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Formation regimes of vortex rings in thermals

Published online by Cambridge University Press:  07 January 2020

Xinping Zhou Open the ORCID record for Xinping Zhou [Opens in a new window] ,
Yangyang Xu  and
Wanqiu Zhang
Xinping Zhou*
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan430074, PR China Department of Mechanics, Huazhong University of Science and Technology, Wuhan430074, PR China
Yangyang Xu*
Affiliation:
Department of Mechanics, Huazhong University of Science and Technology, Wuhan430074, PR China
Wanqiu Zhang
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan430074, PR China Department of Mechanics, Huazhong University of Science and Technology, Wuhan430074, PR China
*
†Email addresses for correspondence: xpzhou08@hust.edu.cn, yangyangxu91@hust.edu.cn
†Email addresses for correspondence: xpzhou08@hust.edu.cn, yangyangxu91@hust.edu.cn
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Abstract

The development of laminar thermals and the formation of buoyant vortex rings in thermals are studied by performing direct numerical simulations. The formation number of buoyant vortex rings in thermals is also analysed. We find that the development of thermals can be classified into three modes: the starting vortex ring dominated mode; the mode with the occurrence of a secondary vortex ring with breakup; and the mode with the occurrence of a secondary vortex ring without breakup. For the latter two modes, owing to the stretching of the thermal cap, the fluid at the leading edge rolls up, and a secondary vortex ring occurs, grows and replaces the starting vortex ring. The boundary of non-occurrence and occurrence of the secondary vortex ring is determined in a space of Richardson number (Ri) and injection duration ($t_{i}$). The final mode occurs only in a small region. For $Ri<0.6$, the secondary vortex ring does not occur even for very long injection duration. The effective Rayleigh number ($Ra_{m}$) is proposed to accommodate the cases $Ri>0.7$ and $t_{i}<5$, with $Ra_{m}$ larger than the critical value (approximates to 1. 95 × 105) for the occurrence of the secondary vortex ring. The formation number of buoyant vortex rings in thermals is beyond the universal formation number of 4 for non-buoyant vortex rings, and increases with the increase of the Richardson number and the injection duration. The switching between the thermal modes by changing the Richardson number and the injection duration has no significant effect on the value of the formation number.

JFM classification

Convection: Plumes/thermals Vortex Flows: Vortex dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 885 , 25 February 2020 , A44
Copyright
© 2020 Cambridge University Press

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