## 1 Introduction
The bubbles not only deformed greatly during the first oscillation cycle but also caused liquid flow in all directions after rupture. His student, [PERSON] [16], conducted an experimental study on the oscillation of bubbles generated by a single spark in a rigid tube with the help of a hydrophone. Under an asymmetric state, secondary cavitation was observed to occur in the tube. [PERSON] et al. [17] placed a tube horizontally in a water tank filled with water, generated electric spark bubbles in the tube, and used a high-speed camera to capture the expansion, rupture, and rebound of the bubbles. When the bubble position is eccentric in the tube, it will migrate to the distal part of the tube at the end of the collapse, and a jet will form in that direction. [PERSON] [18] studied the dynamic behavior of laser-induced bubbles in a tube under different initial conditions. Numerical simulation based on the fluid volume method was implemented using open-source OpenFOAM code. According to experimental observations and numerical analysis, an axial jet pointing toward the front end of the tube was generated during the contraction of the bubble. [PERSON] [19] used high-speed photography to study the dynamics of bubbles generated by electric sparks in a vertical rigid tube. The bubble behavior is affected, to some extent, by the proximity to the tube wall, and the presence of a tube greatly increases the lifetime of the bubble. [PERSON] [20] conducted experimental and theoretical studies on liquid jets generated by electric explosions in water in a centimeter-wide circular tube. The study found that the jet pattern is mainly affected by the tube diameter, with narrow tubes producing conical jets and wide tubes producing annular jets. The jet maintains an almost constant velocity, which increases with the explosion energy and decreases with the tube diameter and the spacing distance. [PERSON] [21] studied the dynamics of cavitation bubbles in a typical type of open tube with different cross-sections. The bubble generates a weak jet in the funnel-shaped part, an inverted cone-shaped jet near the throat, and a cylindrical jet with a rounded end in the funnel-shaped tube. Under the action of internal flow, bubbles seriously threaten the safety of equipment. In order to analyze the movement and deformation of bubbles in the fluid flow inside a pipeline, [PERSON] [22] established a corresponding boundary-element numerical model based on the potential flow theory. Different flow velocity directions lead to different deformations of the later annular bubbles. If the dimensionless parameter of the pipe radius is greater than 5, the influence of the pipe on the bubble can be ignored. In the field of clinical applications, the study of elastic tubes is of great significance in biomedicine, drug delivery, and vascular rupture. The study of the deformation and movement of bubbles in biological tissues can provide guidance for their application in medicine. [PERSON] and [PERSON] [23] studied the impact of bubbles on the surrounding environment by simulating treatment in narrow spaces. In the case where bubbles are formed near the elastic wall, the bubbles come into contact with the elastic wall during growth, and severe large deformation of the elastic wall is observed when the bubbles collapse. By presenting the deformation and temperature increase of the elastic wall, the safety of treatment in narrow spaces can be improved. [PERSON] [24] proposed the use of ultrasound-excited microbubbles in blood vessels for various clinical applications. Axisymmetric coupled boundary-element and finite-element codes and experiments were used to study the effect of the surrounding tubing on the response of the bubbles to acoustic excitation. [PERSON] [25] focused on the mechanism of microscopic damage to the vessel wall caused by the evolution of cavitation bubbles in blood vessels.