Capabilities and Limitations of the Quadratic Constitutive Relation in Corner Flow Prediction

Abstract

The capabilities and limitations of the quadratic constitutive relation in computing streamwise corner flows are investigated using publicly-available data from direct numerical simulations of a square duct flow. The increased accuracy of RANS computations which use the quadratic constitutive relation in corner flows is not due to significantly improved turbulent stress estimates in general. Instead, the reported success of the relation in this flow field, whose structure is governed by the presence of streamwise vortices, is a result of the particular turbulent stress combinations which appear in the mean streamwise vorticity equation being better predicted. Despite this improved prediction, the precise topology of the vorticity production terms deviates from the true distribution, particularly close to the walls, which explains why the strength and position of the corner vortices may not quite correspond to those in the physical flow. In addition, the imperfect estimate of the shear stress term is observed to be the source of additional, non-physical vortices when the QCR coefficient exceeds its recommended value.