Generalized helical vortex pairs
Generalized helical vortex pairs
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广义螺旋涡对
DOI：
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发表时间：
2018
影响因子：
3.7
通讯作者：
S. Le Dizès
中科院分区：
文献类型：
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作者：
E. Durán Venegas;S. Le Dizès
用涡丝方法得到了描述螺旋对反向旋转涡相互作用的新解。假设涡流具有较小的核心尺寸，从而可以使用截止理论根据毕奥-萨伐尔定律计算自诱导速度。这些新的涡结构不具有任何螺旋对称性，但它们具有空间周期性，并且在旋转和平移坐标系中是静止的。它们的属性，如径向变形，帧速度和诱导流，提供作为表征每个解决方案的四个几何参数的函数。当相互作用较弱时，也得到了近似解。这使我们能够提供显式表达式的旋转和平移速度的结构在此限制。一阶修正描述螺旋变形也计算和用于与数值结果进行比较。分析了螺旋线变形引起的涡核尺寸的变化。我们表明，这些变化有一个弱的影响的形状和特性的解决方案，我们已经考虑的参数范围。最后将计算结果应用于旋翼尾迹。它解释了如何这些解决方案可能描述直升机旋翼在垂直飞行的远尾迹。
New solutions describing the interaction of helical pairs of counter-rotating vortices are obtained using a vortex filament approach. The vortices are assumed to have a small core size allowing the calculation of the self-induced velocities from the Biot–Savart law using the cutoff theory. These new vortex structures do not possess any helical symmetry but they exhibit a spatial periodicity and are stationary in a rotating and translating frame. Their properties, such as radial deformation, frame velocity and induced flow, are provided as a function of the four geometric parameters characterizing each solution. Approximate solutions are also obtained when the mutual interaction is weak. This allows us to provide explicit expressions for the rotation and translation velocities of the structure in this limit. First-order corrections describing helix deformation are also calculated and used for comparison with the numerical results. The variation of the vortex core size induced by the helix deformation is also analysed. We show that these variations have a weak effect on the shape and characteristics of the solutions, for the range of parameters that we have considered. The results are finally applied to rotor wakes. It is explained how these solutions could possibly describe the far wake of an helicopter rotor in vertical flight.