激波诱导重-轻型界面不稳定性研究Heavy–Light Interfacial Instability Induced by Shocks

Jiaxuan Li

Ph. D. thesis 2026

Richtmyer–Meshkov（RM）不稳定性是激波与具有初始扰动的流体界面相互作用后产生的典型界面失稳现象，该现象广泛存在于高能量密度物理、天体物理以及惯性约束核聚变（ICF）等科学问题与工程应用中。在ICF点火过程中，激光驱动形成的高强度汇聚激波不可避免地与多模扰动界面相互作用，诱发RM不稳定性并增强燃料掺混，是降低能量增益与制约点火实现的关键因素之一。ICF靶丸内层通常呈重–轻型界面结构；受激光照射不完全对称与触发不同步等因素影响，入射激波扰动及界面扰动均难以避免。相比轻–重型界面，重–轻型界面RM不稳定性的演化规律及其深层机理仍缺乏系统认识。针对激波诱导的重–轻型界面RM不稳定性，本文结合实验、数值模拟与理论建模，重点研究可压缩性效应、模态耦合效应、汇聚几何效应以及扰动入射激波效应的影响规律。 针对传统RM不稳定性实验中固体障碍物对流动与波系干扰这一不足，本文利用超疏水–疏油表面对肥皂膜界面的约束，发展了无需固体障碍物的间断气体界面生成方法，并在多类典型工况下进行了验证。实验与数值对比表明，与传统方法相比，该方法可有效避免由障碍物引入的附加反射波及边界效应，在重–轻型界面、多层界面与较强激波条件下具有更好的适用性。 针对重–轻型界面RM不稳定性的可压缩性效应，开展了不同强度激波冲击单模界面的实验与数值研究，系统评估了若干线性增长率模型的适用范围。基于线性化分析建立了启动阶段模型，阐明了启动阶段与反相阶段的内在联系，并提出更具物理一致性的无量纲参考时刻以归一化振幅增长；进一步揭示了比热比与Atwood数等可压缩物性参数对线性增长特性的影响规律。 针对模态耦合效应，采用奇异摄动法与扰动展开推导了单模与双模界面的匹配渐近展开模态模型，并通过轻–重型与重–轻型界面实验验证了其有效性。该模型能够描述冲击后界面模态振幅的全过程演化，刻画不同基础模态的启动与反相差异，并表明基础模态间耦合不仅影响拍频模态，也会显著作用于非拍频模态。进一步对多模重–轻型界面的气泡与尖钉演化进行分析，发现气泡演化在不同等效波长条件下具有可归一性，而尖钉演化表现出更强的参数敏感性。 针对汇聚几何效应，在开口汇聚激波管中开展了汇聚激波冲击重–轻型单模界面的实验研究，分析了初始振幅波长比、波数等参数对界面演化的影响，并讨论了Bell–Plesset效应与非线性效应在汇聚RM不稳定性中的竞争机制。为改善现有弱非线性模型在较长时间尺度上的适用性，采用Padé 近似对模型进行延展，从而更有效地预测后期振幅演化；并从机理上说明Bell–Plesset效应在汇聚重–轻型界面中促进二次谐波增长、导致气泡发展趋于饱和的作用。 针对扰动入射激波在重–轻型界面上的折射及其后续演化，本文通过求解Klein–Gordon方程建立了扰动透射激波的解析理论，并在单次与多次折射条件下得到验证；在此基础上提出了可显著削弱透射激波扰动的激波–界面参数组合。进一步研究了扰动激波诱导的非标准RM不稳定性，建立了不含经验参数的解析线性模型并通过数值模拟验证。结果表明，随马赫数增大，非标准RM不稳定性的失稳加速程度强于经典RM不稳定性；其关键差异在于波后横向压力梯度引入额外的环量沉积机制。基于所建理论，提出了可显著抑制扰动增长并实现“扰动冻结”的激波与界面扰动组合条件，为非标准RM不稳定性的调控提供理论依据。 Richtmyer–Meshkov (RM) instability is a canonical interfacial instability that arises when a shock interacts with a fluid interface containing initial perturbations. It is ubiquitous in high-energy-density physics, astrophysics, and engineering applications such as inertial confinement fusion (ICF). During the ICF ignition process, intense convergent shocks driven by laser irradiation inevitably interact with interfaces containing multi-mode perturbations, triggering RM instability and enhancing fuel mixing, which constitutes one of the key factors limiting energy gain and ignition success. The inner interfaces of ICF capsules are typically characterized by a heavy–light configuration. Owing to laser asymmetries and timing jitter, both incident shock perturbations and interfacial perturbations are unavoidable. Compared with the light–heavy configuration, the evolution characteristics and underlying physical mechanisms of RM instability at heavy–light interfaces remain insufficiently understood. Focusing on shock-induced RM instability at heavy–light interfaces, this dissertation combines experimental investigations, numerical simulations, and theoretical modeling to systematically study the roles of compressibility effects, mode coupling effects, geometrical convergence effects, and perturbed incident shock effects. To overcome the limitations of traditional RM instability experiments in which solid obstacles introduce flow perturbations and complex wave interactions, a novel method for generating discontinuous gaseous interfaces without solid obstacles is developed by confining soap-film interfaces with super-hydrophobic–oleophobic surfaces. This method is validated under several representative experimental conditions. Comparisons between experiments and numerical simulations demonstrate that the proposed approach effectively eliminates additional reflected waves and boundary effects induced by solid obstacles, and exhibits superior applicability compared with conventional methods, particularly for heavy–light interfaces, multilayer interfaces, and strong shock conditions. To investigate compressibility effects in RM instability at heavy–light interfaces, systematic experimental and numerical studies are conducted for single-mode interfaces subjected to shocks of varying strengths. The applicability of several linear growth-rate models is critically assessed. Based on linearized analysis, a startup-process model is established to elucidate the intrinsic connection between the startup stage and the phase-inversion stage. A more physically consistent non-dimensional reference time is proposed for normalizing amplitude growth. Furthermore, the influence of compressibility-related physical properties, such as the specific heat ratio and the Atwood number, on linear growth characteristics is elucidated. To address mode coupling effects, mode evolution models based on the method of matched asymptotic expansions for single- and dual-mode interfaces are derived using singular perturbation methods combined with perturbation expansion methods, and are validated through experiments on both light–heavy and heavy–light interfaces. The proposed model captures the complete post-shock evolution of interfacial mode amplitudes, characterizes the differences in startup and phase-inversion behaviors among different fundamental modes, and demonstrates that mode coupling affects not only beat modes but also non-beat modes. Further analysis of bubble and spike evolution in multi-mode heavy–light interfaces reveals that bubble growth collapses onto a common trend after normalization under different effective wavelengths, whereas spike growth shows stronger sensitivity to initial parameters. To investigate geometrical convergence effects, experiments are conducted in an open-end convergent shock tube, where convergent shocks interact with single-mode heavy–light interfaces. The influences of initial amplitude-to-wavelength ratio and wavenumber on interfacial evolution are analyzed, and the competing roles of the Bell–Plesset effect and nonlinear effects in convergent RM instability are discussed. To improve the applicability of existing weakly nonlinear models over extended timescales, the models are extended using Padé approximation, enabling more accurate prediction of late-time amplitude evolution. The results indicate that the Bell–Plesset effect in convergent heavy–light interfaces promotes the growth of secondary harmonics, leading to saturation tendencies in bubble development. For the refraction and subsequent evolution of perturbed incident shocks at heavy–light interfaces, an analytical theory for perturbed transmitted shocks is established by solving the Klein–Gordon equation, and is validated under both single and multiple refraction conditions. Based on this theory, combinations of shock and interface parameters that can significantly suppress transmitted shock perturbations are identified. Furthermore, non-standard RM instability induced by perturbed shocks is investigated, and an analytical linear model free of empirical parameters is developed and validated through numerical simulations. The results indicate that, with increasing Mach number, the growth of non-standard RM instability accelerates more strongly than that of classical RM instability. This fundamental difference is attributed to an additional circulation deposition mechanism introduced by transverse pressure gradients in the post-shock flow. Based on the developed theory, combinations of shock and interface perturbations capable of substantially suppressing perturbation growth and achieving “perturbation freeze-out” are identified, providing a theoretical foundation for the manipulation of non-standard RM instability.

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