Artificial neural network-based subgrid-scale velocity enrichment model used for large-eddy simulation of particle clustering and collision rates in isotropic turbulent flows

This study extends our previously proposed artificial neural network (ANN)-based subgrid-scale (SGS) model [Tan and Jin, Phys. Fluids 36, 085170 (2024)] to improve the predictive accuracy of large-eddy simulation (LES) for particle clustering and collision rates. The model integrates a linearized SGS velocity equation with an ANN closure that represents the effects of SGS self-interaction and the pressure gradient, thereby bridging physics-based and data-driven approaches. Using the large-scale velocity and velocity gradient tensor as inputs, the model predicts their combined SGS contribution; SHapley Additive exPlanations analysis is employed to interpret the relative importance of these input features. By solving the linearized governing equations informed by the large-scale flow, we reconstruct the SGS flow fields. The novel contribution of this work lies in validating the dynamic interaction between inertial particles and the reconstructed SGS motions, which is critical for accurately predicting particle clustering, relative motion, and collision rates. In an a priori study, the model's performance in reconstructing SGS fields is validated through analysis of flow structures and probability density functions of velocity gradients. Furthermore, predictions of particle statistics—including the radial distribution function, radial relative velocity, and collision kernel—are compared with results from direct numerical simulation (DNS) and filtered DNS. The results demonstrate that the hybrid physics-informed ANN model effectively reconstructs small-scale velocities and significantly enhances the prediction accuracy of particle clustering and collision statistics in LES.