Ignition limit and shock-to-detonation transition mode of n-heptane/air mixture in high-speed wedge flows

In this work, oblique detonation of n-heptane/air mixture in high-speed wedge flows is simulated by solving the reactive Euler equations with a two-dimensional (2D) configuration. This is a first attempt to model complicated hydrocarbon fuel oblique detonation waves (ODWs) with a detailed chemistry (44 species and 112 reactions). Effects of freestream equivalence ratios and velocities are considered, and the abrupt and smooth transition from oblique shock to detonation are predicted. Ignition limit, ODW characteristics, and predictability of the transition mode are discussed. Firstly, homogeneous constant-volume ignition calculations are performed for both fuel-lean and stoichiometric mixtures. The results show that the ignition delay generally increases with the wedge angle. However, a negative wedge angle dependence is observed, due to the negative temperature coefficient effects. The wedge angle range for successful ignition of n-heptane/air mixtures decreases when the wedge length is reduced. From two-dimensional simulations of stationary ODWs, the initiation length generally decreases with the freestream equivalence ratio, but the transition length exhibits weakly non-monotonic dependence. Smooth ODW typically occurs for lean conditions (equivalence ratio < 0.4). The interactions between shock/compression waves and chemical reaction inside the induction zone are also studied with the chemical explosive mode analysis. Moreover, the predictability of the shock-to-detonation transition mode is explored through quantifying the relation between ignition delay and chemical excitation time. It is demonstrated that the ignition delay (the elapsed time of the heat release rate, HRR, reaches the maximum) increases, but the excitation time (the time duration from the instant of 5% maximum HRR to that of the maximum) decreases with the freestream equivalence ratio for the three studied oncoming flow velocities. Smaller excitation time corresponds to stronger pressure waves from the ignition location behind the oblique shock. When the ratio of excitation time to ignition delay is high (e.g., > 0.5 for n-C₇H₁₆, > 0.3 for C₂H₂ and > 0.2 for H₂, based on the existing data compilation in this work), smooth transition is more likely to occur.