Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-18T08:07:17.726Z Has data issue: false hasContentIssue false
  • English
  • Français

Unsteady confined buoyant plumes

Published online by Cambridge University Press:  26 April 2006

Gilles Desrayaud  and
Guy Lauriat
Gilles Desrayaud
Affiliation:
IBM-France, C3NI, 95 rue de la Galéra, 34090 Montpellier, France
Guy Lauriat
Affiliation:
Laboratoire de Thermique, CNAM, 292 rue Saint-Martin, 75141 Paris Cédex 03, France
Get access Rights & Permissions [Opens in a new window]

Abstract

Two-dimensional time-dependent buoyancy-induced flows above a horizontal line heat source inside rectangular vessels, with adiabatic sidewalls and top and bottom walls maintained at uniform temperature, are studied numerically. Transitions to unsteady flows are performed by direct simulations for various depths of immersion of the source in the central vertical plane of air-filled vessels. For a square vessel and a line source near the bottom wall, the numerical solutions exhibit a sequence of instabilities, called natural swaying motion of confined plumes, beginning with a periodic regime having a high fundamental frequency followed by a two-frequency locked regime. Then, broadband components appearing in the spectra indicate chaotic behaviour and a weakly turbulent motion arises via an intermittent route to chaos. For rectangular vessels of aspect ratio greater than 2 and depths of immersion greater than the width, the flow undergoes a pitchfork bifurcation. This symmetry breaking is driven by the destabilization of an upper unstable layer of stagnant fluid above the plume. Then a subcritical Hopf bifurcation occurs. On the other hand, if the depth of immersion is lower than the width of the vessel, a stable layer of fluid is at rest below the line source. Then penetrative convection sets the whole air-filled vessel in motion and an oscillatory motion of very low frequency arises through supercritical Hopf bifurcation followed by a two-frequency locked state.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 252 , July 1993 , pp. 617 - 646
Copyright
© 1993 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

Beck, J. V., McLain, H. A., Karnitz, M. A., Shonder, J. A. & Segan, E. G. 1988 Heat losses from underground steam pipes. Trans. ASME C: J. Heat Transfer 110, 814–820.Google Scholar
Bérge, P., Pomeau, Y. & Vidal, Ch. 1988 L'Ordre Dans le Chaos. Hermann.
Bill, R. G. & Gebhart, B. 1975 The transition of plane plumes. Intl J. Heat Mass Transfer 18, 513–526.Google Scholar
Brodowicz, K. & Kierkus, W. T. 1966 Experimental investigation of laminar free-convection flow in air above horizontal wire with constant heat flux. Intl J. Heat Mass Transfer 9, 81–94.Google Scholar
Desrayaud, G., Lepeutrec, Y. & Lauriat, G. 1990 Numerical simulation of oscillatory convection in low-Pr fluids. In Notes on Numerical Fluid Mechanics, vol. 27, pp. 49–56. Vieweg.
Eichhorn, R., Lienhard, J. H. & Chen, C. C. 1974 Natural convection from isothermal spheres and cylinders immersed in a stratified fluid. In Proc. 5th Intl Heat Transfer Conf., Tokyo, JSME—SCEJ, vol. 3, pp. 10–14.
Eichhorn, R. & Vedhanayagam, M. 1982 The swaying frequency of line source plumes. In Proc. 7th Intl Heat Transfer Conf., Munich (ed. U. Grigull, E. Hahne, K. Stephan & J. Straub), vol. 2, pp. 407–412. Hemisphere.
Forstrom, R. J. & Sparrow, E. M. 1967 Experiments on the buoyant plumes above a heated horizontal wire. Intl J. Heat Mass Transfer 10, 321–331.Google Scholar
Fujii, T. 1963 Theorey of the steady laminar natural convection above a horizontal line heat source and a point heat source. Intl J. Heat Mass Transfer 6, 597–606.Google Scholar
Fujii, T., Morioka, I. & Uehara, H. 1973 Buoyant plume above horizontal line heat source. Intl J. Heat Mass Transfer 16, 755–768.Google Scholar
Gebhart, B., Jaluria, Y., Mahajan, R. L. & Sammakia, B. 1988 Buoyancy-Induced Flows and Transport. Springer.
Gebhart, B., Pera, L. & Schorr, A. W. 1970 Steady laminar natural convection plumes above a horizontal line heat source. Intl J. Heat Mass Transfer 13, 161–171.Google Scholar
Haaland, S. E. & Sparrow, E. M. 1973 Stability of buoyant boundary layers and plumes, taking into account of nonparallelism of the basic flows. Trans. ASME C: J. Heat Transfer 95, 295–301.Google Scholar
Hasnaoui, M., Bilgen, E. & Vasseur, P. 1990 Natural convection above an array of open cavities heated from below. Numer. Heat Transfer 18A, 463–482.Google Scholar
Hieber, C. A. & Nash, E. J. 1975 Natural convection above a line heat source: higher-order effects and stability. Intl J. Heat Mass Transfer 18, 1473–1479.Google Scholar
Incropera, F. P. & Yaghoubi, M. A. 1980 Buoyancy driven flows originating from heated cylinders submerged in a finite water layer. Intl J. Heat Mass Transfer 23, 269–278.Google Scholar
Jaluria, Y. 1982 Thermal plume interaction with vertical surfaces. Lett. Heat Mass Transfer 9, 107–117.Google Scholar
Lauriat, G. & Desrayaud, G. 1990 Numerical study of oscillatory buoyant plumes above a horizontal line heat source. In Proc. 9th Intl Heat Transfer Conf., Jerusalem (ed. G. Hetsroni), vol. 4, pp. 117–176. Hemisphere.
Leibovich, S., Lele, S. K. & Moroz, I. M. 1989 Nonlinear dynamics in Langmuir circulations and thermosolutal convection. J. Fluid Mech. 198, 471–511 (and Corrigendum 235 (1992), 6901.Google Scholar
Lyakhov, Y. N. 1970 Experimental investigation of free convection above a heated horizontal wire. J. Appl. Mech. Tech. Phys. 11, 355–359.Google Scholar
Mörwald, K., Mitsotakis, K. & Schneider, W. 1986 Higher-order analysis of laminar plumes. In Proc. 8th Intl Heat Transfer Conf., San Francisco (ed. C. L. Tien, V. P. Carrey & J. K. Ferrell), vol. 3, pp. 1335–1340. Hemisphere.
Nawoj, H. J. & Hickman, R. S. 1977 An experimental investigation of the plume velocity field above a horizontal line heat source. Trans. ASME C: J. Heat Transfer 99, 609–613.Google Scholar
Noto, K. 1989 Swaying motion in thermal plume above a horizontal line heat source. J. Thermophys. 3, 428–434.Google Scholar
Noto, K., Matsui, S. & Matsumoto, R. 1982 Observation on vortex pair of plane plume in thermally stratified fluid. In Flow Visualization, vol. 4, pp. 697–702. Springer.
Pera, L. & Gebhart, B. 1971 On the stability of laminar plumes: some numerical solutions and experiments. Intl J. Heat Mass Transfer 14, 975–984.Google Scholar
Pera, L. & Gebhart, B. 1975 Laminar plume interactions. J. Fluid Mech. 68, 259–271.Google Scholar
Peyret, R. 1990 The Chebyshev multidomain approach to stiff problems in fluid mechanics. Comput. Methods Appl. Mech. Engng 80, 129–145.Google Scholar
Schorr, A. W. & Gebhart, B. 1970 An experimental investigation of natural convection wakes above a line heat source. Intl J. Heat Mass Transfer 13, 557–571.Google Scholar
Urakawa, K., Morioka, I. & Kiyota, M. 1983 Swaying motion of the buoyant plume above a horizontal line heat source. In Proc. 1st ASME-JSME Thermal Engng Conf., Honolulu. HI, vol. 3, pp. 215–220.
Wakitani, S. 1985 Non-parallel-flow stability of a two-dimensional buoyant plume. J. Fluid Mech. 159, 241–258.Google Scholar
Wakitani, S. & Yosinobu, H. 1984 Stability characteristics of a natural convection flow above a horizontal line heat source. J. Phys. Soc. Japan 53, 1291–1300.Google Scholar
wolf, A., Swift, J. B., Swinney, H. L. & Vastano, J. A. 1985 Determining Lyapounov exponents from a time series. Physica 16D, 285–317.Google Scholar
Yaghoubi, M. A. & Incropera, F. P. 1978 Natural convection from a heated horizontal cylinder submerged in a shallow water layer. In Proc. 6th Intl Heat Transfer Conf., Toronto, vol. 2, pp. 269–274. Hemisphere.
Yosinobu, H., Onishi, Y., Amano, S., Enyo, S. & Wakitani, S. 1979 Experimental study on instability of a natural convection flow above a horizontal line heat source. J. Phys. Soc. Japan 47, 312–319.Google Scholar
Zia, J. L., Xin, M. D. & Zhang, H. J. 1990 Natural convection in an externally heated enclosure containing a local heat source. J. Thermophys. 4, 233–238.Google Scholar