An airfoil undergoing transonic buffet exhibits a complex combination of unsteady shock-wave and boundary-layer phenomena, for which prediction models are deficient. Recent approaches applying computational fluid mechanics methods using turbulence models seem promising, but are still unable to answer some fundamental questions on the detailed buffet mechanism. The present contribution is based on direct numerical simulations of a laminar flow airfoil undergoing transonic buffet at Mach number M = 0.7 and a moderate Reynolds number R e = 500, 000. At an angle of attack α = 4 ∘ , a significant change of the boundary layer stability depending on the aerodynamic load of the airfoil is observed. Besides Kelvin Helmholtz instabilities, a global mode, showing the coupled acoustic and flow-separation dynamics, can be identified, in agreement with literature. These modes are also present in a dynamic mode decomposition (DMD) of the unsteady direct numerical solution. Furthermore, DMD picks up the buffet mode at a Strouhal number of S t = 0.12 that agrees with experiments. The reconstruction of the flow fluctuations was found to be more complete and robust with the DMD analysis, compared to the global stability analysis of the mean flow. Raising the angle of attack from α = 3 ∘ to α = 4 ∘ leads to an increase in strength of DMD modes corresponding to type C shock motion. An important observation is that, in the present example, transonic buffet is not directly coupled with the shock motion.

中文翻译：

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在 Re = 500,000 的自助条件下层流翼型的模态分析

经历跨音速抖振的翼型表现出不稳定冲击波和边界层现象的复杂组合，对此预测模型是有缺陷的。最近使用湍流模型应用计算流体力学方法的方法似乎很有前途，但仍然无法回答有关详细抖振机制的一些基本问题。目前的贡献是基于在马赫数 M = 0.7 和中等雷诺数 Re = 500, 000 下经历跨音速抖振的层流翼型的直接数值模拟。在攻角 α = 4 ∘ 时，观察到取决于翼型的气动载荷的边界层稳定性。除了开尔文亥姆霍兹不稳定性之外，还可以识别显示耦合声学和流动分离动力学的全局模式，与文献一致。这些模式也存在于非定常直接数值解的动态模式分解 (DMD) 中。此外，DMD 以 S t = 0.12 的 Strouhal 数拾取抖振模式，这与实验一致。与平均流量的全局稳定性分析相比，DMD 分析发现流量波动的重建更加完整和稳健。将攻角从 α = 3 ∘ 提高到 α = 4 ∘ 导致对应于 C 型激波运动的 DMD 模式强度增加。一个重要的观察结果是，在本示例中，跨音速抖振不直接与激波运动耦合。12 与实验相符。与平均流量的全局稳定性分析相比，DMD 分析发现流量波动的重建更加完整和稳健。将攻角从 α = 3 ∘ 提高到 α = 4 ∘ 导致对应于 C 型激波运动的 DMD 模式强度增加。一个重要的观察结果是，在本示例中，跨音速抖振不直接与激波运动耦合。12 与实验相符。与平均流量的全局稳定性分析相比，DMD 分析发现流量波动的重建更加完整和稳健。将攻角从 α = 3 ∘ 提高到 α = 4 ∘ 导致对应于 C 型激波运动的 DMD 模式强度增加。一个重要的观察结果是，在本示例中，跨音速抖振不直接与激波运动耦合。