A numerical study of three-dimensional flow past a sphere is performed through direct integration of the incompressible Navier-Stokes equations. A spectral element method is used for the simulation that employs general doubly-curved hexahedra elements for the spatial discretization, while highorder stiffly stable schemes are used for the time discretization. Viscous "sponges" are used at the outflow that eliminate the explosive numerical instability typically encountered in simulations of external flows. Here, we report results at Reynolds numbers in the range of 30 to 1000, which include steady subcritical axisymmetric states as well as supercritical states with non-axisymmetric vortex shedding. The computed results are in good qualitative and quantitative agreement with available experimental results.
Flow past a sphere is a prototype for axisymmetric wake flows in the same way that flow past a cylinder is a prototype for two-dimensional wake flows. While there have been many experimental and computational studies of cylinder flows (see [1] and references therein), considerably less is known about flows past a sphere. Experimentally, this is mostly due to the many difficulties encountered in obtaining non-intrusive support of the sphere. For the range of Reynolds numbers mentioned above, experiments with fixed spheres are reported in [2, 3, 4, 5, 6, 7, 8, 9, 10], whereas experiments for falling spheres are reported in [11],[12]. Torobin and Gauvin, in a review paper [13], give an extensive list of earlier experimental and theoretical work on the subject. Numerical methods have been successfully developed in the past [14],[15] for flow on the surface of a sphere. For the flow past a sphere results for the steady axisymmetric case are reported in [16],[17],[18], and for the transient axisymmetric case in [19],[20]. Finite difference calculations for high Reynolds number unsteady flow are reported in [21].
