Hostname: page-component-84b7d79bbc-dwq4g Total loading time: 0 Render date: 2024-07-26T18:36:53.609Z Has data issue: false hasContentIssue false
  • English
  • Français

Thermoacoustic and buoyancy-driven transport in a square side-heated cavity filled with a near-critical fluid

Published online by Cambridge University Press:  26 April 2006

Bernard Zappoli ,
Sakir Amiroudine ,
Pierre Carles  and
Jalil Ouazzani
Bernard Zappoli
Affiliation:
CNES, 18 Av. Edouard Belin, 31055 Toulouse Cedex, France
Sakir Amiroudine
Affiliation:
Institut de Mécanique des Fluides, 1 rue Honnorat 13003 Marseille, France
Pierre Carles
Affiliation:
Institut National Polytechnique de Toulouse, Place des Hauts Murats, 31006 Toulouse, France
Jalil Ouazzani
Affiliation:
Arco Fluid, IMT, Technopôle de Château Gombert, 13451 Marseille, France
Get access Rights & Permissions [Opens in a new window]

Abstract

The mechanisms of heat and mass transport in a side-heated square cavity filled with a near-critical fluid are explored, with special emphasis on the interplay between buoyancy-driven convection and the Piston Effect. The Navier–Stokes equations for a near-critical van der Waals gas are solved numerically by means of an acoustically filtered, finite-volume method. The results have revealed some striking behaviour compared with that obtained for normally compressible gases: (i) heat equilibration is still achieved rapidly, as under zero-g conditions, by the Piston Effect before convection has time to enhance heat transport; (ii) mass equilibration is achieved on a much longer time scale by quasi-isothermal buoyant convection; (iii) due to the very high compressibility, a stagnation-point effect similar to that encountered in high-speed flows provokes an overheating of the upper wall; and (iv) a significant difference to the convective single-roll pattern generated under the same conditions in normal CO2 is found, in the form of a double-roll convective structure.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 316 , 10 June 1996 , pp. 53 - 72
Copyright
© 1996 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Amiroudine, S. 1995 Modélisation numérique des phénomènes de transport de chaleur et de masse dans les fluides supercritiques. PhD dissertation, Institut de Mécanique des Fluides, Marseille, France.
Amiroudine, S., Ouazzani, J., Zappoli, B. & Carles, P. 1996 Numerical solutions of 1D unsteady hypercompressible flows using finite volume methods. Eur. J. Mech. (submitted).Google Scholar
Bailly, D., Ermakov, M. & Zappoli, B. 1996 Density relaxation in near critical pure fluids. Phys. Rev. A (to be submitted).Google Scholar
Bonetti, M., Perrot, F., Beysens, D. & Garrabos, Y. 1994 Fast thermalization in supercritical fluids. Phys. Rev. E 49, R4779.Google Scholar
Boukari, H., Shaumeyer, J. N., Briggs, M. E. & Gammon, R. W. 1990 Critical speeding up in pure fluids. Phys. Rev. A 41, 2260.Google Scholar
Boukari, H., Pego, R. L. & Gammon, R. W. 1995 Calculation of the dynamics of gravity-induced density profiles near the liquid-vapor critical point. Phys. Rev. E 52, 1614.Google Scholar
Bravais, P., Zappoli, B. & Mignon, C. 1993 Free convection in the vicinity of the critical point. Presented at the 14th IAF Congress, Gratz, Austria. Acta Astronautica (to appear).
Carles, P. 1995 L'Effet piston et les phénomènes thermoacoustiques dan les fluids supercritiques. PhD dissertation, Institut National Polytechnique de Toulouse, France.
Carpenter, B. M. & Homsy, G. M. 1990 High Marangoni number convection in a square cavity: Part 2. Phys. Fluids A 2, 137.Google Scholar
Garrabos, Y., Bonnetti, M., Beysens, D., Perrot, F., Frohlich, T., Carles, P. & Zappoli, B. Phys. Rev., (in preparation).
Gitterman, M. & Steinberg, V. A. 1970 Criteria of occurrence of free convection in a compressible viscous heat-conducting fluid. J. Appl. Math. Mech. 34, 305.Google Scholar
Gitterman, M. & Steinberg, V. A. 1972 Establishment of thermal equilibrium in a liquid near the critical point. High Temp. 10, 565.Google Scholar
Guenoun, P., Beysens, D., Khalil, B., Garrabos, Y., Kammoun, B., Le Neindre, B. & Zappoli, B. 1993 A thermo cycle around the critical point of CO2 under reduced gravity. Phys. Rev. E 47, 1531.Google Scholar
Heinmiller, P. J. 1970 A numerical solution of the Navier–Stokes equations for supercritical fluid thermodynamic analysis. T.R.W. Rep. 17618-H080-RO-00. Houston, Texas.
Jang, D. S., Jetli, R. & Acharya, S. 1986 Comparisons of the PISO, SIMPLER and SIMPLEC algorithms for the treatment of the pressure-velocity coupling in steady flow problems. Number. Heat Transfer 10, 209.Google Scholar
Klein, H., Wanders, K. & Feuerbacher, B. 1991 Relaxation of non-equilibrium density inhomogeneities in near critical fluids. Adv. Space Res. 11, 181.Google Scholar
Moldover, M. R., Sengers, J. V., Gammon, R. W. & Hocken, R. J. 1979 Rev. Mod. Phys. 51, 79.
Onuki, A. & Ferrell, R. A. 1990 Phys. Rev. A 164, 245.
Onuki, A., Hao, H. & Ferrell, R. A. 1990 Fast adiabatic equilibrium in a single component fluid near the liquid-vapor critical point. Phys. Rev. A 41, 2256.Google Scholar
Paolucci, S. 1982 On the filtering of sound from the Navier–Stokes equations. SAND 82-8257.
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. Hemisphere.
Patankar, S. V. 1985 A calculation procedure for two-dimensional elliptic situations. Number. Heat Transfer 14, 409.Google Scholar
Patankar, S. V. & Spalding, D. P. 1972 A calculation procedure for heat, mass and momentum transfer in three dimensional parabolic flows. Intl J. Heat Mass Transfer 15, 1787.Google Scholar
Spradley, L. W. & Churchill, S. W. 1975 Pressure and buoyancy-driven thermal convection in a rectangular enclosure. J. Fluid Mech. 70, 705.Google Scholar
Stanley, H. E. 1971 Introduction to Phase Transition and Critical Phenomena. Clarendon.
Straub, J. 1965 Dissertation, Technische Universitt, Munchen, Germany (unpublished). Results presented by E. H. Schmidt in Critical Phenomena (ed. M. S. Green & J. V. Sengers), Proc. Conf. on Phenomena in the Neighbourhood of Critical Point (National Bureau of Standard, Washington, DC, 1966).
Straub, J. & Nitsche, K. 1991 In Proc. 11th Symp. on Thermophysica Properties, Boulder, Colorado.
Straub, J. & Nitsche, K. 1993 Isochric heat capacity Cv at the critical point of SF6 under micro and earth-gravity. Results of the German spacelab mission D1. Fluid Phase Equil. 88, 183.Google Scholar
Swinney, H. L. & Henry, D. L. 1973 Dynamics of fluids near the critical point: decay rate of order-parameter fluctuations. Phys. Rev. A 8, 2586.CrossRefGoogle Scholar
Zappoli, B. 1992 The response of a nearly supercritical pure fluid to a thermal disturbance. Phys. Fluids A 4, 1040.Google Scholar
Zappoli, B., Bailly, D., Garrabos, Y., Le Neindre, B., Guenoun, P. & Beysens, D. 1990 Anomalous heat transport by the piston-effect in supercritical fluids under zero gravity. Phys. Rev. A 41, 2224.Google Scholar
Zappoli, B. & Carles, P. 1995 Thermoacoustic nature of the critical speeding-up. Eur. J. Mech. B 14, 41.Google Scholar
Zappoli, B. & Carles, P. 1996 Acoustic saturation of the critical speeding up. Physica D 89, 381–394.Google Scholar
Zappoli, B. & Durand-Daubin, A. 1994 Direct numerical modelling of heat and mass transport in a nearly supercritical fluid. Phys. Fluids 6, 1929.Google Scholar
Zhong, F. & Meyer, H. 1995 Density equilibration near the liquid-vapor critical point of a pure fluid: single phase T > Tc. Phys. Rev. E 51, 3223.Google Scholar