摘要
本文研究了沿其轴向运动的亚声速和超声速旋涡的性状，指出两者完全不同。在加速区，于涡轴附近，亚声速旋涡的横截面流线即横截面上的速度场的向量线为由外向内转的稳定螺旋点形态，空间流线沿其轴向是收缩的，而超声速旋涡的横截面流线为由内向外转的不稳定螺旋点形态，空间流线沿其轴向是散开的。在减速区，两者的情况也恰好相反。此外，当旋涡由加速区过渡到减速区时，两者横截面流线方程在涡轴附近的Ｈｏｐｆ分叉情况也不同，亚声速情况出现稳定的极限环，而超声这情况出现不稳定的极限环。文中还讨论了涡破裂问题，对于亚声速旋涡，其破裂位置发生在减速区。对于超声速旋涡，除非有激波出现，在减速区不会破裂；在加速区。也不会出现破裂点为驻点的破裂形态。文中指出，水洞实验显示不了超声速旋涡的形态，对亚声速旋涡有效的控制方法，不适用于超声速旋涡。
The vortex evolution along its axis is investigated by using topological theory.It is pointed out that . at the axis of vortex is an important parameter to determine the evolution mech- anism of vortex. If λ>0 along the axis,the sectional streamlines near the axis in the transversal plane possess a stable spiral(inward)pattern.If λ<0 along the axis,the transversal streamlines are unstable spiral(out- ward).As the sign of λ changes along the axis from positive to negative or from negative to positive,the flow pattern in the transversal plane willyield a Hopf bifurcation starting from the position where λ=0.Mean-while,the former is a stable limit cycle and the later an unstable one.The vortex bursting is accompanied with an unstable transversal spiralpattern and the decrease of axial velocity. If the vortex is stable initially,i.e. λ>0 in the initial region, the Hopf bifurcation certainly appears inadvance of the bursting point.There are three kinds of vortex burstingwhich are the bubble type,bubble-spiral type,and spiral type. For thesubsonic vortex moving forward along its axis with M_z<1 at high Reyn-olds number,the sign of λ is the same as. and the opposite with.It means that in the adverse pressure region the unstable trans-versal spiral pattern is just accompanied with the decrease of axial veloc-ity. As the vortex moves forward along the axis from the favorable pres-sure to the adverse pressure,the initially stable vortex will becomebursting later through the Hopf bifurcation occuring in the adversepressure region. For the supersonic vortex moving forward along its axiswith M_z>1 at high Reynolds number, the sign of λ is the same as。and the opposite with.It means that in the region of unstablespiral pattern the axial velocity is increased,and that in the region ofstable spiral pattern the axial velocity is decreased.So the vortex inthe supersonic case is not easy to burst except where the shock waveexists.
出处
《空气动力学学报》
CSCD
北大核心
1995年第3期259-264,共6页
Acta Aerodynamica Sinica
关键词
旋涡运动
超声速旋涡
旋涡破裂
拓扑分析
ortex motion,subsonic and supersonic vortex,Hopf bifurcation,vortex bursting,topological analysis.
