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Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (12): 1607-1614.doi: https://doi.org/10.1007/s10483-016-2143-8

• 论文 • 上一篇    下一篇

Effect of surface tension and viscosity on bubble growth of single mode Rayleigh-Taylor instability

Mingjun LI1, Qiaofeng ZHU2, Guibo LI1   

  1. 1. School of Mathematics and System Science, Shenyang Normal University, Shenyang 110034, China;
    2. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan Province, China
  • 收稿日期:2015-10-14 修回日期:2016-05-13 出版日期:2016-12-01 发布日期:2016-12-01
  • 通讯作者: Mingjun LI E-mail:alimingjun@163.com
  • 基金资助:

    Project supported by the National Natural Science Foundation of China (Nos. 11171281 and 11201389)

Effect of surface tension and viscosity on bubble growth of single mode Rayleigh-Taylor instability

Mingjun LI1, Qiaofeng ZHU2, Guibo LI1   

  1. 1. School of Mathematics and System Science, Shenyang Normal University, Shenyang 110034, China;
    2. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan Province, China
  • Received:2015-10-14 Revised:2016-05-13 Online:2016-12-01 Published:2016-12-01
  • Contact: Mingjun LI E-mail:alimingjun@163.com
  • Supported by:

    Project supported by the National Natural Science Foundation of China (Nos. 11171281 and 11201389)

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摘要：

Based on the Zufiria theoretical model, a new model regarding the asymptotic bubble velocity for the Rayleigh-Taylor (RT) instability is presented by use of the complex velocity potential proposed by Sohn. The proposed model is an extension of the ordinary Zufiria model and can deal with non-ideal fluids. With the control variable method, the effect of the viscosity and surface tension on the bubble growth rate of the RT instability is studied. The result is consistent with Cao's result if we only consider the viscous effect and with Xia's result if we only consider the surface tension effect. The asymptotic bubble velocity predicted by the Zufiria model is smaller than that predicted by the Layzer model, and the result from the Zufiria model is much closer to White's experimental data.

关键词: Zufiria model, viscosity, Rayleigh-Taylor (RT) instability, surface tension

Abstract:

Based on the Zufiria theoretical model, a new model regarding the asymptotic bubble velocity for the Rayleigh-Taylor (RT) instability is presented by use of the complex velocity potential proposed by Sohn. The proposed model is an extension of the ordinary Zufiria model and can deal with non-ideal fluids. With the control variable method, the effect of the viscosity and surface tension on the bubble growth rate of the RT instability is studied. The result is consistent with Cao's result if we only consider the viscous effect and with Xia's result if we only consider the surface tension effect. The asymptotic bubble velocity predicted by the Zufiria model is smaller than that predicted by the Layzer model, and the result from the Zufiria model is much closer to White's experimental data.

Key words: viscosity, surface tension, Rayleigh-Taylor (RT) instability, Zufiria model

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