Classification of Similarity Criteria in Combustion Theory and the Problem of Autoignition of a Combustible Mixture by Compression

The dynamic problems of the theory of combustion and explosion are classified from the point of view of competition of the characteristic times of bulk chemical reaction, frontal combustion, heat transfer, gas flow from the vessel, compression (motion of the piston), and heating (cooling) rate. We consider dynamic similarity criteria such as the ratio of the characteristic times in problems of classical thermal explosion, dynamic thermal explosion, flammability limits, combustion in communicating vessels, competition of frontal and volumetric combustion, autoignition by adiabatic compression, competition of frontal combustion and piston motion, as well as compound similarity criteria (such as functions of simple dynamic similarity criteria). The problem of autoignition of a mixture by compression is considered, and a method for obtaining an analytical solution of the problem and an algorithm for the approximate solution based on a special differential criterion are proposed.