Theoretical Analysis Of Cylindrical Bubble Equation With Liquid Compressibility Based On The Perturbation Method

Cavitation is widely present in the operation of fluid machinery,and it may cause adverse effects such as mechanical efficiency and mechanical seal performance degradation.With the deepening of cavitation research,people realized that the study of cavitation phenomena should start with bubble dynamics.In some complex scenes,the bubble shape in the bubble field is not only spherical,but cylindrical bubbles may also appear.In order to solve the above problems,the research on the dynamics of cylindrical bubbles has gradually attracted the attention of scholars.Therefore,this paper has conducted scientific research under these conditions,and the detailed work is as follows:First,this paper uses the small disturbance method to solve the first-order approximate equation of the cylindrical bubble considering the fluid compressibility,and further considers the second-order approximate equation to solve the accuracy of the analytical solution.After perfecting,the expression of the radius of the cylindrical bubble changing with time is obtained,and the movement of the bubble radius can be approximated theoretically.Secondly,through the analysis of the energy dissipation and natural frequency of the cylindrical bubbles in the water,it is found that the energy dissipation term is mainly composed of viscous dissipation and acoustic dissipation.The change in natural frequency is only related to bubble size.Through the method of quantitative analysis,the influence of the main parameters such as bubble balance radius,external sound field frequency and fluid compressibility on the solution of the first-order approximate equation and the second-order approximate equation is studied in detail,and several interaction mechanisms at different stages are discovered.The influencing factors of the analytical solution of the equation are explored,and it is found that the solution of the first-order approximate equation is the main factor affecting the analytical solution,and when the parameters change,the interference of the external sound field has a greater impact on the process of large-size bubble oscillation.Finally,this paper uses the method of phase plane and bifurcation diagram to quantitatively analyze the nonlinear oscillation characteristics of the cylindrical bubble,discusses the influence of the dimensionless amplitude and frequency of the external sound field on the oscillation characteristics of the cylindrical bubble,and determines the bubble The process of sexual chaotic oscillation was identified and analyzed.