TY - JOUR
T1 - Axisymmetry breaking instabilities of natural convection in a vertical bridgman growth configuration
AU - Gelfgat, A. Yu
AU - Bar-Yoseph, P. Z.
AU - Solan, A.
N1 - Funding Information:
This work was supported by the Israel Ministry of Science (Grant 8575-1-98), the Israel Ministry of Immigrant Absorption (to A.Gelfgat), the Israel High Performance Computer Unit, the Fund for Promotion of Research and the Y.Winograd Chair of Fluid Dynamics and Heat Transfer at Technion.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2000/12
Y1 - 2000/12
N2 - A study of the three-dimensional axisymmetry-breaking instability of an axisymmetric convective flow associated with crystal growth from bulk of melt is presented. Convection in a vertical cylinder with a parabolic temperature profile on the sidewall is considered as a representative model. The main objective is the calculation of critical parameters corresponding to a transition from the steady axisymmetric to the three-dimensional non-axisymmetric (steady or oscillatory) flow pattern. A parametric study of the dependence of the critical Grashof number Grcr on the Prandtl number 0≤Pr≤0.05 (characteristic for semiconductor melts) and the aspect ratio of the cylinder 1≤A≤4 (A = height/radius) is carried out. The stability diagram Grcr(Pr, A) corresponding to the axisymmetric - three-dimensional transition is reported for the first time. The calculations are done using the spectral Galerkin method allowing an effective and accurate three-dimensional stability analysis. It is shown that the axisymmetric flow in relatively low cylinders tends to be oscillatory unstable, while in tall cylinders the instability sets in due to a steady bifurcation caused by the Rayleigh-Benard mechanism. The calculated neutral curves are non-monotonous and contain hysteresis loops. The strong dependence of the critical Grashof number and the azimuthal periodicity of the resulting three-dimensional flow indicate the importance of a comprehensive parametric stability analysis in different crystal growth configurations. In particular, it is shown that the first instability of the flow considered is always three-dimensional.
AB - A study of the three-dimensional axisymmetry-breaking instability of an axisymmetric convective flow associated with crystal growth from bulk of melt is presented. Convection in a vertical cylinder with a parabolic temperature profile on the sidewall is considered as a representative model. The main objective is the calculation of critical parameters corresponding to a transition from the steady axisymmetric to the three-dimensional non-axisymmetric (steady or oscillatory) flow pattern. A parametric study of the dependence of the critical Grashof number Grcr on the Prandtl number 0≤Pr≤0.05 (characteristic for semiconductor melts) and the aspect ratio of the cylinder 1≤A≤4 (A = height/radius) is carried out. The stability diagram Grcr(Pr, A) corresponding to the axisymmetric - three-dimensional transition is reported for the first time. The calculations are done using the spectral Galerkin method allowing an effective and accurate three-dimensional stability analysis. It is shown that the axisymmetric flow in relatively low cylinders tends to be oscillatory unstable, while in tall cylinders the instability sets in due to a steady bifurcation caused by the Rayleigh-Benard mechanism. The calculated neutral curves are non-monotonous and contain hysteresis loops. The strong dependence of the critical Grashof number and the azimuthal periodicity of the resulting three-dimensional flow indicate the importance of a comprehensive parametric stability analysis in different crystal growth configurations. In particular, it is shown that the first instability of the flow considered is always three-dimensional.
UR - http://www.scopus.com/inward/record.url?scp=0034501566&partnerID=8YFLogxK
U2 - 10.1016/S0022-0248(00)00842-3
DO - 10.1016/S0022-0248(00)00842-3
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AN - SCOPUS:0034501566
SN - 0022-0248
VL - 220
SP - 316
EP - 325
JO - Journal of Crystal Growth
JF - Journal of Crystal Growth
IS - 3
ER -