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.
Convection in a Czochralski crucible – Part 1: non-rotating crystal
Abstract A Czochralski melt is simulated in a model experiment and by numerical analysis. We use a transparent fluid (0.65 cSt silicone oil with Pr=6.8) which is contained in a transparent sapphire crucible (40 mm inner diameter, 40 mm height, crystalline material). A copper rod (e.g. 14 mm diameter) is used to simulate the growing crystal. An imposed temperature difference between the crucible and the crystal dummy gives rise to convective flow in the fluid. Forced convection by crystal rotation has also been applied but will be treated in part 2 of this paper. Our experiment models to a good degree the growth of oxide and fluoride crystals from noble metal crucibles. Flow visualization and flow velocity measurements are performed. We report the flow patterns observed in the fluid for different parameters (temperature difference, fluid depth, meniscus, free surface cooling). We observe a separated surface tension driven convection roll at the free surface and a “cold jet” beneath the crystal dummy. The flow is strongly affected by thermocapillary forces. The experimental results can be used as benchmarks to test numerical simulation programs for Czochralski growth. Numerical simulations are performed (2D, steady, axisymmetric). The simulation results compare favorably with the experimental data. In a parametric numerical study the relative importance of thermocapillary and buoyant forces is investigated.
Oscillatory thermocapillary convection in open cylindrical annuli. Part 1. Experiments under microgravity
We report results from microgravity experiments on thermocapillary convection in open annuli with outer radius $R_{o}{\,=\,}40\,\hbox{mm}$ and inner radius $R_{i}{\,=\,}20\,\hbox{mm}$ of various aspect ratios $Ar$. The measurements are from more than 230 equilibrated states in the $Ar$–Marangoni-number space. We found time-independent and oscillatory states and report some selected oscillation and Fourier spectra from thermocouple measurements. We measured the critical temperature difference $\uDelta T^{\hspace*{1pt}c}$ for the onset of temperature oscillations in the range $1{\,\le\,}Ar{\,\le\,}8$. We report supercritical oscillation periods and attribute the oscillations in the larger $Ar$ range to hydrothermal waves. This conclusion is supported by the values of the oscillation periods and of the critical Marangoni numbers in that $Ar$ range. The hydrothermal waves exhibit an internal corotating multicellular pattern. For the smaller $Ar$ and near the threshold we report $m$-fold temperature patterns on the free surface with $m$ decreasing for decreasing $Ar$. At $4\uDelta T^{\hspace*{1pt}c}$ these patterns become very irregular. Most of the findings are in accordance with the numerical results reported in Part 2 (Sim et al. (2003)). The experimental $\uDelta T^{\hspace*{1pt}c}$ are higher and the experimental periods $\tau^{c}$ are smaller than the numerical values for Biot number $Bi{\,=\,}0$. However, analysis of the experimental free-surface thermal boundary conditions shows that there was heat input to the free surface. Good agreement with numerical results for $\uDelta T^{\hspace*{1pt}c}$ and $\tau^{\hspace*{1pt}c}$ is obtained with $Bi{\,\ne\,}0$ (heat input).