On The Study Of The Reflection And Diffraction Phenomena Of Gaseous Detonations

The reflection and diffraction phenomenons are both basic research interests of gaseous detonations. The research of the detonation reflection and diffraction can con-tribute to the application of detonations, i.e. the prevention of industrial explosion of combustible gases, the design of propulsion system, and advanced weapon development. However, the detonation reflection and diffraction have characteristics of non-linearity, multiple length scales and strong coupling of physics and chemistry. Thus it is dif-ficult to study such kind of phenomenon. In the present thesis, we developed and modified high resolution schemes for reactive Euler equation with parallel calculation and adoptive mesh refinement techniques and then carried out numerical simulations of detonation reflection and diffraction. The numerical research focused on the intrin-sic dynamics of detonation reflection and diffraction and several important conclusions were also obtained. The main studies of the thesis are described below:1. The full unsteady nonlinear dynamics of detonations are modeled by solutions of the inviscid compressible, time-dependent reactive Euler equations with several chemical reaction models, i.e. detailed chemistry model, a one-step Arrhenius reaction law and a two-step chain branching reaction model. For multi-species reactive Euler equation, a fifth-order WENO scheme is applied to discrete the spatial terms and, a third-order TVD Runge-Kutta scheme is employed to integrate ordinary partial equations. For reactive Euler equation with stiff source terms, a traditional operator-splitting method as well as an additive Runge-Kutta are both introduced to solve the stiff problem. Based on the methods above, a parallel finite difference code is developed to run numerical simulations. In addition, a finite volume code AMROC with adoptive mesh refinement technique is also modified to couple a two-step chain branching reaction model.2. The Mach reflection of a ZND detonation wave on a wedge is investigated nu-merically with high resolution WENO scheme and a two-step chain-branching reaction model as well. The presence of a finite reaction zone thickness renders the Mach re-flection process non self-similar. The variation of the height of the Mach stem with distance of propagation does not correspond to a straight curve from the wedge apex as governed by self-similar three-shock theory. However, the present results indicate that in the near field around the wedge apex, and in the far field where the reaction zone thickness is small compared to the distance of travel of the Mach stem, the behavior appears to be self-similar. This corresponds to the so called frozen and equilibrium limit for strong shock waves and cellular detonations respectively. The critical wedge angle for the transition from regular to Mach reflection is found to correspond to the value determined by self-similar three-shock theory, but not by reactive three-shock theory for a discontinuous detonation front.3. The Mach reflection of cellular detonation waves on a wedge is investigated numerically in attempt to elucidate certain aspects of the phenomenon, i.e. the effect of the cellular instability on the Mach reflection, the dependence of the asymptotic approach to self-similarity in the far field on the reaction zone thickness, the effect of cellular structures on the Mach reflection and the initial development of the Mach stem near the wedge tip. A large distances of travel of Mach stem was carried out in the simulations in order to observe the asymptotic behavior of Mach reflection in the far field. It was found that the Mach reflection of a cellular detonation behaves essentially like that of a ZND detonation wave and the cellular instabilities however, cause the triple-point trajectory to fluctuate. In the vicinity of the wedge tip, the Mach reflection is found to be self-similar since the Mach stem is largely overdriven initially. In the far field, the triple-point trajectory tends towards a straight line indicating that the Mach reflection becomes self-similar asymptotically.4.The detonation diffraction is investigated numerically with a two step chain-branching chemical reaction model and finite volume code AMROC. In present study, we focus on measuring the critical tube diameter of detonation diffraction for both stable and unstable detonations. In order to elucidate different propagation mechanisms of det-onation diffraction for stable and unstable detonations, a three-dimensional simulation is firstly carried out. Three-dimensional detonation diffraction problem in cylindrical or-dinate system is assumed to an axis-symmetric case. Thus a three-dimensional reactive Euler equation can be deduced to be a two-dimensional case by adding a geometrical term into the source terms. The numerical results show that for a stable detonation, the critical tube diameter in a two-dimensional case is found to be 13 A, and 25 A in a three-dimensional case with good agreement with the experimental results. For an unstable detonation, the critical tube diameter in a two-dimensional case is found to be 4-5A.5. A detailed reaction model is employed in simulating two-dimensional cellu-lar detonations propagating through smooth pipe bends in a stoichiometric hydrogen-oxygen mixture diluted by argon. Additive Runge-Kutta methods are applied to solve the stiff reactive Euler equations. The numerical results indicate that, as the regular cellular detonation wave propagating through the bend section, the diffraction near the inner wall causes an increase in detonation cell size while the detonation reflection oc-curring on the bottom wall leads to a decrease in cell size. In addition, an expansion wave is generated continuously. The expansion wave causes the failure as well as the partial failure of the detonations near the inner and outer walls, respectively. The prop-agation mechanism of steady cellular detonations in curved channels is also investigated numerically. Two kinds of propagation modes exist as the detonation is propagating in the curved channel.