The Zeldovich spontaneous reaction wave propagation concept in the fast/modest heating limits (Q2814884)

The unsteady conservation equations for a perfect gas are considered in a finite volume. In order to study gas autoignition, the non-dimensional parameters are presented which can describe the physical conditions for the occurrence of a spontaneous reaction wave and for the validity of the reactive Euler equations. The asymptotic analyses describe both induction and post-induction period models for a fast heat release rate (induction time scale short compared to the acoustic time of the spot), as well as a modest heat release rate (induction time scale equivalent to the acoustic time). The results demonstrate that the transport terms are tiny relative to all other terms in the equations. The physical conditions compatible with the constant-volume heat addition are identified, showing when the thermomechanical response of the gas is governed by the Zeldovich model [\textit{Ya. B. Zeldovich}, ``Regime classification of an exothermic reaction with nonuniform initial conditions'', Combust. Flame 39, No. 2, 211--214 (1980; \url{doi:10.1016/0010-2180(80)90017-6})].