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Interactions between a toroidal bubble and a free surface

Published online by Cambridge University Press:  29 October 2024

Yutong Bi ,
Lang Qin ,
Liufang Yu ,
Bo Li ,
Shuhong Liu Open the ORCID record for Shuhong Liu [Opens in a new window]  and
Zhigang Zuo Open the ORCID record for Zhigang Zuo [Opens in a new window]
Yutong Bi
Affiliation:
State Key Laboratory of Hydroscience and Engineering, and Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, PR China
Lang Qin
Affiliation:
State Key Laboratory of Hydroscience and Engineering, and Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, PR China
Liufang Yu
Affiliation:
Research Institute of Chemical Defence, Beijing 102205, PR China
Bo Li
Affiliation:
State Key Laboratory of Hydroscience and Engineering, and Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, PR China Beijing Key Laboratory of Information Service Engineering, Beijing Union University, Beijing 100101, PR China
Shuhong Liu*
Affiliation:
State Key Laboratory of Hydroscience and Engineering, and Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, PR China
Zhigang Zuo*
Affiliation:
State Key Laboratory of Hydroscience and Engineering, and Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, PR China
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

Toroidal bubbles (TBs) represent cases of vortex rings with a gas–liquid interface where a gas vortex ring is encased within a liquid vortex ring, and can serve as effective media for mass conveyance, process mixing, noise reduction and reaction regulation. In this study, we carry out a systematic study on the interaction between a TB and a free surface. According to the high-speed photographic images from the experiments, we identify strong and weak interactions in terms of the normalized maximum free surface deformation $h_{max}^*$. Then, we perform numerical simulations based on the volume of fluid (VOF) method in the OpenFOAM platform. Based on both the experimental and the numerical results, we conclude that the Froude number, $Fr$, determines the main characteristics during the interaction process. The TB–free surface interaction is essentially the interaction between the liquid vortex ring enveloping the TB and the free surface, supplemented by the TB's complex behaviour. Next, we establish the scaling law of $h_{max}^*$ based on the energy balance condition. Based on this, we provide the critical $Fr$ and the slenderness of the TB, $\eta$, for identifying the strong and weak interactions, and a parametric plot of the interactions in terms of $Fr$ and $\eta$.

JFM classification

Drops and Bubbles: Bubble dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 998 , 10 November 2024 , A28
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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Supplementary material: File

Bi et al. supplementary movie 1

Strong interaction between a TB and a free surface, where Fr = 7.15, Bo = 1.18 × 102 and Ar = 2.21 × 103.
Download Bi et al. supplementary movie 1(File)
File 8 MB
Supplementary material: File

Bi et al. supplementary movie 2

Strong interaction between a TB and a free surface, where Fr = 4.02, Bo = 2.18 × 102 and Ar = 2.69 × 104.
Download Bi et al. supplementary movie 2(File)
File 7.2 MB
Supplementary material: File

Bi et al. supplementary movie 3

Weak interaction between a TB and a free surface, where Fr = 2.94, Bo = 8.21 × 102 and Ar = 6.19 × 104.
Download Bi et al. supplementary movie 3(File)
File 7.2 MB
Supplementary material: File

Bi et al. supplementary movie 4

Weak interaction between a TB and a free surface, where Fr = 0.96, Bo = 1.21 × 10^3 and Ar = 5.59 × 104.
Download Bi et al. supplementary movie 4(File)
File 8.1 MB
Supplementary material: File

Bi et al. supplementary movie 5

Weak interaction between a TB and a free surface, where Fr = 0.86, Bo = 9.99 × 102 and Ar = 5.10 × 104.
Download Bi et al. supplementary movie 5(File)
File 8.6 MB