Abstract

The stability of one-dimensional steady flows of an ideal (inviscid and non-heat-conducting) gas in channels of variable cross section with combustion in a structurally stable detonation wave is studied. The detonation wave represents a discontinuity surface propagating normally to the axis of the channel. It was previously established that, in this formulation, steady flows with combustion in a Chapman–Jouguet detonation wave are always unstable, in contrast to combustion flows in an overcompressed detonation wave. The stability analysis of such flows is reduced to the numerical solution of an initial-boundary value problem describing the evolution of finite flow perturbations between the moving detonation wave and the minimal nozzle cross section (in the case of a sudden contraction) or the exit nozzle cross section. The problem is solved by applying a modified Godunov scheme of higher order accuracy. More specifically, a Riemann solver with switching (between the overcompressed and Chapman–Jouguet detonation waves) with an explicitly represented detonation wave is created. Examples of stable flows and flows collapsing due to large initial perturbations are given, and their dynamics with transitions to a Chapman–Jouguet detonation wave and back are computed.

中文翻译：

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变截面通道内一维带爆波的稳定流的稳定性

摘要

研究了在结构稳定的爆炸波中具有燃烧的可变截面通道中理想气体（无粘性和非导热性）的一维稳态流动的稳定性。爆震波表示垂直于通道轴线传播的不连续表面。先前已经确定，在这种公式中，与超压缩爆震波中的燃烧流相反，在Chapman–Jouguet爆震波中具有燃烧的稳定流始终不稳定。这种流动的稳定性分析被简化为一个初始边界值问题的数值解，该问题描述了运动爆轰波和最小喷嘴横截面（在突然收缩的情况下）或出口喷嘴之间的有限流动扰动的演变。横截面。通过应用改进的高阶精度的Godunov方案可以解决该问题。更具体地说，创建了一个Riemann求解器，该开关具有明确表示的爆震波（在超压缩和Chapman–Jouguet爆震波之间切换）。给出了稳定的流动和由于大的初始扰动而塌陷的流动的例子，并计算了它们在向Chapman–Jouguet爆炸波过渡和向后过渡时的动力学。