Transient growth in the near wake region of the flow past a finite span wing
Transient growth in the near wake region of the flow past a finite span wing
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经过有限翼展机翼的气流近尾流区域的瞬态增长
DOI：
10.1017/jfm.2019.110
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发表时间：
2019
影响因子：
3.7
通讯作者：
L. Jacquin
中科院分区：
文献类型：
--
作者：
Navrose;V. Brion;L. Jacquin
我们研究流过有限展弦比 ($AR$) 机翼的最佳扰动。优化是在完全发展的流动稳定的情况下进行的。对时间范围 ($T$)、雷诺数 ($Re$)、$AR$、迎角和机翼横截面几何形状（平板和 NACA0012 翼型）的参数研究表明，线性最佳扰动的一般形状在探索的参数空间上保持不变。最佳扰动位于机翼表面附近，以弦向周期性结构的形式存在，其强度从根部向尖端递减。以线性最优扰动作为初始条件，对带或不带非线性项的扰动方程进行直接时间积分。在这两种情况下，最佳扰动都会演变为下游行波波包，其速度几乎与自由流的速度相同。波包的能量在近尾流区域增加，并且在非线性模拟中发现在超出涡卷卷起距离时几乎保持恒定。非线性波包导致尖端涡流的位移。在这种情况下，尖端涡流的运动类似于风洞实验中涡流蜿蜒/徘徊期间观察到的运动。在较高 $Re$ 下进行的计算结果表明，即使超出稳定流状态，源自机翼附近的扰动波包也可能导致尖端涡流的蜿蜒。
We investigate optimal perturbation in the flow past a finite aspect ratio ( $AR$ ) wing. The optimization is carried out in the regime where the fully developed flow is steady. Parametric study over time horizon ( $T$ ), Reynolds number ( $Re$ ), $AR$ , angle of attack and geometry of the wing cross-section (flat plate and NACA0012 airfoil) shows that the general shape of linear optimal perturbation remains the same over the explored parameter space. Optimal perturbation is located near the surface of the wing in the form of chord-wise periodic structures whose strength decreases from the root towards the tip. Direct time integration of the disturbance equations, with and without nonlinear terms, is carried out with linear optimal perturbation as initial condition. In both cases, the optimal perturbation evolves as a downstream travelling wavepacket whose speed is nearly the same as that of the free stream. The energy of the wavepacket increases in the near wake region, and is found to remain nearly constant beyond the vortex roll-up distance in nonlinear simulations. The nonlinear wavepacket results in displacement of the tip vortex. In this situation, the motion of the tip vortex resembles that observed during vortex meandering/wandering in wind tunnel experiments. Results from computation carried out at higher $Re$ suggest that, even beyond the steady flow regime, a perturbation wavepacket originating near the wing might cause meandering of tip vortices.