Role of transversal concentration gradient in detonation propagation

The role of a transversal concentration gradient in detonation propagation in a two-dimensional channel filled with an $\text{H}_{2}{-}\text{O}_{2}$ mixture is examined by high-resolution simulation. Results show that, compared to propagation in homogeneous media, a concentration gradient reduces the average detonation velocity because of the delay in reaching downstream reaction equilibrium, leading to a large amount of unreacted $\text{H}_{2}$ and hence significant species fluctuations. The transversal concentration gradient also enhances the cellular detonation instability. Steepening it reduces considerably the number of triple points on the front, lengthens the global detonation front structure on average and consequently increases the deficit of the average detonation velocity. It is further found that the interaction of the leading shock with the transversal concentration gradient influences the formation of local $\text{H}_{2}$ bump and thus the unreacted pocket behind the front, while the transverse wave causes mixing and burning of the residue fuel downstream. Nevertheless, for the steepened concentration gradient, a transverse detonation is present and consumes the fuel in the compressed and preheated zone by the leading shock; consequently, the detonation velocity deficit is not increased significantly for detonation with the single-head propagation mode close to the limit.

Numerical investigations on reignition behavior of detonation diffraction

In this paper, by adopting a fifth-order weighted essentially non-oscillatory (WENO) scheme with a third-order TVD Runge–Kutta time stepping method for two-dimensional reactive Euler equations, a parallel code is developed, and reignition behavior after a self-sustaining detonation from the tube into free space filled with H2/O2 mixtures is investigated. The numerical results show that the initial pressure has a great influence on the detonation cellular width, and that as the initial pressure increases, the cellular width gradually decreases and the cellular shape changes from irregular structure to regular structure, demonstrating the detonation instability to stability transition. When the initial pressure is larger than 1.2 atm, the detonation wave expands over the edge of the splitter plate, reignition can come into being because enough transverse waves collide with each other at the leading edge of the expanding front. When the initial pressure is 1.2 atm, hot spots appear on the front, and ignite the combustible gas near the hot spots after detonation diffraction. When the initial pressure is 1.0 atm, reignition fails. These findings hint that a critical initial pressure exists between 1.0–1.2 atm for direct reignition after detonation diffraction.

On the transition pattern of the oblique detonation structure

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 $1{5}^{\ensuremath{\circ} } $–$1{8}^{\ensuremath{\circ} } $. 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.

Direct initiation of detonation with a multi-step reaction scheme

The problem of direct initiation of detonation, where a powerful ignition source drives a blast wave into a gaseous combustible mixture to generate a Chapman–Jouguet (CJ) detonation, is investigated numerically by using a three-step chain-branching chemical kinetic model. The reaction scheme consists sequentially of a chain-initiation and a chain-branching step, followed by a temperature-independent chain termination. The three regimes of direct initiation i.e. subcritical, critical and supercritical, are numerically simulated for planar, cylindrical and spherical geometries using the present three-step chemical kinetic model. It is shown that the use of a more detailed reaction mechanism allows a well-defined value for the critical initiation energy to be determined. The numerical results demonstrate that detonation instability plays an important role in the initiation process. The effect of curvature for cylindrical and spherical geometries has been found to enhance the instability of the detonation wave and thus influence the initiation process. The results of these simulations are also used to provide further verification of some existing theories of direct initiation of detonation. It appears that these theories are satisfactory only for stable detonation waves and start to break down for highly unstable detonations because they are based on simple blast wave theory and do not include a parameter to model the detonation instability. This study suggests that a stability parameter, such as the ratio between the induction and reaction length, should be considered and a more complex chemistry should be included in future development of a more rigorous theory for direct initiation of detonation.