Asymptotic modelling of self-acceleration of spherical flames

In this paper, we investigate the self-acceleration of the expansion of premixed spherical flames and evolution of the cellular patterns on their surfaces. Asymptotic models are used for the simulations and a spectral numerical algorithm is employed to study flames over large time intervals. Numerous numerical experiments indicate that for large enough time the acceleration of two-dimensional expanding flame slows down but the expansion rate still able to reach values significantly exceeding the burning rate of an exactly circular flame. Simulations of expansion of a three-dimensional flame were carried out by using similar asymptotic model for a spatial segment of the spherical flame. Obtained results indicate that the three-dimensional spherical flame accelerates at much higher rate than the circular one. Wrinkling of the three-dimensional flames is much more intensive and they start to accelerate earlier too.