Analytical and Numerical Study of a Pulsatile Flow in a Porous Tube

Lateral leakage is encountered in many biological and chemical applications such as renal flows and filtration processes. In this paper we report a comprehensive analytical and numerical method to examine pulsatile flow in a porous-walled tube, with leakage flow rate or leakage pressure gradient prescribed. In the first scenario, analytical results have been obtained when the leakage flow rate is small as compared to the axial flow rate. Numerical simulations using ANSYS Fluent were also performed for cases where both the pulsatile Reynolds number based on the amplitude of the mean axial velocity and the leakage ratio, were varied. The results indicate that, the analytical solution for the axial velocity had an increasing deviation from the numerical results with the pulsatile Reynolds number, and the leakage ratio. Interestingly, the analytical radial velocity almost overlapped with its numerical counterpart, for all considered cases. In the second scenario where the pressure-gradient for the leakage is prescribed, an analytical solution was obtained. Importantly, it suggests the criteria, based on the wall permeability, for the application of the analytical method developed herein.