An analysis of the direct initiation of gaseous detonations in a spherical geometry is presented. The full set of constitutive equations is analysed by an asymptotic analysis in the double limit of Mach number close to unity (small heat release) and large thermal sensitivity. The quasi-steady curvature-induced quenching phenomenon is first revisited in this limit. Considering a realistic decrease rate of the rarefaction wave, the unsteady problem is reduced to a single nonlinear hyperbolic equation. The time-dependent velocity of the lead shock is an eigenfunction of the problem when two boundary conditions are imposed to the flow at the lead shock and at the burnt gas side. Following (Linan et al. , C. R. Mec. , vol. 340, 2012, pp. 829–844), the boundary condition in the quasi-transonic flow of burnt gas is expressed in terms of the curvature. Focusing our attention on successful initiation, the time-dependent velocity of the lead shock of a detonation approaching the Chapman–Jouguet regime is the solution of a nonlinear integral equation investigated for stable and marginally unstable detonations. By comparison with the quasi-steady trajectories in the phase space ‘propagation velocity versus radius’, the solution exhibits the unsteady effect produced upon the detonation decay by the long time delay of the upstream-running mode for transferring the rarefaction-wave-induced deceleration across the inner detonation structure from the burnt gas to the lead shock. In addition, a new and intriguing phenomenon concerning pulsating detonations is described. Even if the results are not quantitatively accurate, they are qualitatively relevant for real detonations.

中文翻译：

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小放热气态爆轰直接引爆的分析研究

介绍了在球形几何结构中直接引发气态爆轰的分析。全套本构方程在马赫数接近1（放热小）和热敏度大的双重极限下进行渐近分析。准稳态曲率引起的猝灭现象首先在这个极限中被重新审视。考虑到稀疏波的实际下降率，非定常问题被简化为单个非线性双曲方程。当对铅激波和可燃气体侧的流动施加两个边界条件时，铅激波的时间相关速度是问题的本征函数。继（Linan et al., C. R. Mec., vol. 340, 2012, pp. 829–844）之后，燃气准跨音速流动的边界条件用曲率表示。将我们的注意力集中在成功起爆上，接近查普曼-朱盖区的爆炸的铅激波的时间相关速度是为稳定和边缘不稳定爆炸研究的非线性积分方程的解。通过与相空间“传播速度与半径”中的准稳态轨迹进行比较，该解表现出由于传递稀疏波引起的减速的上游运行模式的长时间延迟对爆轰衰减产生的非稳态效应穿过从燃烧气体到铅激波的内部爆炸结构。此外，还描述了关于脉动爆轰的一种新的有趣现象。即使结果在定量上不准确，它们也与实际爆炸定性相关。