Burning velocities, Markstein lengths, and flame quenching for spherical methane-air flames: A computational study

Computations are for three modes of spherical laminar flame propagation: explosion, implosion, and stationary. The reduced kinetic, C-1, scheme of Mauss and Peters is employed for a range of equivalence ratios under atmospheric conditions, with flame propagation at constant pressure. Save for the richest mixture, the scheme is fully adequate for present purposes. Two burning velocities are computed, one based on the rate of disappearance of unburned gas, the other on the rate of appearance of burned gas. These give the same laminar burning velocity when extrapolated to zero stretch rate. It is necessary to account for two different contributions to the flame stretch rate: one due to the flow field strain rate, the other to the flame curvature. These give rise to different values of Markstein length, which have been evaluated from the three modes of propagation. Flame quenching stretch rates are derived from corresponding Markstein lengths and the mode of quenching is discussed. The relevance of the results to laminar flamelet modeling of turbulent combustion also is discussed. Finally, experimental procedures are suggested for the measurement of the stretch-free laminar burning velocity and the different Markstein lengths.