Extensions of the Falkner-Skan similar solutions to flows with surface curvature.

Abstract

Results of a study of the effects of longitudinal surface curvature on incompressible laminar boundary-layer flows are presented. They were obtained by numerical solution of a generalized Falkner-Skan equation governing similar solutions for flows over curved surfaces. These solutions form a two-parameter family; that is, they depend on a surface curvature parameter in addition to the well-known pressure gradient parameter. The curvature parameter is essentially the inverse square root of the Reynolds number based on freestream conditions and a characteristic radius of curvature. Effects of curvature on skin friction are linear in the curvature parameter. Convex surface curvature produces a decrease in skin friction compared to the zero curvature solution, whereas concave curvature increases skin friction. The magnitude of the correction to skin friction introduced by surface curvature depends on the value of pressure gradient parameter, being smaller for adverse longitudinal pressure gradients than for favorable pressure gradients. It is found, in addition, that concave curvature produces a reduction and convex curvature an increase in the value of momentum and displacement thickness compared to zero curvature solutions. The results also indicate that, for equal flow conditions, boundary-layer thickness is greater for flows with convex surface curvature than for flows with concave curvature.