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The mixing process of gas-liquid-solid three-phase flow is a complex multi-fluid-structure coupling dynamic problem. The relationship between the particle parameters and the physical spatial scale of the flow channel directly affects the calculation convergence. Numerical modeling and mesh processing of fluid-structure bidirectional interaction in the strong shear zone are difficult. Aiming at the above problems, a method of modeling and solving the gas-liquid-solid three-phase flow mixing is proposed. Based on the volume-of-fluid coupled with discrete-element-method model, a three-phase dynamic model considering particle motion is established. By solving the momentum equation, the bidirectional coupling of two-phase fluid and particle is realized. The user-defined function communication interface is developed independently to obtain the interaction force between fluid and particles, and a porous-interphase coupling solution is proposed to describe the trajectory of particles. Taking the mixing process of three-phase flow with strong shear for example, this method is used to study the influence of different aeration conditions on the free surface, velocity distribution and particle suspension characteristics in the physical space of the flow channel. The results show that strong shear and wall action can convert the tangential velocity of the fluid into axial and radial velocity; choosing an appropriate inflation velocity can eliminate the instability of the free surface and increasing the flow velocity of the fluid has a limited effect on the suspension of particles in some areas. The research results can provide a useful reference for studying the interaction mechanism of complex multiphase flow, and also provide technical support for the mixing production control of gas-liquid-solid three-phase particles.
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Keywords:
- three-phase flow /
- solid particles /
- volume of fluid-discrete element method coupling /
- strong shear
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[10] Tan D P, Li L, Yin Z C, Li D F, Zhu Y L, Zheng S 2020 Int. J. Heat Mass Transfer 150 119250
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[11] Alexander S, Alexander D, Markku N, Jan M, Falah A, Maximilian V B, Jochen S, Bernd E 2019 Chem. Eng. Sci. 196 37
Google Scholar
[12] Musango L, John S, Lloyd M 2021 Powder Technol. 378 85
Google Scholar
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Google Scholar
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[15] Bastien D, Juliane R, Louis F, Francois B, Bruno B 2021 Chem. Eng. Sci. 230 116137
Google Scholar
[16] 邵婷, 胡银玉, 王文坦, 金涌, 程易 2013 中国化学工程学报 21 1069
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Shao T, Hu Y Y, Wang W T, Jin Y, Cheng Y 2013 Chin. J. Chem. Eng. 21 1069
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Google Scholar
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Google Scholar
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Google Scholar
[20] Xu W T, Tan Y B, Li M, Sun J L, Xie D, Liu Z 2020 Particuology 49 159
Google Scholar
[21] Sun X, Sakai M 2015 Chem. Eng. Sci. 134 531
Google Scholar
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Google Scholar
[23] Kang Q Q, He D P, Zhao N, Feng X, Wang J T 2019 Chem. Eng. J. 386 122846
Google Scholar
[24] 谭大鹏, 杨涛, 赵军, 计时鸣 2016 物理学报 65 054701
Google Scholar
Tan D P, Yang T, Zhao J, Ji S M 2016 Acta Phys. Sin. 65 054701
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[32] Tamburini A, Cipollina A, Micale G, Brucato A, Ciofalo M 2012 Chem. Eng. J. 193 234
Google Scholar
[33] Jahoda M, Tomaskova L, Mostek M 2009 Chem. Eng. Res. Des. 87 460
Google Scholar
[34] Wang J J, Han Y, Gu X P, Feng L F, Hu G H 2013 AIChE J. 59 1066
Google Scholar
[35] Xie L, Luo Z H 2017 Chem. Eng. Sci. 176 439
Google Scholar
[36] Jovanovic A, Pezo M, Pezo L, Levic L 2014 Powder Technol. 266 240
Google Scholar
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图 1 VOF-DEM耦合计算流程图
Figure 1. VOF-DEM coupling calculation flowchart.
图 2 混合空间结构示意图
Figure 2. Diagram of mixed space structure.
图 3 网格划分 (a) 静子区域网格; (b) 转子区域网格; (c) 叶轮网格
Figure 3. Grids division: (a) Grids of stator region; (b) grids of rotor region; (c) grids of impeller.
图 4 四种网格尺寸在t = 5 s时的轴向速度分布
Figure 4. Axial velocity distribution of four grid sizes at t = 5 s
图 5 t = 5 s时四种充气条件下混合空间内的自由液面 (a) v = 0 m/s; (b) v = 0.01 m/s; (c) v = 0.05 m/s; (d) v = 1 m/s
Figure 5. Free surface under four aeration conditions at t = 5 s: (a) v = 0 m/s; (b) v = 0.01 m/s; (c) v = 0.05 m/s; (d) v = 1 m/s.
图 6 t = 5 s时, 四种充气条件下混合空间内z = 0.15 m高度截面的切向速度矢量图 (a) v = 0 m/s; (b) v = 0.01 m/s; (c) v = 0.05 m/s; (d) v = 1 m/s
Figure 6. Tangential velocity vector in height z = 0.15 m under four aeration conditions at t = 5 s: (a) v = 0 m/s; (b) v = 0.01 m/s; (c) v = 0.05 m/s; (d) v = 1 m/s.
图 7 径向位置r = 60 mm处的轴向高度速度分布 (a) 总速度; (b) 轴向速度; (c) 径向速度; (d) 切向速度
Figure 7. Axial velocity distribution at radial position r = 60 mm: (a) Total velocity; (b) axial velocity; (c) radial velocity; (d) tangential velocity.
图 8 v = 0 m/s时不同时刻的三相混合系统模拟结果
Figure 8. Simulation results of three-phase stirred system at different time when v = 0 m/s.
图 9 v = 0.01 m/s时不同时刻的三相混合系统模拟结果
Figure 9. Simulation results of three-phase stirred system at different time when v = 0.01 m/s.
图 10 v = 0.05 m/s时不同时刻的三相混合系统模拟结果
Figure 10. Simulation results of three-phase stirred system at different time when v = 0.05 m/s.
图 11 v = 1 m/s时不同时刻的三相混合系统模拟结果
Figure 11. Simulation results of three-phase stirred system at different time when v = 1 m/s.
图 12 不同充气工作条件下的RSD随时间的变化
Figure 12. RSD changes with time under different aeration conditions.
表 1 流体和颗粒特性设置
Table 1. Characteristics settings of fluid and particle.
参数 值 空气密度 ${\rho _{\rm{a}}}$/(${\rm{kg}} \cdot {{\rm{m}}^{{ - 3}}}$) 1 空气黏度 ${\mu _{\rm{a}}}$/(${\rm{Pa}} \cdot {\rm{s}}$) 1 × 10–5 水密度 ${\rho _{\rm{w}}}$/(${\rm{kg}} \cdot {{\rm{m}}^{{ - 3}}}$) 1000 水黏度 ${\mu _{\rm{w}}}$/(${\rm{Pa}} \cdot {\rm{s}}$) 0.001 颗粒密度 ${\rho _{\rm{p}}}$/(${\rm{kg}} \cdot {{\rm{m}}^{{ - 3}}}$) 1100 颗粒直径 ${d_{\rm{p}}}$/mm 1 颗粒数目 ${n_{\rm{p}}}$ 10000 颗粒杨氏模量 ${Y_{\rm{P}}}$/${\rm{MPa}}$ 1 颗粒泊松比 ${\nu _{\rm{P}}}$ 0.25 壁面杨氏模量 ${Y_{\rm{w}}}$/${\rm{MPa}}$ 70000 壁面泊松比 ${\nu _{\rm{w}}}$ 0.3 滚动摩擦系数 ${\mu _{\rm{r}}}$ 0.01 静摩擦系数 ${\mu _{\rm{s}}}$ 0.5 恢复系数 ${e_{\rm{r}}}$ 0.5 搅拌桨速度 $\omega $/(${\rm r} \cdot {\rm min }^{ - 1 }$) 400 CFD时间步 $\Delta {t_{\rm{CFD}}}$/${\rm{s}}$ $2 \times {10^{ - 4}}$ DEM时间步 $\Delta {t_{\rm{DEM}}}$/${\rm{s}}$ $2 \times {10^{ - 5}}$ 耦合时间步 $\Delta {t_{{\rm{coupling}}}}$/${\rm{s}}$ $2 \times {10^{ - 4}}$ 
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[1] Delvigne F, Destain J, Thonart P 2005 Chem. Eng. J. 113 1
Google Scholar
[2] Ge M, Ji S M, Tan D P, Cao H Q 2021 Int. J. Adv. Manuf. Tech. 114 3419
Google Scholar
[3] Hosseini S, Patel D, Ein-Mozaffari F, Mehrvar M 2010 Ind. Eng. Chem. Res. 49 4426
Google Scholar
[4] Wang S Y, Jiang X X, Wang R C, Wang X, Yang S W, Zhao J, Liu Y 2017 Adv. Powder Technol. 28 1611
Google Scholar
[5] Panneerselvam R, Savithri S, Surender G D 2009 Ind. Eng. Chem. Res. 48 1611
Google Scholar
[6] Li L, Tan D P, Yin Z C, Wang T, Fan X H, Wang R H 2021 Renew. Energy 175 887
Google Scholar
[7] Li L, Tan D P, Wang T, Yin Z C, Fan X H, Wang R H 2021 Energy 216 119136
Google Scholar
[8] Kasat G R, Khopkar A R, Ranade V V, Pandit A B 2008 Chem. Eng. Sci. 63 3877
Google Scholar
[9] Qi H, Qin S K, Cheng Z C, Teng Q, Hong T, Xie Y 2021 J. Manuf. Processes 64 585
Google Scholar
[10] Tan D P, Li L, Yin Z C, Li D F, Zhu Y L, Zheng S 2020 Int. J. Heat Mass Transfer 150 119250
Google Scholar
[11] Alexander S, Alexander D, Markku N, Jan M, Falah A, Maximilian V B, Jochen S, Bernd E 2019 Chem. Eng. Sci. 196 37
Google Scholar
[12] Musango L, John S, Lloyd M 2021 Powder Technol. 378 85
Google Scholar
[13] Li L, Lu J F, Fang H, Yin Z C, Wang T, Wang R H, Fan X H, Zhao L J, Tan D P, Wan Y H 2020 IEEE Access 8 27649
Google Scholar
[14] Han Y, Cundall P A 2013 Int. J. Numer. Anal. Methods Geomech. 37 10
Google Scholar
[15] Bastien D, Juliane R, Louis F, Francois B, Bruno B 2021 Chem. Eng. Sci. 230 116137
Google Scholar
[16] 邵婷, 胡银玉, 王文坦, 金涌, 程易 2013 中国化学工程学报 21 1069
Google Scholar
Shao T, Hu Y Y, Wang W T, Jin Y, Cheng Y 2013 Chin. J. Chem. Eng. 21 1069
Google Scholar
[17] Blais B, Lassaigne M, Goniva C, Fradette L 2016 J. Comput. Phys. 318 201
Google Scholar
[18] Blais B, Bertrand F 2017 Chem. Eng. Res. Des. 118 270
Google Scholar
[19] Blais B, Bertrand O, Fradette L, Bertrand F 2017 Chem. Eng. Res. Des. 123 388
Google Scholar
[20] Xu W T, Tan Y B, Li M, Sun J L, Xie D, Liu Z 2020 Particuology 49 159
Google Scholar
[21] Sun X, Sakai M 2015 Chem. Eng. Sci. 134 531
Google Scholar
[22] Wu L, Gong M, Wang J T 2018 Ind. Eng. Chem. Res. 57 1714
Google Scholar
[23] Kang Q Q, He D P, Zhao N, Feng X, Wang J T 2019 Chem. Eng. J. 386 122846
Google Scholar
[24] 谭大鹏, 杨涛, 赵军, 计时鸣 2016 物理学报 65 054701
Google Scholar
Tan D P, Yang T, Zhao J, Ji S M 2016 Acta Phys. Sin. 65 054701
Google Scholar
[25] 刘扬, 韩燕龙, 贾富国, 姚丽娜, 王会, 史宇菲 2015 物理学报 64 114501
Google Scholar
Liu Y, Han Y L, Jia F G, Yao L N, Wang H, Shi Y F 2015 Acta Phys. Sin. 64 114501
Google Scholar
[26] Ergun S 1952 Chem. Eng. Prog. 48 89
Google Scholar
[27] Ji S M, Xiao F Q, Tan D P 2010 Sci. China Technol. Sc. 53 100
Google Scholar
[28] Saffman P G 1965 J. Fluid Mech. 22 385
Google Scholar
[29] Tan D P, Ji S M, Fu Y Z 2016 Int. J. Adv. Manuf. Technol. 85 1261
Google Scholar
[30] Li L, Qi H, Yin Z C, Li D F, Zhu Z L, Tangwarodomnukun V, Tan D P 2019 Powder Technol. 360 462
Google Scholar
[31] Lu J F, Wang T, Li L, Yin Z C, Wang R H, Fan X H, Tan D P 2020 Processes 8 760
Google Scholar
[32] Tamburini A, Cipollina A, Micale G, Brucato A, Ciofalo M 2012 Chem. Eng. J. 193 234
Google Scholar
[33] Jahoda M, Tomaskova L, Mostek M 2009 Chem. Eng. Res. Des. 87 460
Google Scholar
[34] Wang J J, Han Y, Gu X P, Feng L F, Hu G H 2013 AIChE J. 59 1066
Google Scholar
[35] Xie L, Luo Z H 2017 Chem. Eng. Sci. 176 439
Google Scholar
[36] Jovanovic A, Pezo M, Pezo L, Levic L 2014 Powder Technol. 266 240
Google Scholar
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