Non-Oberbeck-Boussinesq effects in three-dimensional Rayleigh-Bénard convection

Part of the ERCOFTAC Series book series (ERCO, volume 15)

Abstract

To study the classical problem of Rayleigh-Bénard convection, i.e. a fluid layer confined between a heating-plate at the bottom and a cooling-plate at the top, a common assumption is that all material properties are temperature independent, except for the density ρ within the buoyancy part, that changes like
$$\rho(T) = \rho_0 \left(1 - \alpha \cdot (T-T_0)\right),$$
with a constant isobaric expansion coefficient α. In combination with the condition of an incompressible fluid this is the so-called Oberbeck-Boussinesq (OB) approximation (Boussinesq, 1903; Oberbeck, 1879).

Keywords

Nusselt Number Direct Numerical Simulation Buoyancy Term High Rayleigh Number Viscous Boundary Layer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ahlers, G., Brown, E., Fontenele Araujo, F., Funfschilling, D. Grossmann, S. Lohse, D.: Non-Oberbeck-Boussinesq effects in strongly turbulent Rayleigh-Bénard convection. J. Fluid Mech. 569, 409–445 (2006) MATHCrossRefGoogle Scholar
  2. 2.
    Boussinesq, J. V.: Theorie Analytique de la Chaleur 2. Gauthier-Villars (1903) Google Scholar
  3. 3.
    Chorin, A. J.: A Numerical Method for Solving Incompressible Viscous Flow Problems. Journal of Computational Physics 2, 12–26 (1967) MATHCrossRefGoogle Scholar
  4. 4.
    Gray, D. D., Giorgini, A.: The validity of the Boussinesq approximation for liquids and gases. Int. J. Heat Mass Transfer 19, 545–551 (1976) MATHCrossRefGoogle Scholar
  5. 5.
    Oberbeck, A.: Ueber die Wärmeleitung der Flüssigkeiten bei Berücksichtigung der Strömungen infolge von Temperaturdifferenzen. Annalen der Physik 243, 271–292 (1879) CrossRefGoogle Scholar
  6. 6.
    Shishkina, O., Stevens, R. J. A. M., Grossmann, S., Lohse, D.: Boundary layer structure in turbulent thermal convection and its consequences for the requiered numerical resolution. New J. Physics 12, 075022 (2010) CrossRefGoogle Scholar
  7. 7.
    Shishkina, O., Thess, A.: Mean temperature profiles in turbulent Rayleigh-Bénard convection of water. J. Fluid Mech. 633, 449–460 (2009) MATHCrossRefGoogle Scholar
  8. 8.
    Shishkina, O., Wagner, C.: A fourth order finite volume scheme for turbulent flow simulations in cylindrical domains. Computers & Fluids 36, 484–497 (2007) MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Shishkina, O., Wagner, C.: Boundary and interior layers in turbulent thermal convection in cylindrical containers. Int. J. Computing Science and Mathematics 1, 360–373 (2007) MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Sugiyama K., Calzavarini, E., Grossmann, S., Lohse, D.: Flow organization in two-dimensional non-Oberbeck-Boussinesq Rayleigh-Bénard convection in water. J. Fluid Mech. 637, 105–135 (2009) MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.DLR - Institute of Aerodynamics and Flow TechnologyGöttingenGermany

Personalised recommendations