Numerical analysis of the unsteady character of “spoke pattern” in Bridgman top seeding geometry

Abstract

Three-dimensional (3D) numerical simulations of spoke patterns were performed in a vertical cylinder (similar to the Bridgman top seeding method of single-crystal growth). Calculations were presented for Rayleigh numbers in the range between 10 5 and 10 7 (for the transient region from laminar to turbulent flow). The numerically simulated surface pattern shows unsteady flow behaviour. The spoke pattern was formed due to a buoyancy effect. All velocity components (radial, azimuthal and axial) show fluctuations. The region of the maximum fluctuations for the axial velocity component appears near the axis of symmetry. However the regions of maximum fluctuation for the radial and azimuthal velocity components are near the bottom of the crucible. The analysis of the numerical results shows that fluctuations in “spoke patterns” are driven by temperature fluctuations and by fluctuations of the azimuthal and axial velocity components. The calculated distributions of the kinetic fluctuation energy show that the height of the kinetic fluctuation energy profile depends on the Grashof number. As the Grashof number increases the flow structure becomes unstable and the vertical “cold jet” becomes dominant in the melt.