Haoyang Li

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 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.

The propagation of two-dimensional cellular detonations is investigated numerically using a one-step reversible reaction model. The effect of the average mole weight ratio W_B/W_A of the product and reactant on the one-dimensional Zeldovich–von Neumann–Döring (ZND) detonation and cellular detonation behavior is analyzed in detail. Several interesting cellular detonation phenomena are observed in the numerical simulations. These can be divided into five categories according to the cell patterns of detonation, i.e., regular, relatively regular, irregular, half-cell propagating, and decoupled detonation. The results indicate that differences in cell size under different values of W_B/W_A modify the cellular detonation behavior. The ZND detonation parameters under various W_B/W_A values are studied and related to the cell size. The results show that the reaction zone length and maximum heat release rate are clearly influenced by W_B/W_A. Furthermore, for both ZND detonation and cellular detonation, the reaction zone length decreases as W_B/W_A increases, which effectively reduces the cell size. To elucidate the effects of the reaction zone length on cell size, thermoacoustic instability theory is introduced to investigate the acoustic perturbations in the reaction zone. This allows the correlation between the propagation frequency and cell number along the width of the duct to be determined. Correlation analysis indicates that the cell number has a strong linear dependence on the perturbation frequency.

A normal detonation wave in a gaseous mixture is a transient, multidimensional structure containing triple points (TPs) that collide in pairs and then propagate oppositely. However, the TPs on an oblique detonation wave (ODW) almost propagate along the same direction in most studies. In this study, the reactive Euler equations coupled with a two-step induction–reaction kinetic model are used to solve a two-dimensional wedge-induced ODW. Two novel movement patterns are observed in most cases. Results show that the TPs of the ODW can propagate upstream and even stand on the wave surface. The movement patterns of TPs include downstream, upstream, and steady according to their propagation direction relative to the wedge. We find that the ratio of the post-ODW flow speed U_τ to the transverse wave speed U_T dominates the TP movement types. When the speed ratio U_τ/U_T is approximately equal to 1, the TPs can stand on the wave surface. Above unity, downstream TPs form, and upstream TPs correspond to a value smaller than 1. Furthermore, the inflow Mach number has little influence on U_T, while U_τ changes significantly. This is largely due to the high sensitivity of the ODW angle to the inflow. The high heat release rate benefits upstream TPs, and steady TPs form under a large wedge angle. The results are confirmed by varying the inflow Mach number, wedge angle, and chemical parameters.