Comptes Rendus
An adaptation of the low Mach number approximation for supercritical fluid buoyant flows
Comptes Rendus. Mécanique, Volume 333 (2005) no. 5, pp. 397-404.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2005.03.004
Keywords: Fluid mechanics, Supercritical fluid, Low Mach number, Rayleigh–Bénard instability, Piston effect
Mot 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

1 Laboratoire de modélisation et simulation numérique en mécanique, UMR 6181 du CNRS, les universités Aix-Marseille, technopôle de Château Gombert, 38, rue Frédéric-Joliot-Curie, 13451 Marseille cedex 20, France
2 CNES, 18, avenue Edouard-Belin, 31401 Toulouse cedex 4, France
@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] I. Raspo; B. Gilly; S. Amiroudine; P. Bontoux; B. Zappoli Simulation of convective instabilities inside a supercritical fluid layer under Rayleigh–Bénard configuration, J. Chim. Phys., Volume 96 (1999), p. 1059

[2] S. Amiroudine; P. Bontoux; P. Larroudé; B. Gilly; B. Zappoli 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] G. Accary; I. Raspo; P. Bontoux; B. Zappoli Three-dimensional Rayleigh–Bénard instability in a supercritical fluid, C. R. Mecanique, Volume 332 (2004), p. 209

[4] A. Furukawa; A. Onuki Convective heat transport in compressible fluids, Phys. Rev. E, Volume 66 (2002), p. 016302

[5] M. Gitterman; V.-A. Steinberg 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] P. Carlès; B. Ugurtas The onset of free convection near the liquid–vapour critical point. Part I: Stationary initial state, Physica D, Volume 126 (1999), p. 69

[7] A.-B. Kogan; H. Meyer Heat transfer and convection onset in a compressible fluid: 3He near the critical point, Phys. Rev. E, Volume 63 (2001), p. 056310

[8] A.-B. Kogan; D. Murphy; H. Meyer Onset of Rayleigh–Bénard convection in a very compressible fluid: 3He, near Tc, Phys. Rev. Lett., Volume 82 (1999), p. 4635

[9] K. Nitsche; J. Straub 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] B. Zappoli; D. Bailly; Y. Garrabos; B. Le Neindre; P. Guenoun; D. Beysens Anomalous heat transport by the piston effect in supercritical fluids under zero gravity, Phys. Rev. A, Volume 41 (1990), p. 2224

[11] H. Boukari; J.-N. Schaumeyer; M.-E. Briggs; R.-W. Gammon Critical speeding up in pure fluids, Phys. Rev. A, Volume 41 (1990), p. 2260

[12] A. Onuki; H. Hao; R.-A. Ferrell Fast adiabatic equilibration in a single-component fluid near the liquid–vapor critical point, Phys. Rev. A, Volume 41 (1990), p. 2256

[13] B. Zappoli 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

Cited by Sources:

Comments - Policy