High Resolution WENO Simulation of 3D Detonation Waves

Abstract

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×L 1/2 ), 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.Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Oper...