刘璨^1，2， 何江波¹， 朱江林³， 尹凝霞^1，2， 刘焕牢^1，2， 张佳蕲¹

1. 广东海洋大学 机械工程学院， 广东 湛江 524088； 2. 广东省小家电创新设计及制造工程技术研究中心， 广东 湛江 524048；

3. 南方海洋科学与工程广东省实验室（湛江）， 广东 湛江 524054

引用格式：

刘璨，何江波，朱江林，等. 棒销式砂磨机的气-液-固三相耦合模型的构建与验证［J］. 中国粉体技术，2025，31（6）：1-15.

LIU Can，HE Jiangbo，ZHU Jianglin，et al. Construction and validation of gas-liquid-solid three-phase coupled model for rod-pin sand mills［J］. China Powder Science and Technology，2025，31（6）：1-15.

DOI：10.13732/j.issn.1008-5548.2025.06.014

收稿日期：2024-10-11，修回日期：2025-03-20，上线日期：2025-04-16。

基金项目：国家自然科学基金项目，编号：52175458；广东省质量监督家用电热蒸煮器具检验站（湛江）联合培养研究生示范基地项目，编号：521004010；广东省小家电创新设计及制造工程技术研究中心资助项目，编号：C17080。

第一作者简介：刘璨（1971—），男，教授，博士，硕士生导师，研究方向为先进制造及其检测技术。E-mail：liucanzj@163.com。

摘要：【目的】棒销式砂磨机的工作过程存在复杂的气体、液体和固体的三相耦合现象，为使仿真工况更接近实际工况，构建气-液-固三相耦合仿真模型，提高棒销式砂磨机仿真设计的准确性。【方法】采用离散单元法（discrete element method，DEM）和计算流体动力学（computational fluid dynamics，CFD）分别研究固体相和流体相，并引入流体体积模型（volume of fluid model，VOF）区分流体相所包含的液体相和气体相，分析固体相运动方程、流体相控制方程，确定气-液界面的识别方法和耦合计算方法，制定仿真流程；通过单球落水仿真、颗粒群落水仿真试验分析CFD-DEM-VOF三相耦合模型仿真计算的精度，并进行准确性验证； 在设置仿真参数、进行网格划分及其无关性分析基础上，针对棒销式砂磨机的CFD-DEM-VOF三相耦合模型进行仿真试验；对流体速度、颗粒总能量和颗粒的速度的仿真结果进行分析，并通过实验验证仿真结果。【结果】在单球落水仿真试验中，根据CFD-DEM-VOF三相耦合模型的仿真结果与根据Stokes定律的理论计算结果基本吻合； 在颗粒群落水仿真过程中，液面上升高度的仿真值与理论值之间的相对误差为1.37%，VOF模型的体积守恒性较好；棒销四面体网格边长小于2 mm、研磨桶四面体网格边长小于2.5 mm时，满足网格独立性的精度要求，同时计算量也较少；随着棒销转速的增大，流体速度、颗粒总能量、颗粒平均速度也逐渐增大；当棒销转速为1 400~2 000 r/min时，CFD-DEM-VOF三相耦合模型流体速度的仿真结果与实验结果最为接近；当棒销转速为 1 400~2 200 r/min时，CFD-DEM-VOF三相耦合模型的颗粒总能量仿真值与实验值的最大相对误差为1%。【结论】与仅仅采用流体相、固体相单相模型或固-液两相模型相比，采用CFD-DEM-VOF三相耦合模型设计棒销式砂磨机的计算精度和准确性较高，仿真性能好。

关键词： 棒销式砂磨机；离散单元法；计算流体动力学；流体体积模型；气-液-固三相耦合模型

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 accuracy and reliability of numerical predictions.

Methods A systematic methodology was developed for this simulation study. The discrete element method （DEM） and computational 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 governing equations for solid-phase motion and fluid-phase dynamics，the gas-liquid interface tracking method and the coupled computation 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. Rigorous 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 0.0 280 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%， meeting the accuracy requirements for grid independence while maintaining a reasonable computational load. As the rod-pin rotational 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 experimental 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 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 ranging from 1 400 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.

Keywords：rod-pin sand mill；discrete element method；computational fluid dynamics；volume of fluid model；gas-liquid-solid three-phase coupling model

参考文献（References）

［1］LIMA D A A S，GOMES C A M，MENDONCA S N. Experimental study of clinker grinding in a ball mill and the behavior of the grinding media inside the equipment using DEM［J］. Brazilian Journal of Chemical Engineering，2022，40（2）：469-479.

［2］刘长远. 卧式圆盘搅拌磨机结构及工艺参数研究［D］.秦皇岛：燕山大学，2016.

LIU C Y. Study on structure and technological parameters of horizontal disc stirring mill［D］. Qinhuangdao：Yanshan University，2016.

［3］张国旺. 超细搅拌磨机的流场模拟和应用研究［D］.长沙：中南大学，2005.

ZHANG G W. Study on flow field simulation and application of ultra-fine stirring mill［D］. Changsha：Central South University，2005.

［4］MUZAMMIL A，ALEJANDRO L，MEHRDAD P，et al. Optimisation of the performance of a new vertical roller mill by computational fluid dynamics simulations［J］. Powder Technology，2024，433：119282.

［5］CARVALHO R M D，OLIVEIRA A L R，PETIT H A，et al. Comparing modeling approaches in simulating a continuous pilot-scale wet vertical stirred mill using PBM-DEM-CFD［J］. Advanced Powder Technology，2023，34（9）：104135.

［6］LARSSON S，PÅLSSON B I，PARIAN M，et al. A novel approach for modelling of physical interactions between slurry，grinding media and mill structure in wet stirred media Mills［J］. Minerals Engineering，2020，148：106180.

［7］MITTAL A，KUMAR M，MANGADODDY N. A coupled CFD-DEM model for tumbling mill dynamics：effect of lifter profile［J］. Powder Technology，2024，433：119178.

［8］王建明，邱钦宇，何讯超. 搅拌罐内基于EDEM-FLUENT耦合的多相流混合数值模拟［J］.郑州大学学报（工学版），2018，39（5）：79-84.

WANG J M，QIU Q Y，HE X C. Numerical simulation of multi-phase flow mixing in stirring tank based on EDEM-FLUENT coupling ［J］. Journal of Zhengzhou University （Engineering Science），2018，39（5）：79-84.

［9］WU L，GONG M，WANG J T. Development of a DEM-VOF model for the turbulent free-surface flows with particles and its application to stirred mixing system［J］. Industrial & Engineering Chemistry Research，2018，57（5）：1714-1725.

［10］MARCHELLI F，HOU Q，BOSIO B，et al. Comparison of different drag models in CFD-DEM simulations of spouted beds［J］. Powder Technology，2020，360：1253-1270.

［11］LU H L，GIDASPOW D. Hydrodynamics of binary fluidization in a riser：CFD simulation using two granular temperatures［J］. Chemical Engineering Science，2003，58（16）：3777-3792.

［12］彭恺然，刘红帅，平新雨，等. CFD-DEM耦合模拟中拖曳力模型精度［J］. 吉林大学学报（地球科学版），2021，51（5）：1400-1407.

PENG K R，LIU H S，PING X Y，et al. Accuracy of drag force models in the CFD-DEM method［J］. Journal of Jilin University （Earth Science Edition），2021，51（5）：1400-1407.

［13］RAWIN S，THANASIT W，SUNATE S. Foundation of the Ergun equation for the calculation of minimum fluidizing velocity of solid［J］. Journal of the Thai Society of Agricultural Engineering，2012，18（1）：24-33.

［14］LI J C，WANG P，ZHENG X J. Effects of the Saffman lift force on particle statistics and turbulence modulation in two-phase flow［J］. Physical Review Fluids，2024，9（3）：034301.

［15］李东晖，柳波，张晓仪，等. 撞击流中颗粒运动行为的CFD-DEM模拟［J］. 中国粉体技术，2021，27（5）：11-19.

LI D H， LIU B，ZHANG X Y， et al. CFD-DEM simulation of particle motion behavior in impinging stream［J］. China Powder Science and Technology， 2021， 27（5）： 11-19.

［16］OESTERLÉ B， DINH T B. Experiments on the lift of a spinning sphere in a range of intermediate Reynolds numbers［J］. Experiments in Fluids， 1998， 25（1）： 16-22.

［17］HIRT C W， NICHOLS B D. Volume of fluid （VOF） method for the dynamics of free boundaries［J］. Journal of Computational Physics， 1981， 39（1）： 201-225.

［18］王圣业， 王光学， 董义道， 等. 基于雷诺应力模型的高精度分离涡模拟方法［J］. 物理学报， 2017， 66（18）： 184701.

WANG S Y， WANG G X， DONG Y D， et al. High-order detached-eddy simulation method based on a Reynolds-stress background model［J］. Acta Physica. Sinica， 2017， 66（18）： 184701.

［19］GIBSON M M， LAUNDER B E. Ground effects on pressure fluctuations in the atmospheric boundary layer［J］. Journal of Fluid Mechanics， 1978， 86： 491-511.

［20］WANG Z K， TENG Y J， LIU M B. A semi-resolved CFD-DEM approach for particulate flows with kernel based approximation and Hilbert curve based searching strategy［J］. Journal of Computational Physics， 2019， 384： 151-169.

［21］WANG Z K， LIU M B. On the determination of grid size/smoothing distance in un-/semi-resolved CFD-DEM simulation of particulate flows［J］. Powder Technology， 2021， 394： 73-82.

［22］WANG Z K， LIU M B. Semi-resolved CFD-DEM for thermal particulate flows with applications to fluidized beds［J］. International Journal of Heat and Mass Transfer， 2020， 159： 120150.

［23］张强强. 基于DEM-CFD耦合的颗粒在水中沉降过程仿真分析［D］. 长春： 吉林大学， 2014.

ZHANG Q Q. Simulation analysis of particle settling process in water based on DEM-CFD coupling［D］. Changchun： Jilin University， 2014.

［24］SUN X S， SAKAI M. Three-dimensional simulation of gas-solid-liquid flows using the DEM-VOF method［J］. Chemical Engineering Science， 2015， 134： 531-548.

［25］陈彦如. 湿法卧式超细搅拌磨机的研磨特性与过程模拟研究［D］. 北京： 中国矿业大学（北京）， 2015.

CHEN Y R. Study on grinding characteristics and process simulation of wet horizontal ultra-fine stirring mill［D］. Beijing： China University of Mining & Technology， Beijing， 2015.

［26］于嘉川. 水力旋流器中气-液-固三相流的数值模拟：VOF-DEM方法的应用［D］.天津：天津大学，2021.

YU J C. Application of VOF-DEM method in numerical simulation of gas-liquid-solid three-phase flow in hydrocyclone ［D］. Tianjin：Tianjin University，2021.

［27］FAN X H，TAN D P，LI L，et al. Modeling and solution method of gas-liquid-solid three-phase flow mixing［J］. Acta Physica Sinica，2021，70（12）：124501.

［28］邵冬冬. 立式螺旋搅拌磨机工艺和结构参数研究［D］. 沈阳：东北大学，2020.

SHAO D D. Study on technology and structural parameters of vertical spiral stirring mill［D］. Shenyang：Northeastern University，2020.