### 4.1.7. The Reynolds Stress Model

Two-equation turbulence models ( and based models) offer good predictions of the characteristics and physics of most flows of industrial relevance. In flows where the turbulent transport or non-equilibrium effects are important, the eddy-viscosity assumption is no longer valid and results of eddy-viscosity models might be inaccurate. Reynolds Stress (or Second Moment Closure (SMC)) models naturally include the effects of streamline curvature, sudden changes in the strain rate, secondary flows or buoyancy compared to turbulence models using the eddy-viscosity approximation. You may consider using a Reynolds stress model in the following types of flow:

- Free shear flows with strong anisotropy, like a strong swirl component. This includes flows in rotating fluids.

- Flows with sudden changes in the mean strain rate.

- Flows where the strain fields are complex, and reproduce the anisotropic nature of turbulence itself.

- Flows with strong streamline curvature.

- Secondary flow.

- Buoyant flow.

Reynolds stress models have shown superior predictive performance compared to eddy-viscosity models in these cases. This is the major justification for Reynolds stress models, which are based on transport equations for the individual components of the Reynolds stress tensor and the dissipation rate. These models are characterized by a higher degree of universality. The penalty for this flexibility is a high degree of complexity in the resulting mathematical system. The increased number of transport equations leads to reduced numerical robustness, requires increased computational effort and often prevents their usage in complex flows.

Theoretically, Reynolds stress models are more suited to complex flows, however, practice shows that they are often not superior to two-equation models. An example of this is for wall-bounded shear layers, where despite their (theoretically) higher degree of universality, Reynolds stress models often prove inferior to two-equation models. For wall-bounded flows try to use the SMC-BSL model. It is based on the -equation and automatic wall treatment. For details, see Omega-Based Reynolds Stress Models.

Three varieties of the Reynolds stress model are available that use different model constants:

- Reynolds stress model (LRR-IP)

- QI Reynolds stress model (LRR-IQ)

- SSG Reynolds stress model (SSG)

In general, the SSG model is more accurate than the LRR versions for most flows. This is particularly true for swirling flows. The SSG model is therefore recommended over the other models, which are there for historic reasons and because they are standard models.

Compared to the model, the Reynolds Stresses model has six additional transport equations that are solved for each timestep or outer coefficient loop in the flow solver. The source terms in the Reynolds Stress equations are also more complex than those of the model. As a result of these factors, outer loop convergence may be slower for the Reynolds stress model than for the model.

In principle, the same timestep can be used for all turbulence model variants, but pragmatically the timestep should be reduced for the Reynolds stress model due to the increased complexity of its equations and due to numerical approximations made at general grid interfaces (GGI) and rotational periodic boundary conditions. If convergence is difficult, it is recommended that a or based model solution be obtained first and then a Reynolds stress model solution can be attempted from the converged two-equation solution. It is frequently observed that Reynolds stress models produce unsteady results, where two-equation models give steady-state solutions. This can be correct from a physical standpoint, but requires the solution of the equations in transient mode.

The Reynolds stress models may be used with isotropic or anisotropic turbulent diffusion terms in the Reynolds Stress and Epsilon transport equations. The difference is usually second order as there is often domination by the source terms and the effects of diffusion are small. An exception might be buoyant flows, which can be diffusion dominated. However, the model that uses isotropic turbulent diffusion terms is potentially more robust than the model that uses anisotropic turbulent diffusion terms.

Selection of the appropriate model and settings are carried out on the Fluid Models tab of the Domains form in CFX-Pre.

Further theoretical model information is available in Reynolds Stress Turbulence Models in the CFX-Solver Theory Guide.

Release 18.2 - © ANSYS, Inc. All rights reserved.