A thermal multi-phase flow model for directed energy deposition processes via a moving signed distance function

Thermal multi-phase flow analysis has been proven to be an indispensable tool in metal additive manufacturing (AM) modeling, yet accurate and efficient simulations of metal AM processes remains challenging. This paper presents a flexible and effective thermal multi-phase flow model for directed energy deposition (DED) processes. Departing from the data-fitted or presumed deposit shapes in the literature, we first derive a deposit geometry model based on an energy minimization problem with a mass conservation constraint. Then, an interface-capturing approach based on a signed distance function that moves with the laser is constructed to represent the air–metal interface evolution. The approach can be applied to any type of mesh without requiring the activation process of solid elements in a mesh. The coupled multi-phase Navier–Stokes and energy conservation equations are solved by a variational multi-scale formulation (VMS). A density-scaled continuous surface force (CSF) model is employed to incorporate the Marangoni effect, no penetration boundary condition, and the heat source on the air–metal interface. We utilize the proposed method to simulate two representative metal manufacturing problems. The simulated results are carefully compared with available experimental measurements and computational results from others. The results demonstrate the accuracy and modeling capabilities of the proposed method for metal AM problems.