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A minimal model for curved detonations is studied, illustrating the role of the reaction rate on the detonation speed and its propagation limits. The model is based on a simple extension of the minimal Fickett toy model for detonations based on the kinematic wave equation. The use of a simple depletion rate conditioned on the shock speed serves to illustrate its role in the quasi-steady structure of curved waves and their initiation from a strong blast wave. Calculations of strong initiation from a self-similar explosion illustrate the various asymptotic regimes of the transition to self-sustenance and their link to the steady wave structure. We recover the asymptotic regimes of detonation formation suggested by He and Clavin and modelled in the context of Detonation Shock Dynamics by Stewart and collaborators. Following an analysis using the shock change equation, we identify a unique criterion that permits to infer the critical energy for initiation from the competition between energy release and geometric decay.

When designing high-efficiency spark-ignition (SI) engines to operate at high compression ratios, one of the main issues that have to be addressed is detonation development from a pre-ignition front. In order to control this phenomenon, it is necessary to understand the mechanism by which the detonation is initiated. The development of a detonation from a pre-ignition front was analyzed by considering a one-dimensional constant-volume stoichiometric hydrogen/air reactor with detailed chemistry. A spatially linear initial temperature profile near the end-wall was employed, in order to account for the thermal stratification of the bulk mixture. A flame was initiated near the left wall and the effects of its propagation towards the cold end-wall were analyzed. Attention was given on the autoignition that is manifested within the cold-spot ahead of the flame and far from the end-wall, which is followed by detonation. Using CSP tools, the mechanism by which the generated pressure waves influence the autoignition within the cold-spot was investigated. It is found that the pressure oscillations induced by the reflected pressure waves and the pressure waves generated by the pre-ignition front tend to synchronize in the chamber, increasing the reactivity of the system in a periodic manner. The average of the oscillating temperature is greater in the cold-spot, compared to all other points ahead of the flame. As a result, the rate constants of the most important reactions are larger there, leading to a more reactive state that accelerates the dynamics of the cold-spot and to its autoignition., Comment: Part of this work was presented in the 37th International Symposium on Combustion, 29 July-3 August 2018, Dublin, Ireland

The present study aims to clarify the effect of the polytropic index (i.e., the ratio of specific heats in the context of a perfect gas) on the detonation structure. This is addressed by two-dimensional numerical simulations. To ease the clarification of the role of gasdynamics, a simple Arrhenius kinetic law is used for the chemical model. The activation energy, normalized by the shock temperature, is kept constant to obtain the same reaction rate sensitivity to temperature in all considered mixtures. This procedure dissociates the gasdynamic effects from the chemistry effects. The numerical results reveal that in mixtures with low polytropic indicies, the convective mixing is enhanced compared to mixtures with higher polytropic indicies. The mixing is evaluated using Lagrangian tracers. Moreover, mixtures with low polytropic indicies are found to have a shorter reaction length than mixtures with high polytropic indicies. Also, for the range of parameters considered in this study the results indicate that Mach stem bifurcation in detonations due to jetting is primarily a gasdynamic driven mechanism.

We evaluate the effect of boundary layer losses on two-dimensional H2/O2/Ar cellular detonations obtained in narrow channels. The experiments provide the details of the cellular structure and the detonation speed deficits from the ideal CJ speed. We model the effect of the boundary layer losses by incorporating the flow divergence in the third dimension due to the negative boundary layer displacement thickness, modeled using Mirels' theory. The cellular structures obtained numerically with the resulting quasi-2D formulation of the reactive Euler equations with two-step chain-branching chemistry are found in excellent agreement with experiment, both in terms of cell dynamics and velocity deficits, provided the boundary layer constant of Mirels is modified by a factor of 2. A significant increase in the cell size is found with increasing velocity deficit. This is found to be very well captured by the induction zone increase in slower detonations due to the lower temperatures in the induction zone., Comment: This paper (25 pages, 9 figures) has been published in the Proceedings of the Combustion Institute

We use numerical simulations of the reactive Euler equations to analyze the nonlinear stability of steady-state one-dimensional solutions for gaseous detonations in the presence of both momentum and heat losses. Our results point to a possible stabilization mechanism for the low velocity detonations in such systems. The mechanism stems from the existence of a one-parameter family of solutions found in Semenko et al. (Shock Waves 26 (2), 141-160, 2016).