Study Of Analog System Of Detonations With Loss And Stability Of The Analog System

Non-ideal detonations, i.e., the detonation waves propagating that under the influence of losses or the curvature of the shock front, are very common in practice. Because of the loss term, the detonation wave will propagate at a slower velocity than the Chapman-Jouguet(CJ) velocity. In condensed-phase detonations, the pressure of the detonation exceeds the yielding limits of the confining materials, Momentum and energy losses and a curved detonation wave front are present as a result of the radially expanding flow behind the leading shock front. Due to these losses, a detonation wave propagates at a velocity lower than the Chapman-Jouguet(CJ) velocity, and beyond some critical degree of losses, fails to propagate. Furthermore, losses can result an otherwise stable detonation becoming unstable. Hence, it is of importance to study the effects of losses on condensed-phase detonations.Analog system of detonation is a new way to study detonation in recent years. It is a mathematic model of the Euler system. The Euler system contains too much real physical details. The nonlinear equations of the Euler system bring great mathematical difficulties. Analog system removes unnecessary details of the Euler system, which reduces the mathematical difficulty of the Euler system.In this paper, analog system with loss and reaction mechanism that applicable for the condensed-phase detonation will be used to study the condense-phase detonation. Specific content are as follows:1. The relationship of detonation velocity vs. loss parameter is analytically solved, and a minimal state-dependence of the reaction rate required for this relationship to exhibit a critical behavior(i.e., a turning point) is examined.2. Using normal-mode method, a linear stability analysis is performed to investigate whether the ideal, steady-state detonation structure modeled by this analog system is stable to small one-dimensional perturbations. A radiation(closure) condition is derived and applied at the end of the reaction zone to close the governing equations.3. Analog system with loss can be more unstable than the ideal one. Direct numerical simulation is used to examine the detonation stability near the propagation limits. The stability results agree with the results of the ideal one.