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
URL:
http://dx.doi.org/10.1063/1.869432
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