Laminar Flows Past Oblate Spheroids of Various Thicknesses

Abstract

The effect of high surface curvature of bodies on a surrounding laminar flow field is studied by means of steady axisymmetric flows past oblate spheroids of various thicknesses. For vanishing Reynolds number the Oberbeck solution is discussed. For nonzero Reynolds numbers Re ≤ 100 a numerical program is used which was recently developed by Rimon. The numerical stability of this finite-difference scheme deteriorates rapidly as the oblate spheroids become very thin. For Reynolds numbers 0 and 10 two different types of flows are observed, depending on the thickness of the body: for spherelike oblate spheroids the surface pressure has a maximum at the stagnation point, whereas for disklike bodies this maximum moves toward the edge with decreasing thickness. However, for Re = 100 the maximum pressure is always at the stagnation point, no matter how thin the body is. In the limiting case of the infinitely thin disk the edge becomes a singular body point. Although this limit could not be examined for nonzero Reynolds numbers with the numerical scheme used, the trend in the behavior of the solutions as the thickness decreases is discussed. From a previous analysis of the nature of possible solutions near a singular point, it appears from the numerical results that for Re = 100 the flow is regular at the edge. Since for Re = 0 the solution is weakly singular (pressure and vorticity are infinite at the singular body point), a change in the flow characteristics must occur between Re = 0 and Re = 100.