Comparison of Model and Experimental Results for Material and Energy Flow in a Titanium Evaporation System with Deforming Interfaces

Finite element calculations and measurements are compared for material and energy flow in a system to evaporate pure titanium. A 40 kW electron beam is used to heat the end of a 7.62 cm diameter cylindrical rod which is fed vertically through a water-cooled crucible. Vapor emanates from a liquid pool in which flow is driven strongly by buoyancy and capillary forces. At high evaporation rates, the vapor exerts strong shear and normal forces on the liquid-vapor interface. The MELT finite element code is used to calculate steady-state, axisymmetric flow and temperature fields along with liquid-solid and liquid-vapor interface locations. The influence of the vapor on the liquid top surface is treated using boundary conditions with parameters derived from Monte Carlo simulations. The upper and lower interfaces of the liquid pool are tracked using a mesh structured with rotating spines. Experimental evaporation rates are obtained from measured feed rates, and heat flow rates are determined from measured temperature rises in the cooling water. The finite element model provides a good representation of the measured evaporation rates, heat flows, and lower pool boundary locations.