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Entrainment by turbulent fountains

Published online by Cambridge University Press:  04 February 2016

H. C. Burridge
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
G. R. Hunt*
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
*
Email address for correspondence: gary.hunt@eng.cam.ac.uk

Abstract

Experimental measurements of entrainment by turbulent fountains from circular sources in quiescent uniform environments are presented. Our results span almost four orders of magnitude in the source Froude number ($0.004\leqslant \mathit{Fr}_{0}\leqslant 25$) and thereby encompass the entrainment across all classes of fountain behaviour identified to date. We identify scalings for the entrained volume flux $Q_{E}$, in terms of $\mathit{Fr}_{0}$ and the source volume flux $Q_{0}$, within a number of distinct Froude-number bands corresponding to each class of fountain. Additionally we identify a distinct class of new behaviour, as yet unreported, for $\mathit{Fr}_{0}\lesssim 0.1$.

Type
Papers
Copyright
© 2016 Cambridge University Press 

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References

Baines, W. D. 1975 Entrainment by a plume or jet at a density interface. J. Fluid Mech. 68 (2), 309320.CrossRefGoogle Scholar
Baines, W. D. 1983 A technique for the direct measurement of volume flux of a plume. J. Fluid Mech. 132, 247256.CrossRefGoogle Scholar
Baines, W. D., Corriveau, A. F. & Reedman, T. J. 1993 Turbulent fountains in a closed chamber. J. Fluid Mech. 255, 621646.CrossRefGoogle Scholar
Baines, W. D., Turner, J. S. & Campbell, I. H. 1990 Turbulent fountains in an open chamber. J. Fluid Mech. 212, 557592.CrossRefGoogle Scholar
Bloomfield, L. J. & Kerr, R. C. 1998 Turbulent fountains in a stratified fluid. J. Fluid Mech. 358, 335356.Google Scholar
Burridge, H. C. & Hunt, G. R. 2013 The rhythm of fountains: the length and time scales of rise height fluctuations at low and high Froude numbers. J. Fluid Mech. 728, 91119.Google Scholar
Burridge, H. C. & Hunt, G. R. 2014 Scaling arguments for the fluxes in turbulent miscible fountains. J. Fluid Mech. 744, 273285.CrossRefGoogle Scholar
Burridge, H. C., Mistry, A. & Hunt, G. R. 2015 The effect of source Reynolds number on the rise height of a fountain. Phys. Fluids 27 (4), 047101.Google Scholar
Carazzo, G., Kaminski, E. & Tait, S. 2010 The rise and fall of turbulent fountains: a new model for improved quantitative predictions. J. Fluid Mech. 657, 265284.Google Scholar
Cardoso, S. S. S. & Woods, A. W. 1993 Mixing by a turbulent plume in a confined stratified region. J. Fluid Mech. 250, 277305.CrossRefGoogle Scholar
Cresswell, R. W. & Szczepura, R. T. 1993 Experimental investigation into a turbulent jet with negative buoyancy. Phys. Fluids 11, 28652878.Google Scholar
Ezzamel, A., Salizzoni, P. & Hunt, G. R. 2015 Dynamical variability of axisymmetric buoyant plumes. J. Fluid Mech. 765, 576611.Google Scholar
Hunt, G. R. & Burridge, H. C. 2015 Fountains in industry and nature. Annu. Rev. Fluid Mech. 47, 195220.CrossRefGoogle Scholar
Kaye, N. B. & Hunt, G. R. 2006 Weak fountains. J. Fluid Mech. 558, 319328.Google Scholar
Kumagai, M. 1984 Turbulent buoyant convection from a source in a confined two-layered region. J. Fluid Mech. 147, 105131.Google Scholar
Lin, W. E. & Armfield, S. W. 2000 Very weak fountains in a homogeneous fluid. Numer. Heat Transfer A 38, 377396.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, 2552.Google Scholar
Morton, B. R. 1959 Forced plumes. J. Fluid Mech. 5, 151163.CrossRefGoogle Scholar
Morton, B. R., Taylor, G. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234, 123.Google Scholar
Shrinivas, A. B. & Hunt, G. R. 2014 Unconfined turbulent entrainment across density interfaces. J. Fluid Mech. 757, 573598.CrossRefGoogle Scholar
Sutherland, B. R. 2010 Internal Gravity Waves. Cambridge University Press.CrossRefGoogle Scholar
Williamson, N., Armfield, S. W. & Lin, W. 2011 Forced turbulent fountain flow behaviour. J. Fluid Mech. 671, 535558.CrossRefGoogle Scholar