Prediction of Flows with Porous Inclusions Using the Generalized QGD System of Equation

Many engineering applications involve problems with flows in porous media. The problem becomes even more complicated if in the region under consideration there is a system consisting of a free flow of a pure liquid and solid inclusions considered as a fully saturated porous body. This paper proposes a model for calculating flows in the “free flow–porous medium” system based on the generalized quasi-gasdynamic (QGD) system of equations involving Darcy–Forchheimer terms. By analogy with the papers of other authors, where averaging of the Navier–Stokes equations over an elementary volume is used, the system of QGD equations is averaged over a small representative volume of a computational domain in our model. The model is unified for both subdomains of the system—a free flow and a porous medium. This makes possible to perform calculations throughout the entire computational domain using a homogeneous numerical algorithm. Test calculations of flows in a plane channel with a porous plug and in a lid-driven cavity partially filled with a porous medium are presented. In both cases, a good enough agreement with similar calculations by other authors was obtained.