Transient and geometrical effects in expanding turbulent flames

To study turbulent combustion, experiments with expanding, statistically sp herical flames ignited by a spark are widely used. The goal of the work is to show that certain trends in the behavior of turbulent flame speed S-t, o bserved in such experiments, are substantially affected by the curvature of the mean flame brush and by the ignition conditions. For this purpose, sim ulations of expanding, spherical, premixed flames were performed using the k - epsilon turbulence model and the Turbulent Flame Speed Closure of the b alance equation for a progress variable. Three major trends have been obser ved in the simulations. First, the analysis of various physical mechanisms controlling the increase of S-t has shown that the lime-dependence of the m ean heat release rate, invoked by the model, is of substantial importance f or small kernels only. For moderately large flames, the development of S-t, is mainly controlled by the relaxation of the reduction effect of the mean flame curvature on the flame speed. The second manifestation of the mean c urvature mechanism is the opposite effects of the turbulent length scale L on the speed of asymptotically stationary, planar flames and of moderately large, statistically spherical flames. in the spherical case, a stronger re duction of the flame speed of small kernels is observed in turbulence with a larger scale. As the kernel grows, the reduction effect relaxes and the d ependence of S-t on L reverses. Third, when the ignition energy is close to tho critical value igniting the turbulent mixture, a regime of kernel expa nsion characterized by substantially reduced name speed and burning velocit y can occur even in relatively large, statistically spherical turbulent nam es. The physical cause of this memory effect consists in the formation of a highly dispersed kernel followed by slow after-burning. When the spark ene rgy is kept constant, the increase in turbulent velocity u' increases the c ritical ignition energy and the transformation to the aforementioned regime occurs. This mechanism can contribute to the decrease of S-t with u', obse rved in many experiments. Finally, the suppression of counter-gradient diff usion in spherical flames is discussed at the end of the paper.