SPH Simulation of Multiple Droplets Impact and Solidification on a Cold Surface

The impact and solidification of multiple molten droplets on a cold substrate critically influence the quality and performance of thermally sprayed coatings. We present a Smoothed Particle Hydrodynamics (SPH) model that couples fluid-solid interaction, wetting, heat transfer and phase change to simulate multi-droplet impact and freezing. The model is validated against benchmark cases, including the Young–Laplace relation, wetting dynamics, single-droplet impact and the Stefan solidification problem, showing good agreement. Using the validated model, we investigate two droplets—either centrally or off-centrally—impacting on a cold surface. Simulations reveal two distinct solidification patterns: convex pattern (CVP), which results in a mountain-like splat morphology, and concave pattern (CCP), which leads to a valley-like shape. The criterion for the two patterns is explored with two dimensionless numbers, the Reynolds number Re and the Stefan number Ste. When Re≤17.8, droplets tend to solidify in CVP; at higher Reynolds numbers Re≥18.8, they tend to solidify in CCP. The transition between the two patterns is primarily governed by Re, with Ste exerting a secondary influence. For example, when droplets have Re=9.9 and Ste=5.9, they tend to solidify in a convex pattern, whereas at Re=19.8 and Ste=5.9, they tend to solidify in a concave pattern. Also, the solidification state of the first droplet greatly influences the subsequent spreading and solidification of the second droplet. A parametric study on CCP cases with varying vertical and horizontal offsets shows that larger vertical offsets accelerate solidification and reduce the maximum spreading factor. For small vertical distances, the solidification time increases with horizontal offset by more than 29%; for large vertical distances the change is minor. These results clarify how droplet interactions govern coating morphology and thermal evolution during thermal spraying.