Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-12-03T00:01:43.643Z Has data issue: false hasContentIssue false
  • English
  • Français

A scaling analysis of transient natural convection in a reservoir model induced by iso-flux heating

Published online by Cambridge University Press:  23 December 2014

Peng Yu ,
John C. Patterson  and
Chengwang Lei
Peng Yu*
Affiliation:
School of Civil Engineering, University of Sydney, Sydney, NSW 2006, Australia
John C. Patterson
Affiliation:
School of Civil Engineering, University of Sydney, Sydney, NSW 2006, Australia
Chengwang Lei
Affiliation:
School of Civil Engineering, University of Sydney, Sydney, NSW 2006, Australia
*
†Present address: Institute of High Performance Computing, Agency for Science, Technology and Research (A*STAR), Republic of Singapore. Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This study presents a detailed scaling analysis quantifying the transient behaviour of natural convection in a reservoir model induced by iso-flux surface heating. It is found that horizontal conduction, which has often been neglected in previous analyses, plays an important role in the development of the flow. Depending on the Rayleigh number, three possible pathways through which the flow develops towards the final steady state are identified. A thermal boundary layer initially grows downwards from the surface. When the thermal boundary layer reaches the sloping bottom and becomes indistinct, a horizontal temperature gradient establishes due to the increasing water depth in the offshore direction. A flow is then driven towards the offshore direction by a buoyancy-induced horizontal pressure gradient, which convects away the heat input from the water surface. On the other hand, the horizontal temperature gradient also conducts heat away. The flow behaviour is determined by the interaction between the horizontal conduction and convection. An interesting flow feature revealed by the present scaling analysis is that the region across which the thermal boundary layer encompasses the full water depth shrinks over time at a certain stage of the flow development. The shrinking process eventually stops when this region coincides with a conduction-dominated subregion. The present scaling results are verified by corresponding numerical simulations.

JFM classification

Convection: Buoyant boundary layers Convection: Convection in cavities Geophysical and Geological Flows: Gravity currents
Type
Papers
Information
Journal of Fluid Mechanics , Volume 764 , 10 February 2015 , pp. 219 - 249
Check for updates
Copyright
© 2014 Cambridge University Press 

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

Adams, E. E. & Wells, S. A. 1984 Field measurements on side arms of Lake Anna Va. J. Hydraul. Engng 110, 773–793.CrossRefGoogle Scholar
Bednarz, T., Lei, C. & Patterson, J. C. 2008 An experimental study of unsteady natural convection in a reservoir model cooled from the water surface. Exp. Therm. Fluid Sci. 32, 844–856.CrossRefGoogle Scholar
Bednarz, T., Lei, C. & Patterson, J. C. 2009a A numerical study of unsteady natural convection induced by iso-flux surface cooling in a reservoir model. Intl J. Heat Mass Transfer 52, 56–66.CrossRefGoogle Scholar
Bednarz, T., Lei, C. & Patterson, J. C. 2009b An experiment study of unsteady natural convection in a reservoir model subject to periodic thermal forcing using combined PIV and PIT techniques. Exp. Fluids 47, 107–117.CrossRefGoogle Scholar
Bednarz, T., Lei, C. & Patterson, J. C. 2009c Unsteady natural convection induced by diurnal temperature changes in a reservoir with slowly varying bottom topography. Intl J. Therm. Sci. 48, 1932–1942.CrossRefGoogle Scholar
Farrow, D. E. 2004 Periodically forced natural convection over slowly varying topography. J. Fluid Mech. 508, 1–21.CrossRefGoogle Scholar
Farrow, D. E. & Patterson, J. C. 1994 The daytime circulation and temperature pattern in a reservoir sidearm. Intl J. Heat Mass Transfer 37, 1957–1968.CrossRefGoogle Scholar
Ferziger, J. H. & Perić, M. 1999 Computational Methods for Fluid Dynamics, 2nd edn. Springer.CrossRefGoogle Scholar
Horsch, G. M. & Stefan, H. G. 1988 Convective circulation in littoral water due to surface cooling. Limnol. Oceanogr. 33, 1068–1083.CrossRefGoogle Scholar
Horsch, G. M., Stefan, H. G. & Gavali, S. 1994 Numerical simulation of cooling-induced convective currents on a littoral slope. Intl J. Numer. Meth. Fluids 19, 105–134.CrossRefGoogle Scholar
Lei, C. & Patterson, J. C. 2002a Natural convection in a reservoir sidearm subject to solar radiation: a two-dimensional simulation. Numer. Heat Transfer A 42, 13–32.CrossRefGoogle Scholar
Lei, C. & Patterson, J. C. 2002b Unsteady natural convection in a triangular enclosure induced by absorption of radiation. J. Fluid Mech. 460, 181–209.CrossRefGoogle Scholar
Lei, C. & Patterson, J. C. 2003 A direct stability analysis of a radiation-induced natural convection boundary layer in a shallow wedge. J. Fluid Mech. 480, 161–184.CrossRefGoogle Scholar
Lei, C. & Patterson, J. C. 2005 Unsteady natural convection in a triangular enclosure induced by surface cooling. Intl J. Heat Fluid Flow 26, 307–321.CrossRefGoogle Scholar
Lei, C. & Patterson, J. C. 2006 Natural convection induced by diurnal heating and cooling in a reservoir with slowly varying topography. JSME Intl J. Ser. B 49, 605–615.CrossRefGoogle Scholar
Mao, Y., Lei, C. & Patterson, J. C. 2009 Unsteady natural convection in a triangular enclosure induced by absorption of radiation – a revisit by improved scaling analysis. J. Fluid Mech. 622, 75–102.CrossRefGoogle Scholar
Mao, Y., Lei, C. & Patterson, J. C. 2010 Unsteady near-shore natural convection induced by surface cooling. J. Fluid Mech. 642, 213–233.CrossRefGoogle Scholar
Monismith, S. G. 2007 Hydrodynamics of coral reefs. Annu. Rev. Fluid Mech. 39, 37–55.CrossRefGoogle Scholar
Monismith, S. G., Genin, A., Reidenbach, M. A., Yahel, G. & Koseff, J. R. 2006 Thermally driven exchanges between a coral reef and the adjoining ocean. J. Phys. Oceanogr. 36, 1332–1347.CrossRefGoogle Scholar
Monismith, S. G., Imberger, J. & Morison, M. L. 1990 Convective motions in the sidearm of a small reservoir. Limnol. Oceanogr. 35, 1676–1702.CrossRefGoogle Scholar
Patterson, J. & Imberger, J. 1980 Unsteady natural convection in a rectangular cavity. J. Fluid Mech. 100, 65–86.CrossRefGoogle Scholar
Phillips, O. M. 1970 On flows induced by diffusion in a stably stratified fluid. Deep-Sea Res. 17, 435–443.Google Scholar
Rhie, C. M. & Chow, W. L. 1983 Numerical study of the turbulent flow past an airfoil with trailing edge separation. AAIA J. 21, 1525–1532.CrossRefGoogle Scholar
Sturman, J. J., Oldham, C. E. & Ivey, G. N. 1999 Steady convective exchange flows down slopes. Aquat. Sci. 61, 260–278.CrossRefGoogle Scholar
Wunsch, C. 1970 On oceanic boundary mixing. Deep-Sea Res. 17, 293–301.Google Scholar
Yu, P., Lee, T. S., Zeng, Y. & Low, H. T. 2007 A numerical method for flows in porous and open domains coupled at the interface by stress jump. Intl J. Numer. Meth. Fluids 53, 1755–1775.CrossRefGoogle Scholar
Yu, P., Lei, C. & Patterson, J. C. 2012a Transient behaviour of natural convection in a reservoir model induced by surface heating. J. Therm. Sci. Technol. 7, 211–226.CrossRefGoogle Scholar
Yu, P., Lei, C. & Patterson, J. C. 2012b A numerical simulation of transient near-shore natural convection induced by ramped iso-flux cooling. Intl J. Heat Fluid Flow 38, 107–117.CrossRefGoogle Scholar