An Exact Navier‐Stokes Solution for Three‐Dimensional, Spanwise‐Homogeneous Boundary Layers

Abstract

The plane stagnation flow onto (Hiemenz boundary layer, HBL) and the asymptotic suction boundary layer flow over a flat wall (ASBL) are two boundary layer flows for which the incompressible Navier‐Stokes equations are amenable to exact similarity solutions. The Hiemenz solution has been extended to swept Hiemenz flows by superposition of a third, spanwise‐homogeneous sweep velocity. This solution becomes singular as the chordwise, tangential base flow component vanishes. In this limit, the homogeneous ASBL solution is valid, which however cannot describe the swept Hiemenz flow, because it does not contain any chordwise velocity. This work presents a generalized three‐dimensional similarity solution which describes three‐dimensional spanwise homogeneously impinging boundary layers at arbitrary wall‐normal suction velocities, using a rescaled similarity coordinate. The HBL and the ASBL are shown to be two limits of this solution. Further extensions consist of oblique impingement or different boundary suction directions, such as slip or stretching walls. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)