Numerical Solution of the Incompressible Time-Dependent Viscous Flow past a Thin Oblate Spheroid

Numerical solutions of the transient axisymmetric flow around a thin disk normal to the flow are obtained. The fluid is incompressible, homogeneous, and its flow is governed by the complete Navier-Stokes equations. The Reynolds-number range studied is 10-600. The study investigates the effects that a very large curvature of the body has on the numerical procedure for the solution of the flow field, and the fundamental fluid-dynamical phenomena of separation, of a recirculatory wake, and of vorticity shedding. A time-dependent stream function-vorticity formulation is adopted. The solutions are obtained on an oblate spheroidal grid system. The high curvature has profound adverse effects on the numerical stability and accuracy. This is due to the extreme gradients of vorticity that appear near the edge of the disk. The results show that no vorticity shedding occurs for axisymmetric flow in the Reynolds-number range studied. In addition, some new interesting fluid-dynamical features are revealed. These include a different behavior of the pressure distribution at low and high Reynolds numbers and a local maximum of vorticity inside the wake at the higher Reynolds numbers studied.