Effect of temporal pulsations of a turbulent flow on the flame velocity

Recently, a hypothesis has been proposed that temporal pulsations of a turbulent flow may explain the reduction and even saturation of the flame velocity at large turbulent intensities. However, the study was limited to very anisotropic flows. In this paper, we investigate the effect under more general conditions, which use the dependence of the velocity in the mean direction of propagation. Analytical formulae for the flame velocity in a time-dependent turbulent flow are obtained at low turbulent intensity and generalized to high intensity by using the renormalization method. These results are compared to numerical simulations. We show that the temporal pulsations do not lead to saturation of the flame velocity at high turbulent intensity, even if some effects appear at lower root-mean-square velocity.