第五届分数阶导数理论及其应用国际学术会议纪要

刊名简称刊名全称ISSN小类名称（中文）0269-9648工程：工业PROBABILITY IN THE ENGINEERING AND INFORPROBAB ENG INFORAPPL MATH MODEL A PPLIED MATHEMATICAL MODELLING0307-904X工程：综合0927-6467工程：综合RUSS J NUMER ANARUSSIAN JOURNAL OF NUMERICAL ANALYSIS AN1239-6095环境科学ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MBOREAL ENVIRON R0167-9473计算机：跨学科应用COMPUT STAT DATACOMPUTATIONAL STATISTICS & DATA ANALYSISJ COMB OPTIM JOURNAL OF COMBINATORIAL OPTIMIZATION1382-6905计算机：跨学科应用0094-9655计算机：跨学科应用J STAT COMPUT SIJOURNAL OF STATISTICAL COMPUTATION AND S1387-3954计算机：跨学科应用MATH COMP MODELMATHEMATICAL AND COMPUTER MODELLING OF DMATHEMATICAL AND COMPUTER MODELLING0895-7177计算机：跨学科应用MATH COMPUT MODEMATHEMATICS AND COMPUTERS IN SIMULATION0378-4754计算机：跨学科应用MATH COMPUT SIMUQUEUEING SYST QUEUEING SYSTEMS0257-0130计算机：跨学科应用1615-3375计算机：理论方法FOUNDATIONS OF COMPUTATIONAL MATHEMATICSFOUND COMPUT MATFUZZY SET SYSTFUZZY SETS AND SYSTEMS0165-0114计算机：理论方法COMPUT COMPLEXCOMPUTATIONAL COMPLEXITY1016-3328计算机：理论方法STAT COMPUT STATISTICS AND COMPUTING0960-3174计算机：理论方法COMBINATORICS PROBABILITY & COMPUTING0963-5483计算机：理论方法COMB PROBAB COMPDISCRETE & COMPUTATIONAL GEOMETRY0179-5376计算机：理论方法DISCRETE COMPUT0218-1959计算机：理论方法INT J COMPUT GEOINTERNATIONAL JOURNAL OF COMPUTATIONAL G1521-1398计算机：理论方法J COMPUT ANAL APJOURNAL OF COMPUTATIONAL ANALYSIS AND APMATH PROGRAM MATHEMATICAL PROGRAMMING0025-5610计算机：软件工程BIT BIT NUMERICAL MATHEMATICS 0006-3835计算机：软件工程1365-8050计算机：软件工程DISCRETE MATHEMATICS AND THEORETICAL COMDISCRETE MATH THMATHEMATICAL AND COMPUTER MODELLING0895-7177计算机：软件工程MATH COMPUT MODEMATH COMPUT SIMUMATHEMATICS AND COMPUTERS IN SIMULATION0378-4754计算机：软件工程RANDOM STRUCTURES & ALGORITHMS1042-9832计算机：软件工程RANDOM STRUCT AL0392-4432科学史与科学哲学B STOR SCI MATBollettino di Storia delle Scienze MatemHIST MATH HISTORIA MATHEMATICA0315-0860科学史与科学哲学NEXUS NETW J Nexus Network Journal1590-5896科学史与科学哲学J NONLINEAR SCI J OURNAL OF NONLINEAR SCIENCE0938-8974力学APPL MATH MODEL A PPLIED MATHEMATICAL MODELLING0307-904X力学0253-4827力学APPL MATH MECH-EAPPLIED MATHEMATICS AND MECHANICS-ENGLIS1392-5113力学NONLINEAR ANAL-MNonlinear Analysis-Modelling and ControlNONLINEAR OSCIL N onlinear Oscillations1536-0059力学0044-2267力学ZAMM-Zeitschrift fur Angewandte MathematZAMM-Z ANGEW MATABSTR APPL ANAL A bstract and Applied Analysis 1085-3375数学ACTA MATHEMATICA0001-5962数学ACTA MATH-DJURSHANN MATH ANNALS OF MATHEMATICS0003-486X数学0273-0979数学B AM MATH SOC BULLETIN OF THE AMERICAN MATHEMATICAL SO0010-3640数学COMMUN PUR APPLCOMMUNICATIONS ON PURE AND APPLIED MATHECONSTR APPROX CONSTRUCTIVE APPROXIMATION0176-4276数学DUKE MATH J DUKE MATHEMATICAL JOURNAL0012-7094数学INVENT MATH INVENTIONES MATHEMATICAE0020-9910数学0894-0347数学J AM MATH SOC JOURNAL OF THE AMERICAN MATHEMATICAL SOC0021-7824数学JOURNAL DE MATHEMATIQUES PURES ET APPLIQJ MATH PURE APPL0065-9266数学MEM AM MATH SOC M EMOIRS OF THE AMERICAN MATHEMATICAL SOCPUBL MATH-PARIS P UBLICATIONS MATHEMATIQUES DE L IHES0073-8301数学ADV MATH ADVANCES IN MATHEMATICS0001-8708数学Aequationes Mathematicae0001-9054数学AEQUATIONES MATHAM J MATH AMERICAN JOURNAL OF MATHEMATICS0002-9327数学ANAL APPL Analysis and Applications0219-5305数学ANAL PDE Analysis & PDE1948-206X数学ANN MAT PUR APPLANNALI DI MATEMATICA PURA ED APPLICATA 0373-3114数学0012-9593数学ANN SCI ECOLE NOANNALES SCIENTIFIQUES DE L ECOLE NORMALEB SYMB LOG BULLETIN OF SYMBOLIC LOGIC1079-8986数学BOUND VALUE PROBBoundary Value Problems 1687-2762数学0944-2669数学CALC VAR PARTIALCALCULUS OF VARIATIONS AND PARTIAL DIFFECarpathian Journal of Mathematics1584-2851数学CARPATHIAN J MATCOMBINATORICA COMBINATORICA0209-9683数学COMMENTARII MATHEMATICI HELVETICI0010-2571数学COMMENT MATH HEL0219-1997数学COMMUNICATIONS IN CONTEMPORARY MATHEMATICOMMUN CONTEMP M0360-5302数学COMMUNICATIONS IN PARTIAL DIFFERENTIAL ECOMMUN PART DIFFCOMPUTATIONAL GEOMETRY-THEORY AND APPLIC0925-7721数学COMP GEOM-THEORCOMPOS MATH COMPOSITIO MATHEMATICA0010-437X数学1078-0947数学DISCRETE CONT DYDISCRETE AND CONTINUOUS DYNAMICAL SYSTEMDOC MATH Documenta Mathematica 1431-0643数学FIXED POINT THEOFixed Point Theory 1583-5022数学Fixed Point Theory and Applications 1687-1820数学FIXED POINT THEOFOUNDATIONS OF COMPUTATIONAL MATHEMATICS1615-3375数学FOUND COMPUT MATGEOM FUNCT ANAL G EOMETRIC AND FUNCTIONAL ANALYSIS1016-443X数学GEOM TOPOL GEOMETRY & TOPOLOGY1364-0380数学INDIANA U MATH JINDIANA UNIVERSITY MATHEMATICS JOURNAL0022-2518数学1705-5105数学International Journal of Numerical AnalyINT J NUMER ANALJ ALGEBR COMB JOURNAL OF ALGEBRAIC COMBINATORICS0925-9899数学JOURNAL OF ALGEBRAIC GEOMETRY1056-3911数学J ALGEBRAIC GEOM0095-8956数学J COMB THEORY B J OURNAL OF COMBINATORIAL THEORY SERIES BJ CONVEX ANAL JOURNAL OF CONVEX ANALYSIS0944-6532数学JOURNAL OF DIFFERENTIAL EQUATIONS0022-0396数学J DIFFER EQUATIOJ DIFFER GEOM JOURNAL OF DIFFERENTIAL GEOMETRY0022-040X数学1040-7294数学J DYN DIFFER EQUJournal of Dynamics and Differential Equ1435-9855数学J EUR MATH SOCJOURNAL OF THE EUROPEAN MATHEMATICAL SOCJ FUNCT ANAL JOURNAL OF FUNCTIONAL ANALYSIS0022-1236数学1474-7480数学Journal of the Institute of MathematicsJ INST MATH 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STAlgebraic and Geometric Topology 1472-2739数学ALGEBR GEOM TOPOAlgebra & Number Theory1937-0652数学ALGEBR NUMBER THALGEBR REPRESENTALGEBRAS AND REPRESENTATION THEORY1386-923X数学1239-629X数学ANN ACAD SCI FENANNALES ACADEMIAE SCIENTIARUM FENNICAE-MANNALS OF GLOBAL ANALYSIS AND GEOMETRY0232-704X数学ANN GLOB ANAL GEANN I FOURIER ANNALES DE L INSTITUT FOURIER0373-0956数学ANN PURE APPL LOANNALS OF PURE AND APPLIED LOGIC0168-0072数学0391-173X数学ANN SCUOLA NORM-ANNALI DELLA SCUOLA NORMALE SUPERIORE DI1452-8630数学Applicable Analysis and Discrete MathemaAPPL ANAL DISCR0024-6093数学B LOND MATH SOC B ULLETIN OF THE LONDON MATHEMATICAL SOCICALCOLO CALCOLO0008-0624数学0008-414X数学CAN J MATH CANADIAN JOURNAL OF MATHEMATICS-JOURNALCOMMUNICATIONS IN ANALYSIS AND GEOMETRY1019-8385数学COMMUN ANAL GEOM1534-0392数学COMMUNICATIONS ON PURE AND APPLIED ANALYCOMMUN PUR APPLCOMPUT COMPLEXCOMPUTATIONAL COMPLEXITY1016-3328数学0926-2245数学DIFFER GEOM APPLDIFFERENTIAL GEOMETRY AND ITS APPLICATIOELECTRON J COMB E LECTRONIC JOURNAL OF 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OF COMBINATORIAL DESIGNS1063-8539数学0097-3165数学J COMB THEORY A J OURNAL OF COMBINATORIAL THEORY SERIES AJ COMPUT MATH JOURNAL OF COMPUTATIONAL MATHEMATICS0254-9409数学J EVOL EQU JOURNAL OF EVOLUTION EQUATIONS1424-3199数学1661-7738数学J FIX POINT THEOJournal of Fixed Point Theory and Applic0972-6802数学J FUNCT SPACE APJournal of Function Spaces and ApplicatiJ GEOM ANAL JOURNAL OF GEOMETRIC ANALYSIS1050-6926数学J GRAPH THEOR JOURNAL OF GRAPH THEORY0364-9024数学1025-5834数学J INEQUAL APPLJOURNAL OF INEQUALITIES AND APPLICATIONSJ LOND MATH SOC J OURNAL OF THE LONDON MATHEMATICAL SOCIE0024-6107数学0025-5645数学J MATH SOC JPNJOURNAL OF THE MATHEMATICAL SOCIETY OF J1345-4773数学J NONLINEAR CONVJournal of Nonlinear and Convex AnalysisJ NUMER MATH Journal of Numerical Mathematics 1570-2820数学JOURNAL OF PURE AND APPLIED ALGEBRA0022-4049数学J PURE APPL ALGEJ SYMPLECT GEOM J ournal of Symplectic Geometry1527-5256数学JPN J MATH Japanese Journal of Mathematics0289-2316数学K-THEORY K-THEORY0920-3036数学LINEAR & MULTILINEAR 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中国古生物学会第26届学术年会2011年10月21—23日贵州关岭会议组织机构主办中国古生物学会合作主办中国古生物化石保护基金会支持中国科学技术协会中国科学院国家自然科学基金委员会地球科学部国家古生物化石专家委员会国家基础科学人才培养基金承办贵州关岭自治县人民政府中国科学院南京地质古生物研究所贵州大学协办中国科学院古脊椎动物与古人类研究所中国地质调查局武汉地质矿产研究所现代古生物学和地层学国家重点实验室生物地质与环境地质国家重点实验室中科院脊椎动物进化系统学重点实验室北大地球与空间学院/古生物研究所大会组织委员会顾问委员：吴新智中科院古脊椎动物与古人类所殷鸿福中国地质大学（武汉）汪品先同济大学张弥曼中科院古脊椎动物与古人类所周志炎中科院南京地质古生物研究所戎嘉余中科院南京地质古生物研究所陈旭中科院南京地质古生物研究所邱占祥中科院古脊椎动物与古人类所邱铸鼎中科院古脊椎动物与古人类所项礼文中国地质科学院地质研究所曹瑞骥中科院南京地质古生物研究所穆西南中科院南京地质古生物研究所汪啸风中国地质科学院宜昌地质所郑守仪中科院青岛海洋研究所沙金庚中科院南京地质古生物研究所郝守刚北京大学朱敏中科院古脊椎动物与古人类所主席：杨群中科院南京地质古生物研究所副主席：周忠和中科院古脊椎动物与古人类季强中国地质科学院地质研究所童金南中国地质大学（武汉）孙革沈阳师范大学委员（按姓氏笔画排列）：万晓樵中国地质大学（北京）尹崇玉中国地质科学院地质研究所王军中科院南京地质古生物研究所王元青中科院古脊椎动物与古人类所王文利北京自然博物馆王永栋中科院南京地质古生物研究所王训练中国地质大学（北京）王伟铭中科院南京地质古生物研究所王向东中科院南京地质古生物研究所王宇飞中国科学院植物研究所王成文吉林大学王汝建同济大学邓胜徽中国石油勘探开发研究院冯伟民中科院南京地质古生物研究所冯庆来中国地质大学（武汉）卢立伍中国地质博物馆白志强北京大学任东首都师范大学刘武中科院古脊椎动物与古人类所刘羽国家自然科学基金委员会刘家润南京大学华洪西北大学孙革吉林大学孙元林北京大学孙春林吉林大学孙柏年兰州大学巩恩普东北大学吴亚生中科院地质与地球物理研究所张维中科院地质与地球物理研究所张兆群中科院古脊椎动物与古人类所张兴亮西北大学秘书长：张喜光云南大学李勇长安大学李奎成都理工大学杜品德塔里木油田勘探开发研究院杨群中科院南京地质古生物研究所沈波常州中华恐龙园沈树忠中科院南京地质古生物研究所陈木宏中科院南海海洋研究所陈孝红中国地质科学院宜昌地质所周传明中科院南京地质古生物研究所周忠和中科院古脊椎动物与古人类欧阳辉重庆自然博物馆季强中国地质科学院地质研究所武涛中石化西北勘探开发研究院郑卓中山大学郑晓廷山东省天宇自然博物馆金昌柱中科院古脊椎动物与古人类所姚建新中国地质科学院地质所施贵军南京大学洪天求合肥工业大学姬书安中国地质科学院地质研究所袁训来中科院南京地质古生物研究所高星中科院古脊椎动物与古人类所黄清华大庆油田勘探开发研究院黄智斌中国石油塔里木油田公司彭进贵州大学曾勇中国矿业大学童金南中国地质大学（武汉）谢树成中国地质大学（武汉）詹仁斌中科院南京地质古生物研究所王永栋中科院南京地质古生物研究所副秘书长：蔡华伟中科院南京地质古生物研究所刘建波北京大学张翼中科院古脊椎动物与古人类所纪占胜中国地质科学院地质研究所何卫红中国地质大学（武汉）孙跃武吉林大学单华春中国古生物化石保护基金会王丽霞国家古生物化石专家委员会学术秘书：王博中科院南京地质古生物研究所闫德飞兰州大学胡东宇沈阳师范大学尹士银山东省天宇自然博物馆许晓音常州中华恐龙园中国古生物学会第38期会讯欢迎词尊敬的各位嘉宾、专家和参会代表：欢迎您于金秋十月来到古朴秀丽的贵州关岭，参加中国古生物学会第26届学术年会。

表、植物对可持续发展的贡献、微生物在可持续发展农业中的作用、如何更广泛地社会传播科学知识。

w o r k s h o p 形式更自由，参 与者有更多的机会与专家们讨论交流，效果非常好。

在促进中国和英国植物科学的合作这个w o r k s h o p 中，双方学者在几个领域 达成了合作意向。

(华中农业大学生命科学技术学院胡红红，武汉430070)2019天府偏微分方程国际会议本次会议于2019年7月8~10日在西南财经大学举行。

会议旨在汇集偏微分方程领域的领军人物和专家学者介绍他们 在该领域和相关方向最新的科研进展及其在自然科学和社会科学中的应用;同时会议还为专家学者、教师与青年学生交流他们 的学术研究经验提供一个优秀的跨学科交流平台，互相交流讨论相关领域的发展趋势、研究兴趣以及可能存在的挑战。

本次会议吸引了偏微分方程领域众多专家学者参会，包括奥地利维也纳科技大学A n to n A r n o l d ,美国匹兹堡大学陈新富，首 尔国立大学S e u n g -Y e a l H a ,洛桑联邦理工学院J a n S . H e s t h a v e n ,上海交通大学金石，南方科技大学A le x a n d e r K u r g a n o v ,首都师 范大学李海梁,俄亥俄州立大学楼元，美国明尼苏达大学&香港中文大学(深圳）倪维明，美国布朗大学舒其望,上海交通大学 陶有山,南方科技大学王学锋，加拿大英属哥伦比亚大学魏军城，香港城市大学杨彤等在内的世界级领军人物，以及韩国仁荷大 学Y o u n g -P i l C h o i ,香港中文大学段仁军，清华大学何凌冰，上海交通大学唐敏,香港理工大学王治安，美国佐治亚理工学院姚珧 等在内的学术新星及青年才俊，介绍他们在偏微分方程领域最新的科研进展。

大会共有25个精彩报告，报告主题涵盖了偏微分 方程分析、建模计算及其在相关自然和社会学科中的应用等。

Experimental investigation and numerical simulation for weakening the thermal fluctuations in aT-junctionK.Gao a ,P.Wang b ,T.Lu a ,⇑,T.Song caCollege of Mechanical and Electrical Engineering,Beijing University of Chemical Technology,Beijing 100029,China bSchool of Energy and Power Engineering,Dalian University of Technology,Dalian 116024,China cChina Nuclear Power Technology Research Institute Co.,Ltd,Shenzhen 518124,Chinaa r t i c l e i n f o Article history:Received 25August 2014Received in revised form 17November 2014Accepted 4January 2015Available online 17January 2015Keywords:Experimental investigation Numerical simulation Tee junctionThermal fluctuationa b s t r a c tIn this work,the mixing processes of hot and cold fluids with and without a distributor are predicted by experiments and numerical simulations using large-eddy simulation (LES)on FLUENT platform.Temperatures at different positions of the internal wall and mixing conditions caused by T-junctions at different times are obtained,then the simulated normalized mean and root-mean square (RMS)temperature,velocity vector and temperature contour for the two structures,namely with and without a distributor,are compared.The results show that,compared with the a T-junction without a distributor,the mixing region of hot and cold water in the T-junction with distributor moves to the middle of the pipe,and the inclusion of the distributor reduces the temperature fluctuations of internal wall noticeably and makes the mixing of hot and cold water more efficient.Ó2015Elsevier Ltd.All rights reserved.1.IntroductionTee junction is a familiar structure that is universally used in pipeline systems of power plants,nuclear power plants and chemi-cal plants,it is often applied to mix hot and cold fluid of main and branch pipes.The fluctuations of fluid temperature are transported to the solid walls by heat convection and conduction.This can cause cyclical thermal stresses and subsequent thermal fatigue cracking of the piping (Lee et al.,2009).So far,leakage accidents took place in several light water and sodium cooled reactors due to thermal fati-gue.In 1998,a crack was discovered at a mixing tee in which cold water from a branch pipe flowed into the main pipe in the residual heat removal (RHR)system in a reactor in Civaux,France.Metallur-gical studies concluded that the crack was caused by a high degree of cycle thermal fatigue (Eric Blondet,2002).In 1990,sodium leak-age happened in the French reactor Superphenix (Ricard and Sperandio,1996).It has been established that mixing hot and cold sodium can induce temperature fluctuations and result in thermal fatigue (IAEA,2002).Therefore,it is significant to study how to weaken thermal fatigue of the piping wall to ensure the integrity and safety of the piping system in a nuclear power plant.In the analysis of thermal fatigue,temperature fluctuation is a very important evaluation parameter.A reliable lifetime assess-ment of these components is difficult because usually only thenominal temperature differences between the hot and cold fluids are known,whereas the instantaneous temperatures and heat fluxes at the surface are unknown (Paffumi et al.,2013).Kamaya and Nakamura (2011)used the transient temperature obtained by simulation to assess the distribution of thermal stress and fati-gue when cold fluid flowed into the main pipe from a branch pipe.Numerical simulation of flow in the tee has been carried out Simoneau et al.(2010)to get temperature and its fluctuation curves,and the numerical results were in good agreement with the experimental data.Through the analysis on thermal fatigue stress,it draw the conclusion that the enhanced heat transfer coef-ficient and the temperature difference between hot and cold fluids were primary factors of thermal fatigue failure of tees.Many numerical simulations and experiments have been carried out to evaluate the flow and heat transfer in a mixing tee junction (Metzner and Wilke,2005;Hu and Kazimi,2006;Hosseini et al.,2008;Durve et al.,2010;Frank et al.,2010;Jayaraju et al.,2010;Galpin and Simoneau,2011;Aulery et al.,2012;Cao et al.,2012).Turbulent models such as Reynolds-averaged Navier–Stokes (RANS),Unsteady Reynolds averaged Navier Stokes (URANS),Scale-Adaptive Simulation (SAS),Reynolds stress model (RSM),detached eddy simulations (DES),and LES have all been used in industrial applications.As one of the choices of turbulent model for predicting the mixing flow in tee junctions,the RSM can bemused to describe the momentum conservation of the mixing (Durve et al.,2010;Frank et al.,2010).Turbulent mixing phenomena in a T-junction have been numerically investigated using the k $x/10.1016/j.anucene.2015.01.0010306-4549/Ó2015Elsevier Ltd.All rights reserved.Corresponding author.based baseline Reynolds stress model(BSL RSM)(Frank et al.,2010) for two different cases.Durve et al.(2010)applied the RSM to pre-dict the velocityfield of three non-isothermal parallel jetsflowing in an experiment setup used to simulate theflow occurring at the core outlet region of a fast breeder reactor(FBR),with a Reynolds number of1.5Â104.Theflow in tube of different Reynolds numbers (Re)andflow velocity ratio were studied experimentally with three-dimensional scanning using particle image velocimetry(3D-SPIV) (Brücker,1997).Large-eddy simulation(LES)is an alternative turbulence model with different subgridscale models often employed to predict velocity and temperaturefluctuations.Indeed many numerical studies have shown the capability of LES to model thermalfluctu-ations in turbulent mixing.LES was performed(Lee et al.,2009)to analyze temperaturefluctuation in the tee junction and the simu-lated results were in good agreement with the experimental data. Thermal striping phenomena in the tee junction had been numer-ically investigated using LES(Hu and Kazimi,2006)for two differ-ent mixing cases,and the simulated normalized mean and root-mean square(RMS)was consistent with experimental results. LES in a mixing tee were carried out(Galpin and Simoneau, 2011)in order to evaluate the sensitivity of numerical results to the subgrid scale model by comparing the experimental results, and to investigate the possibility of reducing thefluid computa-tional domain at the inlet.Another simulation that mixing of a hot and a coldfluid stream in a vertical tee junction with an upstream elbow main pipe was carried out with LES(Lu et al., 2013).And the numerical results show that the normalized RMS temperature and velocity decrease with the increases of the elbow curvature ratio and dimensionless distance.In the meantime,many scholars have studied how to weaken the thermalfluctuation.Experiments and simulation were con-ducted(Wu et al.,2003)on a tee junction geometry with a sleeve tube in it.Theflow is divided into three types of jets by theflow velocity ratio in main and branch pipes.Through the analysis of flowfield and velocityfield of various jets types,it indicate that the addition of sleeve tube relieve the thermal shock caused by the coldfluid injection rge-eddy simulation have been used(Lu et al.,2010)to evaluate the thermal striping phe-nomena in tee junctions with periodic porous media,the temper-ature and velocityfield inside the tubes are obtained.The research revealed that the addition of a porous reduces the tem-perature and velocityfluctuations in the mixing tube.As mentioned above,experiments and numerical simulations for both tee junction geometry with a sleeve tube in it(Wu et al., 2003)and for a mixing tee with periodic porous media in it(Lu et al.,2010)have been carried out.The results of previous researches provide a good reference value for this work that anal-yses the role of distributor in weakening the thermalfluctuation of internal piping wall,and this structure has not been studied to date,to the best of our knowledge.In this work,mixing processes have been studied by the experiment and numerically predicted with LES.Then the simulated normalized mean and root-mean square(RMS)temperature,velocity vector and temperature con-tour of the two tees are compared.2.Experiment systemThe Experimentflowchart is presented in Fig.1.The experimen-tal system consists of four main components,a cold water supply line,a hot water supply line,a test section,and a data acquisition unit.The experiment device is shown in Fig.2.Experimentfluid was adjusted to the desired temperature by the heater and chiller, and then was pumped to the test section.After mixing thefluid is returned to the heater for recycling,some of the excessfluid is dis-charged through the overflow pipe.During the mixing of thefluids, the temperature of the mixingfluid is collected and recorded by the thermocouple probe installed on the tube wall.The experiment requires two different structures of the test sec-tion,Fig.3is the T-junction section without the branch liquid dis-tributor and Fig.4is that with the branch liquid distributor.The addition of this structure has two main functions:(1)changing the mixing position of hot and coldfluids:moving the mixing zone to the middle of the tube,and away from the main pipe wall;(2) increasing the intensity of mixing process:adding the fence near the outlet of distributor enhanced the mixed disturbance and the exacerbatedfluid mixing of the inner tube.For the convenience of observing and adjusting the mixing process,the test section is a round pipe made of plexiglass,and other pipes are made of steel. Fig.5is the physical model of the branch liquid distributor.The test conditions in the present experiment are shown in Table1.We collected the instantaneous temperature data of every measurement points by the data collector.The distribution of sam-pling points are shown in Fig.6,there are total eight thermocou-ples in the circumferential direction at each plane.In the T-junction section without the branch liquid distributor,the number of the collected plane is6(x/d m=1,2,3,4,6,8).That is to say there are48thermocouples in the structure without distributor.And in the T-junction section with the branch liquid distributor,the num-ber of the collected plane is5(x/d m=2,3,4,6,8),which means there are40thermocouples in the structure that with the distrib-utor.In both structures,the distance between measuring point the thermocouple probe and the inner wall is30mm.Since the collect-ing frequency of the collector is limited,we use1Hz as the collect-ing frequency after theflowfield is stable,and the total number of collection is800s.Table1shows the specific parameters of the test conditions.NomenclatureT time(s)Pr Prandtl numberLs mixing length of subgrid grid(m)T temperature(K)G acceleration of gravity(m/s2)K von Karman numberCs Smagorinsky numberS ij subgrid strain rate tensorM R momentum ratio of main pipe and branch pipe TÃnormalized mean temperaturesTÃrms normalized RMS temperaturesR d diameter ratioR v velocity ratiox,y,z axial coordinate(m)Greek symbolsqfluid density(kg/m3)b coefficient of thermal expansionl viscosity(Pa s)ltturbulent viscosity(Pa s)k thermal conductivity(w/(m k))C P heat capacity(J/(kg°C))K.Gao et al./Annals of Nuclear Energy78(2015)180–187181182K.Gao et al./Annals of Nuclear Energy78(2015)180–1871\4\11-thermometers 2\5\10-pressure gauge 3\9-flow meter 6-c ooler 7-heater8-overflow 12-test sec tion 13-thermoc ouple data c ollec torFig.1.Experimentflow chart.Fig.5.Physical model of the branch liquid distributor(a)the whole graph(b)theprofile map.Fig.2.Experiment device of thermalfluctuation.Fig.3.Schematic diagram of the T-junction section without the branch liquid distributor.Fig.4.Schematic diagram of the T-junction section with the branch liquid distributor.3.Numerical simulationFig.7is the numerical model based on the experimental section of T junction.The size of the model,boundary conditions are con-sistent with the experiment.In which,hot water enters from the left of main pipe,and cold water enters from the branch pipe,finally the mixingfluidflow out of the right of the main pipe.Dur-ing the calculation,the steady results offlowfield and heat transfer are obtained by Reynolds stress model(RSM)firstly,and then set @q@tþ@q u i@x i¼0ð1Þ@q u i@tþ@q u i u j@x j¼À@ p@x iÀq0bðTÀT0Þgþ@@x jlþltÀÁ@ u i@x jþ@ u j@x i!ð2Þ@q T@tþ@q Tu j@x j¼@@x jkc p@T@x jÀq T00u00j!ð3ÞIn these equations,q,b,l,l t,k and c p represent the density,ther-mal expansion coefficient,molecular viscosity,turbulent viscosity, thermal conductivity and specific heat capacity,respectively.The Smagorinsky–Lilly model is used for the turbulent viscosity,which is described as:lt¼q L2s j S jð4Þj S jTable1Experimental conditions.Main pipe Branch pipeFlow rate (m3/h)Temperature(K)Flow rate(m3/h)Temperature(K)Without distributor0.645304.650.270287.65With distributor0.645304.650.266287.65Fig.6.The distribution of sampling points on the planes.Physical model of T-junction(a)without the branch liquid distributor;(b)with the branch liquid distributor.K.Gao et al./Annals of Nuclear Energy78(2015)180–187183ij ¼12@ u i@x jþ@ u j@x ið7Þwhere k is the Von Karman constant of0.42;d is the distance to the closest wall;C s is the Smagorinsky constant of0.1;V is the volume of the computational cell.4.Results and discussionThe normalized mean and root-mean square temperature are used to describe the time-averaged temperature and temperature fluctuation intensity.The normalized temperature is defined as:ü1NX Ni¼1TÃið8ÞN is the total number of sample times.TÃi¼T iÀT cT hÀT cð9Þwhere T i is the transient temperature,T c is the coldfluid inlet tem-perature and T h is hotfluid inlet temperature.The root-mean square(RMS)of the normalized temperature is defined as:TÃrms¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1X Ni¼1TÃiÀTÃ2rð10Þ184K.Gao et al./Annals of Nuclear Energy78(2015)180–187parison of experimental and numerical resultsAs can be seen from the Fig.8,the numerical normalized mean temperature distributions at the plane x/d m=1and the plane x/ d m=2are in good qualitative agreement and in adequate quantita-tive agreement,and most of them are within the experimental deviation of±20%.Meanwhile,the lifting trends of the data are the same.In the direction of180°,the mean temperatures are both minimal.And with the angle decrease to0°,the temperatures are gradually increased.Quantitative differences between the experi-ment and numerical results are that the normalized mean temper-atures given by LES are larger than the experimental data.That is because we did not add insulation unit on tube wall in the exper-iment,leading the transfer of some heat into the air.And in the process of numerical simulation,we ignored the convective heat transfer between the wall and the air.As shown in Fig.9,although the numerical results and experi-mental results have a little difference at the plane x/dm=2around the location of225°and the plane x/dm=2around the location of 0°and315°,all of them are within the error range that can be accepted.Both the simulations and experimental results give a lar-ger mean temperature in the top half of the main pipe than in the bottom half.This verifies the validity of the LES model for predict-ing the mixing of hot and coldfluids in a tee junction.The normalized RMS temperature on the plane x/d m=1and plane x/d m=2are shown in Fig.10,respectively.Similar to the nor-malized mean temperature,the normalized RMS temperature lines agree very well with the experiment ones.Both of the maximum values appear at the bottom half of the pipe.This indicates that the maximum temperaturefluctuations of main pipe appear on the opposite of the branch pipe inlet in this condition.As shown in Fig.11,the numerical results and the experimental results have the same trend and the numerical data are agreed well with the experimental ones.By comparison with Figs.4and5,dif-ferent from the temperaturefluctuations distribution which with-out the branch liquid distributor,there are two peaks of high fluctuation located at the90°and270°directions along with the tube.This is because the direction is that of the outlet of branch liquid distributor,the coldfluidflowing out from the outlet of branch liquid distributor mixes very fast with the hotfluid,leading to dramatic changes of temperature.In summary,the LES simulation results obtained are generally in good qualitative and quantitative agreement with the experi-mental data for the case of T-junction with/without the branch liquid distributor.Based on this,we analyzed the numerical results further.And the results are reported in the section below.4.2.Numerical results with/without branch liquid distributorThe numerical data were sampled on the inner wall in the plane x/ d m=À1,À0.5,0,0.5,1,2,3,4,6and8.At the same time,the numer-ical data were sampled from points every5mm along the intersec-tional lines of planes of y/d m=0and sections of x/d m=À2,À1,0,1,2, 3,4,5and6,to get the points with the maximum normalized rootK.Gao et al./Annals of Nuclear Energy78(2015)180–187185mean square temperatures in the tee and on the top and bottom walls.Here,the temperature and velocityfields were determined with LES simulations for the case of tee junction with/without branch liquid distributor.The temperature contours and velocity vectors for the T-junction are shown in Figs.12and13,respectively.As can be seen in Fig.12,due to the large branch pipeflow velocity,hot and coldfluid mixing zone is mainly located in both upstream and downstream region of the intersections of the main pipe and the branch pipe.The vigorous mixing offluids in the tube leads to thermalfluctuation on the wall.But in the T-junction with the branch liquid distributor,the mixing region moves to the lower half and downstream region of the main pipe.This indicates that the distributor is advantageous to weaken thermalfluctuations on the wall.The same conclusion can be seen from Fig.13,the dis-tributor weaken thermalfluctuations on the wall of downstream region and the top of the main pipe.186K.Gao et al./Annals of Nuclear Energy78(2015)180–187Fig.14compares the normalized mean temperatures between two tees of different structures.As can be seen,wall temperature changes great in the direction of90°,135°,225°and270°in T-junc-tion with the distributor,because the directions are the distributor outlet directions.This indicates that the coldfluid mixes with hot fluid on the wall afterflows out of the distributor.At the same time,the temperature in the direction of180°also changes dra-matically.That is because the coldfluid moves down in the effects of gravity and buoyancy.As shown in Fig.15,for the tee with distributor,the maximum values of normalized RMS temperature are smaller than that of the tee without distributor in most directions.This indicates that the adding of the distributor can relieve thermalfluctuations on the wall to some extent.And for the T-junction with distributor,tem-perature tends to be stable after the plane of x/d m=6,which indi-cates that twofluids have made a full mixing,while for the initial tee,temperature is still in the dramatic change,and this shows that the improved structure can effectively reduce the mixing length.Fig.16shows the maximum normalized instantaneous temper-aturefluctuations in the tee and on the top and bottom walls in the plane y/d m=0.In the tee,the maximum normalized instantaneous temperaturefluctuations of the case without distributor vary from 0.45to0.8,which means that the hot and coldfluids alternate in this location.However,for the case with distributor,the tempera-turefluctuations in the tee as well as on the top and bottom walls are much smaller than those of the case without distributor.That also implies that the distributor can reduce the temperaturefluctu-ation effectively.The normalized instantaneous temperaturefluctuations cannot describe the relationship between power spectrum density(PSD) and frequency of the temperaturefluctuation.PSD against fre-quency is one of the most important parameter for thermal fatigue analysis,which can directly show how PSD is in a certain fre-quency.The PSDs of the points with maximum temperaturefluctu-ation for the cases with and without distributor against frequency were recorded by fast Fourier transform(FFT)and shown in Fig.17. The temperaturefluctuation of the case without distributor has the highest PSD,at the frequency of0.04Hz,whereas the distributor significantly reduces the PSD of the temperaturefluctuations with the frequency from0.01to0.1Hz.In addition,the PSD of temper-aturefluctuations decreases with the frequency increasing.5.ConclusionsAs thermal stratification can result in thermal fatigue in the pip-ing system of a nuclear power plant,safety and integrity evaluation of the piping system has become an important issue.In this work the temperaturefluctuation has been studied by the experiment and numerically predicted by LES for two types of vertical tee junc-tion:one with distributor in the branch pipe and another without. The numerical results of normalized mean and RMS temperatures for the two structures have been found to be in good qualitative and quantitative agreement with the experimental data,which val-idates the use of LES simulations to evaluate convective mixing in such geometries.At the same time,the simulated normalized mean and root-mean square(RMS)temperature,velocity vector and temperature contour of the two tees are compared.The numerical results show that thefluctuations of temperatures of the tee without the distrib-utor are larger than those of the tee with the distributor,which can be explained by the branch liquid distributor enhancing the mix-ing.Although both tees give the same momentum ratio between the main pipeflow and the branch pipeflow,mixing and convec-tive heat transfer are greatly enhanced by the presence of the branch liquid distributor.These all show that the structure is effec-tive for weakening the thermalfluctuation of tee piping wall when hot and coldfluids mix,and it can make the mixing more sufficient.AcknowledgementsThis work was supported by projects of the National Natural Science Foundation of China(No.51276009),Program for New Century Excellent Talents in University(No.NCET-13-0651),and the National Basic Research Program of China(No.2011CB706900). 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