patterson, J. C. & Imberger, J. 1980 Unsteady natural convection in a rectangular cavity. J. Fluid Mech. 100, 65–86.Google Scholar
Perng, C. Y. & Street, R. L. 1989 Three dimensional unsteady flow simulation: alternative strategies for volume averaged calculation. Intl J. Numer. Meth. Fluids (in press).Google Scholar
Schladow, S. G., Patterson, J. C. & Street, R. L. 1989 Transient flow in a side-heated cavity at high Rayleigh number: a numerical study. J. Fluid Mech. 200, 121–148 (referred to as SPS).Google Scholar
Schladow, S. G. & Street, R. L. 1988 Transient flow in a weakly stratified side-heated cavity. ASME FED 71, 39–41.Google Scholar
Siegel, R. 1958 Transient free convection from a vertical flat plate. Trans. ASME 80, 347–359.Google Scholar
Worster, M. G. & Leitch, A. M. 1985 Laminar free convection in confined regions. J. Fluid Mech. 156, 301–319.Google Scholar