Flow past a rotating sphere in a non-Newtonian, Carreau fluid, up to a Reynolds number of 1000

Abstract

ABSTRACT The flow induced by a sphere rotating inside an incompressible, non-Newtonian, Carreau fluid has been investigated numerically. The rotating sphere is enclosed in a concentric cubic box with solid boundaries. The fluid power-law index varied between 0.2 and 2 thereby covering both shear-thinning and shear-thickening fluids, the Reynolds number varied between 0.01 and 1000 and the Carreau number varied between 1 and 1000. The torque applied on the sphere has been calculated and is presented in tables and figures. It was found that at low Reynolds numbers the torque is independent of the Reynolds number and increases with increasing the power-law index. As the Carreau number increases the torque decreases in shear-thinning fluids and increases in shear-thickening fluids. In all cases, four vortices appear at the vertical plane passing through the sphere centre.