Modeling of heat and mass transfer and electrons scattering in electron beam welding and additive manufacturing

The mathematical formulation of electron beam melting and liquid metal transfer model in wire-based additive manufacturing with temperature dependencies of thermophysical properties is described. A description of the model algorithmic implementation based on the use of numerical methods for solving the Navier-Stokes equations system and the Volume of Fluid (VOF) method for tracking the free surface of a liquid on the cubic mesh cells is given. An iterative method for calculating the pressure field that ensures the fulfillment of the incompressibility condition for a viscous fluid is described. The paper also paid attention to the description of methodology for calculating the forces acting on the free surface of the melt, including surface tension forces and metal vapor pressure forces. One of the key elements of the proposed model is method for volumetric distribution of electron losses calculating, considering their scattering during the interaction of an electron beam with a curved melt surface. Electron beam focusing influence on the distribution of energy losses and the dynamics of penetration channel formation has been studied. An algorithm for visualizing the free surface of the melt based on the use of the Gaussian function, is described.