Turbulence Model Effects on Flow Over an Airfoil
So how do the
different turbulence models
perform in practice? In the figure below, for example, are contour plots of the predicted turbulent viscosity around a transonic airfoil obtained with four different steady-state turbulence models. These models represent the range of commonly used techniques: an algebraic model, a one-equation model, and a duo of two-equation models.
While the Spalart-Allmaras and Chien k-epsilon models are in rough agreement with each other, the SST and Baldwin-Lomax models predict a very different turbulent viscosity distribution. If you were looking solely at performance in the shear layer, you might want to choose either the Spalart of Chien models.
But what if you care more about lift and drag on the airfoil? Well, as the plot below indicates, the more sophisticated models are not always the best ones to use. The figure shows the surface pressure coefficient from different simulations of an RAE 2822 airfoil at 2.3 degrees angle of attack and a Mach number of 0.729.
All the simulations were run using the Wind-US solver. There is nothing unique about Wind-US as applied to this case; the same results can be obtained with almost any compressible code.
The advantage of restricting things to a single code was that it allowed me to run all the cases using, as much as possible, the same settings and algorithms for everything except turbulence model. Therefore, the differences in results are almost entirely due to the different models
The settings were not identical for every case, however, because some of the models were more sensitive than others and required special treatment. For example, some turbulence models required me to initialize the flow using a previous solution (obtained with one of the other models). Also, some cases were run with a reduced time step (“CFL number”) compared to the others.
From the figure above, it is obvious that without a model, the solution never converges, and the answer is garbage. The results from all of the models, however, compare well with experiment for the majority of the airfoil surface.
The only real differences for this case lie in the predicted shock location on the upper surface (shown by the abrupt drop in the top curve that takes place between x/c of 0.5 and 0.6). A close-up of this region is shown below.
You may be surprised to see that the algebraic models (P.D. Thomas, Baldwin-Lomax, and Cebeci-Smith) actually do a better job of predicting the shock position than the other models. This goes to show that, when they work, algebraic models can produce very good results--but there are a lot of cases where they won't work this well.
The next best result is the Chien k-epsilon model, followed by the two one-equation models (Spalart-Almaras and Baldwin-Barth). The two SST variants come next in a virtual tie. Bringing up the rear, so to speak, is the Rumsey-Gatski EASM model.
This is especially ironic, because the EASM model is the most sophisticated of any of those employed here. As you can see, however, increasing sophistication does not always lead to better results.
Keep in mind that this is not really the type of case that the EASM models were designed for. If you have a complex 3-D geometry with not too much compressibility effects but lots of curvature in the flow, then the EASM model may indeed provide a better answer. For simple airfoils like this, however, it's overkill.
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