Numerical Analysis of Low-Reynolds Number Flow around a Sphere

Abstract

Numerical solutions to the Navier-Stokes equation are obtained by using a successive-over-relaxation method for a steady incompressible flow past a sphere at the Reynolds numbers below 1.0, where the Reynolds number is related to the sphere diameter. The numerically-obtained streamlines and the numerically-determined sphere drag agree well with the recent experimental streamlines around a sphere and the recent measurements of the sphere drag respectively at the Reynolds numbers below 0.4. The analytical solutions, the present numerical solutions and the recent experimental results lead to the conclusion that the first-order solution to Oseen's equation represents the most simple and suitable flow-model among the analytical solutions for the steady incompressible flow past a sphere at the Reynolds numbers below 0.4.