Turbulence Model for Flow through Porous Media.

Abstract

The governing equations for turbulent flow through porous media consisting of packed spheres are examined and a O-equation model is proposed. In the process of deriving the governing equations by using the local volume-averaging technique, we consider the eddy viscosity (thermal conductivity) as the algebraic sum of the eddy viscosities (thermal conductivities) estimated from two types of vortices : (1) interstitial vortices of the order of the thickness of the gap width, √(K), which develop in micro-boundary layers between particles, and (2) pseudo vortices of the order of the particle diameter, dp, which reflect the forced distortion of flow due to interruption of the solid particles. Furthermore, we propose the O-equation model, and show that the present turbulence model can predict the flow and heat-transfer characteristics at high Reynolds number, i. e., Forchheimer's flow resistance and the dispersion effect in thermal conductivity, and these phenomena can be explained in terms of vortex transport in porous media.