Physics of Fluids
Feedback | Help | Exit
Search:
   
 
 
 
Previous Article
Combustion mechanism of liquid fuel spray in a gaseous flame
Two-dimensional direct numerical simulation is applied to spray flames stabilized in a laminar counterflow, and the detailed behavior is studied in terms of the droplet group combustion. The stretch r...
Next Article
Splitting and merging of Görtler vortices
The splitting and merging of Görtler vortices are experimentally studied by varying the spacings of vertical wires located 10  mm upstream of a concave surface leading edge of 2.0 ...

Three-dimensional numerical study of natural convection in vertical cylinders partially heated from the side

Phys. Fluids 17, 124101 (2005); doi:10.1063/1.2141430

Published 9 December 2005

You are not logged in to this journal. Log in

D. J. Ma, D. Henry, and H. Ben Hadid
Laboratoire de Mécanique des Fluides et d'Acoustique, UMR CNRS 5509, Ecole Centrale de Lyon/Université Claude Bernard Lyon 1/INSA de Lyon, ECL, 36 avenue Guy de Collongue, 69134 Ecully Cedex, France
Three-dimensional steady and oscillatory flows are simulated in a vertical cylinder partially heated from the side. The vertical wall is heated in a zone at midheight and is insulated above and below this middle zone, while both ends of the cylinder are cooled. The cylinder aspect ratio (A=height/radius) ranges from 2 to 8, whereas a fixed Prandtl number, Pr=0.021, is considered as well as a fixed length of the heated zone, equal to the cylinder radius. Three-dimensional steady and unsteady simulations as well as mode decomposition techniques and energy transfer analyses are used to characterize the flows and their transitions. The flows that develop from the steady toroidal pattern beyond the first instability threshold break the axisymmetry. At small A (2<=A<=2.5), the flow corresponds to a two-roll rotating pattern, which is triggered by a k=2 azimuthal mode as a result of a hydrodynamic instability. At large A (3<=A<=8), the flow is steady and corresponds to a main one-roll pattern in the upper part of the cylinder. The flow is triggered by a k=1 mode as a result of buoyancy effects affecting this unstably stratified upper part (Rayleigh-Bénard instability), but shear effects are involved in the instability for the smaller values of A. These steady flows then transit at a higher threshold to a standing-wave oscillatory one-roll pattern associated with the breaking of symmetry of the previous steady pattern. For intermediate values of A (2.7<=A<=2.9), the transition is toward an oscillatory pattern, but hysteresis phenomena with multiplicity of steady and oscillatory states have been found. Comparisons with experiments performed at aspect ratios A=4 and 8 are then considered and discussed. ©2005 American Institute of Physics
History: Received 9 December 2004; accepted 20 October 2005; published 9 December 2005
Permalink: http://link.aip.org/link/?PHFLE6/17/124101/1
BUY THIS ARTICLE   (US$24)
Download PDF (373 kB) View Cart

KEYWORDS and PACS

Keywords
PACS
  • 47.60.+i
    Flows in ducts, channels, nozzles, and conduits
  • 47.55.Hd
    Stratified flows
  • 47.20.Bp
    Buoyancy-driven hydrodynamic instability
  • 47.20.Ky
    Nonlinearity (including bifurcation theory) (hydrodynamic stability)
  • YEAR: 2005

RELATED DATABASES


To view database links for this article,
you need to log in.
To view database links for this article,
you need to log in.

PUBLICATION DATA

ISSN:
1070-6631 (print)   1089-7666 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (21)
View in Separate Window/Tab
For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. G. Müller and A. Ostrogorsky, "Convection in melt growth," in Handbook of Crystal Growth, edited by D. T. J. Hurle (North-Holland, Amsterdam, 1994), Vol. 2, pp. 711–781.
  2. J. P. Garandet and T. Alboussière, "Bridgman growth: Modeling and experiments," Prog. Cryst. Growth Charact. Mater. 38, 73 (1999).
  3. G. Müller, G. Neumann, and W. Weber, "Natural convection in vertical Bridgman configurations," J. Cryst. Growth 70, 78 (1984).
  4. G. Neumann, "Three-dimensional numerical simulation of buoyancy-driven convection in vertical cylinders heated from below," J. Fluid Mech. 214, 559 (1990).
  5. M. Wanschura, H. C. Kuhlmann, and H. J. Rath, "Three-dimensional instability of axisymmetric buoyant convection in cylinders heated from below," J. Fluid Mech. 326, 399 (1996).
  6. R. Touihri, H. Ben Hadid, and D. Henry, "On the onset of convective instabilities in cylindrical cavities heated from below. I. Pure thermal case," Phys. Fluids 11, 2078 (1999).
  7. J. Baumgartl, W. Budweiser, G. Müller, and G. Neumann, "Studies of buoyancy-driven convection in a vertical cylinder with parabolic temperature profile," J. Cryst. Growth 97, 9 (1989).
  8. A. Yu. Gelfgat, P. Z. Bar-Yoseph, and A. Solan, "Axisymmetry breaking instabilities of natural convection in a vertical Bridgman growth configuration," J. Cryst. Growth 220, 316 (2000).
  9. R. Selver, Y. Kamotani, and S. Ostrach, "Natural convection of a liquid metal in vertical circular cylinders heated locally from the side," J. Heat Transfer 120, 108 (1998).
  10. V. Erenburg, A. Yu. Gelfgat, E. Kit, P. Z. Bar-Yoseph, and A. Solan, "Multiple states, stability and bifurcations of natural convection in a rectangular cavity with partially heated vertical walls," J. Fluid Mech. 492, 63 (2003).
  11. A. Rubinov, V. Erenburg, A. Yu. Gelfgat, E. Kit, P. Z. Bar-Yoseph, and A. Solan, "Three-dimensional instabilities of natural convection flow in a vertical cylinder with partially heated sidewall," ASME J. Heat Transfer 126, 586 (2004).
  12. Computational Methods for Fluid Dynamics, edited by J. H. Ferziger and M. Peric (Springer, Berlin, 1996).
  13. Numerical Heat Transfer and Fluid Flow, edited by S. V. Patankar (Hemisphere, Washington, DC, 1980).
  14. A. Brandt, "Multilevel adaptative computations in fluid dynamics," AIAA Pap. 79-1455, 1979.
  15. J. Kim and P. Moin, "Application of a fractional-step method to incompressible Navier-Stokes equations," J. Comput. Phys. 59, 308 (1985).
  16. R. Verzicco and P. Orlandi, "A finite-difference scheme for the three-dimensional incompressible flows in cylindrical coordinates," J. Comput. Phys. 123, 402 (1996).
  17. G. S. Charlson and R. L. Sani, "On thermoconvective instability in a bounded cylindrical fluid layer," Int. J. Heat Mass Transfer 14, 2157 (1971).
  18. J. C. Buell and I. Catton, "The effect of wall conduction on the stability of a fluid in a right circular cylinder heated from below," ASME J. Heat Transfer 105, 255 (1983).
  19. J. C. Buell and I. Catton, "Effect of rotation on the stability of a bounded cylindrical layer of fluid heated from below," Phys. Fluids 26, 892 (1983).
  20. B. Hof, A. Juel, L. Zhao, D. Henry, H. Ben Hadid, and T. Mullin, "On the onset of oscillatory convection in molten gallium," J. Fluid Mech. 515, 391 (2004).
  21. A. Yu. Gelfgat, P. Z. Bar-Yoseph, and A. L. Yarin, "Stability of multiple steady states of convection in laterally heated cavities," J. Fluid Mech. 388, 315 (1999).

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.


Copyright © American Institute of Physics