Numerical investigation on laminar pulsating flow through porous media

Abstract

In this investigation, the flow friction associated with laminar pulsating flows through porous media was numerically studied. The problem is of interest for understanding the regenerators of Stirling and pulse tube cryocoolers. Two-dimensional flow in a system composed of a number of unit cells of generic porous structures was simulated using a CFD tool, with sinusoidal variations of flow with time. Detailed numerical data representing the oscillating velocity and pressure variations for five different generic porous structure geometries in the porosity range of 0.64 to 0.84, with flow pulsation frequency of 40 Hz were obtained, and special attention was paid to the phase shift characteristics between the velocity and pressure waves. Based on these detailed numerical data, the standard unsteady volume-averaged momentum conservation equation for porous media was then applied in order to obtain the instantaneous as well as cycle-averaged permeability and Forchheimer coefficients. It was found that the cycle-averaged permeability coefficients were nearly the same as those for steady flow, but the cycle-averaged Forchheimer coefficients were about two times larger than those for steady flow. Significant phase lags were observed with respect to the volume-averaged velocity and pressure waves. The parametric trends representing the dependence of these phase lags on porosity and flow Reynolds number were discussed. The phase difference between pressure and velocity waves, which is important for pulse tube cryocooling, depended strongly on porosity and flow Reynolds number.