Is CFD of Reacting Flow Really so Sensitive to the Turbulence Model?

There is a lot of interest in CFD of reacting flow these days, but it's not so easy to get consistently accurate results. This leads to a lot of arm-waving in technical papers on the subject, which almost always ends up with some statement to the effect that, “we'd have gotten better results if our turbulence model was better.” While there is no doubt that turbulence models can affect your results , that line has been wearing a bit thin with me.

Configuration

So, I was happy to have an opportunity to examine the impact of changing the turbulence model on a particular combustion simulation. The case examined here was based on (but not identical to) the experiments of Burrows and Kurkov on supersonic combustion (conducted in the early 1970's at NASA).

In these experiments, hydrogen is injected at Mach 1 from a backward-facing step in a direction parallel to the main supersonic stream of vitiated air, which is traveling at Mach 2.44. The hot air eventually ignites the hydrogen, which burns as it convects downstream.

Results

After tinkering with various options in the code, a “baseline” case was created using the compressible formulation of Menter's SST model. Static temperature contours for this case are pictured below.

Temperature contours in a supersonic combustion case using a compressible SST model


Normally, in this sort of reacting flow simulation, one seeks to match both the location and the extent of the observed combustion region, as well as the distribution of chemical species. In this study, though, the simulations have a different chemical composition in the vitiated air stream, so direct comparison with experiment is not possible.

Instead, the goal is to learn what happens when the turbulence model is changed but everything else remains the same. Thus, what is important here are the differences between the simulations, not the absolute value of any of the predicted quantities. The modified freestream composition helps this, because it tends to move the reaction zone upstream, which makes the effects of the different options more visible.

The baseline results were compared with those from runs which used three other turbulence models: a “standard” (incompressible) SST model, a Chien k-epsilon model, and the Spalart-Almaras one-equation model. Aside from the turbulence model, the same options were used for all the reacting flow simulations (as much as possible).

Below is the same temperature contour data plotted for the case which used the incompressible form of the SST model. While I would have expected more of a difference due to the various compressibility corrections, the solutions hardly changed at all.

Temperature contours in a supersonic combustion case using an incompressible SST model


The third plot, shown below, is of the Chien k-epsilon model results. The Chien model tends to be quite unstable, so for this case, the baseline solution was used as a starting point, and a greatly reduced time step size (CFL number) was employed. While a close examination shows that, compared to the baseline, there is some ignition delay apparent in this case, but nothing very significant.

Temperature contours in a supersonic combustion case using a Chien k-e model


The final contour plot (below) shows the temperature in the Spalart model run. There is a noticeable delay in ignition, which in the Spalart case is roughly five centimeters downstream of the compressible SST prediction. Obviously, this is significant, but by way of comparison, however, keep in mind that, in the original experiments, a twenty centimeter shift resulted just from increasing the freestream static temperature by 45K (starting above 1200K).

Temperature contours in a supersonic combustion case using a Spalart model


Profiles of mole fraction of H2O at the exit plane are shown below for all the different cases. Again, while there are slight differences, the solutions are surprisingly similar for all the different models.

H2O mole fraction at exit plane in supersonic combustion case--effects of varying turbulence model


Conclusions

These results show that, while turbulence modeling may make a big difference in some cases, this particular configuration was not as sensitive to the choice of turbulence model as one might have expected. Obviously, this situation is going to be extremely case dependent, and it is possible that all of the models used here are deficient in the same areas.

At least these results should make you think twice if a reacting flow simulation does not come out right the first time. Don't just give up and blame the turbulence model; there could be a lot more going on.

Further Reading

For example, a prime consideration when setting up a reacting flow simulation is choosing the chemistry options to be used. To learn more about how some of these options affect the results, check out this page on the sensitivity of a combustion simulation to the chemistry treatment.

Beyond that, there are all the other options which can affect a simulation, such as boundary conditions and limiters. To see what kind of affect these can have on this case, read this page on further studies of sensitivity of reacting flow simulations.

When you are ready, return to the CFD applications page and browse through the other sample applications.

Or, head back to the Innovative CFD home page and take a look at the other topics on this site.

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