Turbulent burning, flame acceleration, explosion triggering

The present thesis considers several important problems of combustion theory, which are closely related to each other: turbulent burning, flame interaction with walls in different geometries, flame acceleration and detonation triggering. The theory of turbulent burning is developed within the renormalization approach. The theory takes into account realistic thermal expansion of burning matter. Unlike previous renormalization models of turbulent burning, the theory includes flame interaction with vortices aligned both perpendicular and parallel to average direction of flame propagation. The perpendicular vortices distort a flame front due to kinematical drift; the parallel vortices modify the flame shape because of the centrifugal force. A corrugated flame front consumes more fuel mixture per unit of time and propagates much faster. The Darrieus-Landau instability is also included in the theory. The instability becomes especially important when the characteristic length scale of the flow is large. Flame interaction with non-slip walls is another large-scale effect, which influences the flame shape and the turbulent burning rate. This interaction is investigated in the thesis in different geometries of tubes with open / closed ends. When the tube ends are open, then flame interaction with non-slip walls leads to an oscillating regime of burning. Flame oscillations are investigated for different flame parameters and tube widths. The average increase in the burning rate in the oscillations is found. Then, propagating from a closed tube end, a flame accelerates according to the Shelkin mechanism. In the theses, an analytical theory of laminar flame acceleration is developed. The theory predicts the acceleration rate, the flame shape and the velocity profile in the flow pushed by the flame. The theory is validated by extensive numerical simulations. An alternative mechanism of flame acceleration is also considered, which is possible at the initial stages of burning in tubes. The mechanism is investigated using the analytical theory and direct numerical simulations. The analytical and numerical results are in very good agreement with previous experiments on “tulip” flames. The analytical theory of explosion triggering by an accelerating flame is developed. The theory describes heating of the fuel mixture by a compression wave pushed by an accelerating flame. As a result, the fuel mixture may explode ahead of the flame front. The explosion time is calculated. The theory shows good agreement with previous numerical simulations on deflagration-to-detonation transition in laminar flows. Flame interaction with sound waves is studied in the geometry of a flame propagating to a closed tube end. It is demonstrated numerically that intrinsic flame oscillations coming into resonance with acoustic waves may lead to violent folding of the flame front with a drastic increase in the burning rate. The flame folding is related to the Rayleigh-Taylor instability developing at the flame front in the oscillating acceleration field of the acoustic wave