Fully explicit and self-consistent algebraic Reynolds stress model

Abstract

A fully explicit, self-consistent algebraic expression (for Reynolds stress) which is the exact solution to the Reynolds stress transport equation in the “weak-equilibrium” limit for two-dimensional mean flows for all linear and some quasi-linear pressure-strain models, is derived. Current explicit algebraic Reynolds stress models derived by employing the “weak-equilibrium” assumption treat the production-to-dissipation (P/ɛ) ratio as a constant, resulting in an effective viscosity that can be singular away from the equilibrium limit. In this paper the set of simultaneous algebraic Reynolds stress equations in the weak-equilibrium limit are solved in the full nonlinear form and the eddy viscosity is found to be nonsingular. Preliminary tests indicate that the model performs adequately, even for three-dimensional mean-flow cases. Due to the explicit and nonsingular nature of the effective viscosity, this model should mitigate many of the difficulties encountered in computing complex turbulent flows with the algebraic Reynolds stress models.