A parallel stability analysis of a trailing vortex wake
A parallel stability analysis of a trailing vortex wake
复制标题
尾涡尾流的并行稳定性分析
DOI：
10.1017/jfm.2017.866
复制
发表时间：
2018
影响因子：
3.7
通讯作者：
L. Cattafesta
中科院分区：
文献类型：
--
作者：
Adam M. Edstrand;P. Schmid;K. Taira;L. Cattafesta
在航空和海上应用中会产生拖尾涡流，并产生各种难以控制的不利影响。稳定性分析可以指导流量控制设计者确定合适的频率、波长和位置，这些频率、波长和位置可能会导致不稳定性的激发，最终导致旋涡的破裂。然而，大多数尾涡模型都是远场模型，这使得稳定性分析结果的实施具有挑战性。因此，我们在形成区进行了稳定性分析，其中数值计算的基流既包含二维尾迹，也包含由NACA0012在$5^{CIRC}$迎角和基于弦的雷诺数$Re_{c}=1000$产生的尖端涡旋。平行的时间和空间分析表明，在后缘下游的3根弦上，存在7个不稳定振型：3个来自时间分析，4个来自空间分析。这三个时间不稳定性类似于空间分析中的三个不稳定模，尾迹不稳定性在两种分析中都占主导地位。定域于涡旋的螺旋模与基流同向旋转，这与Batchelor涡模式的逆转$m=-1$不稳定性相反，这可能是由于基流涡旋的形成性质所致。第四种空间模式局限于叶尖涡区。频谱的连续部分包含振荡解和波包解，这促使使用波包分析来分析流场和群速度。全双全局谱的结构和细节将有助于导航有效控制策略的设计空间，以加速持续翼尖漩涡的衰减。
Trailing vortices are generated in aeronautical and maritime applications and produce a variety of adverse effects that remain difficult to control. A stability analysis can direct flow control designers towards pertinent frequencies, wavelengths and locations that may lead to the excitation of instabilities, resulting in the eventual breakup of the vortex. Most models for trailing vortices, however, are far-field models, making implementation of the findings from stability analyses challenging. As such, we perform a stability analysis in the formative region where the numerically computed base flow contains both a two-dimensional wake and a tip vortex generated from a NACA0012 at a $5^{\circ }$ angle of attack and a chord-based Reynolds number of $Re_{c}=1000$ . The parallel temporal and spatial analyses show that at three chord lengths downstream of the trailing edge, seven unstable modes are present: three stemming from the temporal analysis and four arising in the spatial analysis. The three temporal instabilities are analogues to three unstable modes in the spatial analysis, with the wake instability dominating in both analyses. The helical mode localized to the vortex co-rotates with the base flow, which is converse with the counter-rotating $m=-1$ instabilities of a Batchelor vortex model, which may be a result of the formative nature of the base-flow vortex. The fourth spatial mode is localized to the tip vortex region. The continuous part of the spectrum contains oscillatory and wavepacket solutions prompting the utilization of a wavepacket analysis to analyse the flow field and group velocity. The structure and details of the full bi-global spectrum will help navigate the design space of effective control strategies to hasten decay of persistent wingtip vortices.