Three-dimensional oscillatory flow in a thin annular pool of silicon melt

In order to understand the nature of surface patterns on silicon melt in industrial Czochralski furnaces, we conducted a series of unsteady three-dimensional numerical simulations of thermocapillary and thermocapillary–buoyancy flows in thin silicon melt pools in annular containers. The pool is heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces either are adiabatic or allow heat transfer in the vertical direction. With large temperature difference in the radial direction, the simulation can predict two types of oscillatory convections. One is characterized by spoke patterns traveling in the azimuthal direction. The other one is characterized by radially extended roll cells periodically alternating the azimuthal flow directions but are stationary. The small vertical heat flux (3 W/cm 2) does not have significant effects on the characteristics of those oscillatory flows. Details of the flow and temperature disturbances are discussed and the critical conditions for the onset of the oscillatory flow are determined.