Direct simulation of turbulent flow in a square duct: Reynolds-stress budgets

The data base from a direct numerical simulation of turbulent flow in a square duct is used to calculate all the terms in the Reynolds stress transport equations. The simulation of this complex turbulent flow was performed at a Reynolds number of 600 based on the friction velocity and the duct width. The distributions of the Reynolds stress budget terms along the wall bisector show similar dynamics to wall-bounded turbulent flows with one inhomogeneous direction. Budget terms in the vicinity of the corner demonstrate how transport and redistribution of energy and shear stresses between the Reynolds stress components takes place, promoting the turbulence characteristics of secondary flows of the second kind. The redistribution of energy by pressure velocity correlations can be explained by the low pressures at the cores of streamwise vortices. The data base is also used to evaluate a nonlinear turbulence model in its ability to accommodate the anisotropy of the Reynolds stress tensor in this flow. This anisotropy is known to be entirely responsible for the formation of the secondary flow in noncircular ducts and cannot be captured by linear models.