Nonlinear convection regimes in a fluid layer partially filled with an inhomogeneous porous medium

Abstract

We numerically simulate a nonlinear problem of convection excitation in a horizontal single-component-fluid layer heated from below and partially filled with an inhomogeneous porous medium under the gravitational field. Porosity and permeability of the porous medium depend on a vertical coordinate. The porous matrix divides a cavity with the fluid into two layers. Convection in a porous layer and in the fluid layer located above it is described by equations within the Boussinesq approximation. A fluid flow through pores obeys Darcy's law. The nonlinear problem is solved by the Galerkin and finite difference methods. A linear stability problem for mechanical equilibrium is simulated by the shooting method. The Nusselt number versus supercriticality is obtained at a fixed ratio of layer thicknesses and various porosity gradients. It was shown that when porosity grows with depth, convection monotonously arises in the form of the long-wave rolls covering both layers. Additional vortices occur in the fluid layer as supercriticality goes up. They lead to fluid oscillations. In the case of uniform porosity and the porosity decreasing with depth, convection starts up as short-wave rolls localized in the fluid layer. They enhance as supercriticality rises. For a homogeneous medium we recorded a sharp increase in the heat flux with rising supercriticality. It is associated with the penetration of convective motion into a porous layer and enhancement of heat transfer from the lower hot wall of the cavity.