Effect of agglomerate structure on drag force by numerical simulation

doi:10.11949/0438-1157.20230291

Abstract

Abstract:

Viscous particles mostly exist in the gas-solid two-phase system in the form of agglomerates, and the drag force exerted by the fluid on the agglomerates plays a crucial role in the two-phase flow and heat and mass transfer. However, the irregular and porous structure of the agglomerate result in complexities of the drag characteristics. In this study, a series of fractal-like agglomerates are generated by discrete element method (DEM) with a cohesive contact model, and the flow field including the external and interior flow through the agglomerate is resolved by computational fluid dynamic (CFD). The effect of agglomerate structure on drag characteristics at low Reynolds number flows (Re=0.1—10) is investigated. The simulation results show that the flow through the agglomerate is greatly influenced by the agglomerate structure. The permeability of agglomerate is enhanced by increasing agglomerate porosity, resulting in an increase of the contact surface between the fluid and agglomerate, thus increasing the drag force. The drag coefficient for agglomerates with different structures are calculated, which indicates that the drag coefficient of non-spherical agglomerates is influenced not only by structure parameters (size, porosity, fractal dimension) but also by the orientation between the agglomerate and gas flow direction. Finally, a correlation of the drag force coefficients based on the current simulations is proposed for porous agglomerates with fractal-like shapes.

Key words: agglomerate structure, fractals, drag, permeation, computational fluid dynamics

摘要：

黏性颗粒多以聚团形式存在于气固两相系统中，流体施加于聚团的曳力对两相流动及传热传质起着至关重要的作用，而聚团的不规则、分形结构增加了曳力特性的复杂性。基于黏性离散单元方法生成不同分形结构的聚团，利用计算流体力学方法（CFD）直接求解分形聚团内部多孔结构的气流流动，得到了气体流过聚团时的周围与内部流场，研究了低Reynolds数（Re=0.1~10）条件下聚团结构特征对曳力的影响。结果表明：聚团的疏密程度显著影响聚团整体流场分布，多孔疏松结构增强了聚团的渗透性，使其与流体接触面积增加，所受曳力增加。分析不同结构聚团的曳力系数发现：除了聚团孔隙率、分形维数等结构参数的影响，气体流经聚团的方向也影响聚团曳力系数。在此基础上，综合考虑聚团分形维数、聚团与气流的夹角方向、Reynolds数拟合得到聚团曳力系数关联式。

关键词: 聚团结构, 分形, 曳力, 渗透, 计算流体力学

CLC Number:

TQ 021

Daoyin LIU, Bingqi CHEN, Zuyang ZHANG, Yan WU. Effect of agglomerate structure on drag force by numerical simulation[J]. CIESC Journal, 2023, 74(6): 2351-2362.

刘道银, 陈柄岐, 张祖扬, 吴琰. 颗粒聚团结构对曳力特性影响的数值模拟[J]. 化工学报, 2023, 74(6): 2351-2362.

Figures/Tables 17

Fig.1 Agglomerates formed by particle aggregate at different initial velocities

Table 1 Characteristics of typical agglomerates

聚团编号	颗粒速度/(m/s)	回转半径/m	分形维数	无量纲密度	孔隙度/%	投影面积/m²
Agg-Ⅰ-1	0	2.62×10^-5	2.94	0.87	12.73	3.96×10^-9
Agg-Ⅱ-1	0.1	3.12×10^-5	2.74	0.51	48.66	5.22×10^-9
Agg-Ⅲ-1	0.5	4.05×10^-5	2.48	0.24	76.39	3.44×10^-9
Agg-Ⅳ-1	1.0	5.90×10^-5	2.19	0.08	92.39	9.08×10^-9

Fig.2 Computational domain and mesh for flow around and within the agglomerate

Table 2 Simulation parameters for CFD

参数	数值
计算域尺寸/(mm×mm×mm)	0.6×0.3×0.3
组成聚团的原生颗粒粒径/μm	5
组成聚团的原生颗粒个数	1000
原生颗粒密度/(kg/m³)	400
流体密度/(kg/m³)	1.225
流体黏度/(kg/(m·s))	1.7894×10^-5

Table 3 The condition settings for simulations at different Re

聚团编号	分形维数	回转半径/m	无量纲密度	孔隙度/%	投影面积/m²	等效直径/m	Reynolds数	来流速度/(m/s)
Agg-Ⅳ-5	2.35	4.75×10^-5	0.15	85.39	4.18×10^-9	7.30×10^-5	0.1	0.02002
							0.15	0.03002
							0.2	0.04003
							0.5	0.10008
							1	0.20015
							2	0.40031
							5	1.00077
							10	2.00155

Table 4 The condition settings for simulations at different agglomerate orientations

聚团编号	Reynolds数	聚团和来流方向夹角/(˚)	投影面积/(10^-9 m²)	等效直径/(10^-5 m)	来流速度/(m/s)
Agg-Ⅳ-5	0.1	0	4.18	7.30	0.020015
		30	4.64	7.69	0.018995
		60	6.07	8.79	0.016614
		90	6.95	9.41	0.015520
		120	6.67	9.22	0.015847
		150	5.43	8.32	0.017556
		180	4.18	7.30	0.020015

Fig.3 Effect of number of surface cells on the predicted drag coefficient at Re=0.1, 1, 10 for a single particle

Fig.4 Relationship between drag coefficient and Reynolds number for a single particle

Fig.5 Fluid velocity distribution and streamline around different agglomerates at Re=0.1

Fig.6 Viscous force and pressure force of four agglomerates with different fractal dimensions

Fig.7 The ratio between viscous force and pressure force with different fractal dimensions

Fig.8 Pressure calculated based on the projected area of agglomerates with different fractal dimensions

Fig.9 Relationship between drag coefficient and Reynolds number for agglomerates with different fractal structures

Fig.10 Effect of agglomerate orientation on drag coefficient and projected area

Fig.11 Effect of structure characteristics on the simulated drag coefficient

Fig.12 Effect of structure characteristics on the modified drag coefficient

Fig.13 Comparison between prediction of the correlation and simulated results for the drag coefficient

References 41

1	Flesch J C, Spicer P T, Pratsinis S E. Laminar and turbulent shear-induced flocculation of fractal aggregates[J]. AIChE Journal, 1999, 45(5): 1114-1124.
2	刘荣正, 刘马林, 邵友林, 等. 流化床-化学气相沉积技术的应用及研究进展[J]. 化工进展, 2016, 35(5): 1263-1272.
	Liu R Z, Liu M L, Shao Y L, et al. Application and research progress of fluidized bed-chemical vapor deposition technology[J]. Chemical Industry and Engineering Progress, 2016, 35(5): 1263-1272.
3	Wang W, Lu B N, Geng J W, et al. Mesoscale drag modeling: a critical review[J]. Current Opinion in Chemical Engineering, 2020, 29: 96-103.
4	万韶六, 欧阳洁. 颗粒团绕流曳力系数的LBM计算[J]. 化工学报, 2008, 59(1): 58-63.
	Wan S L, Ouyang J. Evaluation of drag coefficient on particles in cluster by using lattice Boltzmann method[J]. Journal of Chemical Industry and Engineering(China), 2008, 59(1): 58-63.
5	祁晗璐, 王嘉骏, 顾雪萍, 等. 黏性颗粒团聚机理及流化特性研究进展[J]. 过程工程学报, 2019, 19(1): 55-63.
	Qi H L, Wang J J, Gu X P, et al. Research progress on agglomeration mechanisms and fluidization behavior of cohesive particles[J]. The Chinese Journal of Process Engineering, 2019, 19(1): 55-63.
6	Chen S, Chen P Z, Fu J H. Drag and lift forces acting on linear and irregular agglomerates formed by spherical particles[J]. Physics of Fluids, 2022, 34(2): 023307.
7	Tsou G W, Wu R M, Yen P S, et al. Advective flow and floc permeability[J]. Journal of Colloid and Interface Science, 2002, 250(2): 400-408.
8	Wu R M, Feng W H, Tsai I H, et al. An estimate of activated-sludge floc permeability: a novel hydrodynamic approach[J]. Water Environment Research, 1998, 70(7): 1258-1264.
9	Wang S W, Liu H P, Yang C Y. Structure and drag characteristics of fluidized nanoparticle agglomerates at the bottom of the bed[J]. Industrial & Engineering Chemistry Research, 2019, 58(42): 19693-19701.
10	Johnson C P, Li X Y, Logan B E. Settling velocities of fractal aggregates[J]. Environmental Science & Technology, 1996, 30(6): 1911-1918.
11	Xiao F, Li X Y, Wang D S. Three-dimensional CFD simulation of the flow field around and through particle aggregates[J]. Colloids and Surfaces A-Physicochemical and Engineering Aspects, 2013, 436: 1034-1040.
12	Rogak S N, Flagan R C. Stokes drag on self-similar clusters of spheres[J]. Journal of Colloid and Interface Science, 1990, 134(1): 206-218.
13	Li D, Bai X F, Li P, et al. A dynamic cluster structure-dependent drag coefficient model applied to the riser in high density circulating fluidized bed[J]. Advanced Powder Technology, 2022, 33(2): 103418.
14	Bhattacharyya S, Dhinakaran S, Khalili A. Fluid motion around and through a porous cylinder[J]. Chemical Engineering Science, 2006, 61(13): 4451-4461.
15	Yu P, Zeng Y, Lee T S, et al. Steady flow around and through a permeable circular cylinder[J]. Computers & Fluids, 2011, 42(1): 1-12.
16	Noymer P D, Glicksman L R, Devendran A. Drag on a permeable cylinder in steady flow at moderate Reynolds numbers[J]. Chemical Engineering Science, 1998, 53(16): 2859-2869.
17	王利民, 邱小平, 李静海. 气固两相流介尺度LBM-DEM模型[J]. 计算力学学报, 2015, 32(5): 685-692.
	Wang L M, Qiu X P, Li J H. Mesoscale LBM-DEM model for gas-solid two-phase flow[J]. Chinese Journal of Computational Mechanics, 2015, 32(5): 685-692.
18	蒋鸣, 周强. 气固流化床介尺度结构形成机制及过滤曳力模型研究进展[J]. 化工学报, 2022, 73(6): 2468-2485.
	Jiang M, Zhou Q. Progress on mechanisms of mesoscale structures and mesoscale drag model in gas-solid fluidized beds[J]. CIESC Journal, 2022, 73(6): 2468-2485.
19	Binder C, Feichtinger C, Schmid H J, et al. Simulation of the hydrodynamic drag of aggregated particles[J]. Journal of Colloid and Interface Science, 2006, 301(1): 155-167.
20	Dietzel M, Sommerfeld M. Numerical calculation of flow resistance for agglomerates with different morphology by the lattice-Boltzmann method[J]. Powder Technology, 2013, 250: 122-137.
21	Dietzel M, Ernst M, Sommerfeld M. Application of the lattice-Boltzmann method for particle-laden flows: point-particles and fully resolved particles[J]. Flow Turbulence and Combustion, 2016, 97(2): 539-570.
22	Wittig K, Nikrityuk P, Richter A. Drag coefficient and Nusselt number for porous particles under laminar flow conditions[J]. International Journal of Heat and Mass Transfer, 2017, 112: 1005-1016.
23	Li X, Ouyang J, Wang X D, et al. A drag force formula for heterogeneous granular flow systems based on finite average statistical method[J]. Particuology, 2021, 55: 94-107.
24	Dodds D, Sarhan A R, Naser J. Experimental and numerical study of drag forces on particles in clusters[J]. Powder Technology, 2020, 371: 195-208.
25	Chen X, Song N, Jiang M, et al. A microscopic gas-solid drag model considering the effect of interface between dilute and dense phases[J]. International Journal of Multiphase Flow, 2020, 128: 103266.
26	Chen X, Ma T, Zhou Q. Theoretical and numerical analysis of drag force at the interface between the dilute and dense phases[J]. Physics of Fluids, 2022, 34(9): 093306.
27	Ma T, Li Y, Zhou Q, et al. Microscale drag model considering the effect of interface between dense and dilute phases for gas-solid suspensions at moderate Reynolds numbers[J]. International Journal of Multiphase Flow, 2022, 157: 104270.
28	Liu D Y, Wang Z, Chen X P, et al. Simulation of agglomerate breakage and restructuring in shear flows: coupled effects of shear gradient, surface energy and initial structure[J]. Powder Technology, 2018, 336: 102-111.
29	Mroczka J, Wozniak M, Onofri F R A. Algorithms and methods for analysis of the optical structure factor of fractal aggregates[J]. Metrology and Measurement Systems, 2012, 19(3): 459-470.
30	Froeschke S, Kohler S, Weber A P, et al. Impact fragmentation of nanoparticle agglomerates[J]. Journal of Aerosol Science, 2003, 34(3): 275-287.
31	Kanniah V, Wu P, Mandzy N, et al. Fractal analysis as a complimentary technique for characterizing nanoparticle size distributions[J]. Powder Technology, 2012, 226: 189-198.
32	Goudeli E, Eggersdorfer M L, Pratsinis S E. Coagulation-agglomeration of fractal-like particles: structure and self-preserving size distribution[J]. Langmuir, 2015, 31(4): 1320-1327.
33	Tenneti S, Subramaniam S. Particle-resolved direct numerical simulation for gas-solid flow model development[J]. Annual Review of Fluid Mechanics, 2014, 46: 199-230.
34	Johnson T A, Patel V C. Flow past a sphere up to a Reynolds number of 300[J]. Journal of Fluid Mechanics, 1999, 378: 19-70.
35	Schlichting H, Gersten K. Fundamentals of boundary-layer theory[M]//Boundary-Layer Theory. Berlin Heidelberg: Springer-Verlag, 2000: 29-49.
36	Rong L W, Dong K J, Yu A B. Lattice-Boltzmann simulation of fluid flow through packed beds of uniform spheres: effect of porosity[J]. Chemical Engineering Science, 2013, 99: 44-58.
37	Mola I A, Fawell P D, Small M. Particle-resolved direct numerical simulation of drag force on permeable, non-spherical aggregates[J]. Chemical Engineering Science, 2020, 218: 115582.
38	Militzer J, Kan J M, Hamdullahpur F, et al. Drag coefficient for axisymmetric flow around individual spheroidal particles[J]. Powder Technology, 1989, 57(3): 193-195.
39	Bushell G C, Yan Y D, Woodfield D, et al. On techniques for the measurement of the mass fractal dimension of aggregates[J]. Advances in Colloid and Interface Science, 2002, 95(1): 1-50.
40	Holzer A, Sommerfeld M. New simple correlation formula for the drag coefficient of non-spherical particles[J]. Powder Technology, 2008, 184(3): 361-365.
41	Beinert S, Kwade A, Schilde C. Strategies for multi-scale simulation of fine grinding and dispersing processes: drag coefficient and fracture of fractal aggregates[J]. Advanced Powder Technology, 2018, 29(3): 707-718.

[1]	Siyu ZHANG, Yonggao YIN, Pengqi JIA, Wei YE. Study on seasonal thermal energy storage characteristics of double U-shaped buried pipe group [J]. CIESC Journal, 2023, 74(S1): 295-301.
[2]	Mingkun XIAO, Guang YANG, Yonghua HUANG, Jingyi WU. Numerical study on bubble dynamics of liquid oxygen at a submerged orifice [J]. CIESC Journal, 2023, 74(S1): 87-95.
[3]	Song HE, Qiaomai LIU, Guangshuo XIE, Simin WANG, Juan XIAO. Two-phase flow simulation and surrogate-assisted optimization of gas film drag reduction in high-concentration coal-water slurry pipeline [J]. CIESC Journal, 2023, 74(9): 3766-3774.
[4]	Lei XING, Chunyu MIAO, Minghu JIANG, Lixin ZHAO, Xinya LI. Optimal design and performance analysis of downhole micro gas-liquid hydrocyclone [J]. CIESC Journal, 2023, 74(8): 3394-3406.
[5]	Jiayi ZHANG, Jiali HE, Jiangpeng XIE, Jian WANG, Yu ZHAO, Dongqiang ZHANG. Research progress of pervaporation technology for N-methylpyrrolidone recovery in lithium battery production [J]. CIESC Journal, 2023, 74(8): 3203-3215.
[6]	Linjing YUE, Yihan LIAO, Yuan XUE, Xuejie LI, Yuxing LI, Cuiwei LIU. Study on influence of pit defects on cavitation flow characteristics of throat of thick orifice plates [J]. CIESC Journal, 2023, 74(8): 3292-3308.
[7]	Linzheng WANG, Yubing LU, Ruizhi ZHANG, Yonghao LUO. Analysis on thermal oxidation characteristics of VOCs based on molecular dynamics simulation [J]. CIESC Journal, 2023, 74(8): 3242-3255.
[8]	Dian LIN, Guomei JIANG, Xiubin XU, Bo ZHAO, Dongmei LIU, Xu WU. Preparation and drag reduction effect of silicon-based liquid-like anti-crude-oil-adhesion coatings [J]. CIESC Journal, 2023, 74(8): 3438-3445.
[9]	Xiaokun HE, Rui LIU, Yuan XUE, Ran ZUO. Review of gas phase and surface reactions in AlN MOCVD [J]. CIESC Journal, 2023, 74(7): 2800-2813.
[10]	Yuying GUO, Jiaqiang JING, Wanni HUANG, Ping ZHANG, Jie SUN, Yu ZHU, Junxuan FENG, Hongjiang LU. Water-lubricated drag reduction and pressure drop model modification for heavy oil pipeline [J]. CIESC Journal, 2023, 74(7): 2898-2907.
[11]	Zihan YUAN, Shuyan WANG, Baoli SHAO, Lei XIE, Xi CHEN, Yimei MA. Investigation on flow characteristics of wet particles with power-law liquid-solid drag models in fluidized bed [J]. CIESC Journal, 2023, 74(5): 2000-2012.
[12]	Zhengtao LI, Zhijie YUAN, Gaohong HE, Xiaobin JIANG. Study of the mechanism of internal circulation regulation during evaporation of NaCl droplets on hydrophobic interface [J]. CIESC Journal, 2023, 74(5): 1904-1913.
[13]	Chenxi LI, Yongfeng LIU, Lu ZHANG, Haifeng LIU, Jin’ou SONG, Xu HE. Quantum chemical analysis of n-heptane combustion mechanism under O₂/CO₂ atmosphere [J]. CIESC Journal, 2023, 74(5): 2157-2169.
[14]	Longfei JIA, Shaotong FU, Xing XIANG, Huahai ZHANG, Tao ZHANG, Limin WANG. Lattice Boltzmann simulations of the effect of particles movement on momentum transfer process [J]. CIESC Journal, 2023, 74(2): 735-747.
[15]	Sheng CHEN, Mengke WANG, Bona LU, Xiufeng LI, Cenfan LIU, Mengxi LIU, Yiping FAN, Chunxi LU. CFD investigation of effects of feedstock oil vaporization on FCC cracking reaction and coking [J]. CIESC Journal, 2022, 73(7): 2982-2995.