A machine learning-based drag model for sand particles in transition flow aided by spherical harmonic analysis and resolved CFD-DEM

Given the importance of drag model in solving fluid–particle interactions in unresolved numerical methods, this study proposed a machine learning (ML)-based drag model for irregular sand particles in transition flow, aided by spherical harmonic (SH) analysis and a resolved computational fluid dynamics-discrete element method (CFD-DEM). Initially, realistic particle shapes were reconstructed by the SH function, and their multi-scale shape features were quantified by the energy spectrums of SH frequencies. A developed fictitious domain method, particularly for irregularly shaped clumps, was proposed to solve fluid–solid interactions within resolved CFD-DEM. Subsequently, the fluid flow past a fixed particle test was repetitively simulated by the resolved CFD-DEM for 270 realistic sand particles, and a dataset consisting of 4220 drag coefficients was finally established. A classic ML algorithm, namely the multi-layer perceptron (MLP) neural network, was then utilized to train a drag model associated with the multi-scale shape features, particle orientations, and flow conditions. Compared with the results from the resolved CFD-DEM, the trained MLP model demonstrates both efficiency and accuracy in predicting the drag coefficients of natural sand particles with irregular shapes. This work provides a more reliable drag model for granular soils and shows its potential for application in large-scale modeling using the unresolved CFD-DEM framework.