Three-dimensional finite element modeling of the flow of a metal melt with a free surface under conditions of a moving laser source

Three-dimensional convective heat and mass transfer in a metal melt bath under the action of a moving laser heat source is considered. The mathematical model with a Lagrangian description is based on the Navier – Stokes equations, continuity and energy, taking into account diffusion, convective and radiative heat losses. Temperature – dependent surface effects are taken into account using surface tension (Marangoni forces) at a dynamic contact angle on a moving three-phase contact line. The numerical solution of the problem is performed by the finite element method with a divergently stable approximation of the main variables. The integration of kinematic and dynamic conditions on a free surface is performed according to the Newmark – Bassac scheme. Verification and validation of the proposed numerical algorithm is performed. The influence of the determining process parameters (laser power and scanning speed) on the geometric dimensions of the melt bath is shown.