Development of Curvature Sensitive Nonlinear Eddy-Viscosity Model

Abstract

Current widely used turbulence closures, except the full second-moment closure, cannot properly account for the suppression of turbulence by convex curvature and the enhancing effect by concave curvature. Particularly, the failure of the explicit algebraic stress model (EASM) to capture the curvature strain effects in curved flows can be attributed to the equilibrium assumption embodied in EASM. Thus, the algebraic stress model (ASM) approach is reexamined in the framework of a generalized curvilinear coordinate system. In the approach, the equilibrium assumption applies only to the gradient part of convective transport while the curvature-related algebraic terms in the Reynolds stress convection process are retained. In this way, a curvature sensitive ASM is derived and is further transformed into an explicit nonlinear eddy-viscosity model in an orthogonal coordinate system. With this newly developed explicit ASM to predict the curved flow in a two-dimensional U duct, it is observed that the turbulence suppression at the convex wall is successfully captured