Particle-resolved large eddy simulation and viscous drag modeling in random sphere arrays with volume fraction effects

This study investigates interphase forces in shock-induced and nozzle-driven dense gas-solid flows, where volume fraction significantly affects gas–solid interactions. Using particle-resolved (PR) large eddy simulation (LES), we simulated airflows through randomly distributed spheres (particle volume fraction φp = 10%–25%, particle Reynolds number Rep = 300–900, particle Mach number Mp = 0.154–1.234) to obtain a viscous drag dataset. Combined with an isolated-sphere viscous drag model [Zhang et al., “A general drag coefficient model for a spherical particle incorporating rarefaction and particle-to-gas temperature ratio effects,” Chem. Eng. Sci. 298, 120442 (2024)], we developed a new viscous drag correlation via least squares-method based nonlinear (LSM-NL) fitting. At a low Mp incompressible flow regime, the Venturi effect dominates: reduced interparticle spacing accelerates flow, increasing shear stress, while higher Rep thins boundary layers and enhances vortex shedding, causing volume fraction correction coefficient ⟨Fd⟩/Fiso to rise with φp, where ⟨Fd⟩ and Fd,iso denote sphere-array averaged viscous drag force (magnitude) and the isolated-sphere viscous drag force predicted by Zhang et al., Chem. Eng. Sci. 298, 120442 (2024). Higher Mp increases pressure drag while reducing viscous effects, decreasing ⟨Fd⟩/Fiso. Subsonic flows show blocking effects at low φp, countered by Venturi effects at φp ≥ 21%. Supersonic flows exhibit persistent shock-induced blocking that reduces ⟨Fd⟩/Fiso with φp and creates non-monotonic Rep dependence. For Rep ≥ 500, compressibility suppresses inertial effects, minimizing ⟨Fd⟩/Fiso variations across Rep. Nozzle flow experiments confirm the model's superior accuracy over existing correlations, demonstrating its effectiveness in capturing complex volume fraction, compressibility, and inertial effects in both subsonic and supersonic regimes for dense gas–solid flow applications.