We examine asymptotically the dynamics of two-dimensional, steady detonation wave propagation and failure for a strongly confined high explosive (HE), in which the width of the explosive is small relative to the reaction zone length. An energy balance equation is derived, which shows how the longitudinal acceleration of subsonic flow behind the detonation shock is influenced both by chemical reaction and by the effects of HE boundary streamline deflection, specifically via the induced rate of change of mass flux through the detonation wave. The latter serves to either counteract or reinforce the acceleration of longitudinal flow, depending on the sign of the gradient of the boundary streamline deflection at the detonation shock. The analysis is valid for general equations of state and chemical reaction rates in the HE. The asymptotically derived form of the energy equation represents an eigenvalue problem for the determination of the steady detonation propagation speed, solved via a shooting method. We explore specific results for ideal and stiffened equations of state, along with a pressure-dependent reaction rate for which changes in the pressure exponent and reaction order are also studied. We consider the influences of both straight and curved HE boundary streamline shapes. The asymptotic analysis reveals significant physical insights into how detonation propagation and failure are affected by strong confinement.

中文翻译：

---

强约束薄通道中的稳定爆轰传播

我们渐近地研究了强约束强炸药 (HE) 的二维稳定爆轰波传播和失效的动力学，其中炸药的宽度相对于反应区长度较小。推导出了一个能量平衡方程，该方程显示了爆炸冲击后亚音速流动的纵向加速度如何受到化学反应和 HE 边界流线偏转的影响，特别是通过爆炸波引起的质量通量变化率. 后者用于抵消或加强纵向流动的加速，这取决于爆震激波处边界流线偏转的梯度符号。该分析适用于 HE 中的一般状态方程和化学反应速率。能量方程的渐近导出形式表示用于确定稳定爆轰传播速度的特征值问题，通过射击方法求解。我们探索了理想状态方程和强化状态方程的具体结果，以及压力相关的反应速率，还研究了压力指数和反应阶数的变化。我们考虑了直线和曲线 HE 边界流线形状的影响。渐近分析揭示了关于强约束如何影响爆轰传播和失效的重要物理见解。以及与压力相关的反应速率，还研究了压力指数和反应顺序的变化。我们考虑了直线和曲线 HE 边界流线形状的影响。渐近分析揭示了关于强约束如何影响爆轰传播和失效的重要物理见解。以及与压力相关的反应速率，还研究了压力指数和反应顺序的变化。我们考虑了直线和曲线 HE 边界流线形状的影响。渐近分析揭示了关于强约束如何影响爆轰传播和失效的重要物理见解。