Axisymmetric stagnation flow obliquely impinging on a circular cylinder

Abstract

Laminar stagnation flow, axisymmetrically yet obliquely impinging on the generators of a circular cylinder, is formulated as an exact solution of the Navier–Stokes equations. The outer stream is composed of a rotational axial flow superposed onto irrotational radial stagnation flow normal to the cylinder. The relative importance of these two flows is measured by a parameter γ. The viscous problem is reduced to a coupled pair of ordinary differential equations governed by a Reynolds number R introduced by Wang (1974). Two-term asymptotic formulae valid for large R are derived for the wall shear stress and for the position and slope of streamline attachment. These results agree well with exact numerical calculations for R>30. In checking the consistency of our solution in the planar limit R→∞ we uncover and correct an error in the work of Dorrepaal (2000) for the position of viscous streamline attachment.