The flow past a spinning sphere in a slowly rotating fluid at small reynolds numbers-A numerical study

The axisymmetric flow due to a uniform stream at infinity past a slowly rotating sphere in a viscous, incompressible, rotating fluid is studied by numerical method and the results are presented mostly in the form of graphs of the streamlines and vorticity lines. The governing equations are the non-linear Navier-Stokes equations. They are written as three coupled, nonlinear, elliptic partial differential equations for the stream function Ψ, vorticity ζ, rotational velocity component Ω. Finite difference method is used for solving the governing equations. Second order derivatives are approximated by central differences of order h2 or k2 and nonlinear terms are approximated by upwind differences of order h or k. A region of reversed flow and vortex formation is found to occur near the front or rear stagnation point or both under certain conditions depending upon the speed of the uniform stream at infinity, the radius of the sphere and the angular velocity of the sphere and fluid. The fluid may rotate in the same or opposite directions of the sphere rotation. © 1993.