Reynolds Number Dependent Porous Media Flow Using the Brinkman Equation

R. Rieck[1], A. Bénard[1], and C. Petty[1]
[1]Michigan State University, Michigan, USA
Published in 2009

Porous media fluid dynamic modeling has been widely explored and utilized in many academic and industrial applications. Cross flow filtration being one attractive application, whereas the fluid and filtrate flow parallel the porous media, and thereby induce shearing stress along the membrane surface to reduce fouling. In modeling porous media flow, it is common to describe the porous domain by global averaging since modeling individual pores becomes computationally expensive. The well known Darcy law describes flow in porous media without accounting for shear induced momentum transfer. The Brinkman equation is an extension of Darcy’s law which accounts for shear induced momentum transfer and has experimentally shown to be significant within many flow regimes. It is theorized that a more robust porous media model can be designed using the COMSOL Brinkman equation with the permeability set as a user defined function of the local pore Reynolds number.