On theoretical modeling of underdriven oblique detonation phenomenon

Polar analysis is an important theoretical method in shock and detonation fields. However, a detonation polar is fundamentally different from the well-established shock polar due to not only the reaction heat release but also its involvement of a so-called underdriven oblique detonation wave (ODW) with a flow deflection angle θ smaller than the Chapman–Jouguet (CJ) angle θCJ, whose traditional modeling is recognized as non-physical in the literature. In this study, a far-field physical model of underdriven ODWs neglecting the initiation zone, as a CJ ODW surface followed by a centered expansion fan, is proposed based on the numerical observations of the flow features of a wedge-induced ODW at θ < θCJ simulated using a finite-rate two-step chain-branching reaction model. Accordingly, the polar segment of underdriven ODWs in terms of pressure p and θ, i.e., the p–θ relation, is quantitatively constructed using a combination of the theoretical solution of a CJ ODW and the Prandtl–Meyer isentropic expansion relation. Thereafter, such physical and mathematical modeling of underdriven ODWs from a far-field perspective is well verified with a series of numerical cases simulated using a quasi-equilibrium reaction model. Finally, a sensitivity analysis is carried out to evaluate the effects of the viscous boundary layer developed on the wedge surface. The results showed that the initiation zone of viscous wedge-induced underdriven ODWs is significantly shorter than that of the inviscid counterparts, but the viscosity effect is negligible from the far-field perspective. This work advances the fundamental understanding of underdriven ODWs and supplements the theoretical modeling of the oblique detonation phenomenon.