Cumulative Effects of Weak Pressure Waves During the Induction Period of a Thermal Explosion in a Closed Cylinder

Abstract

It is shown that the accumulation of small-amplitude gasdynamic perturbations is able to accelerate the process of self-ignition of a homogeneous explosive mixture. For analytical simplicity, the chemical kinetics are represented by a one-step irreversible reaction with a large activation energy. A one-dimensional piston-cylinder geometry is considered, which allows a slow compression of the gas during the induction period. It is assumed that the rates of temperature increase due to the reaction and due to the compression are comparable. A two-timescale asymptotic expansion for small Mach numbers is performed considering the distinguished limit ME = O(1), where E is the non-dimensional activation energy, and M is the Mach number based on a characteristic speed of the gas motion. Gasdynamic-chemical interaction is observed at the second order, where the secular equations describing the evolution on the slow timescale explicitly show a cumulative influence.