In these models, the eddy-viscosity hypothesis is avoided and the individual components of the Reynolds stress tensor are directly computed.
These models use the exact Reynolds stress transport equation for their formulation.
They account for the directional effects of the Reynolds stresses and the complex interactions in turbulent flows.
Reynolds stress models offer significantly better accuracy than eddy-viscosity based turbulence models, while being computationally cheaper than Direct Numerical Simulations (DNS) and Large Eddy Simulations.
models have significant shortcomings in complex, real-life turbulent flows.
Eddy-viscosity based models cannot replicate the behaviour of turbulent flows in the Rapid Distortion limit,[2] where the turbulent flow essentially behaves as an elastic medium (instead of viscous).
The six partial differential equations above represent six independent Reynolds stresses.
) is closed and does not require modelling, the other terms, like pressure strain correlation (
The Production term that is used in CFD computations with Reynolds stress transport equations is Physically, the Production term represents the action of the mean velocity gradients working against the Reynolds stresses.
This accounts for the transfer of kinetic energy from the mean flow to the fluctuating velocity field.
All other terms in the Reynolds Stress Transport Equations are unclosed and require closure models for their evaluation.
The rapid pressure-strain correlation term redistributes energy among the Reynolds stresses components.
This is dependent on the mean velocity gradient and rotation of the co-ordinate axes.
are the coefficients of the rapid pressure strain correlation model.
There are many different models for the rapid pressure strain correlation term that are used in simulations.
The slow pressure-strain correlation term redistributes energy among the Reynolds stresses.
This is responsible for the return to isotropy of decaying turbulence where it redistributes energy to reduce the anisotropy in the Reynolds stresses.
Physically, this term is due to the self-interactions amongst the fluctuating field.
In this model the dissipation only affects the normal Reynolds stresses.
However, as has been shown by e.g. Rogallo,[12] Schumann & Patterson,[13] Uberoi,[14][15] Lee & Reynolds[16] and Groth, Hallbäck & Johansson[17] there exist many situations where this simple model of the dissipation rate tensor is insufficient due to the fact that even the small dissipative eddies are anisotropic.
is assumed to be a function the turbulent Reynolds number, the mean strain rate etc.
Based on extensive physical and numerical (DNS and EDQNM) experiments in combination with a strong adherence to fundamental physical and mathematical limitations and boundary conditions Groth, Hallbäck and Johansson proposed an improved model for the dissipation rate tensor.
However, Groth, Hallbäck and Johansson used rapid distortion theory to evaluate the limiting value of
[20][21] Using this value the model was tested in DNS-simulations of four different homogeneous turbulent flows.
Even though the parameters in the cubic dissipation rate model were fixed through the use of realizability and RDT prior to the comparisons with the DNS data the agreement between model and data was very good in all four cases.
The benefit of this cubic model is apparent from the case of an irrotational plane strain in which the streamwise component of
This is an application of the concept of the gradient diffusion hypothesis to modeling the effect of spatial redistribution of the Reynolds stresses due to the fluctuating velocity field.
1) Unlike the k-ε model which uses an isotropic eddy viscosity, RSM solves all components of the turbulent transport.
2) It is the most general of all turbulence models and works reasonably well for a large number of engineering flows.
4) Since the production terms need not be modeled, it can selectively damp the stresses due to buoyancy, curvature effects etc.