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The flow across a square cylinder is an important test case for the validation of separated flows in the turbulent regime. In the past, it has been regularly used to validate Large Eddy Simulation (LES) models.

Experiments studying the flow across a square cylinder have been available since about the time of Vickery (1966), while modern simulations usually tend to reproduce the results of Lyn and Rodi (1994) whose data set for Re = 22,000 is publicly available.

The flow involves separation and coherent vortex shedding. In trying to benchmark a code with the experimental data, the following items are usually compared:

• Strouhal Number which is the easiest to reproduce.
• Mean recirculation length.
• Global drag and lift statistics, e.g. mean lift coefficient, rms lift coefficient, mean drag coefficient and rms drag coefficient.
• Spatial distributions of time-averaged and phase-averaged velocities, pressure and Reynolds stresses.

References

Experiments

• B. J. Vickery. Fluctuating lift and drag on a long cylinder of square cross section in a smooth and in a turbulent stream. Journal of Fluid Mechanics, 25: 481-494, 1966.
• B. E. Lee. The effect of turbulence on the surface pressure field of a square prism. Journal of Fluid Mechanics, 69(2): 263-292, 1975.
• P. W. Bearman and E. D. Obasaju. An experimental study of pressure fluctuations on fixed and oscillating square-section cylinders. 119: 297-321, 1982.
• I. McLean and I. Gartshore. Spanwise correlations of pressure on a rigid square section cylinder. 41-44:779-808, 1992.
• C. Norberg. Flow around rectangular cylinders: Pressure forces and wake frequencies. Journal of Wind Engineering and Industrial Aerodynamics, 49: 187-196, 1993.
• D. A. Lyn and W. Rodi. The flapping shear layer formed by flow separation from the forward corner of a square cylinder. Journal of Fluid Mechanics, 267: 353-376, 1994.
• D. A. Lyn, S. Einav, W. Rodi, and J.-H. Park. A laser-doppler velocimetry study of ensemble-averaged characteristics of the turbulent near wake of a square cylinder. Journal of Fluid Mechanics, 304: 285-319, 1995.

Computations

• P. R. Voke. Direct and Large Eddy Simulation II, pages 355-422. Kulwer Acadamic Publishers, 1997.
• W. Rodi, J. H. Ferziger, M. Breuer, and M. Pourquie. Status of large eddy simulation: Results of a workshop. ASME Journal of Fluids Engineering, 119: 248-261, 1997.
• A. Sohankar, L. Davidson, and C. Norberg. Large eddy simulation of flow past a square cylinder: Comparison of different subgrid scale models. ASME Journal of Fluids Engineering, 122: 39-47, 2000.