Different simplified and detailed chemical models and their impact on simulations of combustion regimes initiating by the initial temperature gradient in methane/air mixtures are studied. The limits of the regimes of reaction wave propagation depend upon the spontaneous wave speed and the characteristic velocities of the problem. The present study mainly focus to identify conditions required for the development a detonation and to compare the difference between simplified chemical models and detailed chemistry. It is shown that a widely used simplified chemical schemes, such as one-step, two-step and other simplified models, do not reproduce correctly the ignition process in methane/air mixtures. The ignition delay times calculated using simplified models are in orders of magnitude shorter than the ignition delay times calculated using detailed chemical models and measured experimentally. This results in considerably different times when the exothermic reaction affects significantly the ignition, evolution, and coupling of the spontaneous reaction wave and pressure waves. We show that the temperature gradient capable to trigger detonation calculated using detailed chemical models is much shallower (the size of the hot spot is much larger) than that, predicted by simulations with simplified chemical models. These findings suggest that the scenario leading to the deflagration to detonation transition (DDT) may depend greatly on the chemical model used in simulations and that the Zel'dovich gradient mechanism is not necessary a universal mechanism triggering DDT. The obtained results indicate that the conclusions derived from the simulations of DDT with simplified chemical models should be viewed with great caution.

Understanding the mechanisms of explosions is important for minimizing devastating hazards. Due to the complexity of real chemistry, a single-step reaction mechanism is usually used for theoretical and numerical studies. The purpose of this study is to look more deeply into the influence of chemistry on detonation initiated by a spontaneous wave. Results of high resolution simulations performed for one-step models are compared with simulations for detailed chemical models for highly reactive and low reactive mixtures. The calculated induction times for H2/air and for CH4/air are validated against experimental measurements for a wide range of temperatures and pressures. It is found that the requirements in terms of temperature and size of the hot spots, which produce a spontaneous wave capable to initiate detonation, are quantitatively and qualitatively different for one-step models compared to the detailed chemical models. The time and locations when the exothermic reaction affects the coupling between the pressure wave and spontaneous wave are considerably different for a one-step and detailed models. The temperature gradients capable to produce a detonation and the corresponding size of hot spots are much shallower and, correspondingly, larger than those predicted with one-step models. The impact of detailed chemical model is particularly pronounced for the methane-air mixture. In this case, not only the hot spot size is much greater than that predicted by a one-step model, but even at elevated pressure the initiation of detonation by a temperature gradient is possible only if the temperature outside the gradient is so high, that can ignite thermal explosion. The obtained results suggest that the one-step models do not reproduce correctly the transient and ignition processes, so that interpretation of the simulations performed using a one-step model for understanding mechanisms of flame acceleration, DDT and the origin of explosions must be considered with great caution.

We present a high-resolution convergence study of detonation initiated by a temperature gradient in a stoichiometric hydrogen-oxygen mixture using the Pencil Code and compare with a code that employs a fifth order weighted essentially non-oscillating (WENO) scheme. With Mach numbers reaching 10-30, a certain amount of shock viscosity is needed in the Pencil Code to remove or reduce numerical pressure oscillations on the grid scale at the position of the shock. Detonation is found to occur for intermediate values of the shock viscosity parameter. At fixed values of this parameter, the numerical error associated with those small wiggles in the pressure profile is found to decrease with decreasing mesh width δx like δx −1.4 down to δx = 0.2 µm. With the WENO scheme, solutions are smooth at δx = 10 µm, but no detonation is obtained for δx = 5 µm. This is argued to be an artifact of a decoupling between pressure and reaction fronts.