The buffet flow field around supercritical airfoils is dominated by self-sustained shock wave oscillations on the suction side of the wing. Theories assume that this unsteadiness is driven by a feedback loop of disturbances in the flow field downstream of the shock wave whose upstream propagating part is generated by acoustic waves. High-speed particle-image velocimetry measurements are performed to investigate this feedback loop in transonic buffet flow over a supercritical DRA 2303 airfoil. The freestream Mach number is \(M_{\infty } = 0.73\), the angle of attack is \(\alpha = 3.5^{\circ }\), and the chord-based Reynolds number is \({\mathrm{Re}}_{c} = 1.9\times 10^6\). The obtained velocity fields are processed by sparsity-promoting dynamic mode decomposition to identify the dominant dynamic features contributing strongest to the buffet flow field. Two pronounced dynamic modes are found which confirm the presence of two main features of the proposed feedback loop. One mode is related to the shock wave oscillation frequency and its shape includes the movement of the shock wave and the coupled pulsation of the recirculation region downstream of the shock wave. The other pronounced mode represents the disturbances which form the downstream propagating part of the proposed feedback loop. The frequency of this mode corresponds to the frequency of the acoustic waves which are generated by these downstream traveling disturbances and which form the upstream propagating part of the proposed feedback loop. In this study, the post-processing, i.e., the DMD, is highlighted to substantiate the existence of this vortex mode. It is this vortex mode that via the Lamb vector excites the shock oscillations. The measurement data based DMD results confirm numerical findings, i.e., the dominant buffet and vortex modes are in good agreement with the feedback loop suggested by Lee.

Graphic abstract

中文翻译：

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跨音速自助餐的动态模式分解分析

超临界翼型周围的自助流场主要由机翼吸力侧的自持冲击波振荡决定。理论上认为，这种不稳定是由冲击波下游的流场中的扰动反馈回路驱动的，该冲击波的上游传播部分是由声波产生的。进行高速颗粒图像测速仪测量，以研究超临界DRA 2303机翼上跨音速自助流动中的此反馈回路。自由流马赫数为\（M _ {\ infty} = 0.73 \），迎角为\（\ alpha = 3.5 ^ {\ circ} \），基于和弦的雷诺数为\（{\ mathrm { Re}} _ {c} = 1.9 \乘以10 ^ 6 \）。通过稀疏促进动态模式分解处理获得的速度场，以识别对自助流场贡献最大的主导动力学特征。找到了两个明显的动态模式，这些模式确认了所提出的反馈环路的两个主要特征的存在。一种模式与冲击波的振荡频率有关，并且其形状包括冲击波的运动和冲击波下游的再循环区域的耦合脉动。另一个明显的模式代表形成建议的反馈回路的下游传播部分的干扰。该模式的频率对应于由这些下游行进干扰产生的声波的频率，这些声波形成了所提出的反馈环路的上游传播部分。在这项研究中，突出显示后处理，即DMD，以证实该涡旋模式的存在。正是这种涡旋模式通过兰姆向量激发了激波振荡。基于DMD的测量数据证实了数值结果，即主要的自助模式和涡旋模式与Lee建议的反馈回路非常吻合。

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