Simulation of metal droplet deposition with solidification including undercooling and contact resistance effects

A numerical procedure for the deformation and solidification of a metal droplet impinging on a flat surface is developed and a sample calculation is presented. A previously derived second-order ordinary differential equation (ODE) that approximates the splat as a cylinder and describes the droplet size evolution based on the mechanical energy equation in conjunction with kinematic and geometrical compatibility is used. The thermal energy equations for the liquid and solid regions of the splat and the substrate ape separately solved coupled by boundary conditions such as contact resistance and undercooling in a regularized calculation domain produced by algebraic grid generation. The solidified layer thickness is calculated by solving a hyperbolic partial differential equation (PDE) resulting from the interface energy equation at the phase change boundary. Physical processes such as convective heat loss, substrate heat loss, viscous dissipation, and surface tension are modeled through appropriate nondimensional parameters.