Simulations of Detonation Wave Propagation in Rectangular Ducts Using a Three-Dimensional WENO Scheme

Abstract

This paper reports high resolution simulations using a fifth-order weighted essentially non-oscillatory (WENO) scheme with a third order TVD Runge-Kutta time stepping method to examine the features of detonation front and physics in square ducts. The simulations suggest that two and three-dimensional detonation wave front formations are greatly enhanced by the presence of transverse waves. The motion of transverse waves generates triple points (zones of high pressure and large velocity coupled together), which cause the detonation front to become locally overdriven and thus form "hot spots". The transversal motion of these hot spots maintains the detonation to continuously occur along the whole front in two and three-dimensions. The present simulations indicate that the influence of the transverse waves on detonation is more profound in three dimensions and the pattern of quasi-steady detonation fronts also depends on the duct size. For a narrow duct (4LX4L where L is the half reaction length), the detonation front displays a distinctive "spinning" motion about the axial direction with a well-defined period. For a wider duct (20LX20L), the detonation front exhibits a "rectangular mode" periodically, with the front displaying "convex" and "concave" shapes one following the other and the transverse waves on the four walls being partly out-of-phase with each other.