Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-25T12:39:34.185Z Has data issue: false hasContentIssue false
  • English
  • Français

Fountains impinging on a density interface

Published online by Cambridge University Press:  08 January 2008

JOSEPH K. ANSONG ,
PATRICK J. KYBA  and
BRUCE R. SUTHERLAND
JOSEPH K. ANSONG
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada T6G 2G1
PATRICK J. KYBA
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada T6G 2G1
BRUCE R. SUTHERLAND
Affiliation:
Departments of Physics and of Earth and Atmospheric Sciences, University of Alberta, Edmonton, AB, Canada T6G 2G7
Get access Rights & Permissions [Opens in a new window]

Abstract

We present an experimental study of an axisymmetric turbulent fountain in a two-layer stratified environment. Interacting with the interface, the fountain is observed to exhibit three regimes of flow. It may penetrate the interface, but nonetheless return to the source where it spreads as a radially propagating gravity current; the return flow may be trapped at the interface where it spreads as a radially propagating intrusion or it may do both. These regimes have been classified using empirically determined regime parameters which govern the relative initial momentum of the fountain and the relative density difference of the fountain and the ambient fluid. The maximum vertical distance travelled by the fountain in a two-layer fluid has been theoretically determined by extending the theory developed for fountains in a homogeneous environment. The theory compares favourably with experimental measurements. We have also developed a theory to analyse the initial speeds of the resulting radial currents. The spreading currents exhibited two different flow regimes: a constant-velocity regime and an inertia-buoyancy regime in which the front position, R, scales with time, t, as R ∼ t3/4. These regimes were classified using a critical Froude number which characterized the competing effects of momentum and buoyancy in the currents.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 595 , 25 January 2008 , pp. 115 - 139
Copyright
Copyright © Cambridge University Press 2008

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. 1963 Jet diffusion in stagnant ambient fluid. Delft Hydraulics Laboratory, Publication 29.Google Scholar
Baines, W. & Chu, V. 1996 ‘Jets and Plumes’ in Environmental Hydraulics, chap. 2. Kluwer.Google Scholar
Baines, W., Turner, J. & Campbell, I. 1990 Turbulent fountains in an open chamber. J. Fluid Mech. 212, 557–592.CrossRefGoogle Scholar
Bloomfield, L. & Kerr, R. 1998 Turbulent fountains in a stratified fluid. J. Fluid Mech. 358, 335–356.CrossRefGoogle Scholar
Bloomfield, L. & Kerr, R. 2000 A theoretical model of a turbulent fountain. J. Fluid Mech. 424, 197–216.CrossRefGoogle Scholar
Britter, R. 1979 The spread of a negatively buoyant plume in a calm environment. Atmos. Environ. 13, 1241–1247.CrossRefGoogle Scholar
Britter, R. 1989 Atmospheric dispersion of dense gases. Annu. Rev. Fluid Mech. 21, 317–344.CrossRefGoogle Scholar
Chen, J.-C. 1980 Studies on gravitational spreading currents. PhD thesis, California Institute of Technology.Google Scholar
Daviero, G., Roberts, J. & Mile, K. 2001 Refractive index matching in large-scale experiments. Exps. Fluids 31, 119–126.CrossRefGoogle Scholar
Fischer, H., List, E., Imberger, J. & Brooks, N. 1979 Mixing in Inland and Coastal Waters. Academic.Google Scholar
Friedman, P. & Katz, J. 2000 Rise height for negatively buoyant fountains and depth of penetration for negatively buoyant jets impinging an interface. Trans. ASME I: J. Fluids Engng 122, 779–782.Google Scholar
Kapoor, K. & Jaluria, Y. 1993 Penetrative convection of a plane turbulent wall jet in a two-layer thermally stable environment: a problem in enclosure fires. Intl J. Heat Mass Transfer 36, 155–167.CrossRefGoogle Scholar
Kotsovinos, N. 2000 Axisymmetric submerged intrusion in stratified fluid. J. Hydrau Engng ASCE 126, 446–456.CrossRefGoogle Scholar
Lee, J. & Chu, V. 2003 Turbulent Buoyant Jets and Plumes: A Langrangian Approach. Kluwer.CrossRefGoogle Scholar
Lin, Y. & Linden, P. 2005 a A model for an under floor air distribution system. Energy and Buildings 37, 399–409.CrossRefGoogle Scholar
Lin, Y. & Linden, P. 2005 b The entrainment due to a turbulent fountain at a density interface. J. Fluid Mech. 542, 25–52.CrossRefGoogle Scholar
List, E. 1982 Turbulent jets and plumes. Annu. Rev. Fluid Mech. 14, 189–212.CrossRefGoogle Scholar
Lister, J. & Kerr, R. 1989 Viscous gravity currents at a fluid interface. J. Fluid Mech. 203, 215–249.CrossRefGoogle Scholar
McDougall, T. 1981 Negatively buoyant vertical jets. Tellus 33, 313–320.CrossRefGoogle Scholar
Mellor, G. 1996 Introduction to Physical Oceanography. Springer.Google Scholar
Mizushina, T., Ogino, F., Takeuchi, H. & Ikawa, H. 1982 An experimental study of vertical turbulent jet with negative buoyancy. Warme and Stoffubertragung (Thermo and Fluid Dynamics) 16, 15–21.CrossRefGoogle Scholar
Morton, R. 1959 a The ascent of turbulent forced plumes in a calm atmosphere. Intl J. Air Pollution 1, 184–197.Google Scholar
Morton, R. 1959 b Forced plumes. J. Fluid Mech. 5, 151–163.CrossRefGoogle Scholar
Morton, R., Taylor, G. & Turner, J. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234, 1–23.Google Scholar
Noutsopoulos, G. & Nanou, K. 1986 The round jet in a two-layer stratified ambient. Proc. Intl Symp. on Buoyant Flows: Athens-Greece vol. 1–5, 165–183.Google Scholar
Priestley, C. & Ball, F. 1955 Continuous convection from an isolated source of heat. Q. J. R. Met. Soc. 81, 144–156.CrossRefGoogle Scholar
Rawn, A., Bowerman, F. & Brooks, N. 1960 Diffusers for disposal of sewage in sea water. J. Sanitary Engng Div. Proc. ASCE 86, 65–105.CrossRefGoogle Scholar
Rodi, W. 1982 Turbulent Buoyant Jets and Plumes. Pergamon.Google Scholar
Scorer, R. 1959 The behaviour of chimney plumes. Intl J. Air Pollution 1, 198–220.Google ScholarPubMed
Seban, R., Behnia, M. & Abreu, K. 1978 Temperatures in a heated air jet discharged downward. Intl J. Heat Mass Transfer 21, 1453–1458.CrossRefGoogle Scholar
Shy, S. 1995 Mixing dynamics of jet interaction with a sharp density interface. Expl Thermal Fluid Sci. 10, 355–369.CrossRefGoogle Scholar
Timothy, W. 1977 Density currents and their applications. J. Hydraul. Div. 103, HY5, 543–555.Google Scholar
Turner, J. 1966 Jets and plumes with negative or reversing buoyancy. J. Fluid Mech. 26, 779–792.CrossRefGoogle Scholar
Turner, J. 1973 Buoyancy Effects in Fluids. Cambridge University Press.CrossRefGoogle Scholar