The structure of the solution obtained with Reynolds-stress-transport models at the free-stream edges of turbulent flows

Abstract

The behavior of Reynolds-stress-transport models at the free-stream edges of turbulent flows is investigated. Current turbulent-diffusion models are found to produce propagative (possibly weak) solutions of the same type as those reported earlier by Cazalbou, Spalart, and Bradshaw [Phys. Fluids 6, 1797 (1994)] for two-equation models. As in the latter study, an analysis is presented that provides qualitative information on the flow structure predicted near the edge if a condition on the values of the diffusion constants is satisfied. In this case, the solution appears to be fairly insensitive to the residual free-stream turbulence levels needed with conventional numerical methods. The main specific result is that, depending on the diffusion model, the propagative solution can force turbulence toward definite and rather extreme anisotropy states at the edge (one - or two-component limit). This is not the case with the model of Daly and Harlow [Phys. Fluids 13, 2634 (1970)]; it may be one of the reasons why this "old" scheme is still the most widely used, even in recent Reynolds-stress-transport models. In addition, the analysis helps us to interpret some difficulties encountered in computing even very simple flows with Lumley's pressure-diffusion model [Adv. Appl. Mech. 18, 123 (1978)]. A new realizability condition, according to which the diffusion model should not globally become "anti-diffusive", is introduced, and a recalibration of Lumley's model satisfying this condition is performed using information drawn from the analysis.