Dynamics in the Evolution of Spherical Micro-Bubble in Water and Its Control

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Dynamics in the Evolution of Spherical Micro-Bubble in Water and Its Control

更新时间：2025-07-09

- Dynamics in the Evolution of Spherical Micro-Bubble in Water and Its Control
- Vol. 45, Issue 11, Pages: 27-33+90(2011)
- 作者机构：
  
  西安交通大学能源与动力工程学院,西安,710049
- 作者简介：
- 基金信息：
- DOI：
  CLC： O322
- Online First：10 November 2011，
  
  Published：2011
- 稿件说明：
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Dynamics in the Evolution of Spherical Micro-Bubble in Water and Its Control[J]. 2011, 45(11): 27-33+90.
DOI：

Dynamics in the Evolution of Spherical Micro-Bubble in Water and Its Control[J]. 2011, 45(11): 27-33+90. DOI：

摘要

从动力学观点分析了水中球形微气泡无外部激励时平衡态的稳定性及受到声波激励时受迫振荡的复杂动力学行为; 分析了无声波激励时平衡态的稳定性和奇点类型

并对其相应的物理现象进行了解释; 对于受到声波激励的微气泡受迫振荡

结合Poincaré映射法确定了Poincaré映射的不动点

并根据Floquet理论分析了周期解的稳定性及分岔.分析表明:无声波激励时水中球形微气泡的平衡态是一稳定焦点

而受到声波激励时

随着激励频率的升高

微气泡的周期振荡从失稳转变为倍周期运动

进而转变成准周期运动

最终进入混沌状态; 随着压力脉动幅值的增加

微气泡的振荡经过一系列倍周期分岔通向混沌.研究结果揭示了水中球形微气泡的复杂动力学特性

为进一步控制奠定了基础.

Abstract

The stability of the equilibrium state of evolution without external excitation and the complex dynamics of forced oscillation due to sound propagation are discussed for a spherical micro-bubble in water. First

the stability of the equilibrium state of evolution without sound wave propagation was analyzed

and the corresponding type of the singular point was determined. Second

the shooting method was combined with the Poincaré map to obtain the fixed point for forced oscillation due to sound excitation. Third

the stability and bifurcation were examined with the Floquet theory. The results show that from viewpoint of nonlinear dynamics

the equilibrium state is a stable focus for a spherical micro-bubble evolution in water without external excitation. With the increase in sound frequency

the 1-period oscillation becomes unstable

and the oscillation behaves in a double-periodic manner

then in a quasi-periodic manner

and finally chaotically. Additionally

with the increase in the amplitude of the pressure fluctuation

the micro-bubble eventually oscillates chaotically via a series of period-doubling bifurcations.

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Keywords

references

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