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 permeation coefficient prescribed. In the first scenario, the analytical results have been obtained when the leakage flow rate is small as compared to the axial flow rate. Numerical simulations using ansysFluent were performed for cases where both the pulsatile Reynolds number based on the amplitude of the axial velocity and the leakage ratio (ratio of leakage velocity amplitude to the mean axial velocity amplitude) were varied. The comparison between the analytical and the numerical results indicates that the analytical solution for the axial velocity had an increasing deviation from the numerical results with the increasing pulsatile Reynolds number, or increasing leakage ratio. Interestingly, the analytical radial velocity almost overlapped with its numerical counterpart, for all considered cases. In the second scenario where a permeation coefficient for the leakage is prescribed, an analytical solution was obtained. Importantly, the solution in the second scenario suggests the criteria based on the wall permeability for the application of the analytical method developed herein.