Basis of the Lattice Boltzmann Method for Additive Manufacturing

Additive manufacturing (or 3D printing) is constantly growing as an innovative process for the production of complex-shape components. Among the seven recognized 3D printing technologies, powder bed fusion (PBF) covers a very important role for the production of structurally functional components starting from different metal powder. However, being PBF a production process involving very high thermal gradients, non-negligible deformations and residual stresses may affect the 3D printed component. One of the characterizing aspects of PBF is the evolution of the melt pool and the heat exchange with the surrounding solid powder. In literature many attempts to simulate melt pool evolution have been carried out, however the only approaches leading to interesting results rely on the lattice Boltzmann method. In this work, starting from the Boltzmann’s equation, we derive the lattice Boltzmann equation and we introduce the needed assumptions in order to recover the lattice Boltzmann method. Finally, we apply the lattice Boltzmann method to study some interesting problems related to powder bed fusion process, including droplets wetting, thermal convection and solid–liquid phase change.