Effect of two-step chemistry on the critical extinction-pressure drop for pre-mixed flames

A numerical study of the response to a sudden drop in pressure of planar, pre-mixed flames modeled by two different two-step, generic reaction schemes is presented. An increase in the reaction order is found to destabilize the flame, in the sense that it can be extinguished by a smaller pressure drop to or below some critical minimum value. Critical minimum pressures are computed for different chemical reaction schemes, namely: (1) single-step, first-order; (2) single-step, second-order; (3) the Zel’dovich scheme; and (4) the Lindemann mechanism. The computations show that the flame becomes more unstable as the temperature sensitivity to the rate of heat release increases. For the Lindemann mechanism, the critical minimum pressure can be more than that with a single-step, first-order reaction, even when the ratio of the pre-exponential frequency factors of the reaction steps is of the order of unity. Finally, the effect of the increase in the activation energy of the first reaction is to increase the critical minimum pressure, i.e., to also destabilize the flame. This effect is found in all the reaction schemes.