Chapter 5 - Turbulent Heat Transport

Abstract

This chapter illustrates the procedure for obtaining the macroscopic energy equation for a porous medium starting from the local energy equations (for the fluid and solid phases). Then, time averaging is applied followed by volume averaging (or vice versa) using the local thermal equilibrium hypothesis. This procedure leads to the one-energy equation model. The final expanded form of the macroscopic energy equation for a rigid, homogeneous porous medium saturated with an incompressible fluid does not depend on the averaging order, that is, both procedures lead to the same results. The transport equations at the pore-scale were numerically solved using the SIMPLE method on a non-orthogonal boundary-fitted coordinate system. The relaxation process starts with the solution of the two momentum equations, and the velocity field is adjusted in order to satisfy the continuity principle. This adjustment is attained by solving the pressure correction equation. The turbulence model and the energy equations are relaxed to update the κ, ɛ and temperature fields. In many industrial applications, turbulent flow through a packed bed represents an important configuration for efficient heat and mass transfer. A common model used for analyzing such a system is the local thermal equilibrium assumption, where both solid and fluid phase temperatures are represented by a unique value. This model simplifies theoretical and numerical research, but the assumption of local thermal equilibrium between the fluid and the solid is inadequate for a number of problems. Consequently, in many instances it is important to take into account the distinct temperatures for the porous material and for the working fluid.