Scaling the vorticity dynamics in the leading-edge vortices of revolving wings with two directional length scales
Scaling the vorticity dynamics in the leading-edge vortices of revolving wings with two directional length scales
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DOI：
10.1063/5.0024213
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发表时间：
2020-12
影响因子：
4.6
通讯作者：
Nathaniel H. Werner;Junshi Wang;Haibo Dong;A. Panah;Bo Cheng
中科院分区：
文献类型：
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作者：
Nathaniel H. Werner;Junshi Wang;Haibo Dong;A. Panah;Bo Cheng
在旋转翼或扑翼中，径向行星涡倾斜（PVTr）是一种有助于消除前缘涡（LEV）内径向（展向）涡量的机制，而涡量平流则增加其强度。量纲分析预测，PVTr和平流应与机翼展弦比（AR）以相同的方式成比例，假定使用统一的特征长度。然而，作者以前的工作表明，随着AR的增加，涡度平流比PVTr下降得更快，这表明应该应用单独的归一化。在这里，我们的目标是开发一个全面的缩放的PVTr和涡度平流的基础上使用计算流体动力学的模拟结果。对攻角为45°的旋转矩形机翼进行了两组模拟，第一组模拟的翼尖速度保持不变，因此在回转半径处确定的雷诺数（Re）等于110，第二组模拟的机翼角速度保持不变，因此在一个弦长处确定的Re等于63.5。我们提出了两个独立的长度尺度的基础上LEV几何，即，径向和切向方向的翼展和垂直方向的翼弦。LEV在径向和切向的尺寸受到翼展的限制，而垂直深度保持不变。使用两个长度尺度不仅成功地预测了PVTr和涡度平流的尺度，而且还预测了三个方向上平流的相对大小，即，切向平流最强，其次是垂直（下洗），然后是径向，可以忽略不计。
In revolving or flapping wings, radial planetary vorticity tilting (PVTr) is a mechanism that contributes to the removal of radial (spanwise) vorticity within the leading-edge vortex (LEV), while vorticity advection increases its strength. Dimensional analysis predicts that the PVTr and advection should scale with the wing aspect-ratio (AR) in identical fashion, assuming a uniform characteristic length is used. However, the authors’ previous work suggests that the vorticity advection decreases more rapidly than the PVTr as AR increases, indicating that separate normalizations should be applied. Here, we aim to develop a comprehensive scaling for the PVTr and vorticity advection based on simulation results using computational fluid dynamics. Two sets of simulations of revolving rectangular wings at an angle of attack of 45° were performed, the first set with the wing-tip velocity maintained constant, so that the Reynolds number (Re) defined at the radius of gyration equals 110, and the second set with the wing angular velocity maintained constant, so that Re defined at one chord length equals 63.5. We proposed two independent length scales based on LEV geometry, i.e., wing-span for the radial and tangential directions and wing chord for the vertical direction. The LEV size in the radial and tangential directions was limited by the wing-span, while the vertical depth remained invariant. The use of two length scales successfully predicted not only the scaling for the PVTr and the vorticity advection but also the relative magnitude of advection in three directions, i.e., tangential advection was strongest, followed by the vertical (downwash) and then the radial that was negligible.