Analysis of premixed-flame propagation in media with periodic flame-speed variations using the level-set equation

Abstract

Propagation of premixed flames in a nonuniform concentration field is investigated using the level-set approach. In order to eliminate interactions with the fluid dynamic effects, the flow is assumed to be quiescent and of constant density, so that the level set will be moved only by flame propagation. The effects of a nonuniform propagation medium are taken into account by introducing a variable laminar-flame speed, corresponding to nonuniform concentration, which is assumed to be periodic in the transverse direction. Numerical simulations with zero Markstein number show that the level set achieves a steady propagation typically after the characteristic passage time of concentration inhomogeneity. In the steady propagation stage, the level-set distribution exhibits three types of characteristic point. These characteristic points are the leading head at the maximum laminar flame speed, the inflection point at the other extrema of laminar flame speed and the trailing edge with a cusp structure towards the burnt side to ensure the continuity of the level set. Asymptotic analysis is carried out for a distinguished limit where the Markstein length is much smaller than the wavelength but much greater than the flame thickness. Under this condition, centred around the cusp at the trailing edge exists an inner layer with a characteristic length scale of the Markstein length, in order to smooth out the singularity. In the asymptotic analysis, the two-term outer solution and two-term inner solution are obtained to construct a composite expansion of the level-set profile. In addition, the three-term expansion of the overall flame propagation speed, which includes corrections up to the order of the square of the Markstein number, is also obtained to give the overall flame propagation speed as a function of the Markstein number and the degree of concentration inhomogeneity.