Mathematical Modeling of a Melt Pool Driven by an Electron Beam

Physical vapor deposition (PVD) assisted by an electron beam is one of several methods currently used to apply thermal barrier coatings (TBCs) to aircraft components subjected to high-temperature environments. The molten pool of source material inherent in this process shall be the subject of analysis in this investigation. A model of the melt pool and the ingot below shall be generated in an effort to study the fluid flow and heat transfer within the pool. This model shall incorporate all of the following mechanisms for heat transfer into and out of the melt pool/ingot system: electron-beam impingement upon the melt pool surface, absorption of latent heat of evaporation at the melt pool surface, radiation from the melt pool surface, loss of sensible heat carried off with the vapor, and cooling by the crucible containing the melt pool/ingot. Fluid flow within the melt pool model shall be driven by both natural convection and by surface tension gradients on the melt pool surface. Due to the complexity of the differential equations and boundary equations governing the model, this detailed study shall be performed through a finite element analysis. Reduced order models of the system will be generated from this investigation. An analysis will also be performed to ascertain the error introduced into these models by uncertainty in the thermophysical property data used to generate them.