Construction and validation of gas-liquid-solid three-phase coupled model for rod-pin sand mills

LIU Can; HE Jiangbo; ZHU Jianglin; YIN Ningxia; LIU Huanlao; ZHANG Jiaqi

doi:10.13732/j.issn.1008-5548.2025.06.014

Abstract：Objective During the simulation design process of rod-pin sand mills,the study considers the distinct characteristics of gas and liquid phases by incorporating air phase dynamics into the simulation model to establish a gas-liquid-solid three-phase coupled simulation framework.This approach enables a more accurate representation of actual operating conditions,enhancing the accu-racy and reliability of numerical predictions. Methods A systematic methodology was developed for this simulation study.The discrete element method(DEM)and computa-tional fluid dynamics(CFD)were employed to model the solid and fluid phases,respectively.The volume of fluid(VOF)method was incorporated to distinguish between the liquid phase and gas phase within the fluid domain.By analyzing the govern-ing equations for solid-phase motion and fluid-phase dynamics,the gas-liquid interface tracking method and the coupled compu-tation framework were established,and a simulation workflow was developed.The accuracy of the CFD-DEM-VOF three-phase coupled model was evaluated through numerical simulations of single-particle water entry and particle swarm water entry.Rigor-ous verification procedures were implemented.Then,simulation parameters were configured,and computational meshes were generated,alongside grid independence analysis.The validated model was applied to simulate the operational conditions of a rod-pin sand mill.Finally,the simulated results,including slurry flow rate,total particle kinetic energy,and particle velocity distributions,were analyzed and compared with experimental data to validate the model's predictive capability. Results and Discussion In the single-particle water entry simulation,when the dynamic viscosity coefficients of water were 4×10-5,2×10-4,8×10-4,and 2×10-3 Pa·s(corresponding to Reynolds numbers of 107,11.34,1.09,and 0.20,respectively),the time required for particle velocity to stabilize was 0.054 6,0.047 6,0.032 2,and 0.028 0 s,respectively.The time required for the particle velocity to stabilize decreased as the dynamic viscosity coefficient of water increased.The simulation results from the CFD-DEM-VOF three-phase coupling model showed good agreement with the theoretical calculations based on Stokes' law.In the particle swarm water entry simulation,the relative error between the simulated and theoretical values of the liquid surface rise heights was 1.37％,demonstrating the volume conservation capability of the CFD-DEM-VOF three-phase coupling model.The tangential velocity of tetrahedral mesh first increased and then decreased with radial distance,reaching its maximum at a radial distance of 8 mm.When the edge length of the tetrahedral mesh for the rod-pin was less than 2 mm and that for the grinding barrel was less than 2.5 mm,the relative error of tangential velocity of the tetrahedral mesh was 3.23％,meet-ing the accuracy requirements for grid independence while maintaining a reasonable computational load.As the rod-pin rota-tional speed increased,the fluid velocity,total particle kinetic energy,and average particle velocity also increased.For each rotational speed,the CFD-DEM-VOF three-phase coupled model exhibited closer agreement between the simulated and experi-mental values for fluid velocity,total particle kinetic energy,and average particle velocity compared to single-fluid-phase,single-solid-phase,or solid-liquid two-phase models.At rotational speeds ranging from 1 400 r/min to 2 200 r/min,the relative error between the simulated and experimental values for fluid velocity in the CFD-DEM-VOF three-phase coupled model was minimized to 0.25％,representing the closest agreement between simulation and experimental results.At rotational speeds rang-ing from 1 400 r/min to 2 200 r/min,the maximum relative error for total particle kinetic energy was 1％,further validating the model's predictive capability. Conclusion Compared to using single-fluid or solid-phase models or solid-liquid two-phase models,the CFD-DEM-VOF three-phase coupled model demonstrates significantly enhanced computational accuracy and precision in designing rod-pin sand mills,with superior simulation performance.