三维涡环与自由表面的粘性相互作用  

Interactions of Three-dimensional Viscous Vortex Rings with a Free Surface

作　　者：吴锤结[1] 王安 马晖扬[2] 

机构地区：[1]空军气象学院流体力学研究中心,南京211101 [2]中国科技大学研究生院,北京100039

出　　处：《水动力学研究与进展（A辑）》1997年第4期478-496,共19页Chinese Journal of Hydrodynamics

摘　　要：本文用VOF(Volume of Fluid)方法数值模拟了三维涡环与自由表面的粘性相互作用.重点考察了Froude数、Weber数、初始扰动及密度分层对涡环与自由表面相互作用的影响.结果表明:由于粘性的存在,使得涡环与自由表面的相互作用与无粘情形相比有许多不同.粘性的作用主要体现在涡量的耗散和新的二次涡环的产生;对自由表面变形而言,Froude数是主要的控制参数,Froude数越大,自由表面变形越显著,而Weber数的影响作用则不大;在Froude数较大时,涡环与自由表面相互作用会使得自由表面上出现轴对称的快速发展的行波,而当Froude数较小时,自由表面的变形形式较为复杂;当存在初始周向扰动时,水下涡环环量的非均匀分布会在自由表面上留下与实验中观察到的纵向沟槽相对应的水面痕迹.这些非轴对称、短波的表面痕迹正是综合孔径雷达(SAR)所能探测到的;自由表面的存在可削弱流场中的扰动,对流场中的涡环的不稳定性有抑制作用;在密度分层的流体中,水下涡环演化规律仍与均质流体中的定性大致相同,仅在定量数值上有所不同.在密度分层流中,自由表面的存在抑制了内波的发展,因而亦抑制了内波对自由表面的影响,使得密度分层对涡环与自由表面的相互作用影响不大.With the three-dimensional VOF method, the interactions of three-dimensional non-axisymmet-ric vortex rings with a free surface in an uniform or density stratified incompressible viscous fluid are numerically simulated in this paper. The influence of the Froude number, the surface tension, the initial disturbance alone the circumference direction of the ring and the non-constant distribution of density of fluid are studied. The re-sults show that the interaction between a viscous vortex ring and a free surface is different from the inviscid one. The effect of the viscosity is mainly shown in the diffusion of vorticity and the generation of secondary vortex ring. For the deformations of the free surface, the most significant parameter is the froude number. The bigger it is, the larger the deformations will be. The Weber number has only little influence. When the Froude number is large, rapidly developing axisymmetric travelling-waves will appear on the surface. While the Froude number is small, the deformation patterns of the free surface will be quite complex. When the initial flow field is disturbed around in the circumferential direction, due to the uneven distributed vorticity within the vortex ring, there are some corresponding scars on the free surface, which were observed in experiments. These non-axisymmetric short waves can be detected by a synthetic aperture radar (SAR). The free surface can obstruct the disturbance and restrain the instability in the flow field. In a density stratified flow field, the evolution of a vortex ring is al-most the same as in an uniform flow field. in a stratified fluid, the free surface restrains the development of inter-nal waves, resulting in little influence on the interaction between a vortex ring and the free surface.

关 键 词：涡环 自由表面 计算流体力学 VOF 粘性 N-S方程 

分 类 号：O357.1[理学—流体力学]