Structures of wing-tip vortices at low Reynolds numbers and their modelling
Structures of wing-tip vortices at low Reynolds numbers and their modelling
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低雷诺数翼尖涡结构及其建模
DOI：
10.1088/1873-7005/ab9b63
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Yuji Hattori
中科院分区：
文献类型：
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作者：
Hiroshi Koizumi;Yuji Hattori
采用直接数值模拟的方法研究了低雷诺数（Rec= 103）下翼尖涡的结构。在确定翼尖涡的基本特征后，对轴向涡量和速度的分布进行了详细的研究。涡度分布由对称分量、涡核椭圆变形的四极分量和其他小分量组成。涡度的对称分量与Moore-Saffman模型（Moore & Saffman 1973 Proc. R. Soc）基本一致。长。333,491)的三种类型的机翼平台考虑：矩形，椭圆和三角翼。由于从边界层脱落的涡片不完全卷起，边界层分量较小，因此轴向速度对称分量的数值计算结果与Moore-Saffman模型的吻合度不高。然而，Moore-Saffman模型对轴向速度的涡旋分量进行了正确的预测。涡核的椭圆变形由长轴的长径比和方向来表征。椭圆变形在流方向上是不均匀的，这意味着翼尖涡不能总是用二维涡对来模拟。椭圆变形沿流方向的演化可以用边界层近似下的二维涡旋动力学来描述。椭圆涡旋片在应变场中的运动方程正确地预测了方向变化率，但不能预测展弦比的变化率，而导出的涡旋轴对称化方程对展弦比的变化率给出了较好的预测。
The structures of wing-tip vortices at a low Reynolds number (Rec= 103) are studied by direct numerical simulation. After confirming the basic features of the wing-tip vortices, the distributions of axial vorticity and velocity are investigated in detail. The vorticity distribution consists of a dominant symmetric component, quadrupole components responsible for elliptical deformation of the vortex core and the other small components. The symmetric component of vorticity is in reasonable agreement with the Moore-Saffman model (Moore & Saffman 1973 Proc. R. Soc. Lond. 333, 491) for the three types of wing planform considered: the rectangular, elliptic and delta wings. The agreement between numerical results and the Moore-Saffman model is not good for the symmetric component of axial velocity since the boundary layer component is small owing to the incomplete roll-up of the vortex sheet shed from the boundary layer. However, the vortex component of the axial velocity is correctly predicted by the Moore-Saffman model. The elliptical deformation of the vortex core is characterized by the aspect ratio and the direction of the major axis. It is found that the elliptical deformation is not uniform in the streamwise direction, which implies that the wing-tip vortices cannot be always modelled by a two-dimensional vortex pair. The evolution of the elliptical deformation along the streamwise direction is shown to be described by two-dimensional vortex dynamics under the boundary-layer approximation. The equations of motion of an elliptic vortex patch in a straining field predicts correctly the rate of change of the direction, but fails to predict that of the aspect ratio, for which the equation derived for axisymmetrization of vortices gives a good prediction.