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Transition behaviour of weak turbulent fountains

Published online by Cambridge University Press:  11 May 2010

N. WILLIAMSON ,
S. W. ARMFIELD  and
WENXIAN LIN
N. WILLIAMSON*
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia
S. W. ARMFIELD
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia
WENXIAN LIN
Affiliation:
School of Engineering & Physical Sciences, James Cook University, Townsville, Queensland 4811, Australia
*
†Email address for correspondence: [email protected]
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Abstract

Numerical simulations of fully turbulent weak fountain flow are used to provide direct evidence for the scaling behaviour of fountain flow over the Froude number range Fr = 0.1–2.1 and Reynolds number range Re = 20–3494. For very weak flow at Fr < 0.4, the flow mean penetration height, Zm, scales with Zm/R0 = A1Fr2/3 + A2Fr2/3 where R0 is the source radius. A1 and A2 are constants which quantify the separate effects of the radial acceleration of fountain fluid from the source (A1) and the backpressure from the surrounding intrusion, if present, on the upflow (A2). The evidence presented in this work suggests that the mechanisms for the two parts in the scaling of Zm scale with Fr2/3. The intrusion behaviour varies with the Reynolds number (Re) but there is no Re affect on the fountain penetration height. For Re < 250 the radial intrusion flow is subcritical and has different behaviour. For Fr between 0.4 and 2.1 the effect of source momentum flux increases and the flow structure changes to one where there is a coherent upflow and a cap region where the flow stagnates and then reverses. The two regions have separate scaling behaviour such that the overall height, through this transition range of Froude numbers, can be described by Zm/R=C1Fr2/3 + C2Fr2, where C1 and C2 are constants. Over this transition range the effect of source velocity profile is more significant than the Reynolds number effects and the effect of inlet turbulence is minor.

JFM classification

Wakes/Jets: Jets Geophysical and Geological Flows: Gravity currents Waves/Free-surface Flows: Shear waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 655 , 25 July 2010 , pp. 306 - 326
Copyright
Copyright © Cambridge University Press 2010

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References

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Williamson et al. supplementary movie

Movie 1.Visualisation of Re=3494 and Fr=0.4 flow from startup through to quasi-steady flow. Shading indicates non-dimensional scalar concentration φ, from φ=0 (white) to φ=1.0 (black). The surrounding annular re-circulation region is unmixed with ambient fluid and the Kelvin Helmholtz structures flow from the cap region into the intrusion.

Download Williamson et al. supplementary movie(Video)
Video 2.1 MB

Williamson et al. supplementary movie

Movie 2. Visualisation of Re=3494 and Fr=0.97 flow from startup through to quasi-steady flow. Shading indicates non-dimensional scalar concentration φ, from φ=0 (white) to φ=1.0 (black). The surrounding annular re-circulation region is unmixed with ambient fluid and the Kelvin Helmholtz structures flow from the cap region into the intrusion.

Download Williamson et al. supplementary movie(Video)
Video 4.2 MB

Williamson et al. supplementary movie

Movie 3. Visualisation of Re=3494 and Fr=1.4 flow from startup through to quasi-steady flow. Shading indicates non-dimensional scalar concentration φ, from φ=0 (white) to φ=1.0 (black). Ambient fluid is entrained into the annular re-circulation region surrounding the upflow.

Download Williamson et al. supplementary movie(Video)
Video 4.2 MB