中国物理B ›› 2008, Vol. 17 ›› Issue (3): 927-938.doi: 10.1088/1674-1056/17/3/031

• CLASSICAL AREAS OF PHENOMENOLOGY • 上一篇    下一篇

The interaction between multiple bubbles and the free surface

张阿漫, 姚熊亮   

  1. School of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China
  • 收稿日期:2007-09-15 修回日期:2007-10-21 出版日期:2008-03-04 发布日期:2008-03-04
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 50779007).

The interaction between multiple bubbles and the free surface

Zhang A-Man(张阿漫) and Yao Xiong-Liang(姚熊亮)   

  1. School of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China
  • Received:2007-09-15 Revised:2007-10-21 Online:2008-03-04 Published:2008-03-04
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 50779007).

摘要: The flow is assumed to be potential, and a boundary integral method is used to solve the Laplace equation for the velocity potential to investigate the shape and the position of the bubble. A 3D code to study the bubble dynamics is developed, and the calculation results agree well with the experimental data. Numerical analyses are carried out for the interaction between multiple bubbles near the free surface including in-phase and out-of-phase bubbles. The calculation result shows that the bubble period increases with the decrease of the distance between bubble centres because of the depression effect between multiple bubbles. The depression has no relationship with the free surface and it is more apparent for out-of-phase bubbles. There are great differences in dynamic behaviour between the in-phase bubbles and the out-of-phase bubbles due to the depression effect. Furthermore, the interaction among eight bubbles is simulated with a three-dimensional model, and the evolving process and the relevant physical phenomena are presented. These phenomena can give a reference to the future work on the power of bubbles induced by multiple charges exploding simultaneously or continuously.

Abstract: The flow is assumed to be potential, and a boundary integral method is used to solve the Laplace equation for the velocity potential to investigate the shape and the position of the bubble. A 3D code to study the bubble dynamics is developed, and the calculation results agree well with the experimental data. Numerical analyses are carried out for the interaction between multiple bubbles near the free surface including in-phase and out-of-phase bubbles. The calculation result shows that the bubble period increases with the decrease of the distance between bubble centres because of the depression effect between multiple bubbles. The depression has no relationship with the free surface and it is more apparent for out-of-phase bubbles. There are great differences in dynamic behaviour between the in-phase bubbles and the out-of-phase bubbles due to the depression effect. Furthermore, the interaction among eight bubbles is simulated with a three-dimensional model, and the evolving process and the relevant physical phenomena are presented. These phenomena can give a reference to the future work on the power of bubbles induced by multiple charges exploding simultaneously or continuously.

Key words: multiple bubbles, boundary integral, free surface, depression effect, potential flow theory

中图分类号:  (Bubble dynamics)

  • 47.55.dd
02.60.Nm (Integral and integrodifferential equations) 47.11.Hj (Boundary element methods)