一种考虑时延的双气泡耦合振荡模型

A double-bubble coupled oscillation model considering time delay

基于单气泡Keller-Miksis振荡方程,在考虑时延的情况下,建立了一种双气泡耦合振荡计算模型。该模型将气泡振荡的周期分成若干份,初始扰动引起第一个气泡的半径在极短时间内变化而产生振荡并辐射声压,声压在传播一定时间后作用到第二个气泡,第二个气泡同样在短时间内做耦合振荡并反馈到第一个气泡,然后重复此过程。利用数值仿真在此模型的基础上分别研究了气泡振幅、半径、间距等参数对耦合振荡的影响。结果表明:初始扰动越大、两个气泡半径越接近,气泡耦合效应越明显;初始半径和平衡半径较大的气泡对耦合振荡有显著影响,振荡的频率向低频移动;气泡间距越大,耦合效应越弱;在某个特定距离处,气泡耦合效应的阻尼会异常减小或者增大。

Based on the Keller-Miksis oscillation equation of a single bubble, a calculation model of double-bubble coupled oscillation model is established by considering the time delay. The model divides the period of bubble oscillation into several parts. An initial disturbance causes the radius of the first bubble changing in a very short time to generate oscillation and radiate sound pressure. The radiated sound pressure acts on the second bubble after a certain time of propagation. The second bubble also oscillates in a short time and feeds back to the first bubble, and then this process would be repeated over and over again. Based on this model, the effects of bubble oscillation amplitude, radius and spacing on coupled oscillation are studied by numerical simulation. The results show that the stronger the initial disturbance and the closer the radius of the two bubbles, the more obvious the coupling effect;the bubble with larger initial radius and equilibrium radius has a significant influence on the coupled oscillation, and the oscillation shifts to the lower frequency;the larger the bubble spacing the weaker the coupling effect;at a certain distance, the damping of the coupling effect between bubbles will decrease or increase abnormally.