A SMEAR FLOW AROUND A SPINNING SPHERE - NUMERICAL STUDY AT MODERATE REYNOLDS-NUMBERS

In order to contribute to the existing knowledge of the hydrodynamic f orces exerted on a spinning spherical particle, the influence of combi ned shear and rotation on the lift, drag and torque is numerically inv estigated. The Navier-Stokes equations are solved using a finite volum e formulation based on a pressure correction procedure. The accuracy o f the numerical code is tested through comparison with theoretical res ults at small Reynolds numbers and with accepted numerical and experim ental results for a uniform flow at moderate Reynolds numbers. The stu dy is resticted to Reynolds numbers Re-p (based on sphere radius) up t o 20, dimensionless shear rates -0.3 less than or equal to chi(+) less than or equal to + 0.3 and dimensionless angular velocities -2 less t han or equal to omega(+) less than or equal to + 2. At small Reynolds numbers, it is found that the lift force on a spinning sphere in a lin ear shear flow can be obtained by superposing Saffman's or McLauehlin' 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 character istic Reynolds numbers be small enough. At higher Reynolds numbers, th e numerically predicted drag and lift coefficients were found to be si gnificantly 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 t he torque coefficient versus the parameters Re-p, chi(+) and omega(+) is finally proposed. (C) 1998 Elsevier Science Ltd. All rights reserve d.