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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 simulations using a two-dimensional finite volume numerical code solving the time-dependent Navier-Stokes equations under the Low Mach Number approximation. 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 constant 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 incompressible model is not sufficient to simulate natural convective flow for large temperature differences.
KEYWORDS
PAPER SUBMITTED: 2013-08-10
PAPER REVISED: 2014-06-18
PAPER ACCEPTED: 2014-07-01
PUBLISHED ONLINE: 2014-08-10
DOI REFERENCE: https://doi.org/10.2298/TSCI130810084H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Issue 5, PAGES [1509 - 1517]
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

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence