Fluid Dynamics of the Circular Porous Slider

Abstract

A fluid of constant density is forced through the porous bottom of a circular slider which is moving laterally on a flat plane. We assume the radius of the slider is much larger than the gap width between the slider and the plane. The Navier-Stokes equations reduce to a set of nonlinear ordinary differential equations. These equations are solved by three methods: series expansion for small crossflow Reynolds number R, matched asymptotic expansions for large R, and also exact numerical integration. The approximate solutions are compared with the numerical results, which is also an exact solution of the Navier-Stokes. Lift and drag are calculated. If everything else is held fixed, both lift and drag increase rapidly although at different rates, with decreasing gap width.