Laminar flow past a circle in a shear flow

Abstract

A numerical solution of the equations governing time-dependent, viscous, incompressible fluid flow past a circle is presented for Reynolds number 400. The free-stream velocity profile corresponds to the time-averaged flow of a turbulent jet. The location and strength of the jet are adjusted so that the free stream approximates a linear shear flow in the vicinity of the circle. The asymmetry of the free stream causes a shift of the upstream stagnation streamline (the Pilot-tube displacement effect) and small biases in the lift and torque exerted upon the circle. This lift bias is suggested as a contributing factor in the observed stability of raindrops in vertical wind tunnels. Contour plots of the vorticity and stream function are compared with histories of the pressure distribution, drag, lift, torque, and separation angles. These comparisons show how the asymmetry of the free stream manifests itself in terms of fine details within the flow pattern around the circle.