ON Laminar Flows Past Oblate Spheroids of Various Thicknesses.
NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER WASHINGTON D C
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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 R or 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 both Reynolds numbers 0 and 10 two different types of flows are observed, depending on the thickness of the body For sphere-like oblate spheroids the surface pressure has a maximum at the stagnation point, whereas for disk-like bodies this maximum moves towards the edge with decreasing thickness. However, for R 100 the macimum 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 R 100 the flow is regular at the edge. Since for R 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 R 0 and R 100. Author
- Fluid Mechanics