Flame Surface Density.
 

I have a question regarding combustion modelling. In the Tabor and Weller paper "LES of premixed turbulent combustion using flame surface wrinkling model", Flow, turbulence and combustion, 72: 1-28, 2004 is the wrinking factor in effect the ratio of the total subgrid surface area divided by the surface area? This is as stated in the paper. Why is it that the source term in the reaction progress variable that contains the flame surface denity always talks about the sub-grid surface area? What about the filter level surface area? The source term seems to contain the effect of both filter level and subgrid flame surface area. Is all of the surface assumed to be within the small (sub grid ) scales? Any ideas or comments which can shed light on this would be of interest.

Re: Flame Surface Density.
 

Heya,

Firstly, search for other Weller's papers on the subject, including RANS combustion models - the whole derivation of his model from basic principles exists in a (rather obscure) technical report from Imperial College around 1993. The idea is this: if you imagine a flame to be a flat surface, it will propagate normal to itself with laminar flams speed and it will consume fuel - hence the source term in the progress variable. The rate of consumption therefore depends on the laminar flame speed and flame surface area. Turbulence wrinkles the flame, i.e. for the same surface area in the mean direction of propagation, you get more actual surface area. This means (increased surface area) that the fuel consumption is faster, simply from the fact that there is more surface, right? Therefore, you can introduce the variable you're talking about (flame area per unit area) and you'll get the source term.

I think you can now cook up all other necessary LES ingredients, including the separation of the resolved and unresolved scales.

Enjoy,

Hrv

Re: Flame Surface Density.
 

Dear Hrv,

Thank you for you reply. What I am trying to ascertain is the following: People tend to talk about 'flame surface density' (FSD) and never in terms of resolved FSD and sub-grid FSD. My question is does wrinkling act like a modification to the resolved FSD as follows. If the flat surface (which in each cell is all you can capture in the resolved field (?)) is multiplied by a number, say, 1.2 (where this number increase the FSD by 20% ((1.2-1.0)*100) is the wrinkling parameter therefore a means of finding out the degree of wrinkling WITHIN the cell and then increasing the total FSD by 20% to account for this? If this is the case, can the wrinkling paramter takes values less than 1.0? If so,is this in effect flame destruction?

Thanks again Hrv.

Re: Flame Surface Density.
 

A bit too hard for me. The first thing is that here you've got wrinkling (area per unit area) and not FSD (area per unit volume). Secondly, resolved wrinkling exists in LES and does not need to be modelled, only in the sub-grid scales. As for destruction, the definition says that wrinkling cannot be lower than a flat flame (= 1), but beware: in some papers wrinkling is defined such that it is between 1 and inf and in others it is the inverse (i.e. 0 < Ksi < 1). I think the answer to the first question is positive, but I am not sure (or shall I say positive!) :)