Numerical study of unsteady, thermally-stratified shear flows in superposed porous and pure-fluid domains

In this paper we report on numerical simulations of temporally evolving, thermally stratified shear flows in superposed porous and pure-fluid domains. In particular, we study two different types of flows, namely, pressure-driven channel flows and unforced shear layers. Our study is based on a recently developed thermo-mechanical model for flows in the domains of interest. This model follows a mixture-theoretic approach, according to which the medium's porosity is introduced as a concentration parameter, thus allowing the derivation of a single set of equations that is valid simultaneously in both domains. For the types of flows examined herein, our simulations predict the formation of spanwise vortical structures (rollers) at the porous-pure fluid interface. These rollers grow in time thereby inducing fluid circulation inside the porous medium. For the case of pressure-driven channel flows, our simulations further predict the development of plumes of hot and cold fluid due to convective instabilities that interact with the rollers. In the case of unforced shear layers, unstable stratification accelerates the growth of the rollers, which soon start to merge, and enhances fluid mixing. By contrast, the effect of stable stratification is exactly the opposite. Herein we discuss in detail the temporal evolution of the predicted flow structures and the interactions between them, as well as the mechanisms that induce thermal non-equilibrium inside the porous medium.