基于全局线性稳定性分析的翼尖双涡不稳定特征演化机理

相比于机翼产生的孤立翼尖涡，加装小翼之后的翼尖涡表现出双涡甚至多涡结构，并且呈现出更加复杂的不稳定特征。为揭示翼尖双涡结构不稳定特征及其演化机理，采用体视粒子图像测速（SPIV）技术和全局线性稳定性分析（LAS）方法对不同雷诺数和攻角下带双叉弯刀小翼的M6机翼产生的翼尖涡结构在尾迹区的不稳定特征进行研究。试验结果表明，对称布置的双叉弯刀小翼产生的翼尖涡包含上/下小翼产生的主涡（上/下主涡）结构，两者构成近似等强度的同转涡对，在相互靠近的同时以20 rad/s的角速度相互缠绕。对上/下主涡瞬时涡核位置的统计分析表明，翼尖涡摇摆幅值随流向位置逐渐增大，随雷诺数的增加而增大，随攻角的增加先增大后减小。对16倍弦长的尾迹截面处的翼尖双涡结构进行全局时间稳定性分析，不同工况下，上/下主涡最不稳定模态（模态P/模态S）的稳定性曲线变化规律与摇摆幅值的变化规律相一致，表明翼尖涡的摇摆源自于其内在的不稳定性特征。增加流向扰动波数，发现模态P切向波数逐渐增加；而模态S则是径向波数逐渐增加。不同工况下，模态P的切向波数为5~6，扰动波数分布在2.75，5]的区间内，所对应的不稳定放大率均大于模态S，而不稳定放大率最大的模态扰动范围作用在上主涡的整个涡核区域，表明这种大切向波数的扰动模态在翼尖涡流控中的潜在价值，也意味着加装小翼会增加涡结构的个数，增强不稳定性的发展，有助于翼尖涡的快速失稳衰减。

Evolution mechanism of instability features of wingtip vortex pairs based on bi-global linear stability analysis

Compared with isolated wingtip vortices generated by the wings, vortex pairs or even more complex multi-vortices formed after the installation of winglets exhibit more intricate instability characteristics. In this paper, the instability characteristics of wingtip vortices generated by the M6 wings with split winglets under different Reynolds numbers and angles of attack, as well as along the 16 times chord length wake region, are experimentally investigated using the Stereoscopic Particle Image Velocimetry (SPIV) technology and bi-global Linear Stability Analysis (LSA) method. The experimental results show that wingtip vortices contain one upper primary vortex (Vortex-U) and one lower primary vortex (Vortex-L), which are respectively generated by the upper winglet branch and lower winglet branch. These two vortices form an approximately equal strength co-rotating vortex pair, intertwining with each other at the angular velocity of 20 rad/s. The statistical analysis of instantaneous vortex core positions of Vortex-U and Vortex-L show that the wandering amplitudes of the wingtip vortices increase gradually along the streamwise locations and with the increasing Reynolds numbers, while increase first and then decrease with the increasing angles of attack. Moreover, the instability curves of the most unstable modes of Vortex-U/Vortex-L, namely, Model-P/Mode-S, obtained from the temporal bi-global LSA share the same trends with those of wandering amplitudes, indicating that the wandering of wingtip vortices results from their inherent instability characteristics. By increasing the disturbance wavenumber in the flow direction, the tangential wavenumber in Mode-P increases gradually, while in Mode-S, the radial wavenumber increases gradually. Under different flow conditions, the tangential wavenumber of Mode-P is 5-6, the disturbance wavenumber is distributed in 2.75, 5], and the growth rates are always larger than those of Mode-S. Furthermore, the perturbation mode corresponding to the most unstable growth rate covers the whole vortex core region of Vortex-U, suggesting the remarkable prospect of this large tangential wavenumber mode for the wingtip vortex control, as well as indicating that the development of vortex instability can be manipulated by increasing the vortex number.