Direct Numerical Simulation of Buoyancy Driven Turbulence inside a Cubic Cavity

  • R. Puragliesi
  • A. Dehbi
  • E. Leriche
  • A. Soldati
  • M. Deville
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design book series (NNFM, volume 110)


Direct numerical simulation (DNS) of thermally driven turbulent flows inside a fully confined eclosure is performed using state-of-the-art Chebyshev pseudo-spectral methods. The identification of turbulent coherent structures through λ 2 method is presented as well as the direct influence of turbulent eddies on the local Nusselt number and the shear stress distribution at the active walls. Furthermore a first study of turbulent kinetic energy and temperature variance together with the respective production and dissipation terms are reported for Rayleigh number Ra = 109.


Turbulent Kinetic Energy Rayleigh Number Direct Numerical Simulation Local Nusselt Number Shear Stress Distribution 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Batoul, A., Khallouf, H., Labrosse, G.: Une Méthode de Résolution Directe (Pseudo-Spectrale) du Problème de Stokes 2D/3D Instationnaire. Application à la Cavité Entrainée Carrée. C.R. Acad. Sci. Paris 319 Série I, 1455–1461 (1994)zbMATHGoogle Scholar
  2. 2.
    Bejan, A.: Convection heat transfer. Wiley Interscience, Hoboken (1984)zbMATHGoogle Scholar
  3. 3.
    Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods in Fluid Dynamics. Springer Series in Computational Physics. Springer, New-York (1988)zbMATHGoogle Scholar
  4. 4.
    Gottlieb, D., Orszag, S.A.: Numerical Analysis of Spectral Methods: Theory and Applications. SIAM-CBMS, Philadelphia (1977)zbMATHGoogle Scholar
  5. 5.
    Haldenwang, P., Labrosse, G., Abboudi, S.A., Deville, M.: Chebyshev 3D Spectral and 2D Pseudospectral Solvers for the Helmholtz Equation. Journal of Computational Physics 55, 115–128 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Hanjalic, K., Kenjeres, S., Durst, F.: Natural convection in partitioned two-dimensional enclosures at higher rayleigh numbers. International Journal of Heat and Mass Transfer 39(7), 1407–1427 (1996)zbMATHCrossRefGoogle Scholar
  7. 7.
    Hsieh, K.J., Lien, F.S.: Numerical modeling of buoyancy-driven turbulent flows in enclosures. International Journal of Heat and Fluid Flow 25(4), 659–670 (2004)CrossRefGoogle Scholar
  8. 8.
    Jeong, J., Hussain, F.: On the identification of a vortex. Journal of Fluid Mechanics 285, 69–94 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Karniadakis, G.E.M., Israeli, M., Orszag, S.A.: High-Order Splitting Methods for the Incompressible Navier-Stokes Equations. J. Computational Physics 97, 414–443 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Le Quéré, P.: Accurate solutions to the square thermally driven cavity at high Rayleigh number. Computers and Fluids 20(1), 29–41 (1991)zbMATHCrossRefGoogle Scholar
  11. 11.
    Leong, W.H., Hollands, K.G.T., Brunger, A.P.: On a physically-realizable benchmark problem in internal natural convection. Int. J. Heat Mass Transfer 41, 3817–3828 (1998)zbMATHCrossRefGoogle Scholar
  12. 12.
    Leriche, E., Labrosse, G.: High-Order Direct Stokes Solvers with or without Temporal Splitting: Numerical Investigations of their Comparative Properties. SIAM J. Scient. Comput. 22(4), 1386–1410 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Leriche, E., Perchat, E., Labrosse, G., Deville, M.O.: Numerical evaluation of the accuracy and stability properties of high-order direct Stokes solvers with or without temporal splitting. Journal of Scientific Computing 26, 25–43 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Lynch, R.E., Rice, J.R., Thomas, D.H.: Direct Solution of Partial Diiference Equations by Tensor Product Methods. Numerishe Mathematik 6, 185–199 (1964)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Salat, J., Xin, S., Joubert, P., Sergent, A., Penot, F., Le Quéré, P.: Experimental and numerical investigation of turbulent natural convection in a large air-filled cavity. Int. J. Heat and Fluid Flow 23, 824–832 (2004)CrossRefGoogle Scholar
  16. 16.
    Trias, F.X., Soria, M., Oliva, A., Pérez-Segarra, C.D.: Direct numerical simulation of two- and three-dimensional turbulent natural convection flows in a differentially heated cavity of aspect ratio 4. J. Fluid Mech. 586, 259–293 (2007)zbMATHCrossRefGoogle Scholar
  17. 17.
    Tric, E., Labrosse, G., Betrouni, M.: A first incursion into the 3D structure of natural convection of air in a differentially heated cubic cavity, from accurate numerical solutions. Int. J. Heat Mass Transfer 43, 4043–4056 (2000)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • R. Puragliesi
    • 1
  • A. Dehbi
    • 1
  • E. Leriche
    • 2
  • A. Soldati
    • 3
  • M. Deville
    • 4
  1. 1.Paul Scherrer InstitutVilligenSwitzerland
  2. 2.Université Jean-MonnetSaint-ÉtienneFrance
  3. 3.University of UdineUdineItaly
  4. 4.École Polytechnique Fédérale de LausanneSwitzerland

Personalised recommendations