Macroscopic model for porous media in oscillating flow for CFD applications

Abstract

In this paper a macroscopic model for porous media in oscillating flow is derived for CFD applications. In non -linear modelling of thermoacoustic devices, their cores, useful for the energy conversion, cannot be, in general, modelled like a traditional porous media through friction factor and Nusselt number correlations, recovered from steady state. In this work the analytical solutions in the frequency domain of the linearized Navier-Stokes equations are spatially averaged for an oscillating flow between parallel plates case to build a macroscopic model of an equivalent porous media through a complex permeability and Nusselt number. The results, obtained by assuming a zero mean temperature gradient, show that there is a good agreement between macroscopic solution of a porous box (representing a parallel plates stack) and the average of the solutions of oscillating flow between parallel plates, both in terms of temperature and velocity fields.

Application of the porous media approach to a Standing Wave Thermoacoustic Engine for CFD simulations

“…In this work, a macroscopic porous media model, derived from a previous article in case of isothermal case [4] and extended in subsequent work [5], has been applied for the first time to the stack of a SWTAE. The second section briefly reviews the governing equations of the "microscale" and "macroscale", and the third one describes the numerical setup employed in this work.…”