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.
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.
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Mots-clés : Mécanique des fluides, Fluide supercritique, Faible nombre de Mach, Instabilité de Rayleigh–Bénard, Effet piston
Gilbert Accary 1; Isabelle Raspo 1; Patrick Bontoux 1; Bernard Zappoli 2
@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/
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