A discussion on eddy viscosity models on the basis of the large eddy simulation of turbulent flow in a square duct (Q1198335)

In turbulent flow in a noncircular duct a turbulence-driven secondary flow originates which is predicted on the basis of the large eddy simulation computation. The governing second order partial differential equations and some eddy viscosity formulae are set up in a nondimensionalized form, at which a certain Reynolds number is the only parameter to be specified for the computation. The setup of the finite difference calculation with respect to the adopted grid, the spatial derivatives and the time marching scheme is described. The evaluation of the averaged main turbulent flow and of turbulence- driven secondary flow is discussed in detail for two typical Reynolds numbers. Especially the question of the origin of the secondary flow in connection with that of the validity of eddy viscosity models is treated thoroughly. The result is that the secondary flow is produced as a consequence of the imbalance between the gradient of the turbulence stress and that of the corresponding pressure in the region very close to the corner wall of the examined duct of square cross section and that suitable anisotropic eddy viscosity models must be used.