Ecoulements induits par la force gravifique dans une cavité cylindrique en rotation

Resume Une methode numerique du type Tau-Chebyshev est utilisee pour decrire le mouvement d'un fluide de Boussinesq en rotation, soumis a un gradient thermique radial. L'analyse des regimes d'ecoulement axisymetriques est developpee pour des cavites annulaires, lorsque les parametres physiques varient: 0 ≤ Re ≤ 2500; Ra = 10 2 , ± 10 4 , 10 5 ; 0 ≤ Fr ≤ 25. La transition entre les regimes de convection thermique et ceux domines par la rotation resulte de la competition entre les differentes forces : gravifique, centrifuge et de Coriolis. La validite des solutions asymptotiques proposees par Hunter (1966) lorsque Fr ⪡ 1 et Re ⪢ 1, est discutee lorsque Re varie.

[1]  C. W. Gear,et al.  Numerical initial value problem~ in ordinary differential eqttations , 1971 .

[2]  D. Schwabe,et al.  Experiments on buoyant, thermocapillary, and forced convection in Czochralski configuration , 1983 .

[3]  Daniel D. Joseph,et al.  Stability of fluid motions , 1976 .

[4]  R. Hide.  On source-sink flows in a rotating fluid , 1968, Journal of Fluid Mechanics.

[5]  J. L. Hudson,et al.  Centrifugally driven thermal convection in a rotating cylinder , 1969, Journal of Fluid Mechanics.

[6]  A. Robinson.  The symmetric state of a rotating fluid differentially heated in the horizonal , 1959, Journal of Fluid Mechanics.

[7]  M. Crochet,et al.  Finite-element Simulation of Czochralski Bulk Flow , 1983 .

[8]  M. Mihelčić,et al.  Three-dimensional simulations of the Czochralski bulk flow , 1984 .

[9]  W. E. Langlois.  Buoyancy-Driven Flows in Crystal-Growth Melts , 1985 .

[10]  Harvey P. Greenspan,et al.  The Theory of Rotating Fluids. By H. P. GREENSPAN. Cambridge University Press, 1968. 327 pp. £5.50. , 1972, Journal of Fluid Mechanics.

[11]  A. Davey,et al.  On the removal of the singularities from the Riccati method , 1979 .

[12]  C. Temperton.  Fast Mixed-Radix Real Fourier Transforms , 1983 .

[13]  K. Hashimoto,et al.  Thermally driven flow in a gas centrifuge with an insulated side wall , 1976, Journal of Fluid Mechanics.

[14]  J. R. Pincombe,et al.  Numerical predictions for laminar source-sink flow in a rotating cylindrical cavity , 1984, Journal of Fluid Mechanics.

[15]  R. Hide,et al.  Thermal Convection in a Rotating Annulus of Liquid: Effect of Viscosity on the Transition Between Axisymmetric and Non-Axisymmetric Flow Regimes , 1965 .

[16]  H. Riehl,et al.  The general circulation in a steady rotating-dishpan experiment , 1958 .

[17]  Dale B. Haidvogel,et al.  The Accurate Solution of Poisson's Equation by Expansion in Chebyshev Polynomials , 1979 .

[18]  S. Ostrach,et al.  Fluid motion in the Czochralski method of crystal growth , 1984 .

[19]  R. Singleton.  An algorithm for computing the mixed radix fast Fourier transform , 1969 .

[20]  Raymond Hide,et al.  An experimental study of thermal convection in a rotating liquid , 1958, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[21]  C. Hunter.  The axisymmetric flow in a rotating annulus due to a horizontally applied temperature gradient , 1967, Journal of Fluid Mechanics.

[22]  K. Stewartson,et al.  On almost rigid rotations , 1957, Journal of Fluid Mechanics.

[23]  Haroon S. Kheshgi,et al.  Viscous flow through a rotating square channel , 1985 .

[24]  J. M. Owen,et al.  Source–sink flow inside a rotating cylindrical cavity , 1985, Journal of Fluid Mechanics.

[25]  G. D. Davis,et al.  Heat transfer in a vertical rotating annulus - A numerical study , 1982 .

[26]  J. Chew.  DEVELOPMENT OF A COMPUTER-PROGRAM FOR THE PREDICTION OF FLOW IN A ROTATING CAVITY , 1984 .

[27]  D. Gray,et al.  The validity of the boussinesq approximation for liquids and gases , 1976 .

[28]  W. D. Jackson,et al.  Source–sink flows in a rotating annulus: a combined laboratory and numerical study , 1974, Journal of Fluid Mechanics.

[29]  J. Pedlosky,et al.  On the steady motions produced by a stable stratification in a rapidly rotating fluid , 1967, Journal of Fluid Mechanics.

[30]  D. Gottlieb,et al.  Numerical analysis of spectral methods : theory and applications , 1977 .

[31]  A. Conlisk,et al.  Forced convection in a rapidly rotating annulus , 1982, Journal of Fluid Mechanics.

[32]  G. D. Davis,et al.  Convection in a rotating annular cavity , 1984 .

[33]  J. Hyun.  Source-sink flows of a stratified fluid in a rotating annulus , 1984, Journal of Fluid Mechanics.

[34]  A. Hindmarsh.  LSODE and LSODI, two new initial value ordinary differential equation solvers , 1980, SGNM.