Volatilization kinetics in vacuum metallurgy

During metal processing, the melting conducted under vacuum or at low press ures leads to volatile metal losses. It is the case in the metallurgical pr ocessing of the nickel-based, titanium-based or zirconium-based alloys wher e the evaporation losses make it difficult to control the alloy chemical co mposition. A theoretical approach has been carried out involving both an hydrodynamic description of the liquid phase and a kinetic description of the gas phase. In the liquid phase, the coupled transport equations are solved by using t he finite volume method where the turbulence mechanism is described by a k- epsilon model. In the gas phase, the vapour transport is modelled by the Bo ltzmann equation which is solved using a Monte Carlo method : the velocity distribution function of the vapour is approximated by a set of particles, each having a specific velocity and position. For each time step, the parti cle evolution is split in two steps, a free molecular motion and a random c ollision step. At the liquid metal and metallic vapour interface, the volat ilization and recondensation fluxes link the two calculations. The models c alculate the behaviours of the liquid metal and the vapour phase. The recon densation coefficients, which represent the fraction of evaporated molecule s which return to the surface of the liquid, are also given by the simulati on. Simulation results are given for the electron beam melting and refining of a reactive metal under vacuum, a titanium alloy (Ti-6 wt % Al) in particula r, where the control of the chemical composition remains a major difficulty . For standard operating conditions, the recondensation coefficients are cl ose to zero. The small recondensation flux values corroborate the low calcu lated partial pressures above the liquid pool and the expansion of the vapo ur towards the chamber walls. The deviation from Langmuir's law due to reco ndensation is thus negligible in this case. The numerical tool has also bee n used so as to study the influence of the volatilization rate on the recon densation coefficients. The recondensation fluxes increase with the thermal power, and therefore the liquid metal superheat. The aluminium recondensat ion coefficient reaches 20 % in the case of intense evaporation (which is t he case of PVD for instance).