Numerical estimates of convective stability in the inclined layer of a porous medium

Abstract

A numerical study of natural convection in a plane highly porous layer placed in an impenetrable array at different angles of inclination to the horizontal plane is presented. Porosity, thermal conductivity, thermal diffusivity and some other parameters are assumed to be constant for both media. Investigations of convective flows in inclined layers usually consider layers with constant temperature at boundaries. In the present work, temperature is set constant at horizontal boundaries surrounding the impenetrable array, and the vertical boundary is considered as heat insulation. This problem formulation conforms to real conditions of geological sections. The problem has been solved by the finite difference method on non-uniform rectangular grids. For horizontal and vertical grid dimensions, hx> hzat α 45 are taken, respectively Thickness of the permeable layer is chosen as the unit of length. Estimates were made for the critical Rayleigh-Darcy number at different inclinations of the permeable layer, and the corresponding stability curve was plotted. It is shown that with increasing angle the convective flow stability decreases. An increase in the size of the surrounding array leads to a slight decrease in stability. The structural changes that occur in convection also take place. The number of realized convective cells decreases with increasing angle of inclination. This result is qualitatively consistent with the structure of convection in an inclined porous layer with constant temperature at boundaries. It has been found that the distribution of the heat flow over the surface of the surrounding array depends significantly on the depth and orientation of the layer and on the Rayleigh-Darcy number. Positive and negative density anomalies (comparable in amplitude) of the heat flow are intrinsic to the layers with a small angle.