Dynamics of weakly stretched flames: Quantitative description and extraction of global flame parameters

Generalized expressions for the flame response to weak stretch rate variations were derived based on an integral analysis. Together with values of the laminar flame speed, laminar flame thickness, and the one-step overall reaction order and activation energy determined from the computational results of the one-dimensional planar flame, these expressions for the stretched flames were then used to correlate the computational results of the spherical outwardly propagating, spherical inwardly propagating, and counterflow hydrogen/air and propane/air flames. These correlations yielded the laminar flame speeds through linear extrapolation to zero stretch rate, the Markstein lengths representing the sensitivity of the flame response to stretch rate, and the flame Lewis number. Furthermore, it is shown that the extracted Markstein lengths and Lewis numbers from the three flame configurations are largely the same for given equivalence ratio and system pressure, and that these Lewis numbers also agree well with those predicted from the two-reactant flame theory of Joulin and Mitani. The feasibility of a priori quantitative determination of stretch effects on laminar premixed flames is suggested.