Chemical Time Scales

[sandee...@gmail.com]

Hi everyone,

I was wondering if you could share your thoughts on how best to obtain chemical time-scales in Cantera for a premixed/non-premixed flame.

My research shows:

- ignition delay (but this precludes reaction-diffusion influences)

- simple evaluation of the Arrhenius rate constants

- simple ideas like the ratio of some product species mass fraction and its net production rate.

- more involved methods that have to do with analyzing the chemical Jacobian (pyJac et al.) - but it looks like a jacobian matrix cannot be obtained directly. 

I'd like to be able to generate a chemical time-scale database as a function of some reaction progress variable and wondered if someone else had tried this and found a good methodology or even better, able to share some code snippet that does the job. 

This is part of a much larger work that links with a CFD code so the evaluation has to be fast.

Many thanks,

Sandeep.

[Nick Curtis]

Hi Sandeep,

A couple of thoughts.

If you're pregenerating a look-up table that maps a reaction progress variable to a chemical timescale, then the complexity of said time-scale estimate doesn't matter too much since you're doing it before your CFD simulation

On the other hand, if you're building this on the fly during the simulation I can see your reasoning here.

This is a difficult question and an open research question -- one of my collaborators is looking at the similar question of how to classify chemical-stiffness based on the thermo-chemical state.

One simple estimate of chemical time-scale was given in Gou et al. (A dynamic multi-timescale method for combustion modeling with detailed and reduced chemical kinetic mechanisms, 2010) where they simply used the ratio of the species mass fraction and the species consumption rate.  They also extended this to diffusion in later works if I recall correctly.

Alternatively, if you're going for the lookup-table route, something more complex like CEMA or CSP might yield a more accurate estimate.

You can obtain a Jacobian via pyJac, but Cantera doesn't provide access to the finite-difference Jacobian used by CVODE; it's questionable if the use of a finite-difference Jacobian is even accurate enough to yield good results for Jacobian analysis methods (see the recent "On the Consistency of State Vectors and Jacobians" from Hansen & Sutherland)

Best,

Nick

[Sandeep Jella]

Nick,

Thank you for the useful suggestions. My plan is to try both - tabulated chemical time-scales as well as calculations on the fly - to see if it makes a big impact on a turbulent combustion model I'm developing. 

For on-the-fly calcs, I think I found what I was looking for from the Guo paper.  

For the look-up table, CEMA is best for my application, but requires the Jacobian. I am planning to use PyJac for this since you've confirmed Cantera won't spit it out easily. 

Thanks again for your help,

Sandeep.

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