下载文档原格式
文章编号：1008 − 8857(2020)03 − 0173 − 06DOI : 10.13259/j .cnki .eri .2020.03.008泰勒涡流流动及强化传热数值研究叶 立1，牟军杰1，石 艳2，林海波2，童正明1，岳 汉1（1. 上海理工大学 能源与动力工程学院，上海 200093；2. 过程装备与控制工程四川省高校重点实验室，四川 自贡 643000）摘 要：泰勒涡流为叠加于剪切流之上的二次流，其具有强化传热作用，在航空、水处理、制药工程和化工等领域都具有很大的应用价值。
运用Fluent 软件，建立长径比Γ = 30的模型并对同轴套管间的流态演变和传热特性进行了数值模拟。
模拟结果显示了环隙内流体流态随着内筒转速增加的演变过程，表明在存在径向温差的情况下，涡流的存在强化了传热效率。
对不同转速下的强化传热效果进行了对比分析，并确定了最佳状态点。
关键词：泰勒涡流；强化传热；数值模拟中图分类号：TK 124 文献标志码：ASimulation study on flow and enhanced heat transferperformance of Taylor vortex flowYE Li 1，MOU Junjie 1，SHI Yan 2，LIN Haibo 2，TONG Zhengming 1，YUE Han1(1. School of Energy and Power Engineering , University of Shanghai for Science and Technology , Shanghai 200093, China ;2. Sichuan Provincial Key Laboratory of Process Equipment and Control , Zigong 643000, China )Abstract ：Taylor vortex flow , as a secondary flow superimposed on shear flow , enables to enhance the heat transfer of the fluids with wide application in the fields of aviation , water treatment ,pharmaceutical , chemical engineering and so on . A model with an aspect ratio Γ=30 was built using fluent software . And the numerical simulation of flow patterns and heat transfer performance between coaxial sleeves was conducted . The simulation results showed the evolution of flow patterns in the annulus space with the increased rotation speed of inner sleeve , which indicated that the presence of vortex flow could enhance the heat transfer efficiency under the radial temperature difference . The comparative analysis of enhanced heat transfer performance under different rotation speeds was performed . The optimum condition was determined .Keywords ：Taylor vortex ; enhanced heat transfer ; numerical simulation能源研究与信息第 36 卷 第 3 期Energy Research and Information Vol .36 No .3 2020收稿日期：2017 − 02 − 08基金项目：国家自然科学基金资助项目（51306122）；四川省高校重点实验室项目（GK 201401）第一作者：叶立（1977—），女，副教授。
基于ＡＮＳＹＳ的裂隙岩体全充填介质膨胀效应的数值模拟陈 义，王传琪，陈金刚（郑州大学工程力学系，郑州４５０００１）摘 要：依据采矿区裂隙岩体中存在的具有鲜明水理性质的膨胀性充填物，应用有限元分析软件ＡＮＳＹＳ对裂隙全充填的岩体进行了数值模拟计算，重点探讨了膨胀性充填介质对裂隙岩体位移、应力场的影响。
结果表明：裂隙充填物的膨胀效应增大了裂隙岩体各应力的分量，因此当计算的裂隙岩体应力呈非线性分布时，应综合考虑裂隙充填物吸水膨胀效应，否则计算结果将偏于不安全；导致裂隙扩展的楔切效应显著，但裂隙岩体未受到拉张和剪切破坏。
通过将模拟结果与实测结果进行对比分析，验证了该模拟方法的有效性和可靠性。
关键词：裂隙岩体；全充填介质；膨胀效应；ＡＮＳＹＳ；数值模拟中图分类号：Ｘ９３６；ＴＵ４５２ 文献标识码：Ａ 文章编号：１６７１－１５５６（２０１２）０４－０１１５－０４收稿日期：２０１２－０２－１７ 修回日期：２０１２－０３－０６基金项目：国家自然科学基金项目（５０７０９０３０）；郑州大学国家大学生创新性实验项目（０９１０４５９２７）作者简介：陈 义（１９８６—），男，硕士研究生，主要研究方向为安全技术与工程。
Ｅ－ｍａｉｌ：ｃｈｅｎｙｉ１４７８５２＠１６３．ｃｏｍＮｕｍｅｒｉｃａｌ Ｓｉｍｕｌａｔｉｏｎ ｏｆ Ｅｘｐａｎｓｉｏｎ Ｅｆｆｅｃｔ ｏｆ Ｆｕｌｌ－ｆｉｌｌｉｎｇ Ｍｅｄｉｕｍｉｎ ｔｈｅ Ｆｒａｃｔｕｒｅｄ Ｒｏｃｋ Ｂａｓｅｄ ｏｎ ＡＮＳＹＳＣＨＥＮ Ｙｉ，ＷＡＮＧ Ｃｈｕａｎ－ｑｉ，ＣＨＥＮ Ｊｉｎ－ｇａｎｇ（Ｄｅｐａｒｔｍｅｎｔ ｏｆ Ｅｎｇｉｎｅｅｒｉｎｇ Ｍｅｃｈａｎｉｃｓ，Ｚｈｅｎｇｚｈｏｕ Ｕｎｉｖｅｒｓｉｔｙ，Ｚｈｅｎｇｚｈｏｕ４５０００１，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：Ｅｘｐａｎｓｉｖｅ ｍａｔｅｒｉａｌ ｗｈｉｃｈ ｈａｓ ｄｉｓｔｉｎｃｔｉｖｅ ｍｅｃｈａｎｉｃａｌ ｃｈａｒａｃｔｅｒｉｓｔｉｃｓ ａｎｄ ｈｙｄｒａｕｌｉｃ ｐｒｏｐｅｒｔｉｅｓ ｉｓ ａ－ｄｏｐｔｅｄ ａｓ ｆｒａｃｔｕｒｅ ｆｉｌｌｉｎｇｓ，ａｎｄ ｔｈｅ ｆｒａｃｔｕｒｅ ｆｕｌｌｙ ｆｉｌｌｅｄ ｗｉｔｈ ｅｘｐａｎｓｉｖｅ ｆｉｌｌｉｎｇｓ ｉｓ ｓｉｍｕｌａｔｅｄ ｂｙ ＡＮＳＹＳ ＦＥＡｓｏｆｔｗａｒｅ．Ｔｈｅ ｄｉｓｐｌａｃｅｍｅｎｔ ａｎｄ ｓｔｒｅｓｓ ｆｉｅｌｄ ｓｕｂｊｅｃｔｅｄ ｔｏ ｔｈｅ ｅｘｐａｎｓｉｏｎ ｅｆｆｅｃｔ ｏｆ ｆｉｌｌｉｎｇｓ ｉｓ ｅｍｐｈａｔｉｃａｌｌｙ ｄｉｓ－ｃｕｓｓｅｄ．Ｔｈｅ ｎｕｍｅｒｉｃａｌ ｓｉｍｕｌａｔｉｏｎ ｒｅｓｕｌｔｓ ｓｈｏｗ ｔｈａｔ ｔｈｅ ｅｘｐａｎｓｉｏｎ ｅｆｆｅｃｔ ｏｆ ｆｒａｃｔｕｒｅ ｆｉｌｌｉｎｇｓ ｉｎｃｒｅａｓｅｓ ｅａｃｈｓｔｒｅｓｓ ｃｏｍｐｏｎｅｎｔ ｏｆ ｔｈｅ ｆｒａｃｔｕｒｅ，ｓｏ ｔｈｅ ｅｘｐａｎｓｉｏｎ ｅｆｆｅｃｔ ｏｆ ｆｒａｃｔｕｒｅ ｆｉｌｌｉｎｇｓ ｓｈｏｕｌｄ ｂｅ ｔａｋｅｎ ｉｎｔｏ ａｃｃｏｕｎｔ ｉｎｔｈｅ ｓｔｒｅｓｓ ｎｏｎｌｉｎｅａｒ－ｄｉｓｔｒｉｂｕｔｉｏｎ ｃａｌｃｕｌａｔｉｏｎ；ｏｔｈｅｒｗｉｓｅ ｔｈｅ ｃａｌｃｕｌａｔｉｏｎ ｒｅｓｕｌｔ ｉｓ ｐｒｏｂａｂｌｙ ｕｎｓａｆｅ．Ｔｈｅ ｗｅｄｇｅｃｕｔ ｅｆｆｅｃｔ ｗｈｉｃｈ ｌｅａｄｓ ｔｏ ｆｒａｃｔｕｒｅ ｅｘｔｅｎｓｉｏｎ ｉｓ ｒｅｍａｒｋａｂｌｅ，ｂｕｔ ｔｈｅ ｆｒａｃｔｕｒｅ ｉｓ ｎｏｔ ｄａｍａｇｅｄ ｂｙ ｔｅｎｓｉｌｅ ｅｆｆｅｃｔｏｒ ｌｅｄ ｔｏ ｓｈｅａｒ ｆａｉｌｕｒｅ．Ｔｈｒｏｕｇｈ ｃｏｍｐａｒａｔｉｖｅ ａｎａｌｙｓｉｓ，ｔｈｅ ｒｅａｓｏｎａｂｌｅｎｅｓｓ ａｎｄ ｒｅｌｉａｂｉｌｉｔｙ ｏｆ ｔｈｅ ｓｉｍｕｌａｔｉｏｎｍｅｔｈｏｄ ｉｓ ｖｅｒｉｆｉｅｄ．Ｋｅｙ ｗｏｒｄｓ：ｆｒａｃｔｕｒｅｄ ｒｏｃｋ；ｆｕｌｌ－ｆｉｌｌｉｎｇ ｍｅｄｉｕｍ；ｅｘｐａｎｓｉｏｎ ｅｆｆｅｃｔ；ＡＮＳＹＳ；ｎｕｍｅｒｉｃａｌ ｓｉｍｕｌａｔｉｏｎ０ 引 言裂隙岩体具有复杂的力学特性和渗透特性，相关领域的学者对其耦合机制进行了研究。
基于物质点法的土体流动大变形过程数值模拟杨婷婷;杨永森;邱流潮【期刊名称】《工程地质学报》【年(卷),期】2018(026)006【摘要】土体滑坡作为一种自然地质灾害,受自然因素和人类活动的影响在我国时有发生,给周围居民的生命和财产安全带来了很大威胁,日益受到人们的广泛关注.滑坡防治也逐渐成为工程研究的热点之一.土体本质上是一种具有复杂组成结构的颗粒材料堆积体,通过对颗粒流动的模拟可以深入理解自然界中的土体流动现象,如滑坡、泥石流等,进而预测灾害破坏范围及改进相应工程防护措施.但由于土体流动是一个涉及大变形及大位移的复杂流动过程,传统的基于网格的有限元法(FEM)由于网格畸变,并不适合这类问题的研究.本文采用物质点法(MPM)模拟土体流动大变形问题.作为一种源于particle-in-cell(PIC)法的无网格法,兼具欧拉法和拉格朗日法的优点,因而,物质点法在处理大变形问题上具有独特的优势.目前,国内外利用物质点法模拟边坡滑动问题已有不少研究,但对相关参数进行敏感性分析的较少.本文基于物质点法模拟了黏性土体及无黏性土体流动大变形问题,并进行了参数敏感性分析,包括土体材料的内摩擦角、黏聚力、高宽比、底面坡度对土体滑动距离的影响规律.本文计算中采用Drucker-Prager(DP)弹塑性本构模型描述土的非线性特性.研究结果表明:(1)基于物质点法得到的土体的流动形态、滑动距离以及自然休止角等数值模拟结果均与文献中的实验结果基本吻合,验证了物质点法模拟土体大变形力学行为的精度及有效性;(2)随着内摩擦角、黏聚力的增大,滑动距离相应减小;(3)坡度对边坡稳定的影响是显著的,随着底面坡度的增大,滑动距离相应增大;(4)当土柱高宽比较小时,与滑动距离呈线性增长关系.其中,内摩擦角和黏聚力反映了土体的抗剪切性能,因此通过工程措施提高土体的抗剪能力可以降低土体滑坡带来的危害.研究结果为探索土体滑动破坏规律,降低滑动破坏范围提供了可靠的参考.%As a natural geologic disaster, soil landslide is affected by natural factors and human activities. It brings a great threat to the safety of the surrounding residents' life and property, attracting more worries from ndslide prevention and control are also one of the hot spots in engineering research. Soil is essentially a kind of deposits consists of granular material with complicated composition and structure. By means of numerical simulation of granular material flows, we can well understand the phenomena of soil flows in the nature, such as landslide and debris flows. It is therefore possible to predict the landslide hazard zone and to improve the design of engineeringprotection measurements. However, the finite element method (FEM) is not suitable for simulating soil flow with large deformation and large displacement due to the finite element method is sensitive to mesh distortion. In this paper, we simulate the soil flows using the material point method (MPM). MPM is a mesh-free method and originating from the particle-in-cell (PIC) method. It combines the Eulerian description and Lagrangian description and has distinct advantages in solving the large deformation and large displacement problem. Currently, there have been many studies on the simulation of slope sliding using MPM, but less attentions has paid to sensitivity analysis on relevant parameters. In this paper, the large deformations of the cohesive soil and the non-cohesive soil slopes due to gravity are numerically investigated with MPM. The influence of the internal friction angle, the cohesive force,the aspect ratio and bottom surface gradient on the landslide run-out are analysed. In this MPM simulation, the elasto-palstic constitutive models based on the Drucker-Prager (DP) yield criterion is used for modeling nonlinear characters of soil flows. The Drucker-Prager yield criterion is a pressure-dependent model for determining whether a material has failed or undergone plastic yielding. The yielding surface of the Drucker-Prager criterion may be considered depending on the internal friction angle of the material and its cohesion. The simulated results show the following featurs.(a) There are well agreements in the flow pattern, the sliding distance and natural angle of repose between the simulated results and the corresponding experimental results, which validates the ability of MPM to modeling soil flows. (b) The sliding distance decreases with the increase of the internal friction angle and cohesive force. (c) The steepness of the soil slope has significant influence on its stability. The sliding distance increases with the increase of the steepness of the soil slope. (d) For a comparatively small aspect ratio, the sliding distance increases linearly with aspect ratio. It is noteworthy that the internal friction angle and cohesive force of soil reflect its shear resistance. Therefore, the damage due to landslide can be reduced by improving the shear resistance of soil through engineering measurements. The results of the simulation provide a reliable reference to explore the law of the soil sliding hazardous behavior and reduce the sliding damage range.【总页数】10页(P1463-1472)【作者】杨婷婷;杨永森;邱流潮【作者单位】中国农业大学水利与土木工程学院, 北京 100083;中国农业大学水利与土木工程学院, 北京 100083;中国农业大学水利与土木工程学院, 北京 100083【正文语种】中文【中图分类】TU36【相关文献】1.基于有限点法的自由面流动的数值模拟 [J], 卢雨;胡安康;刘亚冲2.基于物质点法的弹体侵彻靶板破甲特性数值模拟 [J], 秦业志;姚熊亮;王志凯;王莹3.基于物质点法的钛合金高速切削数值模拟技术研究 [J], 谷骁勇; 王大勇; 程坦4.基于物质点法的土体强度对边坡失稳滑动距离影响研究 [J], 宰德志;庞锐5.盾构掘进过程土体变形特性数值模拟 [J], 张利民;李大勇因版权原因，仅展示原文概要，查看原文内容请购买。
第52卷第3期2021年3月Safety in Coal Mines Vol.52 No.3 Mar. 2021移动扫码阅读D O I: 10.13347 /j.c n k i.m kaq .2021.03.038李芸卓，苏贺涛，季淮君.采空区注氮对瓦斯爆炸危险区的影响数值模拟[J].煤矿安全，2021,52(3)：211-216.LI Yunzhuo, SU Hetao. Jl Huaijun. Numerical simulation of e'ffect of nitrogen injection on gas explosion hazard in go af[j]. Safety in Coal Mines, 2021. 52(3): 211-216.采空区注氮对瓦斯爆炸危险区的影响数值模拟李芸卓苏贺涛季淮君|二(1.中国地质大学（北京）工程技术学院，北京丨0()083;2.中国地质大学（北京）国土资源部深部地质钻探技术重点实验室,北京100083)摘要：为研究注氮对高瓦斯矿井采空区内瓦斯爆炸危险区的影响，以安徽许疃煤矿3235工作面为实例，使用C0M S0L多物理场耦合模拟软件建立采空区注氮模型，分析了不同注氮流量及注氮位置条件下采空区气体运移规律，并依据线性叠加的数学原理对采空区瓦斯爆炸危险区进行划分，分析其分布特征。
通过对比研究发现：随采空区注氮流量的增加，爆炸所需最低浓度的氧气和爆炸极限内的甲烷，分别有向工作面和采空区移动的趋势，瓦斯爆炸危险区的最大宽度以及面积均呈现减小趋势；注氮位置和瓦斯爆炸所需氧气体积分数的危险区域，在一定范围内呈现负相关性。
关键词：采空区；瓦斯爆炸危险区；注氮流量；注氮口位置；负相关中图分类号:TD712 文献标志码：A文章编号：丨003-496)((202丨）03-02丨卜()6Numerical simulation of effect of nitrogen injection on gas explosion hazard in goafU Yunzhuo'-2, SU Hetao12, JI Huaijun12{\.School o f Engineering and Technology, China University o f Geosciences iBeijing), Beijing100083, China;2.Key Lal)〇rat〇7~y of Deep Geo-drilling Technolog}. Ministry o f Natural Resources, China University oj Ceosciences (Beijing), Beijing100083, China) A bstract：In order to study the effect of nitrogen injection on the gas explosion danger zone in the goaf of high-gas mines, taking the 3235 working face of a coal mine in Anhui Provinc e as an example, the COMSOL niultiphysics coupling simulation software was used to establish a model of nitrogen injection in the goaf, and the gas migration laws of goaf under differen! nitrogen injection flow rates and nitrogen injection positions were analyzed. According to the mathematical principle of linear superposition, the gas explosion hazard area of goaf is divided and its distribution characteristics are analyzed. Through comparative study, it is found that with the increase of nitrogen injection flow in the goaf, the oxygen with the lowest concentration recjuired for the explosion and the methane within the explosion limit have the tendency to move towards the working face and the goaf respectively, and the maximum width and area of the gas explosion hazard area show a trend of decrease. The nitrogen injection position and the hazard area of the volume fraction of oxygen required for a gas explosion showed a negative correlation.Key w ords：goaf; gas explosion danger zone; nitrogen injec tion How rate: nitrogen injection position; negative correlation采空区是煤矿灾害事故的主要源头m。
Abstract:The karst mud limestone of Triassic Badong formation (T2 b) is the serious engineering geological problem newly discovered in the population resettlement project in the Three Gorges Reservoir region. There are very complex structures in mud limestone, involving old structures, new structures and surface deformation structures, which coordinately control the karstification. In the old structures, the local structures such as folds and fault zones control the important segments and layers of karstification; and the mini structures such as joint and layer face popularize the karstification. The surface uplift and river cutting in new tectonic period put forward the unload and loose of rock mass, widening of karstification paths. The surface deformation structures densify the karstification paths and intensify the karstification. The mechanism of karst hazards yields to the regulation of structure controlling over karstification in mud limestone terrain, Three Gorges Reservoir region , which brings about hazards with features of broad range , huge scale and complex structure. The types of karst hazards involve uneven subsidence, fissure, landslide, collapse,mudflow and cave in.三峡库区三叠系巴东组(T2b)泥灰质岩石岩溶是移民迁建中发现的重大工程地质问题。
基于希尔伯特变换结构模态参数识别范兴超;纪国宜【摘要】应用HHT方法对GARTEUR飞机模型模态参数进行识别，通过采用多通带滤波器对信号进行滤波，较好的解决模态混叠问题，采用NExT法对信号预处理，由EMD分解获得较准确的各阶固有模态函数分量（IMF），在EMD分解中使用镜像延拓方法对极值点进行处理来抑制端点效应，然后将分解得到的IMF分量进行希尔伯特变换并结合ITD法识别出各阶固有频率和阻尼比。
最后对悬臂梁进行数值仿真模拟，并将模态参数识别结果和理论值进行对比，并运用此方法进一步识别GARTEUR飞机模型固有模态参数。
%The HHT method is applied to the modal parameter identification of GARTEUR plane model. The multi-channel filter is applied to process the signal for solving the problem of modal aliasing. Meanwhile, the NExT method is adopted to get more accurate individual-order intrinsic mode functions (IMF) form the EMD decomposition. The mirror continuation method is applied to process extreme value points for suppressing the endpoint effect. Then, the natural frequency of each order and the damping ratio are identified with Hilbert transform and ITD method. The numerical simulation of a cantilever beam is carried out and the simulation results are compared with the theoretical results. Finally, the intrinsic modal parameters of the GARTEUR plane model are recognized with this method.【期刊名称】《噪声与振动控制》【年(卷),期】2014(000)003【总页数】5页(P52-56)【关键词】振动与波;模态参数识别;Hilbert-Huang变换;模态阻尼比;镜像延拓【作者】范兴超;纪国宜【作者单位】南京航空航天大学机械结构力学及控制国家重点实验室，南京210016;南京航空航天大学机械结构力学及控制国家重点实验室，南京 210016【正文语种】中文【中图分类】O241.82Hilbert-Huang变换[1]（HHT）是1998年美国华裔科学家Huang提出的一种新的数据处理方法，该方法已应用到地球物理学领域，并取得较好的效果，其主要是由经验模态分解（Empirical Mode Decomposition）和Hilbert变换（Hilbert Transform）两个部分组成，其主要思想是EMD分解[5]。
第21卷 第2期 石油化工高等学校学报 Vol.21 No.2 2008年6月 J OU RNAL OF PETROCH EMICAL UN IV ERSITIES J un.2008 文章编号:1006-396X(2008)02-0059-04S K型静态混合器停留时间分布特性研究孟辉波1, 吴剑华2, 禹言芳2(1.天津大学化工学院,天津300072; 2.沈阳化工学院,辽宁沈阳110142)摘 要: 结合脉冲示踪法利用计算流体力学方法的雷诺时均方程(RNAS)和重整化群的k-ε湍流模型计算SK型静态混合器内的浓度响应曲线。
基于正交实验原理分析流体在不同混合元件长径比、不同监测位置及不同的进口流速下的停留时间分布特性,并计算了平均停留时间和方差来研究各因素之间影响顺序。
结果表明,SK型静态混合器内的液体单相流动的轴向返混系数较小且数量级均为10-2,流动状态接近活塞流;平均停留时间随流体流速的增大而减小,随混合器长度和混合元件长径比的增加而增大。
关键词: 静态混合器; 停留时间分布; 数值模拟; 长径比中图分类号: TQ051.7 文献标识码:ANumerical Simulation of Residence Time Dist ribution in Kenics Static MixerM EN G Hui-bo1,WU Jian-hua2,YU Yan-fang2(1.School of Chemical Engineering&Technology,Tianj in Universit y,Tianj in300072,P.R.China;2.S heny ang I nstitute of Chemical Technology,S heny ang L iaoning110142,P.R.China)Received12J une2007;revised25December2007;acce pted5M arch2008Abstract: The concentration response curves were calculated based on pulse tracer input technique by means of CFD method adopted RANS equations and renormalization group k-εturbulence model.The characteristic of residence time distribution measured at different outlet with different inlet velocities and aspect ratios were ealeulated and analyzed by orthogonal experiment,and the orders of factors were ranked by the range analysis of mean value and square deviation.The results show that the order of axial back mixing coefficient is10-2,and the flowing state of the fluid in the kenics static mixer approaches plug flows.The mean residence time decreases with increasing flow rate of the fluid and increases with the increasing length and aspect ratio of the static mixers.K ey w ords: Static mixer;Residence time distribution(R TD);Numerical simulation;Aspect ratioCorresponding author.Tel.:+86-24-89385408;fax:+86-24-89381016;e-mail:mhb_vip@ 静态混合器由于流程简单、结构紧凑、投资少、能耗省、易于实现连续操作等优点广泛应用于石油化工、生物化工、制药、高分子材料、环保等工业过程,这些过程往往伴随有化学反应及传热,化学反应进行的完全程度与反应物料在反应器内的停留时间的长短有关[1-4]。
In order to understand the static magnetic field under the action of molten droplet oscillation deformation characteristics, the phase field method is adopted to simulate the suspension silicon melt oscillation of the droplet deformation, axial magnetic field on initial shape are analyzed for the second order Legendre function and fourth-order Legendre function the influence of silicon melt droplet motion and deformation. Results found that: as the silicon melt is bigger, the surface tension of the droplet deformation rapidly. Original shape as the fourth-order Legendre function of droplets, due to its interfacial curvature is small, weak internal flow. ShiJiaJing magnetic field, magnetic field part inhibited the droplet flow inside. Along with the increase of the magnetic field strength inside the droplet convection is abate, the droplets faster shrinkage is spherical.The electromagnetic levitation technology is widely apply to measure thermal physical properties of metals and alloys. However, in the process of measuringthermal conductivity, the convection and oscillation due to the surface tension of the melt can lower the accuracy of measurements .Therefore, it is necessary to reduce internal convection of melt in some cases .Yasuda adopts the method of applying alternating magnetic field and static magnetic field at the same time, observe the different strength under the static magnetic field, electromagnetic levitation melt oscillation process copper and nickel. Found that with the increase of static magnetic field, magnetic field intensity, the droplets decrease oscillation behavior. Kobatake people such as the electromagnetic levitation technology, measurement of silicon melt and thermal conductivity of austenitic stainless steel.Measurement with laser heating melting metal, add a static magnetic field, and measured the interior of the melt convection.Yasuda developed a new levitation method, which used the simultaneous imposition of atatic and alternating magnetic fields. Oscillation behavior was measured for pure Cu and pure Ni melts levitated with different magnetic. He finded that imposing static magnetic field ,reduction of oscillation , convection in levitated melt.Study found that strengthening the static magnetic field can be more accurate measurement of thermal conductivity, because it eliminates the internal melt convection effect on the measured value. Due to the metal droplet temperature, opacity, difficult to accurate observation of the internal flow, numerical simulation of this kind of problem appears very necessary.Bojarevics false spectral method is used to simulate the static magnetic field on electromagnetic levitation melting aluminum droplet oscillation process. Tsukada numerical simulation of the static magnetic field conditions of electromagnetic suspension silicon internal convection of liquid droplets, found that the coefficient of thermal conductivity of the measured static magnetic field intensity, increasing the static magnetic field strength inside the droplet velocity attenuation. But at the moment of static magnetic field cases, metallic melts oscillation process study is less, further study on the static magnetic field conditions of oscillation and internal melt convection condition has the vital significance.In recent years, phase field method is used to simulate complex flow interface problems,particularly suitable for simulation with higher density than the metal droplets in a gas environment of behavior. Shi Wanyuan the phase field method is adopted to simulate the silicon melt oscillation behavior of the droplet, the internal flow is analyzed. In this paper, using the phase field method simulating the effect of static magnetic field on liquid drop oscillation deformation.1数学模型与数值方法Assumes that the fluid is incompressible fluid, under cylindrical coordinate system, the control equation of dimensionless quantity as follows:The oscillation behavior of the levitated drop is expressed by using the dimension lessequations of a drop and continuous phase composed of incompressible fluid as follows：Continuity equation0u ∇⋅=(1)momentum equation ()()()()211+e e T u Ha u u p u u J B t R We R ρφηφμφ∂⎛⎫+⋅∇=-∇+∇⋅∇∇+∇+⨯ ⎪∂⎝⎭（2） Cahn Hilliard equation(hereinafter referred to as C-H equation)()1u M t Peφφφμ∂+⋅∇=∇∇∂（3） Type t is time, in the time scale for L ref /u ref (L ref as the characteristic length,u ref characteristicvelocity); u for speed; Pfor the pressure, the pressure gauge for (for the density of the mock object); M for the chemical potential, the chemical potential of scale for ε/αL ref (ε for the thickness of the interface;αis constant,αDescribe fluid interface changes as a function of φ,known as phase variables, φ=1represent the essence of simulation objects, namely, in this paper, the droplets, φ=0represents the environmental fluid and gas-liquid interface is 0<φ<1. ρ(φ)as the nondimensional density, ρ(φ)=φ+(1-φ)λρ(λρ=ρ2/ρ1, said environmental fluid and droplet density ratio);η(φ)is a dimensionless viscosity, η(φ)=φ+(1-φ)λη, (λη=η2 /η1,η2and η1is environmental fluid and viscosity ratio of the droplet,respectively);M (φ)according to the mobility is defined as: M (φ)=φ(1-φ), g is acceleration of gravity; Dimensionless parameter Re , We , Pe , Ha are defined, respectively:1ref ref 1u L Re ρη=,21ref ref 12e u L W ρσ=,0ref Ha L =,2ref ref ref 12Lu Pe M σ= When computing free boundary with Neumann boundary conditions. The initial moment, droplet remains at rest. Initial interface of gas and liquid phase field analytical solutions to balance()112r φ⎛=+ ⎝ r 0to simulate initial size of an object, such as the initial droplet radius; X, y coordinates for the space.Calculation area by uniform discrete staggered grid, the finite difference discrete control equations. Momentum equations of convection item using the QUICK scheme, second-order central differencingscheme in diffusion; C - H equation with convection term five order weighted essentially no oscillation method, diffusion using fourth-order central difference. The velocity and pressure in the momentum equation of coupling using SIMPLEC method.Discrete C - H equation and momentum equation of the Bi - CGStab method to solve.2计算结果和分析2.1Validation of the modelIn order to verify the correctness of the numerical simulation of a computer program, first for the initial shape of fourth-order Legendre function two-dimensional free oscillation of the droplets are simulated, and simulation results were compared with Sussman. Droplet initial amplitude is 0.38, the simulation region for axisymmetric region, geometry size is2×4, divided into 42×82 meshes; Simulation of isothermal process; Parameters for the Re = 2000, We = 2,ρ2/ρ1=0.01, theη2/η1=0.01. Phase field simulation results as shown in figure 1 (a), and Sussman adopt the Level set method simulation results are in good agreement.(a)相场模拟结果(b)Sussman的模拟结果图1初始形状为四阶Legendre函数的液滴随时间的振荡变形过程2.2Original shape as the second-order Legendre function of silicon melt droplet oscillation process(1) Not add static magnetic oscillation process of the dropletThis section suspended the flow of the molten silicon liquid droplets in microgravity environment, the deformation process is simulated. Simulation assumptions for axisymmetric condition, isothermal process.Simulation area by2⨯4 size, initial shape of the droplet r = r for second order Legendre polynomial curve r=R[1+0.5ε(3cos2θ-1], as shown in figure 2. As shown in (a). The droplet radiusR=1, the initial amplitude ε=0.38. The density of air and droplets than ρ2/ρ1=4.84⨯10-4, viscosity ratioη2 /η1=2.53⨯10-2, We=0.63, Cn=0.02. The grid number is 42⨯82. From the figure 2.(b)-2.(d) visible, because the surface tension of the droplet is uneven, the top and bottom surface tension is bigger, the local surface tension is relatively small, the rest are flat surface tension tend to make the droplets is round ball, after a period of time, the shape of the droplet has contracted.When droplets gradually close to the ball, the surface tension is reduced, but due to inertia, the fluid flow inside the droplet convection will not stop immediately, after a period of time, the droplet is stretched along the poles of the convection for the slender rod, as shown in figure 2.(e) and 2.(f).(a)t=0 (b) t=0.3 (c) t=0.6(d)t=0.9 (e) t=1.2 (f) t=1.5Levitation melting silicon droplet deformation process Figure 3 said internal flow of droplet, contour diagram on the left side of the said flow function, flow field on the right side. At first, contraction of the droplet driven poles of flowing fluid in the center to the equatorial region, then return to the poles, along the flow near the surface of the liquid droplets in fluctuation of each distribution has a pair of counter-rotating vortex cell, as shown in figure 3. As shown in (b). As the droplets contraction, near the equator flows radially inward, and form a pair of small vortex cell, as shown in figure 3. As shown in (c). Radial inward flows along the longitudinal squish the droplets, as shown in figure 3. (e) and (3) (f).(a) t=0 (b) t=0.3 (c) t=0.6(d) t=0.9 (e) t=1.2 (f) t=1.5图3熔融硅液滴的流场（2）Static magnetic field effects on droplet internal flowTo analyze the impact of static magnetic field on liquid drop oscillation deformation, here add vertical upward to the droplets of static magnetic field, as shown in figure 4 (a), as shown in the other parameters with the case shown in figure 2. Figure 4 said Ha =50 (magnetic induction intensity B 0=0.3T ) oscillation of the droplet deformation process. From figure can be seen, with no when magnetic field is different: aftermagnetic field, the droplets contraction faster, partly inhibit droplet movement within static magnetic field is illustrated.(a) t =0 (b)t =0.3 (c)t=0.6(d) t =0.9 (e)t =1.2 (f)t =1.5图4 Ha =50磁场强度下液滴的振荡情况Figure 5 compares the t = 1.2 times under different magnetic field strength of silicon melt droplet shape. Visible from the figure, along with the enhancement of the static magnetic field intensity, the droplet faster tend to be spherical.(a) Ha =0 (b) Ha =50B 0(c) Ha=100 (d) Ha=150图5不同磁场强度下t=1.2时刻液滴的形状Figure 5 t = 1.2 times under different magnetic field strength the shape of the dropletsAs shown in figure 6 for t = 1.2, under different magnetic field strength of silicon melt flows inside the droplet. Visible from the figure, along with the enhancement of the magnetic field intensity, the maximum value of stream function is reduced, the droplet movement within recede. When Ha = 150, droplet is nearly spherical, internal flow is very weak.(a) Ha=0，流函数最大值为0.57(b) Ha=50,流函数最大值为0.23(c) Ha=100,流函数最大值为0.14 (d) Ha=150，流函数最大值为0.08图6 不同静磁场强度下的液滴内部流场，t=1.22.3Original shape as the fourth-order Legendre function of silicon melt droplet oscillation processIn order to analyze the initial shape more complex oscillation of the droplet deformation process, here the initial shape of fourth-order Legendre function of silicon melt droplet is simulated, the results are shown in figure 7, the oscillation deformation process and is similar to the results shown in figure 1. But, because of the silicon melt We several smaller, surface tension is bigger, the droplet deformation faster, at t = 0.3 time namely deformation is similar to figure 1, t = 0.6 times of the shape. Its flow field is shown in figure 8, and the initial shape as the second-order Legendre function of silicon melt droplet, the liquid droplets in most of the time its internal flow is weak, this is due to its small surface tension and interface curvature is smaller(a) t=0 (b) t=0.15 (c) t=0.30(d)t=0.45 (e) t=0.60 (f) t=0.9图7初始形状为四阶Legendre函数的悬浮熔融硅液滴的变形过程(a) t=0 (b) t=0.15 (c) t=0.30(d) t=0.45 (e) t=0.60 (f) t=0.9图8液滴内部流场随时间的变化情况With initial shape as the second-order Legendre function of droplet, once add the static magnetic field, the droplets of oscillation is abate, faster to spherical droplets, as shown in figure 9, it said Ha = 50 deformation process of the droplet.(a) t=0 (b) t=0.15 (c) t=0.30(d)t=0.45 (e) t=0.60 (f)t=0.90图9Ha=50时液滴的振荡情况Faster with the increase of magnetic field intensity, contraction of the droplet, closer to spherical, as shown in figure 10. Droplet weakens, internal flow as shown in figure 11.(a)Ha=0 (b)Ha=50 (c)Ha=100图12t=0.9时刻不同静磁场强度下液滴的形状(a) Ha=0,流函数最大值为0.69(b) Ha=50,流函数最大值为0.23(c) Ha=100,流函数最大值为0.16图11t=0.9时刻不同静磁场强度下液滴的内部流场3结论In this paper, the phase field method is adopted to simulate the suspension silicon melt oscillationof the droplet deformation, axial magnetic field on initial shape are analyzed for the second order Legendre function and fourth-order Legendre function the influence of silicon melt droplet motion and deformation. Simulation results show: the silicon melt We several smaller, surface tension is bigger, the droplet deformation rapidly. Original shape as the fourth-order Legendre function of droplets, due to its interfacial curvature is relatively small, the surface tension is small, its flow is second-order Legendre function of droplet flow is weak. ShiJiaJing after magnetic field, droplet contraction faster, partly inhibit droplet movement within static magnetic field is illustrated. Along with the increase of the magnetic field strength inside the droplet convection is abate, the droplets faster shrinkage is spherical.参考文献：[1]Yasuda, H, et al. Levitation of metallic melt by using the simultaneous imposition of the alternating and the static magnetic fields[J]. Journalofcrystalgrowth, 2004. 260(3-4): p. 475-485.[2] H. Kobatake, H. Fukuyama, I. Minato, T. Tsukada, S. Awaji. Noncontact modulated laser calorimetry of liquid silicon in a static magnetic field[J]. Appl. Phys. Lett. 90 (2007) 094102.[3]H. Kobatake, H. Fukuyama, I. Minato, T. Tsukada, S. Awaji. Noncontact measurement of thermal conductivity of liquid silicon in a static magnetic field[J]. Journal. Appl. Phys. 104 (2008) 054901.[4] H. Fukuyama, K. Takahashi, S. Sakashita, H.Kobatake, T. Tsukada, S. Awaji. Noncontact modulated laser calorimetry for liquid austenitic stainless steel in dc magnetic field[J]. ISIJ International. 49 (2009) 1422–1436. [5]Bojarevics, V. and K. Pericleous, Modelling electromagnetically levitated liquid droplet oscillations[J]. ISIJ International, 2003. 43(6): 890-898.Crystal Growth, 2004. 260(3-4): 475-485.[6]T. Tsukada, K.-I. Sugioka, T. Tsutsumino, H. Fukuyama, H. Kobatake. Effect of static magnetic field on a thermal conductivity measurement of a molten droplet using an electromagnetic levitation technique[J]. Int. Heat Mass Transfer 52 (2009) 5152–5157.[7]石万元，张凤超，田小红.相场法模拟悬浮熔融硅液滴内部对流及自由界面变形现象[J]. 西南交通大学学报,2012(04): 692-697.[8]Ding, H., P. Spelt and C. Shu. Diffuse interface model for incompressible two-phase flows with large density ratios[J]. Journal of computational physics, 2007. 226(2): 2078-2095[9]Jing. G S,Shu C W. Efficient implementation of weighted ENO schemes[J]. Computational Physics，1996,126: 202-228．[10]Van Der V orst H A. Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems[J]. Siam Journal on Scientific and Statistical Computing, 1992, 13: 631-644．[11] Sussman, M. and P. Smereka. Axisymmetric free boundary problems[J]. Journal of fluid mechanics, 1997. 341: 269-294.[12] Watanabe, T. Zero frequency shift of an oscillating-rotating liquid droplet [J]. Physics letters , 2008. 372(4): 482-485.[13] Asakuma, Y. et al. Nonlinear oscillations of molten silicon drops in electromagnetic levitator[J]. Journal of chemical engineering of Japan, 2000. 33(6): 861-868.。
