The Flow around an Oscillating sphere : 1st Report, The Case of Periodic Oscillation

The numerical solution of the flow around an oscillating sphere in a uniform flow is presented. The stream function and the vorticity are expanded in Fourier series with respect to time, which are substituted into the Navier-Stokes equations of motion and the continuity equation. Partial differential equations are obtained from the Fourier coefficients as functions of the spatial coordinates. These equations are solved numerically by finite-difference method. Consequently the plots of the streamlines, the equi-vorticity lines, the hydrodynamic factors and the unsteady drag are obtained.