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Low-Reynolds-number fountain behaviour

Published online by Cambridge University Press:  11 July 2008

N. WILLIAMSON ,
N. SRINARAYANA ,
S. W. ARMFIELD ,
G. D. McBAIN  and
W. LIN
N. WILLIAMSON
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW, 2006Australia
N. SRINARAYANA
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW, 2006Australia
S. W. ARMFIELD
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW, 2006Australia
G. D. McBAIN
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW, 2006Australia
W. LIN
Affiliation:
School of Engineering, James Cook University, Townsville, Queensland, 4811Australia
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Abstract

Experimental evidence for previously unreported fountain behaviour is presented. It has been found that the first unstable mode of a three-dimensional round fountain is a laminar flapping motion that can grow to a circling or multimodal flapping motion. With increasing Froude and Reynolds numbers, fountain behaviour becomes more disorderly, exhibiting a laminar bobbing motion. The transition between steady behaviour, the initial flapping modes and the laminar bobbing flow can be approximately described by a function FrRe2/3=C. The transition to turbulence occurs at Re > 120, independent of Froude number, and the flow appears to be fully turbulent at Re≈2000. For Fr > 10 and Re≲120, sinuous shear-driven instabilities have been observed in the rising fluid column. For Re≳120 these instabilities cause the fountain to intermittently breakdown into turbulent jet-like flow. For Fr≲10 buoyancy forces begin to dominate the flow and pulsing behaviour is observed. A regime map of the fountain behaviour for 0.7≲Fr≲100 and 15≲Re≲1900 is presented and the underlying mechanisms for the observed behaviour are proposed. Movies are available with the online version of the paper.

JFM classification

Wakes/Jets: Jets Instability: Instability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 608 , 10 August 2008 , pp. 297 - 317
Copyright
Copyright © Cambridge University Press 2008

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References

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Williamson et al. supplementary movie

Movie 1. Salt-water is injected up into a small fresh water tank. The water is injected from a sudden start and maintained at a constant flow rate throughout the experiment. During an experiment the saline fluid rises and then falls back on itself and finally spreads along the base of the tank. The flow behaviour depends on the Reynolds number and Froude number of the flow. Here visualization of combined flapping and circling behaviour is shown at Re=87.5 and Fr=1.2, with characteristic velocity U0=3.9 cm/s, source radius R0=2.4 mm and density ratio  Δρ/ρf=0.0459. The movie looks down upon the fountain source. Fountain startup behaviour is from 0 to 5 s, two-dimensional flapping exists between 5 and 9 s, circling between 9 and 14 s and two-dimensional flapping behaviour returns again from 14 s onwards.

Download Williamson et al. supplementary movie(Video)
Video 4.9 MB

Williamson et al. supplementary movie

Movie 2. Visualization of flapping/bobbing behaviour at Re=97 and Fr=1.3, with U0=4.3 cm/s, R0=2.4 mm and Δρ/ρf=0.0459.

Download Williamson et al. supplementary movie(Video)
Video 2.9 MB

Williamson et al. supplementary movie

Movie 3. Visualization of sinuous behaviour at Re=158 and Fr=45, with U0=28 cm/s, R0=0.565 mm and Δρ/ρf=0.00718.

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Video 489.5 KB

Williamson et al. supplementary movie

Movie 4. Visualization of sinuous behaviour at Re=26 and Fr=26, with U0=6.9 cm/s, R0=0.38 mm and Δρ/ρf=0.00186.

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Video 1.7 MB

Williamson et al. supplementary movie

Movie 5. Visualization of jet breakdown behaviour at Re=152 and Fr=13, with U0=12 cm/s, R0=1.27 mm and Δρ/ρf=0.00718.

Download Williamson et al. supplementary movie(Video)
Video 5.2 MB