Self-Turbulent Flame Simulation by a Cellular Automaton

Abstract

The analogy between a premixed flame front and a propagating line of sources of fluid volume [1] has been exploited to simulate premixed flames by cellular automata [2,3]. The automaton consists of individual particles moving in a two-dimensional square lattice. Two binary variables (accounting for temperature and fuel concentration) are associated to each individual particle. Thus, a normalized temperature equal to one is assigned to every hot particle and equal to zero to every cold particle. Mean local temperature values, corresponding to the average mesoscopic diffusive-convective thermal field, are obtained by averaging over the lattice on 7×7 boxes around each particle. Analogously, the mesoscopic fuel concentration is obtained by averaging the two-valued scalar variable which is equal to one for unburned particles and equal to zero for burned particles. Every time step, at the border between the unburned and burned regions, some unburned particles transform to burned particles. At these locations a source of fluid is inserted to account for the volume increase of the gas. The transformation from unburned to burned is simulated either by an inflammation temperature criterion or by a probability law which depends on the local mean temperature and concentration values, such as to mimic an Arrhenius law. The local particle sources generate extra (burned and hot) particles which push the neighbor particles along random and radial expansion directions, thus accounting for the potential part of the self-generated convective flow of flame fronts. The simulations have been performed for 800×1600 lattices with periodic lateral boundaries and open front and rear boundaries.