Unsteady hydrodynamic forces on spheroidal bodies

Abstract

The problem of incompressible axisymmetric flow over spheroidal bodies Is considered. The analysis covers steady and unsteady flows of inviscid and viscous fluids. The spheroidal bodies may take the shape of spheres, oblate or prolate spheroids. The study is based on analytical and numerical solutions of the mass an momentum conservation equations. Euler's equations are solved analytically for the case of inviscid flow while the full Navier-Stokes equations are solved numerically for the case of viscous flow. The study focuses on the time variation of the velocity field as well as the hydrodynamic forces due to free-stream oscillations. The method of solution of the full Navier-Stokes equations combines analytical and numerical techniques where the steam function and vorticity are approximated using Legendre functions whereas the resulting differential equations are solved numerically. The parameters involved in the voscous flow problem are the Reynolds number, strouhal number, and the spheroidal body geometry. The study covers Reynolds numbers in the range from 0.1 to 200 and Strouhal numbers in the range from π / 4 to 2π. Results are presented in terms of the drag coefficient, surface vorticity and surface-pressure distributions, and stream line and equi-vorticity pattersns. Detailed analysis of the velocity field including the wake length and angle of separation is also presented.