Reynolds Stress Models (RSM)

In this Method, the Reynolds stress is determined by solving the differential transport equations for each components of Reynolds stresses (Launder et al., 1975; Gibson and Launder, 1978; Launder, 1989). Taking moments from the exact momentum equations, one may derive the exact form of the Reynolds stress transport equation. But the Reynolds stress transport equation contains several unknown terms that need to be modeled in order to close the equations:

	(32.5)

Here, ρ₀ the reference density of the fluid, β is the volume expansion coefficient, the fluctuating fluid temperature, and Ω is the rotation vector. Term (6) and (9) are the culmination of thermal buoyancy and rotation respectively. In Equation (32.5), the following terms do not require any model. The time derivative (term-1), advection/ convection (term-2), molecular diffusion (term-4) turbulent stress production (term-5) and the production by system rotation (term-9). The following terms need to be modeled. The turbulent diffusion due to triple correlations and pressure fluctuations (term-3), the thermal buoyancy (term-6), the pressure strain correlation (term-7) and dissipation rate correlation (8).

The RSM takes into account the effects of swirl, rotation, and rapid changes in the strain rate in a more rigorous manner than other RANS models. However, the RSM predictions are still limited by the closure assumptions used for various terms of Eqn. (32.5), especially the pressure-strain and the dissipation-rate correlations.