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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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References

Batchelor, G. K. 1954 Heat convection and buoyancy effects in fluids. Q. J. R. Meteorol. Soc. 80, 339–358.CrossRefGoogle Scholar
Bond, D. & Johari, H. 2005 Effects of initial geometry on the development of thermals. Exp. Fluids 39, 591–601.CrossRefGoogle Scholar
Bond, D. & Johari, H. 2010 Impact of buoyancy on vortex ring development in the near field. Exp. Fluids 48, 737–745.CrossRefGoogle Scholar
Dabiri, J. O. & Gharib, M. 2004 Delay of vortex ring pinchoff by an imposed bulk counterflow. Phys. Fluids 16, L28–L30.CrossRefGoogle Scholar
Dabiri, J. O. & Gharib, M. 2005 Starting flow through nozzles with temporally variable exit diameter. J. Fluid Mech. 538, 111–136.CrossRefGoogle Scholar
Gao, L. & Yu, S. C. 2016 Vortex ring formation in starting forced plumes with negative and positive buoyancy. Phys. Fluids 28, 113601.CrossRefGoogle Scholar
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140.CrossRefGoogle Scholar
Krueger, P. S., Dabiri, J. O. & Gharib, M. 2006 The formation number of vortex rings formed in uniform background co-flow. J. Fluid Mech. 556, 147–166.CrossRefGoogle Scholar
Lundgren, T. S., Yao, J. & Mansour, N. N. 1992 Microburst modelling and scaling. J. Fluid Mech. 239, 461–488.CrossRefGoogle Scholar
Marugán-Cruz, C., Rodríguez-Rodríguez, J. & Martínez-Bazán, C. 2013 Formation regimes of vortex rings in negatively buoyant starting jets. J. Fluid Mech. 716, 470–486.CrossRefGoogle Scholar
Mohseni, K. & Gharib, M. 1998 A model for universal time scale of vortex ring formation. Phys. Fluids 10, 2436–2438.CrossRefGoogle Scholar
Mohseni, K., Ran, H. & Colonius, T. 2001 Numerical experiments on vortex ring formation. J. Fluid Mech. 430, 267–282.CrossRefGoogle Scholar
Popinet, S. 2003 Gerris: a tree-based adaptative solver for the incompressible Euler equations in complex geometries. J. Comput. Phys. 190, 572–600.CrossRefGoogle Scholar
Popinet, S. 2009 An accurate adaptative solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228, 5838–5866.CrossRefGoogle Scholar
Pottebaum, T. S. & Gharib, M. 2004 The pinch-off process in a starting buoyant plume. Exp. Fluids 37, 87–94.CrossRefGoogle Scholar
Shlien, D. J. 1976 Some laminar thermal and plume experiments. Phys. Fluids 19, 1089–1098.CrossRefGoogle Scholar
Shlien, D. J. & Brosh, A. 1979 Velocity field measurements of a laminar thermal. Phys. Fluids 22, 1044–1053.CrossRefGoogle Scholar
Shlien, D. J. & Thompson, D. W. 1975 Some experiments on the motion of an isolated laminar thermal. J. Fluid Mech. 72, 35–47.CrossRefGoogle Scholar
Shusser, M. & Gharib, M. 2000 A model for vortex ring formation in a starting buoyant plume. J. Fluid Mech. 416, 173–185.CrossRefGoogle Scholar
Sparrow, E. M., Husar, R. B. & Goldstein, R. J. 1970 Observation and other characteristics of thermals. J. Fluid Mech. 41, 793–800.CrossRefGoogle Scholar
Tankin, R. S. & Farhadien, R. 1971 Effects of thermal convection currents on formation of ice. Intl J. Heat Mass Transfer 14, 953–961.CrossRefGoogle Scholar
Taylor, G. I. 1946 Dynamics of a Mass of Hot Gas Rising in Air. Technical Information Division Oak Ridge Operations.Google Scholar
Thompson, D. W. 1970 Effect of interfacial mobility on mass transfer in gas-liquid systems. Ind. Engng Chem. Fundam. 9, 243–248.CrossRefGoogle Scholar
Wang, R.-Q., Law, A. W.-K., Adams, E. E. & Fringer, O. B. 2009 Buoyant formation number of a starting buoyant jet. Phys. Fluids 21, 125104.CrossRefGoogle Scholar