TAFSM

Team for Advanced Flow Simulation and Modeling



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Flow Past a Circular Cylinder

The wake behind a cylinder is a fundamental problem involving smooth bodies of finite thickness and has been the focus of extensive studies, both experimentally and numerically. Until recently most numerical simulations have been restricted to 2D due to lack of computational power, whereas experiments indicate the presence of strong three dimensionality above Re=200.

In this simulation at Re=300, a Karman vortex street is observed in this periodic state, and the corresponding Strouhal number is about 0.205. Visualization of the vorticity magnitude reveals the presence of columnar vortices with their axis aligned with that of the cylinder (See the figure below). In the near-wake these exhibit sinusoidal variations in the axial direction which appear to be fairly regular. With the present mesh we capture 4-5 wavelengths. Further downstream, diffusion cause the vortices to mingle and lose their individual nature.

The mesh used to solve this problem consists of 197,948 nodes and 186,240 hexahedral elements. An implicit time integration method is used to obtain the solution of the coupled nonlinear system with 760,107 unknowns at every time step. This problem is solved on a CM-5. The mesh generator, flow solver, and flow visualization software (based on BoB and Ensight) were developed by the T*AFSM.

References:

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. V. Kalro and T. Tezduyar, "Parallel 3D Computation of Unsteady Flows around Circular Cylinders", Parallel Computing, 23 (1997) 1235-1248.

5. T. Tezduyar and Y. Osawa, "Methods for Parallel Computation of Complex Flow Problems", Parallel Computing, 25 (1999) 2039-2066.