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

TL;DR

This paper establishes criteria for the formation and collapse of large cavitation bubbles in tubes during transients, introducing a new cavitation number and a Rayleigh-type model validated by experiments, aiding hydraulic system design.

Contribution

It proposes a new cavitation number $Ca_2$, combines it with existing criteria, and develops a Rayleigh-type model for bubble dynamics, validated through systematic experiments.

Findings

Large cavitation bubbles occur when $Ca_2<1$ and $Ca_1<1$.

The collapse time of bubbles is given by $T_c=\

The experimental validation supports the analytical models and criteria.

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. (2017)), 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 $T_c=\sqrt{2}\sqrt{lL_{\max}}\sqrt{\frac{\rho}{p_\infty}}$, 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.