Stability of natural convection in superposed fluid and porous layers: Equivalence of the one- and two-domain approaches. (English) Zbl 1156.80330
Summary: Stability analyses of thermal and/or solutal natural convection in a configuration composed by a fluid layer overlying a homogeneous porous medium have been performed using different modeling approaches, especially for the treatment of the interfacial region. Comparisons between the one-domain approach and the two-domain formulation have shown important discrepancies of the marginal stability curves. This note shows that, according to I. Kataoka [Int. J. Multiphase Flow 12, 745–758 (1986; Zbl 0613.76114)], the differentiation of the macroscopic properties of the porous layer at the interface (porosity, permeability, thermal effective diffusivity) must be considered in the meaning of distributions. In that case, the one- and the two-domain approaches are shown to be equivalent and very good agreement is indeed found when comparing the results obtained with both approaches.
MSC:
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
| 76S05 | Flows in porous media; filtration; seepage |
| 76R10 | Free convection |
| 76E05 | Parallel shear flows in hydrodynamic stability |
Citations:
Zbl 0613.76114References:
| [1] | Kataoka, I.: Local instant formulation of two-phase flow, Int. J. Multiphase flow 12, No. 5, 745-758 (1986) · Zbl 0613.76114 · doi:10.1016/0301-9322(86)90049-2 |
| [2] | Nield, D. A.: Onset of convection in a fluid layer overlying a layer of a porous medium, J. fluid mech. 81, 513-522 (1977) · Zbl 0364.76032 · doi:10.1017/S0022112077002195 |
| [3] | Nield, D. A.: The boundary correction for the Rayleigh – Darcy problem: limitations of the Brinkman equation, J. fluid mech. 128, 37-46 (1983) · Zbl 0512.76101 · doi:10.1017/S0022112083000361 |
| [4] | Chen, F.; Chen, C. F.: Onset of finger convection in a horizontal porous layer underlying a fluid layer, J. heat transfer 110, 403-409 (1988) |
| [5] | Carr, M.; Straughan, B.: Penetrative convection in a fluid overlying a porous layer, Adv. water resour. 26, 263-276 (2003) |
| [6] | Carr, M.: Penetrative convection in a superposed porous-medium-fluid layer via internal heating, J. fluid mech. 509, 305-329 (2004) · Zbl 1163.76361 · doi:10.1017/S0022112004009413 |
| [7] | Beavers, G. S.; Joseph, D. D.: Boundary conditions at a naturally permeable wall, J. fluid mech. 30, 197-207 (1967) |
| [8] | Beavers, G. S.; Sparrow, E. M.; Magnuson, R. A.: Experiments on coupled parallel flows in a channel and a bounding porous medium, J. basic eng. 92, 843-848 (1970) |
| [9] | Brinkman, H. C.: A calculation of the viscous force exerted by flowing fluid on a dense swarm of particles, Appl. sci. Res. 1, 27-34 (1947) · Zbl 0041.54204 · doi:10.1007/BF02120313 |
| [10] | Neale, G.; Nader, W.: Practical significance of Brinkman’s extension of Darcy’s law: coupled parallel flow within a channel and a bounding porous medium, Can. J. Chem. eng. 52, 475-478 (1974) |
| [11] | Desaive, T.; Lebon, G.; Henneberg, M.: Coupled capillary and gravity-driven instability in a liquid film overlying a porous layer, Phys. rev. E 64, 066304 (2001) |
| [12] | Hirata, S. C.; Goyeau, B.; Gobin, D.; Carr, M.; Cotta, R. M.: Linear stability analysis of natural convection in superposed fluid and porous layers: influence of interfacial modelling, Int. J. Heat mass transfer 50, No. 7 – 8, 1356-1367 (2007) · Zbl 1118.80003 · doi:10.1016/j.ijheatmasstransfer.2006.09.038 |
| [13] | Arquis, E.; Caltagirone, J.: Sur LES conditions hydrodynamiques au voisinage d’une interface milieu fluide-milieu poreux: application à la convection naturelle, CR acad. Sci. 299-II, 1-4 (1984) |
| [14] | Zhao, P.; Chen, C. F.: Stability analysis of double-diffusive convection in superposed fluid and porous layers using a one-equation model, Int. J. Heat mass transfer 44, 4625-4633 (2001) · Zbl 1043.76024 · doi:10.1016/S0017-9310(01)00102-8 |
| [15] | Schwartz, L.: Méthodes mathématiques pour LES sciences physiques, (1961) · Zbl 0101.41301 |
| [16] | Cotta, R. M.: Integral transforms in computational heat and fluid flow, (1993) · Zbl 0974.35004 |
| [17] | Whitaker, S.: The method of volume averaging, (1999) |
| [18] | Hirata, S. C.; Goyeau, B.; Gobin, D.: Stability of natural convection in superposed fluid and porous layer: influence of the interfacial jump boundary condition, Phys. fluids 19, 058102 (2007) · Zbl 1146.76412 · doi:10.1063/1.2730877 |
| [19] | Hirata, S. C.; Goyeau, B.; Gobin, D.; Cotta, R. M.: Stability of natural convection in superposed fluid and porous layers using integral transforms, Numer. heat transfer 50, No. 5, 409-424 (2006) · Zbl 1118.80003 |
| [20] | Chandrasekhar, S.: Hydrodynamic and hydromagnetic stability, (1961) · Zbl 0142.44103 |
| [21] | S.C. Hirata, Stabilité de la convection thermique et/ou solutale en couches fluide et poreuse superposées, Ph.D. Thesis, Université de Paris, VI, 2007. |
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