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What happens to the vortex structures when the rising bubble transits from zigzag to spiral?

Published online by Cambridge University Press:  04 September 2017

Jie Zhang Open the ORCID record for Jie Zhang [Opens in a new window]  and
Ming-Jiu Ni Open the ORCID record for Ming-Jiu Ni [Opens in a new window]
Jie Zhang
Affiliation:
State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China
Ming-Jiu Ni*
Affiliation:
State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 101408, PR China
*
†Email address for correspondence: mjni@ucas.ac.cn
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Abstract

It has been demonstrated by many experiments carried out over the last 60 years that in certain liquids a single millimetre-sized bubble will rise within an unstable path, which is sometimes observed to transit from zigzag to spiral. After performing several groups of direct numerical simulations, the present work gives a theoretical explanation to reveal the physical mechanism causing the transition, and the results are presented in two parts. In the first part, in which a freely rising bubble is simulated, equal-strength vortex pairs are observed to shed twice during a period of the pure zigzag path, and this type of motion is triggered by the amounts of streamwise vorticities accumulated on the bubble interface, when a critical value is reached. However, when the balance between the counter-rotating vortices is broken, an angular velocity is induced between the asymmetric vortex pairs, driving the bubble to rise in an opposite spiral path. Therefore, although there is no preference of the spiral direction as observed in experiments, it is actually determined by the sign of the stronger vortex thread. In the second part, external vertical magnetic fields are imposed onto the spirally rising bubble in order to further confirm the relations between the vortex structures and the unstable path patterns. As shown in our previous studies (Zhang & Ni, Phys. Fluids, vol. 26 (10), 2014, 102102), the strength of the double-threaded vortex pairs, as well as the imbalance between them, will be weakened under magnetic fields. Therefore, as the vortex pairs become more symmetric, the rotating radius of the spirally rising bubble is observed to decrease. We try to answer the question, put forward by Shew et al. (2005, Preprint, ENS, Lyon), ‘what caused the bubble to transit from zigzag to spiral naturally?’

JFM classification

Drops and Bubbles: Drops and Bubbles Materials Processing Flows: Materials Processing Flows

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Papers
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Journal of Fluid Mechanics , Volume 828 , 10 October 2017 , pp. 353 - 373
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© 2017 Cambridge University Press 

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