三维定常分离流和涡运动的定性分析研究

Analytic Studies for Three Dimensional Steady Separated Flows and Vortex Motion

本文由两部分组成。第一部分研究和分析了物体表面上的分离形态,指出若分离线从奇点始,该奇点为鞍点;若在奇点终,该奇点为结点。若分离线上有很多奇点,其鞍点和结点是交替分布的。分离线的起始,可能有三种形态:一种称之为闭式分离的鞍点起始;一种为正常点起始;一种为鞍、结点组合形态起始。可以把正常点起始和距离很近的鞍、结点组合形态起始称之为开式分离。在一定条件下,闭式分离的形态,先转变为鞍、结点组合的形态,然后过渡到正常点的开式分离。第二部分研究了旋涡沿其轴线发展过程中,其横截面流线形态的发展,指出旋涡轴线上物理量λ=(1/ρ)(ρw/z)是决定流线形态的重要参量。如果λ>0,截面流线在涡心附近是稳定的螺旋点形态。如果λ<0,为不稳定的螺旋点形态,如果λ=0,流线形态是中心型的,当沿涡轴λ由正变负或由负变正时,相应在涡心附近截面流线由稳定螺旋点形态变为不稳定螺旋点形态,或由不稳定螺旋点形态变为稳定螺旋点形态;并且从λ由正到负的变号点起,截面流线产生稳定的极限环,或从λ由负到正的变号点起,产生不稳定的极限环。旋涡破裂只能发生在截面流线为不稳定螺旋点形态的区域中,在通过涡轴的纵向平面内,破裂点处的流线形态是鞍型的。破裂涡的合拢点处在不稳定的极限环区域内。

This paper consists of two parts.In the first part, the distribution rule of singular points along the separation line is given. If the separation line starts from singular point, then this point must be a saddle point. If the separation line ends at the singular point, then this point must be a nodal point or spiral node. If many singular points are distributed at separation line, two saddle points or two nodal points cannot directly connect each other along the separation line. There are three types for starting pattern of separation lines. One starts from a saddle point. We call it as closed separation line. The second starts from regular point which is open separation line. The third is the combination of saddle point with nodal point.In the second part, the development of a vortex along its axis z is studied. Depending on whether λ=(1/p)((?)ρω/(?)z)at the axis z is positive or negative, we will have the transversal streamline being spiral inward vortex ( called as stable ) or spiral outward vortex (called as unstable). Where w is the velocity component along the axis z and p is the density of gas flow. The vortex bursting is accompanied with an unstable spiral. If λ variates from positive to negative along the axis z or from negative to positive, the stable limiting cycle for the transversal, streamline equation or unstable limiting cycle will exist in the region behind the place where λ= 0 . In the longitudinal section at bursting point, the section streamlines are of saddle type. The numerical results given by this paper agree with all qualitative pictures mentioned above.