Prediction of Turbulence-Generated Secondary Mean Flow in a Square Duct

Near-wall second-moment closures have revealed a tendency to severely underpredict the strength of the turbulence-generated secondary flow in noncircular ducts. The aim of this study has been to elucidate the reasons for this failure that seems to be present at both high and low Reynolds numbers. Fully developed three-componential turbulent flow inside a straight square duct has been computed with the quasi-linear SSG second-moment closure and near-wall effects were modeled by elliptic relaxation. The results compared favourably with the reference DNS data, except that the strength of the turbulence-induced secondary flows is significantly underpredicted. A close examination of the generation mechanisms of the mean streamwise vorticity revealed that this discrepancy can be attributed to the secondary shear-stress component, the importance of which is generally overlooked. The normal-stress anisotropy was, however, adequately returned by the model and so was the variation of the friction velocity with Reynolds number over a wide Reynolds-number range. The present study supports the view that the wall-function approach should be abandoned in order to retain a physical appealing representation of the generation mechanisms of mean streamwise vorticity along internal corners. This revised version was published online in July 2006 with corrections to the Cover Date.