Numerical Analysis of Viscous Shear Flows around a Circular Cylinder

Abstract

Numerical solutions of the Navier-Stokes equations for viscous shear flows past an infinitely long circular cylinder are obtained for Reynolds numbers ranging from Re=1 to Re=40. The shear parameters, ε's investigated for each Re are 0.01, 0.05, 0.1, 0.2, 0.5 and 1. The outer boundary condition of the free stream is replaced by adding to a linear shear flow Oseen's exact solution for the perturbation stream function that has been obtained in the questions of the uniform flow, and the stream function, Ψ_s, on the surface is decided by imposing a condition that the pressure is single-valued. Numerical solutions for the drag, lift, moment and pressure distributions are presented, and their dependence on the shear parameter are investigated. The most interesting result is that lift gives rise to minus even in this Reynolds number range. Lastly, flow patterns are shown for Re=20.