Shock buffet on wings encountered in edge-of-the-envelope transonic flight remains an unresolved and disputed flow phenomenon, challenging both fundamental fluid mechanics and applied aircraft aerodynamics. Its dynamics is revealed through the interaction of spanwise shock-wave oscillations and intermittent turbulent boundary-layer separation. Resulting unsteady aerodynamic loads, and their mutual working with the flexible aircraft structure, need to be accounted for in establishing the safe flight envelope. The question of global instability leading to this flow unsteadiness is addressed herein. It is shown for the first time on an industrially relevant configuration that the dynamics of a single unstable oscillatory eigenmode plays a prominent role in near-onset shock buffet on a quasi-rigid wing. Its three-dimensional spatial structure, previously inferred both from experiment and time-marching simulation, describes a spanwise-localised pocket of shear-layer pulsation synchronised with an outboard-propagating shock oscillation. The results also suggest that the concept of a critical global shock-buffet mode commonly reported for two-dimensional aerofoils also applies to three-dimensional finite and swept wings, albeit different modes at play. Specifically, the modern wing design, NASA Common Research Model, with publicly available geometry and experimental data for code validation is studied at a free-stream Mach number of 0.85 with Reynolds number per reference chord of $5.0\times 10^{6}$ and varying angle of attack between 3. 5 ° and 4. 0 ° targeting the instability onset. Strouhal number at instability onset just above 3. 7 ° is approximately 0.39. At the same time, a band of eigenmodes shows reduced decay rate in the Strouhal-number range of 0.3 to 0.7, with additional unstable oscillatory modes appearing beyond onset. Importantly, those emerging modes seem to discretise the continuous band of medium-wavelength modes, as recently reported for infinite swept wings using stability analysis, hence generalising those findings to finite wings. Through conventional time-marching unsteady simulation it is explored how the critical linear eigenmode feeds into the nonlinearly saturated limit-cycle oscillation near instability onset. The established numerical strategy, using an iterative inner–outer Krylov approach with shift-and-invert spectral transformation and sparse iterative linear solver, to solve the arising large-scale eigenvalue problem with an industrial Reynolds-averaged Navier–Stokes flow solver means that such a practical non-canonical test case at a high-Reynolds-number condition can be investigated. The numerical findings can potentially be exploited for more effective unsteady flow analysis in future wing design and inform routes to flow control and model reduction.

中文翻译：

---

机翼冲击自助开始的全局不稳定性

在包络边缘跨音速飞行中遇到的机翼激振仍然是一个悬而未决和有争议的流动现象，对基本流体力学和应用飞机空气动力学都提出了挑战。它的动力学是通过展向冲击波振荡和间歇性湍流边界层分离的相互作用来揭示的。在建立安全飞行包线时需要考虑由此产生的不稳定空气动力载荷及其与柔性飞机结构的相互作用。导致这种流动不稳定的全球不稳定问题在本文中得到解决。首次在工业相关配置上表明，单个不稳定振荡​​本征模式的动力学在准刚性机翼上的接近开始的激波抖振中起着重要作用。其三维空间结构，先前从实验和时间推进模拟中推断出的，描述了与外侧传播的冲击振荡同步的剪切层脉动的展向局部化口袋。结果还表明，通常为二维翼型报告的临界全球冲击自助模式的概念也适用于三维有限和后掠翼，尽管在起作用的模式不同。具体而言，现代机翼设计、NASA 通用研究模型以及用于代码验证的公开几何和实验数据在 0.85 的自由流马赫数下进行研究，每个参考弦的雷诺数为 $5.0\times 10^{6}$ 和不同的攻角在 3。5 ° 和 4。0 ° 之间针对不稳定性开始。刚好高于 3. 7 ° 的不稳定开始时的 Strouhal 数约为 0.39。同时，一个特征模带在 0.3 到 0.7 的 Strouhal 数范围内显示衰减率降低，并且在开始后出现额外的不稳定振荡​​模式。重要的是，这些新兴模式似乎离散了中波长模式的连续带，正如最近使用稳定性分析针对无限后掠翼所报道的那样，因此将这些发现推广到有限翼。通过传统的时间推进非定常模拟，探索了临界线性本征模如何在不稳定开始附近馈入非线性饱和极限循环振荡。已建立的数值策略，使用具有平移和反转谱变换和稀疏迭代线性求解器的迭代内-外 Krylov 方法，使用工业雷诺平均 Navier-Stokes 流求解器解决出现的大规模特征值问题意味着可以研究这种在高雷诺数条件下的实际非规范测试用例。数值结果可能被用于在未来的机翼设计中进行更有效的非定常流动分析，并为流动控制和模型简化提供路线信息。