Ay. Gelfgat et al., Axisymmetry breaking instabilities of natural convection in a vertical bridgman growth configuration, J CRYST GR, 220(3), 2000, pp. 316-325
A study of the three-dimensional axisymmetry-breaking instability of an axi
symmetric convective flow associated with crystal growth from bulk of melt
is presented. Convection in a vertical cylinder with a parabolic temperatur
e profile on the sidewall is considered as a representative model. The main
objective is the calculation of critical parameters corresponding to a tra
nsition from the steady axisymmetric to the three-dimensional non-axisymmet
ric (steady or oscillatory) flow pattern. A parametric study of the depende
nce of the critical Grashof number Gr(cr) on the Prandtl number 0 less than
or equal to Pr less than or equal to 0.05 (characteristic for semiconducto
r melts) and the aspect ratio of the cylinder 1 less than or equal to A les
s than or equal to 4 (A = height/radius) is carried out. The stability diag
ram Gr(cr)(Pr,A) corresponding to the axisymmetric - three-dimensional tran
sition is reported for the first time. The calculations are done using the
spectral Galerkin method allowing an effective and accurate three-dimension
al stability analysis. Tt is shown that the axisymmetric how 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-Ben
ard 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 differe
nt crystal growth configurations. In particular, it is shown that the first
instability of the how considered is always three-dimensional. (C) 2000 El
sevier Science B.V. All rights reserved.