A REYNOLDS STRESS MODEL FOR NEAR-WALL TURBULENCE

A tensorially consistent near-wall second-order closure model is formu lated. Redistributive terms in the Reynolds stress equations are model led by an elliptic relaxation equation in order to represent strongly non-homogeneous effects produced by the presence of walls; this replac es the quasi-homogeneous algebraic models that are usually employed, a nd avoids the need for ad hoc damping functions. A quasihomogeneous mo del appears as the source term in the elliptic relaxation equation - h ere we use the simple Rotta return to isotropy and isotropization of p roduction formulae. The formulation of the model equations enables app ropriate boundary conditions to be satisfied. The model is solved for channel flow and boundary layers with zero and adverse pressure gradie nts. Good predictions of Reynolds stress components, mean flow, skin f riction and displacement thickness are obtained in various comparisons to experimental and direct numerical simulation data. The model is al so applied to a boundary layer flowing along a wall with a 90-degrees, constant-radius, convex bend. Because the model is of a general, tens orially invariant form, special modifications for curvature effects ar e not needed; the equations are simply transformed to curvilinear coor dinates. The model predicts many important features of this flow. Thes e include: the abrupt drop of skin friction and Stanton number at the start of the curve, and their more gradual recovery after the bend; th e suppression of turbulent intensity in the outer part of the boundary layer; a region of negative (counter-gradient) Reynolds shear stress; and recovery from curvature in the form of a Reynolds stress 'bore' p ropagating out from the surface. A shortcoming of the present model is that it overpredicts the rate of this recovery. A heat flux model is developed. It is shown that curvature effects on heat transfer can als o be accounted for automatically by a tensorially invariant formulatio n.