Model of flame dynamics of laminar premixed flame subject to the low frequency equivalence ratio oscillations

The effect of the non-uniform profile of scalar variables, such a fuel at the upstream and temperature at the downstream of the flame zone was discussed theoretically to elucidate; (1) the deviation of motion from the steady state case and (2) the hysteresis of premixed flames response to the equivalence ratio oscillations seen in an experimental and numerical works. One-dimensional integral model for the non-uniform scalar variable profile with low frequency equivalence ratio oscillation has been developed. Here, the wavelength of the oscillation is assumed to be larger than the nominal flame thickness. Through the integral analysis, we obtained the relation of the flame propagation speed for steady and unsteady cases depending on the non-uniform scalar profile at the upstream and downstream of the flame zone. Hysteresis of the flame propagation speed is found due to the transport of fuel and heat by the non-uniform scalar profile at the upstream and downstream of the flame zone. This result qualitatively agreed with the numerical results of a response of the stagnation laminar CH4/air premixed flames for a low equivalence ratio oscillation frequency.