Evaluation of the performance of an analytical-numerical coupled method for droplet impacts on soft material surfaces

Abstract

Impacts between droplets and solid surfaces can commonly cause erosion problem in Engineering applications, including aircraft surface erosion, wind blade leading-edge erosion and steam turbine blade erosion. In practice, the impacted solid surfaces have varied material softness, ranging from stiff metallic coatings to soft materials. An analytical-numerical coupled model (ANCM) for simulating droplet impacts on surfaces, and corresponding material analysis, has been developed in the literature. However, the analytical impact pressure solution of the ANCM model has been derived assuming rigid solid surface. In the current study, we investigate the performance of the ANCM model for droplet impacts on soft materials made of urethane gel phantom, by comparing the ANCM computations to lab-based experiments and numerical simulations based on Smoothed Particle Hydrodynamics (SPH). Parametric studies explore the applicability limit of the ANCM model for droplet impacts on very soft materials at low Young's modulus. It was found that for materials at Young's modulus of $47,400$ Pa or stiffer, which covers most engineering applications, the developed ANCM model performs as expected for an assumed rigid surface. For softer solid materials, the SPH-modeled liquid interacts with the evolving surface geometry and mitigates impact intensity as deformation occurs. The analytical impact loads estimated by ANCM are independent of surface geometry, and hence provide conserved impact impulse in a non-physical way. Results show a critical value of Young's modulus at $E=10,000$ pa for the ANCM model, below which the model exhibits overshoot in total contact force and surface deformation, leading to the formation of steep wall craters.

Figures (13)

• Figure 1: Initial droplet (and material) configuration in the Cartesian coordinate system (a) and corresponding analytical pressure profiles on the rigid surface upon liquid droplet impact in Hao_ANCM, shown at time $t=0.05$ (b), $t=0.1$ (c) and $t=0.3$ (d). $r_0=1$ and $u_0=1$ denote the radius and impact velocity of the droplet, respectively. Subfigures (b-d) have the same axes and pressure limits. All variables in the figure are presented in their dimensionless forms.
• Figure 2: The analytical pressure profiles of Equation \ref{['pre']} are plotted as a function of radius and time. Figure is produced after Nick2023 with the same values on the axes, but (the present figure is) in dimensionless forms, for comparison purpose.
• Figure 3: Required FE elements (with element codes in ABAQUS) and loading conditions in SPH (left) and ANCM (right) models Hao_ANCM. The figure is for illustration purpose and the solid material dimensions are not to scale.
• Figure 4: Numerical FE mesh and simulation parameters in SPH (left) and ANCM (right) models. The same mesh resolution has been used for the solid materials in SPH (left) and ANCM (right) models.
• Figure 5: The temporal evolutions of the impact force on the solid surface, from the experiment in Yuto2024 and the numerical simulations of SPH and ANCM models, are compared. The error bar indicates one standard deviation of three tests in experiments. The analytical solution of Equation \ref{['temp1']}, which is the impact force under the liquid droplet assuming a rigid surface, is also superimposed. The experimental peak force happens at $T_p=0.45\times10^{-3}$. The empirical formula in Zhang estimates the peak force as $F_{emp,p}=0.0247$.