Oscillating flow over oblate spheroids

This paper deals with the problem of oscillating viscous flow over an oblate spheroid. The flow is assumed incompressible and axisymmetric and the motion is governed by the Navier-Stokes equations. The method of solution is based on the series truncation method where the stream function and vorticity are expressed in terms of a finite series of Legendre functions. The effects of the Reynolds and Strouhal numbers on the flow characteristics are studied and compared with previous available solutions. Results are presented for the periodic variation of the drag coefficient, surface vorticity and pressure distributions for Reynolds numbers ranging from 5 to 100 and Strouhal numbers ranging from π/4 to π while keeping the spheroid axis ratio unchanged. The time variation of the velocity field during one complete oscillation is presented in the form of streamline and equi-vorticity patterns. The periodic variation of the angle of separation as well as the length of the separation bubble are also presented. The double boundary layer structure previously observed in the case of a sphere is also detected.