Critical Conditions of Self-Ignition at Bifurcation Points

The results of the main research in the field of self-ignition theory are summarized. For symmetrical vessels, the following are presented: critical conditions of spontaneous ignition in dimensional coordinates, temperature distribution in the vessel, pre-explosive heating of fuel, and the critical size of the vessel at the time of explosion. It is noted that the self-ignition conditions for various vessels differ only by a digital multiplier, which indicates that the shape of the vessel does not affect the physicochemical processes going on in the fuel at the time of the explosion. Each singular point, being a bifurcation point, determines a number that allows finding a single critical condition of self-ignition from the set of solutions to the heat equation. This condition, in the coordinates of its variables, represents a multidimensional surface separating the zone of stationary existence of a combustible system from the zone of “no return,” where a combustible system cannot exist.