Some issues of using Markstein number for modeling premixed turbulent combustion

Various Markstein numbers are considered and the relations between them are discussed using qualitative estimations and numerical simulations of expanding and converging spherical laminar flames. Measurements with expanding spherical flames permit finding the Markstein number characterizing flame speed with respect to products. To model turbulent combustion, the Markstein number characterizing the consumption velocity is required. It differs markedly from various Markstein numbers characterizing flame speeds. The effect of non-linear (with respect to the flame stretch rate) mechanisms on the consumption velocity is studied by analyzing the data of numerical simulations. The relations between the consumption velocity and dame curvature or stretch rate are non-linear and unambiguous for highly curved flames. For weakly curved dames, the non-linear effects are of importance too and prevent from correctly measuring a Markstein number as a physico-chemical parameter.