An analytical-numerical coupled model of liquid droplet impact on solid material surfaces

Abstract

Impacts of liquid droplets on wind turbine blade surfaces, for example sea sprays, can result in material damage through erosion. In this study, we derive an explicit, closed-form analytical approximation for droplet impact and subsequent spreading on a solid surface in inertia-dominated regimes of large Reynolds and Weber numbers. The formulation extends an existing theoretical framework based on inviscid potential flow for a rising expanding disk in an infinite liquid domain. The modified solution provides full spatio-temporal pressure distributions and impact force histories on the impact surface over the entire impact duration, capturing both the early-time self-similar flow and the inertia-driven lamella spreading following the peak impact force. The predicted pressure and force profiles show good agreement with analytical, numerical and experimental results reported in the literature, including accurate reproduction of the well-known ring-shaped pressure distribution. Key quantities, such as the radial location and magnitude of peak pressure, as well as the timing and magnitude of the peak impact force, are predicted analytically with reasonable accuracy. To enable solid material erosion analysis, the analytical liquid-phase solution is coupled with a finite-element (FE) simulation for the solid response. This analytical-numerical coupled method (ANCM) eliminates the need to explicitly simulate droplet fluid dynamics, which is conventionally performed using smoothed particle hydrodynamics (SPH). As a result, for the purpose of material response analysis, the proposed approach achieves grid independence at substantially lower mesh resolutions and reduces computational cost by more than 97% compared to SPH-based simulations, while maintaining or improving numerical accuracy.