Challenges in Study of Single Particles and Particle Swarms

Abstract

Abstract: Numerical simulation of multiphase flows in processing equipment in industry with two-fluid models and Eulerian-Lagrangian approaches requires the constitutive equations describing the interactions between the dispersed phase of high concentration and the continuous phase.The status of research on the forces on dispersed solid and fluid particles is reviewed in this article.As compared with the knowledge on drag of single solid particles,study on particle swarms and on other forces is not sufficient to meet the demand of reliable and efficient numerical simulation of multiphase flows.Thus,thorough study on the particle swarms becomes the key to accurate multi-scale simulation of multiphase flows.Besides,the development of efficient algorithm dealing with the non-uniformity on both equipment and mesoscopic scales is recognized as an important issue to be resolved.The research topics in the near future are suggested.

Key words: particle, drop, bubble, swarm, interphase force, multiphase flow, numerical simulation

摘要： Numerical simulation of multiphase flows in processing equipment in industry with two-fluid models and Eulerian-Lagrangian approaches requires the constitutive equations describing the interactions between the dispersed phase of high concentration and the continuous phase.The status of research on the forces on dispersed solid and fluid particles is reviewed in this article.As compared with the knowledge on drag of single solid particles,study on particle swarms and on other forces is not sufficient to meet the demand of reliable and efficient numerical simulation of multiphase flows.Thus,thorough study on the particle swarms becomes the key to accurate multi-scale simulation of multiphase flows.Besides,the development of efficient algorithm dealing with the non-uniformity on both equipment and mesoscopic scales is recognized as an important issue to be resolved.The research topics in the near future are suggested.

关键词: particle, drop, bubble, swarm, interphase force, multiphase flow, numerical simulation

MAO Zaisha, YANG Chao. Challenges in Study of Single Particles and Particle Swarms[J]. , 2009, 17(4): 535-545.

毛在砂, 杨超. Challenges in Study of Single Particles and Particle Swarms[J]. CIESC Journal, 2009, 17(4): 535-545.

References

1 Sokolichin,A.,Eigenberger,G.,Lapin,A.,LÜbert,A.,“Dynamic numerical simulation of gas-liquid two-phase flows Euler/Euler versus Euler/Lagrange”,Chem.Eng.Sci.,52(4),611-62
2 Jakobsen,H.A.,Lindborg,H.,Dorao,C.A.,“Modeling of bubble column reactors,progress and limitations”,Ind.Eng.Chem.Res.,44 (14),5107-5151(2005).
3 Brackbill,J.U.,Kothe,D.B.,Zemach,C.,“A continuum method for modeling surface tension”,J.Comput.Phys.,100(2),335-354 (1992).
4 Clift,R.,Grace,J.R.,Weber,M.E.,Bubbles,Drops,and Particles, Academic Press,New York,30-33(1978).
5 Kwauk,M.S.,Li,H.Z.,Handbook of Fluidization,Chemical Industry Press,Beijing,106(2008).(in Chinese)
6 Tomiyama,A.,“Struggle with computational bubble dynamics”, Multiphase Sci.Technol.,10,369-405(1998).
7 Hu,S.,Kintner,R.C.,“The fall of single liquid drops through water”, AIChE J.,1(1),42-48(1955).
8 Brucato,A.,Grisafi,F.,Montante,G.,“Particle drag coefficients in turbulent fluids”,Chem.Eng.Sci.,53(18),3295-3314(1998).
9 Lane,G.L.,Schwarz,M.P.,Evans,G.M.,“Modeling of the interaction between gas and liquid in stirred vessels”,In:Proc.10th Eur. Conf.on Mixing,van den Akker,H.E.A.,Derksen,J.J.,eds.,Elsevier,Amsterdam,197-204(2000).
10 Khopkar,A.R.,Rammohan,A.R.,Ranade,V.V.,Dudukovic,M.P., “Gas-liquid flow generated by a Rushton turbine in stirred vessel: CARPT/CT measurements and CFD simulations”,Chem.Eng.Sci., 60(8/9),2215-2229(2005).
11 Blumberg,P.N.,Mohr,C.M.,“Effect of orientation on the settling characteristics of cylindrical particles”,AIChE J.,14(2),331-334 (1968).
12 Fan,L.,Mao,Z.S.,Yang,C.,“Experiment on sedimentation of slender particles with large aspect ratio and correlation of drag coefficient”,Ind.Eng.Chem.Res.,43(23),7664-7670Å2004).
13 Anderson,T.B.,Jackson,R.,“A fluid mechanical description of fluidized beds”,Ind.Eng.Chem.Fundam.,6(11),527-539(1967).
14 Homsy,G.M.,El-Kaissy,M.M.,Didwania,A.,“Instability waves and the origin of bubbles in fluidized beds-II”,Int.J.Multiphase Flow,6(4),305-318(1980).
15 Jakobsen,H.A.,Sanns,B.H.,Grevskott,S.,Svendsen,H.F.,“Modeling of vertical bubble-driven flows”,Ind.Eng.Chem.Res.,36(10), 4052-4074(1997).
16 Kuo,J.T.,Walls,G.B.,“Flow of bubbles through nozzles”,Int.J.Multiphase Flow,14(5),547-564(1988).
17 Sankaranarayanan,K.,Shan,X.,Kevrekidis,I.G.,Sundaresan,S., “Analysis of drag and virtual mass forces in bubbly suspensions using an implicit formulation of the lattice Boltzmann method”,J. Fluid Mech.,452,61-96(2002).
18 Kendoush,A.A.,Sulaymon,A.H.,Mohammed,S.A.M.,“Experimental evaluation of the virtual mass of two solid spheres accelerating in fluids”,Exp.Therm.Fluid Sci.,31(7),813-823(2007).
19 Odar,F.,“Verification of the proposed equation for calculation of the forces on a sphere accelerating in a viscous fluid”,J.Fluid Mech., 25(3),591-592(1966).
20 Zapryanov,Z.,Tabakova,S.,Dynamics of Bubbles,Drops and Rigid Particles,Kluwer Academic,Dordrecht,338,343(1999).
21 Reeks,M.W.,McKee,S.,“The dispersive effects of basset history forces on particle motion in a turbulent flow”,Phys.Fluids,27(7), 1573-1582(1984).
22 Sokolichin,A.,Eigenberger,G.,Lapin,A.,“Simulation of buoyancy driven bubbly flow:Established simplifications and open questions”, AIChE J.,50(1),24-45(2004).
23 You,C.F.,Qi,H.Y.,Xu,X.C.,“Progress in the Basset force research and its application”,Chinese Journal of Applied Mechanics,19(2), 31-33(2002).(in Chinese)
24 Drew,D.A.,Lahey,R.T.Jr.,“The virtual mass and lift force on a sphere in rotating and straining flow”,Int.J.Multiphase Flow,13 (1),113-121(1987).
25 Tomiyama,A.,Sou,A.,Zun,I.,Kanami,N.,Sakaguchi,T.,“Effects of Eötvös number and dimensionless liquid volumetric flux on lateral motion of a bubble in a laminar duct flow”,In:Proceedings of the 2nd International Conference on Multiphase Flow Serizawa,A., Fukano,T.,Bataille,J.,eds.,Elsevier,Amsterdam,3-15(1995).
26 Tomiyama,A.,Tamai,H.,Zun,I.,Hosokawa,S.,“Transverse migration of single bubbles in simple shear flows”,Chem.Eng.Sci.,57 (11),1849-1858(2002).
27 Lahey,Jr.R.T.,Lopez de Bertodano,M.,Jones,Jr.O.C.,Buscaglia, G.,“Phase distribution in complex geometry conduits”,Nucl.Eng. Design,141(1/2),177-201(1993).
28 Antal,S.P.,Lahey,Jr.R.T.,Flaherty,J.E.,“Analysis of phase distribution in fully developed laminar bubbly two-phase flow”,Int.J. Multiphase Flow,17(5),635-652(1991).
29 Zhang,L.,Yang,C.,Mao,Z.S.,“Unsteady motion of a single bubble in highly viscous liquid and empirical correlation of drag coefficient”,Chem.Eng.Sci.,63(8),2099-2106(2008).
30 Zhang,L.,Yang,C.,Mao,Z.S.,“Unsteady motion of a single bubble in non-Newtonian liquids and empirical correlation of drag coefficient”,Ind.Eng.Chem.Res.,47(23),9767-9772(2008).
Pan,T.W.,Joseph,D.D.,Bai,R.,Glowinski,R.,Sarin,V.,“Fluidization of 1204 spheres:Simulation and experiment”,J.Fluid Mech., 451,169-191(2002).
32 Li,J.,Kuipers,J.A.M.,“Gas-particle interactions in dense gas-fluidized beds”,Chem.Eng.Sci.,58(3-6),711-718(2003).
33 Zinchenko,A.Z.,Davis,R.H.,“An efficient algorithm for hydrodynamical interaction of many deformable drops”,J.Comput.Phys., 157(2),539-587(2000).
34 Happel,J.,“Viscous flow in multi-particle systems:Slow motion of fluids relative to beds of spherical particles”,AIChE J.,4(2),197-201 (1958).
35 Happel,J.,Brenner,H.,Low Reynolds Number Hydrodynamics, 2nd edition,Noordhoff,Leydon the Netherlands(1973).
36 Chhabra,R.P.,Bubbles,Drops,and Particles in Non-Newtonian Fluids,2nd edition,Taylor Francis,300-303(2007).
37 Mao,Z.S.,“Numerical simulation of viscous flow through spherical particle assemblage with the modified cell model”,Chin.J.Chem. Eng.,10(2),149-162(2002).
38 Mao,Z.S.,Wang,Y.F.,“Numerical simulation of mass transfer in a spherical particle assemblage with the cell model”,Powder Technol., 134(1/2),145-155(2003).
39 LeClair,B.P.,Hamielec,A.E.,“Viscous flow through particleassemblages at intermediate Reynolds numbers—A cell model for transport in bubbles swarms”,Can.J.Chem.Eng.,49(6),713-720 (1971).
40 Sankaranarayanan,K.,Sundaresan,S.,“Lift force in bubbly suspensions”,Chem.Eng.Sci.,57(17),3521-3542(2002).
41 Mao,Z.S.,Chen,J.Y.,“Numerical approach to the motion and external mass transfer of a drop swarm by the cell model”,In:International Solvent Extraction Conference(ISEC'2002),Sole,K.C.,Cole, P.M.,Preston,J.S.,Robinson,D.J.,eds.,South African Institute of Mining and Metallurgy,Johannesburg,South Africa,227-232(2002).
42 Mao,Z.S.,Chen,J.Y.,“An attempt to improve the cell model for motion and external mass transfer of a drop in swarms at intermediate Reynolds numbers”,In:International Solvent Extraction Conference(ISEC'2005),Fei,W.Y.,Liu,H.Z.,Yan,C.H.,eds.,Beijing, A417(2005).
43 Kumar,A.,Hartland,S.,“Gravity settling in liquid/liquid dispersions”,Can.J.Chem.Eng.,63(3),368-376(1985).
44 Wen,C.Y.,Yu,Y.H.,“Mechanics of fluidization”,Chem.Eng.Prog. Symp.Ser.,62,100-111(1966).
45 Oey,R.S.,Mudde,R.F.,van den Akker,H.E.A.,“Sensitivity study on interfacial closure laws in two-fluid bubbly flow simulations”, AIChE J.,49(7),1621-1636(2003).
46 Koch,D.L.,Hill,R.J.,“Inertial effects in suspension and porous-media flows”,Ann.Rev.Fluid Mech.,33,619-647(2001).
47 Pan,Y.,Dudukovic,M.P.,Chang,M.,“Numerical Investigation of gas-driven flow in 2-D bubble columns”,AIChE J.,46(3),434-449 (2000).
48 Li,J.H.,Kwauk,M.S.,“Exploring complex systems in chemical engineering—The multi-scale methodology”,Chem.Eng.Sci.,58(2), 521-535(2003).

[1]	Xin WU, Jianying GONG, Long JIN, Yutao WANG, Ruining HUANG. Study on the transportation characteristics of droplets on the aluminium surface under ultrasonic excitation [J]. CIESC Journal, 2023, 74(S1): 104-112.
[2]	Wei SU, Dongxu MA, Xu JIN, Zhongyan LIU, Xiaosong ZHANG. Visual experimental study on effect of surface wettability on frost propagation characteristics [J]. CIESC Journal, 2023, 74(S1): 122-131.
[3]	Zhanyu YE, He SHAN, Zhenyuan XU. Performance simulation of paper folding-like evaporator for solar evaporation systems [J]. CIESC Journal, 2023, 74(S1): 132-140.
[4]	Xiaoqing ZHOU, Chunyu LI, Guang YANG, Aifeng CAI, Jingyi WU. Icing kinetics and mechanism of droplet impinging on supercooled corrugated plates with different curvature [J]. CIESC Journal, 2023, 74(S1): 141-153.
[5]	Keke SHAO, Mengjie SONG, Zhengyong JIANG, Xuan ZHANG, Long ZHANG, Runmiao GAO, Zekang ZHEN. Experimental study on the formation and distribution of trapped air bubbles in horizontal ice slice [J]. CIESC Journal, 2023, 74(S1): 161-164.
[6]	Lisen BI, Bin LIU, Hengxiang HU, Tao ZENG, Zhuorui LI, Jianfei SONG, Hanming WU. Molecular dynamics study on evaporation modes of nanodroplets at rough interfaces [J]. CIESC Journal, 2023, 74(S1): 172-178.
[7]	Yifei ZHANG, Fangchen LIU, Shuangxing ZHANG, Wenjing DU. Performance analysis of printed circuit heat exchanger for supercritical carbon dioxide [J]. CIESC Journal, 2023, 74(S1): 183-190.
[8]	Zhiguo WANG, Meng XUE, Yushuang DONG, Tianzhen ZHANG, Xiaokai QIN, Qiang HAN. Numerical simulation and analysis of geothermal rock mass heat flow coupling based on fracture roughness characterization method [J]. CIESC Journal, 2023, 74(S1): 223-234.
[9]	He JIANG, Junfei YUAN, Lin WANG, Guyu XING. Experimental study on the effect of flow sharing cavity structure on phase change flow characteristics in microchannels [J]. CIESC Journal, 2023, 74(S1): 235-244.
[10]	Jiahao SONG, Wen WANG. Study on coupling operation characteristics of Stirling engine and high temperature heat pipe [J]. CIESC Journal, 2023, 74(S1): 287-294.
[11]	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.
[12]	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.
[13]	Ruitao SONG, Pai WANG, Yunpeng WANG, Minxia LI, Chaobin DANG, Zhenguo CHEN, Huan TONG, Jiaqi ZHOU. Numerical simulation of flow boiling heat transfer in pipe arrays of carbon dioxide direct evaporation ice field [J]. CIESC Journal, 2023, 74(S1): 96-103.
[14]	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.
[15]	Jiaqi YUAN, Zheng LIU, Rui HUANG, Lefu ZHANG, Denghui HE. Investigation on energy conversion characteristics of vortex pump under bubble inflow [J]. CIESC Journal, 2023, 74(9): 3807-3820.