# How to compute mixture fraction at each node in a turbulent combustion reactor model?

I need to calculate the spatially-resolved mixture fractions (with respect to both fuel and oxidizer) in a turbulent combustion chamber. The mixture fraction is defined as the mass originating from a single stream (usual fuel) over the total mass in a volume. This should be a fairly simple task, but a good portion of elemental C and O are also coming from diluent streams throughout the combustor. The chemical compositions of each stream, specifically, are fuel: CH4, oxid: O2, and diluent: CO2. I want to find specifically the fuel and oxidizer contribution to the mixture composition at each node. I believe mixture fraction is a built-in output in Chemkin but not Fluent.

If I have to calculate it manually, even if I neglect species diffusion, I still have more than 10 chemical species--way too many unknowns to calculate the mixture fractions from just mole and mass fraction outputs.

Is there a way to compute the mixture fraction for such a model?

## Comments

Hi!

Take a look to the Fluent manual. I am assuming that you are using a non-premixed combustion model in Fluent.

Look for "secondary mixture fraction" (It is an input in the boundary conditions). If a secondary stream (another fuel or oxidant, or a non-reacting stream) is included, the fuel and secondary mixture fractions are simply the elemental mass fractions of the fuel and secondary streams, respectively. The sum of all three mixture fractions in the system (fuel, secondary stream, and oxidizer) is always equal to 1.

Instead of f_fuel + f_oxidizer = 1 you will have f_fuel + f_oxidizer + f_secondary_stream= 1. Fluent will track the the primary and secondary mixture fraction via the governing equation of the non premixed model, so you will always know where you are at.

Does that help?

Thanks,

Gilles

Thank you Gilles,

The solutions I have were actually generated using the species transport model with volumetric reactions only and no TCI.

From the Fluent manual and what what you've suggested, it appears that I should have used the non-premixed combustion model instead.

However, there are multiple inlet slots from which fuel, oxidizer, and diluent gas enters the combustor. Some of which simulating EGR gas (CO2 and O2).

Would it still be possible to obtain the mixture fraction for this setup?

Hi,

Oups my bad. I assumed you were using the non-premixed model. Give it a try if it can working your case, it can be faster than species transports with reactions. It should work as long as all your secondary inlet slots have the same species (remember each inlet can have a different secondary mixture fraction value - so you can have different diluent mixture fraction at each inlet)

If you are using species it is tougher because it is impossible to differentiate, for example, CO2 from combustion and CO2 from an other secondary stream. BUT...

One possible ideas (that I never tested) is to create 2 species with CO2 properties. One will be the CO2 from the combustion, the other (call it CO2_2) from the diluent. In this case you will have to modify the reactions so Fluent treats CO2 and CO2_2 as... CO2. However what you would gain is see what CO2 comes from the fuel stream (will be CO2 mass fraction fn post-processing) and CO2 from diluent (will be CO2_2 mass fraction for example in post-processing)

You can therefore

1) Try a mixture fraction approach. I do not have all the details on your application but check the manual if applicable to your simulation (it should be)

2) Try my idea or a similar one. I never tested it but it should work

Makes sense?

Gilles

Hello Gilles,

Thank you so much for the detailed answer.

I will try rerunning the simulations again per your suggestions.