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On the criteria of large cavitation bubbles in a tube during a transient process

Published online by Cambridge University Press:  02 March 2021

Peng Xu ,
Shuhong Liu ,
Zhigang Zuo  and
Zhao Pan Open the ORCID record for Zhao Pan [Opens in a new window]
Peng Xu
Affiliation:
Department of Energy and Power Engineering, and State Key Laboratory of Hydro Science and Engineering, Tsinghua University, Beijing 100084, PR China Department of Mechanical and Mechatronics Engineering, University of Waterloo, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
Shuhong Liu
Affiliation:
Department of Energy and Power Engineering, and State Key Laboratory of Hydro Science and Engineering, Tsinghua University, Beijing 100084, PR China
Zhigang Zuo*
Affiliation:
Department of Energy and Power Engineering, and State Key Laboratory of Hydro Science and Engineering, Tsinghua University, Beijing 100084, PR China
Zhao Pan*
Affiliation:
Department of Mechanical and Mechatronics Engineering, University of Waterloo, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
*
†Email addresses for correspondence: zhigang200@tsinghua.edu.cn, zhao.pan@uwaterloo.ca
†Email addresses for correspondence: zhigang200@tsinghua.edu.cn, zhao.pan@uwaterloo.ca
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Abstract

Extreme cavitation scenarios, such as water column separations in hydraulic systems during transient processes caused by large cavitation bubbles, can lead to catastrophic destruction. In the present paper, we study the onset criteria and dynamics of large cavitation bubbles in a tube. A new cavitation number $Ca_2 = {l^*}^{-1} Ca_0$ is proposed to describe the maximum length $L_{max}$ of the cavitation bubble, where $l^*$ is a non-dimensional length of the water column indicating its slenderness, and $Ca_0$ is the classic cavitation number. Combined with the onset criteria for acceleration-induced cavitation ($Ca_1<1$, Pan et al., Proc. Natl Acad. Sci. USA, vol. 114, 2017, pp. 8470–8474), we show that the occurrence of large cylindrical cavitation bubbles requires both $Ca_2<1$ and $Ca_1<1$ simultaneously. We also establish a Rayleigh-type model for the dynamics of large cavitation bubbles in a tube. The bubbles collapse at a finite end speed, and the time from the maximum bubble size to collapse is $T_c=\sqrt {2}\sqrt {lL_{max}}\sqrt {{\rho }/{p_\infty }}$, where $l$ is the length of the water column, $L_{max}$ is the maximum bubble length, $\rho$ is the liquid density and $p_{\infty }$ is the reference pressure in the far field. The analytical results are validated against systematic experiments using a modified ‘tube-arrest’ apparatus, which can decouple acceleration and velocity. The results in the current work can guide design and operation of hydraulic systems encountering transient processes.

JFM classification

Drops and Bubbles: Cavitation Drops and Bubbles: Bubble dynamics

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Type
JFM Rapids
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Journal of Fluid Mechanics , Volume 913 , 25 April 2021 , R6
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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