Numerical study on unstable surfaces of oblique detonations

Abstract

In this study, the onset of cellular structure on oblique detonation surfaces is investigated numerically using a one-step irreversible Arrhenius reaction kinetic model. Two types of oblique detonations are observed from the simulations. One is weakly unstable characterized by the existence of a planar surface, and the other is strongly unstable characterized by the immediate formation of the cellular structure. It is found that a high degree of overdrive suppresses the formation of cellular structures as confirmed by the results of many previous studies. However, the present investigation demonstrates that cellular structures also appear with degree of overdrive of 2.06 and 2.37, values much higher than ∼1.8 suggested previously in the literature for the critical value defining the instability boundary of oblique detonations. This contradiction could be explained by the use of differently shaped walls, a straight wall used in this study and a custom-designed curved wedge system so as to induce straight oblique detonations in previous studies. Another possible reason could be due to the low and possibly insufficient resolution used in previously published studies. Hence, simulations with different grid sizes are also performed to examine the effect of resolution on the numerical solutions. Using the present results, analysis also shows that although the characteristic lengths of unstable surfaces are different when the incident Mach number changes, these length scales are proportional to tangential velocities. Hence, the interior time determined by the overdrive degree is identified, and its limitation as the instability parameter is discussed.

Evolution of cellular structures on oblique detonation surfaces

“…Indeed from both experiments [5] and numerical simulations [9][10][11][12][13][14], it was observed that the oblique detonation surface can be unstable with the generation of triple points and fine scale cellular unstable structures very similar to normal cellular detonation. Numerically, it was found by Choi et al [11] using mixtures of different activation energies that these unstable oblique detonation structures cannot be captured without sufficient numerical resolution.…”

Numerical investigation on the induction zone structure of the oblique detonation waves

“…Choi et al [8] studied these small scale structures and demonstrated the coupling relation between the shock and the combustion. Teng et al [9] found out the formation of triple points is hard in the case of high overdrive degree, but it derives from small disturbance and cannot be suppressed thoroughly. The other kind of small scale structures, which is similar to the detonation cell on the normal detonation surface, are also observed and discussed recently [10][11][12].…”

Numerical study of oblique detonation initiations with chain-branching kinetics

“…For the computation, the coordinate is rotated to the direction along the wedge surface. Hence, the Cartesian grid in the rectangular domain enclosed by the dashed line is aligned with the wedge surface, like our previous studies 6,7 .…”

“…For instance, Li et al 3 revealed that the multi-dimensional oblique detonation structure consists of a non-reactive oblique shock, an induction region, a set of deflagration waves, and an oblique detonation surface. The instability of oblique detonation surface has been studied widely, demonstrating the cellular structure formation and evolution 4,5,6,7 . Another research direction is the oblique shock-to-detonation transition, which can be viewed as the initiation process of oblique detonation.…”