Numerical Modeling of Laminar Pulsating Flow in Porous Media

The laminar pulsating flow through porous media was numerically studied. Two-dimensional flows in systems composed of a number of unit cells of generic porous structures were simulated using a computational fluid mechanics tool, with sinusoidal variations in flow with time as the boundary condition. The porous media were periodic arrays of square cylinders. Detailed numerical data for the porosity ranging from 0.64 to 0.84, with flow pulsation frequencies of 20-64 Hz were obtained. Based on these numerical data, the instantaneous as well as the cycle-average permeability and Forchheimer coefficients, to be used in the standard unsteady volume-averaged momentum conservation equation for flow in porous media, were derived. It was found that the cycle-average permeability coefficients were nearly the same as those for steady flow, but the cycle-average Forchheimer coefficients were significantly larger than those for steady flow and were sensitive to the flow oscillation frequency. Significant phase lags were observed between the volume-averaged velocity and the pressure waves. The phase difference between pressure and velocity waves, which is important for pulse tube cryocooling, depended strongly on porosity and the mean-flow Reynolds number.