We present a theory for the evolution of a one-dimensional, steady-state detonation reaction zone to a two-dimensional reaction zone, when the explosive experiences a sudden loss of side-on confinement as a boundary of the explosive is impulsively withdrawn. Our focus is on condensed-phase explosives, which we describe as having a constant adiabatic gamma equation of state and an irreversible, state-independent reaction rate. We consider two detonation models: (i) the instantaneous reaction heat release Chapman–Jouguet (CJ)-limit and (ii) the spatially resolved reaction heat-release Zel’dovich–von Neumann–Döring (ZND) model, in the limit where only a small fraction of the energy release is resolved (the SRHR-limit). Two competing rarefaction waves are generated by this loss of confinement: (i) a smooth wave coming off the full length of the withdrawn boundary and (ii) a singular fan spreading out from the point where the detonation shock and the withdrawn boundary meet. For the CJ-limit, in all cases the singular rarefaction fan eventually dominates the competition to control the steady-state behaviour. For the SRHR-limit, the spatially resolved heat release moderates this competition. When the withdrawal speed is fast, the rarefaction fan dominates; when the withdrawal speed is slower, the smooth rarefaction eventually dominates, although the flow features a fan at early times. By examining the mathematical properties of the steady two-dimensional fan-based solution, we set down a mechanism for this transition in behaviours.

中文翻译：

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爆炸限制失效后的瞬态

我们提出了一种将一维稳态爆轰反应区演变为二维反应区的理论，当炸药的侧面限制突然消失时，炸药的边界被冲动地撤回。我们的重点是凝聚相炸药，我们将其描述为具有恒定的绝热伽马状态方程和不可逆的、与状态无关的反应速率。我们考虑两种爆轰模型：(i) 瞬时反应放热 Chapman–Jouguet (CJ)-limit 和 (ii) 空间分辨反应放热 Zel'dovich–von Neumann–Döring (ZND) 模型，在以下限制中只有一小部分能量释放得到解决（SRHR 限制）。这种约束的丧失产生了两个相互竞争的稀疏波：(i) 从撤回边界的整个长度上发出的平滑波和 (ii) 从爆震激波和撤回边界相遇的点散开的奇异扇形。对于 CJ 限制，在所有情况下，单一稀疏风扇最终会主导竞争以控制稳态行为。对于 SRHR 限制，空间分辨的热释放缓和了这种竞争。提拉速度快时，稀扇占优势；当提取速度较慢时，平滑的稀疏最终占主导地位，尽管流动在早期具有风扇特征。通过检查基于稳定二维风扇的解决方案的数学特性，我们为这种行为转变建立了一种机制。