Motion and orientation of cylindrical and cubic particles in pipe flow with high concentration

第第175期卷第5期Vol.17No.52011年10月CHINAPOWDERSCIENCEANDTECHNOLOGYOct.2011doi：10.3969/j.issn.1008-5548.2011.05.017基于CFD-DEM方法的柱状颗粒在弯管中输送过程的数值模拟卢洲，刘雪东，潘兵（常州大学机械工程学院，江苏常州213016）摘要：针对物料在气力输送过程中特别是弯管部分易破碎的问题，采用在工业、农业以及物流运输业中，弯管应用非常计算流体力学（CFD）和离散单元法（DEM）耦合模拟弯管内的柱状颗粒气力输送过程，对弯径比k分别为1、2、3、4、6的90°弯管内柱状颗粒广泛。

弯管对气-固两相流流动的压降、管壁磨蚀、物的运动状态、碰撞特性、破碎原因及相关的力学特性进行研究。

结果表料破碎有很大的影响，对于弯管压降、磨损的作用机明：球形颗粒与柱状颗粒在输送过程中遵循基本一致的变化规律，同理及其应对措施，一直是研究、设计的重点之一[1]。

目样外部条件下，柱状颗粒的悬浮速度小于球形颗粒。

当k=3时气力输送前对于弯管的研究主要集中在高速输送的数值模拟过程颗粒的破碎率最低。

同时，颗粒与管壁的碰撞是造成颗粒破碎的主研究和管壁磨损的实验研究，对于颗粒在弯管中运动要原因。

关键词：气力输送；柱状颗粒；弯管；数值模拟的磨损机理研究较少。

中图分类号：TQ022.4文献标志码：A多年来，对于弯管部分的气-固两相流的研究都文章编号：1008-5548（2011）05-0065-05是把颗粒作为球形来处理，原因是非球形颗粒的形状非各向同性，处理起来非常复杂。

但是实际应用中，很NumericalSimulationofCylindrical多被输送物的形状更加接近于圆柱状，如小麦、催化ParticlesConveyinginCurvedDucts剂颗粒、包装工业中的碳酸钙等[2]，所以有必要对圆柱UsingCFD-DEMCoupledApproach状颗粒的运动进行研究。

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原本打算每人交一篇论文，但估计一部分同学会网上下载，凑数，所以，我们考试就是词汇，范围包括下面我列出来的和课后的，只要能根据英语写出汉语即可。

下周上课时间我们简单考一下，请大家复习一下。

第一课element（元素）, fundamental particles（基本粒子），protons, neutrons and electrons（质子，中子，电子），chemical identity（化学特性），nucleus （原子核），positively charged （带正电的），uncharged（不带电的），negatively charged （带负电的），electrically neutral（电中性的），atomic number（原子序数），Periodic Table（元素周期表），mass number（质量数），nucleon（核子），carbon（碳），orbital electrons（轨道电子），innermost electron（内壳层电子），naturally occurring（天然存在的），stable isotope（稳定同位素），unstable （不稳定的）or radioactive（放射性的），artificial means（人工手段），chemical bonds（化学键），nuclei（原子核nucleus的复数），chemical symbol（化学符号）, subscript（下角标），superscript （上角标），oxygen（氧），radioactive isotopes（放射性同位素），Hydrogen（氢），nuclear engineering（核工程），heavy hydrogen（重氢）or deuterium（氘），tritium（氚）mass and charge（质量和电荷）, atomic and nuclear physics（原子和原子核物理），atomic mass unit (u)（原子质量单位），one twelfth （十二分之一）carbon 12 （碳12），weighted mean （加权平均数），Avogadro’s Number（阿伏加德罗常数），compounds and molecules（化合物和分子），equal in magnitude and opposite in sign（数量相等，符号相反），electron-volt（电子伏特），mega electron-volt（兆电子伏特）( MeV)，unit electronic charge（单位电荷），potential difference （势差），classical principle（经典原理），conservation of mass（质量守恒定律），mass defect （质量亏损），principle of the equivalence of mass and energy（质能相当原理），interchange of mass and energy（质能转换），laws of conservation of mass and conservation of energy（质量守恒和能量守恒定律），release of energy（能量的释放）, absorption of energy（能量的吸收），equivalence between mass and energy（质能相当），force of electrostatic repulsion between like charge（同种电荷之间的静电排斥力）, force of attraction（吸引力），nuclear force（核力），nucleon（核子），Binding Energy（结合能），energy of chemical binding（化学结合能），Energy Level（能级），ground state of energy（能量基态），nuclear reaction （核反应），excited states or levels （激发态或激发能级），discrete excited states （分立的激发态），spacing of the levels （能级间隔），excitation energy （激发能），average lifetime （平均寿命），decay, or become de-excited（衰变或退激发），emission of high energy electromagnetic radiation （发射高能电磁辐射），fission （裂变），uranium （铀），transuranium elements（超铀元素），radioactive barium 139（放射性钡139），split into fragments （分裂成碎片），intermediate mass elements （中间质量的元素），medium mass number（中等质量数）, chain reaction （链式反应）uranium 235（铀235）, Thorium 232（钍232）, fissionable （可裂变的）, fissile（易裂变的），uranium 233 and plutonium 239（钚239）, low energy neutrons（低能中子），liquid drop model（液滴模型），short range nuclear forces（短程核力）, surface tension （表面张力）, action of the nuclear forces（核力作用），dumbbell shape （哑铃形），Coulomb force of repulsion （库仑排斥力），emission of gamma radiation（发射伽玛辐射），fission fragments （裂变碎片），neutrinos （中微子），macroscopic（宏观的）第二课radiation（辐射），material or electromagnetic origin（物质或电磁起源）, nuclear decay（核衰变），particle accelerator（粒子加速器）, cosmic rays（宇宙射线）, molecules, atoms, electrons, and nuclei（分子，原子，电子，原子核），photons（光子），target（靶），projectile （入射粒子），nuclear energy field（核能领域），nuclear reactor（核反应堆）, inert substances（惰性物质），protective shielding（防护屏），Excitation and Ionization （电离和激发），fluorescent light bulb（荧光灯泡）, vacuum tube （真空管），impart energy to （传递能量），excitation of electrons to higher energy states（激发电子到更高能态），emission of light（发光）.inner orbits （内层轨道），high energy radiation（高能辐射），heavy element target（重元素靶，X-rays due to transitions in the electronic orbits（电子在轨道间跃迁产生的X射线）, bremsstrahlung （韧致辐射），ion pair（离子对），range（射程）, millimeter（毫米），meter （米），Charged particles（带电粒子），fragments of fission （裂变碎片），heavy particles （重离子）, inertia（惯性），electrostatic interaction （静电相互作用），kinetic energy （动能），inversely proportional to（成反比例），million-electron-volt （百万电子伏特）high-speed charged ion （高速带电离子），mutual repulsion （相互排斥），hyperbolic path （双曲线轨迹），scatter（散射），initial energy （初始能量），scattering of the photon（光散射）, ionization by the photon（光电离）, pair production（电子对产生）. Photon-Electron Scattering（光-电子散射），rest mass （静止质量），bound to their nucleus（受原子核的束缚）, free stationary particles（自由静止粒子），physical principles of energy and momentum conservation（能量和动量守恒物理原理. Compton effect（康普顿效应）, scattered backward（背散射），the special theory of relativity （狭义相对论），cross section（截面），Photoelectric Effect（光电效应），incident photon （入射光子），light emission （发光）, Electron-Positron Pair Production（电子正电子对产生），be converted into matter（转变成物质），theory of the equivalence of mass and energy（质能相当理论），law of conservation of charge （电荷守恒定律），be annihilated as material particles（作为物质粒子湮灭）, substance（物质）, attenuation of gamma rays in matter （伽马射线在物质中的衰减），mean free path （平均自由程）,helium 4 （氦4），positive charge（正电荷），density of the material （物质密度），aluminum （铝），health hazard （健康危害），alpha-emitting isotope（α放射性同位素），be ingested in the body(摄入人体)，radioactive isotope（放射性同位素），a spectrum of energies（能谱），ingestion hazard（摄入危害）. penetrating power（穿透本领），radiation hazards （辐射危害），reactor shielding（反应堆屏蔽）.light elements （轻元素），beryllium（铍），Neutron（中子），average lifetime （平均寿命），Neutron Source（中子源），radium 226（镭226），potential scattering （势散射），compound nucleus formation（复合核形成），capture（俘获）。

牛顿流体圆管内非稳态Poiseuille流动特性陈雷;汤苑楠;刘刚;卢兴国【摘要】Poiseuille流动初始阶段存在速度发展的非稳态过程,会对测试结果造成偏差.为分析非稳态Poiseuille流动过程对测量黏度造成的偏差,以不可压缩牛顿流体为例,进行恒流量边界与非定常流量边界下的非稳态Poiseuille流动过程研究.以无量纲黏度和无量纲时间表征非稳态过程,建立数值模型,计算给出恒平均速度边界、从0线性增加平均速度边界和恒压力边界条件下无量纲黏度数值的变化规律.结果表明:非稳态过程中无量纲黏度数值随时间逐渐减小并最终趋于1,且不同边界条件下流动达到稳定对应的无量纲时间为定值.当边界类型确定时,非稳态过程的无量纲黏度数值可视为仅与无量纲时间有关的函数;对于不同类型边界条件,从0线性增加的平均速度边界、恒压力边界、恒平均速度边界条件对应的非稳态过程逐渐缩短.%At the initial stage of Hagen-Poiseuille flow, there is an unsteady process for the velocity developing which will cause deviation on the results of measurement. In order to analyze the deviation caused by the unsteady Poiseuille flow for the viscosity measurement,studies were carried out through a numerical model. Taking the incompressible Newtonian fluid as an example,we studied the unsteady Poiseuille flow process at a constant flow rate and unsteady flow rate boundary conditions. The dimensionless viscosity and dimensionless time were used to reflect the unsteady process and a numerical model was built. The variation rules of the dimensionless viscosity under the boundaries of the constant average velocity,the average ve-locity which increases linearly from 0,and the constant pressure drop were given via numericalcalculations. It was found that dimensionless viscosity falls to 1 with the time increasing and the non-dimensional time is a constant when the flow attains the stable state under different boundary conditions. When the types of boundary conditions are decided,the dimensionless vis-cosity can be viewed as a function only with respect to the dimensionless time in the unsteady process. For different types of boundary conditions,the unsteady processes reduce corresponding to the boundary conditions of the constant average veloci-ty,the constant pressure drop,and the average velocity which increases linearly from 0.【期刊名称】《中国石油大学学报（自然科学版）》【年(卷),期】2018(042)003【总页数】8页(P114-121)【关键词】流变学;非稳态Poiseuille流动;数值模型;边界条件;无量纲黏度;无量纲时间【作者】陈雷;汤苑楠;刘刚;卢兴国【作者单位】中国石油大学(华东)储运与建筑工程学院,山东青岛266580;山东省油气储运安全省级重点实验室,山东青岛266580;中国石化销售有限公司华南分公司,广东广州510000;中国石油大学(华东)储运与建筑工程学院,山东青岛266580;山东省油气储运安全省级重点实验室,山东青岛266580;中国石油大学(华东)储运与建筑工程学院,山东青岛266580;山东省油气储运安全省级重点实验室,山东青岛266580【正文语种】中文【中图分类】O357.1为保证原油管道的安全经济运行，须全面把握原油管道停输再启动过程，许多学者[1-3]开展了胶凝原油管道测试研究。

第２１卷第６期２０２３年６月动力学与控制学报J O U R N A L O FD Y N AM I C SA N DC O N T R O LV o l ．２１N o ．６J u n ．２０２３文章编号:１６７２Ｇ６５５３Ｇ２０２３Ｇ２１(６)Ｇ０１８Ｇ０１３D O I :１０．６０５２/１６７２Ｇ６５５３Ｇ２０２３Ｇ０７６㊀２０２３Ｇ０３Ｇ２２收到第１稿,２０２３Ｇ０５Ｇ０６收到修改稿．∗国家自然科学基金资助项目(１１９０２００１,１２０７２２２１,１２１３２０１０),N a t i o n a lN a t u r a lS c i e n c eF o u n d a t i o no fC h i n a (１１９０２００１,１２０７２２２１,１２１３２０１０)．†通信作者E Ｇm a i l :y a n gt i a n z h i ＠m e ．n e u ．e d u ．c n 输流管道动力学与控制的最新进展∗唐冶１,２㊀高传康２㊀丁千１㊀杨天智３†(１．天津大学力学系,天津㊀３００３５０)(２．安徽工程大学机械工程学院,芜湖㊀２４１０００)(３．东北大学机械工程与自动化学院,沈阳㊀１１０８１９)摘要㊀管道系统在航空航天㊁石油输送㊁深海探测㊁核能工程等工程领域发挥着输送流体的作用．由复杂结构功能设计㊁支承条件㊁内部流体和外部环境等因素引起输流管道中的流体和管道发生强烈地耦合,导致的动力学问题严重限制了输流管道在各种领域中的工程应用．因此,输流管道的复杂动力学行为引起了工程和科学领域学者们的广泛关注,本文综述和讨论了最新的输流管道振动控制的研究和进展．关键词㊀输流管道,㊀动力学,㊀振动控制,㊀最新进展中图分类号:O ３２４;O ３２２文献标志码:AR e v i e wo nD y n a m i c a n dC o n t r o l o fP i p e sC o n v e y i n g Fl u i d a n ∗T a n g Y e １,２㊀G a oC h u a n k a n g ２㊀D i n g Q i a n １㊀Y a n g Ti a n z h i ３†(１．D e p a r t m e n t o fM e c h a n i c s ,T i a n j i nU n i v e r s i t y ,T i a n ji n ㊀３００３５０,C h i n a )(２．S c h o o l o fM e c h a n i c a l E n g i n e e r i n g ,A n h u i P o l y t e c h n i cU n i v e r s i t y,W u h u ㊀２４１０００,C h i n a )(３．S c h o o l o fM e c h a n i c a l E n g i n e e r i n g a n dA u t o m a t i o n ,N o r t h e a s t e r nU n i v e r s i t y ,S h e n y a n g㊀１１０８１９,C h i n a )A b s t r a c t ㊀P i p e l i n e s a r eu s e d t oc o n v e y f l u i d i nt h ee n g i n e e r i n g f i e l d s s u c ha s a e r o s p a c e ,o i l t r a n s po r t a Ｇt i o n ,d e e p Ｇs e a e x p l o r a t i o n ,n u c l e a r p o w e r e n g i n e e r i n g a n d s o o n ．T h e s t r o n g c o u p l i n g b e t w e e n t h e p i p e s a n d f l u i d i s i n d u c e db y t h e c o m p l e xs t r u c t u r a l a n d f u n c t i o n a l d e s i g n ,s u p p o r t c o n d i t i o n s ,i n t e r n a l f l u i d a n d e x t e r n a l e n v i r o n m e n t ,r e s u l t i n g i nd y n a m i c p r o b l e m sw h i c hs e v e r e l y l i m i t t h ee n g i n e e r i n g a p pl i c a Ｇt i o no f t h e p i p e s c o n v e y i n g f l u i d i n v a r i o u s f i e l d s ．T h e r e f o r e ,t h e c o m p l e x d y n a m i c b e h a v i o r o f p i p e s c o n Ｇv e y i n g f l u i dh a s b e e na t t r a c t e dw i d e a t t e n t i o no f s c h o l a r s i ne n g i n e e r i n g an d s c i e n c e ．T h e l a t e s t r e s e a r c h a n d p r o g r e s s i nv i b r a t i o na n d c o n t r o l o f p i p e c o n v e y i n g f l u i d a r e r e v i e w e d a n dd i s c u s s e d i n t h i s p a p e r ．K e y wo r d s ㊀p i p e s c o n v e y i n g f l u i d ,㊀d y n a m i c ,㊀v i b r a t i o n c o n t r o l ,㊀r e c e n t d e v e l o p m e n t 引言输流管道通常是指输送流体的管状结构,作为各种工程系统中的一种重要的基本单元,被广泛地应用于航空航天㊁机械㊁土木㊁海洋㊁生物㊁核能㊁石油能源和动力水能等工程领域,如大型水利工程的压力管道,石油工程中的输油和输气管道,飞机和液体火箭中的输送推进剂管道,海洋钻探中的输油管道,以及核电工业的热交换管道等．由于内部流体和外部环境的作用,管道在传输流体过程中不可避免地出现许多动力学和稳定性问题．在工程中,失稳㊁大幅振动和混沌等复杂行为往往会使输流管Copyright ©博看网. All Rights Reserved.第６期唐冶等:输流管道动力学与控制的最新进展结构破坏㊁精度下降和寿命降低．随着科学技术的发展和进步,各种工程结构㊁机械和传输设备对振动环境㊁稳定性和抗振能力的要求越来越高．因此,研究输流管道振动及其控制问题具有重要的工程意义．输流管系统的振动问题研究可以追溯到十九世纪末,M a r v e lB r i l l o u i n在观察给草坪浇水的橡皮管时,发现流体高速流动引起管道自由端产生一些奇怪的运动,这一现象引起了他的学生B o u r r iér e的兴趣[１],并在１９３９年建立了输流管道的线性方程．但是,二次世界大战使相关研究工作遭遇停滞．直到１９５０年,A s h l e y和H a v i l a n d[２]分析了横跨阿拉伯工程管道的弯曲振动问题．随后,众多学者开始关注输流管系统的固有频率㊁振动波传播㊁稳定性和响应振幅等动力学行为[３Ｇ５]．１９８７年, P aïd o u s s i s[６]精辟地阐述了输流直管的线性振动问题,指出了当流速超过临界值时,悬臂输流管会发生颤振失稳,两端支承管道更容易屈曲失稳．随着研究的不断深入,学者们对输流管道动力学的研究考虑更为一般的三维模型,探索更为复杂的非线性现象．H o l m e s[７]在P aïd o u s s i s的输流管线性振动模型中引入了几何非线性,从而建立了系统的非线性运动方程,开启了非线性动力学的研究热潮．M e n g等[８]基于K a n e方程和R i t z方法,建立了输流管系统全局运动的三维非线性动力学模型,并利用增量谐波平衡方法研究了系统的非线性时域响应．G h a y e s h等[９]提出了悬臂输流管的非线性平面运动模型,应用伪弧长和直接积分方法构造系统的分岔图㊁时间历程图和相图,并指出了随着流速的增加,系统经历超临界的H o p f分岔后而进入颤振失稳．C h a n g和M o d a r r e sＧS a d e g h i[１０]利用有限差分方法讨论了悬臂输流管在基础激励下二维㊁三维概周期运动和混沌运动的流速条件．Lü等[１１]应用G a l e r k i n截断和数值技术研究了具有非线性弹簧耦合的两输流管系统的分岔和同步振动．Z h a n g 等[１２]数值地分析了在一般边界条件下具有附加质量弹簧约束输流管道的三维动力学,并通过分岔图㊁相图㊁功率谱密度图和庞加莱映射图等手段考察了系统分岔和混沌等复杂动力学行为．由于管道内液体流动的特殊性以及控制方程引入非线性后,系统固有频率之间可能存在一定的比例关系,这时模态的相互影响不容忽视,出现了内共振现象[１３]．同济大学的徐鉴教授[１４,１５]采用多尺度方法研究悬臂输流管的内共振,分别推导了３ʒ１㊁２ʒ１和１ʒ１内共振的条件,并用数值方法模拟了３ʒ１内共振下系统的非线性动力学行为．上海大学的陈立群教授[１６]考虑管内流速处于超临界区域,进一步研究了输流管的主共振和２ʒ１内共振,并解释了在稳态响应中发生双跳跃现象的机理．M a o等[１７]关注了超临界输流管在３ʒ１内共振情况下的强迫振动响应,研究发现了跳跃㊁饱和与滞后等现象,并通过数值方法检验了曲线平衡附近的局部分岔行为．管道所载流体经常由泵等装置提供动力,流体流速不可避免地带有脉动．当这种脉动频率和输流管系统的固有频率满足一定关系时,即使是小的脉动激励,也可能引起大的系统响应．因此,脉动流速所引起的参数振动是输流管系统的另一个重要的动力学问题．P a n d a和K a r[１８,１９]采用多尺度方法分析了３ʒ１内共振条件下脉动输流管系统的主㊁组合参数共振,并发现了鞍结分岔及H o p f分岔．北京工业大学的杨晓东教授[２０]讨论了脉动输流黏弹性管道在次谐波共振和组合谐波共振条件下的稳定性．华中科技大学的王琳教授课题组[２１]提出了一种脉动输流管的涡激动力学模型,并采用直接多尺度方法讨论了锁频条件下脉动参数共振对输流管系统涡激振动的影响,研究结果表明,只有锁频效应和脉动参数共振发生在同一阶模态上时,脉动参数共振才会对响应幅值产生明显的影响．北京工业大学的张伟教授课题组[２２]考察了超临界脉动输流管在１ʒ２内共振条件下的超谐波全局动力学,并通过辨别相空间中的多脉冲跳跃轨道说明发生混沌运动的条件．目前,随着解析方法[２３]㊁数值仿真[２４,２５]和实验手段[２６]的不断成熟,学者们更加关注工程实际情形下的输流管道振动问题,如海洋石油天然气钻井系统㊁盐矿卤水输送管路系统．为了满足不同的工程应用,不同形状,复杂约束,输送多相流体的,恶劣的工作环境下的管道动力学行为被大量地研究．同时,引进复合材料如功能梯度材料构造管道调控输流管道振动特性来增强输流管道的强度和提高系统的可靠性,也是另外一个重要的研究方向．此外,虽然振动抑制在工程应用中的需求越来越大,但是,关于输流管道振动控制的研究还是相对较９１Copyright©博看网. All Rights Reserved.动㊀力㊀学㊀与㊀控㊀制㊀学㊀报２０２３年第２１卷少．本文从一般输流直管/曲管㊁不同外形输流管道㊁复杂支承和约束输流管道㊁运动输流管道㊁内流和外流作用下输流管道㊁多相流输流管道㊁复合材料输流管道动力学特性及输流管道的振动控制等方面进行综述,全面地给出输流管道动力学与控制的最新研究进展．１㊀一般输流直管/曲管普通直曲输流管道的研究较为简单,计算工作量小,这种研究模型通常从工程实际中合理假设而得到的．在输流管道系统设计初始阶段,对精度要求不高的动特性预估是可行的．对于普通输流管道,边界条件通常被假设为两端支承和悬臂．T a n等[２７]考虑了T i m o s h e n k o模型,建立了纵横扭耦合振动模型,利用有限差分法和离散傅立叶变换方法,研究了初始幅值㊁外激振力和流速对系统的非线性频率和强迫响应特性的影响．并讨论了T i m o s h e n k o输流管道模型的优势．S a z e s h和S h a m s[２８]研究了高斯白噪声随机激励下悬臂输流管道的动力学,通过随机时间历程和概密度函数探索管道在颤振点附近的随机行为．G i a c o b b i等[２９]针对输流管道应用于海洋平台砖井开采甲烷晶体的工程问题,考虑管道传输高速的气体和沿管长方向变化的热环境,研究了轴向变密度输流管道的动力学,得出管道入口和出口的密度差对系统稳定性影响较大．H i g u c h i等[３０]提出识别悬臂输流管道自激振动的复模态实验技术,构造了输流管道系统发生颤振时的特征模态．L i等[３１]利用谱不变流形方法,对悬臂输流管道的非线性动力学模型进行降维,通过比较降维前后的系统自由振动㊁强迫振动响应㊁周期和概周期分岔以及同宿和异宿轨道等复杂的动力学行为,说明所提出的不变流形降维方法的有效性．Z h a n g和C h e n[３２]利用G a l e r k i n截断和多尺度方法,结合规范性理论和能量相方法,研究了悬臂输流管道在脉动流和外激励作用下的多脉冲跳跃轨道和混沌动力学．当管道内流体增加到临界值的,两端支承输流管道发生屈曲,由原来的绕直线平衡位置运动过渡到绕曲线平衡位置进行运动．目前,传播高速流下管道振动越来越普遍,也成为研究重点之一．T a n 等[３３,３４]针对高速流管道常常产生严重的振动问题,讨论了T i m o s h e n k o输流管道在超临界情况下的主共振㊁超谐波共振和参数振动行为,发现超临界情况下管道动力学行为比亚临界情况下更加复杂．L u等[３５]研究了输流管道在超临界流体作用下发生３ʒ１内共振和应力分布情况,并揭示了抑制内共振提高管道的疲劳生命的机理．Z h u等[３６]考虑黏弹性输流管道的面内和面外耦合作用和欧拉梁理论,利用频响图㊁力幅图㊁吸引盆㊁时间历程图和相图,研究了输流管道在亚临界和超临界情况下三维耦合动力学,说明了当出现２ʒ１内共振时,系统展现典型的跳跃㊁滞后并出现双峰响应．为适应工程操作和适应环境变化的安装,曲率比较大输流曲管在工程中应用比较广泛而被研究者重视,以便实现更加灵活性设计．O y e l a d e和O y e d i r a n[３７]考虑两端简支㊁两端固支和一端固支一端简支边界条件以及轻微弯曲输流曲管的纵横耦合特性,分析了系统在热载荷作用下的非线性动力学．Z h o u等[３８]利用绝对节点坐标方法,建立了悬臂轻微输流曲管的非线性控制方法,经过研究发现即使初始几何形变较小,管道流体引起的静态变形也是非常大的,系统的颤振失稳临界流速依赖于静态平衡构造,同时,关注了后屈曲非线性行为．C zＧe r w i n s k i和Łu c z k o[３９]引入轴向力的非线性成分,利用理论和实验方法分析了系统时间历程图㊁相图㊁运动轨迹㊁振动模态和分岔演化规律．研究了脉动流频率和幅值对输流曲管的各种参数振动影响．C h e n等[４０]以柔性机器人和生物医学为背景,利用绝对节点坐标方法,对具有任意初始构型的柔性输流曲管进行了几何精确性建模,预估了输流曲管的静态变形及稳定性和非线性振动等大变形行为．X u 等[４１]研究了轻微输流曲管涡激振动,他们发现了在稳定流情况下,系统存在针对绕流一三阶模态振动的锁频区域,其振动幅值随着外流体速度增加而增大;在脉动流作用下,系统展现出更加复杂的动力学行为．Y a n等[４２]研究了两端固支输流曲管的静态平衡构型的分岔和稳定性行为,分析了外力㊁流速和弧角对系统非线性响应的影响．２㊀复杂支承和约束管道在工程中,学者们在输流管道系统中增加复杂支承和约束,试图改善系统的动力学环境．Y aＧm a s h i t a等[４３]研究了具有弹性支承和端部质量的０２Copyright©博看网. All Rights Reserved.第６期唐冶等:输流管道动力学与控制的最新进展输流管道动力学,通过理论结合试验的方法关注了H o p f－H o p f耦合和两不稳定模态幅值的演化,在一定的参数区间,存在由H o p f－H o p f耦合而产生的混合模态自激振动．G u o等[４４]运用传递矩阵方法和实验技术,研究了并行输流管道系统在局部位置受到外激励干扰时振动传递问题,并分析了约束㊁流速和压力对振动传递特性的影响．P e n g等[４５]应用哈密顿变分原理,建立了含有运动约束倾斜输流管道的三维非线性运动微分方程,通过数值技术获取系统的相图和振动轨线说明运动规律．E l N a j j a r 和D a n e s h m a n d[４６]关注了沿着管长方向增加质量和弹簧提高横向和纵向管道的临界流速的可能行．A s k a r i a n等[４７]讨论了端部线性弹簧和扭转弹簧约束性输流管道在分数阶黏弹性地基支承情况下的稳定性．K h e i r i[４８]分析了两端强非线性横向和扭转弹簧约束下输流管道的非线性动力学,与悬臂输流管道相比,复杂约束输流管道展现更低的H o p f分岔流速,更高的振动位移幅值．在高流速下,存在概周期和混沌运动．M a o等[４９]利用模态校正结合投影方法,提出了处理具有非线性和非均匀边界的输流管道振动的近似解析方法,该方法利用谐波平衡法将边界非线性和非均匀项进行描述,通过更多谐波判别响应解的收敛性．与多尺度方法的解对比,说明提出的方法有效性．Z h o u等[５０]考虑几何大变形和弹性边界条件,计算了复合材料输流管道失稳临界流速和非线性频率,结果表明平移弹簧的变化对临界流速具有轻微影响,旋转弹簧能提高系统的稳定性．Z h o u等[５１]提出了具有局部刚化的悬臂输流直管和曲管的非线性模型,探索了局部刚段位置和长度对系统非线性静平衡构造和动力学特性的影响．结果表明局部刚段的出现影响两种管道的振动模态,曲管中出现周期１和周期２的运动,而直管中仅出现周期１的运动．P e n g等[５２]研究脉动流输流管道在运动约束作用下的横纵耦合非线性振动,通过相平面图㊁庞加莱映射图和功率谱密度图展现如概周期和混沌运动等复杂的运动规律．L i u 等[５３]提出了悬臂输流管道在松散约束下的涡激振动模型,通过分岔图和A r g a n d图及振型图说明了锁频现象及复杂动力学行为．３㊀运动有大运动叠加的输流管道学者们从工程领域中简化出三种运动管道模型:沿着管道轴线平动抽吸输流管道㊁绕管道轴线旋转的输流管道㊁绕管道径向旋转的输流管道．Y a n 等[５４]建立了沿轴向时变滑动输流管道的非线性动力学模型,研究了系统动力学稳定性和非线性行为,结果表明当流速超过临界值时,颤振幅值随着时间变化而改变,随着滑动率的增加,管道系统更容易失稳,而质量比和重力的增加能提高系统的稳定性．L i a n g等[５５]考虑旋转速度和流速脉动情形,提出了绕管道轴线旋转的输流管道非线性参数振动模型,利用多尺度方法分析了系统稳定性,通过数值方法模拟了系统非线性响应和空间振动形态．L i a n g等[５６]研究了绕管道轴线旋转的多跨功能梯度输流管道的动力学,结果表明引入中间支承可提高系统的稳定性,不同跨度的模态特征能确定管道振动幅值位置．E b r a h i m i和Z i a e iＧR a d[５７]提出了绕管道轴线旋转的悬臂压电输流管道振动模型,考察了流速㊁电阻㊁旋转速度和压电层覆盖角对系统的动力学轨线和稳定性影响．L i a n g等[５８]研究了绕管道轴线旋转的两端支承输流管道在内外流共同作用下的三维动力学．A b d o l l a h i等[５９]进行了绕管道径向旋转的输流管道在环流液体媒介中的稳定性分析,考虑双陀螺力的影响,通过解析和半解析解获取稳定性解．４㊀内流和外流作用下输流管道在工业领域,涉及输流管道同时受到内外流共同影响的系统也是非常常见的,例如,热交换器㊁钻井作业的钻柱和石油勘探,以及在 盐井洞穴 中提取碳氢化合物等．P aïd o u s s i s等[６０]综述了悬臂输流管道在内和反向外流作用下动力学问题．A b d e l b aＧk i等[６１]提出了悬臂输流管系在内外轴向流作用下的全局非线性模型,利用伪弧长延拓方法结合直接数值积分方法计算系统的运动微分方程,预估了不稳定性引起的颤振㊁超临界下的极限环振动和频率受外流的限制程度㊁重力㊁质量比等参数的影响．Z h o u等[６２,６３]利用能量方法推导了悬臂输流管道在轴向激励下的非线性三维控制方程,通过非线性数值方法预测了系统的非线性响应,流速在亚临界条件下,轴向激励能够产生共振响应,超临界情况下,轴向激励在某些特定区间能使系统稳定,非平面周期自激振动演化成平面概周期或周期运动．J i a n g 等[６４]研究了两端支承输流管道在轴向内外流作用１２Copyright©博看网. All Rights Reserved.动㊀力㊀学㊀与㊀控㊀制㊀学㊀报２０２３年第２１卷下的稳定性和三维非线性动力学,揭示了一些有趣动力学现象如周期㊁概周期和混沌运动等．A b d e lＧb a k i等[６５]提出了悬臂输流管系在部分限制外流作用下的非线性理论模型,探索了环向区域的参数对动力学行为影响,通过实验验证了提出模型的有效性．M i n a s和P aïd o u s s i s等[６６]搭建了悬臂管系在内外流作用下实验平台,上部环绕部分由一个同心圆的刚性圆柱形管组成,并安装在一个装满水的水箱中．水从管道上部流入,在其自由端排入水箱,理论和实验预测了环状流强烈地影响管系失稳．B u t t 等[６７]提出了悬挂吸水管道系统在内外流作用下线性模型,研究了一定内外流速比下的系统复模态,结果表明在足够高外流速下,系统失稳主要由一阶颤振引起．C h e h r e g h a n i[６８]利用实验方法研究了悬臂输流管道在反向环流作用下动力学问题,当外内流速比较低时,系统失稳由二阶模态颤振引起;当外内流速比较高时,管道经历静变形,伴随着高速内流引起的周期和混沌等复杂动力学行为．D a n eＧs h m a n d等[６９]执行了部分限制悬臂管道在内和反向外流作用下的耦合双向流固耦合分析．Z h o u 等[７０]建立了端部锥形悬臂输流管道在内外轴向流作用下的动力学模型,研究了系统失稳边界和模态及非线性振动幅值和形态．５㊀多相流输流管道在石油和天然气开采领域,存在石油和天然气混合油气井,为降低成本,通常采用油气混合输送模式,这是典型的气液两相流．较普通的单相流㊁多相流造成许多缺点,如承载能力的降低㊁流体物理性质的变化㊁流体流动的中断和系统效率的降低等[７１]．这些缺陷为动力学设计带来相应的挑战,如空间密度变化引起流速的暂态变化,进而引起参数振动等．因此,研究多相流输流管道的振动特性具有重要的设计意义．E b r a h i m iＧM a m a g h a n i等[７２]提出了立管传输气液两相流的数学模型,应用G a l e rＧk i n截断和特征值分析得到了如气体体积分数㊁流速㊁结构阻尼和重力参数对系统稳定性的影响．G u o 等[７３]研究了管中管系统在热环境和二相流作用下的动力学特性和稳定性,通过A r g a n d图㊁稳定图㊁时间历程图说明了在超临界流作用下,不同于单相流,二相流系统展现了二管道耦合颤振失稳．M a和S r i n i l[７４]数值研究了传递气液两相流倾斜弯曲输流管道的平面动力学．L i u等[７５]采用绝对节点坐标方法,建立了海洋立管在内部二相流作用下的非线性数学模型．通过时域和频域的变化,说明了提出建模方法的有效性．O y e l a d e和O y e d i r a n[７６]利用哈密顿变分原理,建立了传递二相流水平管道的非线性控制方程,分析了初始变形㊁体积分数和质量比对系统的频率㊁临界流速㊁响应位移分岔和混沌的影响．Z h o u等[７７]研究了传递气液两相流倾斜输流管道的自由振动和稳定性,结果表明,倾斜引起的重力对系统振动特性具有重要的影响,随着倾斜角度加大,系统临界气体速度和振动频率降低,系统更容易失稳;对于给定倾斜角,系统对表面气体/液体速度的动态响应与质量比直接相关．E b r a h i m iＧM a m a g h a n i等[７８]通过特征值求解,研究了两端支承输送二相流管道系统的稳定性,同时给出了非线性振动频率闭式解,结果表明系统稳定性随着液相密度的降低而提高,提高气体分数和流体混合速度可增大系统非线性振动频率．C h a n g等[７９]研究了含气液两相流输流管道在洋流作用下的涡激锁频特性,利用哈密顿变分原理,建立了管道系统平面运动微分方程,范德波尔振动模型模拟洋流的涡激力,N e w m a r kＧβ和四阶龙哥库塔法求解系统动力学响应．得到了锁频区间随着液相速度㊁纤维方向角的增大而向右移动,而轴向张力增大使锁频区域向左移动．X i e等[８０]针对多相流引起的流体变密度,研究了输流管道经历涡激振动情况下的非线性参数振动行为,结果表明,当内部流体密度在不同系统固有频率附近波动时,管道的振动会变得不均匀或非周期性,位移量会增加或减少．随着内部流体波动幅度的增大,密度较大时,这些现象就会变得更加明显．随后,X i e等[８１]将变密度输流管道扩展到系统经历c r o s sＧf l o w和i nＧl i n e耦合涡激振动的动力学响应分析,给出了在不同参数共振下的管道系统不同模态被激励的动力学特性．６㊀复合材料输流管道动力学特性复合材料是由两种或两种以上的材料复合而成的新材料,从而能改善材料的力学性能．比较典型的功能梯度材料由体积含量在空间位置上可连续变化的两组分材料组成．在制造这种材料时,通过改变组分的体积指数率而使该材料具有物理属性分布沿着某一方向连续梯度变化的性质．与传统２２Copyright©博看网. All Rights Reserved.第６期唐冶等:输流管道动力学与控制的最新进展材料相比,功能梯度材料拥有很多优点,例如,缓解或消除材料的应力集中,提高结构连接强度和增强结构抗热腐蚀性能等[８２]．因此,在工程领域中制造重要部件广泛采用这样的材料．最近,学者们为了优化动力学特性而将功能梯度材料引入输流管系统．R e d d y等[８３]提出应用功能梯度材料构造管道来提高传递热流体的稳定性,采用谐波平衡法和龙格库塔法获取系统时域和频域响应．在前屈曲构造,一阶和二阶主参数振动不稳定区域发生偏差;在后屈曲状态下,通过间歇过渡路径㊁循环折叠分岔㊁周加倍分岔和亚临界分岔而产生混沌运动．L u等[８４]分析了内共振和轴向功能梯度材料对输流管道疲劳寿命的影响,应用G a l e r k i n截断和直接多尺度方法得到主共振和３ʒ１内共振情况下的可解性条件,研究结果表现内共振缩短轴向功能梯度管道的疲劳寿命,降低功能梯度分布系数有利于降低系统共振响应和最大应力．Z h u等[８５Ｇ８７]研究了多孔功能梯度输流管道在初始变形下后屈曲静态和动态特性,在弹性地基下的非线性自由和强迫振动,以及三维非线性动力学．G u o等[８８]提出了随机轴向功能梯度材料构造输流管道系统的有效统计性固有频率分析方法．L i u和L i[８９]考虑高阶圆柱梁模型和几何非线性,建立了功能梯度输流管道在弹性地基下的非线性控制方法和边界条件,采用微分求积方法确定系统的非线性频率和幅频响应,并揭示了几何和物理参数对系统动力学行为影响．C h a n g等[９０]预估了具有初始变形下弹性地基功能梯度输流管道静态屈曲和后屈曲动力学特性．除此之外,B a b a e i[９１]利用二步扰动法,研究了功能梯度碳纳米管增强输流管道的热前屈曲和后屈曲的频率响应受几何特性㊁地基刚度㊁碳纳米管增强分布形式和体积分数的影响．G h a d i r i a n等[９２]基于T i m o s h e n k o梁模型,研究了功能梯度碳纳米管增强输流管道的非线性自由振动和稳定性．R e n等[９３]针对工程中飞机中输流管道存在内流和外载荷联合作用下流固耦合振动,研究了功能梯度石墨烯增强输流管道在前屈曲和后屈曲情况下碰撞动力学和突跳行为受流速㊁碰撞速度㊁结构材料和几何因子的影响．结果表明,随着碰撞能量提高,流体促使后屈曲管道展现对称的双稳态特征,结构阻尼对响应影响较大．L i和L i u[９４]考虑高阶剪切变形梁模态,建立了各项异性复合材料输流管道在弹性地基下的非线性振动模型,利用微分求积方法和迭代算法确定了非线性频率和幅频响应．G u o等[９５]关注了悬臂弹性连接双复合材料输流管道系统的流固耦合失稳和分岔特性,通过A r g a n d图分析了颤振失稳,利用分岔图㊁时间历程和相图等非线性动力学分析手段,研究了系统在后屈曲情况下的周期和概周期等复杂现象,并发现了二管道的纤维排布方法能打破系统对称稳定性区间和分岔行为．G u o等[９６,９７]研究了具有时变张力复合材料输流管道在亚临界和超临界下的非线性动力学,以及在热环境下的屈曲和后屈曲行为．７㊀输流管道的振动控制输流管道动力学分析的最终目的是振动控制,减少管道振动幅值,改善其工作的动力学环境,提高机械系统运转的可靠性．目前,对于输流管道的振动控制研究主要分为优化设计结构的控制㊁被动控制和主动控制．工程中应用的输流管道,安装和设计是固定的,因此外激励频率的变化范围也是一定的．通过理论分析和实验方法,调谐管道参数㊁支承位置㊁材料和结构布置方式等,可实现系统固有频率和模态的避免共振的调控,实现管道的振动控制．S h o a i b 等[９８]通过对带隙的实验分析,利用周期性惯性放大机构来减弱输流管道的振动．通过考虑轴向运动和旋转运动,L i a n g等[９９]提出了一种新的输送流体声子晶体(P C)管模型,并发现了耦合区域的振动自抑制行为．L y u等[１００]根据带隙产生的机理提出了一种超薄压电晶格来抑制输流管道的振动．在旋转局部共振输流管道的基础上,L i a n g等[１０１]人提出了一种新的动态超材料结构．结果表明,局部谐振管更容易形成低频带隙,有利于振动抑制．以往的研究主要集中在通过系统本身的优化设计来抑制输流管道的振动．通过引入特定的阻尼力,提出被动控制,以达到更好的减振效果．被动控制方法由于结构设计简单,不需要外部能源,能有效地减小结构在高频段的振动,已被广泛应用于结构振动的抑制．K h a z a e e等[１０２]提出了一种由两个线性弹簧㊁一个轻质量块和一个线性阻尼器组成的被动非线性吸振器,它以接地和非接地的形式与管道连接,以实现对输流管道的振动抑制．D i n g 等[１０３]使用由三个线性弹簧组成的准零刚度系统作３２Copyright©博看网. 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Lateral Migration and Nonuniform Rotation of Biconcave Particle Suspended inPoiseuille Flow*WEN Bing-Hai(闻炳海)1,2,3,CHEN Yan-Yan(陈艳燕)4,ZHANG Ren-Liang(张任良)1,ZHANG Chao-Ying(张超英)3**,FANG Hai-Ping(方海平)11Shanghai Institute of Applied Physics,Chinese Academy of Sciences,Shanghai2018002University of Chinese Academy of Sciences,Beijing1000493College of Computer Science and Information Engineering,Guangxi Normal University,Guilin5410044Department of Physics,Zhejiang Normal University,Jinhua321004(Received25January2013)A biconcave particle suspended in a Poiseuille flow is investigated by the multiple-relaxation-time lattice Boltz-mann method with the Galilean-invariant momentum exchange method.The lateral migration and equilibrium of the particle are similar to the Segré-Silberberg effect in our numerical simulations.Surprisingly,two lateral equilibrium positions are observed corresponding to the releasing positions of the biconcave particle.The upper equilibrium positions significantly decrease with the increasing Reynolds number,whereas the lower ones are almost insensitive to the Reynolds number.Interestingly,the regular wave accompanied by nonuniform rotation is exhibited in the lateral movement of the biconcave particle.It can be attributed to the fact that the biconcave shape in various postures interacts with the parabolic velocity distribution of the Poiseuille flow.A set of contours illustrate the dynamic flow field when the biconcave particle has successive postures in a rotating period.PACS:47.11.Qr,47.11.−j DOI:10.1088/0256-307X/30/6/064701The phenomena of inertia-induced cross-stream migration of suspended particles in Poiseuille flow have received wide interest since the classical investigations,[1]which reported that neutrally buoy-ant spheres in a pipe flow would migrate away from the wall and reach a certain lateral equilibrium posi-tion,namely the Segré-Silberberg effect.After many theoretical,experimental and numerical efforts were made to investigate and analyze the phenomena,[2−6] recently researching interests turned to the biolog-ical flows,especially the movement of cells or col-loid particles in a tube flow.[7−11]The lateral mi-gration of vesicles is considered as the interplay be-tween nonlinear character of a Poiseuille flow and vesi-cle deformation.[8]Theoretical analysis ascribed the cross-stream shift to the ratio of the inner over the outer fluid viscosities.[9]The more recent studies ob-served that vesicles presented two motion patterns(os-cillation and vacillating breathing)[10]or a phase dia-gram of shapes(bullet,croissant and parachute).[11] The red blood cell of human beings could be the most famous vesicle in biological flows.Without a cell nucleus,it generally exhibits a biconcave shape in rest state and some viscoelastic deformations in blood flow.[12−14]However,sizeable disparities can still be noticed among numerical simulations and ex-perimental observations due to its tiny size and com-plex characteristics.[10−16]It is therefore meaningful to obtain some credible benchmarks by simple mod-els in order to understand the essential behaviors of particles with various geometries.For example,the investigations of an ellipse in sedimentations,[17]shear flow[18]and Poiseuille flow[4]can make active contri-butions to the research of blood circulation of birds, whose red blood cell is oval or elliptical in shape with a nucleus inside.In this Letter,we use a simple model to in-vestigate a biconcave particle suspended in a two-dimensional Poiseuille flow by the lattice Boltzmann method,[19−22]which has developed into an alterna-tive and promising numerical scheme for simulating complex fluid flows.The multiple-relaxation-time model can be written as[23−25]f i(x+e iδt,t+δt)−f i(x,t)=−M−1·S·[m−m(eq)],(1) where f i(x,t)is the particle distribution function at lattice site x and time t,moving along the direc-tion defined by the discrete speeds e i,andδt is the time step;m and m(eq)represent the velocity mo-ments of the distribution functions and their equilib-ria,respectively;M is a linear transformation matrix mapping between moment space and discrete veloc-ity space;S is a diagonal matrix of nonnegative re-laxation rates.The hydrodynamic force can be eval-uated simply and efficiently by the momentum ex-change method in the lattice Boltzmann method.[26,27] Taking Galilean invariance[28]into account,Wen et al.recently proposed a Galilean-invariant momentum exchange method by introducing the relative velocity into the interfacial momentum transfer,[29]F(x s)=(e i−v)f i(x f,t)−(e¯i−v)f¯i(x b,t).(2)*Supported by the National Natural Science Foundation of China under Grant Nos10825520and11162002,and the National Basic Research Program of China under Grant No2012CB932400.**Corresponding author.Email:****************.cn©2013Chinese Physical Society and IOP Publishing Ltdwhere x f and x b are of a fluid node and a boundary node on a fluid-solid link,respectively.The boundary has a vector velocity v at the point of intersection x s. It is demonstrated to greatly enhance the hydrody-namic accuracy and robustness of moving boundaries in dynamic fluid.In particular,the algorithm meets full Galilean invariance and is independent of bound-ary geometries.The total hydrodynamic force and torque acting on the solid particle are evaluated byF=∑︁F(x s),T=∑︁(x s−R)×F(x s),(3)where R is the mass center of the solid particle,and the summation runs over all the fluid-solid links.Fig.1.Schematic diagram of a biconcave particle sus-pended in a Poiseuille flow.Figure1illustrates a schematic diagram of a bi-concave particle suspended in a Poiseuille flow.Both densities of the fluid and the particle are1g/cm3.The width of the channel is0.1cm and the kinematic vis-cosity isυ=0.01cm2/s.The Reynolds number is de-fined to characterize the flow domain by Re=HU/υ, where U is the mean velocity of the Poiseuille flow without particle and H is the width of the channel. The biconcave shape of a red blood cell was described by Fung et al.[30]as follows:y=12[︁1−(xR)2]︁1/2[︁C0+C1(xR)2+C2(xR)4]︁,(4)where C0=0.81,C1=7.83,C2=−4.39and R=2.91.The noncircular geometry of a biconcave particle will lead to regular wave and nonuniform rota-tion,and these will impact the fluid field of Poiseuille far more than a circular particle.[27]Therefore,we con-figure a large computing scale to improve the simulat-ing accuracy,as well as a longer channel to eliminate the influence of the inlet and outlet.The width of the computational domain is H=100lattice units,the length is20times the width,and the particle radius is R=15lattice units.The relaxation rates are given by S=diag(0,1.64,1.54,0,1.9,0,1.9,1/0.6,1/0.6). Thus,a second of movement covers300000time steps of the evolution computation.An iterative interpola-tion algorithm is utilized to solve the realtime posi-tions of biconcave boundary and the computing error is restricted to less than1×10−6.The second-order in-terpolation boundary condition[31]is adopted to com-pute the distribution functions bounced back from the curved particle boundary.The pressure boundary condition[32]is applied both at the inlet and outlet of the channel in order to drive fluid flow and form a Poiseuille flow.With the parallel optimization of Intel OpenMP,a following simulation which contains60s of particle movement performs18-million time steps and takes about60h on a HP Z600computer with12cores inside.0000000Fig.2.The migrating trajectories of a biconcave particle in a Poiseuille flow with two Reynolds numbers(a)Re=3 and(b)Re=12.The particles in the red and the blue trajectories are released at0.02and0.04cm away from the low wall,respectively.The black trajectories represent the classic Segré-Silberberg effect in which the particle is a cir-cle.Fig.3.The impact of Reynolds numbers on(a)the fi-nal equilibrium positions and(b)the rotating period of the particle.The particles in the red and blue lines are released at0.02and0.04cm away from the low wall,re-spectively.The biconcave particles are released at0.02and 0.04cm in the low half of the flow field and at the cen-ter of the channel in the horizontal direction,respec-tively.The lattices will be redrawn when the particle moves more than two lattice lengths in the horizontal direction in order to keep the particle in the middle of the channel all the time.Figure2draws the trajec-tories of the particle at the Reynolds numbers 3and 12,respectively.The lateral migration and equilib-rium with periodic wave are clearly observed.We also present the trajectories of the classic Segré-Silberberg effect with the circular particle of radius 15as com-parisons.As shown in Fig.2,it is usual that a sin-gle lateral equilibrium position is located between the wall and the centerline of the channel for the classic Segré-Silberberg effect.[2,6,8,10]Surprisingly,two lat-eral equilibrium positions are exhibited for biconcave particles and they are located at both sides of the equi-librium position of the circular particle.The smaller the Reynolds number is,the more slowly the particle reaches the equilibrium and the farther the two equi-librium positions separate.These trends can be seen more clearly in Fig.3(a),in which a set of Reynolds numbers are simulated.The upper equilibrium positions become significantly low with the increase of the Reynolds number,whereas the lower ones are almost insensitive to the Reynolds number.It should be noted that the horizontal axis in Fig.3uses a binary logarithmic coordinate.(b)0.00.20.40.60.81.002468w (r a d /s )PeriodY (c m )Fig.4.(a)The trajectory and orientation and (b)theangle velocity of the biconcave particle in a single rotating period.Although the biconcave particle in a Poiseuille flow behaves like the Segré-Silberberg effect,it includes ad-ditional regular wave andnonuniform rotationdue tothenoncirculargeometry.Explicitly,we definearo-tatingperiod asatimeintervalinwhich abiconcaveparticlerotates around.As shown in Fig.3(b),the rotating periods are monotonic decreasing with the increase of the Reynolds numbers.Notably,the ro-tating periods of the upper equilibrium positions are always longer than the lower ones and the gaps be-tween them show a continuous narrowing.These oc-cur as a result of the parabolic velocity distribution of a Poiseuille flow.The speeds of flow at the upper posi-tions are higher than those at the lower ones,and the velocity differences reduce continuously since they ap-proach each other along with the increasing Reynoldsnumbers.The trajectory and angle velocity of the biconcave particle in a single period in equilibrium state are il-lustrated in Fig.4,together with the orientations of the particle in various typical positions.The Reynolds number is 3and the particle starts from 0.02cm away from the low wall and rotates clockwise.The migrat-ing trajectory reaches the ridges when the particle an-gle is about 0πand 1π,and two steeper sub-ridges at about 0.5πand 1.5π.Noticeably,the ridges match the minimum angle velocities whereas the sub-ridges match the maximum ones.The peaks of the trajectory have a little lag relative to the angle of the biconcave particle.Four similar troughs lie about 0.25π,0.75π,1.25πand 1.75π.Their corresponding angle velocities are moderate while change is fast.The mechanism of lateral migration in the Segré-Silberberg effect is usually explained by the inertia effect.[6]The additional wave and nonuniform rota-tion in our simulations are due to the interaction of the biconcave shape and the parabolic velocity distri-bution.The fluid velocity at the upper part of the particle is always faster than that at the lower part and the difference drives the particle to rotate inces-santly.The changes of the posture would impact the hydrodynamic forces exerted by the fluid flow.It can be indicated in Fig.4that the biconcave particle exerts a dropping force in the angle range of about 0–0.25πand a lifting force in the angle range of about 0.75–1π.The flow field around the biconcave particle is care-fully investigated by the following contour diagrams.-6T10-5-6T10-5Fig.5.The contours of vertical velocities of the fluid around the biconcave particle:(a)–(f)corresponding to the first six positions in Fig.4(a).Since a Poiseuille flow is a well-defined laminar flow,the vertical velocity of the present flow field orig-inates totally from the wave and rotation of the bicon-cave particle and is far more sensitive to the particle motion than the horizontal velocity.Therefore we ap-ply the contour of the vertical velocity to character-ize the flow field.Figures 5(a)–5(f)are the counter-parts of the first six locations in Fig.4(a).Figure 5(a)is at the highest position with a horizontal posture and the smallest angle velocity,and the flow is mild and bilaterally balanced.Figures5(c)and5(e)are at the troughs with sloping postures,and the flows are strong.Figures5(b)and5(f)draw the rising and falling stages,and thus the upward and downward flows dominate the flow field,respectively.Figure5 illustrates the successive changes and depicts the dy-namic flow field vividly.In summary,we perform a series of numerical sim-ulations of a biconcave particle migrating laterally in a Poiseuille flow by the lattice Boltzmann method with multiple relaxation times.The hydrodynamic force is evaluated by the Galilean-invariant momentum ex-change method.Because of the interaction of the biconcave shape and the parabolic velocity distribu-tion,two lateral equilibrium positions are found for the biconcave particle corresponding to its releasing points.This makes a remarkable distinction to the classic Segré-Silberberg effect,in which a single equi-librium position is observed for a circle or sphere.Ex-tending the simulations to a range of Reynolds num-bers,we observe that the upper equilibrium positions significantly decrease with the increasing Reynolds number while the lower ones are almost insensitive to the Reynolds number.Inside a single rotating pe-riod,the biconcave particle moves with regular wave and the nonuniform angle velocity.The dynamic flow fields around the particle are illustrated vividly by the contours of the vertical velocities when the bicon-cave particle has successive postures.The investiga-tion will be expanded to combine with the viscoelastic membrane[12]in order to enrich the understanding of the behaviors of red blood cells and other vesicles in dynamic fluid.The authors thank Shanghai Supercomputer Cen-ter of China for the support of computation. References[1]Segre G and Silberberg A1962J.Fluid Mech.14115[2]Karnis A,Goldsmith H L and Mason S G1966Can.J.Chem.Eng.44181[3]Asmolov E S1999J.Fluid Mech.38163[4]Qi D,Luo L,Aravamuthan R and Strieder W2002J.Stat.Phys.107101[5]Zhang C Y,Tan H L,Liu M R,Kong L J and Shi J2005Chin.Phys.Lett.22896[6]Matas J P,Morris J F and Guazzelli E2004J.Fluid Mech.515171[7]Fang H P,Wang Z W,Lin Z F and Liu M R2002Phys.Rev.E65051925[8]Kaoui B,Ristow G H,Cantat I,Misbah C and Zimmer-mann W2008Phys.Rev.E77021903[9]Danker G,Vlahovska P M and Misbah C2009Phys.Rev.Lett.102148102[10]Shi L L,Pan T W and Glowinski R2012Phys.Rev.E86056308[11]Coupier G,Farutin A,Minetti C,Podgorski T and MisbahC2012Phys.Rev.Lett.108178106[12]Li H B,Yi H H,Shan X W and Fang H P2008Europhys.Lett.8154002[13]Jiang L G,Wu H A,Zhou X Z and Wang X X2010Chin.Phys.Lett.27028704[14]Dupire J,Socol M and Viallat A2012Proc.Natl.Acad.Sci.U.S.A.10920808[15]Fedosov D A,Caswell B and Karniadakis G E2010Biophys.J.982215[16]Shen Z Y and He Y2012Chin.Phys.Lett.29024703[17]Xia Z H,Connington K W,Rapaka S,Yue P T,Feng J Jand Chen S Y2009J.Fluid Mech.625249[18]Huang H B,Yang X,Krafczyk M and Lu X Y2012J.FluidMech.692369[19]Qian Y H,d’Humières D and Lallemand P1992Europhys.Lett.17479[20]Qian Y H and Orszag S A1993Europhys.Lett.21255[21]Chen S Y,Chen H D,Martinez D and Matthaeus W1991Phys.Rev.Lett.673776[22]Chen S Y and Doolen G D1998Annu.Rev.Fluid Mech.30329[23]d’Humières D1992Prog.Aeronaut.Astronaut.159450[24]Lallemand P and Luo L S2000Phys.Rev.E616546[25]Luo L S,Liao W,Chen X,Peng Y and Zhang W2011Phys.Rev.E83056710[26]Li H B,Lu X Y,Fang H P and Qian Y H2004Phys.Rev.E70026701[27]Wen B H,Li H B,Zhang C Y and Fang H P2012Phys.Rev.E85016704[28]Qian Y H and Zhou Y1998Europhys.Lett.42359[29]Wen B H,Zhang C Y,Tu Y S,Wang C L and Fang H P2013arXiv:1303.0625[physics.flu-dyn][30]Fung Y C1981Biomechanics:Mechanical Properties ofLiving Tissues(New York:Springer Verlag)[31]Lallemand P and Luo L put.Phys.184406[32]Zou Q S and He X Y1997Phys.Fluids91591。

vray百科名片vrayVRay是由chaosgroup和asgvis公司出品，中国由曼恒公司负责推广的一款高质量渲染软件。

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目录简介V-Ray for 3dmaxVray for Cinema4Dvray for SketchupVray的工作流程VRay的渲染参数VRay 灯光VRay 材质简介V-Ray for 3dmaxVray for Cinema4Dvray for SketchupVray的工作流程VRay的渲染参数VRay 灯光VRay 材质∙VRay 阴影∙使用vray如何加快max的渲染速度展开简介VRay渲染器提供了一种特殊的材质——VrayMtl。

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V-Ray for 3dmax目前世界上出色的渲染器却为数不多，如：Chaos Software公司的vray, SplutterFish 公司的brazil,Cebas公司的Finalrender,Autodesk公司的Lightscape，还有运行在Maya上的Renderman等。

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VR在3dmax的界面V-Ray for 3dmax是3dmax的超级渲染器,是专业渲染引擎公司Chaos Software公司设计完成的拥有Raytracing（光线跟踪）和Global Illumination(全局照明)渲染器，用来代替Max 原有的Scanline render（线性扫描渲染器），VRay还包括了其他增强性能的特性，包括真实的3d Motion Blur(三维运动模糊)、Micro Triangle Displacement(级细三角面置换)、Caustic(焦散)、通过VRay材质的调节完成Sub-suface scattering(次表面散射)的sss效果、和Network Distributed Rendering(网络分布式渲染)等等。

Flow3d软件简介Flow3d software profilePublished: 2009-5-20 11:21:43 source: China - build China die casting web casting industry and Trade Information Center flagship online text and FLOW-3D] [simulation tool of high efficient, engineers can according to self define various physical models, used in various engineering fields. By accurately predicting free surface flow (free-surface, flows), the FLOW-3D can assist you in improving the existing process in the engineering field.FLOW-3D is a full set of software that does not require additional grid generation modules or post-processing modules.A fully integrated graphical user interface allows users to quickly complete simulation project settings to result output.Mesh and geometry Meshing & Geometry:Structured finite difference method meshMulti block grid technology supports embedded or connected grid blocks.Fractional areas/volumes (FAVOR) technology enables efficient and precise definition of geometric appearanceFree mesh settingsBuilt in basic geometry generatorYou can read various CAD format filesFlow type options Flow, Type, Options:In pipe flow, pipe outflow, and free surface flow modelSupport three-dimensional, two-dimensional or one-dimensional problem calculationTransient flow calculationSupport Cartesian coordinate system or cylindrical coordinate systemSupports non viscous, viscous, laminar, and turbulent flows Multiple quantitative values, specified calculations Coordinate axis calculationTwo phase flowHeat transfer calculation (including phase change) Saturated and unsaturated porous materialFlow definition options Flow, Definition, Options:General initial conditionsBoundary conditionsSymmetryRigid wallContinuousCycleSpecified pressureSpecify speedOutflowMesh overlapStill waterReboot optionsContinuation simulation calculationFrom the previous simulation, the overlapping data is computed . add, remove or change the model parametersNumeric model options Numerical, Modeling, Options:.Volume-of-Fluid (VOF) method tracing fluid boundary --TruVOFEfficient geometric definition of.Fractional areas/volumes (FAVOR). one order, two order and three order flow calculation advection.Sharp fluid interface trackingImplicit solution and explicit solution calculationSupport Point, line, relaxation, and GMRES pressure solversUser defined variables, sub programs, and outputsA computational iteration tool for executing programsFluid model options Fluid, Modeling, Options:A single incompressible fluid - confined or with free surfacesTwo types of incompressible fluids - miscible, or, with, sharp, interfaces, etc.Compressible fluids - subsonic, transonic, supersonicSaturated fluidAcoustic phenomenaMass particles of different density / diameterHot model option Thermal Modeling Options:Natural convectionForced convectionFluid and solid heat conductionFluid and solid heat transferThermal conduction.Designated heat fluxSpecified temperatureHeat transfer from fluid / object to spaceEnergy distribution / concentration in a fluid or solid The heat radiation of the Yi.Viscous heatPhysical model option Physical Modeling Options: Erosion and erosion depositsCavitationPhase change (liquid gas, liquid solid)Surface tensionThermosyphon phenomenonAdhesion of contact surfaceRoughness of contact surfaceSteam and bubblesCuring and melting (heat-of-transformation, table)Mass / momentum / energy generation settingDistributed mass / energy generatorShear change, viscosity model of density change and temperature dependenceThixotropic viscosityElastic tensionElectric fieldInsulation phenomenonElectroosmosisElectrostatic particlesElectric drive phenomenonJoule heatingCoil gasMolecular and turbulent diffusionSpecial physical model Special, Physical, Models:Six degrees of freedom, general moving objects, --user, specified, motion, or, fully-coupled, with, rigid, motion, body, etc.Rotating objectsLinear and, quadratic, flow, losses)Collision modelMetal casting model Metal, Casting, Models:Curing / melting (heat-of-transformation, table)Curing shrinkageTwo element segregation during solidificationThe rate of cure affected by latent heat release Thermal cyclingDefect trackingCavitation modelLost foam casting modelSemi solid material modelSand mould moisturePlunger head movementBack pressure and exhaustSand core blowingTurbulence model Turbulence, Models:.Prandtl mixing length.One-equation transport.Two-equation, k-, epsilon, transport.RNG (renormalized, group, theory).Large eddy simulationPorous material model Porous, Media, Models:Variable pore settingDirectional pore settingThe general fluid loss. 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2 Curve Fillet 两曲线倒圆角2-D Distance 平面距离2D Exchange 二维交换3-D Distance 空间距离A Single Symbol 单个符号Above Plane 在平面上面Above Text 在文本上面Absolute coordinate system （ ACS ）绝对坐标系Accept Result 接受产生的结果Active view 激活视图Actual 实际的Add a components 加一个组件Add Attribute Search to Filter 给过滤器加属性搜索特性Add Exclude Filter 加排除过滤器Add Proximity Filter 加接近的过滤器Add Tangent Edges 加相切边Add to Filter 加到过滤器Add View to Drawing 加视图到图纸Add View 加视图Add Zone to Filter 加区域到过滤器Adding a view distance 加一个视图的距离Adding anorthographic view加一个正投影视图Adding entries 加记录Adding members toassembly 加成员到装配体中Adding poles 加极点Additional GD&Tsymbols 增加的形位公差符号Adjacency Tolerance邻接公差Adjacent EdgesDeviation 邻接边偏差Advantages overinterpart expressions超过部件间表达式的优点After Text 在文本后面Align 对齐Align curve 曲线对齐Align View 对齐视图Aligning drawingviews 视图对齐Alignment Method 对齐方法Alignment options对齐选项All But Selected 除被选择之外的所有对象All Components 所有组件All Objects 所有对象Allow DuplicateValues 允许相同的值Allow substitution允许替换Along curve 沿曲线Along direction沿某一方向Along driver normals沿驱动的法向Along face normals沿表面的法向Along fixed vector沿定固定矢量方向Along vector 沿矢量方向Alternate Solution替换方法Alternate Thickness改变的厚度Alternates 替换Always Confirm 一直确认Analysis andReporting Functions分析和报告功能Analysis Data SetFunctions 分析数据集功能Analysis Functions分析功能Analysis type 分析类型Analyze Angle 分析角度Analyze Distance 分析距离Analyzing 分析Anchor andorientation point 锚点和方位点Anchor point 锚点Angle 角度Angle tolerance 角度公差Angle 角度Angled extensions 角度延伸Angular 角度的Angular dimensions 角度尺寸Angular Format 角度的格式Angular law 角度规律Angular 角度的Angularity 角状Animation 动画Anisotropic material 各向异性材料Annotation Editor 注释编辑器Annotation Preferences 注释设置ANSI Diameter Symbol ANSI直径符号ANSI Spherical Diameter Symbol ANSI球形直径符号ANSI Standard Section Line Display ANSI标准截面线显示Ansys solver Ansys 求解器ANT 装配导航工具Apex string 顶点线Apparent intersection point 表观交叉点Appended 附加的Appended Text 附加的文本Appended textcontrols 附加文本控制Application context应用上下文Applications 应用Applications of WAVEWAVE的应用Apply Filter 使用过滤器Approximate Rho近似的 Rho 值Aquamarine 碧绿色Arc 弧Arc Center 弧中心Arc Length 弧长Arc/Circle 圆弧/圆周Arc/ellipse center弧/椭圆的中心ArchitecturalFeet/Inches 建筑上的英寸/英尺Arclength 弧长Area Fill 区域填充Area law 面积规律Arow segment 箭头段Arrow line display箭头线显示Arrow Lines 箭头线Arrow Position 箭头位置Arrowhead 箭头ASCII 美国信息交换标准码Aspect Ratio 纵横比Assemblies Clearance装配间隙Assembly 装配Assembly analysis装配体分析AssemblyCrosshatching 装配剖面线Assembly Filtering装配过虑Assembly Hidden LineRemoval 装配隐藏线去除Assembly Modeling装配建模Assembly Navigator装配导航器Assembly NavigatorTool 装配导航工具Assembly part 装配部件Assembly preferences装配参数预设置Assembly views 装配视图Assembly Zone 装配区域Associate Note 相关注释Associated Objects 关联对象Associative direction关联方向Associative offsets相关偏置Associative taperplane reference point 相关的拔模面参考点Associative ViewScale 相关视图比例Associative 关联的Associativity 相关性Associativity Manager 关联性管理器Associativity ofutility symbols实用符号的相关性At angle to vector 与矢量方向成角度Attached Target 附着的目标体Attachment methods 附着方式Attribute editor 属性编辑器Attribute Filter 属性过滤器Attribute Name 属性名Attribute Type 属性类型Attributes 属性Attributes From All Objects 从所有对象得到的属性Attributes From One Object 从一个对象的属性Attributes hierarchy 属性级别Auto dimension 自动尺寸标注Auto Ordinate Dimensions 自动坐标尺寸标注Automatic 自动的Automatic Placement自动放置Automatic Preview 自动预览Automatic Rectangle自动生成矩形Automatic Update 自动更新Auto-size Cells 自动大小的单元Auxiliary 辅助的Auxiliary View 辅助视图Axis 轴Axisymmetric analysis轴对称分析Axisymmetric loading轴对称加载BBackground 背景Ball 球形Ball End Groove 球端槽Bandwidth 带宽Base Angle 基本角Base Diameter 基本直径Base part 基础部件Base point 基点Base View 基本视图Baseline 基线Basic concepts ofGeometric Tolerancing几何公差的基本概念Basic Curves 基本曲线Batch Check 批量检查Bead 小球垫圈Before Text 在文本前Below Plane 在平面下Below Text 在文本下Bend AllowanceFormula 弯边许用公式Bend Position 弯边位置Bend Report 弯边报告Bend segment 弯边段Bend sequence table弯边顺序表Bezier spline 贝塞尔样条Bi-directionalAssociativity双向相关性Bilateral 双面的Bill of Material (BOM)材料明细表Binormal 副法线Blank 隐藏Blank Component 隐藏组件Blank Node 隐藏节点Blanking 隐藏Blend 倒圆Blend All Instances给所有的引用倒圆角Blend solid edge实体边缘倒圆Blend types倒圆类型Blending function倒圆功能Block 块Blue 蓝色Body extents (物)体范围Body of revolution 旋转体Body 体Boolean operation 布尔运算Boss 凸台Bottom 俯视图Bottom-up modeling 自底向上建模Bound by objects由物体确定边界Boundary边界Boundary point 边界点Boundary types 边界类型Bounded Plane 具有边界的平面Bounded Planes 边界平面Box 最小盒子方法Break Line/Detail 截断线/局部放大图Break-Out Section View 截除的剖视图Bridge 桥接Bridge Curve 桥接曲线Bridge Depth 桥接深度Bridge Sheet 桥接片体Bridge Skew 桥接扭曲Bridge Surface 桥接面Broken Links打断的链接Brown 褐色B-spline B-样条线B-surfaceB-曲面Built-in 内置的Bundle 捆Bundle_id捆的标识符By corners按拐角分段By equal segments按等长分段By Equation按方程式By Face Normals 通过面法向By input arc lengthsegments 按输入的弧长分段By knotpoint segments按节点分段By law curve按规律曲线By points通过点By poles 通过极点By segments按段数By tolerance按公差CCalculatorcapabilities计算器功能Callouts插图的编号Callouts and Symbols插图的编号和符号CAM Objects CAM 对象CAM Views CAM视图Cancel 取消Cancel Chain 取消链Canned layout储存的布局Canned view储存的视图Cartesian笛卡尔（直角坐标系）Categorise分类Category 目录Center 中心Center Justify 中心对齐Center Line withExtension 有延伸线的中心线Center Line 中心线Center Point 中心点Centerline Component中心线元件Centerline Projection中心线投影Centerline ProjectionDefinition 中心线投影定义Centerline ProjectionDefinition 中心线投影定义Centerline Projection Vector 中心线投影矢量CGM CGM格式文件Chain 链Chain Curves 链状曲线Chaining 链接Chaining Tolerance链公差Chamfer 倒角Chamfer edges 边缘倒角Chamfer Offset 倒角偏移Change Degree 改变阶数Change Edge 改变边Change Margin 改变边缘Change Reference Set 改变引用集Change stiffness 改变刚度Change weights 改变权值Character字符Character Size 字符大小Character Spacing 字符空间Characteristic 特性Check for overlaps 重叠部分检查Check Geometry 检查几何体Check Overlapping 检查重叠Check-In 签到Checking the format检查格式Child Components 子组件Choose alignmentoptions 选择对齐选项Choose an option 选择一个选项Choose Attributes 选择属性Choose edit option选择编辑选项Choose Expressions选择表达式Choose method 选择方法Choose Named Object选择命名的对象Choose Part File 选择UG文件Choose view displayoptions 选择视图显示选项Chordal Deviation 弦长偏差Chordal Tolerance 弦长公差Circle 圆Circle array圆形阵列Circular boundary圆形边界Circular extension圆形延伸CL file刀位文件CL Point 刀位点Clamp 装夹Class Selection 分类选择Class selectionsubfuction分类选择子功能Class selection tools分类选择工具Clear 清除Clearance analysis间隙分析Clearance zone间隙区域Cliff Edges 悬崖边Cliff Edge Overflows悬崖边溢流Clock Instance 顺时针引用分布Clone assembly克隆装配Cloning 克隆Close Part 关闭部件Close 关闭Closed Arrowhead 封闭箭头Closed bodies封闭体Closed definingpoints 封闭的定义点Closed in U U 向封闭Closed in V V 向封闭Code set 代码集Coincident 共点Collapse 装配树合并Collapse All 使所有装配树合并Color 颜色Color legend 颜色图标Color， font and width option 颜色、线型和宽度选项Color/Font/Width Preferences 颜色、线型和宽度预设置Column 列Column degree 列的阶数Combined curve projections 组合曲线的投影Combined Projection组合投影Common Fraction 公共片断Common tools 公共工具Comp Name 部件名Component 组件Component members 组件成员Component object 组件对象Components addexisting part 向组件中加入已存的部件Components Arrays组件阵列Components Filters 组件过滤器Components Operations 组件操作Components Sets 组件集Composite FCF 组合的FCFComposite Featurecontrol Frame 组合特征控制框架Computed curves计算的曲线Concentric 同心的Concentric Circles同心圆Concentricity 同心Concrete 具体的ConcurrentEngineering并行工程Conditionalannotation条件注释Conduit 导管Conduit Tools 导管工具Cone 圆锥Cone Depth 圆锥深度Cone direction圆锥方向Cone origin圆锥底面圆心Confirm with Ctrl-MB1用Ctrl加鼠标左键确认Confirmation 确认Conic 二次曲线Conic Rho 二次曲线Rho 值Conical Taper 二次方拔模Connection 连接Constant 常量Constant Offsets 常量偏移CONSTANT PARAMETERCURVE 等参曲线CONSTANT X-OFFSET 常X向偏移Constrain options约束选项Constraint Direction约束方向Constraints约束Constructed curves构造的曲线Construction Points构造点Contact mesh接触网格ContainmentInterference包容干涉Contiguous邻近的Continuity Checks连续性检查Continuity method连续性方式Continuity type连续性类型Contour 轮廓Contour Curve轮廓曲线Contour Length 轮廓长度Contour lines轮廓线Contour plot轮廓图Control Point控制点Control Polygon控制多边形Control structure 控制结构Control vertex 控制顶点Convert 转换Convert dependency 转换相关性ConvertNon-Associative GD&T 转换非关联的GD&T Coordinate system 坐标系统Coordinate SystemAxis 坐标系统轴Copy 拷贝Copy component 拷贝组件Copy Filter 拷贝过滤器Copy geometry 拷贝几何体Copy method 拷贝方法Copy Object 拷贝对象Copy Path 拷贝路径Copy To Filter 拷贝到过滤器Copy Views 拷贝视图Copying drawing views 拷贝图纸视图Counterbore 台阶孔Counterclockwise 逆时针Countersink 埋头孔Course objectives 课程目的Create 建立, 生成, 创建Create a ComponentsArrays 建立组件阵列Create a cylindricalcenterline 建立圆柱体的中心线Create a half sectionview 建立一个半剖视图Create a HelicalSpline 建立一个螺旋样条线Create a linearcenterline 建立一条线型中心线Create a new drawing建立一个新的图纸Create a revolvedsection view 建立一个旋转剖视图Create a simplesection view 建立一个简单剖视图Create a Tabular Note建立一个表格说明Create an offsetcenter point 建立一个偏置的中心点Create an unfoldedsection cut 建立一个展开的剖视图Create and EditingAssemblies 建立和编辑装配Create animation建立动画Create AssemblyDiagram 建立装配图表Create Auto OrdinateDimension 建立自动坐标尺寸Create Auxiliary View建立辅助视图Create BreakoutSection View 建立截除的剖视图Create Crosshatching生成剖面线Create Detail View生成详细视图Create Dimension 标注尺寸Create Drawing 建立图纸Create explode views建立爆炸视图Create family members建立族的成员Create Filter 生成过滤器Create GD&T Symbols建立形位公差符号Create GD&T symbolswith a leader 建立带引导线的形位公差符号Create GDT Symbol 建立(标注)GDT符号Create GeometricExpression 建立几何表达式Create ID Symbol 建立(标注)ID符号Create InferredDimension 建立(标注)推测尺寸Create Kanji 生成Kanji汉字Create Label 建立(标注)标记Create Leader 建立(标注)引导线Create linked part 建立链接部件Create Named Filter 建立命名的过滤器Create new level 建立新的一级Create New Multiple Datum Reference 建立新的多基准面参考Create New Part 建立新部件Create Note 建立注释Create on Dimension 在尺寸上建立Create on Edge 在边上建立Create on Extension 在延伸线上建立Create on Point 在点上建立Create or Edit Datums 建立或编辑基准面Create or Select symbol to edit 建立或选择符号来编辑Create Ordinate Dimension 生成坐标尺寸Create OrdinateMargin 生成坐标尺寸标注边界Create Ordinate Set 建立坐标组Create Path 建立路径Create pattern data 建立模式数据Create ProximityFilter 建立相近的过滤器Create Section Line生成截面线Create Section View生成界面视图Create Section Views建立剖视图Create text with aleader 建立带引导线的文本Create ToleranceFeature 生成公差特征Create Tolerance ViewOrientation 生成公差视图方向Create UtilitySymblos 建立实用符号Create Utility Symbol生成ID符号Create with Leader建立带箭头标注Create without Leader建立不带箭头标注Create/Edit Datum 建立/编辑基准面Created in an assembly在一个装配中建立Cross section横截面Cross Splines交叉样条线Cross strings交叉线串Crosshairs 光标十字交叉线Crosshatch and AreaFill Tolerance 剖面线和区域填充公差Crosshatching 剖面线Crosshatchingadjacency tolerance剖面线邻近公差CSYS 坐标系CSYS Method 坐标系方法Cubic 三次的Cubic fit surface三次拟合曲面Current CrosshatchFile 当前剖面线文件Current Directory 当前目录Current Layout当前布局Current parameters 当前参数Current Part 当前部件Current Set 当前组Current view当前视图Cursor 光标Cursor location 光标定位Curvature曲率Curvature analysis曲率分析Curvature comb曲率梳Curvature method曲率方法Curve 曲线Curve analysis曲线分析Curve analysisdisplay 曲线分析显示Curve Chamfer 曲线倒直角Curve creation 曲线建立Curve divide curve 用曲线分割曲线Curve extension 曲线延伸Curve fit creation methods 曲线拟合的建立方式Curve fit with template 使用模板来拟合曲线Curve mesh 曲线网格Curve to face option 曲线到表面的选项Custom menubar 客户化菜单条Cut Angle 剖切角Cut Filter 剖切过滤器Cut line 剖切线Cut Object 剖切对象Cut Position 剖切位置Cut segment 剖切段Cut Through Model 通过模型剖切Cyan 蓝绿色Cycle 周期，循环Cylinder 圆柱体Cylindrical 圆柱的CylindricalCenterline 圆柱中心线CYLINDRICAL CROSSSECTION 圆柱剖切Cylindrical Face 圆柱面CYLINDRICALORIENTATION 圆柱方位Cylindrical targetarea end point 圆柱目标区域端点Cylindrical targetarea start point 圆柱目标区域起点DDark Red 暗红色Dashed 虚线Dashed Hidden Edges虚线隐藏边Data Base 数据基础（库）Data Model 数据模型Data Points数据点集Date/Time 日期和时间Datum基准Datum axis基准轴Datum Editor基准编辑器DATUM IDENTIFIER 基准标识器Datum plane基准平面Datum Plane-DualConstraints基准平面－双约束Datum Plane-SingleConstraints基准平面－单约束DEBUG CONTROL 调试控制Default缺省Default Radius 缺省半径Define 定义Define Torus 定义圆环Define ArrowDirection 定义箭头方向Define Component Set定义组件集Define Cut Direction定义切削方向Define Direction 定义方向Define Filter 定义过滤器Define Hinge Line 定义铰链线Define offsetposition 定义偏移位置Define reference line定义参考线Define Section Line定义截面线Define Symbol 定义符号Define View Boundary定义视图边界Defining a UGExpression table定义一个UG 表达式表Defining Face定义表面Defining Holes,within bounded plane 在边界平面内定义孔Defining points 定义点集Defining the Assembly Structure 定义装配结构Defining the datum origin 定义基准原点Defining the plotter 定义绘图仪Defining the section view display 定义剖视图显示Deform Sheet 变形片体Degree 阶数Degree greater than maximum 阶数大于最大值Degree less than minimum 阶数小于最小值Degree-of-Freedom arrows自由度箭头Degree-of-Freedom indicators自由度指示器Delay interpart updates 延迟部件间更新Delayed update 延迟更新Delete 删除Delete all edits 删除所有编辑Delete Drawing 删除图纸Delete Feature 删除特征Delete Filter 删除过滤器Delete Object 删除对象Delete Path 删除路径Delete positioningdimention删除定位尺寸Delete selected edits删除选择的编辑Delete selectederasures 删除选择的擦除Delete Toolpath 删除刀轨Deleteing parentgeometry删除父几何体Deleting a utilitysymbol删除一个实用符号Delta 增量Delta Offset 增量偏置Dependent 相关Depth 深度Derivative Vector派生矢量Description 描述Descriptor 描述符Deselect isoclines取消选择等参线Deselection 取消选择Design in Context按上下文设计Design rule 设计法则Design Template 设计模板Destinationcoordinate system 目标坐标系统Destination Layer目标层Destination Point目标点Detail 详图Detail center inparent view 在父视图中的详图中心Detail Design 详细设计Detail Filtering 细节过滤Detail of Section 剖面详图Detail View 详细视图Deviation 偏差Deviation Analysis偏差分析Deviation check 偏差检查Diagram 图表Dialog 对话框Dialog Bar 对话工具条Dialog Bar Fields对话工具条区域Dialog Manager 对话管理Dialog Preferences对话框参数预设置Diameter Symbol 直径符号Diameter 直径Die Engineering 冲模工程Die_punch_radius 模具冲压半径Digital Pre-Assembly (DPA) 数字预装配Dimension Constraints 尺寸约束Dimension Filter 尺寸过滤器Dimension Local Settings 尺寸局部设置Dimension Precision尺寸精度Dimensions 尺寸Direction 方向Direction Method定向方式Direction point定向点Directory 目录Directory EntrySection 目录登录区Discard 放弃Discontinuity inCurve 曲线不连续Display Dimensions显示尺寸Display Drawing 显示图纸Display File 显示文件Display InstanceEditor 显示引用特征编辑器Display label 显示标记Display Object 显示对象Display Options 显示选项Display Parent 显示父Display Prefrences显示参数预设置Display Selected Part显示所选部件Display Type 显示类型Displayed Part 显示部件Distance and Angle距离及角度Distance Normal toCurve 垂直于曲线的距离Distance Tolerance距离公差Distance Value 距离值Distance 距离Distortion Method 变形方法Distortion 变形Divide Curve 分割曲线Divided Circle 分割圆周Divided Hexagon 分割了的六边形Divided Square 分割了的正方形Divided Symbols 分割符号Document Tag 文件标签Dotted Dashed 点划线Double offset chamfer双边偏置倒角Double-Arc-Blend双圆弧倒圆Dove Tail Slot 燕尾槽Draft Angle 拔模角度Draft Height 拔模高度Drafting 制图Drafting Annotation制图标注Drafting Application制图应用DraftingAssociativity 制图相关性Drafting ObjectAlignment 制图对象对齐Drafting ObjectAlignment Preferences制图对象对齐预设置Drafting ObjectColor/Font/Width 制图对象颜色/字体、宽度Drafting Preferences制图预设置Drafting SymbolFilter 制图符号过滤器Drafting Symbols制图符号Drag 拖曳Drawing 图纸Drawing Borders 图纸边框Drawing Layout 图纸布置Drawing Member View Display Settings 图纸成员视图显示设置Drawing Member View Render Sets 图纸成员视图着色集Drawing Operations 制图操作Drawing Sheet 图页Drawing View Boundaries 图纸视图边界Drawing Views 图纸视图Drive Curves 驱动曲线Driver Type 驱动类型Dual Constraints 双重约束Dual Dimension Format and Units 双尺寸格式和单位DXF to Unigraphics 从DXF转换到UG Dynamic Deviation Analysis 动态偏差分析EEdge and Cross Tangents 边缘与相交切线Edge and Normals 边缘与法线Edge Blend 边倒圆角Edge Chamfer 边倒直角Edge Curvature 边缘曲率Edge deviation边缘偏差Edge Hiding Edge边缘隐藏边缘Edge Only 仅边缘Edge to Face 边缘到表面Edit 编辑Edit a Tabular Note编辑表格注释Edit Alignment 对齐编辑Edit Angle Feature编辑角度特征Edit Annotation 编辑注释Edit Arc Length 编辑弧长Edit Boolean 编辑布尔运算Edit Breakout SectionView 编辑剖切视图Edit Centerline 编辑中心线Edit Characteristics编辑特性Edit CrosshatchBoundary 编辑剖面线边界Edit Current Drawing编辑当前图纸Edit Curve 编辑曲线Edit Curve Parameters编辑曲线参数Edit DimensionAssociativity 编辑尺寸相关性Edit Dimensions 编辑尺寸Edit Drafting ObjectAssociativity 编辑绘图对象的相关性Edit Drawing 编辑图纸Edit During Update更新期间编辑Edit Entire Segments编辑整段Edit Extract Region编辑抽取的区域Edit Feature 编辑特征Edit FeatureParameters 编辑特征参数Edit Fillet 编辑倒角Edit Free Form Feature编辑自由特征Edit ID Symbol 编辑ID符号Edit Linked Region编辑链接区域Edit Margin 编辑坐标尺寸定位边缘Edit objectpreferences 编辑对象预设置Edit Object Segments编辑对象段Edit Ordinate (Set)Origin 编辑坐标尺寸原点Edit Ordinate DimDoglegs 编辑坐标尺寸拐线Edit OrdinateDimension 编辑坐标尺寸Edit Positioning编辑位置Edit Scale 编辑比例Edit Search Filter编辑搜索过滤器Edit Section Line编辑剖切线Edit Sheet Boundary编辑片体边界Edit Sketch Dimension 编辑草图尺寸Edit Solid Density编辑实体密度Edit Spline by Addinga Point 通过添加点来编辑样条Edit Structure 编辑结构Edit V Degree 编辑V向阶次Edit View Display Preferences 编辑视图显示预设置Editing ,Moving Poles 编辑，移动极点Editing DimensionText 编辑尺寸文本Editing Drafting Objects 编辑草图对象Editing GD&T Symbols 编辑形位公差符号Editing ID Symbols 编辑ID符号Editing Ordinate Dimensions 编辑坐标尺寸Editing Text 编辑文本Editing the Display of Drawing Views 编辑图纸视图的显示Editing the Section Line Segments 编辑剖面线段Editing UtilitySymbols 编辑实用符号Element Size 元素尺寸Ellipse 椭圆Emphasize Work Part强调工作部件Empty List 空的列表Empty Reference set空的引用集End Curvatures 端点曲率End Point 终点End Slopes 端点斜率End Tangent Overflow溢流至切线结束Ends-apex-rho 端点－顶点－RHOEnds-apex-shoulder端点－顶点－肩点Ends-slope-cubic端点－斜率－三次曲线Ends-slopes-hilite端点－斜率－高亮Ends-slopes-rho端点－斜率－RHOEnds-slopes-shoulder端点－斜率－肩点EngineeringFeet/Inches 工程英尺/英寸Enter Radius 键入半径Entering dimensionedit mode 进入尺寸编辑模式Entire Part 整个部件Entire Part Condition整个部件条件Entity Origin 实体原点Entries Options 记录选项Environment Variable环境变量Equal Arc LengthSegments 等弧长分段Equal Arclength 等弧长Equal Length 等长度Equal Radius 等半径Erase Objects 擦除对象Error Messages 错误信息Evaluating Concepts评估概念Existing Line 存在线Existing Part 存在的部件Existing Point 存在点Exit Unigraphics退出UGExpand 扩展Expand All 扩展所有的Exploded Views 爆破视图Exporting a Drawing输出一张图纸Expression 表达式Expression Editior表达式编辑器Expression Name 表达式名Extend Factor 扩展因子Extended Tangents 延伸相切Extension Line 1 延伸线1Extension Line 2 延伸线2Extension Line Display 延伸线的显示Extension Lines 延伸线Extension Sheet 延伸片体Extension Surface 延伸曲面Extensions 延伸External 外部的Extract 抽取Extract Attributes 抽取属性Extract Curve 抽取曲线Extract Expressions 抽取表达式Extract Geometry 抽取几何体Extract Isoline 抽取等参线Extracted Edges 抽取边Extracted Sketch 抽取的草图Extruded Body 抽取的实体FFabrication 制作,构成Face 表面Face Analysis 表面分析Face Analysis Display面分析显示Face Blend 面倒圆Face Edges 面的边Face Normals 表面法线Face Pair Feature成对面特征Face to Face 表面到表面Facepair_DEF 成对面_定义特征Facepair_SEL 成对面_选择特征Facet 小平面Facet Edge 小平面的边Faceted Body 用小平面表示的体Factor 因素Family Member 族成员Family of Parts 部件族Family Table 族表Fast Font 快速生成字体FEA 有限元分析Feature 特征Feature Dependency特征依付Feature Edit 特征编辑Feature Name 特征名Feature Operation 特征操作Feature Playback 特征回放Feature Selection 特征选择Feature Sets 特征集Feature Type 特征类型Feedrates 进给率FEM 有限元建模File 文件File Extensions 文件扩展名File Pull Dwon Menu文件选项下拉菜单Fillet 圆角Fillet Sheet 圆角片体Fillet-Bridge 圆角-桥接Fillet-Rho 圆角－RhoFillet-Shoulder圆角－肩点Filter 过滤器Filter Box 过滤器输入框Filter by choosingcurve types 通过选择曲线类型过滤Filter by choosingface types 通过选择面的类型过滤Filter Methods 过滤方法Filtering 过滤Filtering andFiltering Mode 过滤和过滤模式Filters 过滤器Find Component 找部件Find Object 找对象Find Selected Components 找所选择的组件Find Work Part 找工作部件First Cross String第一交叉线串First Offset 第一偏置First Primary String 第一主线串First Section String 第一截面线串First Set 第一组First Side String 第一侧边线Fit Methods 拟合方法Fit Splines 拟合样条Fit to Preview Window 拟合倒预览窗口Five-points-slope 五点－斜率Fixed 固定Fixed Length Method 固定长度方法Fixture 夹具Flag Section 标志区Flange 凸缘Flange 法兰，轮缘, 凸缘Flange Type 凸缘类型Flange Width 法兰宽度FLEXlm User GuideFLEXlm 用户指南Folded RadiusDimension 折线半径标注Font 字体Font Character 字符Font line 字行Font Object Library字体库Font Table 字体表Forced Direction受力方向FOREIGN CURVE 外来曲线Foreign expression外来表达式Form Feature 成型特征Form Feature BossCreation 成型特征：凸台建立Form Feature PadCreation 成型特征：凸垫建立Form/Unform 成型/不成型Formatting Options格式选项Forming Table 成型表Frame Height Factor框架高度因子Free Form Feature自由形状特征Free State 自由状态Freeze Parts 冻结部件Freeze Parts inSession 冻结进程中的部件Freezing Entries冻结记录Freezing parts 冻结部件Fringes 边缘，条纹From Point Cloud 从点云From Poles 从极点Front 前视图Full Circle 整圆Full CircularCenterline 整圆中心线Fully loaded 全部加载Fully-constrained全约束Functions 功能GGateway 入门Gaussian Radius 高斯半径GD&T Exercises形位公差练习GD&T Symbol Placement形位公差符号放置GD&T Symbols 形位公差符号General Concepts通用概念General Conic 一般二次曲线General Flange 通用凸缘General FunctionSpecifics 通用功能General Pocket 通用腔General Spline通用样条线Geometric Constraint 几何约束Geometric Tolerancing 几何公差Geometry Linker 几何体链接器Geometry Navigator 几何体导航器Geometry View 几何视图Global Layer Mask全局层屏蔽Graph view 图形视图Graphics window 图形窗口Graphics WindowColors 图示窗口颜色Gray 灰色Green 绿色Grid 栅格Grid Lines 栅格线Groove 槽GSM （Graphics Schematics Module）原理图模块Guide Curve 引导曲线Guide String 引导线HH-Adapative Meshing H－自适应网格生成Half Angle 半角Half Section Cut 半剖Hard copy 硬拷贝Hard Interference硬干涉Harness 电路设计模块Harness List 电路列表Header position 标题位置Hedgehog 刺猬状Helix 螺旋线Hexagon 六边形Hicken Sheet 增厚的片体Hidden Line 隐藏线hidden line removal隐藏线去除High quality image高质量图像Hinge Line 铰链线Hole 孔Hole Depth 孔深Hole Diameter 孔直径Hollow 挖空Hollow Enhancements挖空增强功能Hollow feature 挖空特征Hollow Solid 挖空实体Horizontal Dimension水平尺寸Horizontal Margin 水平坐标尺寸标注边界Horizontal Reference水平参考Horizontal 水平的Horz and Vert Dim 水平和垂直尺寸Hyperbola 双曲线IID Symbol ID符号ID Symbol Size ID符号大小IGES IGES标准Import Family TableSpreadsheet 输入部件族电子表格ImportedFeatures/Datums 输入的特征/基准面Imported Tolerances输入的公差Imported View 输入视图In group 成组Inactive 不激活的Include Tangent Faces包括相切面Inconsistentlyconstrained 约束不一致Increment Size 增量大小Indicate polygonvertex 标记多边形顶点Individual Layer Mask单独层的屏蔽Infer Dimensions 推测尺寸Infer from Edge 从边推测Inferred Dimension推断尺寸Inflection 变形Information 信息Information to be displayed 显示的信息Information Window 信息窗口Inherit 继承Inner Tangent Line 内切线Inset Flange 插入凸缘Inside Radius 内接半径Inside/Crossing 内部/相交Instance 引用特征Instance Array Dialog 引用排列对话框Instance Feature 引用特征Instance Type 引用类型Instance view 引用视图Interactive Check 交互检查Interactive Function 交互功能Interactive Step 交互步骤Interactivetechniques 交互技术Interferes 干涉Internal error 内部错误Interpart Dependencies 部件间的相关性Interpart Expressions 部件间表达式Interpart Modeling部件间建模Interpolate 插补Interpolation methods插补方法Intersect 相交Intersect 相交，交叉Intersect Angle atTarget 在相切点的交角Intersect Angle 交角Intersection curve相交曲线Intersection point交点Intersectiontolerance 相交公差Intersects with Plane与平面相交Invalid face code 无效的面代码Invalid Last DateValue 无效的最后数据值Invalid name 无效的名称Invalid orunsupported systemattribute name 无效的或不支持的系统属性名Invalid Part 无效的部件Invalid reference setname 无效的引用集名Invalid selection 无效的选择Invisible HiddenEdges 无效的隐藏边Invisible 不可见Invlaid edge code 无效的边代码Isolate Component 隔离组件Isolate FilteredComponents 隔离过滤后的组件Isometric 正轴侧的Isometric View正轴侧视图IsoparametricTrim/Divide 等参数修剪/分割Isoparmetric Element等参元Isotropic Material各向同性材料GGateway 入门Gaussian Radius 高斯半径GD&T Exercises形位公差练习GD&T Symbol Placement形位公差符号放置GD&T Symbols 形位公差符号General Concepts通用概念General Conic 一般二次曲线General Flange 通用凸缘General FunctionSpecifics 通用功能General Pocket 通用腔General Spline。