Classification of similarity criteria in combustion theory and the problem of auto-ignition of the combustible mixture under compression

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