Experimental Modelling of Czochralski Melt Flow with a Slow Crystal Dummy Rotation
This study examines the e ect of slow crystal dummy rotation on three-dimensional oscillatory instability and time-dependent supercritical ow states in a Czochralski melt ow experimental model. To enable further comparison with numerical modelling, the experiments are carried out using a 20 cSt silicone oil as an experimental liquid and in a large diameter crucible, which allows one to work in a narrow temperature interval, so that temperature dependence of all the thermophysical properties of the experimental liquid can be neglected. The measurements con rm, partially qualitatively and partially quantitatively, earlier numerical predictions on destabilization ofthe Czochralski convective ow by a slow rotation. A simple power dependence of ow oscillations frequency on the Grashof and rotational Reynolds numbers that ts all the experimental runs was found.
Experimental study of cold plume instability in large Prandtl number Czochralski melt: Parametric dependences and scaling laws
Abstract A parametric experimental study of the cold plume instability that appears in the large-Prandtl-number Czochralski melt flows is reported. The critical temperature difference (the critical Grashof number) and the frequency of appearing oscillations were measured for varying Prandtl numbers, aspect ratios of the melt, and crystal/crucible radii ratio. The measurements were carried out by two independent and fully non-intrusive experimental techniques. The results are reported as dimensional and dimensionless parametric dependences, and then are joined into relatively simple empirical relations showing how the critical Grashof number and the frequency of emerging oscillations depend on other parameters.
Stability of convective flows in cavities: solution of benchmark problems by a low‐order finite volume method
A problem of stability of steady convective flows in rectangular cavities is revisited and studied by a second‐order finite volume method. The study is motivated by further applications of the finite volume‐based stability solver to more complicated applied problems, which needs an estimate of convergence of critical parameters. It is shown that for low‐order methods the quantitatively correct stability results for the problems considered can be obtained only on grids having more than 100 nodes in the shortest direction, and that the results of calculations using uniform grids can be significantly improved by the Richardson's extrapolation. It is shown also that grid stretching can significantly improve the convergence, however sometimes can lead to its slowdown. It is argued that due to the sparseness of the Jacobian matrix and its large dimension it can be effective to combine Arnoldi iteration with direct sparse solvers instead of traditional Krylov‐subspace‐based iteration techniques. The same replacement in the Newton steady‐state solver also yields a robust numerical process, however, it cannot be as effective as modern preconditioned Krylov‐subspace‐based iterative solvers. Copyright © 2006 John Wiley & Sons, Ltd.