Problem in mean temperature and mean compressibility calculation in thermophysical library for premixed flame

Hello

The calculation of mean temeperature and mean compressibility i.e. T and psi, in the thermophysical library for a premixed turbulent flame has been problematic since an earlier version of OpenFOAM-v1.6. Please find the attached pdf file for a detailed description. The latestest OpenFOAM-v1712 has the same problem. The relavant code is $WM_PROJECT_DIR/src/thermophysicalModels/reactionThermo/psiuReactionThermo/heheuPsiThermo.C in which the member function of calculation() calculates the mean temperatrue and compressibility psi.

Moreover, it is misleading to consider regress progress variable "b" in solver XiFoam as a mass fraction of some products in the premixed flame as implemented in OpenFOAM; see code $WM_PROJECT_DIR/src/thermophysicalModels/reactionThermo/mixtures/homogeneousMixture/homogeneousMixture.C. The reason is that the regress progress variable "b" is based on the Bray-Mossy-Libby model of premixed flame in which the unburned and burned mixture is seperated by a infinitely thin flame front. The "b" has a physical meaning of probability of finding the unburned mixture, not some mass fraction.

I hope that I managed to explain the problem, otherwise please contact me if there is anything unclear.

Kind regards Chenehsan_yasari_ab.pdf

## Reattaching the author to the issue ticket: @chenhu ##