Viscous Vortex Ring Instability and Multistage Bifurcation

ZHANG Yajie; DU Ruiheng; WEI Yanju; YANG Yajing

doi:10.7652/xjtuxb202204009

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Viscous Vortex Ring Instability and Multistage Bifurcation

更新时间：2025-07-09

- Viscous Vortex Ring Instability and Multistage Bifurcation
- Vol. 56, Issue 4, Pages: 83-90(2022)
- 作者机构：
  
  1. 西安交通大学能源与动力工程学院,西安,710049
  2. 西安交通大学机械结构强度与振动国家重点实验室,西安,710049
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb202204009
  CLC： O351.2
- Online First：10 April 2022，
  
  Published：2022
- 稿件说明：
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ZHANG Yajie, DU Ruiheng, WEI Yanju, et al. Viscous Vortex Ring Instability and Multistage Bifurcation[J]. 2022, 56(4): 83-90.
DOI：

ZHANG Yajie, DU Ruiheng, WEI Yanju, et al. Viscous Vortex Ring Instability and Multistage Bifurcation[J]. 2022, 56(4): 83-90. DOI： 10.7652/xjtuxb202204009.

摘要

为了探究液滴撞击液池形成涡环的长期演化行为

以不同浓度的甘油水溶液为对象

研究其在滴入水池后的形态变化

通过高速摄像机对整个过程进行捕捉

发现其由初始液滴形态转变为涡环再到涡环失稳的一系列演化行为

之后分析其失稳与分叉的变化规律与主要影响因素。最后建立了涡环下沉速度的物理模型并进行了数学推导

建立了涡环前锋与尾部的运动无量纲表达式。研究表明

液滴入池后形成的涡环均不会一直稳定生长

而是在某一时刻发生失稳

失稳时刻与液滴本身属性有关。涡环解体为数个下沉的“手指”

在其下沉一定距离后

“手指”前锋沿其运动方向的垂向发生分叉

分叉后继续下沉

并重复出现自相似的分叉行为

且新产生的分叉前锋开始会获得一定程度的相对加速

最终涡环分解为一簇形如“皇冠”的分叉树。自始至终

其前锋与尾部运动均符合衰减运动的规律。本文对于由液滴撞击液池形成的涡环在池中的演变过程进行了时间和空间的拓展

且其由稳定涡环到突然失稳从而转变为分叉树的行为对流体中最复杂的湍流现象的形成机理具有一定的启发意义。

Abstract

In order to explore the long-term evolution and vortex rings when the droplet impacts pool

this paper studies the morphologic changes of glycerin aqueous solution with different concentrations when the solution drops in the pool. The whole process is captured by high-speed camera

and a series evolution processes were found. The initial droplet changes to vortex ring and then it is at instable vortex ring state. Change law and main influencing factors of instability and bifurcation are also analyzed. Finally

we have set a physical model of the vortex ring sinking velocity

performed mathematical derivation

and established a kinematic dimensionless expression for the front and tail of vortex ring. The result shows that the vortex ring forming after the solution drops in the pool does not always grow stably

but enter an instable state at a certain time. The time when instability occurs is related to the attribute of the droplet. The vortex ring would break down into several sinking “fingers”. After sinking for a certain depth

the “finger” front would bifurcate vertically along its movement direction and then continues to sink with similar bifurcation process. The new bifurcation front begins to obtain a certain relative acceleration

and finally the vortex ring breaks down into a cluster of bifurcation trees like “crowns”. During the whole period

its front and tail movements are in accordance with the law of attenuation movement. In this paper

the evolution process of the vortex ring which forms when the droplet impacts the pool is expanded spatially and temporally

and its transformation

from stable ring to instable ring suddenly and to bifurcation tree

has some inspirational significance for us to explore the formation mechanism of the most complex turbulence phenomenon in the fluid.

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