The position of points of maximum and minimum shear stress upstream of cylinders mounted normal to flat plates

Abstract

Boundary layer separation upstream of cylinders mounted normal to a flat plate leads to the formation of horseshoe vortices around the bases of these cylinders, which can be either laminar or turbulent, depending upon the state of the upstream boundary layer. Therefore, a point of zero shear stress (at the separation position) and a point of maximum shear stress (beneath the main vortex) exists upstream of such cylinders. These particular points are of interest in many fields of fluid mechanics (flow in heat exchangers, wing body junctions, etc.). In this paper, formulae are presented which relate these positions to the following parameters: 1. (a) a boundary layer displacement thickness Reynolds number; 2. (b) the ratio of boundary layer displacement thickness to cylinder diameter; 3. (c) the ratio of cylinder height to cylinder diameter; 4. (d) the ratio of the boundary layer form parameter to the equivalent zero pressure gradient form parameter. Data from a number of experimental and theoretical investigations of low Mach number laminar and turbulent vortex systems are used in the derivation of these formulae.