On the transition pattern of the oblique detonation structure

<jats:title>Abstract</jats:title><jats:p>Oblique detonation waves are simulated to study the evolution of their morphology as gasdynamic and chemical parameters are varied. Although two kinds of transition pattern have previously been observed, specifically an abrupt transition and a smooth one, the determining factors for the transition pattern are still unclear. Numerical results show that the transition pattern is influenced by the inflow Mach number, chemical activation energy and heat release. Despite the fact that these parameters were known to influence the detonation instability, the transition pattern variation cannot be predicted according to the instability criterion. In this study, the difference in the oblique shock and detonation angles is proposed as the criterion to determine the transition pattern with the aid of shock-polar analysis. It is found that the smooth transition will appear when the angle difference is small, while the abrupt transition will occur when the difference is large. The shift from the smooth transition to the abrupt transition occurs when the angle difference is about <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112012004788_inline1" /><jats:tex-math>$1{5}^{\ensuremath{\circ} } $</jats:tex-math></jats:alternatives></jats:inline-formula>–<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112012004788_inline2" /><jats:tex-math>$1{8}^{\ensuremath{\circ} } $</jats:tex-math></jats:alternatives></jats:inline-formula>. The previously proposed criterion using the characteristic time ratio is also examined and compared with the present angle difference criterion, and the latter is proved to provide better results.</jats:p>