Detonation Stability with Reversible Kinetics

Abstract

Detonation propagation is unsteady due to the innate instability of the reaction zone structure. Up until the present, investigations of detonation stability have been exclusively concerned with model systems using the perfect gas equation of state and primarily single-step irreversible reaction mechanisms. This study investigates detonation stability characteristics with reversible chemical kinetics models. To allow for more general kinetics models, we generalize the perfect gas, one-step irreversible kinetics, linear stability equations to a set of equations using the ideal gas equation of state and a general reaction scheme. We linearly perturb the reactive Euler equations following the method of Lee and Stewart (1990) and Short and Stewart (1998). Our implementation uses Cantera (Goodwin, 2005) to evaluate all thermodynamic quantities and evaluate generalized analytic derivatives of quantities dependent on the kinetics model. The computational domain is the reaction zone in the shock-fixed frame such that the left boundary conditions are the perturbed shock jump conditions which we have derived for a general equation of state and implemented for an ideal gas equation of state. At the right boundary, the system must satisfy a radiation condition requiring that all waves travel out of the domain. Unlike the case of a single reversible reaction, in a truly multistep kinetics model, the radiation boundary condition cannot be solved analytically. In this work, we provide a general methodology for satisfying the appropriate boundary condition. We then investigate the effects of reversibility on the characteristics of the instability in one and two dimensions. These characteristics are quantified by the unstable eigenvalues as well as the shape of the base flow and eigenfunctions. We show that there is an exchange of stability as a function of reversibility. To confirm the results our work, we have performed unsteady calculations. We show that we can match the frequencies predicted by our linear stability calculations near the stability threshold.