Thermomechanical Stability of a Stationary Front of Gasless Combustion at the Presence of Heat Losses

Abstract

ABSTRACT The problem on exothermic reaction front stability to thermomechanical perturbations is formulated for the conditions of plane strains. The coupling between thermal and mechanical processes and heat losses into surrounding materials are taken into account. It is assumed that the reaction rate depends on temperature and stress work that leads to two sensitivity coefficient introduction—to the temperature and to stresses. A stationary problem solution is obtained in the approximation of a narrow reaction zone and after linearization of terms responsible for the coupling in the thermal conductivity equation. The stability problem is solved using the method of small perturbations. The result is presented in the form of three equations for attenuation decrements and complex frequency. It was found that the coupling between different phenomena changes the limit of combustion stability; the dependence of the reaction rate on the stress work is the reason for the appearance of the lower limit of stable combustion.