7 - Three-dimensional numerical models for periodically fully-developed heat and fluid flows within porous media

Abstract

The chapter discusses 3D numerical models for heat and fluid flows within porous media. Despite its three-dimensional geometrical complexities, macroscopic hydrodynamic and thermodynamic behavior in porous media can be obtained from the direct application of first principles to viscous flow and heat transfer at a pore scale. Recent investigations on three-dimensional numerical models for periodically fully-developed flow and heat transfer in anisotropic porous media are reviewed in the chapter The chapter focuses on laminar flows around collections of spheres and cubes, laminar forced convective flows through a bank of cylinders in yaw, and turbulent flows through a bank of square cylinders in a regular arrangement. It describes the exhaustive numerical computations carried out to determine macroscopic parameters, such as the permeability and the interfacial heat transfer coefficient, and compares the results against available empirical formulas. A quasi-three-dimensional calculation procedure is proposed and its details are also presented in the chapter. This economical procedure is used to obtain results for three-dimensional heat and fluid flow through a bank of cylinders in yaw. The large eddy simulation (LES) study for turbulence in porous media is carried out to elucidate complex turbulent flow characteristics associated with the porous media.