Three-dimensional numerical simulation for detonation waves using WENO schemes

Abstract

The numerical method and the simulation results of propagation of three-dimensional detonation waves in a rectangular duct are reported. The systems of conservative laws of inviscid fluid combined with the one-step chemical reaction model are discretized in a Cartesian coordinates using the fifth-order WENO (Weighted Essentially NonOscillatory) scheme, and the final discretized variables are solved with a 3rd order TVD Rouge-Kutta method. Then, the process of the formation of the detonation pattern from the premixed gaseous state in 3D space is observed from the simulation results. The simulation result reveals that there are significant differences between the three-dimensional and two-dimensional detonations. As expected, the detonation structure and the reaction process are more complex in three-dimensional case. The simulation shows that under an initial disturbance, the detonation front finally develops to an unsteady three-dimensional distorted pattern and which translates between the walls. For a narrow duct, the flow front displays an unmistakenly spinning motion with a period. For the wide duct, the flow front shows a quasi-steady "rectangular mode" periodically. It is shown that the detonation mechanism depends on the coupling between the pressure and the velocity. The reaction process is dominated by the hot "spot" (zone with high pressure and high velocity) sweeping along the transverse direction for 2D and 3D detonations.