声场驱动下泡壁运动方程的理论分析

Theoretical Analysis of Bubble Wall Motion Equations under Sound Field

声场驱动条件下的泡壁运动方程一直是泡动力学领域的重要研究内容。当泡壁运动方程用于预测高马赫数下的气泡振荡特性时,为满足计算精度的需求,应该充分考虑液体的可压缩性。在声场驱动条件下,本文数值研究了含二阶马赫数修正的泡壁运动方程(简称“二阶方程”)在不同马赫数条件下对气泡振荡特性重要物理量的预测。围绕声场振幅和声场频率两个物理参数,将二阶方程与一阶马赫数修正的泡壁运动方程(简称“一阶方程”)的预测结果进行深入地对比分析。研究发现,在高马赫数条件下,一阶方程和二阶方程预测的气泡半径、泡壁速度和泡壁加速度均存在较大的差异,导致二者所预测的声耗散功率和热耗散功率也存在较为明显的差异。本研究为声场驱动下的泡动力学领域提供了理论模型的选择依据。

The investigation of the bubble wall motion equation driven by the sound field is always essential for the field of bubble dynamics.When the bubble wall motion equation is employed to predict the bubble oscillation characteristics with the high Mach number,the compressibility of the liquid should be fully considered to satisfy the requirements of calculation accuracy.In the present paper,based on the predictions of important physical quantities related to bubble oscillation characteristics,the bubble wall motion equation with the second-order Mach number correction(“second-order equation”for short)driven by the sound field is numerically investigated with different Mach numbers.Moreover,in terms of the acoustic amplitude and frequency,the predictions by the second-order equation and the first-order Mach number correction(“first-order equation”for short)are fully compared.The study shows that the differences of the bubble radius,bubble wall velocity and bubble wall acceleration predicted by the two equations respectively with the high Mach number are obvious.As a result,both the radiation and thermal dissipated power predicted by the two equations are different.This study provides a basis for the selection of theoretical models for the application field of bubble dynamics driven by sound field.