[论文解读] Detonation propagation in weakly confined gases

Youssef K. Wahba, XiaoCheng Mi+2 more|arXiv (Cornell University)|Mar 25, 2026

Combustion and Detonation Processes被引用 0

一句话总结

该论文使用 CFD 与两层气体模型，通过声障抗和层厚来对弱约束配置中的爆轰行为进行分类，并建立分析框架以预测前导冲击、欠驱/超驱状态，以及相图。

ABSTRACT

This study investigates the propagation of detonations along a layered configuration where a reactive gas is weakly confined by a hotter inert layer. CFD simulations are performed using a single-step, non-Arrhenius reaction model designed to suppress cellular instabilities, enabling formulation of a theoretical framework directly compared with simulation results. The simulations reach a quasi-steady state, revealing distinct flowfield regimes that depend on the acoustic-impedance ratio and relative layer thicknesses, with some detonations exhibiting velocity deficits while others propagate above the ideal Chapman-Jouguet (CJ) speed. Analytical models are developed to interpret these regimes. When a precursor shock is observed in the inert layer, the detonation is overdriven; this is modeled using shock-polar analysis and velocity estimates based on the approach of Mitrofanov (Acta Astronaut. 3:995-1004, 1976). An analytical criterion for precursor shock onset is proposed. In underdriven scenarios, the detonation front exhibits positive curvature, analyzed using a geometric construction wherein the relationship between wave speed and front curvature is evaluated a priori. A simplified characteristic-based model captures the decay of the shock wave in the inert layer, after which shock-polar analysis determines the resulting wave interaction. Predictions from these models are assembled into a phase map delineating regions of overdriven and underdriven behavior, along with corresponding shock interactions, in the space of acoustic impedance and area ratios. This map is compared directly with CFD results. The combined numerical-theoretical framework clarifies transition mechanisms governing layered detonations and provides insights into detonation dynamics relevant to rotating detonation engines in which the detonation is bounded by hotter combustion products from a previous cycle.

研究动机与目标

• 研究在两层通道中较热的惰性层弱约束下，反应性气体爆轰如何传播。
• 识别依赖于声阻抗比和层厚的流场分型。
• develop analytical models to interpret CFD-observed regimes and predict transitions between overdriven and underdriven detonations.

提出的方法

• 使用单步、非 Arrhenius 模型在惰性层弱约束下对反应层进行二维 CFD 模拟，以抑制细胞不稳定性。
• 对变量进行无量纲化，并建立可调 A2/A1 与声阻抗比 Z 的两层通道（在所有情形中 Z<1）。
• 采用 MUSCL-Hancock 方案和 HLLC 流型求解器求解反应性欧拉方程，并对化学源项进行 Strang 分裂。
• 通过热点引燃引发爆轰，并运行至准稳态以测量爆轰速度和冲击结构。
• 建立解析构造（Kantrowitz 型 choke 判据、Eyring 几何构造、极坐标分析、以及 Mitrofanov 的两层方法）以解释观测到的分型。

Figure 1 : Schematic representation of the problem, showing terminal shock structures relative to the detonation front: (a) attached shock (behind the front); (b) precursor shock (ahead of the front).

实验结果

研究问题

• RQ1 在惰性层中前导冲击的起始准则如何随面积比 A2/A1 和声阻抗比 Z 变化？
• RQ2 欠驱与超驱爆轰如何在惰性层的流场及反应层相互作用中表现？
• RQ3 是否能构建一个分析相图，以区分附着、前导和分离冲击在 Z 与 A2/A1 的函数下的分界？
• RQ4 前缘曲率与冲击相互作用如何解释相对于 CJ 速度的速度损失或超驱？

主要发现

• CFD 模拟揭示五种爆轰行为（情况 A–E），取决于 Z 和 A2/A1，包括带普通反射或马赫反射的欠驱，以及由反应层驱动的前导冲击、以及分离冲击。
• 推导出 Kantrowitz 型 choke 判据，通过将面积比与阻抗关联来预测前导冲击的起始，得到临界 A2/A1 的关系。
• 欠驱动爆轰（Z > Z_Kant）表现出正前沿曲率和由反应层–惰性界面发出的声学奇点，前沿曲率通过 Eyring 构造进行分析。
• 超驱动情形（前导冲击 κ<0）通过 Mitrofanov 的两层方法与极坐标分析来预测冲击–爆轰相互作用。
• 构建了一个相图，将超驱/欠驱行为与冲击相互作用与 Z 和 A2/A1 联系起来，并与 CFD 结果进行了验证。

Figure 2 : Initial conditions showing abrupt initiation via a high-pressure, high-temperature region.