Hydrodynamic stability of flow between rotating porous cylinders with radial and axial flow

Abstract

A linear stability analysis was carried out for axial flow between a rotating porous inner cylinder and a concentric, stationary, porous outer cylinder when radial flow is present for several radius ratios. The radial Reynolds number, based on the radial velocity at the inner cylinder and the inner radius, was varied from −15 to 15, and the axial Reynolds number based on the mean axial velocity and the annular gap was varied from 0 to 10. Linear stability analysis for axisymmetric perturbations results in an eigenvalue problem that was solved using a numerical technique based on the Runge–Kutta method combined with a shooting procedure. At a given radius ratio, the critical Taylor number at which Taylor vortices first appear for radial outflow decreases slightly for small positive radial Reynolds numbers and then increases as the radial Reynolds number becomes more positive. For radial inflow, the critical Taylor number increases as the radial Reynolds number becomes more negative. For a given radial Reynolds number, increasing the axial Reynolds number increases the critical Taylor number for transition very slightly. The critical wave velocity decreases slightly for small positive radial Reynolds numbers, but increases for larger positive and all negative radial Reynolds numbers. The perturbed velocities are very similar to those for no axial flow.