Pattern formation in a stochastic model of cancer growth
考虑多不确定性因素影响的电压暂降评估
第10卷第12期Vo l .10,No .12宜宾学院学报J ou rnal of Yibin Un i versity2010年12月Dec .,2010收稿日期51修回作者简介陈武(),男,四川广安人,硕士,主要从事电能质量分析与控制及绿色智能电网研究考虑多不确定性因素影响的电压暂降评估陈武(成都电业局温江供电局,四川成都611130)摘要:电压暂降严重程度取决于诸多不确定性因素,变压器相移特性与故障点过渡阻抗对电压暂降传播及幅值有着重要影响.基于变压器相移特性矩阵,对系统中级联变压器引起的电压相移特性进行数学建模,给出了多级变压器相移特性传递矩阵;同时,基于概率理论,对过渡阻抗进行随机建模;提出一种基于对称分量,相序网络及矩阵变换理论的电压暂降评估新方法.以9节点网络和I EEE 230节点测试系统为例进行仿真,并与传统方法得出的评估结果进行比较,结果证明,该方法能够正确反映过渡阻抗及变压器对电压暂降的影响,评估结果准确,方法原理简单,适用于任意规模的电力网络.关键词:电压暂降;暂降传播;相移特性;过渡阻抗中图分类号:T M 41 文献标志码:A 文章编号:1671-5365(2010)12-0069-05A sse ss m en t of Volta ge Sa g Con si der i n g Un cer ta i n ty Fa c tor sCHEN Wu(Chengdu Wenjiang Power Supply Bureau,Chengdu 611130,China )Ab stract:The severity of voltage sags in power syste m depend s on m any uncertain ty factors,and the transfor mer phase shift char 2acteristics and f ault i mpedance at fault l ocation s have great influence on voltage sag p r opagation and its m agn itude .The p hase sh ift of transf or mer in cascade in v o ltage sags based on the transfor mer phase shift characteristics matrix,a v o ltage sag p hase shift p r op 2agation matrix of multi 2transf o r mers w ere analyz ed,and a stochastic model to rep r esent fau lt i mpedance based on p r obability theory was estab lished .A ne w method t o calculate v o ltage sags on the basis of sequence c omponen ts,phase sequence net wo r k and matrix tran sf or mati on theory was suggested .Two exa mp les based on a n ine 2node net work and the I EEE 230test syste m ,which illu strates the a pp licability of such a method,wer e given .The method can be a pp lied t o the arbitr ary net wo r k s due to its accuracy calculation r esu lt and si mp le p rincip le .K ey word s:voltage sags;sag p r op agation;p hase shift char acteristics ;fau lt i mpedance 电压暂降(Voltage Sags)是最常见且引起经济损失最为严重的电能质量事件之一[1],国际电气与电子工程师协会(I EEE )将电压暂降定义为:工频电压有效值降至0.1～0.9p.u .,持续时间在0.5个周波到1分钟之间的电磁扰动[2].电压暂降通常由短路故障、开关操作、变压器以及电容器的投切、雷击引起的绝缘子闪络或线路对地放电以及过负荷、大型负荷(如大型电动机)启动与加速等因素造成.其中,短路故障是最为常见的原因之一[3-4].现代工业过程控制系统中的可编程逻辑控制器、可调速驱动装置、计算机、交流接触器等设备对电压暂降都极为敏感,由于敏感设备的故障可能导致非常巨大的经济损失[5-7],因此,准确评估电压暂降对于电网运行管理人员有效找出系统脆弱区域、提出合理的暂降抑制策略以降低用户经济损失而言具有重要的理论价值和现实意义.电压暂降特特征量主要包括:暂降幅值,暂降持续时间,暂降频次,相角跳变等[8].现有电压暂降评估方法主要有基于实测与模型仿真的方法[9],临界距离法[10]、故障点法[11]、解析式法[12].其中,解析式法以其较高的评估精度、不受电力系统规模限制的特点得到广泛应用.电压暂降评估精度一方面取决于所采用的分析方法,同时也依赖于电力系统中多种不确定性因素[8,9,13-17],如故障位置、故障类型、故障率、网络拓扑、故障前的电压运行水平、继电保护装置动作情况、变压器绕组联结方式、分接头变化、线路投运方式、线路阻抗参数、系统接地阻抗、发电机运行计划及线路时变故障率等[2,8,9,12-17].文献[8]以I EEE 214节点测试系统为例,采用电磁暂态仿真软件重点分析了网络拓扑对电压暂降传播的影响,指出变压器绕组联结方式对电压暂降传播有着重要影响,特别是Y /△接法的变压器对系统电压暂降影响尤为显著.文献[12]基于等值观点,以故障分量的电压正序分量为基准,将电压负序分量作60°偏:2010-09-1:2010-10-10:1984-移,对系统中单台△/Y接法的变压器引起的电压相移进行了分析.文献[13]采用SI M P OW软件仿真的方式,同样分析了变压器对电压暂降传播的影响,并以图例方式给出了电压经单台变压器和多台级联变压器(以下简称多级变压器)传播后的相量图,给出了关于考虑单台变压器相移特性影响的变压器原、副两边各序电流与各序电压的关系式.目前,对于实际系统中大量存在的多级变压器对电压暂降的影响尚未见到更多研究成果.现有电压暂降评估中,一般假设故障为金属性短路.实际上,对于一个特定系统而言,含有过渡阻抗的各种类型故障是广泛存在的[9,18-19],文献[9]指出在考虑过渡阻抗后,电压暂降评估精度明显提高.文献[18]基于Matlab/ Si m ulink电力系统仿真库,构建了I EEE29节点测试系统,通过仿真分析指出,过渡阻抗对电压暂降评估结果影响极大,其对重合闸后的暂态过程有重要影响.上述研究方法存在的主要问题在于,需进行大量仿真,当系统规模大、故障点多时,实用性差.针对多级变压器相移特性和故障阻抗和的客观存在,本文基于变压器两侧电压相量的变换矩阵,结合对称分量法及矩阵运算法则中的乘法结合律,推导出电压暂降经多级变压器传递后的变压器相移特性传递矩阵;同时,计及过渡阻抗对电压暂降的影响,对网络中各种类型故障的过渡阻抗进行了随机建模;提出基于变压器相移特性传递矩阵的电压暂降评估新方法,以单相接地短路、两相相间短路、三相短路为例,重点分析系统发生平衡故障及不平衡故障时,方法的正确性、适用性.1 过渡阻抗随机模型电力系统中的短路故障一般都不是金属性的,而是在短路点存在过渡阻抗.过渡阻抗Zg是指当系统短路时,短路电流从一相流到另一相或从相导线流入地的途径所通过的物质电阻,这包括电弧电阻、中间物质电阻、相导线与地之间的接触电阻、金属杆塔的接地电阻等.在相间短路时,过渡阻抗主要由电弧电阻构成[19].一般情况下,高压输电线路相间短路的电弧电阻初始值可考虑为4～8Ω;输电线路对杆塔放电造成接地短路时,其过渡阻抗可考虑为5～7Ω,对输电线路经媒介(如树枝等)放电造成短路时,其过渡阻抗较大,可能上百欧[20].电弧电阻值具有随机统计特性,它由电源、变压器容量、导体截面、相间距离、短路点远近和大地导电率等多种因素决定[21],本文结合文献[22]的研究成果,认为过渡阻抗Z为一服从正态分布的随机变量文中假设相间短路及接地短路情况下,过渡阻抗主要由电弧电阻构成,其值在[5,]之间服从正态分布,取该区间[5,]中点6做为过渡阻抗的均值,再根据3σ原则[23],知其方差为1/3,即有过渡阻抗Z g服从正态分布N～(6,1/3),其概率密度函数表达式为f(Zg)=12πσexp-(Zg-μ)22σ2(1)式中μ,σ分别为过渡阻抗Zg的均值与方差.2 变压器相移模型2.1 单台变压器相移特性矩阵对于变压器两侧的各相电压相量有如下关系[24]: U se c=PAP-1U p ri(2)式中Us e c[Ua,Ub,Uc]T,表示变压器二次侧A,B,C三相电压相量构成的列向量;U p r i[U A,U B,U C]T,表示变压器一次侧A,B,C三相电压相量构成的列向量,P为对称分量变换矩阵;A为变压器类型特征矩阵(本文称之为变压器相移特性矩阵),当系统发生短路故障时,如果故障点零序电流分量能够通过变压器传播,则有A(1,1)=1,否则为0;P-1为P的逆矩阵.其中:P=1111a2a1a a2,P-1=131111a a21a2a,a=e j120°A=A(1,1)0001∠α0001∠-α,α为变压器相移角度.常用联结方式的变压器相移角度[25]及A(1,1)元素取值如表1统计.表1 常用变压器相移角度及A(1,1)取值联结组号相移角度A(1,1)Y,d1130°0D,y11-30°0Y,d1130°0Y,y00°0Y,y00°12.2 多级变压器相移特性传递矩阵图1 变压器级联 对于故障分量经多级变压器传递的情况,如图1所示根据节相关公式,便可推导出当图所示系统中f 点发生短路故障时,节点处的各相电压相量假设故障分量经台变压器后传递到点,根据节式(),有07 宜宾学院学报 第10卷 g.77.2.11k.n k 2.12:U a k fU b k f U c k f =(PA n P-1)(PA n-1P-1)…(PA1P-1)U A kfU B kfU C kf(3)式中:A i(i=1,2,…,n)为第i台变压器的相移特性矩阵;U akf ,U bkf,U ck f为当f点故障时,考虑变压器相移影响后节点k处A,B,C三相电压相量;U A k f,U B kf,U C kf为当f点故障时,未考虑变压器相移影响时节点k处A,B,C三相电压相量.由矩阵乘法结合律及PP-1=E(E为单位矩阵),式(3)可进一步变为:U ak fU bk fU ck f =PAnAn-1…A1P-1U AkfU BkfU Ckf(4)又根据对称分量变换矩阵,有: U Ak f(0)U Ak f(1) U A k f(2)=P-1U AkfU BkfU C kf(5)式中:U Akf(0),U Akf(1),U Ak f(2)分别为当f点故障时,未考虑变压器相移影响时节点k处A相电压U A kf的零序、正序、负序电压分量.结合式(4)(5),有:U a kfU b kf U c kf =PA n A n-1…A1P-1U A kfU B kfU C kf=PA n A n-1…A1U A kf(0)U A kf(1)U A kf(2)(6)当故障分量所经变压器的绕组联结方式一致时,式(6)可变为: U a bc k f=PA n U A kf(012)(7)式中:U a bck f表示f点故障时,考虑变压器相移影响后节点k 处A,B,C三相电压相量;U A kf(012)表示f点故障时,未考虑变压器相移影响时节点k处A相电压零序、正序、负序分量.当变压器联结方式不同时,式(6)可写为:U a bc k f=PA3U A k f(012)(8)A3=An An-1…A1(9)本文即将A3定义为f点与k点之间n台变压器的相移特性传递矩阵.因此,只要已知故障点与被评估点间压器台数及相应的绕组联结方式,就能确定出A3,从而求取k点电压暂降幅值.对于电压暂降频次计算可参考文献[26].3 考虑过渡阻抗及变压器相移影响的电压暂降评估模型3 评估算法对于如图所示网络,当系统中任意线路q上的f 点处发生短路故障时,设其过渡阻抗为Z,则节点处的电压计算公式为[26]U akfU bkfU ckf=PAnAn-1…A1U Ak f(0)U Ak f(1)U Ak f(2)(10)图2 系统网架结构 以A相发生单相接地故障为例,有:U Akf(0)U B kf(1)U C kf(2)=-Z(0)k fV A p r e f(f)Z(1)f f+Z(2)ff+Z(0)ff+3ZgV A p r ef(k)-Z(1)kfV Ap r ef(f)Z(1)ff+Z(2)ff+Z(0)f f+3Z g-Z(2)k fV A p r e f(f)Z(1)f f+Z(2)ff+Z(0)ff+3Zg(11)式中:Z(1)ff、Z(2)f f、Z(0)f f分别为故障点f的正序、负序、零序自阻抗;Z(1)k f、Z(2)kf、Z(0)kf分别为故障点f与节点k之间的正序、负序、零序转移阻抗,V A pref(k)、V A pref(f)分别为k、f点处A相故障前运行电压.将式(11)代入式(10)即可求得节点k各相电压,从而确定出暂降最为严重的相.其它类型故障情况下A相各序电压计算公式见文献[25].3.2 评估过程(1)当网络中故障分量不经变压器传播时,由(5)知:U AkfU B kfU C kf=PU Akf(0)U A kf(1)U A kf(2)即可确定节点k处电压暂降情况.(2)当故障分量从f点传播至k点仅通过一台变压器时,仅需在式(6)中,令n=1即可.(3)对于故障分量经多级变压器传递的情况,应首先求出故障分量的流通路径,确定出故障分量所经变压器的台数,用式(9)确定出各变压器电压相移特性传递矩阵.(4)据式(7)或式(8)评估电压暂降幅值.(5)计算电压暂降频次算法评估流程如图317 第12期 陈武:考虑多不确定性因素影响的电压暂降评估.12p-g k..图3 算法评估流程4 仿真分析4.1 相移特性矩阵的应用图4 9节点网络 为说明方法的正确性及适用性,以9节点测试系统[12]为例,结构如图4所示.利用M atlab 编制应用程序进行电压暂降评估,系统由150k V 传输网和20k V 配电网两个电压等级网络组成,变压器联结方式为D ,y11联结,且二次侧中性点为直接接地方式.由此可知,变压器电压相移特性矩阵为:A =00001∠-30°001∠30°当系统150kV 侧发生短路故障时,由于故障分量只经过一台变压器传播到20kV 侧,因此,当传输网发生故障时,对于节点6的电压暂降情况,则有:U akfU b f U f=U Akf (0)U Af ()U f ()=00.866-0.5i0.866+0.5i66566+5U Ak f (0)U Af ()U f ()()结合式()计算结果及文献[6]所提解析式法进行电压暂降计算,其电压幅值及暂降频次评估结果如图5,这与文献[12]评估结果一致.由评估结果可知:计及过渡阻抗影响后,系统暂降频次区间变化显著,由此反映出本文分析方法的正确性.图5 传输网单相短路时节点6处电压幅值及暂降频次4.2 大型环网测试为进一步验证所提理论及方法的适用性,以IEEE -30节点测试系统为例[3,26],评估系统中特定节点的电压暂降频次,该测试系统含6台发电机、30条母线、37条线路和4台变压器,其中一台为Y 0,d11联结,其余均为Y,d11联结,网络结构如图6所示.网络中故障类型分布及各线路的故障率等统计数据详见文献[17].图6 IEEE -30节点标准测试系统 假设一年中系统共发生1000次故障,结合本文提出的方法对节点26与节点30进行电压暂降频次计算.对比图与图所示电压暂降频次评估结果后可知考虑过度电阻后,系统电压暂降严重程度显著降低,尤其是区间[,6]内的电压暂降频次变化明显这表明,过渡阻抗是影27 宜宾学院学报 第10卷 k ck P A k 1Ak 20-0.8-0.i -0.80.i 0i-ik 1Ak 21212278:00..响电压暂降频次评估精度的一个重要因素,在今后相关研究中,应当充分考虑过渡阻抗对电压暂降的影响.图8 系统两相短路时节点26、30处暂降频次5 结论短路故障是引起系统电压暂降的主要原因之一,故障分量经变压器传播时,将发生相位偏移,从而引起暂降幅值及其类型发生变化,同时,由于过渡阻抗的存在,系统电压暂降严重程度显著降低.因此,在电压暂降评估过程中,应当充分考虑变压器相移及过渡阻抗对系统电压暂降的影响.本文基于变压器相移特性矩阵,采用叠加原理、对称分量法及阻抗矩阵对系统中的平衡故障及不平衡故障进行了分析计算,首次提出了多级变压器相移特性传递矩阵概念及其确定方法,分析了故障分量经变压器传播及过渡阻抗存在时电压暂降的变化趋势.9节点网络和I EEE 230节点测试系统验证了方法的正确性及其适用性.所提方法具有一定理论价值和明显的工程应用前景,把电力系统电压暂降评估的工程应用向前推进了一步参考文献:[1]I EEE Recom m ended Practice for Monit o ring Electric Po wer Quality[S ].I EEE St andard 1159,New York,1995:122,9223.[2]郝志国,杨淑英.电压凹陷预测与评估[D ].北京:华北电力大学,2005:7.[3]李娟娟.电网电压骤降的分析评估及其抑制措施[D ].福州:福州大学,2005:8.[4]Bo ll en M H J .Underst anding P ower Qualit y Proble m s :Voltage Sags andI n t errup ti on s[M ].s er Power Engi nerring .Piscata way,NJ:IEEE Press ,2000:1392252.[5]McGranaghanM F,M uell erD R ,SamotyjM J.Voltage Sags i n I ndustrialSyst em s[J ].IEEE Transacti ons on I ndu s t ry App licati on,1993,29(3):3972402.[6]肖先勇,王希宝,薛丽丽,等.敏感负荷电压凹陷敏感度的随机估计方法[J ].电网技术,2007,31(22):30233.[7]M ilanovi c J V ,Gup t a C P .Pr obabilistic A ss ess m en t of Financial 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Probabi lit o the a il u re o the P r otec tion st em J .EEEransac tion s on Pow er e live r 200211:2229.8图5 程序流程图3 结束语本文所设计的医用输液保护系统能够对输液过程进行自动监测,可以在药液不足时自动关闭输液管实现止液并及时报警,从而减轻护理工作的劳动强度,更好地达到治疗效果和服务目的,在一定程度上提高输液的安全性,从而提高医院的整体护理水平.参考文献:[1]江勇,段文群.一种面向医院的输液监控系统的设计[J].医疗装备,2009(12):19221.[2]陆蔚华,刘苏.便携式输液器———人性化设计理念实践[J].工程图学学报,2008(2):1582162.[3]祖龙飞,李赛飞.输液报警止液系统的研究[J].医疗装备,2009(1):33234.[4]白驹珩,雷晓平.单片计算机及其应用[M].成都:电子科技大学出版社,2005:16217.[5]吴晓娜.接近开关的正确选用[J].中国科技信息,2008(14):1622163.【编校:王露】(上接73页)[17]Park C H,J ang G,Thomas R J.The Influence of Generator Schedu li ngand Ti m e2Varying Fault R ates on Voltage Predicti on[J].IEEE Transac2 t i ons on PowerD el i very,2008,23(2):124321250.[18]高琳,田立军.电压骤降评估方法研究[D].济南:山东大学,2007:44247.[19]贺家李,宋从矩.电力系统继电保护原理[M].北京:中国电力出版社,1994:102.[20]李晓明.现代高压电网继电保护原理[M].北京:中国电力出版社,2007:425.[21]李瑞生,索南加乐.750k V输电线路的特殊问题及其对线路保护的影响[J].继电器,2006,34(3):124.[22]Marti nez J A,M artin A J.Voltage Sag Stud i es i n Distributi on Net wo rks2Part II:Vo lt age Sag A ss ess men t[J].I 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CFD model of a Hydrocyclone
CFD model of a HydrocyclonePeng Xu∗ and Arun S MujumdarMinerals, Metals and Materials Technology Centre (M3TC), Faculty of Engineering, National University of Singapore, Singapore 117576AbstractThe hydrocyclone is an industrial apparatus used commonly to separate by centrifugal action dispersed solid particles from a liquid suspension. It is widely used in the mineral and chemical processing industries because of its simplicity in design and operation, high capacity, low maintenance and operating costs as well as its small physical size. The computational fluid dynamic (CFD) technique is used for design and optimization as it provides a good means of predicting equipment performance of the hydrocyclone under a wide range of geometric and operating conditions with lower cost. The objective of this study is to numerically investigate the properties of hydrocyclone and explore several innovative designs which offer high separation efficiency at low energy cost as well as reduced erosion-induced wear.In this study several turbulence models are tested and compared with experimental results. Also, the effect of the hydrocyclone geometry e.g. inlet duct shape on the erosion rate within the hydrocyclone is calculated and the hot spots of wear are indicated. Additionally, several new designs are presented and studied numerically for their erosion characteristics, pumping power requirements and collection efficiency.* Email: mpev6@.sg, Tel. +65-65168870.1. IntroductionThe hydrocyclone is a mechanical separation device to separate dispersed solid particles from a liquid suspension fed to it by centrifugal action, it is broadly used in industry because of its simplicity in design and operation, high capacity, low maintenance and operating costs as well as its small physical size [1]. Experimental investigation using the LDA technique [2] is a relatively difficult technique and very expensive as well while empirical models can be used only within the limits of the experimental data from which the empirical parameters are determined. In view of these shortcomings, mathematical models based on the basic fluid mechanics are highly desirable to intensify innovation. The computational fluid dynamic (CFD) technique is gaining popularity in process design and optimization, it provides a good means of predicting equipment performance of the hydrocyclone under a wide range of geometric and operating conditions, and also offers an effective way to design and optimize the hydrocyclones [3-17].Erosion of parts of the internal wall of the hydrocyclone is a critical issue in mineral processing both from both safety and economic considerations. The injected solid particles, such as sand and ore particles, impinge at high vellocity on the inside surfaces of the components of the hydrocyclone, causing mechanical wear and eventual failure of the devices. Therefore, the erosion-induced wear should be taken into account together with separation efficiency and energy cost for optimizing and designing hydrocyclones. As testing for erosion of industrial devices generally requires special equipment and methodology, further modeling effort is needed for advancing our capability in predicting wear of hydrocyclones.This work presents results of a CFD model of a hydrocyclone based on Fluent version 6.3. First, results using different turbulence models viz. k-ε, RSM and LES, are compared with published experimental results for a 75mm standard hydrocyclone [18]. The air core formation and geometry will be predicted with CFD model. Then, in order to study the effect of the fed inlet on erosion rate, four designs of a 75mm hydrocyclone fitted with different inlets are compared.2. Model description2.1 Turbulence ModelThe turbulence model is the key component in the description of the fluid dynamics of the hydrocyclone. The free surface, air core and presence of solid particles make the swirling turbulent flow highly anisotropic, which adds to the difficulty for modeling hydrocyclones using CFD. Three kinds of turbulence models, k-ε model, RSM and LES, are often adopted for modeling the turbulent flow in hydrocyclones.In mineral processing, the fluid suspensions processed are generally dilute (<10%), thus the incompressible Navier-Stokes equations supplemented by a suitable turbulence model are appropriate for modeling the flow in hydrocyclones. The k-εmodel is a semi-empirical model with the assumption that the flow in fully turbulent and the effects of molecular viscosity are negligible. Comparing with standard k-εmodel, the RNG k-εmodel is more responsive to the effects of rapid strain and streamline curvature and presents superior performance for the highly swirling flow in a hydrocyclone. While, the Reynolds stress model (RSM) closes the Reynolds-averaged Navier-Stokes equations (RANS) by solving transport equations for the individual Reynolds stresses withoutisotropic eddy-viscosity hypothesis and together with an equation for the dissipation rate. The quadratic pressure strain (QPS) model in RSM has been demonstrated to give superior performance in a range of basic shear flow comparing with standard linear pressure strain (LPS) model [7]. Large eddy simulation (LES) provides an alternative approach in which large eddies are explicitly resolved in a time-dependent simulation using the filtered Navier-Stokes equations. Both of Smagorinsky-Lilly subgrid-scale model (SLM) [13,14] and renormalization group (RNG) subgrid-scale model [15] have ever been adopted for simulation of hydrocyclone with better performance. It should be pointed out that LES model requires highly accurate spatial and temporal discretization, finer mesh than a comparable RANS simulation, and more compute resources.Therefore, four turbulence models, RNG k-ε, QPS RSM, and SLM and RNG LES will be performed in 75mm standard hydrocyclone. And the numerical results will be compared with each other and that of experiment.2.2 Multiphase modelAnother striking feature of the flow field is the presence of an air core in the hydrocyclone. The centrifugal force generated by the tangential acceleration pushes the fluid to the wall and creates a low pressure in the central axis, which gives the right conditions to suck air into the device and form an air core.The VOF model can simulate two or more immiscible fluid phases, in which the position of the interface between the fluids is of interest. In VOF method, the variable density equations of motion are solved for the mixture, and an additional transport equation for the volume fraction of each phase is solved, which can track the interface between the air core and the liquid in hydrocyclone. The single momentum equation issolved throughout the domain, and the resulting velocity field is shared among the phases. Thus, the VOF model can be adopted for modeling the air core in hydrocyclone. However, for the dense slurry, the more sophisticated Eulerian multiphase model will be more suitable.2.3 Particle TrackingIn most mineral processing operations, the solid phase is sufficiently dilute (<10%). Hence discrete phase model (DPM) can be employed, the fundamental assumption of which is that the dispersed second phase occupies a low volume fraction can be used to track solid particle movement. The Lagrangian DPM follows the Euler-Lagrange approach. The fluid phase is treated as a continuum by solving the time-averaged Navier-Stokes equations, while the dispersed phase is solved by tracking a large number of particles through the calculated flow field. The dispersed phase can exchange momentum, mass, and energy with the fluid phase.The dispersion of particles can be accounted for with a stochastic tracking model, in which the turbulent dispersion of particles is predicted by integrating the trajectory equations for individual particles and using the instantaneous fluid velocity. Also, unsteady tracking is used, where at the end of each time step the trajectory is updated with the instantaneous velocity. As for the slurry feed concentrations in excess of 10% by volume, the DPM is not suitable and Eulerian multiphase model is more appropriate for tracking particles in hydrocyclone.2.4 Erosion ModelThe impingement of solid particles with hydrocyclone walls can cause considerable wear, which is an issue of great industrial concern, both from safety and economicconsiderations. The damage induced by the erosion can cause equipment failure. Hence, estimation of potential erosion of the hydrocyclone wall is important to predict the lifetime of the equipment; it is useful to know how it is affected by geometry and different operating conditions. Because of experimental difficulties, CFD analysis is an effective tool to investigate the erosion rate of hydrocyclone.Particle erosion and accretion rates can be computed at wall boundaries using the following model equations. The erosion rate is defined as [19]()1()()b v N p p erosion p m C d f v R A α==∑& (1)where ()p C d is a function of particle diameter, α is the impact angle of the particle pathwith the wall face, ()f α is a function of impact angle, v is the relative velocity, ()b v is a function of relative particle velocity, and A is the area of the cell face at the wall. The three functions C , f and b can be defined as boundary conditions at the wall; however the default values are not updated to reflect the material being used. Therefore, these parameters have to be updated for different materials. It is known that one of the main parameters which influence the erosion rate is the particles impingement angle. The impingement angle function can be used as the following model and defined by a piece-linear profile [20-21]2()sin(2)3sin ()f ααα=− for o 18.43α≤ (2a)2()cos ()/3f αα= for o 18.43α> (2b)To calculate the erosion rate from Eq. (1), the diameter function and velocity exponent function are adopted as 1.8E-09 and 1.73.[19,22] The CFD model records the number, velocity, mass and the impact angle of the various particles for each of the grids that formthe internal geometry of the hydrocyclone. Then, the erosion rate of the hydrocyclone walls is determined using Eqs. (1) and (2).2.5 Simulation resultsIn this work, the simulations are conducted using Fluent CFD software package (version 6.3.26). The geometry of the 75mm standard hydrocyclone is the same as Hsieh's experiment [18] (figure 1(a)). In the simulation, the velocity inlet boundary condition and pressure outlet boundary conditions for vortex finder and spigot are applied. And the inlet flow rate is kept as 1.12 kg/s and the pressure at the two outlets is 1atm. The physical constants of the liquid phase were set to those of water. The solid particle density is 2700 kg/m3 and its wt fraction is 4.8%, which is injected at the inlet. The flow problem is simulated with three-dimensional unstructured mesh of hexahedral cells (figure 1(b)). Trial numerical results indicated that the solution is independent of the characteristics of the mesh size.(a) (b)Figure. 1. (a) Schematic dimensions of the standard hydrocyclone with stream lines, (b)Grid representation used in simulation.3. Model ValidationThe simulated flow field, air core and separation results are compared with experimental results to validate the model. In order to explore the inner flow field in hydrocyclone, three different horizontal planes situated 60, 120 and 170mm from the top wall of 75mm standard hydrocyclone are selected to give a general description of velocity field. On each plane, the axial and tangential velocity profiles are compared with those of the experimental results. The comparison results show that the predicted axial and tangential velocities of the RNG k-ε turbulence model are far from the experimental results while the performances of QPS RSM, SML LES and RNG LES models can capture the velocity profiles. Comparison between the latter three turbulence models indicates that the although the QPS RSM and SML LES models perform better near the center, the RNG LES model can track the turbulent velocities near the wall better. Furthermore, the absolute error is little for the axial velocity and nearly zero for tangential velocity near wall. Another point should be noted that the QRS RSM turbulence model combing with VOF multiphase model can lead to numerical stability, while the LES model consumes significantly more computing resources and times.The ability to predict well the development of the air core in the hydrocyclone is a test of the CFD model. The predicted air core and general mass balances are calculated and compared with experiments as listed in Table 1. For RNG k-ε turbulence model, there is no obvious air core after reaching steady state, while the predicted air core diameters with QPS RSM, SLM LES and RNG LES are 10.6mm, 11.5mm and 10.45mm respectively, which are all close to the experimental value 10mm. In all, QPS RSM, SLM LES and RNG LES can be used for modeling a hydrocyclone.A x i a l V e l o c i t y (m /s )Radius (m)Radius (m)T a n g e n t i a l Ve l o c i t y (m /s )Radius (m)A x i a l V e l o c i t y (m /s )Radius (m)T a n g e n t i a l V e l o c i t y (m /s )Radius (m)A x i a l V e l o c i t y (m /s )Radius (m)T a n g e n t i a l V e l o c i t y (m /s )FIG. 2. Axial and tangential velocity profile- comparison with experimental results at (a)-(b) 60mm, (c)-(d) 120mm, and (e)-(f) 170mm from the top wall of 75mm standardhydrocyclone.Table 1. General mass balance for four different turbulent modelsExperiment RNGk-εQPSRSMSLMLESRNGLESFeed flow rate (kg/s) 1.117 1.12 1.12 1.12 1.12Overflow flow rate (kg/s) 1.062 0.882 1.072 1.071 1.03Underflow flow rate (kg/s) 0.055 0.238 0.058 0.053 0.09Split ratio (%) 95.1 78.75 95.7 95.6 92.0Pressure drop (kPa) 46.7 38.3 41.13 40.2 38.4Air core diameter (mm) 10.0 0.2 10.6 11.5 10.454. Erosion RateThere are many parameters affecting the erosion rate, such as flow rate, design of the inlet, geometry and dimensions of the hydrocyclone and slurry properties etc. can affect the erosion rate, among which the inlet has a very important effect on the wear characteristics of hydrocyclone. Thus, as a preliminary work, we will calculate erosion rate for hydrocyclone with four different inlets and discuss the influence of the design of inlet ducting on wear characteristics of hydrocyclone. . In order to compare the effect of the inlet geometry on the erosion rate, the same fluid and particle velocity 2.25m/s are adopted for each case, the flow rate of solid particles is set as 0.05kg/s, particle diameter is 11.5µm. In calculation of the erosion rate of hydrocyclone, the interactions of the solid particles and the continuous phase need to be taken into account.Fig. 3 shows the erosion rate of the inner wall of the simulated hydrocyclones fitted with different inlets. Table 2 lists the maximum and average erosion rates and computed pressure drop for each case. Although the standard hydrocyclone with tangential inlet (fig. 3(a)) has been widely used in mineral processes, the erosion rate for it is the highest compared with the other three designs. Also, obvious wear hot spot can be found at the bottom of the cone section, where the erosion rate is very high. The maximum andintegral erosion rates are 3.72E-4 and 1.87E-6 kg/(m 2s), respectively. However, the pressure drop is the lowest, 32.8 kPa. For the modified tangential inlet (fig. 3(b)), there is no obvious wear hot spot, but the erosion rate is still high compared with the involute inlet. The maximum and average erosion rates are 7.61E-7 and 4.72E-8 kg/(m 2s), respectively, and the pressure drop is very high (81.7kPa). For the involute inlet which can provide a smooth transition from pressure energy to rotational momentum, the distribution of erosion rate is relatively uniform and the value is low. For the circular involute inlet, the maximum computed erosion rate is only 4.32E-7 kg/(m 2s) and the average value is 2.91E-8 kg/(m 2s) while for the elliptical involute inlet, the maximum and integral erosion rates are 4.37E-7 and 3.90E-8 kg/(m 2s), respectively. Moreover, the pressure drop of circular involute inlet (45.7kPa) is much smaller than that of elliptical involute inlet (72.3kPa). It can be seen from fig. 4 that the erosion rate at the inlet is nearly zero, while the erosion rate for conical section and spigot is much higher than that of cylindrical section and vortex finder.(a) (b) (c) (d)Figure.3. Computed local erosion rates of the inner wall of tested hydrocyclone fittedwith different inlets: (a) standard tangential inlet, (b) modified tangential inlet, (c)circular involute inlet and (d) elliptical involute inlet.Table 2. Computed Erosion rate for four inlet duct designs5. ConclusionsFour turbulence models, RNG k-ε, QPS RSM, SLM LES and RNG LES, were used to predict the aerodynamic performance of a 75mm standard hydrocyclone. The comparison of numerical and experimental results indicates that the RNG k-ε turbulence model is not suitable for modeling the highly swirling flows in hydrocyclones, while QPS RSM, SML LES and RNG LES models can capture well the velocity profiles and predict the formation of air core. With a VOF multiphase model, the air core formation was analyzed in detail and the diameter of steady air core was successfully predicted. The effects of inlet on the erosion rate were investigated with the RNG LES model. The involute inlet can eliminate the wear hot spot and lower the level of concentrated wear. This is only a preliminary study of the design and optimization process concerning erosion rate of a hydrocyclone. In our future study, other parameters and conditions such as inlet flow rate, particle characteristics etc. which can affect erosion rate will be investigated as all of the performance parameters should be taken into account for good design and operation of the hydrocyclone and to increase its service life.Inlet Pressure drop (kPa) Maximum Erosion rate ( kg/(m 2s)) Face average erosion rate ( kg/(m 2s))Standard tangential inlet 32.8 3.72E-4 1.84E-6Modified tangential inlet 81.7 7.62E-7 4.72E-8Circular involute inlet 45.7 4.32E-7 2.91E-8Elliptical involute inlet 72.3 4.37E-7 3.90E-8AcknowledgementsThis work was supported by M3TC at NUS, partial support of the National Natural Science Foundation of China through grant number 10572052, as well as the Foundation for Study Abroad of Education of Ministry of China is also acknowledged.Reference[1] Svarovsky, L. Hydrocyclones; Holt: Rinehart and Winston, 1984.[2] Dai, G.Q.; Chen, W.M.; Li, J.M.; Chu, L.Y. Experimental study of solid-liquid two-phase flow in a hydrocyclone. Chemical Engineering Journal 1999, 74, 211-216.[3] Boysan, F.; Ayers, W.H.; Swithenbank, J. Fundamental mathematical-modellingapproach to cyclone design. Chemical Engineering Research and Design 1982, 60, 222-230.[4] Fraser, S.M.; Rasek, A.M.; Abdel; Abdullah, M.Z. Computational and experimentalinvestigations in a cyclone dust separator. Journal of Process MechanicalEngineering 1997, 211, 247-257.[5] He, P.; Salcudean, M.; Gartshore, I.S. A numerical simulation of hydrocyclones.Chemical Engineering Research and Design 1999, 77, 429-441[6] Ma, L.; Ingham, D.B.; Wen, X. Numerical modelling of the fluid and particlepenetration through small sampling cyclones. Journal of Aerosol Science 2000, 31, 1097-1119.[7] Cullivan, J.C.; Williams, R.A.; Cross, C.R. Understanding the hydrocycloneseparator through computational fluid dynamics. Chemical Engineering Research and Design 2003, 81, 455-465.[8] Schuetz, S.; Mayer, G.; Bierdel, M.; Piesche, M. Investigations on the flow andseparation behaviour of hydrocyclones using computational fluid dynamics.International Journal of Mineral Processing 2004, 73, 229–237.[9] Cullivan, J.C.; Williams, R.A.; Dyakowski, T.; Cross, C.R. New understanding of ahydrocyclone flow field and separation mechanism from computational fluiddynamics. Minerals Engineering 2004, 17, 651-660.[10] Nowakowski, A.F.; Cullivan, J.C.; Williams, R.A.; Dyakowski, T. Application ofCFD to modeling of the flow in hydrocyclones. Is this a realizable option or still a research challenge? Minerals Engineering 2004, 17, 661-669.[11] Narasimha, M.; Sripriya, R.; Banerjee, P.K. CFD modelling of hydrocyclone--prediction of cut-size. International Journal of Mineral Processing 2005, 71, 53–68.[12] Delgadillo, J.A.; Rajamani, R.K. A comparative study of three turbulence-closuremodels for the hydrocyclone problem. International Journal of Mineral Processing 2005, 77, 217-230.[13] Brennan, M. CFD simulations of hydrocyclones with an air core: Comparisonbetween large eddy simulations and a second moment closure. ChemicalEngineering Research and Design 2006, 84, 495-505.[14] Narasimha, M.; Brennan, M.; Holtham, P.N. Large eddy simulation ofhydrocyclone—prediction of air-core diameter and shape. International Journal of Mineral Processing 2006, 80, 1-14.[15] Delgadillo, J.A.; Rajamani, R.K. Exploration of hydrocyclone designs usingcomputational fluid dynamics. International Journal of Mineral Processing 2007, 84, 252-261.[16] Wang, B.; Chu, K.W.; Yu, A.B. Numerical study of particle—Fluid flow inhydrocyclone. Industrial & engineering chemistry research 2007, 46, 4695-4705. [17] Hsu, Chih-Yuan; Wu, Rome-Ming. Hot zone in a hydrocyclone for particles escapefrom overflow. Drying Technology 2008, 26, 1011-1017.[18] Hsieh, K.T. Phenomenological Model of the Hydrocyclone; Ph.D. Thesis, Universityof Utah, USA, 1988.[19] Fluent V6.3, User's guide. Fluent Inc.: Centerra Resource Park, 10 Cavendish Court,Lebanon NH 03766, 2006.[20] Finnie, I. Erosion of surfaces by solid particles. Wear 1960, 3, 87–103.[21] Mazur, Z.; Campos-Amezcua, R.; Urquiza-Beltrán, G.; García-Gutiérrez, A.Numerical 3D simulation of the erosion due to solid particle impact in the main stop valve of a stream turbine. Applied Thermal Engineering 2004, 24, 1877-1891. [22] Edwards, J.K.; McLaury, B.S.; Shirazi, S.A. Modeling solid particle erosion inelbows and plugged tees. Journal of Energy Resources Technology 2001, 123, 277-284.。
非线性偏微分方程
FINITE DIMENSIONAL REDUCTION OF NONAUTONOMOUS DISSIPATIVESYSTEMSAlain MiranvilleUniversit´e de Poitiers Collaborators:Long time behavior of equations of the formy′=F(t,y)For autonomous systems:y′=F(y)In many situations,the evolution of the sys-tem is described by a system of ODEs:y=(y1,...,y N)∈R N,F=(F1,...,F N)Assuming that the Cauchy problemy′=F(y),y(0)=y0,is well-posed,we can define the family of solv-ing operators S(t),t≥0,acting on a subset φ⊂R N:S(t):φ→φy0→y(t)This family of operators satisfiesS(0)=Id,S(t+s)=S(t)◦S(s),t,s≥0We say that it forms a semigroup onφQualitative study of such systems:goes back to Poincar´eMuch is known nowadays,at least in low di-mensionsEven relatively simple systems can generate very complicated chaotic behaviorsThese systems are sensitive to perturbations: trajectories with close initial data may diverge exponentially→Temporal evolution unpredictable on ti-me scales larger than some critical value→Show typical stochastic behaviorsExample:Lorenz systemx′=σ(y−x)y′=−xy+rx−yz′=xy−bzObtained by truncature of the Navier-Stokes equationsGives an approximate description of a layer of fluid heated from belowSimilar to what is observed in the atmosphereFor a sufficiently intense heating:sensitive dependence on the initial conditions,repre-sents a very irregular convection→Butterfly effectVery often,the trajectories are localized in some subset of the phase space having a very complicated geometric structure(e.g.,locally homeomorphic to the product of R m and a Cantor set)→Strange attractor(Ruelle and Takens)Main feature of a strange attractor:dimen-sionSensitivity to initial conditions:>2(dimen-sion of the phase space≥3,say,3)Contraction of volumes:its volume is equal to0→noninteger,strictly between2and3→Fractal dimensionExample:Lorenz system:dim F A=2.05...Distributed systems:systems of PDEsφis a subset of an infinite dimensional func-tion space(e.g.,L2(Ω)or L∞(Ω))Solution:y:R+→φt→y(t)x→y(t,x)If the problem is well-posed,we can define the semigroup S(t):S(t):φ→φy0→y(t)The analytic structure of a PDE is much more complicated than that of an ODE:the global well-posedness can be a very difficult problemSuch results are known for a large class of PDEs→it is natural to investigate whether the notion of a strange attractor extends to PDEsSuch chaotic behaviors can be observed in dissipative PDEsChaotic behaviors arise from the interaction of•Energy dissipation in the higher part of the Fourier spectrum•External energy income in the lower part•Energyflux from the lower to the higher modesThe trajectories are localized in a”thin”in-variant region of the phase space having a very complicated geometric structure→the global attractor1.The global attractor.S(t)semigroup acting on E:S(t):E→E,t≥0S(0)=Id,S(t+s)=S(t)◦S(s),t,s≥0 Continuity:x→S(t)x is continuous on E,∀t≥0A set A⊂E is the global attractor for S(t)if(i)it is compact(ii)it is invariant:S(t)A=A,t≥0(iii)∀B⊂A,lim t→+∞dist(S(t)B,A)=0dist(A,B)=supa∈A infb∈Ba−b EEquivalently:∀B⊂φbounded,∀ǫ>0,∃t0= t0(B,ǫ)s.t.t≥t0implies S(t)B⊂UǫThe global attractor is uniqueIt is the smallest closed set enjoying(iii)It is the maximal bounded invariant setTheorem:(Babin-Vishik)We assume that S(t)possesses a compact attracting set K, i.e.,∀B⊂E bounded,lim t→+∞dist(S(t)B,K)=0Then S(t)possesses the global attractor A.The global attractor is oftenfinite dimen-sional:the dynamics,restricted to A isfinite dimensionalFractal dimension:Let X be a compact setdim F X=lim supǫ→0+ln Nǫ(X)ǫNǫ(X):minimum number of balls of radius ǫnecessary to cover XIf Nǫ(X)≤c(1Theorem:(H¨o lder-Ma˜n´e theorem)Let X⊂E compact satisfy dim F X=d and N>2d be an integer.Then almost every bounded linear projector P:E→R N is one-to-one on X and has a H¨o lder continuous inverse.This result is not valid for other dimensions (e.g.,the Hausdorffdimension)If A hasfinite fractal dimension,then,fixing a projector P satisfying the assumptions of the theorem,we obtain a reduced dynamical system(S),S= P(A),which isfinite dimensional(in R N)and H¨o lder continuousDrawbacks:(S)cannot be realized as a system of ODEs which is well-posedReasonable assumptions on A which would ensure that the Ma˜n´e projectors are Lipschitz are not knownComplicated geometric structure of A and AThe lower semicontinuitydist(A0,Aǫ)→0asǫ→0is more difficult to prove and may not hold It may be unobservable:∂y∂x2+y3−y=0,x∈[0,1],ν>0y(0,t)=y(1,t)=−1,t≥0A={−1}There are many metastable”almost station-ary”equilibria which live up to t⋆≡eν−12.Inertial manifolds.A Lipschitzfinite dimensional manifold M⊂E is an inertial manifold for S(t)if(i)S(t)M⊂M,∀t≥0(ii)∀u0∈E,∃v0∈M s.t.S(t)u0−S(t)v0 E≤Q( u0 E)e−αt,α>0,Q monotonicM contains A and attracts the trajectories exponentiallyConfirms in a perfect way thefinite dimen-sional reduction principle:The dynamics reduced to M can be realized as a Lipschitz system of ODEs(inertial form)Perfect equivalence between the initial sys-tem and the inertial formDrawback:all the known constructions are based on a restrictive condition,the spectral gap condition→The existence of an inertial manifold is not known for several important equations, nonexistence results for damped Sine-Gordon equations3.Exponential attractors.A compact set M⊂E is an exponential at-tractor for S(t)if(i)It hasfinite fractal dimension(ii)S(t)M⊂M,∀t≥0(iii)∀B⊂E bounded,dist(S(t)B,M)≤Q( B E)e−αt,α>0,Q monotonicM contains AIt is stillfinite dimensional and one has a uni-form exponential control on the rate of at-traction of trajectoriesIt is no longer smoothDrawback:it is not unique→One looks for a simple algorithm S→M(S)Initial construction:non-constructible and valid in Hilbert spaces onlyConstruction in Banach spaces:Efendiev, Miranville,Zelik→Exponential attractors are as general as global attractorsMain tool:Compact smoothing property on the difference of2solutionsLet S:E→E.We consider the discrete dynamical system generated by the iterations of S:S n=S◦...◦S(n times)Theorem:(Efendiev,Miranville,Zelik)We consider2Banach spaces E and E1s.t.E1⊂E is compact.We assume that•S maps theδ-neighborhood Oδ(B)of a bounded subset B of E into B•∀x1,x2∈Oδ(B),≤K x1−x2 ESx1−Sx2 E1Then the discrete dynamical system gener-ated by the iterations of S possesses an ex-ponential attractor M(S)s.t.(i)M(S)⊂B,is compact in E anddim F M(S)≤c1(ii)S M(S)⊂M(S)(iii)dist(S k B,M(S))≤c2e−c3k,k∈N,c3>0 (iv)The map S→M(S)is H¨o lder continu-ous:∀S1,S2,dist sym(M(S1),M(S2))≤c4 S1−S2 c5,c5>0, wheredist sym(A,B)=max(dist(A,B),dist(B,A))S =supSh Eh∈Oδ(B)Furthermore all the constants only depend on B,E,E1,δand K and can be computed explicitly.Remarks:1)We have a mapping S→M(S)and,due to the H¨o lder continuity,we can construct continuous families of exponential attractors2)Exponential attractors for a continuous semigroup S(t):Prove that∃t⋆>0s.t.S⋆=S(t⋆)satisfies the assumptions of the theorem→M⋆for S⋆If(x,t)→S(t)x is Lipschitz(or H¨o lder)on B×[0,t⋆],setS(t)M⋆M=∪t∈[0,t⋆]We again have a mapping S(t)→M(S)which is H¨o lder continuous3)For damped hyperbolic equations:asymp-totically smoothing property4.Finite dimensional reduction of nonau-tonomous systems.Systems of the form∂yDrawback:the uniform attractor has infinite dimension in general.Example:∂yThe family{A(t),t∈R}is a pullback attrac-tor for U(t,τ)if(i)A(t)is compact in E,∀t∈R(ii)U(t,τ)A(τ)=A(t),∀t≥τ(iii)∀B⊂E bounded,dist(U(t,t−s)B,A(t))=0lims→+∞Remarks:1)The pullback attractor is unique2)If the system is autonomous,we recover the global attractor3)In general,A(t)hasfinite fractal dimen-sion,∀t∈RDrawback:The forward convergence does not hold in generalExample:y′=f(t,y),where f(t,y)=−y if y≤0,(−1+2t)y−ty2 if t∈[0,1],and y−y2if t≥1Then A(t)={0},∀t∈R,but every trajectory starting from a neighborhood of0leaves this neighborhood never to enter it againThe forward convergence does not hold be-cause the rate of attraction is not uniform in t→This can be solved by constructing ex-ponential attractorsWe can construct a family{M(t),t∈R}, called nonautonomous exponential attractor, s.t.(i)dim F M(t)≤c1,∀t∈R,c1independent of t(ii)U(t,τ)M(τ)⊂M(t),∀t≥τ,(iii)∀B⊂E bounded,dist(U(t,τ)B,M(t+τ))≤Q( B E)e−αt,t∈R,t≥τ,α>0,Q monotonic(iii)implies the pullback attraction,but also the forward attraction→(i)and(iii)yield a satisfactoryfinite di-mensional reduction principle for nonautono-mous systemsRemarks:1)The time dependence is arbitrary2)The map U(t,τ)→{M(t),t∈R}is also H¨o lder continuous。
人类染色体畸变
Medical Genetics
(1) Euploidy is the condition of having a normal number of structurally normal chromosomes.
Euploid human females have 46 chromosomes (44 autosomes and two X chromosomes).
Medical Genetics
Trisomy is having three chromosomes of a particular type. A common autosomal trisomy in humans in Down syndrome, or trisomy 21, in which a person has three instead of the normal two chromosome 21s. Trisomy is a specific instance of polysomy, a more general term that indicates having more than two of any given chromosome.
Medical Genetics
Another type of aneuploidy is triploidy. A triploid individual has three of every chromosome, that is, three haploid sets of chromosomes. A triploid human would have 69 chromosomes (3 haploid sets of 23).
Medical Genetics
胰腺癌PDX模型研究进展
胰腺癌PDX模型研究进展卢彧，任学晨，周成亮，陈昊，康迎新，樊勇，康博雄，刘永永，王琛兰州大学第二医院，兰州730030摘要：近年来，胰腺癌的发病率和死亡率在世界范围内呈明显上升趋势，但目前其发病机制尚不完全清楚。
由于胰腺癌具有复杂的生物学行为，需要精确的临床前模型来充分展现肿瘤特征，从而研究其发病机制。
现有的胰腺癌临床前模型有细胞系移植模型、基因工程动物模型、类器官模型等，这些模型都不能准确反映胰腺癌的形态学、病理学以及增殖、侵袭等生物学行为，更不能模拟胰腺癌的基因组特征。
人源肿瘤异种移植（PDX）模型是将人类肿瘤组织植入免疫缺陷小鼠的皮下或原位，当肿瘤生长至足够大时，摘取肿瘤组织于新的小鼠体内继续培养，从而完成传代。
相较于细胞系移植模型、基因工程动物模型等传统的临床前模型，PDX模型较好地保留了胰腺癌的肿瘤微环境，同时能够模拟肿瘤来源的异质性、遗传学和组织学特征，是胰腺癌临床前研究和药物筛选的首选模型，已经在识别肿瘤标志物、临床前药物评价、临床精准化疗、胰腺癌转移及神经浸润等研究中得到广泛应用。
未来还需要将PDX模型合理优化，进一步提高其代表原发肿瘤特征的潜力，使之成为改善胰腺癌患者预后的最佳临床前工具。
关键词：胰腺癌；人源肿瘤异种移植模型；临床前模型doi：10.3969/j.issn.1002-266X.2021.10.024中图分类号：R735.9文献标志码：A文章编号：1002-266X（2021）10-0095-04近年来，胰腺癌的发病率和死亡率在世界范围内呈明显上升趋势。
据统计，我国胰腺癌的死亡率在所有恶性肿瘤中居第六位［1］。
虽然胰腺癌的治疗取得了很大进展，但在消化系统肿瘤中其总体生存率仍然较低［2］。
胰腺癌预后不良与其基因组的复杂性、异质性以及难以早期诊断和缺乏有效治疗方案等有关。
因此，深入研究胰腺癌发生、发展的分子生物学机制，对提高其诊疗水平具有重要意义。
目前，对胰腺癌的研究依赖高拟合度的临床前模型，如细胞系移植模型、基因工程动物模型、类器官模型等。
EMT有关基因
MINI REVIEW ARTICLEpublished:17September2013doi:10.3389/fonc.2013.00221 Role of epithelial-mesenchymal transition in pancreatic ductal adenocarcinoma:is tumor budding the missing link? Eva Karamitopoulou1,2*1Clinical Pathology Division,Institute of Pathology,University of Bern,Bern,Switzerland2Translational Research Unit,Institute of Pathology,University of Bern,Bern,SwitzerlandEdited by:Inti Zlobec,University of Bern, SwitzerlandReviewed by:Parham Minoo,University of Calgary, CanadaQianghua Xia,The Children’s Hospital of Philadelphia,USA*Correspondence:Eva Karamitopoulou,Clinical Pathology Division,Institute of Pathology,University of Bern, Murtenstrasse31,CH-3010Bern, Switzerlande-mail:eva.diamantis@pathology.unibe.ch Pancreatic ductal adenocarcinoma(PDAC)ranks as the fourth commonest cause of cancer death while its incidence is increasing worldwide.For all stages,survival at5years is<5%. The lethal nature of pancreatic cancer is attributed to its high metastatic potential to the lymphatic system and distant ck of effective therapeutic options contributes to the high mortality rates of PDAC.Recent evidence suggests that epithelial-mesenchymal transition(EMT)plays an important role to the disease progression and development of drug resistance in PDAC.Tumor budding is thought to reflect the process of EMT which allows neoplastic epithelial cells to acquire a mesenchymal phenotype thus increasing their capacity for migration and invasion and help them become resistant to apoptotic signals. In a recent study by our own group the presence and prognostic significance of tumor budding in PDAC were investigated and an association between high-grade budding and aggressive clinicopathological features of the tumors as well as worse outcome of the patients was found.The identification of EMT phenotypic targets may help identifying new molecules so that future therapeutic strategies directed specifically against them could potentially have an impact on drug resistance and invasiveness and hence improve the prognosis of PDAC patients.The aim of this short review is to present an insight on the morphological and molecular aspects of EMT and on the factors that are involved in the induction of EMT in PDAC.Keywords:pancreatic cancer,epithelial-mesenchymal transition,tumor budding,prognosis,biomarkerPANCREATIC CANCERPancreatic ductal adenocarcinoma(PDAC)is a common can-cer with dismal prognosis(1)that escapes early detection and resists treatment(2).Most patients have advanced stage dis-ease at presentation with a median survival of less than1year (1,3).Surgical resection is the only potentially curative treat-ment of PDAC(3).Classical histomorphological features like tumor size,blood vessel,or lymphatic invasion,and presence of lymph node metastases constitute essential prognostic deter-minants in pancreatic cancer and are invariably included in the pathology reports,with tumor stage being the most important of all(3).The lethal nature of PDAC has been attributed to the propensity of PDAC cells to rapidly disseminate to the lym-phatic system and distant organs(4).However,even patients with completely resected,node-negative PDACs eventually die of their disease.Within this context and considering the fact that the management of PDAC remains suboptimal and that adjuvant therapy has resulted to limited progress,the identification of addi-tional reliable and reproducible prognostic markers that would enable better patient stratification and eventually provide a guide toward a more successful and individualized therapy,is mandatory (1,5).EPITHELIAL-MESENCHYMAL TRANSITIONEpithelial-mesenchymal transition is a biologic process that allows epithelial cells to undergo the biochemical changes that enable them to acquire a mesenchymal phenotype,including enhanced migratory capacity,invasiveness,elevated resistance to apoptosis, and increased production of extracellular matrix(ECM)compo-nents(6,7).EMT is characterized by loss of cell adhesion,down regulation of E-cadherin expression,acquisition of mesenchy-mal markers(including N-cadherin,Vimentin,and Fibronectin), and increased cell motility(6).Both EMT and mesenchymal-epithelial transition(MET),the reversion of EMT,are essential for developmental and repair processes like implantation,embryo for-mation,and organ development as well as wound healing,tissue regeneration,and organfibrosis(8).However,EMT also occurs in neoplastic cells that have undergone genetic and epigenetic changes.These changes affect both oncogenes and tumor sup-pressor genes that enable cancer cells to invade and metastasize. Moreover,some neoplastic cells may go through EMT retaining many of their epithelial properties while other cells are becoming fully mesenchymal(9).Many molecular processes are involved in the initiation of EMT including activation of transcription factors,expression of specific cell-surface proteins,reorganization and expression of cytoskeletal proteins,production of ECM-degrading enzymes,and changes in the expression of specific microRNAs(miRNAS).The above fac-tors can also be used as biomarkers to detect cells in EMT state(10). EMT has been linked to cellular self-renewal programs of cancer stem cells and apoptosis-anoikis resistance,which are features of therapeutic resistance(11).The zincfinger transcription factors Snail,Slug,Zeb1,and Twist repress genes responsible for the epithelial phenotype and represent important regulators of EMT(6,7,12).In PDAC Snail expression has been reported to be seen in nearly80%of the cases and Slug expression in50%(13).Snail expression was inversely correlated with E-cadherin expression and decreased E-cadherin expression was associated with higher tumor grade. Similarly,poorly differentiated pancreatic cancer cell lines showed higher levels of Snail and lower levels of E-cadherin compared with moderately differentiated cell lines(13)while silencing of Zeb1leaded to up-regulation of E-cadherin and restoration of an epithelial phenotype(14).Zeb1expression in PDAC also corre-lated with advanced tumor grade and worse outcomes(14–16) and was shown to be primarily responsible for the acquisition of an EMT phenotype,along with increased migration and inva-sion in response to NF-κB signaling in pancreatic cancer cells (16).EMT AND TUMOR BUDDINGTumor budding reflects a type of diffusely infiltrative growth con-sisting of detached tumor cells or small cell clusters of up tofive cells at the invasive front of gastrointestinal carcinomas(17–22). Tumor buds represent a non-proliferating,non-apoptotic,highly aggressive subpopulation of tumor cells that display migratory and invasive capacities(23).The aim of tumor buds seems to be the invasion of the peritumoral connective tissue,the avoidance of the host’s defense andfinally the infiltration of the lymphatic and blood vessels with the consequence of local and distant metastasis. The EMT process by allowing a polarized cell to assume a more mesenchymal phenotype with increased migratory capacity,inva-siveness,and resistance to apoptosis seems to play a major role in the development of tumor buds.In fact,tumor buds are thought to result from the process of EMT.Thus,although formally tumor budding cannot be equated with EMT,several similarities between the two processes,including activation in WNT signaling,can be shown(24).The detachment of tumor buds from the main tumor body is accomplished by loss of membranous expression of the adhesion molecule E-cadherin.Activation of WNT sig-naling is further suggested by nuclear expression of b-catenin in tumor-budding cells,as well as increase of laminin5gamma2and activation of Slug and Zeb1(24,25).The presence of high-grade tumor budding has been consis-tently associated with negative clinicopathologic parameters in gastrointestinal tumors(26–30).In a previous study from our group we could show that tumor budding occurs frequently in pancreatic cancer and is a strong,independent,and reproducible, highly unfavorable prognostic factor that may be used as a para-meter of tumor aggressiveness and as an indicator of unfavorable outcome,even within this group of patients with generally poor prognosis.Moreover,tumor budding was proven to have a more powerful prognostic ability than other more classic prognostic fac-tors including TNM stage,thus adding relevant and independent prognostic information(31).EMT AND miRNAsMicroRNAS are small non-coding RNAs of18–25nucleotides, excised from60to110nucleotide RNA precursor structures (32).MiRNAs are involved in crucial biological processes, including development,differentiation,apoptosis,and pro-liferation,through imperfect pairing with target messenger RNAs of protein-coding genes and the transcriptional or post-transcriptional regulation of their expression(33,34).Recent studies illustrate the role of miRNAs on the regula-tion of gene expression and proteins in metastasis.For exam-ple,it has been shown that miR-10b,which is up-regulated by EMT transcription factor Twist,is associated with increased invasiveness and metastatic potential(35,36).Furthermore,it was shown that the miR-200family(miR-200a,miR-200b,miR-200c,miR-141,and miR-429)and miR-205play critical roles in regulating EMT by directly targeting the mRNAs encoding E-cadherin repressors Zeb1and Zeb2(37).Moreover,recent studies showed that members of the miR-200family by induc-ing EMT can regulate the sensitivity to epidermal growth fac-tor receptor(EGFR)in bladder cancer cells and to gemcitabine in pancreatic cancer cells(38).Conversely,Zeb1represses the transcription of miR-200genes by directly binding to their promoter region,thereby forming a double-negative feedback loop(39).On the other hand,miR-200family can also pro-mote the conversion of mesenchymal cells to epithelial-like cells (MET)suggesting that these miRNAs may also favor metastatic outgrowth.Recent studies aiming at the evaluation of miRNAs in pan-creatic cancer have shown that specific miRNAs are dysregulated in PDAC while the higher expression of some miRNA species was able to distinguish between benign and malignant pancre-atic tissue(40).For example,miR-21was shown to be over-expressed in79%of pancreatic cancers as opposed to27%of chronic pancreatitis(41).In resected PDAC specimens high lev-els of miR-200c expression strongly correlated with E-cadherin levels and were associated with significantly better survival rates compared with patients whose tumors had low levels of miR-200c expression(42).CHEMORESISTANCE AND EMTCells undergoing EMT become invasive and develop resistance to chemotherapeutic agents.Moreover,EMT can be induced by chemotherapeutic agents,and stress conditions such as exposure to radiation or hypoxia(43,44).Up-regulation of Twist has been shown to be associated with resistance to paclitaxel in nasopharyngeal,bladder,ovarian,and prostate cancers(45).In colorectal cancer cell lines,chronic expo-sure to oxaliplatin leaded to the development of the ability to migrate and invade with phenotypic changes resembling EMT(spindle-cell shape,loss of polarity,intercellular separa-tion,and pseudopodia formation)by the oxaliplatin-resistant cells(46).Pancreatic cancer remains today an extremely lethal disease largely because of its resistance to existing treatments(47).EMT has been shown to contribute significantly to chemoresistance in several cancers,including pancreatic cancer(30,48,49).Induction of gemcitabine resistance in previously sensitive cell lines resulted in development of an EMT phenotype and was associated with an increased migratory and invasive ability compared to gemc-itabine sensitive cells(49).Moreover,gene expression profiling ofchemoresistant cells showed a strong association between expres-sion of the EMT transcription factors Zeb1,Snail,and Twist and decreased expression of E-cadherin(39,50).Silencing of Zeb1 with siRNA resulted to MET(51)and restored chemosensitivity (14).Interestingly,maintenance of chemoresistance in cell lines that have undergone EMT is dependent on Notch and NF-κB signaling(30).Inhibition of Notch-2down regulates Zeb1,Snail, and Slug expression,attenuates NF-κB signaling,and reduces the migratory and invasive capacity of the gemcitabine resistant cells(30).Epithelial-mesenchymal transition can also confer resistance to targeted agents.For example,lung cancer cell lines that have undergone EMT,became resistant to the growth inhibitory effects of EGFR kinase inhibition(erlotinib)in vitro and in xenografts(47)as well as other EGFR inhibitors such as gefitinib and cetuximab(48)Thus,EMT can lead to resis-tance to multiple agents and result to rapid progression of the tumor.Clarifying the correlation between EMT and drug resistance may help clinicians select an optimal treat-ment.CONCLUSIONPancreatic cancer remains an extremely lethal disease partly because of the poor response to existing treatments.Accumulat-ing evidence suggests that EMT plays an important role in PDAC progression,is associated with stem cell features of the PDAC cells and seems to significantly contribute to the chemoresistance of pancreatic cancer.Moreover,is associated with more aggressive tumor characteristics and with poor patient survival.Because of its role in therapy response and tumor progression,targeting EMT could potentially reduce drug resistance and have a great impact in the survival of PDAC patients.Tumor budding thought to be the result of the EMT process is commonly observed in PDAC and high-grade tumor budding has been proven to have an independent adverse prognostic impact in the survival of PDAC patients.Figure1depicts tumor bud-ding as a possible transition between a fully epithelial and a fully mesenchymal phenotype of the tumor cells in PDAC.Moreover, cancer cells in tumor buds have been shown to have EMT and cancer stem cell characteristics.The further characterization of the budding cells at a protein and gene level in order to iden-tify a“molecular budding-promoting profile”will lead to a better understanding of the tumor-stroma interaction at the area of the invasive front and help to further elucidate the similarities between budding cells,EMT process and cancer stem cells in pancreatic cancer.Investigating these issues will allow us to gain further insight into pancreatic carcinogenesis,and provide us with a platform on which to build future studies leading to the identification of new therapeutic interventions.REFERENCES1.Hidalgo M.Pancreatic cancer.NEngl J Med(2010)362:1605–17.doi:10.1056/NEJMra09015572.Tuveson DA,Hingorani SR.Duc-tal pancreatic cancer in humans and mice.Cold Spring Harb Symp Quant Biol(2005)70:65–72.doi:10.1101/ sqb.2005.70.0403.Fernandez-del-Castillo C,JimenezRE,Steer ML.Surgery in the treatment of exocrine pancreas and prognosis.In:Tanabe KK,edi-tor(2013).Available from:www.4.Li Y,Kong D,Ahmad A,Bao B,Sarkar FH.Pancreatic cancer 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S,Parikh N,Gallick GE.Development and characterizationof gemcitabine-resistant pancre-atic tumor cells.Ann Surg Oncol(2007)14:3629–37.doi:10.1245/s10434-007-9583-550.Shimono Y,Zabala M,ChoRW,Lobo N,Dalerba P,QianD,et al.Downregulation ofmiRNA-200c links breast cancerstem cells with normal stemcells.Cell(2009)138:592–603.doi:10.1016/j.cell.2009.07.01151.Conroy T,Paillot B,Francois E,Bugat R,Jacob JH,Stein U,etal.Irinotecan plus oxaliplatin andleucovorin-modulatedfluorouracilin advanced pancreatic cancer–aGroupe Tumeurs Digestives of theFederation Nationale des Centres deLutte Contre le Cancer study.J ClinOncol(2005)23:1228–36.doi:10.1200/JCO.2005.06.050Conflict of Interest Statement:Theauthor declares that the research wasconducted in the absence of anycommercial orfinancial relationshipsthat could be construed as a potentialconflict of interest.Received:24July2013;accepted:11August2013;published online:17Sep-tember2013.Citation:Karamitopoulou E(2013)Role of epithelial-mesenchymal tran-sition in pancreatic ductal adenocar-cinoma:is tumor budding the miss-ing link?Front.Oncol.3:221.doi:10.3389/fonc.2013.00221This article was submitted to Gastroin-testinal Cancers,a section of the journalFrontiers in Oncology.Copyright©2013Karamitopoulou.Thisis an open-access article distributed underthe terms of the Creative CommonsAttribution License(CC BY).The use,distribution or reproduction in otherforums is permitted,provided the origi-nal author(s)or licensor are credited andthat the original publication in this jour-nal is cited,in accordance with acceptedacademic practice.No use,distribution orreproduction is permitted which does notcomply with these terms.。
CAFE模型机理及应用
第21卷第10期2009年10月 钢铁研究学报 Journal of Iron and Steel ResearchVol.21,No.10October 2009基金项目:国家自然科学基金资助项目(50874007)作者简介:王金龙(19782),男,博士生,讲师; E 2m ail :wangjlong78@ ; 修订日期:2009204216CAFE 模型机理及应用王金龙1, 赖朝彬1,2, 王福明1, 张炯明1, 任 嵬1(1.北京科技大学冶金与生态工程学院,北京100083; 2.新余钢铁公司,江西新余338001)摘 要:分析了CA FE 法模拟凝固过程微观组织的物理本质、数值计算方法,并应用CA FE 法模拟了易切削钢9SMn28的三维微观组织,优化了9SMn28的成分。
在CA FE 模型中,形核密度用高斯分布来描述;枝晶尖端生长动力学用KGT 模型进行计算;枝晶生长的择优取向是<100>方向,并可实现枝晶生长的竞争机制;FE 与CA 耦合是通过FE 节点和CA 元胞之间的插值实现的。
易切削钢9SMn28微观组织模拟结果与实验吻合较好,确定的碳、磷、锰、硅、硫的最佳质量分数分别为0115%、0110%、112%、0108%、0136%,并对优化结果进行了模拟,有效地改善了9SMn28的凝固组织。
关键词:元胞自动机2有限元模型;模拟;微观组织中图分类号:T G 142 文献标识码:A 文章编号:100120963(2009)1020060204Mechanism and Application of CAFE MethodWAN G Jin 2long 1, L A I Chao 2bin 1,2, WAN G Fu 2ming 1, ZHAN G Jiong 2ming 1, REN Wei 1(1.School of Metallurgical and Ecological Engineering ,University of Science and Technology Beijing ,Beijing 100083,China ; 2.Xinyu Iron and Steel Co ,Xinyu 338001,Jiangxi ,China )Abstract :The CA FE method simulated 3D 2microstructure in solidification processes was analyzed.The CA FE method is the combination of cellular automaton (CA )model with finite element (FE )method which is a macro 2micro coupling model ,and this method can simulate the competitive growth of columnar grains and equiaxed grains ,the formation of columnar region ,relationship between grain boundary orientation and hot grads ,colum 2nar 2to 2equiaxed transition ,and the shape of equiaxed grains in non 2isothermal temperature field ,etc.The nuclea 2tion density is described by Gaussian distribution in the CA FE model.Calculation of kinetics of the dendrite tip growth is done according to the model of KGT.The crystallographic orientation <100>is selected preferentially ,and the competition of crystal growth is developed directly.The coupling of FE and CA is realized through the in 2terpolation between FE mesh and CA cells.Based on the CAFE method ,3D 2microstructure of 9SMn28free cutting steel was simulated in solidification processes ,and the simulation results are consistent with those of experiment.The composition of 9SMn28f ree cutting steel was optimized ;the optimum C ,P ,Mn ,Si and S contents are 0115%,0110%,112%,0108%and 0136%,respectively.The optimization results were also simulated and the solidifica 2tion structure is improved obviously.K ey w ords :cellular autometion 2finite element model ;simulation ;microstructure 凝固过程的微观组织模拟是指在晶粒尺度上对铸件凝固过程进行模拟,对铸件凝固过程的微观模拟和做少量实验即可预测铸件凝固组织和力学性能。
裂缝各向异性油藏孔隙度和渗透率计算方法
; 同时有如下关系 : ( 3)
[ 16 ]
k i = kf i + k b , i = Ⅰ, Ⅱ, Ⅲ. 采用随机裂缝模型 关系 : φ f = 0 . 029 6 kf / b .
2
, 则裂缝孔隙度 φ f 与方
向平均裂缝渗透率 kf 、 平均裂缝宽度 b 之间有如下
( 4)
3 孔隙度与渗透率的计算
2 基础数据处理
根据岩心分析 、 测井解释及薄片分析等资料统 计得到裂缝宽度分布及裂缝平均宽度。 裂缝密度 L fd 指的是沿垂直于裂缝方向单位长 度内裂缝的条数 。 以单井单层段为目标 ,将裂缝测井 的解释结果进行统计分析 ,结果见表 1 , 由此计算该 井段上的裂缝密度 。
表 1 裂缝测井解释结果
作者简介 : 张吉昌 (1969 - ) ,男 ( 汉族) ,辽宁沈阳人 ,高级工程师 ,中国矿业大学博士研究生 ,从事油藏地质与开发研究工作 。
第 30 卷 第 5 期 张吉昌 ,等 : 裂缝各向异性油藏孔隙度和渗透率计算方法
・6 3 ・
分裂缝与基质的贡献 , 难以提供油藏的微观结构特 征 。文献 [ 13215 ] 提出了裂缝性油藏静动态综合建 模的思路 ,但大都局限于定性或经验方法 ,且没有考 虑裂缝渗透率的各向异性特点 。笔者将静动态研究 相融合 ,尝试建立完善而实用的裂缝性油藏孔隙度 和渗透率的定量计算方法 。
…
152 155 160
油藏总各向异性渗透率张量 K 由裂缝渗透率 张量 Kf 和基质渗透率 k b 组成 。 记 I 为二阶单位张 量 , 则有 K = Kf + k b I .
( 2)
考虑井筒方向与裂缝间夹角的影响 , 确定裂缝 密度的公式为
m
催化氧化技术
ቤተ መጻሕፍቲ ባይዱ
We use PEEM measurements as well as measurements of the CO2 formation rate during CO oxidation and we extract the corresponding probability distributions.Two maxima are rather asymmetric with respect to width and height, a behavior reminiscent. The dynamic is also strongly asymmetric, a result which is again in accord with findings from optical bistability. We conclude that the barrier height and width for Pd(111) is smaller than those for the Ir(111) system.
This system fulfills the conditions necessary for a long time analysis in the framework of reactiondiffusion systems without taking into account a variable associated with the structural composition of the surface.The underlying reaction-diffusion system is based on the Langmuir-Hinshelwood mechanism and is not excitable. For small values of Y the initial slope for the CO2 rate in the Pd(111) system studied here is linear. we investigate experimentally the long time scale behavior of the CO2 rate for four equidistant Y values within the hysteretic regime in the presence of only intrinsic noise.
专业英语
Life on a planet of its own: regulation of RNA polymerase I transcription in the nucleolus Wei xiao qiao Abstract: Mammalian cells contain 100 or more copies of tandemly repeated ribosomal RNA (rRNA)
genes per haploid genome. These genes are transcribed with high efficiency to keep up with the cell’s metabolic activity and demand for ribosomes. Alterations in cell proliferation are accompanied by profound changes in the transcription rate of rRNA genes. Thus, by responding to changes in the cellular environment, transcription by RNA polymerase I (PolI) ultimately determines ribosome production and the potential for cell growth and proliferation. There are several comprehensive reviews that discuss regulation of rRNA synthesis in vertebrates and yeast[1]. However, new data have been produced even since the latest of these reviews that uncover the mechanisms that link PolI transcription to cellular physiology. Keywords：RNA polymerase I, Itranscrition, nucleolus,PolI,tif ia