A SHEAR FLOW AROUND A SPINNING SPHERE: NUMERICAL STUDY AT MODERATE REYNOLDS NUMBERS

Abstract

In order to contribute to the existing knowledge of the hydrodynamic forces exerted on a spinning spherical particle, the influence of combined shear and rotation on the lift, drag and torque is numerically investigated. The Navier–Stokes equations are solved using a finite volume formulation based on a pressure correction procedure. The accuracy of the numerical code is tested through comparison with theoretical results at small Reynolds numbers and with accepted numerical and experimental results for a uniform flow at moderate Reynolds numbers. The study is resticted to Reynolds numbers Re p (based on sphere radius) up to 20, dimensionless shear rates −0.3≤ χ +≤+0.3 and dimensionless angular velocities −2≤ ω +≤+2. At small Reynolds numbers, it is found that the lift force on a spinning sphere in a linear shear flow can be obtained by superposing Saffman's or McLaughlin's results and Rubinow and Keller's results. Compared with the case of uniform flow, the drag is slightly affected by the shear rate, but is not altered by the rotation of the sphere, provided that the characteristic Reynolds numbers be small enough. At higher Reynolds numbers, the numerically predicted drag and lift coefficients were found to be significantly affected by the grid parameters, so that reliable results are restricted to the torque, which has not been studied by any author yet at particle Reynolds numbers exceeding unity. A correlation for the torque coefficient versus the parameters Re p, χ + and ω + is finally proposed.