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The initiation features of two-dimensional, oblique detonations from a wedge in a stoichiometric hydrogen-air mixture are investigated via numerical simulations using the reactive Euler equations with detailed chemistry. A parametric study is performed to analyze the effect of inflow pressure P 0 , and Mach number M 0 on the initiation structure and length. The present numerical results demonstrate that the two transition patterns, i.e., an abrupt transition from a multi-wave point connecting the oblique shock and the detonation surface and a smooth transition via a curved shock, depend strongly on the inflow Mach number, while the inflow pressure is found to have little effect on the oblique shock-to-detonation transition type. The present results also reveal a slightly more complex structure of abrupt transition type in the case of M 0 = 7.0, consisting of various chemical and gasdynamic processes in the shocked gas mixtures. The present results show quantitatively that the initiation length decreases with increasing M 0 , primarily due to the increase of post-shock temperature. Furthermore, the effect of M 0 on initiation length is independent of P 0 , but given the same M 0 , the initiation length is found to be inversely proportional to P 0 . Theoretical analysis based on the constant volume combustion (CVC) theory is also performed, and the results are close to the numerical simulations in the case of high M 0 regardless of P 0 , demonstrating that the post-oblique-shock condition, i.e., post-shock temperature, is the key parameter affecting the initiation. At decreasing M 0 , the CVC theory breaks down, suggesting a switch from chemical kinetics-controlled to a wave-controlled gasdynamic process. For high inflow pressure P 0 at decreasing M 0 , the CVC theoretical estimations depart from numerical results faster than those of low P 0 , due to the presence of the non-monotonic effects of chemical kinetic limits in hydrogen oxidation at high pressure.

a b s t r a c tIn this study, numerical simulations using the inviscid Euler equations with one-step Arrhenius chemistry model are carried out to investigate the effects of activation energy and wedge angle on the stability of oblique detonation surfaces. Two kinds of cellular structure are studied, one is featured by a single group of transverse waves traveling upstream, referred to as LRTW (left-running transverse waves), and the other is featured by additional RRTW (right-running transverse waves). The present computational simulation reveals the formation of un-reacted gas pockets behind the cellular oblique detonation. Numerical smoked foil records are produced to show the emergence of the two types of transverse waves and the evolution of the unstable cellular structure of the oblique detonation. The transverse wave dynamics, including the colliding, emerging and splitting types, are found to be similar to the normal detonation propagation, demonstrating the instability mechanism is originated from the inherent instability of cellular detonations. Statistical analysis on the cellular structure is carried out to observe quantitatively the influences of activation energy and wedge angle. Results from the parametric study show that high activation energy and low wedge angle are favorable to the LRTW formation. However, the condition for the RRTW formation is more complex. In the case of low activation energy, small wedge angle is beneficial to the RRTW formation, as to the LRTW formation. In contrary, for high activation energy, there appears one moderate wedge angle favoring the RRTW formation and giving the shortest length between the onset of both LR and RR transverse waves. For quantitative comparison, we analyze the variation of two distances with the wedge angle, one is between the detonation initiation and LRTW formation points, and the other between LRTW and RRTW formation points. Results show the latter is relatively less pronounced than the former, indicating the RRTW formation depends mainly on the activation energy and the generation of LRTW.

In this study, the onset of cellular structure on oblique detonation surfaces is investigated numerically using a one-step irreversible Arrhenius reaction kinetic model. Two types of oblique detonations are observed from the simulations. One is weakly unstable characterized by the existence of a planar surface, and the other is strongly unstable characterized by the immediate formation of the cellular structure. It is found that a high degree of overdrive suppresses the formation of cellular structures as confirmed by the results of many previous studies. However, the present investigation demonstrates that cellular structures also appear with degree of overdrive of 2.06 and 2.37, values much higher than ∼1.8 suggested previously in the literature for the critical value defining the instability boundary of oblique detonations. This contradiction could be explained by the use of differently shaped walls, a straight wall used in this study and a custom-designed curved wedge system so as to induce straight oblique detonations in previous studies. Another possible reason could be due to the low and possibly insufficient resolution used in previously published studies. Hence, simulations with different grid sizes are also performed to examine the effect of resolution on the numerical solutions. Using the present results, analysis also shows that although the characteristic lengths of unstable surfaces are different when the incident Mach number changes, these length scales are proportional to tangential velocities. Hence, the interior time determined by the overdrive degree is identified, and its limitation as the instability parameter is discussed.