Effects of curvature and vorticity in rotating flows on hydrodynamic forces acting on a sphere

The angular velocity and the lift force on a spherical particle in rotating flows are studied by numerical simulation to investigate the effects of the curvature of the streamlines and the vorticity of the undisturbed background flow. The particle centre is fixed in space, and the rotating motion of the particle is studied in two types of rotating flows: free vortex (irrotational flow) and forced vortex (a rigidly-rotating flow). In both vortices, the angular velocity of the particle is found to exhibit self-similarity with respect to the curvature of the background flow in a range of particle Reynolds number between 5 and 100. Based on this finding, the angular velocity is represented, irrespective of the free and forced vortices, by a single correlation equation of the curvature, the vorticity and the particle Reynolds number. As for the lift force, the effect of the particle rotation induced by the background flow is non-negligible for both vortices. The lift force on a single freely-/non-rotatable particle in a free/forced vortex is found to be represented by linear combination of the following three effects; the streamline curvature and vorticity of the background flow, and the angular velocity of the particle rotation.