Hostname: page-component-76fb5796d-vvkck Total loading time: 0 Render date: 2024-04-27T18:33:33.698Z Has data issue: false hasContentIssue false
  • English
  • Français

Forced turbulent fountain flow behaviour

Published online by Cambridge University Press:  08 February 2011

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 and Physical Sciences, James Cook University, Townsville, QLD 4811, Australia
*
†Email address for correspondence: n.williamson@usyd.edu.au
Get access Rights & Permissions [Opens in a new window]

Abstract

Numerical simulations of turbulent fountain flow are used to investigate the important energy and mass transfer mechanisms present in the forced fountain flow regime, which has been reported to exist at Froude numbers (Fr) greater than 3. The flow is equivalent to a negatively buoyant jet with three flow streams, the inner upflow (IF), the outer downflow (OF) and the surrounding ambient fluid (AF). Simulation results are presented for Fr = 4 and 7 at Reynolds number Re = 3350. The mean fountain penetration height scales with the previously reported relation Zm/R0 = 2.46Fr, where R0 is the source radius, but the assumptions behind analytical derivations of the relation are not supported by the present results. The results suggest that the OF may be relatively well described by the dynamics of a pure line plume surrounding the IF but with higher entrainment owing to the unsteady pulsing behaviour of the flow entering the OF from the IF. The length scale for a pure plume appears to apply at Fr = 7 in the OF and a degree of self-similarity exists. Comparisons with previous results suggest the IF is not fully developed at Fr = 7 and entrainment into the IF from the OF may not occur until Fr > 15.

JFM classification

Wakes/Jets: Jets Convection: Plumes/thermals
Type
Papers
Information
Journal of Fluid Mechanics , Volume 671 , 25 March 2011 , pp. 535 - 558
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abraham, G. 1967 Jets with negative buoyancy in homogeneous fluid. J. Hydaul. Res. 5, 235–248.CrossRefGoogle Scholar
Baddour, R. E. & Zhang, H. 2009 Density effect on round turbulent hypersaline fountain. J. Hydraul. Engng 135, 57–59.CrossRefGoogle Scholar
Baines, W. D., Turner, J. S. & Campbell, I. H. 1990 Turbulent fountains in an open chamber. J. Fluid Mech. 212, 557–592.CrossRefGoogle Scholar
Bloomfield, L. J. & Kerr, R. C. 1998 Turbulent fountains in a stratified fluid. J. Fluid Mech. 358, 335–356.CrossRefGoogle Scholar
Bloomfield, L. J. & Kerr, R. C. 2000 A theoretical model of a turbulent fountain. J. Fluid Mech. 424, 197–216.CrossRefGoogle Scholar
Boguslawski, L. & Popiel, Cz. O. 1979 Flow structure of the free round turbulent jet in the initial region. J. Fluid Mech. 90, 531–539.CrossRefGoogle Scholar
Campbell, I. H. & Turner, J. S. 1989 Fountains in magma chambers. J. Petrol. 30, 885–923.CrossRefGoogle Scholar
Cresswell, R. W. & Szczepura, R. T. 1993 Experimental investigation into a turbulent jet with negative buoyancy. Phys. Fluids A 5, 2865–2878.CrossRefGoogle Scholar
Demetriou, J. D. 1978 Turbulent diffusion of vertical water jets with negative buoyancy (in Greek). PhD thesis, National Technical University of Athens, Department of Civil Engineering.Google Scholar
Hunt, G. R. & Coffey, C. J. 2009 Characterising line fountains. J. Fluid Mech. 623, 317–327.CrossRefGoogle Scholar
Huppert, H. E. 1982 The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech. 121, 43–58.CrossRefGoogle Scholar
Kaminski, E., Tait, S. & Carazzo, G. 2005 Turbulent entrainment in jets with arbitrary buoyancy. J. Fluid Mech. 526, 361–376.CrossRefGoogle Scholar
Kaye, N. B. & Hunt, G. R. 2006 Weak fountains. J. Fluid Mech. 558, 319–328.CrossRefGoogle Scholar
Leonard, B. P. & Mokhtari, S. 1990 Beyond first-order upwinding: the ultra-sharp alternative for non-oscillatory steady state simulation of convection. Intl J. Numer. Meth. Engng 30, 729–766.CrossRefGoogle Scholar
Lin, W. & Armfield, S. W. 2000 a Direct simulation of weak axisymmetric fountains in a homogeneous fluid. J. Fluid Mech. 403, 67–88.CrossRefGoogle Scholar
Lin, W. & Armfield, S. W. 2000 b Very weak axisymmetric fountains in a homogeneous fluid. Numer. Heat Transfer A 38, 377–396.Google Scholar
Lin, Y. J. P. & Linden, P. F. 2005 The entrainment due to a turbulent fountain at a density interface. J. Fluid Mech. 542, 25–52.CrossRefGoogle Scholar
List, E. J. 1982 Turbulent jets and plumes. Annu. Rev. Fluid Mech. 14, 189–212.CrossRefGoogle Scholar
Marugán-Cruz, C., Rodríguez-Rodríguez, J. & Martínez-Bazán, C. 2009 Negatively buoyant starting jets. Phys. Fluids 21, 117101.CrossRefGoogle Scholar
Mi, J., Nobes, D. S. & Nathan, G. J. 2001 Influence of jet exit conditions on the passive scalar field of an axisymmetric free jet. J. Fluid Mech. 432, 91–125.CrossRefGoogle Scholar
Mizushina, T., Ogino, F., Takeuchi, H. & Ikawa, H. 1982 An experimental study of vertical turbulent jet with negative buoyancy. Wärme-und Stoffübertragung 16, 15–21.CrossRefGoogle Scholar
Morton, B. R. 1959 Forced plumes. J. Fluid Mech. 5, 151–163.CrossRefGoogle Scholar
Morton, B. R., Taylor, G. I. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. 234, 1–23.Google Scholar
Pantzlaff, L. & Lueptow, R. M. 1999 Transient positively and negatively buoyant turbulent round jets. Exp. Fluids 27, 117–125.CrossRefGoogle Scholar
Papanicolaou, P. N. & Kokkalis, T. J. 2008 Vertical buoyancy preserving and non-preserving fountains, in a homogeneous calm ambient. Intl J. Heat Mass Transfer 51, 4109–4120.CrossRefGoogle Scholar
Sendan, R. A., Behnia, M. M. & Abreu, K. E. 1978 Temperatures in a heated air jet discharged downward. Intl J. Heat Mass Transfer 21, 1453–1458.Google Scholar
Suzuki, Y. J., Koyaguchi, T., Oqawa, M. & Hachisu, I. 2005 A numerical study of turbulent mixing in eruption clouds using a three-dimensional fluid dynamics model. J. Geophys. Res. 110, B08201.CrossRefGoogle Scholar
Turner, J. S. 1966 Jets and plumes with negative or reversing buoyancy. J. Fluid Mech. 26, 779–792.CrossRefGoogle Scholar
Williamson, N., Armfield, S. W. & Lin, W. 2008 a Direct numerical simulation of turbulent intermediate Froude number fountain flow. ANZIAM J. 50, C16–C30.CrossRefGoogle Scholar
Williamson, N., Armfield, S. W. & Lin, W. 2010 Transition behaviour of weak turbulent fountains. J. Fluid Mech. 655, 306–326.CrossRefGoogle Scholar
Williamson, N., Srinarayana, N., Armfield, S. W., McBain, G. D. & Lin, W. 2008 b Low-Reynolds-number fountain behaviour. J. Fluid Mech. 608, 297–317.CrossRefGoogle Scholar
Zhang, H. & Baddour, R. E. 1997 Maximum vertical penetration of plane turbulent negatively buoyant jets. J. Engng Mech. 123, 973–977.Google Scholar
Zhang, H. & Baddour, R. E. 1998 Maximum penetration of vertical round dense jets at small and large Froude numbers. J. Hydraul. Engng 124, 550–553.CrossRefGoogle Scholar

Williamson et al. supplementary movies

Movie 1.Visualisation of Re=3350 and Fr=4 flow from startup through to fully developed flow. Shading indicates non-dimensional scalar concentration φ, from φ=0 (white) to φ=1.0 (black).

Download Williamson et al. supplementary movies(Video)
Video 11.9 MB

Williamson et al. supplementary movie

Movie 2. Visualisation of Re=3350 and Fr=7 flow from startup through to fully developed. Shading indicates non-dimensional scalar concentration φ, from φ=0 (white) to φ=1.0 (black).

Download Williamson et al. supplementary movie(Video)
Video 8.6 MB

Williamson et al supplementary movie

Movie 3. Visualisation of Re=3350 and Fr=7 flow in the ambient fluid and fountain outer-downflow, after the flow is fully developed. Shading indicates non-dimensional azimuthal vorticity, ωθ = dur/dz -duz/dr, from ωθ=-1.0 (red) to ωθ=1.0 (blue). Thick line indicates non-dimensional scalar concentration φ=0.05. The velocity vectors (not scaled to magnitude) indicate flow direction and illustrate how entrainment is linked to pulses of fluid entering the downflow from the top of the fountain.

Download Williamson et al supplementary movie(Video)
Video 10.8 MB