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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 2086-2092 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In this study the effect of rigid side walls on the onset of solutal convection in the melt is investigated for upward solidification of a binary alloy. The physics is described by the Navier–Stokes equations in the Boussinesq approximation and by the balance of solute, which is coupled with the appropriate boundary conditions. By using a Tau–Chebyshev spectral method the numerical resolution of the perturbed system has been carried out for two alloys: lead–tin, which is the reference in the literature, and lead–thallium, which is currently under study. For both cases the lateral confinement has a stabilizing effect for all the aspect ratios that have been considered.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 1873-1879 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The onset of solutal convection during directional solidification of a binary alloy growing in a cylinder is determined for the axisymmetric and selected nonaxisymmetric flow states. The Tau–Chebyshev projection method is used to solve the system of linearized partial differential equations. The Pb–Tl and Pb–Sn alloy systems are investigated, which, respectively, correspond to k=1.1 and to k=0.3. A critical convective pattern with an azimuthal wave number α=1 is obtained when the aspect ratio β of the cylinder is less than about 6.5. At this value a transition to axisymmetric modes (α=0) is evidenced. Finally, the comparison with previous results for growth in a vertical slot shows the enhancement of the hydrodynamic stability associated to the 3-D confinement by the cylinder.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Journal of Crystal Growth 96 (1989), S. 652-666 
    ISSN: 0022-0248
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Journal of Computational Physics 55 (1984), S. 115-128 
    ISSN: 0021-9991
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Computer Science , Physics
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Journal of Crystal Growth 96 (1989), S. 652-666 
    ISSN: 0022-0248
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 393-409 
    ISSN: 0271-2091
    Keywords: generalized Stokes problem ; Chebyshev spectral method ; thermosolutal convection ; directional solidification ; vertical Bridgman problem ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The paper presents a Chebyshev-Fourier collocation method for solving the unsteady 3D Navier-Stokes equations in a cylindrical domain. The numerical scheme uses primitive variables and the incompressibility constraint is satisfied by applying iteratively a correction to the pressure field. The method, due to Cahouët and Chabard (Int. j. numer. methods fluids,8, 869-895 (1988)) and originally developed in the framework of finite elements, is checked with respect to the present high-order approach. Several tests are carried out in Cartesian geometries, successively 2D and 3D, then a comparison is performed in a cylindrical domain with two different sets of radial collocation nodes: Gauss-Lobatto nodes and Gauss-Radau points. Although quite acceptable results are obtained with the latter chain, a general decrease in efficiency is noticeable in the collocation method. This is interpreted as the consequence of two factors: the collocation formulation is not symmetric and the Fourier analysis, used as heuristic guide by CahouMt and Chabard, loses its efficiency in a non-equidistant grid, especially in a cylindrical geometry.We present an application to the study of thermosolutal convection induced by unidirectional solidification of a binary alloy. The latter grows from a Pb-30%Tl liquid phase in a cylindrical crucible corresponding to the vertical Bridgman upward configuration. We study the influence of the flow patterns on the crystal composition.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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