NUMERICAL STUDY OF NATURAL CONVECTION IN A SQUARE CAVITY UNDER NON-BOUSSINESQ CONDITIONS

Abstract

Natural convection in a differentially heated cavity has been carried out under large temperature gradient. The study has been performed by direct simula-tions using a two-dimensional finite volume numerical code solving the time-dependent Navier-Stokes equations under the Low Mach Number approxima-tion. The LMN model constitutes an important numerical problem for low speed flows. It is based on the filtering of acoustic waves from the complete Navier-Stokes equations. Various simulations were conducted including con-stant or variable transport coefficients and both small and large temperature differences. A comparison between an incompressible code based on the Boussinesq approximation and the LMN compressible code shows that the in-compressible model is not sufficient to simulate natural convective flow for large temperature differences.

Keywords

Dates

  • Submission Date2013-08-10
  • Revision Date2014-06-18
  • Acceptance Date2014-07-01
  • Online Date2014-08-10

DOI Reference

10.2298/TSCI130810084H

References

  1. Paolucci, S., On the filtering of sound from the Navier-Stokes equations, Technical Report 82-8257, Sandia National Laboratories, 1982
  2. Suslov, S.A. and Paolucci, S., Nonlinear analysis of convection flow in a tall vertical enclosure under non-Boussinesq conditions, J. Fluid Mech. 344 (1997), pp.1-41.
  3. Codina, R., A stabilised finite element method for generalised stationary incompressible flows, Method Appl. Mech. Eng., 190 (2001), pp. 2681-2706
  4. Vierendeels, J., Merci, B. and Dick, E., A multigrid method for natural convective heat transfer with large temperature differences, Journal of Computational and Applied Mathematics, 168 (2004), pp. 509-517
  5. Bouafia,M. and Daube, O., Natural convection for large temperature gradients around a square solid body within a rectangular cavity, Int. J. Heat and Mass Transfer, 50 (2007), pp. 3599-3615
  6. Chenoweth, D.R. and Paolucci, S., Natural convection in an enclosed vertical air layer with large horizontal temperature differences, J. Fluid Mech, 169 (1986), pp. 173-210
  7. White, F. M., Viscous Fluid Flow, McGraw-Hill, 1974
  8. Patankar, SV., Numerical heat transfer and fluid flow, McGraw-Hill, 1980
  9. Vierendeels, J., Riemslagh, K. and Dick, E., A Multigrid Semi-Implicit Line-Method for Viscous Incompressible and Low-Mach Number Flows on High Aspect Ratio Grids, J. Comput. Phys., 154 (1999), pp. 310-341
  10. Heuveline, V., On higher-order mixed FEM for low Mach number flows: application to a natural convection benchmark problem, Int. J. Numer. Methods Fluids, 41 (2003), pp. 1339-1356
  11. Mizushima, J. & Gotoh, K., Nonlinear evolution of the disturbance in a natural convection induced in a vertical fluid layer, J. Phys. Soc. Japan, 52 (1983), pp. 1206-121