Modelling of Natural Convection Flows with Large Temperature Differences: A Benchmark Problem for Low Mach Number Solvers. Part 1. Reference Solutions

Patrick Le Quéré; Catherine Weisman; Henri Paillère; Jan Vierendeels; Erik Dick; Roland Becker; Malte Braack; James Locke

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 39, Issue: 3, page 609-616
  • ISSN: 0764-583X

Abstract

top
There are very few reference solutions in the literature on non-Boussinesq natural convection flows. We propose here a test case problem which extends the well-known De Vahl Davis differentially heated square cavity problem to the case of large temperature differences for which the Boussinesq approximation is no longer valid. The paper is split in two parts: in this first part, we propose as yet unpublished reference solutions for cases characterized by a non-dimensional temperature difference of 0.6, Ra = 106 (constant property and variable property cases) and Ra = 107 (variable property case). These reference solutions were produced after a first international workshop organized by CEA and LIMSI in January 2000, in which the above authors volunteered to produce accurate numerical solutions from which the present reference solutions could be established.

How to cite

top

Le Quéré, Patrick, et al. "Modelling of Natural Convection Flows with Large Temperature Differences: A Benchmark Problem for Low Mach Number Solvers. Part 1. Reference Solutions." ESAIM: Mathematical Modelling and Numerical Analysis 39.3 (2010): 609-616. <http://eudml.org/doc/194278>.

@article{LeQuéré2010,
abstract = { There are very few reference solutions in the literature on non-Boussinesq natural convection flows. We propose here a test case problem which extends the well-known De Vahl Davis differentially heated square cavity problem to the case of large temperature differences for which the Boussinesq approximation is no longer valid. The paper is split in two parts: in this first part, we propose as yet unpublished reference solutions for cases characterized by a non-dimensional temperature difference of 0.6, Ra = 106 (constant property and variable property cases) and Ra = 107 (variable property case). These reference solutions were produced after a first international workshop organized by CEA and LIMSI in January 2000, in which the above authors volunteered to produce accurate numerical solutions from which the present reference solutions could be established. },
author = {Le Quéré, Patrick, Weisman, Catherine, Paillère, Henri, Vierendeels, Jan, Dick, Erik, Becker, Roland, Braack, Malte, Locke, James},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Natural convection; non-Boussinesq; low Mach number.},
language = {eng},
month = {3},
number = {3},
pages = {609-616},
publisher = {EDP Sciences},
title = {Modelling of Natural Convection Flows with Large Temperature Differences: A Benchmark Problem for Low Mach Number Solvers. Part 1. Reference Solutions},
url = {http://eudml.org/doc/194278},
volume = {39},
year = {2010},
}

TY - JOUR
AU - Le Quéré, Patrick
AU - Weisman, Catherine
AU - Paillère, Henri
AU - Vierendeels, Jan
AU - Dick, Erik
AU - Becker, Roland
AU - Braack, Malte
AU - Locke, James
TI - Modelling of Natural Convection Flows with Large Temperature Differences: A Benchmark Problem for Low Mach Number Solvers. Part 1. Reference Solutions
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 39
IS - 3
SP - 609
EP - 616
AB - There are very few reference solutions in the literature on non-Boussinesq natural convection flows. We propose here a test case problem which extends the well-known De Vahl Davis differentially heated square cavity problem to the case of large temperature differences for which the Boussinesq approximation is no longer valid. The paper is split in two parts: in this first part, we propose as yet unpublished reference solutions for cases characterized by a non-dimensional temperature difference of 0.6, Ra = 106 (constant property and variable property cases) and Ra = 107 (variable property case). These reference solutions were produced after a first international workshop organized by CEA and LIMSI in January 2000, in which the above authors volunteered to produce accurate numerical solutions from which the present reference solutions could be established.
LA - eng
KW - Natural convection; non-Boussinesq; low Mach number.
UR - http://eudml.org/doc/194278
ER -

References

top
  1. R. Becker, M. Braack and R. Rannacher, Numerical simulation of laminar flames at low Mach number with adaptive finite elements. Combustion Theory and Modelling, Bristol3 (1999) 503–534.  
  2. R. Becker, M. Braack, Solution of a stationary benchmark problem for natural convection with high temperature difference. Int. J. Thermal Sci.41 (2002) 428–439.  
  3. D.R. Chenoweth and S. Paolucci, Natural Convection in an enclosed vertical air layer with large horizontal temperature differences. J. Fluid Mech.169 (1986) 173–210.  
  4. G. de Vahl Davis, Natural convection of air in a square cavity: a benchmark solution. Int. J. Numer. Methods Fluids3 (1983) 249–264.  
  5. G. de Vahl Davis and I.P. Jones, Natural convection of air in a square cavity: a comparison exercice. Int. J. Numer. Methods Fluids3 (1983) 227–248.  
  6. FEAT User Guide, Finite Element Analysis Toolbox, British Energy, Gloucester, UK (1997).  
  7. D.D. Gray and A. Giorgini, The Validity of the Boussinesq approximation for liquids and gases. Int. J. Heat Mass Transfer15 (1976) 545–551.  
  8. P. Le Quéré, Accurate solutions to the square differentially heated cavity at high Rayleigh number. Comput. Fluids20 (1991) 19–41.  
  9. P. Le Quéré, R. Masson and P. Perrot, A Chebyshev collocation algorithm for 2D Non-Boussinesq convection. J. Comput. Phys.103 (1992) 320–335.  
  10. W.L. Oberkampf and T. Trucano, Verification and validation in Computational Fluid Dynamics. Sandia National Laboratories report SAND2002-0529 (2002).  
  11. H. Paillère and P. Le Quéré, Modelling and simulation of natural convection flows with large temperature differences: a benchmark problem for low Mach number solvers, 12th Séminaire de Mécanique des Fluides Numérique, CEA Saclay, France, 25–26 Jan., 2000.  
  12. S. Paolucci, On the filtering of sound from the Navier-Stokes equations. Sandia National Laboratories report SAND82-8257 (1982).  
  13. J.C. Patterson and J. Imberger, Unsteady natural convection in a rectangular cavity. J. Fluid Mech.100 (1980) 65–86.  
  14. V.L. Polezhaev, Numerical solution of the system of two-dimensional unsteady Navier-Stokes equations for a compressible gas in a closed region. Fluid Dyn.2 (1967) 70–74.  
  15. J. Vierendeels, K. Riemslagh and E. Dick, A Multigrid semi-implicit line-method for viscous incompressible and low-Mach number flows on high aspect ratio grids. J. Comput. Phys.154 (1999) 310–341.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.