细长体截面绕流中的一种临界状态

基金项目: 国家自然科学基金资助项目(10172017);航空基础科学基金资助项目(02A51048)

A Critical Pattern of Crossflow Around a Slender

Institute of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100083, P. R. China

摘要: 应用拓扑分析的方法研究了细长体截面绕流拓扑结构的演变过程．指出随着细长体背涡的发展，导致截面流场的拓扑结构发生变化，会出现一种临界流动状态．在这种临界流态下，流场中会出现一种高阶奇点．这种高阶奇点的指数为-3/2．这种高阶奇点是结构不稳定的，稍有扰动就会产生分叉，使流场的拓扑结构发生变化．
- 细长体 /
- 高阶奇点 /
- 分叉 /
- 结构稳定性
Abstract: Topological structure of a slender crossflow was discussed with topological analysis.It is pointed that the development of slender vortices leads to the change of topological structure about cross flow,and a critical flow pattern will appear.There is a high-order singular point in this critical flow pattern.And the index of the high-order singular is -3/2.The topological structure of this singular point is instable,so bifurcation will occur and the topological structure of flowfield will be changed by little disturbance.
- slender /
- high-order singular point /
- bifurcation /
- structure stability

[1]	Allen H J,Perkins E W.Characteristcs of flow over inclined bodies of revolution[R]. NACA RMA,50L07,1951.
[2]	Nielsen J N.Nonlinearities in missile aerodynamics[R]. AIAA Paper,78-21，1978.
[3]	Ericsson L E.Karman vortex shedding and the effect of body motion[J].AIAA J,1980，18(8)：935—944. doi: 10.2514/3.50837
[4]	Keener E R，Chapman G T.Similarity in vortex asymmetric over slender bodies and wings[J].AIAA J,1977，15(9)：1370—1372. doi: 10.2514/3.60795
[5]	Lowson M V，Ponton A J.Symmetry breaking in vortex flows on conical bodies[J].AIAA J,1992,30(6)：1576—1583. doi: 10.2514/3.11103
[6]	陆启韶.常微分方程的定性方法和分叉[M].北京:北京航空航天大学出版社，1989.
[7]	张芷芬,丁同仁,黄文灶,等.微分方程定性理论[M].北京:科学出版社，1985.
[8]	Hunt J C R,Abell C J,Peterka J A,et al.Kinematical studies of the flows around free or surface-mounted obstacles; applying topology to flow visualization[J].Journal of Fluid Mechanics,1978,86(1)：179—200. doi: 10.1017/S0022112078001068

点击查看大图