Convective motions in liquid metals for material processings. Numerical simulation of oscillation regimes and effect of rotation

The paper is concerned with the numerical simulation and the analysis of some kinds of flow regimes which can develop in Bridgman and Czochralski systems for material processings. The flows in the liquid phase are investigated considering two-dimensional and axisymmetric models. The time-dependent regimes were studied for a zero-Prandtl-number fluid layer confined inside a two-dimensional cavity of aspect ratio (length-to-height) A=4, involving a stress-free upper surface and submitted to a horizontal temperature gradient. The range of Grashof number was varied up to the conditions at which the flow goes from oscillatory to chaotic type behaviours. The combined influence of the temperature gradients and of the rotations of the crucible and of the seed/crystal was investigated for a Czochralski model. The axisymmetric regimes were studied for a Pr_m=0.015 liquid melt confined inside a cylindrical crucible of aspect ratio (height-to-radius) A_m=2, and coupled to a viscous encapsulant liquid layer (10<Pr_e<1200) of aspect ratio A_e=0.5. A number of steady and (transient) time-dependent flow patterns are identified.     

Steady and oscillatory convection in vertical cylinders heated from below. Numerical simulation of asymmetric flow regimes

Three-dimensional buoyancy driven flows in vertical cylinders are simulated with a finite difference technique. Asymmetric convective flows are studied for three values of the (length-to-radius) aspect ratio A. One result concerns the occurrence of asymmetric convection in a flat A=0.485 cylinder for Pr=6.7, near the threshold and up to 3Ra_c (where Ra_c is the critical Rayleigh number and Pr is the Prandtl number). Complex (steady and time-dependent) supercritical regimes have been simulated in cylinders of aspect ratios A=2 and A=4 for Pr=0.02 and in ranges of Ra up to 8Ra_c and 6Ra_c, respectively. The flow patterns are analysed graphically and discussed with respect to a weakly nonlinear analysis and to experiments. In a particular case, A=4 and Pr=0.02, an oscillatory motion has been obtained and some features of the flow pattern are shown during a period.