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Research Papers: Fundamental Issues and Canonical Flows

A Unified Energy Feature of Vortex Rings for Identifying the Pinch-Off Mechanism

[+] Author and Article Information
Yang Xiang, Suyang Qin

J.C. Wu Center for Aerodynamics,
School of Aeronautics and Astronautics,
Shanghai Jiao Tong University,
Shanghai 200240, China

Hong Liu

J.C. Wu Center for Aerodynamics,
School of Aeronautics and Astronautics,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: hongliu@sjtu.edu.cn

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 14, 2017; final manuscript received July 20, 2017; published online September 20, 2017. Assoc. Editor: Francine Battaglia.

J. Fluids Eng 140(1), 011203 (Sep 20, 2017) (12 pages) Paper No: FE-17-1154; doi: 10.1115/1.4037506 History: Received March 14, 2017; Revised July 20, 2017

Owing to the limiting effect of energy, vortex rings cannot grow indefinitely and thus pinch off. In this paper, experiments on the vortex rings generated using a piston-cylinder apparatus are conducted so as to investigate the pinch-off mechanisms and identify the limiting effect of energy. Both theoretical and experimental results show that the generated vortex rings share a unified energy feature, regardless of whether they are pinched-off or not. Moreover, the unified energy feature is quantitatively described by a dimensionless energy number γ, defined as γ=(E/I2Γωmax) and exhibiting a critical value γring = 0.14 ± 0.01 for the generated vortex rings. This unified energy feature reflects the limiting effect of energy and specifies the target of vortex ring formation. Furthermore, based on the tendency of γ during vortex ring formation, criteria for determining the two timescales, i.e., pinch-off time and separation time, which correspond to the onset and end of pinch-off process, respectively, are suggested.

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Figures

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Fig. 1

Schematic of the experimental setup with a piston-cylinder apparatus

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Fig. 2

Velocity programs of piston in six cases

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Fig. 3

A dyed vortex ring

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Fig. 4

Streamline pattern

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Fig. 5

The configuration of vortex ring with different methods. Left: vorticity contour; middle: Q-criterion contour; right: streamline pattern.

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Fig. 6

Velocity distribution along the vertical axis

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Fig. 7

Normalized circulation of the total jet and the leading vortex ring as a function of formation time for all cases

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Fig. 8

Temporal formation of a vortex ring with the Q-criterion and streamline pattern in case C1. Left: flow field based on the Q-criterion, Right: flow field based on the streamline pattern: (a) T* = 1.0, (b) T* = 4.0, (c) T* = 4.8, (d) T* = 6.0, (e) T* = 7.0, and (f) T* = 7.0.

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Fig. 10

Formation of the vortex region based on the Q-criterion and its flow visualization in case C2: (a) T* = 3.0 and (b) T* = 6.0

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Fig. 11

Evolution of the vortex region based on the Q-criterion and its flow visualization in case C4: (a) T* = 5.8, (b) T* = 6.5, and (c) T* = 8.0

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Fig. 9

Circulation of the vortex core of the leading vortex ring during the formation process

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Fig. 13

Variation of the dimensionless energy number γ of the total jet against formation time T*

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Fig. 14

Variation of the dimensionless energy number γ of the leading vortex ring against formation time T*

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