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Explosion triggering by an accelerating flame.

The analytical theory of explosion triggering by an accelerating flame is developed. The theory describes the structure of a one-dimensional isentropic compression wave pushed by the flame front. The condition of explosion in the gas mixture ahead of the flame front is derived; the instant of the explosion is determined provided that a mechanism of chemical kinetics is known. As an example, it is demonstrated how the problem is solved in the case of a single reaction of Arrhenius type, controlling combustion both inside the flame front and ahead of the flame. The model of an Arrhenius reaction with a cutoff temperature is also considered. The limitations of the theory due to the shock formation in the compression wave are found. Comparison of the theoretical results to the previous numerical simulations shows good agreement.