Modeling of heat and fluid flow in granular layers using high-order compact schemes and volume penalization method

Abstract

The article presents a novel computational algorithm for modeling of heat and mass transfer processes around neighboring solid objects and inside granular layers. It is based on a volume penalization approach formulated in the framework of an immersed boundary technique, which allows using Cartesian computational meshes for modeling of solid objects with virtually arbitrarily complex shapes and in any form of contact (point-to-point, point-to-surface, etc.). The spatial discretization is performed using a high-order compact discretization/interpolation method on the meshes in which the locations of velocity, density, and temperature are partially staggered with respect to the locations of pressure nodes. Compared to the conventional collocated node arrangement, the present approach has a stabilizing effect, which is very desirable in case of a sudden change of geometry inside the computational grids, especially when high-order discretization is applied. The formulated algorithm is verified based on the following test cases: (i) three hot solid spherical objects immersed in a stream of cold flow; (ii) two granular beds with hundreds of hot solid objects placed in a flowing cold fluid. The results are compared to the solutions obtained using ANSYS-Fluent software and experimental data. In all the cases, the agreement of the results is very good.