Research On Linear And Nonlinear Sound Propagation Problems In Liquids With Bubbles

The problem of acoustic propagation in liquids with bubbles is an important problem in the field of acoustic cavitation and it is the theoretical basis for many ultrasonic applications.In this paper,the propagation characteristics of acoustic wave in the liquid with bubbles is studied by applying the effective medium theory and the perturbation method,and based on this,a theoretical model is established.In order to explore the change of acoustic field in liquids with bubbles,we apply the model to analyze the propagation characteristics of linear acoustic wave and second-order harmonics in liquids with a single kind bubble,and the propagation characteristics of linear acoustic wave in liquids with multiple mixed bubbles.In the study of this paper,the following work is done based on the perspective of acoustic propagation in liquid with bubbles:(1)The propagating characteristics of acoustic wave in viscous liquids were investigated.First,based on three basic laws of physics,the wave equation and the effective wave number of the linear acoustic wave and the second harmonic are obtained by applying the perturbation method;and then,the relationship that the amplitude of the second harmonic is related to the viscosity and nonlinear parameters of the liquid is numerically simulated.Finally,it is found that the viscosity and nonlinear parameters of the liquid have an influence on the nonlinear effect of the acoustic wave,which is that the nonlinear effect of the acoustic wave is stronger with increase of the viscosity coefficient and the nonlinear parameter,and at the same time,the viscosity of the liquid effects the attenuation coefficient of the acoustic wave,which is that the rate of acoustic attenuation are larger with the increase of the attenuation coefficient.(2)The vibration of a single bubble in a liquid caused the acoustic waves is analyzed.First,by comparing the simulation results of Rayleigh-Plesset equation and Keller equation,it is found that the compressibility of the liquid inhibits the resonance of the bubbles in a compressible liquid,such that the resonance peak of the bubble vibration and the half width of the resonance region in the compressible liquid are smaller than the peak and half widths in the incompressible liquid.Then,the linear vibration equation of the bubble is obtained through using the perturbation method to linearize the Keller vibration equation.The result reveals that the nonlinear effect of bubble vibration in the resonance region is very strong;at this time,the bubble vibration cannot be analyzed by linearization,but the bubble vibration can be analyzed by linearization in the non-resonant region.(3)The problem of acoustic propagation in liquids with a single kind of bubble is studied.Firstly,by applying the effective medium theory,the wave equation of acoustic wave is analyzed,and by introducing the volume fraction of gas in the liquid,the wave equation and the bubble vibration equation with the wave equation link up,thus obtaining the effective wave number of linear sound wave and second harmonic.Secondly,the change of the attenuation coefficient of linear acoustic wave with the viscosity coefficient of liquid and the vibration of bubble in liquid is explored through numerical simulation.It is found that the effect of liquid viscosity and the bubbles on acoustic wave promote each other,and the influence of the bubbles on the attenuation coefficient of acoustic wave is exerted by the bubble vibration and the interaction between bubbles.Finally,the change of the second-order harmonic amplitude with the gas volume fraction,liquid viscosity coefficient and nonlinear parameters is investigated.The results show that the main factor affecting the second-order harmonic in the near-field region of the sound source is the gas volume fractions and nonlinear parameters,while the main factor affecting second-order harmonics in the far-field region of the sound source is the viscosity of the liquid.(4)The problem of acoustic propagation in liquids with multiple mixed bubbles has been studied.Firstly,the change of the gas volume fraction with the kind and distribution of bubbles is analyzed when multiple bubbles are contained in the liquid,and the expression of the gas volume fraction is obtained.Secondly,the wave equation and effective wave number expression of linear acoustic wave in liquid with multiple mixed bubbles are obtained by using effective medium theory.Finally,numerical simulation is used to analyze the influence of the number of bubble kind and bubble distribution on the attenuation coefficient and sound velocity of the acoustic wave.The results show that the acoustic resonance propagation is suppressed,and as the number of bubbles increases,the suppression effect is stronger,and the resonance absorption region of the acoustic wave is more stable when two or more kinds mixed bubbles are present in the liquid.In this paper,the problem of acoustic propagation in liquids with bubbles is studied by effective medium theory and perturbation method.The wave equation and the effective wave number of the second-order harmonics of acoustic waves in liquid with a single kind of bubble and the linear acoustics waves in liquids with multiple mixed bubbles are investigated,and the effect of the liquid viscosity,bubble size and distribution,and nonlinear parameters on propagation of acoustic wave is analyzed.This type of knowledge gives us a deeper understanding of the problem of acoustic propagation in liquids with bubbles and is an important complement to the knowledge of acoustic cavitation.