Improved drag force calculation in CFD-DEM using coarse cell for dilute large-sized particles: Effective projected area for drag force distribution

This study addresses a critical challenge in CFD-DEM simulations: the accurate assignment of drag force to fluid mesh cells when the cell size exceeds particle sizes. Traditional particle centroid method (PCM) approaches often lead to abrupt drag force variations as particles cross cell boundaries due to their discrete nature. To overcome this limitation, we propose a novel algorithm that computes an analytical solution for the effective projected area (EPA) of particles within computational cells, aligned with the relative velocity direction. The drag force is then proportionally scaled according to this EPA calculation. The paper presents a specific implementation case of our algorithm, focusing on scenarios where a cell vertex resides within a particle boundary. For EPA determination, we introduce an innovative classification approach based on face-windward surface relations. Extensive validation involved 100,000 test cases with varying cell-particle relative positions (all constrained by the vertex-in-particle condition), systematically classified into 18 types using our scheme. Results demonstrate that all computed EPA values remain within theoretical bounds, confirming the classification's comprehensiveness. Through 5 classic particle movement simulations, we show that our method maintains continuous EPA variation across time steps - a marked improvement over PCM's characteristic discontinuities. Implementation within the CFD-DEM framework for single-particle sedimentation yields terminal velocities that closely match experimental data while ensuring smooth drag force transitions between fluid cells. Compared to PCM, the present method reduces the relative error in terminal settling velocity by approximately 43 %. Moreover, comparative studies of dual-particle sedimentation demonstrate our algorithm's superior performance relative to conventional PCM approaches. For Particle 1, the terminal vertical velocity predicted by the present method reduces the relative error by approximately 17 % compared to PCM. These advances significantly enhance simulation fidelity for particle-fluid interaction problems where cell-particle size ratios challenge traditional methods.