Numerical simulation of bubble breakup phenomena in a narrow flow field

合集下载

直线感应加速器束流崩溃不稳定性数值模拟

第15卷　第4期强激光与粒子束Vol.15,No.4 2003年4月HIGH POWER LASER AND PAR TICL E B EAMS Apr.,2003　文章编号:　100124322(2003)0420397204直线感应加速器束流崩溃不稳定性数值模拟Ξ张开志1,　林郁正2,　王华岑1(1.中国工程物理研究院流体物理研究所,四川绵阳621900;　2.清华大学加速器实验室,北京100084) 摘　要:　在理论分析的基础上,开发了直线感应加速器束流崩溃不稳定性数值模拟程序。

描述了利用该程序开展的研究工作,这些研究揭示了束流崩溃不稳定性的一般规律,分析了相关参数对束流崩溃不稳定性的影响,最后提出了直线感应加速器束流崩溃不稳定性抑制方法。

关键词:　直线感应加速器;　束流崩溃不稳定性;　横向阻抗;　横向尾场;　质心横向位移;　数值模拟中图分类号:　TL50 文献标识码:　A 直线感应加速器中的束流崩溃不稳定性(BBU)是束流脉冲与感应加速腔相互作用的结果。

束流脉冲经过加速腔时将在其中激励起横向尾场,而横向尾场又将使束流质心产生横向高频振荡,这两种因素互相耦合,最终导致束流崩溃不稳定性。

由于束流崩溃的过程非常复杂,采用解析分析方法得出的结论比较粗略[1],必须采用数值模拟以及试验才能进行比较全面深入的研究。

1　数值模拟原理将束流脉冲等分成m个束片,研究它们在n个加速腔中的运动。

束流脉冲经过加速腔时,将受到加速电场,横向尾场和螺线管线圈磁场的作用,因而能量、动量和质心的横向位移都会发生变化。

将加速腔分成漂移段和加速间隙两段,在漂移段只考虑轴向磁场的作用,我们假定在一个加速腔中,螺线管磁场是均匀分布的。

从文献[1]中的理论分析出发,可以导出第i个加速腔漂移段中第j个束片的质心横向位移r d(i,j)和横向动量r′d(i,j)的递推关系r d(i,j)=r(i-1,j)cos(kβl)+r′(i-1,j)/[kβsin(kβl)](1a)r′d(i,j)=-r(i-1,j)kβsin(kβl)+r′(i-1,j)cos(kβl)(1b)式中:kβ=qB/2m0cβγ,q是电荷,B是螺线管线圈磁场;l是加速腔长度。

气升式环流反应器内气液两相流动CFD数值模拟的研究

23.Couvert A.Roustan M.Chatellier P Two-phase hydrodynamic study of a rectangular air-lift loop reactor with an
internal baffle 1999
24.Couvert A.Bastoul D.Roustan M Prediction of liquid velocity and gas hold-up in rectangular air-lift reactors of different scales 2001
36.Warsito.Ohkawa M.Kawata N.Uchida S Cross-sectional distributions of gas and solid holdups in slurry bubble column investigated by ultrasonic computed tomography 1999
45.Iguchi M.Kondoh T.Morita Z I.Nakajima K Velocity and turbulence measurements in a cylindrical bath subject to
centric bottom gas injection 1995(02)
46.Deshpande N S.Joshi J B Simultaneous measurements of gas and liquid phase velocities and gas hold-up using laser Doppler velocimeter 1997
10.Visnovsky G.Claus J D.Merchuk J C Cultivation of Insect Cells in Bioreactors:Influence of Reactor Configuration and Superficial Velocity 2003

A numerical investigation of non-spherical reboundingbubbles

(Received 27 June 1991 and in revised form 18 February 1992)
The motion of buoyant transient cavities with non-condensible contents is investigated numerically using a boundary-integral method. The bubble contents are described by an adiabatic gas law. Motion is considered in the neighbourhood of a rigid boundary, in an axisymmetric geometry. We investigate whether the noncondensible contents will resist the formation of jets. It is found that jets form upon collapse and, in general, completely penetrate the bubble before it rebounds, but circumstances are identified under which the non-spherical bubble will rebound prior to this occurrence. I n these cases the bulk of the jet growth occurs upon rebound. Furthermore, the interaction between the buoyancy force causing jet formation upwards, and the Bjerknes attraction of the rigid boundary causing jet formation towards it, is investigated and general principles discussed which allow the behaviour to be interpreted. The concept of the Kelvin impulse is utilized.

基于EMMS方法的鼓泡塔反应器CFD及群平衡模拟

基于EMMS方法的鼓泡塔反应器CFD及群平衡模拟王珏;杨宁【摘要】The energy-minimization multi-scale (EMMS) model has been introduced to improve the population balance modeling (PBM) of gas-liquid flows. The energy for bubble breakup and coalescence can be obtained from the EMMS model and then used to derive a correction factor for the coalescence rate. This new model is applied in this study to simulate the bubble columns of high flow rates. Simulations using the three different models, namely, the constant-bubble-size model, the CFD-PBM model and the CFD-PBM-EMMS model, are compared with experimental data. The simulation of CFD-PBM-EMMS gives better prediction for bubble size distribution and liquid axial velocity at different heights as well as the overall and local gas holdup. The relative error of global gas holdup reduces to 5% or 15%, and the mean relative error of local gas holdup reduces to 8% or 17% for 0.16 m·s-1 or 0.25 m·s-1 of superficial gas velocity.%能量最小多尺度(energy-minimization multi-scale,EMMS)方法已经被应用于气液体系中群平衡(population balance model,PBM)模型的改进.EMMS模型可计算气泡破碎聚并过程的能量,进而获得聚并速率的修正因子.应用这一模型对高气速鼓泡塔进行了模拟计算,并进一步对比了均一尺径模型、CFD-PBM模型以及CFD-PBM-EMMS模型的模拟结果与实验数据.结果表明,在高表观气速条件下,基于EMMS方法的群平衡模型可以更加准确地预测鼓泡塔中不同高度的气泡尺径分布和轴向液速,同时提高了对整体气含率和局部气含率的模拟准确性.在表观气速为0.16 m·s-1和0.25 m·s-1时,CFD-PBM-EMMS模型对气泡尺径分布的预测精度更高,同时整体气含率模拟的相对误差下降为5%和15%,局部气含率模拟平均相对误差下降为8%和17%.【期刊名称】《化工学报》【年(卷),期】2017(068)007【总页数】11页(P2667-2677)【关键词】计算流体力学;群平衡模型;鼓泡塔;气含率;气泡尺径分布【作者】王珏;杨宁【作者单位】中国科学院过程工程研究所多相复杂系统国家重点实验室,北京100190;中国科学院大学,北京 100049;中国科学院过程工程研究所多相复杂系统国家重点实验室,北京 100190【正文语种】中文【中图分类】TQ021.1鼓泡塔反应器具有结构简单、操作简便、良好的传热传质效率等优点，被广泛应用于化学工程、生物工程、石油工程等领域[1]。

多相流模型经验谈

多相流模型经验谈多相流的介绍：Currentlytherearetwoapproachesforthenumericalcalculationofmultiphaseflows:theEuler-La grangeapproachandtheEuler-Eulerapproach.TheEuler-LagrangeApproach:TheLagrangiandiscretephasemodelinFLUENTfollowstheEuler-Lagr angeapproach,thisapproachisinappropriateforthemodelingofliquid-liquidmixtures,fluidizedbeds,oranyapplicationwhMIteration,theparticlesourcetermsarerecalculated.LengthScale:controlstheintegrationtimestepsizeusedtointegratetheequationsofmotionfort heparticle.Asmaller valuefortheLengthScaleincreasestheaccuracyofthetrajectoryandheat/masstransfercalculat ionsforthediscretephase.LengthScalefactor:AlargervaluefortheStepLengthFactordecreasesthediscretephaseintegrat iontimestep.颗粒积分方法：numerics叶中trackingscheme选项1）implicitusesanimplicitEulerintegrationofEquation23.2-1whichisunconditionallystablefor allparticlerelaxationtimes.2）trapezoidalusesasemi-implicittrapezoidalintegration.（梯形积分）3）analyticusesananalyticalintegrationofEquation23.2-1wheretheforcesareheldconstantdurin gtheintegration.4）runge-kuttafacilitatesa5thorderRungeKuttaschemederivedbyCashandKarp[47]. Youcaneitherchooseasingletrackingscheme,orswitchbetweenhigherorderandlowerordertracki ngschemesusingan12FluidFlowTimeSteptoinjecttheparticles,orwhetheryoupreferaParticleTimeStepSizeindepend entofthefluidflowtimestep.Withthelatteroption,youcanusetheDiscretePhaseModelincombinationwithchangesin thetimestepforthecontinuousequations,asitisdonewhenusingadaptiveflowtimestepping.随机轨道模型的参数：numberoftries:AninputofzerotellsFLUENTtocomputetheparticletrajectorybasedonthemeancon tinuousphasevelocityfield(Equation23.2-1),ignoringtheeffectsofturbulenceontheparticletrajectories.Aninput of1orgreatertellsFLUENTtoincludeturbulentvelocityfluctuationsintheparticleforcebalanceasinEquation23.2 -20.Ifyouwantthecharacteristiclifetimeoftheeddytoberandom(Equation23.2-32),enabletheRando mEddyLifetimeoption.YouwillgenerallynotneedtochangetheTimeScaleConstant(CLinEquation23.2-23)fromitsdefaul tvalueof0.15,unlessyouareusingtheReynoldsStressturbulencemodel(RSM),inwhichcaseavalueof0.3isrecomm ended.液滴颗粒碰撞与破碎碰撞：破碎：有两种模型，TAB模型适合低韦伯数射流雾化以及低速射流进入标态空气中的情况。

原子能院电子直线加速器技术的研究与应用

VACUUMELECTRONICS•加速器专辑•原子能院电子直线加速器技术的研究与应用杨京鹤，王国宝，王修龙，曾自强，朱志斌，余国龙，佟迅华，张立锋，吴青峰，韩广D,刘保杰(中国原子能科学研究院核技术应用研究所"匕京102413)摘要：加速器技术作为核技术应用的源头技术之一，推动了核科学技术与应用的发展。

中国原子能科学研究院是中国核科学技术的发祥地，在中低能电子直线加速器研究与应用方面进行了持续研究，取得了多项成果，研究开发了具有自主知识产权、型谱化、系列化的无损检测电子直线加速器和电子辐照直线加速器，在工业、农业、安全等领域得到了有效应用，在我国国防建设、国民经济发展中发挥了重要作用％关键8:直线加速器；电子束;无损检测；电子辐照中图分类号:TL53文献标志码：A文章编号:1002-8935(2021)01-0011-03doi：10.16540/11-2485/tn.2021.01.02Research and Application of Electron Linear Accelerator Technology at CIAEYANG Jing-he,WANG Guo-bao,WANG Xiu-ong,ZENG Zi-qiang,ZHU Zhi-bin,YU Guo-long, TONG Xun-hua,ZHANG Li-feng,WU Qing-feng,HAN Guang-wen,LIU Bao-jie (..Department of Nuclear Technology Application,China Institute of Atomic Energy,Beijing102413,China)Abstract:Accelerator is one of the source technologies of nuclear technology application,which promotes the development of nuclear science technology and application.China Institute of Atomic Energy is the birthplace of nuclear science technology in China.The low-energy and medium-energy electron linear accelerator technologies were researched and developed there.Serial non-destructive test and irradiation linear accelerators with independent intellectual property rights had been developed successfully.They are used in many fields such as industry,agriculture,security,etc.,and play important roles in China's national defense construction and national economic development.Keywords:Linear accelerator,Electron beam,Non-destructive testing,Electron irradiation电子加速器是研究开发历史最早的粒子加速器类型,在核科学与技术领域发重用％20世纪40年代以来,,波技术的快速进步,采用射频微波电子的电子器取式发展,在大型高能器科研设施和紧凑的中低能应用型器方到应用％原子能科研究低能电子器方的研究较早,并在80年代开始进行科技成果转化，攻克了一批技术难题,研发了一批具的电子器装置,t电子器在民用领域的发展,本文综述原子能电子直线加速器技术方面的研究与应用情况％1原子能院电子直线加速器的发展背景原子能的电子器技术用国防与科研领域(1),,民经济的发展,工业、医疗、农业等领域对应用型器的需求日趋强烈,在20世纪80年代,原子能器团队在强流短脉冲电子器研究等项目的基础上,提岀无损探伤器和电子辐器两个方向的科技化。

journal of fluid mechanics 文献

标题: Two-dimensional and axisymmetric viscous flow in apertures作者: Dabiri, Sadegh; Sirignano, William A.; Joseph, Daniel D.Flow Visualization Using Cavitation Within Blade Passage of an Axial Waterjet Pump RotorDavid Y. Tan,Rinaldo L. Miorini,Jens Keller and Joseph KatzCAVITATION PHENOMENA WITHIN REGIONS OF FLOW SEPARATION.Katz, Joseph Source:Journal of Fluid Mechanics, v 140, p 397-436, Mar 1984Two-dimensional and axisymmetric viscous flow in apertures作者: Dabiri, Sadegh; Sirignano, William A.; Joseph, Daniel D.Interaction between a cavitation bubble and shear flow作者: Dabiri, Sadegh; Sirignano, William A.; Joseph, Daniel D.Direct numerical evidence of stress-induced cavitation作者: Falcucci, G.; Jannelli, E.; Ubertini, S.; 等.标题: Non-spherical bubble dynamics in a compressible liquid. Part 1. Travelling acoustic wave作者: Wang, Q. X.; Blake, J. R.标题: Cavitation in linear bubbles作者: Brenner, Michael P.标题: Numerical simulations of non-spherical bubble collapse作者: Johnsen, Eric; Colonius, Tim标题: Simulation ofcavitationbubbles in a convergent-divergent nozzlewaterjet作者: Qin, Z.; Bremhorst, K.; Alehossein, H.; 等.The influence of the sleeve's orifices geometric patterns on the fluid flow through a hydraulic resistance作者:Sfarlea, I (Sfarlea, I.)[ 1 ] ; Bode, F (Bode, F.)[ 1 ] ; Opruta, D (Opruta, D.)[ 1 ]标题: NUMERICAL SIMULATION OF ORIFICE CAVITATING FLOWS USING TWO-FLUID AND THREE-FLUID CAVITATION MODELS作者: Darbandi, Masoud; Sadeghi, HamedFlow instability due to cryogenic cavitation in the downstream of orifice 作者: Lee, Changjin; Roh, Tae-Seong来源出版物: JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY标题: A STUDY ON FLOW THROUGH AN ORIFICE WITH PREDICTIONOF CAVITATION AND HYDRAULIC FLIP作者: Darbandi, Masoud; Sadeghi, Hamed书籍团体作者: ASME标题: ANALYSIS OF THERMAL EFFECTS IN ACAVITATING ORIFICE USING RAYLEIGH EQUATION AND EXPERIMENTS 作者: Grazia, De Giorgi Maria; Daniela, Bello; Ficarella, Antonio书籍团体作者: ASME会议: 17th International Conference on Nuclear Engineering 会议地点: Brussels, BELGIUM会议日期: JUL 12-16, 2009标题: Simulations of cavitation in orifice and venturis作者: Ahuja, Vineet; Hosangadi, Ashvin丛书编者: Moatamedi, M会议: Joint Conference of the ASME Pressure Vessels and Piping Division/8th International Conference on Creep and Fatigue at Elevated Temperatures会议地点: San Antonio, TX会议日期: JUL 22-26, 2007标题: Effects on pipe vibrations of cavitation in an orifice and inglobe-style valves作者: Caillaud, Sebastien; Gibert, Rene-Jean; Moussou, Pierre; 等.丛书编者: Paidoussis, MP会议: 6th Symposium on Fluid-Structure Interactions, Aeroelasticity and Flow-Induced Vibration and Noise 会议地点: Vancouver, CANADA会议日期: JUL 23-27, 2006会议赞助商: ASME, Pressure Vessels & Piping Div标题: Flow and cavitation characteristics of a damping orifice in water hydraulics作者: Liu Yinshui; Zhu Bihai; Zhu Yuquan; 等.来源出版物: PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART A-JOURNAL OF POWER AND ENERGY 卷: 220期: A8页: 933-942 DOI: 10.1243/09576509JPE323出版年: DEC 2006标题: Investigation of cavitation near the orifice of hydraulic valves作者: Gao, H.; Lin, W.; Tsukiji, T.来源出版物: PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART G-JOURNAL OF AEROSPACE ENGINEERING 卷: 220期: G4页:253-265 DOI: 10.1243/09544100JAER O26出版年: AUG 2006标题: Effects of orifice internal flow on breakup characteristics oflike-doublet injectors作者: Jung, K; Khil, T; Yoon, Y来源出版物: JOURNAL OF PROPULSION AND POWER 卷: 22期: 3页: 653-660 DOI: 10.2514/1.20362出版年: MAY-JUN 2006被引频次: 6 (来自所有数据库)标题: Visualization of cavitation in high-pressure diesel fuel injectororifices作者: Li, Haiyun; Collicott, Steven H.来源出版物: ATOMIZATION AND SPRAYS 卷: 16期: 8页: 875-886 DOI: 10.1615/AtomizSpr.v16.i8.20出版年: 2006被引频次: 8 (来自所有数据库)标题: Experimental study of thermal cavitation in an orifice作者: De Giorgi, Maria Grazia; Chiara, Fabio; Ficarella, Antonio书籍团体作者: ASME会议: 8th Biennial Conference on Engineering Systems Design and Analysis 会议地点: Turin, ITALY会议日期: JUL 04-07, 2006会议赞助商: ASME来源出版物: Proceedings of the 8th Biennial Conference on Engineering Systems Design and Analysis, Vol 1 页: 523-529出版年: 2006被引频次: 0 (来自所有数据库)Cavitation Inception and Head Loss Due to Liquid Flow Through Perforated Plates of Varying ThicknessD. Maynes,G. J. Holt and J. BlotterToward Improved Closure Relations for the Turbulent Kinetic Energy Equation in Bubble-Driven Flows1. Martin Wörner*,2. SercanErdoganArticle first published online: 17 MAY 2013DOI: 10.1002/cite.201200243A TRANSPORT EQUATION MODEL FOR SIMULATINGCAVITATION FLOWS IN MINIATURE MACHINESYAO ZHANG∙State Key Laboratory of Hydroscience& Engineering, TsinghuaUniversity, Beijing, 100084, ChinaXIANWU LUO∙Corresponding author.∙State Key Laboratory of Hydroscience& Engineering, TsinghuaUniversity, Beijing, 100084, ChinaSHUHONG LIU∙State Key Laboratory of Hydroscience& Engineering, TsinghuaUniversity, Beijing, 100084, ChinaHONGYUAN XU∙State Key Laboratory of Hydroscience& Engineering, TsinghuaUniversity, Beijing, 100084, ChinaDevelopment of Cavitation in Refrigerant (R-123) Flow InsideRudimentary Microfluidic SystemsThermodynamic analysis of capillary flows in the presence ofhydrodynamic slip1. A. Laouir1,*,2. D. Tondeur2A Series Pressure Drop Representation for Flow Through Orifice TubesT. A. Jankowski,S. P. Ashworth,E. N. Schmierer and F. C. Prenger[+] Author and Article InformationEstimation of Cavitation Limits From Local Head Loss CoefficientRaúl Sánchez, Francisco V. Laguna, Leonor Rodríguez-Sinobas and Luis Juana[+] Author and Article InformationI mpact of Orifice Length/Diameter Ratio on 90 deg Sharp-Edge Orifice FlowWith Manifold Passage Cross FlowW. H. Nurick, D. G. Talley, P. A. Strakey and T. Ohanian[+] Author and Article InformationNumerical simulation and extended validation of two-phasecompressible flow in diesel injector nozzles1. F J Salvador*2. S Hoyas3. R Novella4. J Martínez-LópezX. Yang, A. Holke, S. A. Jacobson, J. H. Lang, M. A. Schmidt, and S.D. Umans, “An electrostatic, on/off microvalve designed for gas fuel deliveryfor the MIT microengine,”J. Microelectromech. Syst.13, 660 (2004).D. J. Laser and J. G. Santiago, ―A review of micropumps,‖J. Micromech.4.P. Woias, ―Micropumps—summarizing the first two decades,‖Proc.SPIE4560, 39 (2001).5.N.-T. Nguyen, X. Huang, and T. K , Chuan, ―A review of micropumps,‖J. Fluids Eng.124, 384 (2002)./10.1115/1.145907519.C. -M. Ho and Y.-C. Tai, ―Micro-electro-mechanical-systems (MEMS) and fluidflows,‖Annu. Rev. Fluid Mech.30, 579 (1998)./10.1146/annurev.fluid.30.1.57920.P. Gravesen, J. Branebjerg, and O. S. Jensen, ―Microfluidics—a review,‖J.Micromech. Microeng.3, 168 (1993)./10.1088/0960-1317/3/4/00221.H. A. Stone, A. D. Strooch, and A. Ajdari, ―Engineering flows in small devices:Microfluidics toward a lab-on-a-chip,‖Annu. Rev. Fluid Mech.36, 381 (2004)./10.1146/annurev.fluid.36.050802.12212422.T. Hasegawa, M. Suganuma, and H. Watanabe, ―Anomaly of excess pressure drops of the flow through very small orifices,‖Phys. Fluids9, 1 (1997)./10.1063/1.86917023.G. Stemme, G. Kittilsland, and B. Norden, ―A sub-micron particle filter insilicon,‖Sens. Actuators, A21–23, 904 (1990).24.G. M. Mala and D. Li, ―Flow characteristics of water in microtubes,‖Int. J. HeatFluid Flow20, 142 (1999)./10.1016/S0142-727X(98)10043-7G. L. Morini, “Single-phase convective heat transfer in microchannels: A review of experimental results,”Int. J. Therm. Sci.43,631 (2004).26. Cavitation Enhanced Heat Transfer in MicrochannelsBrandon Schneider,Chandan Mishra,Gregory S. Cole,Yoav Peles,Robert P. Scaringe,Ali Koşar and Chih-Jung Kuo26.C. Mishra and Y. Peles, ―Cavitation in flow through a micro-orifice inside a silicon microchannel,‖Phys. Fluids17, 013601(2005)./10.1063/1.182760227.C. Mishra and Y. Peles, ―Size scale effects on cavitating flows through micro-orifices entrenched in rectangular microchannels,‖J. Microelectromech. Syst.14, 987 (2005).28. R. E. A. Arndt, ―Cavitation in fluid machinery and hydraulic structures,‖Annu. Rev. Fluid Mech.13, 273 (1981)./10.1146/annurev.fl.13.010181.00142129. R. T. Knapp, J. W. Daily, and F. G. Hammit, Cavitation (McGraw-Hill, NewYork, 1970).30.C. E. Brennen, Cavitation and Bubble Dynamics (Oxford University Press, Oxford, UK, 1995).31. J. W. Holl, ―Nuclei and cavitation,‖J. Basic Eng.92, 681 (1970).35.F. R. Young, Cavitation (McGraw-Hill, New York, 1989).S. Pennathur, Y. Peles, and A. H. Epstein, Cavitation at Micro-Scale in MEMS Fluid Machinery,” Proc. ASME Int. Mech. Engg. Congress and Expos, New Orleans, LA, 2002, p. 87.39.D. P. Schmidt, C. J. Rutland, and M. L. Corradini, ―Fully compressible,two-dimensional model of small, high-speed, cavitating nozzles,‖Atomization Sprays9, 255 (1999).40. W. Yuan and G. H. Schnerr, ―Numerical simulation of two-phase flow in injection nozzles: Interaction of cavitation and external jet formation,‖J. FluidsEng.125, 963 (2003)./10.1115/1.162568739.D. P. Schmidt, C. J. Rutland, and M. L. Corradini, ―Fully compressible,two-dimensional model of small, high-speed, cavitating nozzles,‖Atomization Sprays9, 255 (1999).40. W. Yuan and G. H. Schnerr, ―Numerical simulation of two-phase flow in injection nozzles: Interaction of cavitation and external jet formation,‖J. FluidsEng.125, 963 (2003)./10.1115/1.162568741. L. C. Ganippa, G. Bark, S. Andersson, and J. Chomiak, ―Cavitation: A contributory factor in the transition from symmetric to asymmetric jets in cross-flow nozzles,‖Exp. Fluids36, 627 (2004).43.B. Freudig, S. Tesch, and H. Schubert, ―Production of emulsions in high-pressure homogenizers—Part II: Influence of cavitation on droplet breakup,‖LifeSci.3, 266 (2003).44. Y. Tomita and A. Shima, ―Mechanisms of impulsive pressure generation and damage pit formation by bubble collapse,‖J. Fluid Mech.169, 535 (1986).42. W. Y. Lee, M. Wong, and Y. Zohar, ―Pressure loss in constriction microchannels,‖J. Microelectromech. Syst.11, 236 (2002)./10.1109/JMEMS.2002.100740245. J. P. Tullis, Hydraulics of Pipelines (Wiley, New York, 1989).43.B. Freudig, S. Tesch, and H. Schubert, ―Production of emulsions in high-pressure homogenizers—Part II: Influence of cavitation on droplet breakup,‖LifeSci.3, 266 (2003).44. Y. Tomita and A. Shima, ―Mechanisms of impulsive pressure generation and damage pit formation by bubble collapse,‖J. Fluid Mech.169, 535 (1986).49. Y. Yan and R. B. Thorpe, ―Flow regime transitions due to cavitation in the flow through an orifice,‖Int. J. Multiphase Flow16,1023 (1990)./10.1016/0301-9322(90)90105-R50. J. W. Ball, J. P. Tullis, and T. Stripling, ―Predicting cavitation in sudden enlargements,‖J. Hydraul. Div., Am. Soc. Civ. Eng.101,857 (1975).51. J. P. Tullis, ―Cavitation scale effects for valves,‖J. Hydraul. Div., Am. Soc. Civ. Eng.99, 1109 (1973).52. K. Ramamurthi and K. Nandakumar, ―Characteristics of flow through smallsharp-edged cylindrical orifices,‖Flow Meas. Instrum.10, 133 (1999)./10.1016/S0955-5986(99)00005-9标题: Experimental study on cavitation characteristics of waterhydraulic orifice作者: Liu, YS; Wu, ZJ; Yang, YS; 等.丛书编者: Lu, YX; Wang, QF; Wei, L会议: 6th International Conference on Fluid Power Transmission and Control (ICFP 2005) 会议地点: Zhejiang Univ, Hangzhou, PEOPLES R CHINA会议日期: APR 05-08, 2005标题: Numerical study of inlet and geometry effects on discharge coefficients for liquid jet emanating from a plain-orifice atomizer作者: Yeh, CL来源出版物: CHINESE JOURNAL OF MECHANICS-SERIES A 卷: 18期: 3页: 153-161出版年: SEP 2002标题: Experimental investigation of the flow characteristics of small orifices and valves in water hydraulics作者: Zhu, BK; Huang, Y; Zhang, TH; 等.来源出版物: PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART E-JOURNAL OF PROCESS MECHANICAL ENGINEERING 卷: 216期:E4页: 235-245出版年: 2002标题: Hydraulic characteristics of multistage orifice tunnels作者: Zhang, QY; Chai, BQ来源出版物: JOURNAL OF HYDRAULIC ENGINEERING-ASCE 卷: 127期: 8页: 663-668 DOI: 10.1061/(ASCE)07 33-9429(2001)127:8(663)出版年: AUG 2001被引频次: 3 (来自所有数据库)标题: Unstable cavitation behavior in a circular-cylindrical orifice flow作者: Sato, K; Saito, Y来源出版物: JSME INTERNATIONAL JOURNAL SERIES B-FLUIDS AND THERMALENGINEERING 卷: 45期: 3页: 638-645 DOI: 10.1299/jsmeb.45.638出版年: AUG 2002标题: Simulations of turbulent, cavitating flows in an injector slot/orifice 作者: Xu, C; Blaisdell, GA; Heister, SD丛书编者: Power, H; Brebbia, CA会议: 1st International Conference on Computational Methods in Multiphase Flow 会议地点: ORLANDO, FL会议日期: MAR 14-16, 2001会议赞助商: WessexInstTechnol; Univ Cent Florida标题: Visualization of internal flow in a cavitating slot orifice作者: Henry, ME; Collicott, SH来源出版物: ATOMIZATION AND SPRAYS 卷: 10期: 6页: 545-563出版年: NOV-DEC 2000被引频次: 12 (来自所有数据库)标题: Prediction of noise generated by orifice plates in liquid systems using a modified form of IEC 534-8-4 : 1994作者: Cairns, C; Whitson, RJ; Strachan, P; 等.丛书编者: Rahman, M; Brebbia, CA会议: 3rd International Conference on Advances in Fluid Mechanics 会议地点: MONTREAL, CANADA会议日期: MAY, 2000会议赞助商: WessexInstTechnol; Dalhousie Univ标题: Compromise orifice geometry to minimize pressure drop作者: Zhang, ZJ; Cai, JM来源出版物: JOURNAL OF HYDRAULIC ENGINEERING-ASCE 卷: 125期: 11页: 1150-1153 DOI: 10.1061/(ASCE )0733-9429(1999)125:11(1150)出版年: NOV 1999标题: Characteristics of flow through small sharp-edged cylindrical orifices作者: Ramamurthi, K; Nandakumar, K来源出版物: FLOW MEASUREMENT AND INSTRUMENTATION 卷: 10期: 3页: 133-143 DOI: 10.1016/S0955-5986( 99)00005-9出版年: SEP 1999被引频次: 43 (来自所有数据库)标题: The effect of manifold cross-flow on the discharge coefficient of sharp-edged orifices作者: Strakey, PA; Talley, DG来源出版物: ATOMIZATION AND SPRAYS 卷: 9期: 1页: 51-68出版年: JAN-FEB 1999被引频次: 8 (来自所有数据库)标题: The effect of oil type on flow and cavitation properties in orifices and annular clearances作者: Koivula, T; Ellman, A; Vilenius, M丛书编者: Burrows, CR; Edge, KA会议: Bath Workshop on Power Transmission and Motion Control (PTMC 99) 会议地点: UNIV BATH, BATH, ENGLAND会议日期: SEP 08-10, 1999会议赞助商: Univ Bath; CtrPowrTransmiss& Motion Control来源出版物: BATH WORKSHOP ON POWER TRANSMISSION AND MOTION CONTROL (PTMC 99) 页: 151-165出版年: 1999标题: Some characteristics of variable orifice nozzle geometrics for diesel injection作者: Soteriou, C; Smith, M; Andrews, R; 等.书籍团体作者: PROFESSIONAL ENGINEERING PUBLISHING LIMITED FOR INST OF MECHANICAL ENGINEERS; PROFESSIONAL ENGINEERING PUBLISHING LIMITED FOR INST OF MECHANICAL ENGINEERS会议: Conference on Fuel Injection Systems 会议地点: INST MECH ENGN, LONDON, ENGLAND会议日期: DEC 01-02, 1999会议赞助商: InstMechEngn, Combust Engines Grp; Lucas Diesel Syst来源出版物: FUEL INJECTION SYSTEMS 丛书: INSTITUTION OF MECHANICAL ENGINEERS SEMINAR卷: 1999期: 17页: 135-161出版年: 1999被引频次: 0 (来自所有数据库)标题: Diesel injection - laser light sheet illumination of the developmentof cavitation in orifices作者: Soteriou, C; Smith, M; Andrews, R书籍团体作者: INST MECH ENGINEERS会议: International Conference on Combustion Engines and Hybrid Vehicles 会议地点: INST MECH ENGINEERS HEADQUARTERS, LONDON, ENGLAND会议日期: APR 28-30, 1998会议赞助商: InstMech Engineers, Automobile Div; InstMech Engineers, Combust Engines Grp; Lucas Varity; SAE, UK; SociedadTecnicosAutomocion; Inst Marine Engines; Inst Elect Engineers; Japan SocMech Engineers来源出版物: INTERNATIONAL CONFERENCE ON COMBUSTION ENGINES AND HYBRID VEHICLES 丛书: IMECHE CONFERENCE TRANSACTIONS卷: 1998期: 4页: 137-158出版年: 1998标题: Effect of cavitation on flow and turbulence in plain orifices forhigh-speed atomization作者: He, L; Ruiz, F来源出版物: ATOMIZATION AND SPRAYS 卷: 5期: 6页: 569-584出版年: NOV-DEC 1995被引频次: 41 (来自所有数据库)Thompson, A. S., 2009, ―Experi mental Characterization of Flow Induced Vibration in Turbulent Pipe Flow,‖ M.S. thesis, Brigham Young University, Provo, UT.21Holt, G. J., 2011, ―Experimental Characterization of Baffle Plate Influence on Turbulent and Cavitation Induced Vibrations in Pipe Flow,‖ M.S. thesis, Brigham Young University, Provo, UT.Gilbarg, D., 1960, “Jets andCavities,”Handbuch der Physik, Band IX, Stromungsmechanik III, S.Fluuge, andC.Truesdell, eds., Springer-Verlag, Berlin, pp. 310–445.Pressure Losses and Limiting Reynolds Numbers for Non-Newtonian Fluids in Short Square-Edged Orifice PlatesButteurNtambaNtamba and Veruscha Fester[+] Author and Article InformationDissipation and Cavitation Characteristics of Single-Hole OrificesTullis, J. P., and Govindarajan, R., 1973, “Cavitation and Size Scale Effects for Orifices,” ASCE J. Hydr. Div., 99, pp. 417–430.umachi, F., Yamabe, M., and Oba, R., 1960, “Cavitation Effect on the Discharge Coefficient of the Sharp-Edged Orifice Plate,” ASME J. Basic Eng., 82(1), pp. 1–6. [CrossRef]Kolodzie, P. A., and Van Winkle, M., 1957, “Discharge Coefficients Through Perforated Plates,”AICHE J., 3, pp. 305–312. [CrossRef]Brennen, C. E., 1995, Cavitation and Bubble Dynamics, Oxford University Press, Oxford.9Holl, J. W., 1970, ―Nuclei and Cavitation,‖ ASME J. Basic Eng., 92(4), pp. 681–688. [CrossRef]Au-Yang, M. K., 2001, Flow Induced Vibration of Power and Process Plant Components: A Practical Workbook, ASME Press, New York.7Blevins, R. D., 1984, Applied Fluid Dynamics Handbook, Van Nostrand Reinhold Company, New York.Arndt, R. E. A., 1981, “Cavitation in Fluid Machinery and Hydraulic Structures,” Ann. Rev. Fluid Mech., 13, pp. 273–326. [CrossRef]Tullis, J. P., Powers, J. J., III, Shiers, P. F., and Hall, W. W., 1980, “Perforated Plates as Hydraulic Energy Dissipators,”Computer and Physical Modeling in Hydraulic Engineering, G.Ashton, ed., ASCE, Reston, VA, pp. 62–73.1Weaver, D. S., Ziada, S., Au-Yang, M. K., Chen, S. S., Padoussis, M. P., and Pettigrew, M. J., 2000, ―Flow-Induced Vibrations in Power and Process Plant Components: Progress and Prospects,‖ ASME J. Pressure Vessel Technol., 122(3), pp. 339–348. [CrossRef]2Testud, P., Moussou, P., Hirschberg, A., and Auregan, Y., 2007, ―Noise Generated by Cavitating Single-Hole and Multi-Hole Orifices in a Water Pipe,‖ J. Fluids Struct., 23, pp. 163–189. [CrossRef]Bohra, L. K., Mincks, L. M., and Garimella, S., 2004, “Pressure Drop Characteristics of Viscous Fluid Flow Through Orifices,” ASME Heat Transfer/Fluids Engineering Summer Conference, Charlotte, NC, July. Johansen, F. C., 1930, ―Flow Through Pipe Orifices at Low Reynolds Numbers,‖ Proc. R. Soc. London, Ser. A, 126 (801), pp. 231–245. [CrossRef]2Medaugh, F. W., and Johnson, G. D., 1940, ―Investigation of the Discharge and Coefficients of Small Circular Orifices,‖ Civil Engineering, 7 (7), pp. 422–424.3Alvi, S. H., Sridharan, K., and Lakshmana Rao, N. S., 1978, ―Loss Characteristics of Orifices and Nozzles,‖ ASM E J. Fluids Eng., 100 (3), pp. 299–307. [CrossRef]4Lakshmana Rao, N. S., Sridharan, K., and Alvi, S. H., 1977, ―Critical Reynolds Number for Orifice and Nozzle Flows in Pipes,‖ J. Hydraul. Res., 15 (2), pp. 167–178. [CrossRef]5Telis-Romero, J., Polizelli, M. A., Gabas, A. L., and TelisV. R. N., 2005, ―Friction Losses in Valves and Fittings for Viscoplastic Fluids,‖ Can. J. Chem. Eng., 83 , pp. 186–193. [CrossRef]6Bohra, L. K., Mincks, L. M., and Garimella, S., 2004, ―Pressure Drop Characteristics of Viscous Fluid Flow Through Orifices,‖ ASME Heat Tran sfer/Fluids Engineering Summer Conference, Charlotte, NC, July.7Edwards, M. F., Jadallah, M. S. M., and Smith, R., 1985, ―Head Losses in Pipe Fittings at Low Reynolds Numbers,‖ Chem. Eng. Res. Des., 63 , pp. 43–50. Available at /cgi-bin/somsid.cgi?type=header&record=17488Samanta, A. K., Banerjee, T. K., and Das, S. K., 1999, ―Pressure Losses in Orifices for the Flow of Gas-Non-Newtonian Liquids,‖ Can. J. Chem. Eng., 77 (3), pp. 579–583. [CrossRef]9ESDU International PLC, 2007, ―Incompressible Flow Through Orifice Plates–A Review of the Data in the Literature,‖ Data Item No. TN 07007.10Benedict, R. P., 1977, ―Loss Coefficients for Fluid Meters,‖ ASME J. Fluid s Eng., 99 (1) pp. 245–248. [CrossRef]11Ginsburg, I. P., 1963, "Applied Fluid Dynamics", Israel Program for Scientific Translations, Jerusalem.12Ward-Smith, A. J., 1971, "Pressure Losses in Ducted Flows", Butterworths, London.13McNeil, D. A., and Stuart, A. D., 2005, ―Highly Viscous Liquid Flow in Pipeline Components,‖ Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 219 (3), pp. 267–281. [CrossRef]14McNally Institute, 2010, ―Pump, Centrifugal Pumps, PD Pumps, Seals and Mechanical Seals Data,‖15White, F. M., 1999, "Fluid Mechanics", 4th ed., McGraw-Hill, New York.16Acheson, D. J., 1990, "Elementary Fluid Mechanics", Oxford University Press, New York.17Swamee, P. K., 2005, ―Discharge Equations for Venturimeter and Orificemeter,‖ J. Hydraul. Res., 43 (4), pp. 417–420. [CrossRef]18Miller, D. S., 1978, "Internal Flow Systems", BHRA Fluid Engineering, Cranfield, Bedfordshire.19Hooper, W. B., 1981, ―The Two-K Method Predicts Head Losses in Pipe Fittings,‖ Chem. Eng., August 24 , pp. 96–100.20Polizelli, M. A., Menegalli, F. C., Telis, V. R. N., and Telis-Romero, J., 2003, ―Friction Losses in Valves and Fittings for Power-Law Fluids,‖ Braz. J. Chem. Eng.,20 (4), pp. 455–463. [CrossRef]21Slatter, P. T., 1996, ―The Laminar/Turbulent Transition—An Industrial Problem Solved,‖ British Hydromechanics Research Group 13th International Conference on Slurry Handling and Pipeline Transport (Hydrotransport 13), Johannesburg, South Africa, Sept. 3–5.22Fester, V. G., Mbiya, B., and Slatter, P., 2008, ―Energy Losses of Non-Newtonian Fluids in Sudden Pipe Contractions,‖ Chem. Eng. J., 145 , pp. 57–63. [CrossRef]23ANSI/API, 1995, ―Manual of Petroleum Measurement Standards. Chapter 14—Natural Gas Fluids Measurement, Section 3—Concentric, Square-Edged Orifice Meters,‖ Aga Report No. 3, Part 1, Gpa 8185-90, ANSI/API 2530-1991, Parts 1, 2, 3, and 4.24Massey, B. S., 1970, "Mechanics of Fluids", 2nd ed., Van Nostrand Reinhold, New York.25Slatter, P. T., and Pienaar, V. G., 1999, ―Establishing Dynamic Similarity for Non-Newtonian Fittings Loss,‖ British Hydromechanics Research Group 14th International Conference on Slurry Handling and Pipeline Transport (Hydrotransport 14), Maastricht, The Netherlands, pp. 245–254.26Govier, G. W., and Aziz, K., 1972, "The Flow of Complex Mixture in Pipes", Van Nostrand Reinhold, New York.27Hanks, R. W., 1979, ―The Axial Laminar Flow of Yield Pseudoplastic Fluids in a Concentric Annulus,‖ Ind. Eng. Chem. Process Des. Dev., 18 (3), pp. 488–493. [CrossRef]28Lazarus, J. H., and Slatter, P. T., 1987, ―A Method for Rheological Characterization of Tube Viscometer Data,‖ J. Pipelines, 7 , pp. 165–176.29Miller, D. S., 1996, "Internal Flow: A Guide to Losses in Pipe and Duct Systems", BHRA Group, Cranfield, Bedfordshire.30Lakshmana Rao, N. S., and Sridharan, K., 1972, ―Orifice Losses for Laminar Approach Flow,‖ J. Hydraul. Div., 98 (11), pp. 2015–2034. Available at/cgi/WWWdisplay.cgi?12791731Rangaraju, K. G. and Jain, A. K., 1978, ―Energ y Loss Due to Sharp Edged Orifice Meters,‖ Irrig. Power, 35 (3) pp. 401–406. Available at /Record/IND7903051232Shima, N., 1984, ―Loss and Discharge Characteristics of a Flow of Polymer Solutions Through Pipes Orifices,‖ Bu ll. JSME, 27 (225), pp. 443–449. [CrossRef]33Humpherys, A. S., 1987, ―Energy Dissipation in Low Pressure Irrigation Pipelines: II Orifices,‖ Trans. ASAE, 30 (1), pp. 176–182. Available at /473/1/596.pdfY. Tomita and A. Shima, “Mechanisms of impulsive pressure generation and damage pit formation by bubble collapse,”J. Fluid Mech.169, 535 (1986).C.-T. Hsiao, G. L. Chahine, and H.-L. Liu, ―Scaling effect on prediction of cavitation inception in a line vortex flow,‖J. Fluids Eng.125, 53 (2003)./10.1115/1.1521956Y. Kuhn de Chizelle, S. L. Ceccio, and C. E. Brennen, “Observations and scaling of traveling bubble cavitation,”J. Fluid Mech.293, 99 (1995).Cavitation Bubbles Near BoundariesAnnual Review of Fluid MechanicsS. Gopalan, J. Katz and O. Knio, ―The flow structure in the near field of jets and its effect on cavitation inception,‖J. Fluid Mech.398, 1 (1999)./10.1017/S0022112099006072G. L. Chahine and Y. T. Shen, “Cavitation bubbles near boundaries.”J. Fluids Eng.108, 99 (1986).标题: Growth, oscillation and collapse of vortex cavitation bubbles作者: Choi, Jaehyug; Hsiao, Chao-Tsung; Chahine, Georges; 等.来源出版物: JOURNAL OF FLUID MECHANICS 卷: 624页: 255-279 DOI: 10.1017/S0022112008005430出版年: APR 10 2009标题: Prediction of tip vortex cavitation inception using coupled spherical and nonspherical bubble models and Navier-Stokes computations作者: Hsiao, CT; Chahine, G79.I. D. Pearce and A. Lichtarowicz, ―Discharge performance of long orifices with cavitating flow,‖ Proceedings of Second Fluid Power Symposium, Guildford,UK, 1971.A. Yamaguchi and T. Suzuki, “Cavitation in hydraulic fluids. Part 3: Oncavitation in long orifices,”J. Fluid Control12, 21 (1980).J. P. Tullis, “Cavitation scale effects for valves,”J. Hydraul. Div., Am. Soc. Civ. Eng.99, 1109 (1973).Flow characteristics of a micro-orificeAmmourah, S.A.a, Benim, A.C.b, Maqableh, A.M.c, Khadrawi, A.F.c, Al-Nimr, M.A.dA criterion for flow mechanisms through vertical sharp-edged orifice and model for the orifice discharge coefficientCao, R., Liu, Y., Yan, C.Flow characteristics of a micro-orificeAmmourah, S.A.a, Benim, A.C.b, Maqableh, A.M.c, Khadrawi, A.F.c, Al-Nimr, M.A.dCharacteristics of R-123 two-phase flow through micro-scale short tube orifice for design of a small cooling systemJin, S.a, Sung, T.a, Seo, T.b, Kim, J.a∙Experimental study of discharge coefficient and cavitation for different nozzle geometries ∙Kim, S.R., Ku, K.W., Hong, J.G., Lee, C.W.CFD analysis of flowfield and cavitation in aSharp-Edged circular orificeKyparissis, S.D.a, Margaris, D.P.bOFFICE CAVITATION AND ITS EFFECT ON SPRAY MIXING.(1976) Journal of Fluids Engineering, Transactions of the ASME, 98 Ser 1 (4), pp.681-687. Cited 154 times.Cavitation indices for high pressure orifice plate energydissipators(1988) International Journal of Mechanical Sciences, 30 (9), pp. 637-657.The effect of orifice plate geometry upon discharge coefficient (1990) Flow Measurement and Instrumentation, 1 (3), pp. 133-140. Cited 12 times.Flow regime transitions due to cavitation in the flow through an orifice(1990) International Journal of Multiphase Flow, 16 (6), pp. 1023-1045. Cited 46 times.Andrews, K.A., Sabersky, R.H.Flow Through an Orifice From a Transverse Stream(1990) Journal of Fluids Engineering, 112 (4), pp. 524-526. Cited 4 times.DecemberAlajbegovic, A.Three-Dimensional Cavitation Calculations in Nozzles(1999) 2nd Annual Meeting Institute ForMultifluid Science and TechnologySanta Barbara, California, USA, MarchYuan, W., Sauer, J., Schnerr, G.H.Modeling and computation of unsteady cavitation flows in injection nozzles(2001) Mecaniqueet Industries, 2 (5), pp. 383-394. Cited 36 times.doi: 10.1016/S1296-2139(01)01120-4Sato, K., Saito, Y.(2001) Unstable Cavitation Behavior In a Circular-Cylindrical Orifice Flow4th International Symposium on Cavitation, Pasadena, California, USA, JuneBorutzky, W., Barnard, B., Thoma, J.An orifice flow model for laminar and turbulent conditions(2002) Simulation Modelling Practice and Theory, 10 (3-4), pp. 141-152. Cited 38 times. Archer, A.A predictive model for cavitation erosion downstream orifices (2002) American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED, 257 (1 A), pp. 403-409.doi: 10.1115/FEDSM2002-31012Vortmann, C., Schnerr, G.H., Seelecke, S.Thermodynamic modeling and simulation of cavitating nozzle flow (2003) International Journal of Heat and Fluid Flow, 24 (5), pp. 774-783. Cited 29 times.doi: 10.1016/S0142-727X(03)00003-1Yagi, Y., Murase, M., Sato, K., Hattori, S.Mechanism of cavitation erosion at the exit of a long orifice(2003) Proceedings of the ASME/JSME Joint Fluids Engineering Conference, 1 B, pp. 1359-1364. Cited 2 times.ISBN: 0791836967Chen, Y., Lu, C.-J., Wu, L.Modelling and computation of unsteady turbulent cavitation flows (2006) Journal of Hydrodynamics, 18 (5), pp. 559-566. Cited 21 times.doi: 10.1016/S1001-6058(06)60135-2De Giorgi, G.M., Chiara, F., Ficarella, A.Experimental Study of Thermal Cavitation in an Orifice(2006) 8th ASME Conference On Engineering Systems Design and Analysis, 1, pp. 523-529.。

Design and characterization of bubble-splitting distributor for scaled-out multiphase microreactors

Design and characterization of bubble-splitting distributor for scaled-out multiphasemicroreactorsDuong A.Hoang,Cees Haringa,Luis M.Portela,Michiel T.Kreutzer,Chris R.Kleijn,Volkert van Steijn ⇑JM Burgers Centre for TU Delft Process Technology Guidelines on how to operate a bubble-splitting distributor.a r t i c l e i n f o Article history:Received 17June 2013Received in revised form 5August 2013Accepted 14August 2013Available online 2September 2013Keywords:Microbubble Bubble breakup Conﬁnement Numbering upAsymmetric breakupa b s t r a c tThis paper reports an analysis of the parallelized production of bubbles in a microreactor based on the repeated break-up of bubbles at T-junctions linked in series.We address the question how to design and operate such a multi-junction device for the even distribution of bubbles over the exit channels.We study the inﬂuence of the three primary sources leading to the uneven distribution of bubbles:(1)nonuniformity in the size of bubbles fed to the distributor,(2)lack of bubble break-up,and (3)asymmetric bubble breakup caused by asymmetries in ﬂow due to fabrication tolerances.Based on our theoretical and experimental analysis,we formulate two guidelines to operate the multi-junction bubble distributor.The device should be operated such that:(i)the capillary number exceeds a critical value at all junctions,Ca >Ca crit ,to ensure that all bubbles break,and (ii)the parameter (l s /w )ÁCa 1/3is sufﬁciently large,with l s /w the distance between the bubbles normalized by the channel width.More quantitatively,(l s /w )ÁCa 1/3>2for fabrication tolerances below 2%,which are typical for devices made by soft lithography.Furthermore,we address the question whether including a bypass channel around the T-junctions reduces ﬂow asymmetries and corresponding nonuniformities in bubble size.While bubble nonuniformities in devices with and without bypass channels are comparable for fabrication tolerances of a few percent,we ﬁnd that incorporating a bypass channels does have a beneﬁcial effect for larger fabrication tolerances.The results presented in this paper facilitate the scale-out of bubble-based microreactors.Ó2013Elsevier B.V.All rights reserved.1.IntroductionMultiphase microreactors have emerged as an attractive class of reactors for the production of ﬁne chemicals and pharmaceuticals [1,2],for the synthesis of micro-and nanoparticles [3–7],and for high-throughput screening applications [8–11].Besides excellent heat and mass transfer characteristics in microreactors,continuous ﬂow chemistry basedon the conﬁnement of reactions in picoliter1385-8947/$-see front matter Ó2013Elsevier B.V.All rights reserved./10.1016/j.cej.2013.08.066Corresponding author at:Department of Chemical Engineering,Delft University of Technology,Julianalaan 136,2628BL Delft,The Netherlands.Tel.:+31152787194.E-mail address:v.vansteijn@tudelft.nl (V.van Steijn).to nanoliter bubbles or droplets(a)enhances mixing,(b)reduces axial dispersion,and(c)prevents precipitation at walls and clog-ging of channels such that higher yields and selectivities are ob-tained[10,12].Despite the conceptually simple idea of numbering-up as a strategy to increase throughput,parallelization of segmentedﬂows remains a challenge in practice[13].One basic approach to in-crease throughput of segmentedﬂow microreactors is to produce droplets or bubbles in each individual channel[14–24].With a few notable exceptions[25–27],this approach requires that the supply of theﬂuids to all these channels is identical,as differences inﬂow lead to corresponding differences in the volume,frequency, and speed of the bubbles or droplets.Integrating resistive channels upstream of the segmentedﬂow channels minimizes cross-talk be-tween the channels and ensures a constant supply ofﬂuids,which is not affected by the dynamic pressureﬂuctuations in the seg-mentedﬂow channels[17,28].de Mas et al.[17]showed that the pressure drop over the resistive channels should be two orders of magnitude larger than the pressure drop over the segmentedﬂow channels.Fulﬁlling this requirement is particularly challenging for gas–liquidﬂows,because the low viscosity of gas requires resistive gas channels that are roughly two orders of magnitude smaller in width than the segmentedﬂow channels.These channels should be fabricated with high precision,as small difference in their hydrodynamic resistance lead to differences in the features of the segmentedﬂows running in parallel.An alternative approach that does not require on-chip integra-tion of resistive feed channels is to feed a segmentedﬂow to the chip,and split the bubbles or droplets at a series of successive junc-tions[29–33].To obtain segmentedﬂows with an identical bubble volume and bubble spacing in all channels downstream the bubble distributor,two key questions need to be addressed:(1)how to en-sure breakup at all junctions,(2)how to minimize asymmetries in ﬂow.Theﬁrst question can be addressed based on the understand-ing of breakup of bubbles or droplets at single T-junctions. Whether a droplet breaks primarily depends on its length relative to the channel width,l/w,and on the capillary number,Ca[34–39]. Of secondary importance is the viscosity contrast between the two phases[40,41].The second question can be addressed by consider-ing the differences in hydrodynamic resistances of the channels due to fabrication inaccuracies.As well known for single T-junc-tions,a difference in velocity in the two exiting arms leads to the asymmetric breakup of bubbles[34,42–45].Consequently,the size of the bubbles and their distance apart is different in the two exit-ing arms.For a multi-junction device,Adamson et al.[29]identi-ﬁed a second cause for unequalﬂow distribution:if bubbles enter downstream T-junctions at times that are not precisely coor-dinated,the backpressure generated when the bubbles split causes an imbalance in the pressure drops across the two exiting arms of the upstream T-junctions.This also leads to asymmetries in seg-mentedﬂows.They showed that this source of variation is reduced by designing the system such that the magnitude of the pressure pulses is negligible with respect to the total pressure drop over the branches.Another clever trick to reduce the inﬂuence of pres-sure pulses at downstream T-junctions is to reduce the coupling between the successive T-junctions by incorporating a pressure-equalizer at the T-junctions in the form of a bypass-like structure [32].Although this concept has been demonstrated,no quantative data is available on the inﬂuence on this bypass.Summarizing the work done on multi-junction bubble and droplet distributors,we conclude that–although there are some pointers on how to design and operate these devices–there is no systematic study how key operating conditions inﬂuence the performance,and to what extend polydispersity is reduced by incorporating a pressure equalizer.In this paper,we start with a discussion on the different design strategies and explain why a design thatﬁxes the relative length of the bubbles or droplets is favorable over other types of design.We then identify three primary sources leading to the uneven distribu-tion of bubbles and systematically study their inﬂuence on the uni-formity of the size of bubbles in the downstream channels of a multi-junction device.Additionally,we quantify to what extend ﬂow asymmetries are reduced with the use of a pressure equalizer. In short,this paper teaches how to design and operate a multi-junction bubble distributor.2.Theory on the design and operation of a multi-junction bubble distributor2.1.DesignNon-breaking bubbles are one of the main sources of polydis-persity.A straightforward approach to ensure breakup at all suc-cessive junctions is to design the network such that l/w and Ca are kept the same at all junctions.Operating the device above the transition line(Ca crit=f(l/w))at theﬁrst junction then ensures breakup at all successive junctions.But,in the planar networks that are commonly used in theﬁeld of microﬂuidics Ca and l/w can-not beﬁxed at the same time.This is easily seen from the fact that theﬂow rate entering a junction hw i v i equals twice theﬂow rate in the two exiting channels hw i+1v i+1that lead to the next junctions, with h the channel height,w the channel width,v the bubble veloc-ity,and i the index of the junction.Hence,v iþ1¼1w iiþ1v i.Deﬁning the capillary number based on the bubble velocity,the viscosity of the compartments between the bubbles,l,and the interfacialNomenclaturea i design constant for i th junction needed in Eq.(6)(–)b design parameter(–)c interfacial tension(N/m)g fraction of breaking bubbles(–)l dynamic slug viscosity(Pa s)Ca capillary number,l v/c(–)CV coefﬁcient of variation(–)a,b constants in Leshansky’s equation for the critical capil-lary numberC constant needed in Eq.(3)C1ÀC4constants needed in Eq.(4)h channel height of planar device(m)i index of channel or junction(–)l bubble length(m)l bp bypass length(m)l s slug length(m)l average bubble length(m)r(l)standard deviation in bubble length(m)m number of non-breaking bubbles(–)n number of bubbles(–)q volumetricﬂow rate(m3/s)R hydrodynamic resistance(Pa s/m3)u(x)deviation in parameter xv i average channel velocity(single phaseﬂow)or bubble velocity(two phaseﬂow)in the i th generation(m/s)w i channel width of i th generation(m)546 D.A.Hoang et al./Chemical Engineering Journal236(2014)545–554tension,c,according to Ca=l v/c,we henceﬁnd that the capillary number decreases at successive junctions according toCa iþ1¼1w iiþ1Ca i.Similarly,the volume of a bubbleﬂowing into ajunction$hw i l i equals twice the volume of the daughter droplesleaving the junction$hw i+1l i+1.Hence,l iþ1¼12w iw iþ1l i such that therelative length decreases at successive junctions according tol iþ1=w iþ1¼1w2i2iþ1l i=w i.This simple analysis shows thatﬁxing Ca re-quires a reduction in width by a factor2in successive junctions, whereas a21/2reduction is needed toﬁx the relative length l/w [29].Fixed l/w-designs[29]andﬁxed Ca-designs[30]have both been demonstrated,as well as designs in which the width of the channels isﬁxed such that both Ca and l/w decrease at successive junctions[34].These three design strategies are illustrated in Fig.1a–c for a network in which segmentedﬂow is distributed over four channels by breaking the incoming stream of bubbles at two successive generations of T-junctions.Of course,other choices are possible for w i/w i+1=2b,but for the sake of simplicity we limit the discussion to designs with aﬁxed w(b=0,Fig.1a),aﬁxed l/w (b=0.5,Fig.1b),and aﬁxed Ca(b=1,Fig.1c).To compare these different designs,we calculate the values of Ca and l/w required in the feed channel(i)and in the channels downstream of theﬁrst junction(ii)to obtain a desired Ca and l/w in the output channels(iii).This desired point is indicated by a star in the(l/w,Ca)map sketched in Fig.1d and lies above the transition line.Below this line(shaded area),breakup does not occur.As shown for theﬁxed width device(b=0),relatively long bubbles or droplets need to be fed to theﬁrst junction at relatively high Ca.Both these requirements pose a problem,because long droplets or droplets might spontaneously breakup[29],while operating at high Ca leads to the formation of satellites during breakup[30].By contrast,theﬁxed Ca-design(b=1)requires a feed of short bubbles or droplets to theﬁrst junction,which are exceedingly difﬁcult to break.For the example discussed here, the bubble length in channels(i)and(ii)is below the required length for pared to theﬁxed-width andﬁxed-Ca de-signs,theﬁxed l/w-design(b=0.5)can be operated at relatively low values of Ca and l/w,while ensuring that breakup occurs at all successive junctions.We therefore focus on theﬁxed relative length-design in this paper.We conclude this section on the design by illustrating the de-sign methodology for theﬁxed relative length-design based on a practical example.Suppose one aims to produce a gas–liquid seg-mentedﬂow in8parallel channels that each have a height and width of50l m,with bubbles having a length of200l m.One then uses a cascade with three generations.For a desired bubble veloc-ity in these exit channels of10cm/s,the corresponding capillary number can be calculated using theﬂow properties.Taking,for example,a viscosity of1mPa s and an interfacial tension of 5mN/m,Ca=2Â10À2.Knowing the relative length and capillary number in the8exit channels,one calculates the relatively length and capillary number in the channels leading to the T-junctions of the last generation andﬁnds l/w=4,Ca=2.8Â10À2.To ensure that bubbles break at all junctions of the device,it is sufﬁcient to check whether the capillary number in the channels leading to the last generation of T-junctions is larger than the critical capillary num-ber for the desired relative length l/w=4.As explained later in Sec-tion 4.4,the critical capillary number can be calculated using Ca crit=0.98(l/w)À3.60.After conﬁrming that Ca>Ca crit,the only thing left to do is to calculate the relative length and velocity of the bubbles that need to be fed to the multi-junction device.2.2.OperationThroughout this paper,we quantify the nonuniformity in bub-ble size based on the coefﬁcient of variation CV.Unless stated otherwise,we use the following deﬁnition:CV¼rðlÞlð1Þwith l and r(l)the average bubble length and the standard deviation in bubble length.2.2.1.Inﬂuence of non-breaking bubbles on size uniformityWe now quantify the inﬂuence of non-breaking bubbles on the size uniformity.For a single T-junction,it is straightforward to cal-culate how the polydispersity is inﬂuenced in case m out of n incoming bubbles do not break.The coefﬁcient of variation,CV out, of the bubbles leaving the two arms of the T-junction depends on the coefﬁcient of variation,CV in,of the incoming bubbles,and on the breakup fraction deﬁned as g=(nÀm)/n according toCV2outþ1CV2inþ1¼g1ÀgðÞ2þ1ð2ÞTo demonstrate the sensitivity of CV out on the break-up fraction,we calculate CV out for several values of g for the case CV in=0.This shows that1%non-breaking bubbles(g=0.99)already leads to a polydisperse size distribution with a value of CV out=0.07.For5% and10%non-breaking bubbles,the coefﬁcients of variation are 0.15and0.21,respectively.This simple analysis hence shows the importance to ensure that all bubbles break.2.2.2.Inﬂuence ofﬂow asymmetries due to fabrication errors on size uniformityEnsuring that all bubbles break is a necessary but not sufﬁ-cient condition to ensure a narrow size distribution.We now fo-cus on the question how asymmetries inﬂow that are caused by fabrication errors inﬂuence the polydispersity.This analysisalso D.A.Hoang et al./Chemical Engineering Journal236(2014)545–554547reveals how polydispersity in bubble size at the exit of the paral-lel channels is inﬂuenced by the size uniformity of the bubbles fed to the bubble distributor.For the sake of simplicity,we start the analysis by considering a single T-junction.We hereby con-sider fabrications errors only in the height of the channels.For microchannels fabricated using soft lithography,this assumption is justiﬁed by the fact that tolerances in channel width or length are typically much smaller than tolerances in channel height.We assume that the height of one of the exit channels is h Àu (h ),while the height of the second exit channel is h +u (h ).The differ-ence in height leads a difference velocities,v Àu (v )and v +u (v ).Consequently,the lengths of the two daughter droplets follow from (v +u (v ))/(l +u (l ))=(v Àu (v ))/(l Àu (l ))[34].Similarly,the length of the compartments (slugs)between the bubbles or drop-lets after split-up follows from (v +u (v ))/(l s +u (l s ))=(v Àu (v ))/(l s Àu (l s )).For channels of equal length,the number of bubbles and compartments is n Àu (n )and n +u (n )in the channels with higher and lower velocity respectively,according to (v +u (v ))/(v Àu (v ))=(n Àu (n ))/(n +u (n )).To understand how the relative ﬂow asymmetry,u (v )/v ,depends on the relative error in channel height u (h )/h ,the capillary number,the height-to-width ratio of the channel,h /w ,and the dimensionless length of the compart-ment between bubbles,we equate the pressure drop over the two exiting channels.To predict the pressure drop over a channel of width w and height h <w through which n bubbles of length l and n slugs of length l s ﬂow at a velocity v ,we use a similar expression as in Refs.[46–48]D p ¼n 12l l s 1À0:63h 1h2v þnC c 2w þ2h3Ca ðÞ2=3ð3Þwith l the viscosity of the compartments between the bubbles,c the interfacial tension and C an order one constant [46,49,50].We hereby neglect the viscous pressure drop over the gas bubbles,and deﬁne the capillary number as Ca =l v /c .Substituting the expressions for the lengths of the bubbles and liquid compartments,the bubble velocity,the number of compartments,and the channel height,we ﬁnd expressions for the two pressure drops over the two exiting channels.Equating these pressure drops and solving for u (v )/v under the assumption u (v )/v (1yieldsu ðv Þv¼C 3ÀC 1ðÞl sw Ca 1=3þðC 4ÀC 2ÞC 1þC 3ðÞl sCa 1=3ÀðC 2þC 4Þ=3ð4ÞwithC 1¼121À0:63h w 1þu ðh Þh h i w 2h21þu ðh Þh !À2C 2¼2C 1þw h 1þu ðh Þh!À1 !32=3C 3¼121À0:63h w1Àu ðh Þh h i w 2h 21Àu ðh Þh !À2C 4¼2C 1þw 1Àu ðh Þ!À1 !32=3As expected for the single phase limit (long slugs,high velocity)andsmall fabrication errors,this reduces to u ðv Þv %2þ0:63h w 1À0:63h wu ðh Þh.This simple model teaches how a small difference in channel heightleads to asymmetries in ﬂow for a single T-junction.We now extend the analysis to a multi-junction device.For a cascade device with k generations,it is straightforward to show that the coefﬁcient of variation for the bubbles collected at the 2k exiting channels,CV out ,depends on the coefﬁcient of variation ofthe bubbles fed to the device,CV in ,and the asymmetries in ﬂow at the different generations,(u (v )/v )i ,according toCV 2outþ1CV in þ1¼Y k i ¼11þu ðv Þv 2i !ð5ÞWe hereby used the simplifying assumption that the ﬂow asymme-tries at the junctions in the same generation are identical.For theﬁxed relative length design considered in this study,with narrow-ing channels immediately after the T-junctions,the ﬂow asymme-tries can be written asu ðv Þvi¼C 3ÀC 1ðÞa i l s w ÀÁ0Ca 1=30þðC 4ÀC 2ÞC 1þC 3ðÞa i l sw ÀÁ0Ca 1=30ÀðC 2þC 4Þ=3ð6Þwith a i ¼2Ài =6;l s ÀÁthe dimensionless length of the compartments between the bubbles fed to the multi-junction device,and Ca 0the capillary number based on the velocity in the feed channel.In the three-generation network used in this work,we do not narrow the channel in the third generation,such that a 1=2À1/6,a 2=2À2/6,and a 3=2À5/3.For this design,Fig.2a shows how the uniformity of sizeof the bubbles leaving the 8exit channels depends on ðl s 0=w 0ÞCa 1=3for three values of u (h )/h .For large ðl s 0=w 0ÞCa 1=30,the uniformity of548 D.A.Hoang et al./Chemical Engineering Journal 236(2014)545–554the bubble size is nearly constant and approaches ﬂow uniformitiesfor single phase ﬂow.For ðl s 0=w 0ÞCa 1=3approaching zero,the nonuni-formity sharply increases.The contribution of each generation to the nonuniformitiy in the size of bubbles leaving the device is shown in Fig.2b.This ﬁgure shows that ﬂow asymmetries in the ﬁnal gener-ation of T-junctions are the main cause of nonuniformities in bubble size for the design used in this work.In summary,the model (Eqs.(5)and (6))developed in this section enables one to predict the nonuniformity in bubble size at the exit of a multi-junction device caused by (i)nonunifor-mity in the size of bubbles fed to the distributor,and (ii)differ-ence in channel height due to fabrication errors.We note that this model is different from the model proposed by [29],who identiﬁed pressure pulses caused by bubbles entering down-stream channels as the main source of ﬂow asymmetries.Since we consider ﬂows at higher values of the capillary number (Ca >0.01)in this paper,the magnitude of such pressure pulses (c /w )[47],is negligible compared to the pressure drop over a channel (Eq.(3)).We can hence ignore pressure pulses generated by breaking bubbles or bubbles entering the narrowing channel segments.Inﬂuence of the bypass.Including a bypass around the T-junction can reduce ﬂow asymmetries considerably.This is easily seen from an analysis based on hydrodynamic resistances as shown in Fig.3.The asymmetry in relative velocity can be expressed in terms of the ﬂow rates,q br and q bl ,in the two branches between the T-junc-tion and the exits of the bypass,as u (v )/v =(q br Àq bl )/(q br +q bl ).It is straightforward to show that the asymmetry in velocity depends on the hydrodynamic resistances of the bypass,the two branches between the T-junction and the exit of the bypass,and the two channels leading to the exit of the device according tou ðv Þv¼R br ÀR bl þR l ÀR r ðÞR b R b þR l þR rR br þR bl þR l þR r ðÞbR b þR l þR rð7ÞFor a bypass with a low resistance (R b ?0),the ﬂow assymmetry hence only depends on the difference in hydrodynamic resistance of the two short branches of the bypass u (v )/v =(R br ÀR bl )/(R br +R bl ).In case no bubbles are present in the short branches except the breaking bubble,ﬂow asymmetries in a bypass device can be approximated by the single phase limit u ðv Þv %2þ0:63h w 1À0:63h wu ðh Þh de-rived before.For distances between the bubbles exceeding the dis-tance between the T-junction and the exit of the bypass (l s >l bp ),we hence expect that the coefﬁcient of variation depends on the fabri-cation inaccuracy and is independent of the conditions as long as the device is operated above the critical capillary number.It is important to note that for slugs shorter than the length of the by-pass (l s <l bp ),bubbles preceeding the breaking bubble likely block the exit of the bypass.With the bypass shut off under these condi-tions,devices with and without a bypass obviously yield the same coefﬁcient of variation.3.ExperimentalWe fabricated our devices in PDMS using standard soft lithogra-phy techniques [51].Channels are sealed against PDMS coated glass slides using an air plasma.The devices consist of a T-junction bubble maker,an additional liquid inlet,and three generations of T-junctions as shown in Fig.4a and b.While the size of the bubbles is controlled by the ﬂow rate of gas q G and liquid q L injected at the bubble maker,the velocity or distance between the bubbles is con-trolled using a second liquid stream q L 2injected from the side channel shown in Fig.4a.We used a ﬁxed relative length design to study the distribution of bubbles over the eight parallel exit chan-nels.The width of the feed channel is w 0=100l m.To ﬁx the rela-tive length of the droplets,we narrowed the channels leading to the second and third generation of T-junctions to w 1=71l m and w 2=50l m,respectively.The fabrication inaccuracy in the widths of the channels is below 1l m.To quantify the effect of pressure equalizers,we studied the distribution of bubbles in devices with-out and with bypass channels around the T-junctions (Fig.4c).The height of the channels in the devices with and without bypass were h =41±1l m and h =43±1l m,respectively.We complementedbypassl bpFig.3.A bypass channel around in ﬂow.This can be understood from analogy with the electrical circuit (b)(c)bypass12345678(a)q L2q Lq GA steady stream of bubbles is produced at a T-junction from a liquid injected at ﬂow rates q G and q L .The additional liquid stream side channel at a rate q L 2enables the independent control of the the bubbles and their distance apart.Once spaced out,the bubbles distributed over 8parallel channels by splitting them at three successive (b)and with (c)a bypass channel.Scale bars:500l m.D.A.Hoang et al./Chemical Engineering Journal 236(2014)545–554549the experiments in the multi-junction devices with experiments performed in single T-junctions to reveal the inﬂuence of the height-to-width ratio of the channels on the transition line be-tween breakup and non-breakup.We used three single T-junction splitters with aspect ratios of h/w=0.27,0.59and0.94.We used HFE-7500(3M,l=1.2mPa s,c=16.2mN/m)and air as workingﬂuids,without the addition of surfactants.The liquid ﬂow rates were controlled using two individual syringe pumps (Harvard pico plus11).Theﬂow rates were in the range 3<q L<20l m/min and4<q L2<100l m/min.A steady airﬂow was supplied from aﬁxed pressure source and controlled using a reducing valve in the range between2and6bar.Air was injected into the microﬂuidic device through a4À7m long capillary tube with internal diameter of25l m.The pressure drop over this tube is much larger than the pressure drop over the chip.This ensures a steady airﬂow rate,which is independent of(temporal)events in the chip such as bubble breakup.We conﬁrm that for the range of gas and liquidﬂow rates used in this work,we did not observeﬂuc-tuations in the speed of bubbles caused by pressureﬂuctuations arising from the gas pressure source or the mechanics of the syr-inge pump.To image theﬂow,we used a high speed camera(Phan-tom V9.1,Vision Research)attached to an inverted microscope (Axiovert200M,Zeiss).We extracted the length of the bubbles, their distance apart,and their velocity from the images.We used a magniﬁcation and frame rate such that the inaccuracy in the length and velocity measurements is below2%.4.Results4.1.Inﬂuence of non-breaking bubbles on size uniformityIn aﬁrst set of experiments,we studied the inﬂuence of non-breaking bubbles on size uniformity.To study this inﬂuence separately from the inﬂuence ofﬂow asymmetries caused by fab-rication inaccuracies,we operated the device at sufﬁciently largevalues ofðl s=wÞ0ÁCa1=3such that the contribution ofﬂow asymme-tries to the coefﬁcient of variation is negligible.For typical fabrica-tion inaccuracies in this work(u(h)/h<0.02),this requires that weoperated the device beyondðl s=wÞ0ÁCa1=3>1:75as can be seenfrom Fig.2b.Based on the model in Section2.2.1,we expect that the coefﬁ-cient of variation is small in case all bubbles break(g=1).This, in turn,is expected when the device is operated such that the cap-illary number is beyond the critical capillary number at all T-junc-tions.For theﬁxed relative length design used in this study,the capillary number,Ca2,at theﬁnal generation of T-junctions is the smallest.We hence expect small coefﬁcients of variation for Ca2> Ca crit.By contrast,CV out is expected to sharply increase for decreas-ing g.We tested these hypotheses by measuring CV out as a function of Ca.To this end,we recorded movies at the eight exit channels and measured the length of all bubblesﬂowing through each exit channel for a given time window.We adjusted Ca such that the length of the bubbles in the feed stream is comparable in all exper-iments(3.1<l0/w0<3.8).We used the average bubble lengths measured upstream of the last junctions to calculate the critical va-lue of the capillary number for each experiment based on Leshan-sky’s relation Ca crit=a(l/w)b,where we used a=0.98and b=À3.60as explained later in Section4.4.For capillary numbers below the critical capillary number,we indeedﬁnd that a signiﬁcant fraction of bubbles fed to the distrib-utor does not breakup as illustrated in the snapshot of the eight exit channels in Fig.5a.By contrast,all bubbles break(g=1)when operating the device beyond the critical capillary number(Fig.5b). The corresponding histograms of the bubble length measured at the eight exit channels show a large spread in bubble length for Ca<Ca crit,while a narrow size distribution is obtained for Ca>Ca crit as shown in Fig.5c.For these two examples,the corresponding values of the coefﬁcient of variation based on all bubbles leaving the device are CV out=0.21and CV out=0.05, respectively.In addition to the two examples shown in Fig.5a,we further illustrate the inﬂuence of Ca on CV out for a wider range of Ca/Ca crit. For Ca2/Ca crit>1,weﬁnd that the coefﬁcient of variation is small(a)12345678(b)(c)exit 1exit 2100200300400exit 3exit 443012exit 6exit 7exit 8exit 5100200300400100200300400400NNNη =0.62η = 1η = 1η = 0.62η = 1η = 0.62η = 1η = 0.62η = 1η = 0.62η = 1η = 0.62η = 1η = 0.62η = 1η = 1500 μm500 μm4301243012430124301243012550 D.A.Hoang et al./Chemical Engineering Journal236(2014)545–554。

新世纪大学英语系列教材综合教程3词汇

U1biased偏袒一方placement安置、就业安排counselor顾问assure使确信reliable可靠的，可信赖的busboy餐厅勤杂工dumpy矮胖的syndrome综合症bus收拾碗碟mouthy夸夸其谈的yuppie雅皮士snob势利小人silverware银质制品napkin餐巾for fear of害怕dread害怕truckstop公路边的廉价餐馆germ病毒expense account账户开支flirt调情卖俏wrap sb around one’s little finger 随心所欲地支配某人regular常客、老主顾mascot吉祥物pepper胡椒粉in place在适当位置上crumb面包屑visible可见的get/be done with做完，结束hover徘徊in the background不显眼，在幕后scrawl乱写乱画count the days热切地盼望jeopardy危险empty走出procession行列，游行队伍mess杂乱saucer茶托、茶杯碟crooked弯曲的dozens of很多clean up清理stern苛刻的严格的peek微露出、隐约可见tableware餐具U2gnawing折磨人的pang一阵剧痛defy使不可能、违抗overwhelming巨大的、势不可当的given考虑到、倘若indulge沉溺于crush迷恋、热恋fancy喜欢、想要bubble气泡，泡沫interact相互影响gender性别social联谊会unhesitant坚定的groom修饰exhilarated被动的、兴高采烈的settled固定的give and take 相互让步foundation基础、根据affection感情、挚爱school学派、流派blossom开花a meeting of minds彼此深刻的理解nurture培养、使发展flesh肉体lavishly浪费的ideal理想era时代constraint限制束缚restraint抑制、遏制unpretentious不装腔作势的curl弯曲remindful起提醒作用bygone以前的holiness神圣proximity最近接近jump赶浪头随大流haste急速急忙compatibility和谐共处合得来via通过借助于sensibility敏锐的brag自夸吹嘘horrify恐怖的hook up勾搭baggage行李state of affairs局势情况purely完全的仅仅originate开始发源mindset推理distort曲解lust愿望，渴望acquire得到获得selflessness无私forge建立…关系bond纽带、关系frivolous轻佻的、轻浮的U3criterion标准、准则label标签、标记thin浅薄的classical经典的、传统的philosopher哲学家distinguish辨别、区分utility有用、实用impermanent暂时的ground原因、理由break up结束、解散in so far as到…的程度regulate控制、管理object目的、目标incidental附带的、次要的saying谚语tribulation苦难statesman政治家orator演说家ethic伦理as to有关，关于purity纯洁equality公正、公平liberality慷慨greed贪心virtue美德possess拥有superiority优势surpass胜过commitment忠诚、承诺good有道德的行为、利益virtuous品德高的、有美德的blind捆绑、结合altruistic无私的U4childishly愚蠢的master race优等民族nationalistic民族主义discipline训练，管教have an eye on sth.以…为目标sophomore大学二年级学生pit沙坑under wraps不对外泄露的hot under the collar易怒的qualify获取资格foul犯规disgustedly厌恶的handshake握手slang俚语supremacy至上，最高权威muscular肌肉发达的blond金发的strikingly惊人地、引人注目的chiseled脸部鲜明的ebb（潮水）落，退quarters住处peak高峰的，最高点的congratulate祝贺despite尽管stand看台fake冒充，假装grip紧握melt融化plating镀层carat克拉U5ray光束filter通过，透过raring渴望的，极想的nightfall黄昏behavioral行为的attribute归因于eccentricity古怪的conditioning训练，熏陶label把…称为chronobiology时间生物学physician内科医生given特定的，规定的detect发现metabolic代谢的rate比率cycle周期，循环accelerate加速efficiency效率circadian昼夜规律的leading重要的sponsor赞助，资助physiologist生理学家authority权威equip装备coordinate使协调capacity力量associate同事、同伴interval间隔reading读数subtract减去，剪掉graph图表familiarize使熟悉take advantage of利用（注：文档可能无法思考全面，请浏览后下载，供参考。

分子动力学模拟的英文

分子动力学模拟的英文Molecular dynamics simulation is a computational method used to study the physical movements of atoms and molecules. It involves solving Newton's equations of motion for a system of interacting particles, typically using numerical methods. This technique allows researchers to gain insights into the dynamic behavior of materials, biological systems, and other complex systems at atomic or molecular scales.The fundamental principle of molecular dynamics simulation is to represent the system of interest as a collection of interacting particles. These particles can be atoms, molecules, or clusters of atoms/molecules, depending on the level of detail required for the simulation. The interactions between particles are typically describedusing force fields, which are mathematical functions that describe the potential energy of the system as a functionof the positions and orientations of the particles.The simulation process begins with the selection of aninitial configuration for the system. This can be obtained from experimental data, or it can be generated randomly or using specific algorithms. Once the initial configurationis set, the forces acting on each particle are calculated using the force field. These forces are then used to compute the accelerations of the particles according to Newton's second law of motion. The velocities and positions of the particles are then updated using these accelerations, typically using a time-stepping algorithm such as theVerlet algorithm.The simulation continues by iterating this process over time, allowing the system to evolve dynamically. As the simulation proceeds, the particles move and interact with each other, leading to changes in the system's structureand properties. By monitoring these changes, researcherscan gain insights into the dynamic behavior of the system and how it responds to external perturbations or changes in conditions.Molecular dynamics simulations can be used to study a wide range of systems and phenomena. In materials science,they can be used to understand the atomic-scale mechanisms underlying material properties such as mechanical strength, thermal conductivity, and electrical conductivity. In biology, they can be used to study the dynamics of proteins, nucleic acids, and other biomolecules, revealing insights into their function and interactions with other molecules.In addition to providing fundamental understanding of these systems, molecular dynamics simulations can also be used to predict and design new materials or molecules with desired properties. For example, they can be used to screen potential drug candidates or optimize the performance of materials for specific applications.However, it is important to note that molecular dynamics simulations have limitations. The accuracy of the results depends on the quality of the force field used to describe the interactions between particles. While manyforce fields have been developed and validated fordifferent types of systems, they may not always accurately represent the complex interactions that occur in real systems. Furthermore, molecular dynamics simulations arecomputationally intensive and may require significant resources to run, especially for large systems or long simulation times.Despite these limitations, molecular dynamics simulations have become a valuable tool in many fields of science and engineering. They provide a unique means to study the dynamic behavior of complex systems at atomic or molecular scales, complementing experimental techniques and enabling the discovery of new materials and molecules with improved properties.。

Fluent流体数值模拟软件中英对照

abort异常中断，中途失败，夭折，流产，发育不全，中止计划［任务］accidentally偶然地，意外地accretion 增长activation energy 活化能active center活性中心addition 增加adjacent相邻的aerosol浮质(气体中的悬浮微粒，如烟，雾等)，［化］气溶胶，气雾剂，烟雾剂Air flow circuits 气流循环ambient周国的，周用环境amines 胺amplitude广阔，丰富,振幅，物理学名词annular环流的algebraic stress model(ASM)代数应力模型algorithm 算法align排列，使结盟，使成一行alternately 轮流地analogy模拟，效仿analytical solution 解析解anisotropic各向异性的anthracite 无烟煤apparent显然的，外观上的，近似的approximation 近似arsenic神酸盐assembly 装配associate 联合,联系assume假设assumption 假设atomization 雾化axial轴向的Axisymmetry轴对称的BBaffle挡流板battlement 城垛式biography 经历bituminous coal 烟煤blow-off water 排污水blowing devices鼓风（吹风）装置body force体积力boiler plant锅炉装置（车间）Boiling 沸腾Boltzmann玻耳兹曼Bounded central differencing：有界中心差分格式Brownian rotation 布朗转动bulk庞大的bulk density堆积密度burner assembly燃烧器组件burnout 燃尽Ccapability性能，（实际）能力，容量，接受力carbon monoxide COcarbonate碳酸盐carry-over loss 飞灰损失Cartesian迪卡尔坐标的casing箱，壳，套catalisis 催化channeled有沟的，有缝的char焦炭、炭circulation circuit 循环回路circumferential velocity 圆周速度clinkering 熔渣clipped截尾的clipped Gaussian distribution 截尾髙斯分布closure （模型的）封闭cloud of particles 颗粒云close proximity 距离很近cluster颗粒团coal off-gas煤的挥发气体coarse粗糙的coarse grid疏网格，粗网格Coatingcoaxial R 轴的coefficient of restitution 回弹系数;恢复系数coke 碳collision 碰撞competence 能力competing process同时发生影响的competing-reactions submodel 平行反应子模型component部分分量composition 成分computational expense 计算成本cone shape圆锥体形状configuration 布置，构造confined flames 有界燃烧confirmation证实，确认，批准Configuration 构造，外形conservation守恒不火conservation equation 守恒方程conserved scalars 守恒标量considerably 相当地consume 消耗contact angle 接触角contamination 污染contingency偶然，可能性，意外事故，可能发生的附带事件continuum连续体Convection 对流converged收敛的conveyer输运机convolve 卷cooling wall 水冷壁correlation 关联（式）correlation function 相关函数corrosion 腐蚀，锈coupling联结,接合,耦合crack裂缝，裂纹creep up （水）渗上来，蠕升critical 临界critically 精密地cross-correlation 互关联cumulative 累积的curtain wall护墙，幕墙curve曲线custom习惯，风俗，＜动词单用〉海关，（封建制度下）左期服劳役，缴纳租税，自定义，v偶用作〉关税V.定制，承接左做活的Cyan青色cyano叙（基），深蓝，青色cyclone旋风子，旋风，旋风筒cyclone separator旋风分离器［除尘器］cylindrical柱坐标的cylindrical coordinate 柱坐标Ddead zones 死区decompose 分解decouple解藕的cooling duct 冷却管coordinate transformation 坐标转换Cp：等压比热defy 使成为不可能 demography 统计 deposition 沉枳derivative with respect to 对…的导数derivation 引出，来历,出处，（语言）语源,词源 design cycle 设计流程 desposit 积灰，结垢deterministic approach 确上轨道模型 deterministic 宿命的 deviation 偏差 devoid 缺乏devolatilization 析出挥发分,液化作用 diffusion 扩散 diffusivity 扩散系数digonal 二角（的），对角的,二维的 dilute 稀的 diminish 减少direct numerical simulation 直接数值模拟 discharge 释放 discrete 离散的discrete phase 分散相，不连续相 discretization ［数］离散化 deselect 取消选泄 dispersion 弥散 dissector 扩流锥dissociate thermally 热分解 dissociation 分裂dissipation 消散,分散,挥霍,浪费,消遣，放荡，狂饮 distribution of air 布风 divide 除以 dot line 虚线drag coefficient 牵引系数，阻力系数 drag and drop 拖放 drag force 曳力 drift velocity 漂移速度 driving force 驱［传,主］动力 droplet 液滴 drum 锅筒dry-bottom-furnace 固态排渣炉 dry-bottom 冷灰斗，固态排渣 duct 管 dump 渣坑dust-air mixture 一次风 EEBU-Eddy break up 漩涡破碎模型 eddy 涡旋effluent 废气，流出物 elastic 弹性的electro-staic precipitators 静电除尘器Deforming ：变形 Density ：密度emanate散发，发岀，发源，［罕］发散，放射embrasure 喷口，枪眼emissivity ［物］发射率empirical经验的endothermic reaction 吸热反应enhance 增，涨enlarge 扩大ensemble组，群，全体enthalpy 焰entity实体entrain携带,夹带entrained-bed 携带床Equation 方程equilibrate保持平衡equilibrium化学平衡ESCIMO——Engulfment （卷吞）Stretching （拉伸）Coherence （粘附）Interdiffusion-interaction （相互扩散和化学反应）Moving-observer （运动观察者）exhaust用尽，耗尽，抽完，使精疲力尽排气排气装巻用不完的，不会枯竭的exit出口，排气管exothermic reaction 放热反应expenditure支出，经费expertise 经验explicitly明白地，明确地extinction 熄灭的extract抽出，提取evaluation评价，估计,赋值evaporation 蒸发（作用）Eulerian approach 欧拉法Ffacilitate推动，促进factor把…分解fast chemistry快速化学反应fate天数，命运，运气，注定，送命，最终结果feasible可行的，可能的feed pump给水泵feedstock 填料Filling 倒水fine grid密网格，细网格finite difference approximation 有限差分法flamelet小火焰单元flame stability火焰稳定性flow pattern 流型fluctuating velocity 脉动速度fluctuation脉动,波动flue烟道（气）flue duck 烟道fluoride氟化物fold夹层块forced-and-induced draft fan 鼓引风机forestall 防止Formulation:公式，函数fouling 沾污fraction碎片部分，百分比fragmentation 破碎fuel-lean flamefuel-rich regions富燃料区，浓燃料区fuse熔化，熔融Ggas duct 烟道gas-tight烟气密封gasification 气化（作用）gasifier气化器Gauge厚度，直径，测量仪表，估测。

王玉梅toelf词汇随身携带版2

adj.
令人惊异的
amazement
n.
惊愕，惊异
ambience
n.
周围环境，气氛
ambitious
adj.
有雄心的，渴望成功的
ambition
n.
雄心，抱负
ambivalent
adj.
有矛盾情绪的，举棋不定的
ambivalence
n.
矛盾心理
scramble
vt.
攀爬；搅乱，使混杂
amble
vi.
admit
vt.
准许进入
vt.
承认
admittedly
adv.
公认地；诚然，无可否认地
adorn
vt.
装饰
adornment
n.
装饰；装饰品
unadorned
adj.
未装饰的，朴实的
advent
n.
出现，到来
adventure
n.
冒险经历
adventurous
adj.
喜欢冒险的，敢做敢为的
adventurer
n.
谴责；控告
accustomed
adj.
习惯了的
acquaintance
n.
熟人
acquaint
v.
熟悉
acquisition
n.
获得
activate
vt.
刺激，使活动
actively
adv.
活跃地，积极地
acute
adj.
灵敏的，敏锐的
adj.
剧烈的；很严重的
acumen
n.
敏锐，聪明
addict
abbreviate

中英文力学对准

一般力学类：分析力学 analytical mechanics拉格朗日乘子 Lagrange multiplier拉格朗日[量] Lagrangian拉格朗日括号 Lagrange bracket循环坐标 cyclic coordinate循环积分 cyclic integral哈密顿[量] Hamiltonian哈密顿函数 Hamiltonian function正则方程 canonical equation正则摄动 canonical perturbation正则变换 canonical transformation正则变量 canonical variable哈密顿原理 Hamilton principle作用量积分 action integral哈密顿-雅可比方程 Hamilton-Jacobi equation作用--角度变量 action-angle variables阿佩尔方程 Appell equation劳斯方程 Routh equation拉格朗日函数 Lagrangian function诺特定理 Noether theorem泊松括号 poisson bracket边界积分法 boundary integral method并矢 dyad运动稳定性 stability of motion轨道稳定性 orbital stability李雅普诺夫函数 Lyapunov function渐近稳定性 asymptotic stability结构稳定性 structural stability久期不稳定性 secular instability弗洛凯定理 Floquet theorem倾覆力矩 capsizing moment自由振动 free vibration固有振动 natural vibration暂态 transient state环境振动 ambient vibration反共振 anti-resonance衰减 attenuation库仑阻尼 Coulomb damping同相分量 in-phase component非同相分量 out-of -phase component超调量 overshoot 参量[激励]振动 parametric vibration模糊振动 fuzzy vibration临界转速 critical speed of rotation阻尼器 damper半峰宽度 half-peak width集总参量系统 lumped parameter system 相平面法 phase plane method相轨迹 phase trajectory等倾线法 isocline method跳跃现象 jump phenomenon负阻尼 negative damping达芬方程 Duffing equation希尔方程 Hill equationKBM方法 KBM method, Krylov-Bogoliu- bov-Mitropol'skii method马蒂厄方程 Mathieu equation平均法 averaging method组合音调 combination tone解谐 detuning耗散函数 dissipative function硬激励 hard excitation硬弹簧 hard spring, hardening spring谐波平衡法harmonic balance method久期项 secular term自激振动 self-excited vibration分界线 separatrix亚谐波 subharmonic软弹簧 soft spring ,softening spring软激励 soft excitation邓克利公式 Dunkerley formula瑞利定理 Rayleigh theorem分布参量系统 distributed parameter system优势频率 dominant frequency模态分析 modal analysis固有模态natural mode of vibration同步 synchronization超谐波 ultraharmonic范德波尔方程 van der pol equation频谱 frequency spectrum基频 fundamental frequencyWKB方法 WKB methodWKB方法Wentzel-Kramers-Brillouin method缓冲器 buffer风激振动 aeolian vibration嗡鸣 buzz倒谱cepstrum颤动 chatter蛇行 hunting阻抗匹配 impedance matching机械导纳 mechanical admittance机械效率 mechanical efficiency机械阻抗 mechanical impedance随机振动 stochastic vibration, random vibration隔振 vibration isolation减振 vibration reduction应力过冲 stress overshoot喘振surge摆振shimmy起伏运动 phugoid motion起伏振荡 phugoid oscillation驰振 galloping陀螺动力学 gyrodynamics陀螺摆 gyropendulum陀螺平台 gyroplatform陀螺力矩 gyroscoopic torque陀螺稳定器 gyrostabilizer陀螺体 gyrostat惯性导航 inertial guidance 姿态角 attitude angle方位角 azimuthal angle舒勒周期 Schuler period机器人动力学 robot dynamics多体系统 multibody system多刚体系统 multi-rigid-body system机动性 maneuverability凯恩方法Kane method转子[系统]动力学 rotor dynamics转子[一支承一基础]系统 rotor-support- foundation system静平衡 static balancing动平衡 dynamic balancing静不平衡 static unbalance动不平衡 dynamic unbalance现场平衡 field balancing不平衡 unbalance不平衡量 unbalance互耦力 cross force挠性转子 flexible rotor分频进动 fractional frequency precession半频进动half frequency precession油膜振荡 oil whip转子临界转速 rotor critical speed自动定心 self-alignment亚临界转速 subcritical speed涡动 whirl固体力学类：弹性力学 elasticity弹性理论 theory of elasticity均匀应力状态 homogeneous state of stress 应力不变量 stress invariant应变不变量 strain invariant应变椭球 strain ellipsoid均匀应变状态 homogeneous state of strain应变协调方程 equation of strain compatibility拉梅常量 Lame constants各向同性弹性 isotropic elasticity旋转圆盘 rotating circular disk 楔wedge开尔文问题 Kelvin problem布西内斯克问题 Boussinesq problem艾里应力函数 Airy stress function克罗索夫--穆斯赫利什维利法 Kolosoff- Muskhelishvili method基尔霍夫假设 Kirchhoff hypothesis板 Plate矩形板 Rectangular plate圆板 Circular plate环板 Annular plate波纹板 Corrugated plate加劲板 Stiffened plate,reinforcedPlate中厚板 Plate of moderate thickness弯[曲]应力函数 Stress function of bending 壳Shell扁壳 Shallow shell旋转壳 Revolutionary shell球壳 Spherical shell[圆]柱壳 Cylindrical shell锥壳Conical shell环壳 Toroidal shell封闭壳 Closed shell波纹壳 Corrugated shell扭[转]应力函数 Stress function of torsion 翘曲函数 Warping function半逆解法 semi-inverse method瑞利--里茨法 Rayleigh-Ritz method松弛法 Relaxation method莱维法 Levy method松弛 Relaxation量纲分析 Dimensional analysis自相似[性] self-similarity影响面 Influence surface接触应力 Contact stress赫兹理论 Hertz theory协调接触 Conforming contact滑动接触 Sliding contact滚动接触 Rolling contact压入 Indentation各向异性弹性 Anisotropic elasticity颗粒材料 Granular material散体力学 Mechanics of granular media热弹性 Thermoelasticity超弹性 Hyperelasticity粘弹性 Viscoelasticity对应原理 Correspondence principle褶皱Wrinkle塑性全量理论 Total theory of plasticity滑动 Sliding微滑Microslip粗糙度 Roughness非线性弹性 Nonlinear elasticity大挠度 Large deflection突弹跳变 snap-through有限变形 Finite deformation 格林应变 Green strain阿尔曼西应变 Almansi strain弹性动力学 Dynamic elasticity运动方程 Equation of motion准静态的Quasi-static气动弹性 Aeroelasticity水弹性 Hydroelasticity颤振Flutter弹性波Elastic wave简单波Simple wave柱面波 Cylindrical wave水平剪切波 Horizontal shear wave竖直剪切波Vertical shear wave体波 body wave无旋波 Irrotational wave畸变波 Distortion wave膨胀波 Dilatation wave瑞利波 Rayleigh wave等容波 Equivoluminal wave勒夫波Love wave界面波 Interfacial wave边缘效应 edge effect塑性力学 Plasticity可成形性 Formability金属成形 Metal forming耐撞性 Crashworthiness结构抗撞毁性 Structural crashworthiness 拉拔Drawing破坏机构 Collapse mechanism回弹 Springback挤压 Extrusion冲压 Stamping穿透Perforation层裂Spalling塑性理论 Theory of plasticity安定[性]理论 Shake-down theory运动安定定理 kinematic shake-down theorem静力安定定理 Static shake-down theorem 率相关理论 rate dependent theorem载荷因子load factor加载准则 Loading criterion加载函数 Loading function加载面 Loading surface塑性加载 Plastic loading塑性加载波 Plastic loading wave简单加载 Simple loading比例加载 Proportional loading卸载 Unloading卸载波 Unloading wave冲击载荷 Impulsive load阶跃载荷step load脉冲载荷 pulse load极限载荷 limit load中性变载 nentral loading拉抻失稳 instability in tension加速度波 acceleration wave本构方程 constitutive equation完全解 complete solution名义应力 nominal stress过应力 over-stress真应力 true stress等效应力 equivalent stress流动应力 flow stress应力间断 stress discontinuity应力空间 stress space主应力空间 principal stress space静水应力状态hydrostatic state of stress对数应变 logarithmic strain工程应变 engineering strain等效应变 equivalent strain应变局部化 strain localization应变率 strain rate应变率敏感性 strain rate sensitivity应变空间 strain space有限应变 finite strain塑性应变增量 plastic strain increment 累积塑性应变 accumulated plastic strain 永久变形 permanent deformation内变量 internal variable应变软化 strain-softening理想刚塑性材料 rigid-perfectly plastic Material刚塑性材料 rigid-plastic material理想塑性材料 perfectl plastic material 材料稳定性stability of material应变偏张量deviatoric tensor of strain应力偏张量deviatori tensor of stress 应变球张量spherical tensor of strain应力球张量spherical tensor of stress路径相关性 path-dependency线性强化 linear strain-hardening应变强化 strain-hardening随动强化 kinematic hardening各向同性强化 isotropic hardening强化模量 strain-hardening modulus幂强化 power hardening塑性极限弯矩 plastic limit bending Moment塑性极限扭矩 plastic limit torque弹塑性弯曲 elastic-plastic bending弹塑性交界面 elastic-plastic interface弹塑性扭转 elastic-plastic torsion粘塑性 Viscoplasticity非弹性 Inelasticity理想弹塑性材料 elastic-perfectly plastic Material极限分析 limit analysis极限设计 limit design极限面limit surface上限定理 upper bound theorem上屈服点upper yield point下限定理 lower bound theorem下屈服点 lower yield point界限定理 bound theorem初始屈服面initial yield surface后继屈服面 subsequent yield surface屈服面[的]外凸性 convexity of yield surface截面形状因子 shape factor of cross-section 沙堆比拟 sand heap analogy屈服Yield屈服条件 yield condition屈服准则 yield criterion屈服函数 yield function屈服面 yield surface塑性势 plastic potential能量吸收装置 energy absorbing device能量耗散率 energy absorbing device塑性动力学 dynamic plasticity塑性动力屈曲 dynamic plastic buckling塑性动力响应 dynamic plastic response塑性波 plastic wave运动容许场 kinematically admissible Field静力容许场 statically admissibleField流动法则 flow rule速度间断 velocity discontinuity滑移线 slip-lines滑移线场 slip-lines field移行塑性铰 travelling plastic hinge塑性增量理论 incremental theory ofPlasticity米泽斯屈服准则 Mises yield criterion普朗特--罗伊斯关系 prandtl- Reuss relation特雷斯卡屈服准则 Tresca yield criterion洛德应力参数 Lode stress parameter莱维--米泽斯关系 Levy-Mises relation亨基应力方程 Hencky stress equation赫艾--韦斯特加德应力空间Haigh-Westergaard stress space洛德应变参数 Lode strain parameter德鲁克公设 Drucker postulate盖林格速度方程Geiringer velocity Equation结构力学 structural mechanics结构分析 structural analysis结构动力学 structural dynamics拱 Arch三铰拱 three-hinged arch抛物线拱 parabolic arch圆拱 circular arch穹顶Dome空间结构 space structure空间桁架 space truss雪载[荷] snow load风载[荷] wind load土压力 earth pressure地震载荷 earthquake loading弹簧支座 spring support支座位移 support displacement支座沉降 support settlement超静定次数 degree of indeterminacy机动分析 kinematic analysis 结点法 method of joints截面法 method of sections结点力 joint forces共轭位移 conjugate displacement影响线 influence line三弯矩方程 three-moment equation单位虚力 unit virtual force刚度系数 stiffness coefficient柔度系数 flexibility coefficient力矩分配 moment distribution力矩分配法moment distribution method力矩再分配 moment redistribution分配系数 distribution factor矩阵位移法matri displacement method单元刚度矩阵 element stiffness matrix单元应变矩阵 element strain matrix总体坐标 global coordinates贝蒂定理 Betti theorem高斯--若尔当消去法 Gauss-Jordan elimination Method屈曲模态 buckling mode复合材料力学 mechanics of composites 复合材料composite material纤维复合材料 fibrous composite单向复合材料 unidirectional composite泡沫复合材料foamed composite颗粒复合材料 particulate composite层板Laminate夹层板 sandwich panel正交层板 cross-ply laminate斜交层板 angle-ply laminate层片Ply多胞固体 cellular solid膨胀 Expansion压实Debulk劣化 Degradation脱层 Delamination脱粘 Debond纤维应力 fiber stress层应力 ply stress层应变ply strain层间应力 interlaminar stress比强度 specific strength强度折减系数 strength reduction factor强度应力比 strength -stress ratio横向剪切模量 transverse shear modulus 横观各向同性 transverse isotropy正交各向异 Orthotropy剪滞分析 shear lag analysis短纤维 chopped fiber长纤维 continuous fiber纤维方向 fiber direction纤维断裂 fiber break纤维拔脱 fiber pull-out纤维增强 fiber reinforcement致密化 Densification最小重量设计 optimum weight design网格分析法 netting analysis混合律 rule of mixture失效准则 failure criterion蔡--吴失效准则 Tsai-W u failure criterion 达格代尔模型 Dugdale model断裂力学 fracture mechanics概率断裂力学 probabilistic fracture Mechanics格里菲思理论 Griffith theory线弹性断裂力学 linear elastic fracturemechanics, LEFM弹塑性断裂力学 elastic-plastic fracture mecha-nics, EPFM断裂 Fracture脆性断裂 brittle fracture解理断裂 cleavage fracture蠕变断裂 creep fracture延性断裂 ductile fracture晶间断裂 inter-granular fracture准解理断裂 quasi-cleavage fracture穿晶断裂 trans-granular fracture裂纹Crack裂缝Flaw缺陷Defect割缝Slit微裂纹Microcrack折裂Kink椭圆裂纹 elliptical crack深埋裂纹 embedded crack[钱]币状裂纹 penny-shape crack预制裂纹 Precrack 短裂纹 short crack表面裂纹 surface crack裂纹钝化 crack blunting裂纹分叉 crack branching裂纹闭合 crack closure裂纹前缘 crack front裂纹嘴 crack mouth裂纹张开角crack opening angle,COA裂纹张开位移 crack opening displacement, COD裂纹阻力 crack resistance裂纹面 crack surface裂纹尖端 crack tip裂尖张角 crack tip opening angle,CTOA裂尖张开位移 crack tip openingdisplacement, CTOD裂尖奇异场crack tip singularity Field裂纹扩展速率 crack growth rate稳定裂纹扩展 stable crack growth定常裂纹扩展 steady crack growth亚临界裂纹扩展 subcritical crack growth 裂纹[扩展]减速 crack retardation止裂crack arrest止裂韧度 arrest toughness断裂类型 fracture mode滑开型 sliding mode张开型 opening mode撕开型 tearing mode复合型 mixed mode撕裂 Tearing撕裂模量 tearing modulus断裂准则 fracture criterionJ积分 J-integralJ阻力曲线 J-resistance curve断裂韧度 fracture toughness应力强度因子 stress intensity factorHRR场 Hutchinson-Rice-Rosengren Field守恒积分 conservation integral有效应力张量 effective stress tensor应变能密度strain energy density能量释放率 energy release rate内聚区 cohesive zone塑性区 plastic zone张拉区 stretched zone热影响区heat affected zone, HAZ延脆转变温度 brittle-ductile transitiontemperature剪切带shear band剪切唇shear lip无损检测 non-destructive inspection双边缺口试件double edge notchedspecimen, DEN specimen单边缺口试件 single edge notchedspecimen, SEN specimen三点弯曲试件 three point bendingspecimen, TPB specimen中心裂纹拉伸试件 center cracked tension specimen, CCT specimen中心裂纹板试件 center cracked panelspecimen, CCP specimen紧凑拉伸试件 compact tension specimen, CT specimen大范围屈服large scale yielding小范围攻屈服 small scale yielding韦布尔分布 Weibull distribution帕里斯公式 paris formula空穴化 Cavitation应力腐蚀 stress corrosion概率风险判定 probabilistic riskassessment, PRA损伤力学 damage mechanics损伤Damage连续介质损伤力学 continuum damage mechanics细观损伤力学 microscopic damage mechanics累积损伤 accumulated damage脆性损伤 brittle damage延性损伤 ductile damage宏观损伤 macroscopic damage细观损伤 microscopic damage微观损伤 microscopic damage损伤准则 damage criterion损伤演化方程 damage evolution equation 损伤软化 damage softening损伤强化 damage strengthening 损伤张量 damage tensor损伤阈值 damage threshold损伤变量 damage variable损伤矢量 damage vector损伤区 damage zone疲劳Fatigue低周疲劳 low cycle fatigue应力疲劳 stress fatigue随机疲劳 random fatigue蠕变疲劳 creep fatigue腐蚀疲劳 corrosion fatigue疲劳损伤 fatigue damage疲劳失效 fatigue failure疲劳断裂 fatigue fracture疲劳裂纹 fatigue crack疲劳寿命 fatigue life疲劳破坏 fatigue rupture疲劳强度 fatigue strength疲劳辉纹 fatigue striations疲劳阈值 fatigue threshold交变载荷 alternating load交变应力 alternating stress应力幅值 stress amplitude应变疲劳 strain fatigue应力循环 stress cycle应力比 stress ratio安全寿命 safe life过载效应 overloading effect循环硬化 cyclic hardening循环软化 cyclic softening环境效应 environmental effect裂纹片crack gage裂纹扩展 crack growth, crack Propagation裂纹萌生 crack initiation循环比 cycle ratio实验应力分析 experimental stressAnalysis工作[应变]片 active[strain] gage基底材料 backing material应力计stress gage零[点]飘移zero shift, zero drift应变测量 strain measurement应变计strain gage应变指示器 strain indicator应变花 strain rosette应变灵敏度 strain sensitivity机械式应变仪 mechanical strain gage 直角应变花 rectangular rosette引伸仪 Extensometer应变遥测 telemetering of strain横向灵敏系数 transverse gage factor 横向灵敏度 transverse sensitivity焊接式应变计 weldable strain gage 平衡电桥 balanced bridge粘贴式应变计 bonded strain gage粘贴箔式应变计bonded foiled gage粘贴丝式应变计 bonded wire gage 桥路平衡 bridge balancing电容应变计 capacitance strain gage 补偿片 compensation technique补偿技术 compensation technique基准电桥 reference bridge电阻应变计 resistance strain gage温度自补偿应变计 self-temperature compensating gage半导体应变计 semiconductor strain Gage集流器slip ring应变放大镜 strain amplifier疲劳寿命计 fatigue life gage电感应变计 inductance [strain] gage 光[测]力学 Photomechanics光弹性 Photoelasticity光塑性 Photoplasticity杨氏条纹 Young fringe双折射效应 birefrigent effect等位移线 contour of equalDisplacement暗条纹 dark fringe条纹倍增 fringe multiplication干涉条纹 interference fringe等差线 Isochromatic等倾线 Isoclinic等和线 isopachic应力光学定律 stress- optic law主应力迹线 Isostatic亮条纹 light fringe 光程差optical path difference热光弹性 photo-thermo -elasticity光弹性贴片法 photoelastic coating Method光弹性夹片法 photoelastic sandwich Method动态光弹性 dynamic photo-elasticity空间滤波 spatial filtering空间频率 spatial frequency起偏镜 Polarizer反射式光弹性仪 reflection polariscope残余双折射效应 residual birefringent Effect应变条纹值 strain fringe value应变光学灵敏度 strain-optic sensitivity 应力冻结效应 stress freezing effect应力条纹值 stress fringe value应力光图 stress-optic pattern暂时双折射效应 temporary birefringent Effect脉冲全息法 pulsed holography透射式光弹性仪 transmission polariscope 实时全息干涉法 real-time holographicinterfero - metry网格法 grid method全息光弹性法 holo-photoelasticity全息图Hologram全息照相 Holograph全息干涉法 holographic interferometry 全息云纹法 holographic moire technique 全息术 Holography全场分析法 whole-field analysis散斑干涉法 speckle interferometry散斑Speckle错位散斑干涉法 speckle-shearinginterferometry, shearography散斑图Specklegram白光散斑法white-light speckle method云纹干涉法 moire interferometry[叠栅]云纹 moire fringe[叠栅]云纹法 moire method云纹图 moire pattern离面云纹法 off-plane moire method参考栅 reference grating试件栅 specimen grating分析栅 analyzer grating面内云纹法 in-plane moire method脆性涂层法 brittle-coating method条带法 strip coating method坐标变换 transformation ofCoordinates计算结构力学 computational structuralmecha-nics加权残量法weighted residual method有限差分法 finite difference method有限[单]元法 finite element method配点法 point collocation里茨法 Ritz method广义变分原理 generalized variational Principle最小二乘法 least square method胡[海昌]一鹫津原理 Hu-Washizu principle 赫林格-赖斯纳原理 Hellinger-Reissner Principle修正变分原理 modified variational Principle约束变分原理 constrained variational Principle混合法 mixed method杂交法 hybrid method边界解法boundary solution method有限条法 finite strip method半解析法 semi-analytical method协调元 conforming element非协调元 non-conforming element混合元 mixed element杂交元 hybrid element边界元 boundary element强迫边界条件 forced boundary condition 自然边界条件 natural boundary condition 离散化 Discretization离散系统 discrete system连续问题 continuous problem广义位移 generalized displacement广义载荷 generalized load广义应变 generalized strain广义应力 generalized stress界面变量 interface variable 节点 node, nodal point[单]元 Element角节点 corner node边节点 mid-side node内节点 internal node无节点变量 nodeless variable杆元 bar element桁架杆元 truss element梁元 beam element二维元 two-dimensional element一维元 one-dimensional element三维元 three-dimensional element轴对称元 axisymmetric element板元 plate element壳元 shell element厚板元 thick plate element三角形元 triangular element四边形元 quadrilateral element四面体元 tetrahedral element曲线元 curved element二次元 quadratic element线性元 linear element三次元 cubic element四次元 quartic element等参[数]元 isoparametric element超参数元 super-parametric element亚参数元 sub-parametric element节点数可变元 variable-number-node element拉格朗日元 Lagrange element拉格朗日族 Lagrange family巧凑边点元 serendipity element巧凑边点族 serendipity family无限元 infinite element单元分析 element analysis单元特性 element characteristics刚度矩阵 stiffness matrix几何矩阵 geometric matrix等效节点力 equivalent nodal force节点位移 nodal displacement节点载荷 nodal load位移矢量 displacement vector载荷矢量 load vector质量矩阵 mass matrix集总质量矩阵 lumped mass matrix相容质量矩阵 consistent mass matrix阻尼矩阵 damping matrix瑞利阻尼 Rayleigh damping刚度矩阵的组集 assembly of stiffnessMatrices载荷矢量的组集 consistent mass matrix质量矩阵的组集 assembly of mass matrices 单元的组集 assembly of elements局部坐标系 local coordinate system局部坐标 local coordinate面积坐标 area coordinates体积坐标 volume coordinates曲线坐标 curvilinear coordinates静凝聚 static condensation合同变换 contragradient transformation形状函数 shape function试探函数 trial function检验函数test function权函数 weight function样条函数 spline function代用函数 substitute function降阶积分 reduced integration零能模式 zero-energy modeP收敛 p-convergenceH收敛 h-convergence掺混插值 blended interpolation等参数映射 isoparametric mapping双线性插值 bilinear interpolation小块检验 patch test非协调模式 incompatible mode 节点号 node number单元号 element number带宽 band width带状矩阵 banded matrix变带状矩阵 profile matrix带宽最小化minimization of band width波前法 frontal method子空间迭代法 subspace iteration method 行列式搜索法determinant search method逐步法 step-by-step method纽马克法Newmark威尔逊法 Wilson拟牛顿法 quasi-Newton method牛顿-拉弗森法 Newton-Raphson method 增量法 incremental method初应变 initial strain初应力 initial stress切线刚度矩阵 tangent stiffness matrix割线刚度矩阵 secant stiffness matrix模态叠加法mode superposition method平衡迭代 equilibrium iteration子结构 Substructure子结构法 substructure technique超单元 super-element网格生成 mesh generation结构分析程序 structural analysis program 前处理 pre-processing后处理 post-processing网格细化 mesh refinement应力光顺 stress smoothing组合结构 composite structure流体动力学类：流体动力学 fluid dynamics连续介质力学 mechanics of continuous media介质medium流体质点 fluid particle无粘性流体 nonviscous fluid, inviscid fluid连续介质假设 continuous medium hypothesis流体运动学 fluid kinematics水静力学 hydrostatics 液体静力学 hydrostatics支配方程 governing equation伯努利方程 Bernoulli equation伯努利定理 Bernonlli theorem毕奥-萨伐尔定律 Biot-Savart law欧拉方程Euler equation亥姆霍兹定理 Helmholtz theorem开尔文定理 Kelvin theorem涡片 vortex sheet库塔-茹可夫斯基条件 Kutta-Zhoukowskicondition布拉休斯解 Blasius solution达朗贝尔佯廖 d'Alembert paradox 雷诺数 Reynolds number施特鲁哈尔数 Strouhal number随体导数 material derivative不可压缩流体 incompressible fluid 质量守恒 conservation of mass动量守恒 conservation of momentum 能量守恒 conservation of energy动量方程 momentum equation能量方程 energy equation控制体积 control volume液体静压 hydrostatic pressure涡量拟能 enstrophy压差 differential pressure流[动] flow流线stream line流面 stream surface流管stream tube迹线path, path line流场 flow field流态 flow regime流动参量 flow parameter流量 flow rate, flow discharge涡旋 vortex涡量 vorticity涡丝 vortex filament涡线 vortex line涡面 vortex surface涡层 vortex layer涡环 vortex ring涡对 vortex pair涡管 vortex tube涡街 vortex street卡门涡街 Karman vortex street马蹄涡 horseshoe vortex对流涡胞 convective cell卷筒涡胞 roll cell涡 eddy涡粘性 eddy viscosity环流 circulation环量 circulation速度环量 velocity circulation 偶极子 doublet, dipole驻点 stagnation point总压[力] total pressure总压头 total head静压头 static head总焓 total enthalpy能量输运 energy transport速度剖面 velocity profile库埃特流 Couette flow单相流 single phase flow单组份流 single-component flow均匀流 uniform flow非均匀流 nonuniform flow二维流 two-dimensional flow三维流 three-dimensional flow准定常流 quasi-steady flow非定常流unsteady flow, non-steady flow 暂态流transient flow周期流 periodic flow振荡流 oscillatory flow分层流 stratified flow无旋流 irrotational flow有旋流 rotational flow轴对称流 axisymmetric flow不可压缩性 incompressibility不可压缩流[动] incompressible flow 浮体 floating body定倾中心metacenter阻力 drag, resistance减阻 drag reduction表面力 surface force表面张力 surface tension毛细[管]作用 capillarity来流 incoming flow自由流 free stream自由流线 free stream line外流 external flow进口 entrance, inlet出口exit, outlet扰动 disturbance, perturbation分布 distribution传播 propagation色散 dispersion弥散 dispersion附加质量added mass ,associated mass收缩 contraction镜象法 image method无量纲参数 dimensionless parameter几何相似 geometric similarity运动相似 kinematic similarity动力相似[性] dynamic similarity平面流 plane flow势 potential势流 potential flow速度势 velocity potential复势 complex potential复速度 complex velocity流函数 stream function源source汇sink速度[水]头 velocity head拐角流 corner flow空泡流cavity flow超空泡 supercavity超空泡流 supercavity flow空气动力学 aerodynamics低速空气动力学 low-speed aerodynamics 高速空气动力学 high-speed aerodynamics 气动热力学 aerothermodynamics亚声速流[动] subsonic flow跨声速流[动] transonic flow超声速流[动] supersonic flow锥形流 conical flow楔流wedge flow叶栅流 cascade flow非平衡流[动] non-equilibrium flow细长体 slender body细长度 slenderness钝头体 bluff body钝体 blunt body翼型 airfoil翼弦 chord薄翼理论 thin-airfoil theory构型 configuration后缘 trailing edge迎角 angle of attack失速stall脱体激波detached shock wave 波阻wave drag诱导阻力 induced drag诱导速度 induced velocity临界雷诺数critical Reynolds number前缘涡 leading edge vortex附着涡 bound vortex约束涡 confined vortex气动中心 aerodynamic center气动力 aerodynamic force气动噪声 aerodynamic noise气动加热 aerodynamic heating离解 dissociation地面效应 ground effect气体动力学 gas dynamics稀疏波 rarefaction wave热状态方程thermal equation of state喷管Nozzle普朗特-迈耶流 Prandtl-Meyer flow瑞利流 Rayleigh flow可压缩流[动] compressible flow可压缩流体 compressible fluid绝热流 adiabatic flow非绝热流 diabatic flow未扰动流 undisturbed flow等熵流 isentropic flow匀熵流 homoentropic flow兰金-于戈尼奥条件 Rankine-Hugoniot condition状态方程 equation of state量热状态方程 caloric equation of state完全气体 perfect gas拉瓦尔喷管 Laval nozzle马赫角 Mach angle马赫锥 Mach cone马赫线Mach line马赫数Mach number马赫波Mach wave当地马赫数 local Mach number冲击波 shock wave激波 shock wave正激波normal shock wave斜激波oblique shock wave头波 bow wave附体激波 attached shock wave激波阵面 shock front激波层 shock layer压缩波 compression wave反射 reflection折射 refraction散射scattering衍射 diffraction绕射 diffraction出口压力 exit pressure超压[强] over pressure反压 back pressure爆炸 explosion爆轰 detonation缓燃 deflagration水动力学 hydrodynamics液体动力学 hydrodynamics泰勒不稳定性 Taylor instability 盖斯特纳波 Gerstner wave斯托克斯波 Stokes wave瑞利数 Rayleigh number自由面 free surface波速 wave speed, wave velocity 波高 wave height波列wave train波群 wave group波能wave energy表面波 surface wave表面张力波 capillary wave规则波 regular wave不规则波 irregular wave浅水波 shallow water wave深水波deep water wave重力波 gravity wave椭圆余弦波 cnoidal wave潮波tidal wave涌波surge wave破碎波 breaking wave船波ship wave非线性波 nonlinear wave孤立子 soliton水动[力]噪声 hydrodynamic noise 水击 water hammer空化 cavitation空化数 cavitation number 空蚀 cavitation damage超空化流 supercavitating flow水翼 hydrofoil水力学 hydraulics洪水波 flood wave涟漪ripple消能 energy dissipation海洋水动力学 marine hydrodynamics谢齐公式 Chezy formula欧拉数 Euler number弗劳德数 Froude number水力半径 hydraulic radius水力坡度 hvdraulic slope高度水头 elevating head水头损失 head loss水位 water level水跃 hydraulic jump含水层 aquifer排水 drainage排放量 discharge壅水曲线back water curve压[强水]头 pressure head过水断面 flow cross-section明槽流open channel flow孔流 orifice flow无压流 free surface flow有压流 pressure flow缓流 subcritical flow急流 supercritical flow渐变流gradually varied flow急变流 rapidly varied flow临界流 critical flow异重流density current, gravity flow堰流weir flow掺气流 aerated flow含沙流 sediment-laden stream降水曲线 dropdown curve沉积物 sediment, deposit沉[降堆]积 sedimentation, deposition沉降速度 settling velocity流动稳定性 flow stability不稳定性 instability奥尔-索末菲方程 Orr-Sommerfeld equation 涡量方程 vorticity equation泊肃叶流 Poiseuille flow奥辛流 Oseen flow剪切流 shear flow粘性流[动] viscous flow层流 laminar flow分离流 separated flow二次流 secondary flow近场流near field flow远场流 far field flow滞止流 stagnation flow尾流 wake [flow]回流 back flow反流 reverse flow射流 jet自由射流 free jet管流pipe flow, tube flow内流 internal flow拟序结构 coherent structure 猝发过程 bursting process表观粘度 apparent viscosity 运动粘性 kinematic viscosity 动力粘性 dynamic viscosity 泊 poise厘泊 centipoise厘沱 centistoke剪切层 shear layer次层 sublayer流动分离 flow separation层流分离 laminar separation 湍流分离 turbulent separation 分离点 separation point附着点 attachment point再附 reattachment再层流化 relaminarization起动涡starting vortex驻涡 standing vortex涡旋破碎 vortex breakdown 涡旋脱落 vortex shedding压[力]降 pressure drop压差阻力 pressure drag压力能 pressure energy型阻 profile drag滑移速度 slip velocity无滑移条件 non-slip condition 壁剪应力 skin friction, frictional drag壁剪切速度 friction velocity磨擦损失 friction loss磨擦因子 friction factor耗散 dissipation滞后lag相似性解 similar solution局域相似 local similarity气体润滑 gas lubrication液体动力润滑 hydrodynamic lubrication 浆体 slurry泰勒数 Taylor number纳维-斯托克斯方程 Navier-Stokes equation 牛顿流体 Newtonian fluid边界层理论boundary later theory边界层方程boundary layer equation边界层 boundary layer附面层 boundary layer层流边界层laminar boundary layer湍流边界层turbulent boundary layer温度边界层thermal boundary layer边界层转捩boundary layer transition边界层分离boundary layer separation边界层厚度boundary layer thickness位移厚度 displacement thickness动量厚度 momentum thickness能量厚度 energy thickness焓厚度 enthalpy thickness注入 injection吸出suction泰勒涡 Taylor vortex速度亏损律 velocity defect law形状因子 shape factor测速法 anemometry粘度测定法 visco[si] metry流动显示 flow visualization油烟显示 oil smoke visualization孔板流量计 orifice meter频率响应 frequency response油膜显示oil film visualization阴影法 shadow method纹影法 schlieren method烟丝法smoke wire method丝线法 tuft method。

70t单管RH冶金传输行为的数值模拟

第50卷第6期2019年6月中南大学学报(自然科学版)Journal of Central South University(Science and Technology)V ol.50No.6Jun e 2019 70t单管RH冶金传输行为的数值模拟窦为学1,2，雷洪3，朱苗勇1(1.东北大学冶金学院，辽宁沈阳，110819；2.敬业钢铁有限公司，河北石家庄，040500；3.东北大学材料电磁过程研究教育部重点实验室，辽宁沈阳，110819)摘要：为了深入了解70t单管RH内的冶金传输过程，分别采用欧拉−欧拉方法、示踪剂输运方程和碳氧质量分数输运偏微分方程组描述RH内钢液流动行为、混匀过程和脱碳过程。

数值模拟结果表明：随着真空度由250Pa降低到50Pa，循环流量和混匀时间保持不变，钢液中碳质量分数由81.8×10−6降低到34.3×10−6；随着底吹氩气量由100L/min增大到500L/min，循环流量由23.1t/min增加到42.2t/min，均混时间由179s下降到100s，钢液中碳质量分数由72.6×10−6下降到47.5×10−6。

预测的脱碳曲线与工业实验数据符合良好；提高单管RH底吹氩气量，有利于提高循环流量，减少均混时间，降低钢液中碳元素质量分数。

关键词：单管RH；真空精炼；均混时间；脱碳；数值模拟中图分类号：TF769.4文献标志码：A文章编号：1672-7207(2019)06−1284−07Numberical simulation for metallurgical transfer in70t singlesnorkel RHDOU Weixue1,2,LEI Hong3,ZHU Miaoyong1(1.School of Metallurgy,Northeastern University,Shenyang110819,China;2.Jingye Iron and Steel Limited Company,Shijiazhuang040500,China;3.Key Laboratory of Electromagnetic Processing of Materials,Ministry of Education,Northeastern University,Shenyang110819,China)Abstract:In order to get a deep insight into the metallurgical transfer process in70t single snorkel RH,Euler−Euler approach,tracer transfer model and partial differential equations for carbon and oxygen transfer were respectively applied to describe the fluid flow,mixing process,and decarburization process in RH.Numerical results show that,while the vacuum degree falls from250to50Pa,the circulation flow rate and mixing time almost remain unchanged,and the carbon mass fraction decreases from81.8×10−6to34.3×10−6.While the ladle bottom blowing argon flow rate rises from 100to500L/min,the circulation flow rate rises from23.1to42.2t/min,the mixing time decreases from179to100s, and carbon mass fraction decreases from72.6×10−6to47.5×10−6.The predicted carbon mass fraction is in good agreement with the industrial experimental result.Increasing the flow rate of argon blown into the single snorkel RH is beneficial to increase the flow rate and reduce the mixing time and carbon mass fraction in liquid steel.Key words:single snorkel RH;vacuum refining;mixing time;decarburization;numerical simulationDOI:10.11817/j.issn.1672-7207.2019.06.003收稿日期：2018−12−24；修回日期：2019−02−13基金项目(Foundation item)：国家自然科学基金与宝钢联合资助项目(U1460108)(Project(U1460108)supported by the National Natural Science Foundation of China and Shanghai Baosteel)通信作者：雷洪，博士，教授，从事高品质钢的精炼和连铸理论与工艺研究；E-mail:***************第6期窦为学，等：70t单管RH冶金传输行为的数值模拟钢液真空循环脱气法是西德鲁尔钢铁公司(Ruhrstahl)和赫拉欧斯公司(Hereaeus)共同设计开发的一种钢液炉外精炼方法，简称RH法。

心里健康英文作文高级词汇

心里健康英文作文高级词汇英文，。

Mental health is a topic close to my heart, as it's something I've struggled with in the past. Understanding advanced vocabulary related to this subject can be empowering and can help articulate complex emotions and experiences.One term often used in discussions about mental health is "psychological resilience." Psychological resilience refers to one's ability to adapt to stressful situations or crises. It's like having a sturdy ship that can weather the stormy seas of life. For example, when I lost my job unexpectedly, my psychological resilience helped me bounce back and find new opportunities.Another important concept is "self-care." Self-care encompasses activities and practices that promote well-being and reduce stress. This could be anything frompracticing mindfulness meditation to indulging in arelaxing bubble bath. Self-care is like giving yourself a recharge so you can tackle life's challenges with renewed energy and focus."Emotional intelligence" is also crucial formaintaining good mental health. It involves recognizing, understanding, and managing our own emotions, as well as empathizing with the emotions of others. For instance, when my friend was going through a tough breakup, I tapped into my emotional intelligence to offer support and empathy.Now, let's explore some advanced vocabulary related to mental health in Chinese.中文：心理健康是我非常关心的话题，因为我过去曾经有过这方面的困扰。

文丘里式气泡发生器气泡碎化特性研究

文丘里式气泡发生器气泡碎化特性研究唐文偲;阎昌琪;孙立成;刘卫;李华【摘要】熔盐堆在运行过程中须不断地去除氙等气体裂变产物。

熔盐堆除气系统中气泡发生器的作用是通过向回路中注入一定量的直径为0.5 mm的小气泡，在扩散作用下吸收熔盐中的氙，最终气泡被分离出来，达到除氙的目的。

在橡树岭国家实验室设计的基础上，本文为钍基熔盐研究堆设计气泡发生器，并在专门建造的水回路中对其工作特性进行了可视化研究。

利用高速摄像系统跟踪气泡的运动和碎化过程，分析气液相流速对碎化后气泡尺寸的影响。

结果表明：在实验条件下，当气体流量一定时，气泡尺寸随液体流量的增大而减小；当液体流量一定时，气泡尺寸随气体流量的增加而增大。

%During the operation of a molten salt reactor , the continuous removal of gaseous fission product 135 Xe from the circulating fuel has to be provided .As one of the key devices in the off-gas removal system ,the bubble generator is for generating tiny bubbles with average bubble diameter around 0.5 mm . Firstly , certain amount of helium bubbles are injected to the fuel , the bubbles absorb 135 Xe , and then these bubbles containing 135 Xe are stripped out of the fuel for removing 135 Xe in the liquid fuel . In the present study ,a new bubble generator was designed for TMSR referenced to the design of ORNL . Meanwhile , a water test loop was fabricated for visualization observation on the performance of the bubble generator .T he movement and breakup of the bubbles were recorded by a high speed camera .The effect of gas and liquid flow rates on generated bubble diameter was also analyzed . The results show that under experimental conditions ,with the increase ofliquid flow rate ,the bubble size decreases with the increase of liquid flow rate when the gas flow rate remains unchanged ;the bubble size increases with the gas flow rate when the liquid flow rate is constant .【期刊名称】《原子能科学技术》【年(卷),期】2014(000)005【总页数】5页(P844-848)【关键词】熔盐堆;气泡发生器;文丘里;气泡碎化【作者】唐文偲;阎昌琪;孙立成;刘卫;李华【作者单位】哈尔滨工程大学核安全与仿真技术国防重点学科实验室，黑龙江哈尔滨 150001;哈尔滨工程大学核安全与仿真技术国防重点学科实验室，黑龙江哈尔滨 150001;哈尔滨工程大学核安全与仿真技术国防重点学科实验室，黑龙江哈尔滨 150001;中国科学院上海应用物理研究所，上海 201800;中国科学院上海应用物理研究所，上海 201800【正文语种】中文【中图分类】TL334反应堆在运行过程中，堆中会产生氙、氪等中子吸收截面较大的裂变气体，氙和氪是反应堆运行中最重要的中子毒物，会对反应堆运行过程中反应性的变化产生重要影响。

基于界面追踪法的双液滴流动特性数值模拟

基于界面追踪法的双液滴流动特性数值模拟林圣享;张莹;夏珍;洪垚【摘要】The motion and deformation of Two parallel free-falling droplets in the gravitational field had been simulated which were based onFTM(front-tracking method).The situations of different parameters,which are Reynolds number(Re)、Eotvos number(Eo)and droplet initial center distance,have been studied by this meth-od.The results show that:when the distance is large(Lc/D≥4),the impact is little.But the characteristics of the droplet's movement are determined by the Re and Eo;when the two droplets are close(Lc/D=2),the deformation of droplet is asymmetric,and the droplet will repel each other;when Eo is large,the deformation of droplet is pro-nounced,and the droplet repels each other more,the velocity of vertical positions smaller; when Re is large, the deformation is more frequent.%基于界面追踪法(front-tracking method,FTM)建立了重力场中多个气液界面间相互耦合的数值模型.以两个液滴的自由落体运动为研究对象,在不同Reynolds数(Re)、Eotvos数(Eo)和液滴初始中心距的情况下进行数值分析.研究结果表明:当液滴初始中心距较大(Lc/D≥4)时,两个液滴间的相互作用很小,对液滴的变形和运动过程不产生影响,而此时液滴的运动特性由Re和Eo决定;当液滴初始中心距较小(Lc/D=2)时,液滴在下落过程中的变形是不对称的,并且液滴会相互排斥,在大Re和Eo时,这种现象更加明显.【期刊名称】《科学技术与工程》【年(卷),期】2017(017)028【总页数】6页(P14-19)【关键词】界面追踪法;两相流;界面形态演化;直接数值模拟【作者】林圣享;张莹;夏珍;洪垚【作者单位】南昌大学机电工程学院,南昌330031;南昌大学机电工程学院,南昌330031;南昌大学机电工程学院,南昌330031;南昌大学机电工程学院,南昌330031【正文语种】中文【中图分类】O359液滴在气体中的运动是非常典型的多相流动过程，其广泛存在于自然现象和工程实际当中，并呈现出独特的流体特性[1,2]，特别是当多个液滴一起出现时，其运动过程更加复杂。

匀强电场作用下分散相液滴的变形和破裂

匀强电场作用下分散相液滴的变形和破裂梁猛;李青;王奎升;刘竞业;陈家庆【摘要】基于Cahn-Hilliard方程的相场方法，建立了在匀强电场作用下液滴的变形和破裂行为模型。

从微观角度研究分散相液滴变形过程中电荷密度、电场强度和电场力的分布规律以及流场和电场分布，探讨了微观液滴变形机理；采用数值模拟方法研究了电场强度、液滴直径和界面张力对液滴变形的影响，结果表明电场强度越强，液滴直径越大，界面张力越小，液滴变形量越大；分析了液滴的两种主要破裂方式，其破裂主要取决于连续相和分散相物性条件，为电破乳技术提供了理论基础。

%Through coupling hydrodynamics and electrostatics, a phase field method based on Cahn-Hilliard formulation was used to predict the deformation and breakup of dispersed phase droplets in a uniform electric field. The distribution of charge density, electric field strength and electric field force on the droplet surface as well as the distribution of flow field and electric field were studied from the micro-perspective. The micro-droplet deformation mechanism was established. The influence of electric field strength, droplet diameter and interfacial tension on the deformation was predicted by numerical simulation. The results showed that strong electric field intensity, large droplet diameter or small interfacial tension could cause larger degree of droplet deformation. The droplet mainly ruptured from its middle or the two ends. Rupture mainly depended on the physical properties of the continuous phase and dispersed phase. The above study would provide a theoretical basis for complex electric demulsification.【期刊名称】《化工学报》【年(卷),期】2014(000)003【总页数】6页(P843-848)【关键词】相场方法;数值模拟;变形;破裂;匀强电场;界面;数学模型【作者】梁猛;李青;王奎升;刘竞业;陈家庆【作者单位】北京化工大学机电工程学院，北京 100029;北京化工大学机电工程学院，北京 100029;北京化工大学机电工程学院，北京 100029;北京化工大学理学院，北京 100029;北京石油化工学院机械工程学院，北京 102617【正文语种】中文【中图分类】TE624.1原油生产过程中，对原油乳状液脱水是最重要的生产环节[1]。

气泡雾化施药喷嘴的设计和试验的开题报告

气泡雾化施药喷嘴的设计和试验的开题报告一、题目气泡雾化施药喷嘴的设计和试验二、研究背景农药喷雾是现代农业生产中的重要环节之一。

传统农药喷雾主要通过液体喷雾的形式进行，但其存在诸多问题，如喷雾效果不佳、浪费农药、对环境造成污染等。

因此，气泡雾化喷雾技术应运而生，它将液体农药雾化成微小气泡，喷洒到植物表面，从而提高了农药的利用率和喷洒效果，大大降低了农药使用量，降低了农业环境污染，受到了广泛关注。

气泡雾化喷雾技术需要通过喷嘴将液体农药变成微小气泡，但喷嘴的设计和制作并不简单，需要考虑气泡大小、稳定性、喷洒均匀度等因素，从而保证喷雾效果。

因此，本文将对气泡雾化喷嘴的设计和试验进行研究。

三、研究内容1. 气泡雾化喷嘴的设计方案，包括双吹管喷嘴和圆管喷嘴两种方案。

2. 基于COMSOL多物理场仿真软件，对不同方案下的气泡雾化喷嘴进行数值模拟，并分析不同参数对气泡大小、稳定性、均匀度的影响。

3. 按照实验设计方案，建立气泡雾化喷嘴的实验测试平台，对双吹管喷嘴和圆管喷嘴的雾化效果进行对比试验。

4. 通过试验数据分析和仿真结果比对，对双吹管喷嘴和圆管喷嘴的优缺点进行评估并提出改进建议。

四、研究意义气泡雾化喷嘴是一种新型的农药喷雾技术，其在提高农药利用效率、减少农药浪费、降低环境污染等方面具有非常重要的意义。

本文将对气泡雾化喷嘴的设计和试验进行深入研究，为该技术在农业生产中的应用提供有力的支持。

五、研究方法本文将采用多种研究方法，包括理论分析、数值模拟和实验测试等。

其中，理论分析主要是对气泡雾化喷嘴的原理和流体力学学基础进行分析；数值模拟将采用COMSOL多物理场仿真软件，对不同喷嘴方案的喷雾效果进行数值模拟；实验测试将采用自行设计的测试平台，对双吹管喷嘴和圆管喷嘴的雾化效果进行试验。

六、进度计划本文的研究时间为一年，大致进度计划如下：第一季度：调研文献，确定研究方向和目标第二季度：设计气泡雾化喷嘴的方案，并进行数值模拟第三季度：建立实验测试平台，进行喷嘴雾化效果的试验第四季度：整理分析试验、仿真数据，撰写论文并进行答辩七、参考文献1. Yu Q, Han J, Zhao K, et al. Bubble sizes and bubble breakup mechanism in bubble column[J]. Chemical Engineering Science, 2012, 69: 153-162.2. Hu M, Wu H, Liu F, et al. Simulation on gas-liquid mixing in a rectangular microchannel under different gas-liquid flow rates[J]. Chemical Engineering Journal, 2018, 345: 487-496.3. Li G, Li Y, Chen X, et al. Bubble column: Experiment and simulation on bubble cloud characteristics[J]. Chemical Engineering Science, 2019, 206: 88-101.4. 刘一鸣. 气液两相流在农药喷雾中的应用研究[J]. 农业装备与机械化, 2015, 10(11): 45-48.5. 张强,李平,石聪聪,等. 液体气泡雾化喷雾对植物叶面农药的覆盖学研究[J]. 农业装备与机械化, 2018, 12(10): 28-35.。

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。