[Une adaptation de l'approximation faible nombre de Mach aux écoulements de convection naturelle dans les fluides supercritiques]
Cette Note décrit un filtrage acoustique des équations régissant la convection naturelle dans un fluide supercritique due à un faible chauffage. L'approximation faible nombre de Mach obtenue prend en compte la compressibilité du fluide par rapport à la pression hydrostatique. Par la simulation numérique directe de l'écoulement d'un fluide supercritique en configuration de Rayleigh–Bénard, nous montrons que la stratification en densité peut être prise en compte sans effort numérique supplémentaire et qu'elle est fondamentale pour la prédiction du seuil d'instabilité convective induite par un faible chauffage.
This Note describes an acoustic filtering of the equations governing the supercritical fluid buoyant flow driven by a weak heating. The resulting low Mach number approximation takes into account the compressibility of the fluid with respect to the hydrostatic pressure. Using the direct numerical simulation of a supercritical fluid flow in the Rayleigh–Bénard configuration, we show that the density stratification may be taken into account without further numerical effort and is fundamental for the prediction of the convective instability threshold induced by a weak heating.
Accepté le :
Publié le :
Mot clés : Mécanique des fluides, Fluide supercritique, Faible nombre de Mach, Instabilité de Rayleigh–Bénard, Effet piston
@article{CRMECA_2005__333_5_397_0,
author = {Gilbert Accary and Isabelle Raspo and Patrick Bontoux and Bernard Zappoli},
title = {An adaptation of the low {Mach} number approximation for supercritical fluid buoyant flows},
journal = {Comptes Rendus. M\'ecanique},
pages = {397--404},
publisher = {Elsevier},
volume = {333},
number = {5},
year = {2005},
doi = {10.1016/j.crme.2005.03.004},
language = {en},
}
TY - JOUR AU - Gilbert Accary AU - Isabelle Raspo AU - Patrick Bontoux AU - Bernard Zappoli TI - An adaptation of the low Mach number approximation for supercritical fluid buoyant flows JO - Comptes Rendus. Mécanique PY - 2005 SP - 397 EP - 404 VL - 333 IS - 5 PB - Elsevier DO - 10.1016/j.crme.2005.03.004 LA - en ID - CRMECA_2005__333_5_397_0 ER -
%0 Journal Article %A Gilbert Accary %A Isabelle Raspo %A Patrick Bontoux %A Bernard Zappoli %T An adaptation of the low Mach number approximation for supercritical fluid buoyant flows %J Comptes Rendus. Mécanique %D 2005 %P 397-404 %V 333 %N 5 %I Elsevier %R 10.1016/j.crme.2005.03.004 %G en %F CRMECA_2005__333_5_397_0
Gilbert Accary; Isabelle Raspo; Patrick Bontoux; Bernard Zappoli. An adaptation of the low Mach number approximation for supercritical fluid buoyant flows. Comptes Rendus. Mécanique, Volume 333 (2005) no. 5, pp. 397-404. doi : 10.1016/j.crme.2005.03.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2005.03.004/
[1] Simulation of convective instabilities inside a supercritical fluid layer under Rayleigh–Bénard configuration, J. Chim. Phys., Volume 96 (1999), p. 1059
[2] Direct numerical simulation of instabilities in a two-dimensional near-critical fluid layer heated from below, J. Fluid Mech., Volume 442 (2001), p. 119
[3] Three-dimensional Rayleigh–Bénard instability in a supercritical fluid, C. R. Mecanique, Volume 332 (2004), p. 209
[4] Convective heat transport in compressible fluids, Phys. Rev. E, Volume 66 (2002), p. 016302
[5] Criteria for the commencement of convection in a liquid close to the critical point, High Temp. (USSR), Volume 8 (1970) no. 4, p. 754
[6] The onset of free convection near the liquid–vapour critical point. Part I: Stationary initial state, Physica D, Volume 126 (1999), p. 69
[7] Heat transfer and convection onset in a compressible fluid: 3He near the critical point, Phys. Rev. E, Volume 63 (2001), p. 056310
[8] Onset of Rayleigh–Bénard convection in a very compressible fluid: 3He, near Tc, Phys. Rev. Lett., Volume 82 (1999), p. 4635
[9] The critical hump of Cv under microgravity, results from D-Spacelab experiment ‘Wärmekapazität’, Proceedings of the 6th European Symp. on Material Sci. under Microgravity Conditions, ESA SP-256, 1987, p. 109
[10] Anomalous heat transport by the piston effect in supercritical fluids under zero gravity, Phys. Rev. A, Volume 41 (1990), p. 2224
[11] Critical speeding up in pure fluids, Phys. Rev. A, Volume 41 (1990), p. 2260
[12] Fast adiabatic equilibration in a single-component fluid near the liquid–vapor critical point, Phys. Rev. A, Volume 41 (1990), p. 2256
[13] The response of a nearly supercritical pure fluid to a thermal disturbance, Phys. Fluids A, Volume 4 (1992), p. 1040
[14] S. Paolucci, On the filtering of sound from the Navier–Stokes equations, Technical report, Sandia National Laboratories USA, SAND82-8257, December 1982
[15] G. Accary, I. Raspo, A 3D finite volume method for the prediction of a supercritical fluid buoyant flow in a differentially heated cavity, Computers & Fluids, in press
Cité par Sources :
Commentaires - Politique
Three-dimensional Rayleigh–Bénard instability in a supercritical fluid
Gilbert Accary; Isabelle Raspo; Patrick Bontoux; ...
C. R. Méca (2004)
Unsteady two-dimensional convection in a bottom heated supercritical fluid
Isabelle Raspo; Bernard Zappoli; Patrick Bontoux
C. R. Méca (2004)
Thermoconvective instabilities in supercritical fluids
Sakir Amiroudine; Bernard Zappoli
C. R. Méca (2004)