Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-20T05:32:34.516Z Has data issue: false hasContentIssue false
  • English
  • Français

Throughflow effects on convective instability in superposed fluid and porous layers

Published online by Cambridge University Press:  26 April 2006

Falin Chen
Falin Chen
Affiliation:
Institute of Applied Mechanies. National Taiwan University, Taipei, Taiwan 10764, ROC
Get access Rights & Permissions [Opens in a new window]

Abstract

We implement a linear stability analysis of the convective instability in superposed horizontal fluid and porous layers with throughflow in the vertical direction. It is found that in such a physical configuration both stabilizing and destabilizing factors due to vertical throughflow can be enhanced so that a more precise control of the buoyantly driven instability in either a fluid or a porous layer is possible. For ζ = 0.1 (ζ, the depth ratio, defined as the ratio of the fluid-layer depth to the porous-layer depth), the onset of convection occurs in both fluid and porous layers, the relation between the critical Rayleigh number Rcm and the throughflow strength γm is linear and the Prandtl-number (Prm) effect is insignificant. For ζ ≥ 0.2, the onset of convection is largely confined to the fluid layer, and the relation becomes Rcm ∼ γ2m for most of the cases considered except for Prm = 0.1 with large positive γm where the relation Rcm ∼ γ3m holds. The destabilizing mechanisms proposed by Nield (1987 a, b) due to throughflow are confirmed by the numerical results if considered from the viewpoint of the whole system. Nevertheless, from the viewpoint of each single layer, a different explanation can be obtained.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 231 , October 1991 , pp. 113 - 133
Copyright
© 1991 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

Beavers, G. S. & Joseph, D. D. 1967 Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197–207.Google Scholar
Beck, J. L. 1972 Convection in a box of porous material saturated with fluid. Phys. Fluids 15, 1377–1383.Google Scholar
Chen, F. & Chen, C. F. 19SS Onset of finger convection in a horizontal porous layer underlying a fluid layer. Trans. ASME C: J. Heat Transfer 110, 403–409.
Chen, F. & Chen, C. F. 1989 Experimental investigation of convective instability in a superposed fluid and porous layer when heated from below. J. Fluid Mech. 207, 311–321.Google Scholar
Chen, F., Chen, C. F. & Pearlstein, A. J. 1991 Convective instability in superposed fluid and anisotropic porous layers. Phys. Fluids A 3, 556–565.Google Scholar
Combarnous, M. A. & Bories, S. A. 1975 Hydrothermal convection in saturated porous media. Adv. Hydrosc. 10, 231–307.Google Scholar
Georgiadis, J. G. & Catton, I. 1986 Prandtl number effect on Benard convection in porous media, Trans. ASME C: J. Heat Transfer 108, 284–290.Google Scholar
Gershuni, G. B. & Zhukhovttskh, E. M. 1976 Canvective Stability of Incompressible Fluids, pp. 235–240. Israel Program for Scientific Translations.
Homsy, G. M. & Sherwood, A. E. 1976 Convective instabilities in porous media with through flow. AIChE J. 22, 168–174.Google Scholar
Jones, M. C. & Peesichetti, J. M. 1986 Convective instability in packed beds with throughflow. AIChE J. 32, 1555–1557.Google Scholar
Krishnamurti, R. 1975 On cellular cloud patterns. Part 1: mathematical model. J. Atmos. Sci. 32, 1353–1363.Google Scholar
MacDonald, I. F., El-Sayed, m. S-, Mow, K. & Dullien, F. A. L. 1979 Flow through porous media - the Ergun equation revisited. Indust. Engng Chem. Fundam. 18, 199–208.Google Scholar
Nield, D. A. 1977 Onset of convection in a fluid layer overlying a layer of a porous medium. J. Fluid Mech. 81, 513–522.Google Scholar
Nield, D. A. 1987a Convective instability in porous media with throughflow. AIChE J. 33, 1222–1224.Google Scholar
Nield, D. A. 1987 Throughflow effects in the Rayleigh-Bénard convective instability problem. J. Fluid Mech. 185, 353–360.Google Scholar
Nield, D. A. & Joseph, D. D. 1985 Effect of quadratic drag on convection in a saturated porous medium. Phys. Fluids 28, 995–997.Google Scholar
Shvartsblat, D. L. 1968 The spectrum of perturbations and convective instability of a plane horizontal fluid layer with permeable boundaries. Appl, Math. Mech. (PMM) 32, 266–271. (Transl. from Prikl. Mat. Mekh.)Google Scholar
Shvartsblat, D. L. 1969 Steady convective motions in a plane horizontal fluid layer with permeable boundaries. Fluid Dyn. 4, 54–59. (Transl. from Izv. Akad. Nauk SSSR, Fiz. Zhid. I Gaza.)Google Scholar
Shvartsblat, D. L. 1971 Chislennoe issledovanie statsionarnogo konvektivnoge dvizheniya v ploskon gorizontal'nom, sloe zhidkosti. Uchen. Zap. Perm Univ. No. 248; Gidrodinamika 3, 97.Google Scholar
Somerton, C. W. & Catton, I. 1982 On the thermal instability of superposed porous and fluid layers. Trans. ASME C: J. Heat Transfer 104, 160–165.Google Scholar
Somerville, R. C. J. & Gal-Chen, T. 1979 Numerical simulation of convection with mean vertical motion. J. Atmos. Sci. 36, 805–815.Google Scholar
Sutton, F. M. 1970 Onset of convection in a porous channel with net through flow. Phys. Fluids 13, 1931–1934.Google Scholar
Taslim, M. E. & Narusawa, U. 1989 Thermal stability of horizontal superposed porous and fluid layers. Trans. ASME C: J. Heat Transfer 111, 357–362.Google Scholar
Ward, J. C. 1964 Turbulent flow in porous media. J. Hydraul. Div. ASCE 90, 1–13.Google Scholar
Wooding, R. A. 1960 Rayleigh instability of a thermal boundary layer in flow through a porous medium. J. Fluid Mech. 9, 183–192.Google Scholar