High resolution WENO simulation of 3D detonation waves

In this paper, we develop a three-dimensional parallel solver using the fifth order highresolution weighted essentially non-oscillatory (WENO) finite difference scheme to perform extensive simulation for three-dimensional gaseous detonations. A careful study is conducted for the propagation modes of the three-dimensional gaseous detonation wave-front structure in a long square duct with different widths under different initial perturbations. The numerical results indicate that, with a transverse sinusoidal perturbation of the initial ZND profile, when the width of the duct is less than the cellular width (4.5×L1/2), unstable detonations can trigger a spinning motion in the duct. The detonation wave propagates in a single-headed spinning motion, with a distinctive “ribbon” displayed on the four walls. In this case, the measured pitch-to-diameter ratio is approximately 3.42, which is slightly larger than the theoretically predicted value 3.128 for a round duct. When the channel width is greater than the cellular width, detonation waves propagate in an out-of-phase rectangular mode. With a transverse cosine perturbation of the initial ZND profile, the front of the stable detonation has a rectangular structure, and regular cellular patterns and in-phase “slapping waves” can be observed clearly on the four walls. The width-to-length ratio of the cellular patterns is approximately 0.5. For a mildly unstable detonation, its front has an in-phase rectangular structure at the early stage, then the wave-front becomes flat. Over time, but it still maintains an in-phase rectangular structure after reigniting. For highly unstable detonations, the wave-front has a rectangular structure at the early stage. After a low pressure stage for a very long time, detonation occurs once again. At this time, the detonation front structure becomes very twisted, and the triple-lines become asymmetrical. Finally, a spinning detonation mode is triggered. With a symmetrical perturbation mode along the diagonals of the detonation front, for the stable detonation, an diagonal detonation is formed and the detonation front maintains a diagonal structure, but no “slapping waves” appears on the walls. The width-to-length ratio of the cellular structure is equal to that in the rectangular structure. For mildly unstable and highly unstable detonations, the front has a diagonal structure at the early stage. After a short period of time, the diagonal structure of the detonation front cannot be maintained, and it ultimately evolves into a spinning detonation.