Numerical simulation and experimental validation of inter-phase forces in dynamic process of liquid-solid fluidization

doi:10.11949/0438-1157.20200368

Abstract

Abstract:

Choosing the appropriate interphase force model is the key to CFD modeling of liquid-solid fluidization dynamic characteristics. Measured overall solids holdups are validated by Richardson-Zaki correlation under steady-state operating conditions. Then five drag formulas including Wen-Yu, Gidaspow, Syamlal-O??Brien, Dallavalle and TGS are assessed in the contraction and expansion processes by using Euler-Euler two-fluid model with the kinetic theory of granular flow. Furthermore, the influence of the classical lift model suggested by Moraga et al. on CFD predictions and the influence mechanism of main inter-phase forces are discussed. The results compared with the experimental data show that the response time of bed contraction process predicted by Syamlal- O??Brien or TGS drag model is more accurate than those by the others. Moreover, TGS drag model shows the most reasonable prediction in overall solids holdup. For the bed expansion process, TGS drag model gives more reliable prediction in the response time and overall solids holdup than the other models. The main reason behind the best hydrodynamic performance with TGS drag model in this study is that the modeling basis of TGS drag model is consistent with the dynamic behaviors of particles in liquid-solid system. The lift model has little influence on the CFD results, and thus it can be ignored in the modelling of inter-phase force for the dynamic characteristics according to the homogeneous liquid-solid fluidized system investigated in this study.

Key words: CFD, experimental validation, fluidized-bed, liquid-solid two-phase flow, dynamic characteristics, inter-phase forces

摘要：

选择恰当的相间作用力模型是液固流态化动态特性CFD建模的关键。首先采用Richardson-Zaki关联式验证了稳态操作条件下整体固含率的实验结果，然后在基于颗粒动理学理论的欧拉-欧拉双流体模型中比较了Wen-Yu、Gidaspow、Syamlal-O’Brien、Dallavalle和TGS 5个曳力计算公式对液固流化床收缩和膨胀特性的数值模拟结果，进而探讨了Moraga等提出的升力模型影响行为及主要相间作用力影响机制。与实验测量数据比较结果表明：收缩过程中Syamlal-O’Brien和TGS曳力模型对响应时间预测较为准确，TGS曳力模型对整体固含率的预测精度较高；膨胀过程中TGS曳力模型对响应时间和整体固含率的预测优于其他模型。整体而言，基于静止颗粒群绕流直接模拟得到的TGS曳力模型忽略了颗粒-颗粒相互作用，与液固散式体系中颗粒动力学特性相符合。升力模型对动态特性模拟结果影响较小，CFD模拟时根据选择体系可予以适当忽略。

关键词: 计算流体力学, 实验验证, 流化床, 液固两相流, 动态特性, 相间作用力

CLC Number:

TQ 021.1

Yi ZHANG,Bing LI,Yulong BAI,Kai ZHANG. Numerical simulation and experimental validation of inter-phase forces in dynamic process of liquid-solid fluidization[J]. CIESC Journal, 2020, 71(11): 5129-5139.

张仪,李兵,白玉龙,张锴. 液固流态化动态过程中相间作用力的数值模拟及实验验证[J]. 化工学报, 2020, 71(11): 5129-5139.

Figures/Tables 12

References 36

1	金涌, 祝京旭, 汪展文, 等. 流态化工程原理[M]. 北京: 清华大学出版社, 2001.
	Jin Y, Zhu J X, Wang Z W, et al. Fluidization Engineering Principles[M]. Beijing: Tsinghua University Press, 2001.
2	Epstein N. Applications of liquid-solid fluidization[J]. International Journal of Chemical Reactor Engineering, 2003, 1: 1-16.
3	Slis P L, Willemse T W, Kramers H, et al. The response of the level of a liquid fluidized bed to a sudden change in the fluidizing velocity[J]. Applied Scientific Research, Section A, 1959, 8: 209-218.
4	Richardson J F, Zaki W N. Sedimentation and fluidization(Ⅰ)[J]. Transactions of the Institution of Chemical Engineers, 1954, 32: 35-53.
5	Fan L T, Schmitz J A, Miller E N. Dynamics of liquid-solid fluidized bed expansion[J]. AIChE Journal, 1963, 9(2): 149-153.
6	Gibilaro L G, Waldram S P, Foscolo P U. A simple mechanistic description of the unsteady state expansion of liquid-fluidized beds[J]. Chemical Engineering Science, 1984, 39(3): 607-610.
7	Asif M, Petersen J N, Kaufman E N, et al. A dynamic model of the hydrodynamics of a liquid fluidized bed[J]. Industrial & Engineering Chemistry Research, 1994, 33(9): 2151-2156.
8	Thelen T V, Ramirez W F. Bed-height dynamics of expanded beds[J]. Chemical Engineering Science, 1997, 52(19): 3333-3344.
9	Liu D, Fu Y. Dynamics of fine particles in liquid-solid fluidized beds[J]. Particuology, 2007, 5(6): 363-375.
10	尤东光, 雍玉梅, 杨超, 等. 流量变化对液固流化床瞬态流化特性的影响[J]. 化工学报, 2012, 63(8): 2356-2364.
	You D G, Yong Y M, Yang C, et al. Effect of fluidizing flux change on liquid-solids fluidization characteristics[J]. CIESC Journal, 2012, 63(8): 2356-2364.
11	Chen Z, Gibilaro L G, Foscolo P U. Two-dimensional voidage waves in fluidized beds[J]. Industrial & Engineering Chemistry Research, 1999, 38(3): 610-620.
12	张锴, Brandani S. 流化床内颗粒流体两相流的CFD模拟[J]. 化工学报, 2010, 61(9): 2192-2207.
	Zhang K, Brandani S. CFD simulation of particle-fluid two-phase flow in fluidized beds[J]. CIESC Journal, 2010, 61(9): 2192-2207.
13	Zhang K, Wu G, Brandani S, et al. CFD simulation of dynamic characteristics in liquid-solid fluidized beds[J]. Powder Technology, 2012, 227: 104-110.
14	Dallavalle J M. Micrometrics: The Technology of Fine Particles[M]. London: Pitman, 1948.
15	Enwald H, Peirano E, Almstedt A E. Eulerian two-phase flow theory applied to fluidization[J]. International Journal of Multiphase Flow, 1996, 22: 21-66.
16	刘大有. 二相流体动力学[M]. 北京: 高等教育出版社, 1993.
	Liu D Y. Fluid Dynamics of Two-phase Systems[M]. Beijing: Higher Education Press, 1993.
17	祁海鹰, 戴群特, 陈程. 大型流态化多相流数值模拟的关键科学问题——曳力模型的理论分析[J]. 力学与实践, 2014, 36(3): 269-277.
	Qi H Y, Dai Q T, Chen C. The key scientific problems in the Eulerian modeling of large-scale multi-phase flows— drag model[J]. Mechanics in Engineering, 2014, 36(3): 269-277.
18	毛在砂. 颗粒群研究: 多相流多尺度数值模拟的基础[J]. 过程工程学报, 2008, 8(4): 645-659.
	Mao Z S. Knowledge on particle swarm: the important basis for multi-scale numerical simulation of multiphase flows[J]. The Chinese Journal of Process Engineering, 2008, 8(4): 645-659.
19	黄社华, 李炜. 粘性流中刚性颗粒非恒定运动的附加质量力[J]. 武汉大学学报(工学版), 2002, 35(4): 13-17.
	Huang S H, Li W. On added mass force acting on a small particle moving unsteadily in viscous flows[J]. Engineering Journal of Wuhan University, 2002, 35(4): 13-17.
20	由长福, 祁海鹰, 徐旭常. Basset力研究进展与应用分析[J]. 应用力学学报, 2002, 19(2): 31-33.
	You C F, Qi H Y, Xu X C. Progresses and applications of Basset force[J]. Chinese Journal of Applied Mechanics, 2002, 19(2): 31-33.
21	Cornelissen J T, Taghipour F, Escudie R, et al. CFD modelling of a liquid-solid fluidized bed[J]. Chemical Engineering Science, 2007, 62(22): 6334-6348.
22	Ye X, Chu D, Lou Y, et al. Numerical simulation of flow hydrodynamics of struvite pellets in a liquid-solid fluidized bed[J]. Journal of Environmental Sciences-China, 2017, 57(7): 391-401.
23	张仪, 白玉龙, 骆丁玲, 等. 液固散式流态化CFD模拟中曳力模型的影响[J]. 化工学报, 2019, 70(11): 4207-4215.
	Zhang Y, Bai Y L, Luo D L, et al. Effect of drag models on CFD simulations for homogeneous liquid-solid fluidization[J]. CIESC Journal, 2019, 70(11): 4207-4215.
24	Zbib H, Ebrahimi M, Einmozaffari F, et al. Comprehensive analysis of fluid-particle and particle-particle interactions in a liquid-solid fluidized bed via CFD-DEM coupling and tomography[J]. Powder Technology, 2018, 340: 116-130.
25	Koerich D M, Lopes G C, Rosa L M. Investigation of phases interactions and modification of drag models for liquid-solid fluidized bed tapered bioreactors[J]. Powder Technology, 2018, 339: 90-101.
26	Felice R D. Hydrodynamics of liquid fluidisation[J]. Chemical Engineering Science, 1995, 50(8): 1213-1245.
27	Garside J, Aldibouni M R. Velocity-voidage relationships for fluidization and sedimentation in solid-liquid systems[J]. Industrial & Engineering Chemistry Process Design and Development, 1977, 16(2): 206-214.
28	Ding J, Gidaspow D. A bubbling fluidization model using kinetic theory of granular flow[J]. AIChE Journal, 1990, 36(4): 523-538.
29	Wen C Y, Yu Y H. Mechanics of fluidization[J]. Chemical Engineering Progress Symposium Series, 1966, 62: 100-111.
30	Gidaspow D. Multiphase Flow and Fluidization: Continuumand and Kinetic Theory Descriptions[M]. Boston: Academic Press, 1994.
31	Syamlal M, O􀆳Brien T J. Simulation of granular layer inversion in liquid fluidized beds[J]. International Journal of Multiphase Flow,1988, 14(4): 473-481.
32	Tenneti S, Garg R, Subramaniam S. Drag law for monodisperse gas-solid systems using particle-resolved direct numerical simulation of flow past fixed assemblies of spheres[J]. International Journal of Multiphase Flow, 2011, 37(9): 1072-1092.
33	Drew D A, Lahey R T. Analytical modelling of multiphase flow[C]//Roco M C. Particulate Two-Phase Flow. Boston, MA: Butterworth-Heinemann, 1993: 509-566.
34	Moraga F J, Bonetto F J, Lahey R T, et al. Lateral forces on spheres in turbulent uniform shear flow[J]. International Journal of Multiphase Flow, 1999, 25(6): 1321-1372.
35	Mazzei L, Lettieri P. CFD simulations of expanding/contracting homogeneous fluidized beds and their transition to bubbling[J]. Chemical Engineering Science, 2008, 63(24): 5831-5847.
36	王勤辉, 杨秋辉, 吴学成, 等. 多相流中颗粒旋转运动特性的研究进展[J]. 化工学报, 2011, 62(9): 2381-2390.
	Wang Q H, Yang Q H, Wu X C, et al. Research progress of particle rotation characteristics in multi-phase flows[J]. CIESC Journal, 2011, 62(9): 2381-2390.

Description	Contraction		Expansion
Description	case 1	case 2	case 3	case 4
experiments
bed height before sudden change in operating velocity, h₀/mm	530	675	400	505
liquid concentration before sudden change in operating velocity, ε_l_,0	0.717	0.778	0.625	0.703
liquid operating velocity before the sudden change, u₀/(mm·s^-1)	41	54	25	38
liquid operating velocity after the sudden change, u₁/(mm·s^-1)	25	38	41	54
liquid temperature/℃	20 — 23
simulations
inlet boundary condition	uniform velocity inlet
liquid inlet velocity, u₁/(mm·s^-1)	25	38	41	54
outlet boundary condition	pressure outlet, 1.013×10⁵Pa
wall boundary condition	no slip for liquid phase, free slip for solid phase
initial bed height, h₀/mm	530	675	400	505
initial liquid velocity in the bed(u_l_,in = u₀/ε_l_,0), u_l,_in/(mm·s^-1)	57	69	40	54

Description	Contraction		Expansion
Description	case 1	case 2	case 3	case 4
experiments
bed height before sudden change in operating velocity, h₀/mm	530	675	400	505
liquid concentration before sudden change in operating velocity, ε_l_,0	0.717	0.778	0.625	0.703
liquid operating velocity before the sudden change, u₀/(mm·s^-1)	41	54	25	38
liquid operating velocity after the sudden change, u₁/(mm·s^-1)	25	38	41	54
liquid temperature/℃	20 — 23
simulations
inlet boundary condition	uniform velocity inlet
liquid inlet velocity, u₁/(mm·s^-1)	25	38	41	54
outlet boundary condition	pressure outlet, 1.013×10⁵Pa
wall boundary condition	no slip for liquid phase, free slip for solid phase
initial bed height, h₀/mm	530	675	400	505
initial liquid velocity in the bed(u_l_,in = u₀/ε_l_,0), u_l,_in/(mm·s^-1)	57	69	40	54

Case	Experimental result	Simulated result/error
Case	Experimental result	Wen-Yu	Gidaspow	Syamlal-O’Brien	Dallavalle	TGS
case 1 (h₀= 530 mm, u₀= 41 mm·s^-1, u₁= 25 mm·s^-1)	0.375	0.425/13.2%	0.421/12.2%	0.4436/16.2%	0.400/6.6%	0.380/1.3%
case 2 (h₀= 675 mm, u₀= 54 mm·s^-1, u₁= 38 mm·s^-1)	0.297	0.341/14.7%	0.316/6.4%	0.327/10.1%	0.321/8.0%	0.300/0.9%

Case	Experimental result	Simulated result/error
Case	Experimental result	Wen-Yu	Gidaspow	Syamlal-O’Brien	Dallavalle	TGS
case 1 (h₀= 530 mm, u₀= 41 mm·s^-1, u₁= 25 mm·s^-1)	0.375	0.425/13.2%	0.421/12.2%	0.4436/16.2%	0.400/6.6%	0.380/1.3%
case 2 (h₀= 675 mm, u₀= 54 mm·s^-1, u₁= 38 mm·s^-1)	0.297	0.341/14.7%	0.316/6.4%	0.327/10.1%	0.321/8.0%	0.300/0.9%

[1]	Yingying TAN, Xiaoqing LIU, Lin WANG, Lisheng HUANG, Xiuzhen LI, Zhanwei WANG. Experimental study on startup dynamic characteristics of R1150/R600a auto-cascade refrigeration cycle [J]. CIESC Journal, 2023, 74(S1): 213-222.
[2]	Kaijie WEN, Li GUO, Zhaojie XIA, Jianhua CHEN. A rapid simulation method of gas-solid flow by coupling CFD and deep learning [J]. CIESC Journal, 2023, 74(9): 3775-3785.
[3]	Chao NIU, Shengqiang SHEN, Yan YANG, Bonian PAN, Yiqiao LI. Flow process calculation and performance analysis of methane BOG ejector [J]. CIESC Journal, 2023, 74(7): 2858-2868.
[4]	Xin DONG, Yongrui SHAN, Yinuo LIU, Ying FENG, Jianwei ZHANG. Numerical simulation of bubble plume vortex characteristics for non-Newtonian fluids [J]. CIESC Journal, 2023, 74(5): 1950-1964.
[5]	Airan ZHOU, Ping LU, Jianhui XIA, Dongqin LI, Jie GUO, Ming DU, Lichun DONG. Scarring analysis and numerical simulation of TiCl₄ oxidation reactor in chloride process of titanium dioxide [J]. CIESC Journal, 2023, 74(4): 1499-1508.
[6]	Laiming LUO, Jin ZHANG, Zhibin GUO, Haining WANG, Shanfu LU, Yan XIANG. Simulation and experiment of high temperature polymer electrolyte membrane fuel cells stack in the 1—5 kW range [J]. CIESC Journal, 2023, 74(4): 1724-1734.
[7]	Wenxuan XU, Jinbo JIANG, Xin PENG, Rixiu MEN, Chang LIU, Xudong PENG. Comparative study on leakage and film-forming characteristics of oil-gas seal with three-typical groove in a wide speed range [J]. CIESC Journal, 2023, 74(4): 1660-1679.
[8]	Jinsheng REN, Kerun LIU, Zhiwei JIAO, Jiaxiang LIU, Yuan YU. Research on the mechanism of disaggregation of particle aggregates near the guide vanes of turbo air classifier [J]. CIESC Journal, 2023, 74(4): 1528-1538.
[9]	Weizheng ZHANG, Jijun ZHAO, Xuezhong MA, Qixuan ZHANG, Yixiang PANG, Juntao ZHANG. Analysis of turbulence effect on face groove cooling performance of high-speed mechanical seals [J]. CIESC Journal, 2023, 74(3): 1228-1238.
[10]	Qian LIU, Xianglan ZHANG, Zhiping LI, Yulong LI, Mengxing HAN. Screening of deep eutectic solvents and study on extraction performance for oil-hydroxybenzene separation [J]. CIESC Journal, 2022, 73(9): 3915-3928.
[11]	Yafei LI, Jianqiang DENG, Yang HE. Numerical study on non-equilibrium condensation and flashing mechanisms in rapid expansion process of transcritical CO₂ [J]. CIESC Journal, 2022, 73(7): 2912-2923.
[12]	Luyue HUANG, Chang LIU, Yongyi XU, Haoruo XING, Feng WANG, Shuangchen MA. Development of CDI two-dimensional concentration mass transfer model and experimental validation [J]. CIESC Journal, 2022, 73(7): 2933-2943.
[13]	Tienan LI, Bidan ZHAO, Peng ZHAO, Yongmin ZHANG, Junwu WANG. CFD-DEM simulation of the force acting on immersed baffles during the start-up stage of a gas-solid fluidized bed [J]. CIESC Journal, 2022, 73(6): 2649-2661.
[14]	Xiaoqiang FAN, Zhengliang HUANG, Jingyuan SUN, Jingdai WANG, Xiaofei WANG, Xiaobo HU, Guodong HAN, Yongrong YANG, Wenqing WU. Development of cloudy gas-liquid fluidized bed ethylene polymerization process and high performance products [J]. CIESC Journal, 2022, 73(6): 2742-2747.
[15]	Yan LI, Ahui TIAN, Yi ZHOU. Characteristics of scalar transport and chemical reaction in reactive dual jets [J]. CIESC Journal, 2022, 73(5): 1947-1963.