Abstract The response of a NACA0012 airfoil impacted by vortical gusts is investigated performing Direct Numerical Simulations of the two-dimensional incompressible flow. Taylor vortices of different diameter and intensity located at different vertical separations with respect to the airfoil are deployed in the free stream. These vortices, which are characterized by its compact distribution of vorticity, are advected downstream to interact with the airfoil, set at a fixed angle of attack. For the low Reynolds number used in these simulations ( R e = 1000 ), the effect of the different parameters defining the vortical gust and the impact is characterized. It is found that the change in the time evolution of the variation of the lift coefficient with respect to the steady state, Δ C l ( t ) , is fairly independent on the angle of attack, at least in the range of α considered in this study. Furthermore, it is found that the time at which the peak in Δ C l is produced scales with the diameter of the viscous core of the vortex and the free-stream velocity, D ∕ U ∞ . On the other hand, the maximum value of Δ C l is roughly proportional to the non-dimensional vortex circulation, but varies non-linearly with the vertical distance between the vortex and the airfoil. This dependency can be captured by scaling Δ C l with the relative intensity of the vertical velocity induced over the airfoil and the free-stream velocity ( w h ∕ U ∞ ), where the former is defined as an integral of the vortex velocity profile over the chord of the airfoil. Using this scaling, the profiles of Δ C l ( t U ∞ ∕ D ) ∕ ( w h ∕ U ∞ ) collapse over a single curve for the different vortex intensities, sizes and vertical separations considered in the present study, specially during the initial evolution of the vortical gust impact. The self-similar profile of Δ C l ( t U ∞ ∕ D ) ∕ ( w h ∕ U ∞ ) is found to depend on the velocity profile of the vortex (i.e., Taylor vortices versus Lamb–Oseen vortices). However, the peak aerodynamic force and the time to peak aerodynamic force seem to scale with D ∕ U ∞ and w h ∕ U ∞ irrespective of the velocity profile of the vortex, suggesting that our definition of w h is sufficiently robust.

中文翻译：

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低雷诺数下旋风阵风对翼型的影响分析

摘要 NACA0012 机翼受旋风阵风影响的响应通过二维不可压缩流的直接数值模拟进行了研究。位于相对于翼型的不同垂直间隔处的不同直径和强度的泰勒涡在自由流中展开。这些涡流的特点是其涡量分布紧凑，向下游平流与机翼相互作用，设置在固定的迎角。对于这些模拟中使用的低雷诺数 (Re = 1000)，定义了旋风阵风和冲击的不同参数的影响是特征化的。发现升力系数相对于稳态的变化随时间的变化ΔC l ( t ) 与攻角相当独立，至少在本研究中考虑的 α 范围内。此外，发现产生 Δ C l 峰值的时间与涡旋粘性核心的直径和自由流速度 D ∕ U ∞ 成比例。另一方面，ΔC l 的最大值与无量纲涡流环流大致成正比，但随涡流与翼型之间的垂直距离呈非线性变化。这种依赖性可以通过用翼型上引起的垂直速度和自由流速度 (wh ∕ U ∞ ) 的相对强度来缩放 Δ C l 来捕获，其中前者被定义为涡流速度分布在整个翼型上的积分。翼型的弦。使用这种缩放比例，对于不同的涡流强度，Δ C l ( t U ∞ ∕ D ) ∕ ( wh ∕ U ∞ ) 的轮廓在一条曲线上坍塌，本研究中考虑的尺寸和垂直间隔，特别是在涡旋阵风影响的初始演变过程中。发现 Δ C l ( t U ∞ ∕ D ) ∕ ( wh ∕ U ∞ ) 的自相似分布取决于涡旋的速度分布（即泰勒涡旋与兰姆-奥森涡旋）。然而，峰值气动力和达到峰值气动力的时间似乎与 D ∕ U ∞ 和 wh ∕ U ∞ 成比例，而与涡旋的速度分布无关，这表明我们对 wh 的定义足够稳健。