Fully-Explicit and Self-Consistent Algebraic Reynolds Stress Model

A fully-explicit, self-consistent algebraic expression for the Reynolds stress, which is the exact solution to the Reynolds stress transport equation in the `weak equilibrium' limit for twodimensional mean ows 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=") ratio implicitly, resulting in an e ective viscosity that can be singular away from the equilibrium limit. In the present paper, the set of simultaneous algebraic Reynolds stress equations are solved in the full non-linear form and the eddy viscosity is found to be non-singular. Preliminary tests indicate that the model performs adequately, even for three dimensional mean ow cases. Due to the explicit and non-singular nature of the e ective viscosity, this model should mitigate many of the di culties encountered in computing complex turbulent ows with the algebraic Reynolds stress models. This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681-0001.