feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 9 (1997), S. 3149-3161 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We numerically investigate the two-dimensional (2-D) convective flow developing in the liquid phase above an alloy growing in the upward Bridgman configuration of directional solidification. Using a time-dependent approach, we are able to describe the various cycles of hysteresis that connect the different branches of stable steady solutions. The main trends of the present results show that the bifurcation diagram, composed of the branches, found in previous works for the partition coefficient k=0.3, remains qualitatively valid for k=1.1: for a small frontal width the leading primary bifurcation is subcritical, while a transcritical bifurcation occurs for larger front. We bring the new complementary feature that the subcritical bifurcation becomes supercritical when the front width tends to zero. Furthermore, for an intermediate frontal width, we address the question of the nature of upper stability limits on various stable steady branches. We show that the limit occurs via either a steady secondary bifurcation or a Hopf bifurcation that initiates an unsteady solution branch which is followed up to chaos. The related route is a subharmonic cascade. When following this chaotic branch, a striking relaminarization process towards a steady secondary branch occurs. Finally we shortly investigate the case of a twice larger frontal width, for which several cycles of hysteresis are equally reported. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 2
    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
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...