Adjusting Reacting Flow Model Parameters: Use With Care

There is a lot of interest in CFD of reacting flow these days, but it's not so easy to reliably get accurate results from these simulations. As a result, there is often a strong temptation to try to adjust various model parameters to get better results. This practice has a long history in turbulence modeling, where researchers have created optimized versions of various models for almost every flow configuration imaginable. The problem is that very few of these models have any generality; move too far from the configuration used in the optimization, and the results go haywire.

A related issue is that the use of CFD as a predictive tool is problematic if your models must be closely calibrated for each case. If you are running a completely new configuration, you won't have data to use in calibration. Ultimately, what is required is a more sophisticated model which better captures the physics of the problem. These models are under development, but what can a CFD user do in the meantime? There are times when you know the results are off, and you do have at least some experimental data to compare with. In that case, you may be able to adjust some settings and improve your results.

To illustrate this, I have returned to the supersonic combustion experiments of Burrows and Kurkov in the early 1970's. In these experiments, pure 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 vitiated air stream is made up of 20.3% O2, 43.8% N2, and 35.9% H2O. The hot air eventually ignites the hydrogen, which burns as it convects downstream.

This is the same basic geometry used to examine the effects of turbulence model , the effects of various chemistry options and the impact of other solver options on simulation of reacting flow , except that those cases had a different chemical makeup of the primary flow of vitiated air. For the current work, the same baseline solver options were used with the Wind-US Navier-Stokes solver.

As the temperature contours below illustrate, the baseline solver configuration results in the reaction region shifting significantly toward the exit, compared with the previous reacting flow runs with the more oxygen-rich mixture. We know from the Burrows and Kurkov report ( NASA TM-X-2828 ) that combustion initiation was observed at approximately 18 cm downstream of the injection point. Clearly the results of the baseline case are not catching this at all.

Baseline Burrows and Kurkov results

Given that we don't want to have to go to the boss with such poor results, we ask ourselves if there might be some setting we could tweak to get closer to the experiments. As it happens, there are quite a few, but to keep things manageable, we'll focus on just three of them here: including the effects of “effective binary diffusion”, varying the turbulent Schmidt number, and modifying the turbulent Prandtl number.

The “effective binary diffusion” model (EBD for short) refers to an improved model of intermolecular interactions (compared to a more conventional Wilke's Law viscosity). Transport properties are computed using an approximation of the “effective” diffusivity of each species with respect to the mixture. The temperature contours that result from this reacting flow simulation are shown below. As you can see, this model moves the combustion region in the right direction (about 4 cm), but by itself, it is not enough to enable us to match the experiments.

Burrows and Kurkov case with effective binary diffusion

The next “tweak” to look at is the effect of modifying the turbulent Prandtl number. This non-dimensional parameter provides a simple method of measuring the relationship between the excess shear stress and heat flux due to turbulence. The appropriate value for this quantity is somewhat ambiguous, with experimentally measured values ranging between 0.7 and 0.9 in many reacting flow cases, but some measurements put it at less than 0.5. The Reynolds analogy assumes a turbulent Prandtl number of 1.0. The Wind-US code uses a default value of 0.9.

When the Burrows and Kurkov reacting flow case is re-run using a value of 0.5, the resulting temperature contours indicate that the reaction zone has moved beyond the computational domain. Thus, we certainly do not want to decrease this quantity if we wish to match the ignition point of the experiments.

Burrows and Kurkov case with Prt=0.5

The last of the three “knobs” we are tweaking for this case is the turbulent Schmidt number. This is a non-dimensional number which describes the relationship between eddy viscosity and eddy mass diffusivity. The default in the Wind-US code is 0.9. In contrast, experimental evidence indicates that this quantity can vary quite a bit, especially in shear layers. Thus, as with turbulent Prandtl number, varying this number can be a reasonable thing to do.

The plot below shows (once more) temperature contours for this case when run with a turbulent Schmidt number of 0.5. In this case, the combustion region has moved significantly upstream, although not quite as far as the experimentalists observed.

Burrows and Kurkov case with Sct=0.5

Now that we have examined the effect of each of our three “knobs” in isolation, we can start using them in combination to zero in on the desired result. As a first guess, let's activate the effective binary diffusion, set the turbulent Prandtl number to 1.0, and drop the turbulent Schmidt number to 0.7. The resulting temperature contours are shown in the plot below. While the temperature contours indicate that the initiation of combustion has moved slightly upstream from the Schmidt number of 0.5 case, the peak temperature temperature may even have dropped a bit.

Burrows and Kurkov case with effective binary diffusion, Prt=1.0, and Sct=0.5

A second attempt at combining all three “tweaks” was run. This time, the turbulent Schmidt number was set to 0.5, the turbulent Prandtl number was 1.0, and the effective binary diffusion algorithm was employed. The temperature contours for this case are shown below. At last it appears that we have ignition at the right spot.

Burrows and Kurkov results with effective bindary diffusion, Prt=1.0, and Sct=0.5

But before you run off to show the boss the good reacting flow simulation results, you might want to check a few other things. For example, you might want to look at cross-sections of the H2O mole fraction at the exit plane (shown below). In this case, it is obvious that all of our tweaking has not resulted in us truly capturing everything that was going on in the experiment; the combustion region (which is closely related to the peak in H2O concentration) is too close to the wall in the CFD.

Burrows and Kurkov results- H2O mole fraction at exit plane

Oh well, back to the drawing board. You can console yourself with the thought that the baseline CFD was actually a reasonably close match to the computational analysis that Burrows and Kurkov performed for their report. It turns out that the best results for this reacting flow case have been obtained when it is run without the upstream duct and the experimentally measured profiles are imposed at the start of the test section.

As I said at the beginning of this page, getting a reacting flow calculation correct is not easy. As we see in this example, while you can tweak things to match one aspect or another of your comparison data, such tweaking will not necessarily result in capturing all of the relevant physics of the problem.

So, while it can be useful, “tweaking” models to improve your results should be used with great care.

When you are ready, return to the CFD tips and tricks page and browse through the other helpful hints.

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

If you have any questions, additions, or corrections regarding reacting flow simulations or any other CFD topic, please feel free to contact me

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