Kepeng Yao

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.

The present study delves into the examination of the stereoscopic cells and wavefront structures characterizing the propagation of three-dimensional detonation waves within square ducts. Leveraging numerical solutions derived from three-dimensional reactive Euler equations, incorporating an induction-exothermic reaction kinetic model, this work reveals the distinct classification of three modes of detonation waves based on the direction of propagation and the phase characteristics of transverse shock waves on the wavefront. This paper delineates the presence of two different types of phenomena: duct wall slapping waves due to shock–wall collisions and internal slapping waves resulting from shock interactions. Furthermore, this investigation exposes the existence of two distinct types of triple-wave lines on the wavefront: the first comprising a strong Mach disk, a weak Mach disk, and a transverse shock wave; the second characterized by a weak Mach disk, an incident shock wave, and a transverse shock wave. Notably, the pressure behind the first type of triple-wave line is observed to be the highest. It elucidates the transition from two- to three-dimensional detonation waves, revealing that the prevalence of transverse shock waves on the wavefront in the rectangular and diagonal modes is twofold and quadruple, respectively, when compared to their two-dimensional counterparts within identical ducts/channels.

This study investigates the characteristics of stable and unstable cells and wavefronts of detonation waves propagating in annular channels with different inner radii and channel widths using two-dimensional Euler equations along with a two-step induction-exothermic reaction kinetics. The results reveal that the effect of annular channels on the detonation cell structure depends on both the inner radius and channel width. To quantify this effect, a parameter σ is introduced, representing the ratio of the inner and outer radii of the channel. We have discovered that for values of the parameter σ exceeding a critical value σs, the detonation wavefront demonstrates characteristics similar to those observed in a straight channel scenario. On the contrary, when σ is below σs, the wavefront becomes distorted, potentially leading to Mach reflection as σ decreases further to another critical value σm. Additionally, the interaction among expansion waves induced by the inner walls leads to an augmented induced length and the potential occurrence of localized decoupling of the detonation wave, particularly for unstable detonation waves. However, it is worth noting that the re-initiation of the detonation wave may be triggered by the formation of hotspots resulting from the interaction between transverse shock waves and the detonation wave. This study aims to characterize the propagation characteristics of detonation waves within annular channels, with the objective of providing valuable insights for the design and optimization of annular chamber configurations in systems involving detonation.

The stationary characteristics of the oblique detonation wave (ODW) induced by the double wedge with an expansion corner are investigated using two-dimensional Navier–Stokes equations along with a two-step induction-exothermic kinetic model. The results show that the detached ODW can be reattached by expansion waves induced by the double wedge so that the standing window of ODW can be expanded. The re-standing position of ODW depends on the location and strength of the expansion waves, which are governed by the first wedge length L and the corner angle between the first and second wedge surface θ_C. There is a critical angle reattachment that determines whether the ODW can be reattached by expansion waves, and this critical angle increases as wedge length increases. However, the detached ODW cannot be reattached when the wedge length is increased to a critical value regardless of the wedge corner. The re-standing position moves downstream with the increment of θ_C until the last Mach wave tangent to the subsonic zone behind the strong overdriven ODW because no more Mach waves interact with the initiation zone. Moreover, the comparison of viscous and inviscid fields demonstrates that a shorter wedge length is necessary for the viscous field to reattach the ODW because the recirculation zone forms a gas wedge that extends the first wedge surface.