The effect of chemical reaction kinetics on the structure of gaseous detonations

In order to elucidate the effect of chemical kinetics on the dynamic structure of a detonation, an investigation is carried out by means of high-resolution numerical simulations of the reactive Euler equations. The chemical description ranges, with increasing complexity, from simplified single-step reaction kinetics to complex models with detailed chemical reaction rates.;To clarify the importance of chain-branching reactions and to resolve the drawbacks associated with the single-step Arrhenius model, a thorough analysis of the pulsating detonation using a two-step reaction mechanism, consisting of a thermally neutral induction step followed by a main reaction layer, has been carried out. It is found that the dynamics of detonation structure depend not only on the temperature sensitivity of the reaction but also the shape of the reaction zone characterized by the length of induction and main heat release layer. From the parametric study, a relevant non-dimensional stability parameter χ and its associated neutral stability curve have been determined. These results are further generalized to more complicated kinetic models of detonation in real gaseous mixtures. They provide a tool to elucidate different experimental observations on the detonation structure such as the cell regularity, the effect of argon dilution and the propagation mechanism. An improved model for the prediction of the characteristic cell size of a detonation is also formulated by including the present stability parameter χ.;To deduce a global method to examine the transient reaction structure of the detonation, the head-on collision problem of a detonation with a shock wave has been proposed. The present study concerned with the effect of chemical kinetics on the unsteady dynamics of the head-on collision phenomenon. Numerical simulations have demonstrated that the unsteady interaction involves a relaxation process consisting of a quasi-steady period and an overshoot for the transmitted detonation subsequent to the frontal collision, followed by the asymptotic decay to a CJ detonation. Due to the change of chemical kinetics as a result of the increase in the thermodynamic state of the reactive mixture froth shock compression, the transmitted pulsating detonation can be stabilized with smaller amplitude and period oscillation. These observations are in agreement with experimental evidence obtained from smoked foils where significant decrease in detonation cell size after a region of relaxation is observed when the detonation collides head-on with a shock wave.;To illustrate the unsteady dynamics of the detonation structure and its dependence on chemical kinetics, a one-dimensional pulsating detonation with one-step kinetics has been investigated. Different nonlinear dynamics of the pulsating front are observed by varying the global temperature sensitivity of the chemical process. Numerical results have suggested that the route to higher oscillation modes may follow closely the Feigenbaum scenario of a period-doubling cascade leading to the existence of chaos as observed in many generic nonlinear systems. The remarkable similarity between a simple nonlinear dynamical system and the pulsating detonation structure suggests that the use of a nonlinear oscillator model can be considered to explore the role of chemical kinetics on the instability spectrum of the oscillatory front.