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Flow Past a Sphere

Wakes behind spheres are aften encountered in engineering applications and have attracted considerable amount of experimental investigation. At Reynolds numbers beyond 300 laminar hairpin vorticies are periodically shed with uniform strength and frequency. The Strouhal number corresponding to the shedding freqency is in the range of 0.120-0.160. In this 3D problem, we simulate incompressible flow past a sphere at a Reynolds number of 400. Here the Reynolds number is based on the free-stream velocity and the diameter of the sphere. We observe periodic shedding of hairpin vortices with a Strouhal number of about 0.134, which is in good agreement with experiment. The figure below shows magnitude of vorticity at one time step.

The mesh used to solve this problem consists of 85,020 nodes and 150,976 tetrahedral elements. An implicit time integration method is used to obtain the solution of the coupled nonlinear system with 615,703 unknowns at every time step. This problem was solved on a CM-5. The mesh generator, flow solver, and flow visualization software (based on BoB) were developed by the T*AFSM.


1. T.J.R. Hughes, T.E. Tezduyar and A.N. Brooks, "Streamline Upwind Formulations for Advection-Diffusion, Navier-Stokes, and First-order Hyperbolic Equations", Proceedings of the Fourth International Conference on Finite Element Methods in Fluid Flow, University of Tokyo Press, Tokyo (1982).

2. T.E. Tezduyar, "Stabilized Finite Element Formulations for Incompressible Flow Computations", Advances in Applied Mechanics, 28 (1991) 1-44.

3. T.E. Tezduyar, S. Mittal and R. Shih, "Time-accurate Incompressible Flow Computations with Quadrilateral Velocity-Pressure Elements", Computer Methods in Applied Mechanics and Engineering, 87 (1991) 363-384.

4. T.E. Tezduyar, S. Mittal, S.E. Ray and R. Shih, "Incompressible Flow Computations with Stabilized Bilinear and Linear Equal-order-interpolation Velocity-Pressure Elements", Computer Methods in Applied Mechanics and Engineering, 95 (1992) 221-242.

5. V. Kalro and T.E. Tezduyar, "3D Computation of Unsteady Flow past a Sphere with a Parallel Finite Element Method", Computer Methods in Applied Mechanics and Engineering, 151 (1998) 267-276.