Counterflow Diffusion flame mixture fraction greater than 1

[Chris Neal]

From Peter's book "Turbulent Combustion", I was under the impression that the mixture fraction varies between 0 and 1. I ran a hydrogen/oxygen combustion case using the CounterflowDiffusionFlame python object, and when I plot the mixture fraction variable(computed using a small amount of argon at the fuel side), I see the value exceed 1. I'm using the template from http://cantera.github.io/docs/sphinx/html/cython/examples/onedim_diffusion_flame_batch.html to generate the opposed flow solutions.  My desire is to eventually be able to write the solution variables in terms of the mixture fraction instead of the physical space coordinates. 

[Ray Speth]

Chris,

I think once you have a moderately complex diffusion model (the mixture-averaged model counts), you start to see some interesting non-intuitive behavior such as this, or such as superadiabatic temperatures in premixed flames. It would not surprise me if the only case in which the variation of the mixture fraction was guaranteed to be monotonic was if all species had the same diffusion coefficients.

I'd also think that implementing a real diffusion model in mixture fraction space would be quite challenging.

Regards,

Ray

[Chris Neal]

Thanks for the insight Ray. That might explain the unity Lewis number assumption that is very often made in flamelet calculations. I thought having the UnityLewisTransport transport option in the physical space was just a sort of 'icing on the cake' that made things computationally easier. It's unfortunate(for me) that it might be a critical assumption to get valid flamelet solutions.