12.3.3. Strategies for Model Optimization

Most users are intimidated/scared of the prospect to modify turbulence model coefficients. Part of the reason for this lies in the interconnectedness of coefficients in conventional turbulence models, where any change to any coefficient can have detrimental effects even on the simplest flows, like flat plate boundary layers (which users typically do not want to modify). Still, a conservative attitude is also commendable for the GEKO model, even though the effects of coefficient changes are much more predictable. The model should therefore only be adjusted if other sources of error have been minimized (it is not always the turbulence model's fault if things do not match). In addition, modifications should be guided by experimental data as far as possible.

The following topics are discussed:

12.3.3.1. GEKO Defaults

The defaults for the GEKO model have been selected to match the SST models performance as closely as possible for the building block flows. Especially for boundary layers, the defaults predict very close results to those of the SST model. The SST model is used in many industrial CFD simulations already, so the default selected for the GEKO model provides a fairly save conversion from SST to GEKO.

There is another 'fix point' in coefficient settings. With the combination =1.0, =1.0, which automatically sets =0.0 from the correlation CMixCor (note again that =0.0 renders passive, as it is a sub-model to ). This setting is an exact transformation of the standard model (except for the wall treatment and the realizability limiter). Users who have used the model successfully in the past, are therefore advised to use these settings.

Figure 12.211: Comparison of velocity profiles for flow around the NACA-4412 airfoil [32] shows a comparison of GEKO model settings for the NACA 4412 airfoil [32] against their 'reference' model. Two model pairs are clearly visible (GEKO-1, RKE) and (GEKO-175, SST) – each pair giving almost identical results.

Figure 12.211: Comparison of velocity profiles for flow around the NACA-4412 airfoil [32]

12.3.3.2. Optimizing Coefficients

C_SEP: The most important coefficients for most applications is . It controls the separation points/lines from smooth body-separation. In case the flow is dominated by boundary layers, users should only modify this coefficient and explore if values within the range given by Equation (2.10) are sufficient for obtaining improved results. Again, increasing will lead to stronger/earlier separation. When changing one should in a first step keep all other coefficients at their default values.
C_NW: The coefficient should only be changed if detailed near wall or surface information needs to be matched and if this cannot be achieved by optimizing alone. The most prominent example would be optimizations with respect to heat transfer coefficients or oil-flow pictures from experiments. Increasing will increase heat transfer and wall shear stress levels in non-equilibrium regions.
C_MIX: In some cases, standard settings (or models) under-estimate the turbulent mixing in free shear flows. The coefficients will allow an adjustment under such scenarios. Increasing will increase eddy-viscosity levels in such zones. It should be noted that this is only possible within physical limits. E.g. in some cases, strong mixing is observed behind bluff bodies. Such effects often result from vortex shedding and cannot be covered fully by a steady state turbulence model run. However, increasing , can improve such situations relative to default settings (see Figure 12.209: GEKO-1.75 solution under variation of . Left: Velocity U Middle: Eddy-viscosity ratio. Right: using UDF-based function [28]). In case changes to do not show the desired influence, it is advisable to check the blending function . It should be recalled that is only effective in regions where . In case, is de-activated by in the region of interest, modifications to the function might be required.
C_JET: The coefficient is subtle. As the name implies it should only be considered when jets are present in the domain. Regions with round jets should best be computed with =1.75-2.00 as otherwise the effect of is not strong enough to achieve the desired effect. In case these settings for are not suitable in the entire domain, one can set these values also locally through UDF access. For highly accurate jet simulations also set CJET_AUX =4.0 (it activates the function more aggressively).

In summary – for the free shear flows, the GEKO-1 model behaves like the underlying model, with good spreading rates for the mixing layer and plane jet but an over-prediction of spreading for the round jet. When increasing one also needs to adjust to maintain proper spreading for the mixing layer. This is automatically achieved through a correlation relating these two coefficients (=). To avoid over-prediction of spreading rates for jets, with increasing , the coefficient is introduced. A value of =2 and =0.9 provides correct asymptotic spreading for both, the round and the plane jet. In case stronger mixing is required, the coefficient can be increased relative to its correlation value. In some cases, it might even be desirable to modify the blending function to obtain an even stronger effect for mixing layers near walls (see 3.7).

,: The coefficients and are also available for other models. They can be activated in combination with GEKO as required by the simulation.
Wall Distance Free: The GEKO model can also be run without a need for computing the wall distance. This is desirable for cases with moving grids/geometries. If the 'wall-distance-free' option is selected the coefficients / are de-activated. In order to still achieve proper mixing layer growth, set =1.