In reacting flow simulation, the species mass fraction may become less than 0 or larger than 1 (i.e., Z<0, Z>1), which is unphysical.

What's the general way to overcome it?

Thanks.

-ma

For negative mass fraction - correct by resetting to 0. For excessively high values, actually the condition is even more strict than you suggest: the sum of mass fractions should be 1. A corrective measure I use is to re-normalize the mass fractions of all species such that the sum is 1. These corrections should be applied within the iterative solution.

I hope this helps.

Hi Ma,

It is also usefull to identify why you are observing this unphysical behavior. It could be a usefull exercise to check whether there is any coding problem. the known problems that results in this kind of behavior are usually:

1) unbounded numerical schemes;

2) diffusion fluxes that can not lead to \sum Yk = 1 (for example, if you are using unity Lewis number).

3) implicit segragated solver.

The solution are (1) to use more appropriate scheme/approximation/solver or (2) to do Rami's tricks.

Note: there is an additional trick that is as follow (a) solve for NS-1 species, (b) force all solved mass fractions to be between 0. and 1., (c) compute the unsolved species as Y_{NS} = 1. - \sum_{NS-1} Yk. This trick works resonnably if species NS is not reacting (such as helium, nitrogen....)

Hoppe this help. Julien

Hi, Rami and Julien,

Thanks a lot for your helpful suggestions.

Since my code/solver has already been set up, I'll have to use the post-remedy as you and Rami mentioned. I later checked Oran and Poris's book "numerical simulation of reactive flow", which also referred to this kind of remedy.

A consequent question is that: When we post-remedy the mass fractions, shall we also modify the conserved varable (Q4=rho*et, in 2D)?

I tested my reacting Euler solver for a non-reacting flow problem (a species contact surface moving from a tube to a unconfined region), and found that: (1) without post-remedy of mass fraction, the temperature field is correct but the mass fraction may reach 1.2 somewhere even with small CFL. (2) with post-remedy of mass fraction, the mass fraction field becomes correct but the temperature reaches unphysically high somewhere. (3) with post-remedy of mass fraction and an ad-hoc remedy of conserved variable Q4, both temperature and mass fraction field are correct.

I would like to know if someone has encountered the similar problem or situation.

Thanks a lot.

- Ma

I met with problems of Y around 0 or 1, say -0.001 or 1.002 , but not so large as 1.2. In that case, I would first to check if there is unconvervative thing that artificailly produces mass. It may be BC, dissipation scheme, a diffusive flux that did not met conservation. etc.

A trick is suggested by Patankar in his book "Numerical Heat Tranfer and Fluid Flow" on pp. 144-145.

The "tricks" applied to Y=1.2 can lead to serious loss of accuracy, up to and including unphysical behavior. This is a case where the best cure is to use decent numerical methods to begin with. For example, the species equations in strongly conservative form is essential, as is a molecular diffusion method in which the fluxes sum to exactly zero without some kind of "fudge" or "trick". There can still be problems with chemical reactions overshooting the 0 and 1 limits, but good numerical methods and sufficient temporal resolution will keep that problem under control. While the tricks that were mentioned have all been widely used, they are best avoided when possible, in my experience, as they introduce uncontrolled approximations into the numerical results. It is worth the small extra effort to use appropriate numerical methods from the start rather than patch poor ones after the fact.

Dean,

I quite agree with you that a good scheme should be used in the first place. However, as you also mentioned, "There can still be problems with chemical reactions overshooting the 0 and 1 limits, but good numerical methods and sufficient temporal resolution will keep that problem under control". My tricks are simple correction to these deviations.

If you have better ways to control these - especially when dealing with "stiff" chemical kinetics, I would be glad to learn them from you (or any other poster).

Rami

[Joshua_X]

Hi guys?
I really like this kind of discussion. Is anybody interested in the negative mass fraction of product at the cold boundary?

http://www.cfd-online.com/Forums/mai...-boundary.html

anybody could help? Because to me the species equation:

d2Y/dx2-dY/dx=-w

always let the mass fraction of reactant increase and make the mass fraction of product decrease (no matter what kind of ignition concept used)