An asymptotic analysis of radiant and hypergolic heterogeneous ignition of solid propellants

Abstract

An asymptotic analysis, in the limit of large activation energies, is presented for the ignition of a solid propellant undergoing an exothermic heterogeneous Arrhenius reaction with a gaseous oxidizer. The analysis is carried out for hypergolic or shock tube ignition conditions, and also for ignition under a radiant flux with in-depth absorption of the radiation. The asymptotic analysis illustrates how, for sufficiently large radiant fluxes, a short reaction stage, ending in thermal runaway, follows a much longer inert heating stage. A closed form expression is found to relate the ignition time to the radiant flux and physico-chemical propellant characteristics. An analytical expression is also found for the ignition time under hypergolic or shock tube ignition conditions. The existing numerical calculations of the ignition time, for hypergolic ignition cases and for ignition under a radiant flux with surface absorption, are very accurately correlated by the closed form expressions resulting from this asymptotic analysis. These expressions take also into account the effects of in-depth absorption.