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 quasisteady detonation fronts also depends on the duct size. For a "narrow" duct (4L × 4L 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 (20L × 20L), 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.

Adaptive mesh refinement based simulations of three-dimensional detonation combustion in supersonic combustible mixtures with a detailed reaction model

“…Gradually, more transverse wave surfaces and triple lines are generated in the overdriven detonation because of the essential instability, as shown from In the previous 3D detonation simulations in rectangular channels with simplified reaction models or detailed reaction models, the results show different models of detonation fronts: a rectangular mode, a diagonal mode and even a spinning mode [41,43,45,46,77] . However, for the simulation here, none of these detonation modes is observed.…”

“…While there are undoubtedly similarities between 2D numerical simulations and experimental researches for detonation initiation and propagation in supersonic combustible mixtures [37] , the mechanism might be better analyzed and explained with 3D calculations. The simplified reaction models are usually utilized in 3D simulations of detonation combustion [40][41][42][43][44][45][46][47] . However, some fine features which normally characterized by chain-branching reaction processes cannot be resolved through these simplified models.…”

Numerical Simulation of Deflagration to Detonation Transition in a Straight Duct: Effects of Energy Release and Detonation Stability

“…For all the three examples above, the accuracy of the simulated results is deemed good as these results are in agreement with analysis and other works. Interested readers may refer to [29,30] for details. Other comparisons with analysis are made for the 1D simulation of detonation again with good concurrence.…”

“…The governing equations describing the fluid flow and the detonation propagation are the three-dimensional Euler equations with a source term which represents the chemical reaction process. In conservative form, these are written as [29][30][31] …”

“…The system of conservation laws of inviscid fluid combined with the one-step chemical reaction model are discretized spatially in the eigenvector space in Cartesian coordinates using the fifth-order WENO (Weighted Essentially NonOscillatory) scheme, and the final discretized variables are solved with a 3rd order TVD (Total Variation Diminishing) Runge-Kutta method in time [29,30]. The computer code for the pure Euler flow (no chemical reaction) has been validated for the steady flow of oblique shock wave past a wedge, and the unsteady flow in one-dimensional shock tubes for both the so called Lax and Sod problems.…”