Hysteresis phenomenon of the oblique detonation wave

Hysteresis phenomenon of the oblique detonation wave (ODW) is numerically studied. Two-dimensional unsteady reactive Euler equations are numerically solved as governing equations with a two-step reduced reaction mechanism. Wedge angle variation is realized by modifying inflow direction. It is found that hysteresis phenomenon does exist in ODW problem, i.e., the final state of the ODW is closely relevant to initial condition. Two types of hysteresis are discovered in this study: the hysteresis of upstream-downstream triple point and the hysteresis of smooth-abrupt transition pattern. Detonation/Shock polar analysis on primary triple point structure of abrupt ODW demonstrates that the precursor shock of the ODW near primary triple point is actually a strong shock solution and therefore characterized by local detachment behavior which is responsible for primary triple point's upstream moving. Similar to hysteresis of shock reflection, irreversibility is the mechanism for ODW's hysteresis. It is found that hysteresis will disappear when the wedge angle is smaller than a certain value, which means that it may be impossible to obtain a standing Chapman-Jouguet (CJ) ODW without ignition delay or with short ignition delay at a CJ wedge angle via hysteresis.