Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-06T02:14:55.235Z Has data issue: false hasContentIssue false
  • English
  • Français

Solutions and stability criteria of natural convective flow in an inclined porous layer

Published online by Cambridge University Press:  20 April 2006

J. P. Caltagirone  and
S. Bories
J. P. Caltagirone
Affiliation:
Laboratoire d'Energétique et Phénomènes de Transfert, Unité Associée CNRS n° 873, Ecole Nationale d'Arts et Métiers, Esplanade des Arts et Métiers, 33405 TALENCE CEDEX (France)
S. Bories
Affiliation:
Institut de Mécanique des Fluides de Toulouse, Laboratoire associé CNRS n° 5, E.N.S.E.E.I.H.T., 2 rue Charles Camichel, 31071 TOULOUSE CEDEX (France)
Get access Rights & Permissions [Opens in a new window]

Abstract

Previous experiments on natural convection in a differentially heated porous layer with large lateral dimensions gave evidence for different configurations of flow. Depending on the values of the Rayleigh number, the inclination and the longitudinal extension of the layer, the three main structures observed correspond to a two-dimensional unicellular flow, polyhedral convective cells and longitudinal coils. In this paper there is a definition of the conditions necessary for these types of flow to exist using a linear stability theory and it is shown that the experimentally observed structures can be theoretically predicted by a three-dimensional numerical model based upon Galerkin's spectral method. Finally, the results of this model are used to show the influence of initial conditions on the setting up of the stationary flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 155 , June 1985 , pp. 267 - 287
Copyright
© 1985 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

Bories, S. & Combarnous, M. 1973 Natural convection in a sloping porous layer. J. Fluid Mech. 57, 63–79.Google Scholar
Bories, S., Combarnous, M. & Jaffrenou, J. Y. 1972 Observations des differentes formes d'ecoulements thermoconvectifs dans une couche poreuse inclinée. C.R. Acad. Sci. Paris A 275, 857–860.Google Scholar
Bories, S. & Monferran, L. 1972 Condition de stabilité et échange thermique par convection naturelle dans une couche poreuse inclinée de grande extension. C.R. Acad. Sci. Paris B 274, 4–7.Google Scholar
Caltagirone, J. P. 1975 Thermoconvective instabilities in a porous layer. J. Fluid. Mech. 72, 269–287.Google Scholar
Caltagirone, J. P. 1981 Convection in porous medium. In Convective Transport and Instability Phenomena, (ed. G. Braun) pp. 199–232, Karlsruhe.
Caltagirone, J. P. & Bories, S. 1980 Solutions numériques bidimensionnelles et tridimensionnelles de l'écoulement de convection naturelle dans une couche poreuse inclinée. C.R. Acad. Sci. Paris B 190, 197–200.Google Scholar
Caltagirone, J. P., Meyer, G. & Mojtabi, A. 1981 Structurations thermoconvectives tridimensionnelles dans une couche poreuse horizontale. J. Méc. 20, 219–232.Google Scholar
Chan, B. K. C., Ivey, C. M. & Barry, J. M. 1970 Natural convection in inclosed porous media with rectangular boundaries. Trans. ASME C: J. Heat Transfer 92, 21–27.Google Scholar
Combarnous, M. & Bories, S. 1975 Hydrothermal convection in saturated porous media. Adv. Hydrosci. 10, 231–307.Google Scholar
Gottlieb, P. & Orszag, S. A. 1977 Numerical Analysis of Spectral Methods, Theory and Applications. Regional Conf. Series in Applied Maths, vol. 26. Arrowsmith.
Horne, R. N. 1979 Three-dimensional natural convection 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
Jaffrennou, J. Y. & Bories, S. 1974 Convection naturelle dans une couche poreuse inclinée. Rapport interne G.E. 14. Institut de Mecanique des Fluides de Toulouse.
Schubert, G. E. & Straus, J. M. 1979 Three-dimensional and multicellular steady and unsteady convection in fluid-saturated porous media at high Rayleigh numbers. J. Fluid Mech. 94, 25–38.Google Scholar
Straus, J. M. & Schubert, G. E. 1979 Three-dimensional convection in a cubic box of a fluidsaturated porous material. J. Fluid Mech. 91, 155–165.Google Scholar
Walch, J. P. 1980 Convection naturelle dans une boîte poreuse inclinée: contribution à l'étude du cas stable. Thèse Université Paris VI.
Walch, J. P. & Dulieu, B. 1979 Convection naturelle dans une boîte rectangulaire légèrement inclinée contenant un milieu poreux. Intl J. Heat Mass Transfer 22, 1607–1612.Google Scholar
Walch, J. P. & Dulieu, B. 1982 Convection de Rayleigh–Bénard dans une cavité poreuse faibiement inclinée. Journal de Physiques Letters. 43, L103–107.Google Scholar
Walker, K. L. & Homsy, G. M. 1978 Convection in a porous cavity. J. Fluid Mech. 87, 449–474.Google Scholar
Weber, J. E. 1975 Thermal convection in a tilted porous layer. Intl J. Heat Mass Transf. 18, 474–475.Google Scholar