Abstract This study presents an investigation of the aerodynamic damping of light dynamic stall phenomena on a pitching NACA 0012 airfoil via Dynamic Modal Decomposition (DMD) and Proper Orthogonal Decomposition (POD) techniques. DMD analysis predicts a dominant mode having the same frequency of the pitching excitation and contributing all of the aerodynamic damping of the system. The temporal orthogonality of the DMD technique renders all other DMD modes orthogonal to both the dominant DMD mode as well as the pitching motion, resulting in zero aerodynamic work due to these DMD modes. However, the lack of temporal orthogonality of POD modes implies several modes contributing to the aerodynamic damping of the system. The leading-edge suction and the trailing-edge vortex were considered the most energetic features by the two most dominant POD modes and was also observed as the most significant spatial feature in the dominant DMD mode shape. A recently developed Hilbert transform-based methodology was extended here for computing chord-wise intra-cycle aerodynamic damping distribution. This method shows large variations of the intra-cycle aerodynamic damping distribution obtained from DDES surface pressure data over the cycle, which poses a challenge to extract meaningful information for possible flow control applications. However, the dominant DMD modal aerodynamic damping distribution shows no intra-cycle variations and predicts negative damping hot-spots near the leading and trailing edges of the chord. Such conclusions are significantly different than observed for an attached flow case or observed in a related study considering a deep dynamic stall regime at lower Reynolds number.

中文翻译：

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基于模态分析的俯仰翼型轻动力失速气动阻尼研究

摘要 本研究通过动态模态分解 (DMD) 和适当正交分解 (POD) 技术对俯仰 NACA 0012 机翼上的轻动态失速现象的气动阻尼进行了研究。DMD 分析预测主模式具有相同的俯仰激励频率并贡献系统的所有气动阻尼。DMD 技术的时间正交性使所有其他 DMD 模式与主要 DMD 模式和俯仰运动正交，由于这些 DMD 模式导致空气动力功为零。然而，POD 模式缺乏时间正交性意味着有几种模式有助于系统的空气动力学阻尼。前缘吸力和后缘涡流被认为是两种最主要的 POD 模式中能量最高的特征，并且也被观察为主要 DMD 模式形状中最重要的空间特征。最近开发的基于 Hilbert 变换的方法在这里被扩展，用于计算弦向内循环空气动力学阻尼分布。该方法显示了从 DDES 表面压力数据获得的循环内循环空气动力学阻尼分布的巨大变化，这对为可能的流量控制应用提取有意义的信息提出了挑战。然而，占主导地位的 DMD 模态空气动力学阻尼分布没有显示出周期内变化，并预测弦的前缘和后缘附近会出现负阻尼热点。