Mathematical modeling of aluminum evaporation during electron-beam cold-hearth melting of Ti-6Al-4V ingots

A mathematical model was developed to describe the kinetics of aluminum evaporation during the electron-beam cold-hearth melting of titanium alloys. The analysis treated the diffusion of aluminum to the surface of the melt, chemical reaction between the melt and vapor phases at the surface, and the transport of aluminum into the vacuum chamber. The kinetics equation was combined with appropriate mass and energy balance equations to determine the effect of melting rate, the electron-beam power input to the melt pool in the hearth and the mold, and charge chemistry on the composition of the cast ingot. The model was validated by comparison to measurements for Ti-6Al-4V processed under a wide range of conditions.