4.1.5. The k-omega and SST Models

One of the main problems in turbulence modeling is the accurate prediction of flow separation from a smooth surface. Standard two-equation turbulence models often fail to predict the onset and the amount of flow separation under adverse pressure gradient conditions. This is an important phenomenon in many technical applications, particularly for airplane aerodynamics because the stall characteristics of a plane are controlled by the flow separation from the wing. For this reason, the aerodynamic community has developed a number of advanced turbulence models for this application. In general, turbulence models based on the -equation predict the onset of separation too late and under-predict the amount of separation later on. This is problematic, as this behavior gives an overly optimistic performance characteristic for an airfoil. The prediction is therefore not on the conservative side from an engineering stand-point. The models developed to solve this problem have shown a significantly more accurate prediction of separation in a number of test cases and in industrial applications. Separation prediction is important in many technical applications both for internal and external flows.

Currently, the most prominent two-equation models in this area are the based models of Menter [9]. The based Shear-Stress-Transport (SST) model was designed to give highly accurate predictions of the onset and the amount of flow separation under adverse pressure gradients by the inclusion of transport effects into the formulation of the eddy-viscosity. This results in a major improvement in terms of flow separation predictions. The superior performance of this model has been demonstrated in a large number of validation studies (Bardina et al. [76]).

For theoretical details on the based models, see The k-omega Models in Ansys CFX in the CFX-Solver Theory Guide.

The SST model is recommended for accurate boundary layer simulations. To benefit from this model, a resolution of the boundary layer of more than 10 points is required. For details, see Modeling Flow Near the Wall.

For free shear flows, the SST model is mathematically identical to the model.

The SST model was developed to overcome deficiencies in the and BSL models. Therefore, using the SST model over these models is recommended. Details of the differences between the three based models available in CFX is available. For details, see The k-omega Models in Ansys CFX in the CFX-Solver Theory Guide.

One of the advantages of the formulation is the near wall treatment for low-Reynolds number computations where it is more accurate and more robust. For details, see Automatic Near-Wall Treatment for Omega-Based Models.

The convergence behavior of the model is often similar to that of the model. Because the zonal models (BSL and SST) include blending functions in the near wall region that are a function of wall distance, an additional equation is solved to compute the wall distance at the start of simulations (the first few iterations). This is done automatically by the CFX-Solver.

Similar to all RANS models, the SST model exaggerates flow separation from smooth surfaces under the influence of adverse pressure gradients. A modified SST model, called the Reattachment Modification (RM) model, may improve separation and reattachment predictions. For details, see The Reattachment Modification (RM) Model in the CFX-Solver Theory Guide.

The Generalized k-Omega (GEKO) model is a two-equation model, based on the k-Omega model formulation, but with the flexibility to tune the model over a wide range of flow scenarios. For details, see GEKO model.

4.1.5.1. GEKO model

The GEKO model’s main parameters are:

  • Separation Coefficient

    • The Separation Coefficient is the main parameter for adjusting separation predictions for boundary layers.

    • This parameter affects all flows. Increasing this parameter reduces eddy viscosity, leading to more sensitivity to adverse pressure gradients for boundary layers and leading to lower spreading rates for free shear flows (compensated by the Mixing Coefficient, which is described below).

  • Near Wall Coefficient

    • The Near Wall Coefficient affects mostly the inner part of wall boundary layers (limited to no impact on free shear flows).

    • For most applications, you can use a value of 0.5 (the default).

    • Increasing the Near Wall Coefficient leads to higher wall shear stress and wall heat transfer rates in non-equilibrium flows. In particular, the Near Wall Coefficient has a strong effect on heat transfer predictions in reattachment and stagnation regions.

    • The effect on non-generic flows (such as vortices) seems to be moderate (although this has not been systematically tested).

  • Mixing Coefficient

    • The Mixing Coefficient parameter affects only free shear flows. It has no impact on boundary layers due to the blending function.

    • Increasing the Mixing Coefficient leads to larger eddy viscosity in free shear flows, leading to higher spreading rates of the velocity profile and higher levels of turbulence kinetic energy.

    • For each value of the Separation Coefficient, there is an optimal value of the Mixing Coefficient that maintains optimal free shear flows. This value can be approximated as:

      0.35 * sign(Separation Coefficient - 1) * ( | Separation Coefficient -1 | ) ^ 0.5

  • Jet Coefficient

    • Affects mostly jet flows. The Jet Coefficient allows you to adjust the spreading rate of jet flows while maintaining the spreading rate of mixing layers. Increasing the Jet Coefficient while the Mixing Coefficient is active decreases the spreading rate for jets.

    • You can usually use a value of 0.9 (the default). For round jets, set the Separation Coefficient to a value between 1.75 and 2.00 and leave the Jet Coefficient at 0.9.

    • The Jet Coefficient has no effect in the case of a Mixing Coefficient of 0.

      With reduction in the Separation Coefficient and the corresponding reduction in the Mixing Coefficient, the effect of the Jet Coefficient vanishes.

    • The Jet Coefficient is active in a sub-model of the Mixing Coefficient (but has no impact for a Mixing Coefficient of 0).

The GEKO model is affected by the following advanced parameters:

The GEKO model is also affected by a blending function, which deactivates the effects of both the Mixing Coefficient and the Jet Coefficient inside boundary layers. The default blending function is sufficient in most cases. If required, you can specify a user-defined blending function. The blending function should be formulated such that a value of 1 is used inside boundary layers and a value of 0 is used for free flows.