Anisotropic modelling of thermal convection in multilayered porous media

Abstract

The principle of large-scale anisotropy due to small-scale layering is applied to thermal convection. The motion takes place in a bounded porous medium heated from below. The medium is periodically layered with respect to permeability and thermal conductivity. The onset of convection as well as slightly supercritical convection are investigated. Anisotropic modelling proves useful even for small numbers of layers as long as the motion is of ‘large-scale convection’ type (Masuoka et al. 1978). The modelling always fails for motion of ‘local convection’ type.

Three-dimensional numerical simulations of free convection in a layered porous enclosure

“…Mckibbin and Tyvand [9] investigated the conditions under which thermal con-53 vection in a layered porous medium can be comparable to that for an anisotropic 54 porous medium. They pointed out that a multilayer system can be modeled by 55 an analog anisotropic system when there is no confinement of convection in the 56 layered system.…”

Convection and Heat Transfer in Layered Sloping,warm-Water Aquifers

“…For example, McKibbin & O'Sullivan (1981) and McKibbin (1992) investigated thermally-driven convection in horizontal layered porous media. McKibbin & Tyvand (1982) studied the correspondence between layering and anisotropy and how the results for either one could inform those for the other. Lim et al (2008) and McKibbin (2008), using Green functions, found analytic expressions for the airborne concentration and ground deposits of volcanic ash that falls though a stratified atmosphere.…”

Numerical techniques for simulating groundwater flow in the presence of temperature gradients

“…In these works the Rayleigh number is calculated using permeability and thermal properties of the bottom layer and the temperature difference and thickness of the whole system. In the case of a stratified system which consists of a large number of thin layers, the Rayleigh number is based on the effective vertical permeability and conductivity calculated using an averaging procedure [12]. The multilayered structure markedly affects the critical Rayleigh number.…”

“…The critical Rayleigh number was first calculated in [7] for a homogeneous porous medium saturated by a single-phase fluid. This work was further advanced in [10,11,12,13] through incorporating more realistic features such as inhomogeneity and anisotropy of a porous medium. Linear stability problems of two-phase liquid-vapour thermal convection in porous media were consid-C1117 ered by numerous authors, mainly in works related to geothermal reservoir modelling, cf.…”