A Comparison of Second-Moment Closure Models in the Prediction of Vortex Shedding From a Square Cylinder Near a Wall

A computational study is presented that examines the capability of various second-moment closure models in the prediction of two-dimensional, nonstationary flow around a square cylinder in proximity to a wall. The linear return-to-isotropy/isotropization-of-production model $RTI+IP$ and the nonlinear $SSG$ pressure-strain models were combined with the $DH$ and modified $LUM$ diffusion models in the computations. In terms of global activity, the drag is well-predicted in terms of both magnitude and variation with cylinder-to-wall gap width $S/D.$ The Strouhal number St was reasonably well-predicted in terms of magnitude, but the predicted trend with decreasing $S/D$ was incorrect for all model combinations. The lift was not well-predicted in terms of magnitude or trend. Prediction of the detailed flow structure in the vicinity of the cylinder and in the wake was favourable, though the magnitudes of some velocity and Reynolds-stress components were over-predicted. It was argued that the large differences between the results at the intermediate gap width may be due to the difference between the measured and predicted critical gap widths. On the basis of the predicted global and detailed activity, the modified $LUM$ model combined with the nonlinear $SSG$ model was suggested as being the most viable combination for future studies.