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Time-dependent convection in a fluid-saturated porous cube heated from below

Published online by Cambridge University Press:  26 April 2006

S. Kimura ,
G. Schubert  and
J. M. Straus
S. Kimura
Affiliation:
Government Industral Research Institute, Tohoku-Nigatake 4-2-1, Sendai 983, Japan
G. Schubert
Affiliation:
Department of Earth and Space Sciences, University of California, Los Angeles, CA 90024-1567, USA
J. M. Straus
Affiliation:
Laboratory Operations, The Aerospace Corporation, PO Box 92957, Los Angeles, CA 90009, USA
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Abstract

A numerical scheme based on the pseudospectral method has been implemented in order to study three-dimensional convection in a fluid-saturated cube of porous material. With increasing Rayleigh number R, convection first evolves from a symmetric steady state (S) to a partially non-symmetric steady state (S’, physical symmetry in the vertical direction is preserved). The transition Rayleigh number is about 550. At a Rayleigh number of 575 the flow becomes oscillatory P(1) with a single frequency that increases with R. At a value of R between 650 and 680 the oscillation becomes quasi-periodic with at least two fundamental frequencies. It returns to a simply periodic state in a narrow range about R = 725. A further increase of R transforms the simply periodic state again to a quasi-periodic state. The sequence of three-dimensional time-dependent states resembles previously studied two-dimensional cases in that evolution from more complex states to less complex states occurs with increasing R. The partial symmetry breaking prior to the onset of time dependence is unique to the three-dimensional flows, but a dependence of the S → S’ transition on the step size in R suggests the possibility that S → S’ might not occur prior to S → P(1) for sufficiently small steps in R. The quasi-periodic flows sometimes exhibit intermittency, causing difficulty in exactly defining their spectral characteristics.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 207 , October 1989 , pp. 153 - 189
Copyright
© 1989 Cambridge University Press

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References

Aidun, C. K. & Steen, P. H. 1986 Transition to oscillatory convective heat transfer in fluidsaturated porous medium. AIAA/ASME 4th Joint Thermophysics and Heat Transfer Conf., AIAA paper 86–1264.
Aidun, C. K. & Steen, P. H. 1987 Transition to oscillatory heat transfer in a fluid-saturated porous medium. J. Thermophys. 1, 268–273.Google Scholar
Beck, J. L. 1972 Convection in a box of porous material saturated with fluid. Phys. Fluids 15, 1377–1383.Google Scholar
Caltagirone, J. P. 1975 Thermoconvective instabilities in horizontal porous layers. J. Fluid Mech. 72, 269–287.Google Scholar
Gary, J. & Kassoy, D. R. 1981 Computation of steady and oscillatory convection in saturated porous media. J. Comput. Phys. 40, 120–142.Google Scholar
Gary, J., Kassoy, D. R., Tradjeran, H. & Zebib, A. 1982 The effects of significant viscosity variation on convective heat transfer in water-saturated porous media. J. Fluid Mech. 117, 233–249.Google Scholar
Gollub, J. P. & Benson, S. V. 1980 Many routes to turbulent convection. J. Fluid Mech. 100, 449–470.Google Scholar
Gottleib, D. & Orszag, S. A. 1977 Numerical Analysis of Spectral Methods: Theory and Applications. SIAM.
Holst, P. H. & Aziz, K. 1972 Transient three-dimensional natural convection motion in a confined porous medium. Intl. J. Heat Mass Transfer 15, 73–90.Google Scholar
Horne, R. N. 1979 Three-dimensional natural convection motion in a confined porous medium heated from below. J. Fluid Mech. 92, 751–766.Google Scholar
Horne, R. N. & Caltagirone, J. P. 1980 On the evolution of thermal disturbances during natural convection in a porous medium. J. Fluid Mech. 100, 385–395.Google Scholar
Horne, R. N. & O'Sullivan, M. J. 1974 Oscillatory convection in a porous medium heated from below. J. Fluid Mech. 66, 339–352.Google Scholar
Howard, L. N. 1964 Convection at high Rayleigh number. In Proc. 11th Intl Congr. Appl. Mech., Munich, pp. 1109–1115. Springer.
Kessler, R. 1987 Nonlinear transition in three-dimensional convection. J. Fluid Mech. 174, 357–379.Google Scholar
Kimura, S., Schubert, G. & Straus, J. M. 1986 Route to chaos in porous-medium thermal convection. J. Fluid Mech. 116, 305–324.Google Scholar
Kimura, S., Schubert, G. & Straus, J. M. 1987 Instabilities of steady, periodic, and quasiperiodic modes of convection in porous media. Trans. ASME C: J. Heat Transfer 109, 350–335.Google Scholar
Koster, J. N. & Müller, V. 1984 Oscillatory convection in vertical slots. J. Fluid Mech. 139, 363–390.Google Scholar
MacLaughlin, J. B. & Orszag, S. A. 1982 Transition from periodic to chaotic thermal convection. J. Fluid Mech. 122, 123–142.Google Scholar
Marcus, P. S. 1981 Effects of truncation in model representations of thermal convection. J. Fluid Mech. 103, 241–255.Google Scholar
Moore, D. R. & Weiss, N. O. 1973 Two-dimensional Rayleigh-Bénard convection. J. Fluid Mech. 58, 289–312.Google Scholar
Orszag, S. A. 1971 Numerical simulation of incompressible flows within simple boundaries. Stud. Appl Maths 50, 293–327.Google Scholar
Schubert, G. & Straus, J. M. 1979 Three-dimensional and multi-cellular steady and unsteady convection in fluid-saturated porous media at high Rayleigh numbers. J. Fluid Mech. 94, 25–36.Google Scholar
Schubert, G. & Straus, J. M. 1982 Transitions in time-dependent thermal convection in fluid-saturated porous media. J. Fluid Mech. 121, 301–313.Google Scholar
Steen, P. H. 1983 Pattern selection for finite amplitude convection states in boxes of porous media. J. Fluid Mech. 136, 219–242.Google Scholar
Steen, P. H. & Aidun, C. K. 1988 Time-periodic convection in porous media: transition mechanism. J. Fluid Mech. 196, 263–290.Google Scholar
Straus, J. M. 1974 Large amplitude convection in porous media. J. Fluid Mech. 64, 51–63.Google Scholar
Straus, J. M. & Schubert, G. 1979 Three-dimensional convection in a cubic box of fluid-saturated porous material. J. Fluid Mech. 91, 155–165.Google Scholar
Zebib, A. & Kassoy, D. R. 1978 Three-dimensional natural convection motion in a confined porous medium. Phys. Fluids 21, 1–3.Google Scholar