A cellular automata model for expanding turbulent flames

Cellular automata models based on population dynamics, introduced by Von Neumann in the 1950s, has been successfully used to describe pattern development and front propagation in many applications, such as crystal growth, forest fires, fractal growth in biological media, etc. We, herein, explore the possibility of using a cellular automaton, based on the population dynamics of flamelets, as a low-order model to describe the dynamics of an expanding flame propagating in a turbulent environment. A turbulent flame is constituted by numerous flamelets, each of which interacts with their neighborhood composed of other flamelets, as well as unburned and burnt fluid particles. This local interaction leads to global flame dynamics. The effect of turbulence is simulated by introducing stochasticity in the local interaction and hence in the temporal evolution of the flamefront. Our results show that the model preserves various multifractal characteristics of the expanding turbulent flame and captures several characteristics of expanding turbulent flames observed in experiments. For example, at low turbulence levels, an increase in global burning rate leads to an increase in the turbulence level, while beyond a critical turbulence level, the expanding flame becomes increasingly fragmented, and consequently, the total burning rate decreases with increasing turbulence. Furthermore, at an extremely high turbulence level, the ignition kernel quenches at its nascent state and consequently loses its ability to propagate as an expanding flame.