基于Runge-Kutta法分析刚性平面附近空化气泡的动力学

Analysis of Cavitation Bubbles DynamicsNear Rigid Planes by Runge-Kutta Method

用镜像空化泡等效替代刚性平面,得到超声场中刚性平面附近空化泡的动力学方程.运用Runge-Kutta法数值计算了该方程,并和自由声场中空化泡动力学方程的数值解进行对比分析.结果表明:刚性平面对空化气泡脉动具有抑制作用;气泡内的气体绝热系数和液体粘度系数越小,气泡溃灭速度越大,对平面的作用也越大.研究结果有利于认识空化气泡对刚性壁面的作用机制.

The dynamic equation of the cavitation bubble near the rigid plane in ultrasonic field is obtained by replacing the rigid plane with the mirror image cavitation bubble.The revised equation is numerically calculated through the Runge-Kutta method and compared with the numerical solution of the bubble’s equation in the free sound field.The results show that the rigid plane can inhibit the pulsation of cavitation bubble.The smaller the adiabatic coefficient of the gas in the bubble and the viscosity coefficient of the liquid,the greater the bubble collapse velocity and the greater the effect on the plane.These results are helpful to understand the action mechanism of cavitation bubbles on rigid walls.