Comparative analysis of numerical algorithms for modeling complex solid‒liquid flow in a vertical conveying system with ceramic and expanded polystyrene particles

This work presents a numerical investigation of a supported upflow vertical pipe model conveying a two-phase particle–liquid flow, focusing on elucidating the turbulent motion dynamics of the particle–liquid interactions. Two numerical methods, computational fluid dynamics coupled with the discrete element method (CFD–DEM) and discrete phase model (CFD–DPM), were employed and validated against experimental measurements. The study involved ceramic particles and expanded polystyrene particles with diameters of 2.32 mm and 1.79 mm, respectively, representing materials with heavier and lighter densities than water. Validation of the CFD–DEM/DPM models across various flow conditions demonstrated the applicability and accuracy of the CFD–DEM method in simulating this flow system, successfully predicting the main flow characteristics. Furthermore, the CFD–DEM approach exhibited minor average deviation errors, highlighting its superior accuracy in capturing the experimental dynamics. The findings revealed that under all operating conditions with applying lift force, the time-averaged variables—including particle volume fraction, axial liquid velocity, and axial particle velocity—exhibited maximum values at the pipe center, gradually decreasing radially toward the wall. The volume fraction profiles indicated that ceramic particles were almost uniformly distributed at low flow rates, while higher flow rates led to their concentration toward the center of the pipe. Conversely, the distribution of the lighter polystyrene particles showed a wall peaking at both low and high flow rates, with the peaking effect diminishing as the flow rate increased. The force analysis revealed that the drag, lift, and interparticle forces dominate the upflow of the conveying vertical pipe, greatly affecting the flow dynamics. The results obtained from this investigation are anticipated to contribute significantly to optimizing hydraulic conveying systems.