Analytical and numerical investigation of successive metallic alloy droplets impacting onto a surface: Regime maps and scaling laws based on energy analysis

Abstract

This study investigates the impact dynamics of two molten Al7075 droplets under varying Weber numbers ($1\le \mathrm{We}\le 60$) and diameter ratios ($0.5\le D_r\le 2$) through numerical simulations using OpenFOAM software and response surface modeling with the Kriging method. Key parameters, including collision spread factor, maximum spread factor, collision time, and time to maximum spreading, are analyzed. The Kriging method demonstrates superior accuracy over Non-Parametric Regression (NPR) method, particularly in predicting spread factors and time-related dynamics, as indicated by its lower relative error. Results show that higher Weber numbers enhance the dominance of inertial forces, accelerating spreading, while lower Weber numbers lead to slower dynamics due to surface tension effects. Smaller second droplets cause more lateral spreading during collisions at lower Weber numbers, whereas at higher Weber numbers, the influence of diameter ratio diminishes as inertia prevails. The maximum spread factor significantly increases with rising Weber numbers, highlighting the correlation between impact velocity and spreading behavior. Larger diameter ratios further amplify maximum spread factors, indicating a strong influence of kinetic energy in spreading dynamics, while smaller ratios restrict spreading, especially at lower Weber numbers. For the first time, two analytical models for maximum spread factor are proposed based on energy analysis, with Model 2, which accounts for energy loss, showing better alignment with numerical results than Model 1. Moreover, a new scaling law for time to maximum spreading reveals an inverse relationship with Weber number. The study also provides regime maps that offer valuable insights for optimizing droplet impact processes in industrial applications.