Freely Propagating Flames and Radiation

[g3]

Hi,

I tried to use the radiation model for a freely propagating flame in Cantera 2.3.0a3. For Hydrogen/Oxygen and Methane/Oxygen flames, where temperatures are very high, turning on radiation does not change the flame speeds. With the two attached scripts, which are just modified versions of the example script, I get the following results:

Flame speeds for a stoichiometric H2/O2 flame at 10 bar:

mixture-averaged transport:          12.278033 m/s

multi component + soret:             11.468347 m/s

multi component + soret + radiation: 11.468272 m/s

Flame speeds for a stoichiometric CH4/O2 flame at 1 bar:

mixture-averaged transport:          3.149871 m/s

multi component + soret:             3.109421 m/s

multi component + soret + radiation: 3.109487 m/s

Am I using the radiation model incorrectly or is the flame speed independent of this radiation model?

[Ray Speth]

Hi,

According to the output from f.show_solution(), for the H2/O2 flame, the radiative heat release rate in the burned gas is about 3.5e7 W/m^3. In contrast, the maximum heat release rate from the reactions is about 3.5e13 W/m^3, or six orders of magnitude larger. Assuming that the calculation of the radiative heat release rate is correct, then it's not surprising that this has essentially no effect on the flame speed.

Regards,

Ray

[g3]

If radiation is negligible even at high pressures and temperatures, are there any cases (in the context of combustion) where this radiation model is relevant?

[Bryan W. Weber]

Hi,

If I had to guess, combustion where soot plays a large role would be one case where radiation might be more important.

Regards,

Bryan

[g3]

Makes sense. Since this radiation model takes only H2O and CO2 into account but not soot it is probably not relevant for most combustion applications. I'm curious if you can think of any cases or conditions outside of combustion where this simple radiation model becomes relevant.

[Ray Speth]

Hi,

I think heat loss from gas-phase radiation is a bit more important in diffusion flame configurations. For the simple diffusion flame example included with Cantera, the maximum temperature drops by 15 K. This is admittedly still fairly small, but more of an effect than what you're seeing in the case of premixed flames. And there is of course the issue that radiation from soot will likely be a more important factor for diffusion flames.

Regards,

Ray

[Lee]

Radiation can play a significant role in diffusion flames, particularly at low strain rates where the residence time competes more directly with radiation time scales. The attached figure shows the s-curve for a CH4/air counterflow diffusion flame at 1 atm with radiation (red) and without (blue). Radiation effects are weak near the critical point \chi ~O(10-100), where mass gradients are steep and the primary balance is between diffusion and reaction. On the other hand, radiation is relatively strong when the flow time scales are long (\chi <~1), leading to large thermal deficits in the steady solution.

These effects are discussed in more detail by Pitsch et al, Proc Combust Inst, 27(1):1057-1064, 1998.

http://dx.doi.org/10.1016/S0082-0784(98)80506-7

In the premixed case, you will likely see stronger radiative losses (i.e. lower temperatures) if you extend your domain far downstream of the flame to simulate longer residence times. This will mainly affect the burned gas region, however, and only weakly impact flame speed. 

[g3]

Thanks for the info, Lee. That is very interesting. Was the T-chi curve computed with Cantera's radiation model or was soot radiation included too?

Regarding premixed/freely propagating flames: When extending the domain to more than 10 m, the temperature in the burnt gas drops below the fresh gas temperature (< 300 K) but even then the flame speed does not really change. Only for extremely rich methane flames outside of the flammability limit (phi > 1.5) I can see a more significant difference. For example with Gri3.0 at 1 bar, 300 K, phi = 2.15 and 1 m domain length:

flame speed multicomponent transport+soret:           0.0307 m/s

flame speed multicomponent transport+soret+radiation: 0.0171 m/s

But since phi = 2.15 is way outside of the flammability limit these results are probably not very relevant.

[Andrius Ambrutis]

Dear colleagues,

I'm facing a problem regarding cantera usage to generate burning velocities of syngas mixtures. While code works perfect while generating mixtures composed of H2, CO, H2O and Air, it often fails to some 1D problems with addition of CO2 or high fractions of Air. Without radiation I can generate around 90% of data points, and I assume it is fine as in some regions burning might not still happen. However, with enabling radiation, I can only generate around 40% of points at the same conditions. And I know that Cantera fails as for example it find solution at 470 K and 400000 Pa, as well as 470 K and 700000 Pa but fails with 470 K and 600000 Pa, or finds solution under lower temperature but fails with higher. Also, some solutions are strange and stays around 0.3 m\s, like it gives 0.2999999 m\s and at higher temperature only 0.11 m\s.

I tried width from 0.01 to 0.1, but at 0.1 Cantera can even give negative velocity at low temperatures.

Also we tried various refinement parameters, sometimes even reducing slove and curve to 0.05

Step size was varied and I tried up to 1500 step size with 3500 max step size but it still fails and simulation takes forever.

We try to use USC2.yaml mechanism which is heavy and after all failure I even tried to use Davis.yaml (lighter version of USC2) to generate initial guess for USC2 but in that case I only noticed large jumps in temperatures and velocities, which some volocities even becoming -650555055 or something like that.

Maybe you have any insights or advices regarding what I do wrong and how to improve it?

```
            gas.TPX = To, Po, composition
            print(gas())

            # Create and solve flame object
            flame = ct.FreeFlame(gas, width=width)
            flame.inlet.X = gas.X
            flame.inlet.T = gas.T

            flame.energy_enabled = True
            flame.radiation_enabled = True
            

            flame.set_refine_criteria(ratio=2.0, slope=0.1, curve=0.1, prune=0.01)
            flame.set_time_step(1e-5, [10, 40, 80, 150, 500])
            flame.max_time_step_count = 1000
            flame.solve(loglevel=loglevel, auto=True)
            flame.save(f'syngas_falme_at_{Po}Pa_{To}K.yaml', name="solution", description="Initial syngas flame", overwrite=True)
```

Thank you for your time.

Best regards,

Andrius