Abstract Unsteady pressures, forces, and pitching moments generated by foils experiencing vibratory motion in an incompressible, attached flow configuration are studied within this work. Specifically, two-dimensional, unsteady potential flow and unsteady Reynolds-Averaged Navier–Stokes calculations are performed on various Joukowski foils undergoing sinusoidal, variable amplitude, small-scale pitching motion at a chord-based Reynolds number of 10 6 over a range of reduced frequencies between 0.01–100. These calculated results from both approaches are compared directly to predictions from implementing the Theodorsen model, which treats foils as infinitely thin, flat plates that shed a planar sheet of vorticity. The effects of relaxing these seemingly strict conditions are explored, and the particular terms which control the unsteady responses are identified and discussed. For increasing pitch amplitudes and reduced frequencies the shed wake is seen to become quite non-planar and to form coherent vortex structures. Despite this wake behavior, the normalized airfoil responses at the disturbance reduced frequency are seen to be largely unaffected. However, non-negligible responses are generated across a wide range of other frequencies. Potential flow calculations for symmetric Joukowski foils show that there is marginal effect of foil thickness at reduced frequencies less than one. For higher reduced frequency conditions however, the unsteady lift response is seen to experience both an amplification of level and a phase shift relative to the Theodorsen model. A specific augmenting expression is developed for this behavior through analysis within the potential flow framework.

中文翻译：

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考虑翼厚度和尾流运动的小尺度俯仰运动引起的翼型不稳定响应

摘要 在这项工作中，研究了由箔在不可压缩的附着流配置中经历振动运动产生的不稳定压力、力和俯仰力矩。具体来说，二维非定常势流和非定常雷诺平均纳维-斯托克斯计算是在各种 Joukowski 箔上进行的，这些 Joukowski 箔在基于弦的雷诺数为 10 6频率在 0.01–100 之间。将这两种方法的这些计算结果直接与实施 Theodorsen 模型的预测进行比较，该模型将箔视为无限薄的平板，可以摆脱平面涡旋片。探索放宽这些看似严格的条件的影响，并确定并讨论了控制非稳态响应的特定术语。对于增加的俯仰幅度和降低的频率，可以看到脱落的尾流变得非常非平面并形成相干的涡旋结构。尽管有这种尾流行为，在扰动降低频率下的归一化翼型响应被认为在很大程度上不受影响。然而，在广泛的其他频率范围内会产生不可忽略的响应。对称 Joukowski 箔的势流计算表明，在频率低于 1 的降低频率下，箔厚度存在边际效应。然而，对于更高的降低频率条件，相对于 Theodorsen 模型，不稳定的提升响应会经历电平放大和相移。