Second-order boundary-layer flow with hard suction

Abstract

The two-dimensional and axisymmetric compressible laminar boundary-layer flow over an arbitrary body with a porous wall is studied for the case in which suction at the wall is very high. Particular attention is paid to the second-order boundary-layer effects for the limiting case of hard suction, which leads to a singular perturbation problem. An important result is that curvature effects disappear and only displacement effects play a role in determining second-order behavior. It is shown that the second-order equations for the inner solution are greatly simplified, and analytical closed-form solutions are obtained for the shear stress and heat transfer at the wall. The shear stress is proportional to the suction-mass flux and the velocity at the outer edge of the boundary layer. The heat transfer is independent of second-order effects. In the example of the supersonic flow along a flat plate with homogeneous suction, the second-order boundary-layer effects lead to an increase of the drag.