Some new results on Markstein number predictions

he flame speed of a premixed flame is known to depend on curvature and local flow conditions, i.e. flame stretch. For flames in unconfined environments, both theory and experiment predict for weakly-stretched flames a linear relationship between flame speed and stretch, and the sensitivity of this dependence is given in terms of the Markstein number. In this paper we first review known theoretical results concerning Markstein numbers and present some new results showing an explicit dependence on equivalence ratio and variable transport properties. We also present new theoretical predictions regarding stretch effects on premixed flames in enclosed vessels. Specifically, we derive an expression for flame speed in a constant volume vessel. The inherent unsteadiness associated with the increasing pressure gives rise to a more complicated expression for flame speed. We find that flame propagation is strongly influenced by geometry, and the corresponding "Markstein" numbers must be interpreted differently from the constant-pressure case. We use our model to examine the propagation of a spherical flame in a closed vessel and relate our results to recent experimental measurements.