飞行器尾涡对的不稳定性建模  

Instability of Aircraft Multiple Trailing Vortex Pairs

作　　者：陈俪芳 王志博[1] 孙刚[1] 

机构地区：[1]复旦大学航空航天系,上海200433

出　　处：《应用数学和力学》2016年第8期863-872,共10页Applied Mathematics and Mechanics

基　　金：国家重点基础研究发展计划(973计划)(2014CB744802)~~

摘　　要：为了确定飞行器尾流的保持距离和诱导失稳运动性质,首先在一阶近似Biot-Savart定律的基础上,推导了任意多个涡对的诱导运动模型,进而利用线性组合方法得到涡系诱导运动的对称以及反对称模态,并结合模态矩阵特征值的性质描述对称分布涡系的稳定性.因为尾涡结构的不稳定性依赖于相应的模态矩阵特征值的取值,所以在利用对称分布的二涡对的模态验证所推导的模态矩阵理论的正确性的基础上,进一步给出了三涡对的模态矩阵对应的失稳模态.理论推导和特征值的计算显示随着涡丝数量的不断增加,三涡系的不稳定性增强,并且涡系对扰动的放大作用增强.For aircrafts the wake vortex separation and the disturbance-induced vortex instability draw more and more concerns.A 1st-order approximation of the Biot-Savart law was used to build the induced motion model for arbitrarily multiple vortex pairs.Symmetric and antisymmetric modes of the induced motion of vortex pairs were deduced with the linear combination method.The properties of the modal matrix eigenvalues were obtained to describe instability of the multiple vortex pairs.The modes of 2 vortex pairs were used for validation of the proposed model,which was thereafter extended to 3 vortex pairs to give the instable modes corresponding to the modal matrices.The theoretical analysis and eigenvalue calculation show that,with the increase of the number of vortex filaments,the instability of the 3 vortex pairs will rise,and the amplification effects of the vortex system on the disturbance will highten.

关 键 词：涡丝 模态矩阵 特征值 尾涡失稳 

分 类 号：O355[理学—流体力学]