Conditions for the development of Rayleigh-Taylor instability on the spherical flame front

Abstract

The instability of the flame front is one of the actual problems of modern fluid and gas mechanics. Depending on the processes determining the growth of inhomogeneities, the hydrodynamic (Darrieus-Landau), diffusive-thermal, and Rayleigh-Taylor instabilities are distinguished for a free spherical flame. The present work is devoted to the conditions for the development of the latter. Rayleigh-Taylor instability arises at the interface of two fluids of different density in the presence of acceleration directed from the lighter to the heavier one. When the flame propagates, combustion products with less density move with acceleration in a denser gas. When the acceleration vector and the density gradient at the flame front are co-directed, instability develops. To investigate the development of instabilities, a series of experiments was carried out. Transparent latex shells were filled with a pre-prepared hydrogen-air mixture. In different series of experiments, the percentage of hydrogen changed. The flame was ignited by a spark discharge with energy of 1 mJ, a spark gap located in the center of the shell. Registration of the flame front propagation was performed using the schlieren method implemented in the shadow device IAB-451 and the high-speed VideoSprint camera. The video was shot at a frame rate of 500 to 1000 fps with an exposure of 500 μs. To automate the processing of images in the Matlab environment, a program is written that converts a set of images of the expanding flame front into a dependence of the mean radius on time. It is found that at the initial stage of propagation there are both acceleration and deceleration of the flame front. Experimentally obtained propagation parameters of the flame front are supplemented by calculations carried out on an analytical model from the literature.