Numerical Simulation of Three Dimensional Tur

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外文翻译----三维注射成型流动模拟的研究

附录Numerical Filling Simulation of Injection MoldingUsing Three—Dimensional ModelAbstract：Most injection molded parts are three-dimensional, with complex geometrical configurations and thick／thin wall sections．A 3D simulation model will predict more accurately the filling process than a 2.5D mode1.This paper gives a mathematical model and numeric method based on 3D model，in which an equal-order velocity-pressure interpolation method is employed successfully．The relation between velocity and pressure is obtained from the discretized momentum equations in order to derive the pressure equation．A 3D control volume scheme is employed to track the flow front．The validity of the model has been tested through the an analysis of the flow in cavity．Key words：three dimension；equal-order interpolation；simulation；injection molding1 IntroductionDuring injection molding，the theological response of polymer melts is generally non-Newtonian and no isothermal with the position of the moving flow front．Because of these inherent factors，it is difficult to analyze the filling process．Therefore，simplifications usually are used．For example，in middle-plane technique and dual domain technique[1], because the most injection molded parts have the characteristic of being thin but generally of complex shape，the Hele-Shaw approximation [2] is used while an analyzing the flow, i.e.．The variations of velocity and pressure in the gapwise (thickness) dimension are neglected．So these two techniques are both 2.5D mold filling models，in which the filling of a mold cavity becomes a 2D problem in flow direction and a 1D problem in thickness direction．However, because of the us e of the Hele-Shaw approximation，the information that 2.5D models can generate is limited and incomplete．The variation in the gapwise (thickness) dimension of the physical quantities with the exception of the temperature，which is solved by finite difference method，is neglected．With the development of molding techniques，molded华东交通大学理工学院毕业设计（论文）parts will have more and more complex geometry and the difference in the thickness will be more and more notable，so the change in the gapwise (thickness) dimension of the physical quantities can not be neglected．In addition，the flow simulated looks unrealistic in as much as the melt polymer flows only on surfaces of cavity, which appears more obvious when the flow simulation is displayed in a mould cavity．3D simulation model has been a research direction and hot spot in the scope of simulation for plastic injection molding．In 3D simulation model，velocity in the gapwise (thickness) dimension is not neglected and the pressure varies in the direction of part thickness，and 3 D finite elements are used to discretize the part geometry．After calculating，complete data are obtained(not only surface data but also internal data are obtained)．Therefore, a 3D simulation model should be able to generate complementary and more detailed information related to the flow characteristics and stress distributions in thin molded parts than the one obtained when using a 2.5D model(based on the Hele-Shaw approximation)．On the other hand，a 3D model will predict more accurately the characteristics of molded parts having thick walled sections such as encountered in gas assisted injection molding．Several flow behaviors at the flow front．such as “fountain flow”．which 2.5D model cannot predict, can be predicted by 3D mode1. Meanwhile, the flow simulation looks more realistic inasmuch as the overall an analysis result is directly displayed in 3D part geometry or transparent mould cavity．This Paper presents a 3 D finite element model to deal with the three—dimensional flow, which employs an equa1-order velocity-pressure formulation method [3,4]．The relation between velocity and pressure is obtained from the discretized momentum equations, then substituted into the continuity equation to derive pressure equation．A 3D control volume scheme is employed to track the flow front．The validity of the model has been tested through the analysis of the flow in cavity．2 Governing EquationsThe pressure of melt is not very big during filling the cavity, in addition，reasonable mold structure can avoid over big pressure，so the melt is considered incompressible．Inertia and gravitation are neglected as compared to the viscous force．With the above approximation，the governing equations，expressed in cartesian coordinates，are as following：Momentum equationsContinuity equationEnergy equationwhere, x，y，z are three dimensional coordinates and u, v，w are the velocity component in the x, y, z directions．P，T，ρandη denote pressure，temperature, density and viscosty respectively．Cross viscosity model has been used for the simulations：where，n,γ，r are non-Newtonian exponent，shear rate and material constant respectively．Because there is no notable change in the scope of temperature of the melt polymer during filling，Anhenius model[5] for η0 is employed as following：where B，Tb，β are material constants.3 Numerical Simulation Method3.1 Velocity-Pressure RelationIn a 3D model，since the change of the physical quantities are not neglected in the gapwise (thickness) dimension，the momentum equations are much more complex than those in a 2.5D mode1．It is impossible to obtain the velocity—pressure relation by integrating the momentum华东交通大学理工学院毕业设计（论文）equations in the gapwise dimension，which is done in a 2.5D model. The momentum equations must be first discretized，and then the relation between velocity and pressure is derived from it. In this paper, the momentum equations are discretized using Galerkin’s method with bilinear velocity-pressure formulation．The element equations are assembled in the conventional manner to form the discretized global momentum equations and the velocity may be expressed as followingwherethe nodal pressure coefficients are defined aswhere represent global velocity coefficient matrices in the direction of x, y, z coordinate respectively. denote the nodal pressure coefficients thedirection of x, y, z coordinate respectively. The nodal values for are obtained byassembling the element-by-element contributions in the conventional manner. N，is element interpolation and i means global node number and j , is for a node, the amount of the nodes around it.3.2 Pressure EquationSubstitution of the velocity expressions (2) into discretized continuity equation, which is discretized using Galerkin method，yields element equation for pressure:The element pressure equations are assembled the conventional manner to form the global pressure equations．3.3 Boundary ConditionsIn cavity wall, the no- slip boundary conditions are employed, e.g.On an inlet boundary,3.4 Velocity UpdateAfter the pressure field has been obtained，the velocity values are updated using new pressure field because the velocity field obtained by solving momentum equations does not satisfy continuity equation．The velocities are updated using the following relationsThe overall procedure for fluid flow calculations is relaxation iterative，as shown in Fig.l and the calculation is stable without pressure oscillation．3.5 The Tracing of the Flow FrontsThe flow of fluid in the cavity is unsteady and the position of the flow fronts values with time．Like in 2.5D model, in this paper, the control volume method is employed to trace the position of the flow fronts after the FAN(Flow Analysis Network)[6]. But 3D control volume is a special volume and more complex than the 2D control volume．It is required that 3D control volumes of all nodes fill the part cavity without gap and hollow space. Two 3D control volumes are shown in Fig．2．华东交通大学理工学院毕业设计（论文）4 Results and DiscussionThe test cavity and dimensions are shown in Fig.3(a)．The selected material is ABS780 from Kumbo. The pa rametric constants corresponding to then, γ,B, Tb and β of the five-constant Cross-type Viscosity model are 0．2638, 4．514 ×le4 Pa, 1.3198043×le-7 Pa *S, 1．12236 ×1e4K，0．000 Pa-1．Injection temperature is 45℃，mould temperature is 250℃, injection flow rate is 44．82 cu. cm／s. The meshed 3D model of cavity is shown in Fig. 3(b).“Fountain flow” is a typical flow phenomenon during filling．When the fluid is injected into a relatively colder mould，solid layer is formed in the cavity walls because of the diffusion cooling，so the shear near the walls takes place and is zero in the middle of cavity, and the fluid near the walls deflects to move toward the walls．The fluid near the center moves faster than the average across the thickness an d catches up with the front so the shape of the flow front is round like the fountain．The round shape of the flow front of the example in several filling times predicted by present 3D model and shown in Fig．4(a)，conforms to the theory and experiments．Contrarily, the shape of the flow front predicted by 2.5D model and shown in Fig．4(b) do not reveal the“Fountain flow”．The flow front comparison at the filling stage is illustrated in Fig．5．It shows that the predicted results based on present 3D model agree well with that based on Moldflow 3D mode1．The gate pressure is illustrated in Fig．6，compared with the prediction of Moldflow 3D model．It shows that the predicted gate pressure of present 3D model is mainly in agreement with that based on Moldflow 3D mode1．The major reason for this deviation is difference in dealing with the model an d material parameters．华东交通大学理工学院毕业设计（论文）5 ConclusionsA theoretical model and numerical scheme to simulate the filling stage based on a 3D finite element model are presented．A cavity has been employed as example to test the validity. 3D numeral simulation of the filling stage in injection moulding is a development direction in the scope of simulation for plastic injection molding in the future．The long time cost is at present a problem for 3D filling simulation，but with the development of computer hardware and improvement in simulation technique，the 3D technique will be applied widely．华东交通大学理工学院毕业设计（论文）三维注射成型流动模拟的研究摘要:大多数注射成型制品都是具有复杂的几何轮廓和厚壁或薄壁的制品。

有自由面渗流分析的三维数值流形方法

第32卷第3期岩土力学 V ol.32 No.3 2011年3月 Rock and Soil Mechanics Mar. 2011收稿日期：2009-12-27基金项目：国家自然科学基金项目(No. 50839004，No.51079110 )；教育部新世纪优秀人才支持计划项目（No. NCET -07-0632）。

第一作者简介：姜清辉，男，1972年生，博士，教授，主要从事岩土力学数值计算方法与岩土工程稳定分析方面的教学与研究工作。

E-mail ：jqh1972@文章编号：1000－7598 (2011) 03－879－06有自由面渗流分析的三维数值流形方法姜清辉1, 2，邓书申2，周创兵2（1. 武汉大学土木建筑工程学院武汉 430072；2. 武汉大学水资源与水电工程科学国家重点实验室，武汉430072）摘要：提出了求解有自由面渗流问题的三维数值流形方法，通过构造任意形状流形单元的水头函数，推导了流形单元的渗透矩阵和无压渗流分析的总体控制方程，并给出了自由面的迭代求解策略和渗透体积力的计算方法。

典型算例的数值分析表明，该方法采用数学网格覆盖整个材料区域，在自由面的迭代求解过程中数学网格保持不变，只考虑自由面以下渗流区的介质，只对自由面以下的流形单元形成总体渗透矩阵，具有精度高、收敛速度快、编程简单等优点，而且能够通过单纯形积分精确计算被自由面穿越单元的渗透作用力，因此，特别适用于有自由面渗流问题的模拟。

关键词：三维渗流；数值流形方法；自由面；数学网格；流形单元中图分类号：O342 文献标识码：AThree-dimensional numerical manifold method for seepageproblems with free surfacesJIANG Qing-hui 1,2 , DENG Shu-shen 2 , ZHOU Chuang-bing 2(1.School of Civil and Architectural Engineering, Wuhan University, Wuhan, 430072, China;2.State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, 430072, China)Abstract: A three-dimensional numerical manifold method for seepage problems with free surfaces is proposed. The hydraulic potential functions for arbitrarily shaped manifold element are constructed and the element conductivity matrix is derived in detail. The global governing equations for unconfined seepage analysis are established by minimizing the flow dissipation energy. The proposed method employs the tetrahedral mathematical meshes to cover the whole material volume. In the process of iterative solving for locating the free surface, the numerical manifold method can strictly realize the seepage analysis of the saturated domain on the condition of mathematical meshes keeping unchanged. Furthermore, the seepage force acting on the transitional elements cut by the free surface can be accurately calculated by the manifold method. Therefore, the proposed method is featured in high accuracy, fast convergence rate and simple programming, especially applicable to simulate the unconfined seepage problem with free surface. Key words: three-dimensional seepage; numerical manifold method; free surface; mathematical mesh; manifold element1 引言在采用传统的有限元方法求解无压渗流问题时，主要存在两类解法：调整网格法和固定网格法。

微孔端面机械密封间液膜的CFD数值模拟

微孔端面机械密封间液膜的CFD数值模拟丁雪兴;王燕;佘志刚;毛亚军【摘要】Three-dimensional spatioal model was founded for the liquid membrane among micro-pore end surfaces by using Pro/E software. The model was latticed by using the Gambit software, a numerical simulation was made with Fluent software for the three-dimension flow field in the internal micro-scale gaps under a special condition of the micro-pores etched on one face of the seal. The distributions of pressure and velocity within the flow field and the liquid leakage were obtained. These three performances were resimulated in the case of different depth to diameter ratios ε. The influence of the depth to diameter ratio on the sealing performance of the end mechanical seals was analyzed in the condition of identical film thick ness. The result showed that when ε = 0. 1, the leakage would be minimal and an optimal sealing effectcould be obtained.%应用Pro/E软件建立微孔端面间液膜的三维立体模型,Gambit软件对模型进行划分网格,F1uent软件对微孔端面间特定工况下的内部微间隙三维流场进行数值模拟,得到流场的压力分布、速度分布以及泄漏量.改变微孔深径比再次模拟,得到不同参数下流场所对应的压力分布、速度分布及泄漏量,分析在同一液膜厚度情况下,微孔深径比对端面机械密封性能的影响.结果表明:当深径比ε=0.1时泄漏量最小,可获得最佳密封效果.【期刊名称】《兰州理工大学学报》【年(卷),期】2011(037)002【总页数】5页(P39-43)【关键词】机械密封;端面微孔;泄漏量;CFD【作者】丁雪兴;王燕;佘志刚;毛亚军【作者单位】兰州理工大学,石油化工学院,甘肃,兰州,730050;兰州理工大学,石油化工学院,甘肃,兰州,730050;兰州理工大学,石油化工学院,甘肃,兰州,730050;陕西延长石油油气勘探公司,陕西,延安,716000【正文语种】中文【中图分类】TB421994年，以色列教授 Etsion［1－2］提出微孔端面机械密封的概念.激光加工多孔端面机械密封是一种动压型机械密封，在密封环端面上加工有规则分布的球形微孔.每一个微孔像一个微动力轴承，当两密封面相对运动时，在孔的上方及其周围区域产生明显的动压效应，可大大降低密封端面间的摩擦扭矩［3］.目前，国内外学者大多利用有限差分法［3－5］，通过公式计算求解雷诺方程的方法研究微孔端面密封动静态特性，采用CFD软件方法进行数值模拟研究的较少.利用CFD软件进行建模，可以考虑任意孔型的结构型式［5］，并且可以更全面、准确、直观地反映微孔端面密封流体动特性［6－7］.随着计算流体力学（CFD）和计算机技术的发展，各种计算流体力学软件日趋成熟，使得对密封环端面微凹腔内流场直接进行数值模拟变成可能［8］.本文利用ANSYS-FLUENT软件对微孔端面间特定工况下的内部微间隙三维流场进行数值模拟，得到流场的压力分布、速度分布以及泄漏量.改变操作参数再次模拟，得到不同参数下流场的压力分布及泄漏量，并分析操作参数对微孔端面机械密封的影响.1 Fluent计算模型建立图1是具有微孔的密封副结构示意图，静环表面采用激光加工出球冠形微孔，微孔沿径向呈放射状分布，沿周向呈等间距分布，密封面不直接接触，密封面间形成一定密度的液膜，假定液膜压力沿液膜厚度方向不变化，密封流体黏度保持不变，并忽略密封曲率影响［4］.图1 具有微孔的密封副结构示意图Fig.1 Micro-pores seal pair structure diagram1.1 几何模型的建立1.1.1 建立几何模型计算模型的三维几何建模采用Pro／E软件，计算区域选定为密封转轴与其配合壁面间隙内的全三维空间，如图2b的一列径向孔栏.利用Pro／E建模后的液膜模型如图3所示，选取的是同一径向相邻的四元体模型.图2 具有半球形微孔的机械密封Fig.2 Mechanical seal with hemispherical micro-pores1.1.2 网格化分本文网格划分采用TGrid单元方案，并采用Gambit非结构化网格划分方法，对同一径向相邻四元体模型直接进行网格划分，如图4所示为计算区域网格.图3 利用Pro／E建模后的液膜模型.3 Liquid membrane model set up by using Pro／E modeling图4 计算区域网格Fig.4 Mesh in computational zone1.2 密封环工作的基本假设机械密封的流体润滑理论的主要内容是流体膜润滑，即由流体膜承载保持密封和润滑的成膜理论，其主要控制方程为雷诺（Reynolds）方程［9－11］.忽略一些对问题研究重点和预期的结果没有影响或影响很小的因素［8］，作者作出以下基本假设：1）忽略体积力的作用，如重力或磁力；2）与黏性力比较，可以忽略惯性力的影响，包括流体加速度的惯性力和流体膜的弯曲的离心力；3）在沿流体膜厚度方向上，不计压力的变化，因为膜厚一般为微米数量级，在膜厚范围内，事实上压力不可能发生明显的变化；4）密封流体介质为牛顿（Newton）流体，即剪切力正比于剪应变率；5）流体在摩擦界面上无滑动，即附着于界面上的流体质点的速度与界面上该点的速度相同；6）流体在密封面间的流动为层流，流体膜中不存在涡流和湍流；7）整个机械密封润滑系统的温度处处相等，因此不考虑润滑剂的黏度和密度随温度的变化；8）两密封面不接触，其间存在液膜，且液膜厚度在密封表面各处相等；9）流体为不可压缩流体，密度不随压力变化.10）不考虑流体的表面张力效应. 1.3 边界条件凹腔开在下面的静环上，故液膜下部有突起.内侧压力为大气压，外侧压力为密封介质压力，流体因为压力差从外径向内径流动，在孔栏的径向边界上，对应半径处的压力分别相等，且液膜压力沿周向的变化率在对应半径处相等［4］，除进、出口以外两侧为周期性边界条件，即本模型进出口分别采用压力入口pressure inlet 及压力出口pressure outlet边界条件；上、下表面采用壁面wall边界条件，上表面为旋转壁面，下表面为静止壁面，除进、出口以外两侧为周期性边界条件.压力的数值大小、壁面的运动形式以及速度值将在FLUENT中具体设定.密封环表面为标准壁面条件，采用速度无滑移条件.采用旋转参考坐标系来模拟动静环之间的相互运动.2 模型计算结果2.1 求解方法求解器选择分离的隐式求解器，压力差值格式为标准差值，压力速度耦合采用SIMPLEC算法.扩散项的离散格式采用中心差分格式，对流项的离散格式采用二阶迎风格式.本模型为含有旋转的流动，压力差值方式选择Presto.本模型采用的收敛准则为默认准则，即小于10－3.2.2 算例给定的密封环端面结构参数和工况参数为：内径ri＝10.8 mm，外径ro＝13.5 mm，环境压力（内压）pi＝pa＝0.101 3 MPa，介质压力（外压）po＝0.60795 MPa，流体黏度μ＝0.015 Pa·s，转速n＝3 000 r／min，微孔密度sp＝0.5，微孔半径rp＝50μm，液膜厚度h0＝3μm，微孔深径比分别选为ε＝0.08，0.10，0.20，0.30，微孔深度分别为hp1＝8μm，hp2＝10μm，hp3＝20μm，hp4＝30μm.分别对4组数据进行建模，网格划分，导入FLUENT进行计算，得到深径比不同时的压力分布和速度分布，如图5和图6所示.2.3 模拟结果分析2.3.1 不同深径比的压力沿径向的分布图7表示微孔深径比对无量纲平均动压力的影响.由图可知，微孔深径比对动压效应有较大的影响，深径比在0.1左右时，平均动压力最大，说明微孔深径比存在最佳值，据Etsion试验研究结果［12］表明，在深径比为0.07时，密封面的承载能力最大，两者比较可知，模拟结果与试验结果接近.2.3.2 不同深径比的速度沿径向的分布由图8可知，当ε＝0.1时，产生的流速最低.这与图7产生的压力结果吻合，说明在ε＝0.1时，存在最佳深径比.2.3.3 不同深径比的泄漏量曲线关系由FLUENT软件直接读出4组不同深径比的泄漏量，由Origin软件绘制曲线图，可得微孔深度对泄漏量的影响规律（见图9）.由图9可知，当液膜厚度h0＝3μm，密封压力和密封环转速不变的情况下，随着微孔深度的增加，泄漏量的变化经历先快速下降再慢速上升的过程.在深径比ε＝0.1，hp＝10 μm时，可得泄漏量值最小.2.4 模拟结果与文献结果对比图10为微孔深径比对无量纲平均动压力的影响.由图可知，微孔深径比对动压效应有较大的影响，深径比ε＝0.1左右时，无量纲平均动压力最大，说明微孔深径比存在最佳值.这与文献［13］的数值模拟结果吻合，因此，当深径比ε＝0.1时泄漏量最小，可获得最佳密封效果.图5 同一径向不同深径比四元体压力分布图（kPa）Fig.5 Diagram of pressure distribution in four-tropic body with different depth／diameter ratio in identical radial direction（kPa）图6 同一径向不同深径比四元体速度分布图（m／s）Fig.6 Diagram of velocity distribution in four-tropic body with different depth／diameter ratio on identical radius（m／s）图7 不同深径比的压力沿径向的分布Fig.7 Radial distribution of pressure for different depth／diameter ratio图8 不同深径比的速度沿径向的分布Fig.8 Radial distribution of velocity for different depth／diameter ratio图9 不同深径比与泄漏量的关系Fig.9 Leakage for different depth／diameter ratio图10 微孔深径比对无量纲平均动压力影响的结果对比Fig.10 Comparison of influence of micro-pores depth／diameter ration on mean dimensionlessdynamic pressure3 结论1）通过对4种不同深径比微孔端面密封所产生的压力、速度以及它们的泄漏量比较可知，当液膜厚度h0＝3μm时，通过FLUENT软件模拟的结果得到：当深径比ε＝0.1，微孔深度hp＝10μm时，泄漏量最小.2）本文只针对同一膜厚情况下，深径比与泄漏量之间的关系，此研究为今后对不同膜厚以及其他几何参数改变的研究提供了依据.致谢：本文得到兰州理工大学博士基金项目（BS05200901）资助，在此表示感谢. 参考文献：［1］ ETSION I，BURETEIN L.A model for mechanical seals with regular microsurface structure ［J］.Tribology Transactions，1996，39（3）：667-683.［2］ ETSION I，MICHEAL O.Enhancing sealing and dynamic performance with partially porous mechanical face seals［J］.Tribology Transactions，1994，37（4）：701-710.［3］于新奇，蔡仁良.激光加工的多孔端面机械密封的性能数值分析［J］.现代制造工程，2004（7）：66-68.［4］李国栋.激光加工多孔端面机械密封性能研究及结构优化［D］.兰州：兰州理工大学，2009.［5］丁雪兴，程香平，杜鹃.机械密封混合摩擦微极流体弹性润滑的数值模拟［J］.兰州理工大学学报，2008，34（4）：70-73.［6］侯煜.CFD环形间隙泄漏量及摩擦力的仿真计算［D］.太原：太原理工大学，2007.［7］叶建槐，刘占生.高低齿迷宫密封流场和泄露特性CFD研究［J］.汽轮机技术，2008（4）：81-84.［8］陈汇龙，翟晓.基于多重网格法和CFD的多孔端面机械密封数值分析比较［J］.润滑与密封，2009（10）：36-40.［9］王福军.计算流体动力学分析［M］.北京：清华大学出版社，2004. ［10］温诗铸，杨沛然.弹性流体动力润滑［M］.北京：清华大学出版社，1992. ［11］杨沛然.流体润滑数值分析［M］.北京：国防工业出版社，1998. ［12］ ETSION I，BURETEIN L.Proceeding of 15th International Conference on Fluid Seal［C］.London：Professional Engineering Publishing Limited，1997：3-10.［13］于新奇，蔡仁良.激光加工多孔端面机械密封的动压分析［J］.华东理工大学学报，2004，30（8）：481-484.。

三维解析仿真的英语作文

三维解析仿真的英语作文Three-Dimensional Computational Modeling.Three-dimensional (3D) computational modeling is the process of creating a mathematical representation of a three-dimensional object. This representation can be used to simulate the behavior of the object under different conditions. 3D computational modeling is used in a wide variety of fields, including engineering, medicine, and manufacturing.In engineering, 3D computational modeling is used to simulate the behavior of structures and machines. This information can be used to design structures that are safe and efficient. In medicine, 3D computational modeling is used to simulate the behavior of organs and tissues. This information can be used to diagnose diseases and develop new treatments. In manufacturing, 3D computational modeling is used to simulate the behavior of products during the manufacturing process. This information can be used tooptimize the manufacturing process and reduce product defects.There are many different types of 3D computational modeling software available. The type of software used will depend on the specific application. Some of the most popular 3D computational modeling software programs include ANSYS, COMSOL, and Siemens NX.3D computational modeling is a powerful tool that can be used to simulate the behavior of objects in a variety of different fields. This information can be used to design safer and more efficient structures, diagnose and treat diseases, and optimize the manufacturing process.Benefits of 3D Computational Modeling.There are many benefits to using 3D computational modeling. Some of the most notable benefits include:Increased accuracy: 3D computational models are more accurate than traditional 2D models. This is because 3Dmodels can take into account the effects of all three dimensions of space.Reduced time and cost: 3D computational modeling can save time and cost by reducing the need for physical testing. Physical testing can be expensive and time-consuming, and it is not always possible to test all possible scenarios.Improved communication: 3D computational models can be used to communicate complex designs and concepts more easily. This can help to reduce errors and improve collaboration between different teams.Applications of 3D Computational Modeling.3D computational modeling is used in a wide variety of applications, including:Engineering: 3D computational modeling is used to simulate the behavior of structures and machines. This information can be used to design structures that are safeand efficient.Medicine: 3D computational modeling is used to simulate the behavior of organs and tissues. This information can be used to diagnose diseases and develop new treatments.Manufacturing: 3D computational modeling is used to simulate the behavior of products during the manufacturing process. This information can be used to optimize the manufacturing process and reduce product defects.Future of 3D Computational Modeling.The future of 3D computational modeling is bright. As computer hardware and software continue to improve, 3D computational models will become even more accurate and sophisticated. This will open up new possibilities for using 3D computational modeling in a wide variety of applications.One of the most exciting developments in 3Dcomputational modeling is the use of artificialintelligence (AI). AI can be used to automate the process of creating and running 3D computational models. This will make it easier for engineers, scientists, and other professionals to use 3D computational modeling in their work.Another exciting development in 3D computational modeling is the use of virtual reality (VR). VR can be used to create immersive 3D environments that allow users to interact with 3D computational models. This can make it easier to understand complex designs and concepts.3D computational modeling is a powerful tool that is transforming the way we design, build, and heal. As computer hardware and software continue to improve, 3D computational modeling will become even more powerful and versatile. This will open up new possibilities for using 3D computational modeling in a wide variety of applications.。

外文翻译--三维注射成型流动模拟的研究

中文2900字附录Numerical Filling Simulation of Injection MoldingUsing Three—Dimensional ModelAbstract：Most injection molded parts are three-dimensional, with complex geometrical configurations and thick／thin wall sections．A 3D simulation model will predict more accurately the filling process than a 2.5D mode1.This paper gives a mathematical model and numeric method based on 3D model，in which an equal-order velocity-pressure interpolation method is employed successfully．The relation between velocity and pressure is obtained from the discretized momentum equations in order to derive the pressure equation．A 3D control volume scheme is employed to track the flow front．The validity of the model has been tested through the an analysis of the flow in cavity．Key words：three dimension；equal-order interpolation；simulation；injection molding1 IntroductionDuring injection molding，the theological response of polymer melts is generally non-Newtonian and no isothermal with the position of the moving flow front．Because of these inherent factors，it is difficult to analyze the filling process．Therefore，simplifications usually are used．For example，in middle-plane technique and dual domain technique[1], because the most injection molded parts have the characteristic of being thin but generally of complex shape，the Hele-Shaw approximation [2] is used while an analyzing the flow, i.e.．The variations of velocity and pressure in the gapwise (thickness) dimension are neglected．So these two techniques are both 2.5D mold filling models，in which the filling of a mold cavity becomes a 2D problem in flow direction and a 1D problem in thickness direction．However, because of the us e of the Hele-Shaw approximation，the information that 2.5D models can generate is limited and incomplete．The variation in the gapwise (thickness) dimension of the physical quantities with the exception of the temperature，which is solved byfinite difference method，is neglected．With the development of molding techniques，molded parts will have more and more complex geometry and the difference in the thickness will be more and more notable，so the change in the gapwise (thickness) dimension of the physical quantities can not be neglected．In addition，the flow simulated looks unrealistic in as much as the melt polymer flows only on surfaces of cavity, which appears more obvious when the flow simulation is displayed in a mould cavity．3D simulation model has been a research direction and hot spot in the scope of simulation for plastic injection molding．In 3D simulation model，velocity in the gapwise (thickness) dimension is not neglected and the pressure varies in the direction of part thickness，and 3 D finite elements are used to discretize the part geometry．After calculating，complete data are obtained(not only surface data but also internal data are obtained)．Therefore, a 3D simulation model should be able to generate complementary and more detailed information related to the flow characteristics and stress distributions in thin molded parts than the one obtained when using a 2.5D model(based on the Hele-Shaw approximation)．On the other hand，a 3D model will predict more accurately the characteristics of molded parts having thick walled sections such as encountered in gas assisted injection molding．Several flow behaviors at the flow front．such as “fountain flow”．which 2.5D model cannot predict, can be predicted by 3D mode1. Meanwhile, the flow simulation looks more realistic inasmuch as the overall an analysis result is directly displayed in 3D part geometry or transparent mould cavity．This Paper presents a 3 D finite element model to deal with the three—dimensional flow, which employs an equa1-order velocity-pressure formulation method [3,4]．The relation between velocity and pressure is obtained from the discretized momentum equations, then substituted into the continuity equation to derive pressure equation．A 3D control volume scheme is employed to track the flow front．The validity of the model has been tested through the analysis of the flow in cavity．2 Governing EquationsThe pressure of melt is not very big during filling the cavity, in addition，reasonable mold structure can avoid over big pressure，so the melt is considered incompressible．Inertia and gravitation are neglected as compared to the viscous force．With the above approximation，the governing equations，expressed in cartesian coordinates，are as following：Momentum equationsContinuity equationEnergy equationwhere, x，y，z are three dimensional coordinates and u, v，w are the velocity component in the x, y, z directions．P，T，ρandη denote pressure，temperature, density and viscosty respectively．Cross viscosity model has been used for the simulations：where，n,γ，r are non-Newtonian exponent，shear rate and material constant respectively．Because there is no notable change in the scope of temperature of the melt polymer during filling，Anhenius model[5] for η0 is employed as following：where B，Tb，β are material constants.3 Numerical Simulation Method3.1 Velocity-Pressure RelationIn a 3D model，since the change of the physical quantities are not neglected in the gapwise (thickness) dimension，the momentum equations are much more complex than those in a 2.5Dmode1．It is impossible to obtain the velocity—pressure relation by integrating the momentum equations in the gapwise dimension，which is done in a 2.5D model. The momentum equations must be first discretized，and then the relation between velocity and pressure is derived from it. In this paper, the momentum equations are discr etized using Galerkin’s method with bilinear velocity-pressure formulation．The element equations are assembled in the conventional manner to form the discretized global momentum equations and the velocity may be expressed as followingwherethe nodal pressure coefficients are defined aswhere represent global velocity coefficient matrices in the direction of x, y, z coordinate respectively. denote the nodal pressure coefficients thedirection of x, y, z coordinate respectively. The nodal values for are obtained byassembling the element-by-element contributions in the conventional manner. N，is element interpolation and i means global node number and j , is for a node, the amount of the nodes around it.3.2 Pressure EquationSubstitution of the velocity expressions (2) into discretized continuity equation, which is discretized using Galerkin method，yields element equation for pressure:The element pressure equations are assembled the conventional manner to form the global pressure equations．3.3 Boundary ConditionsIn cavity wall, the no- slip boundary conditions are employed, e.g.On an inlet boundary,3.4 Velocity UpdateAfter the pressure field has been obtained，the velocity values are updated using new pressure field because the velocity field obtained by solving momentum equations does not satisfy continuity equation．The velocities are updated using the following relationsThe overall procedure for fluid flow calculations is relaxation iterative，as shown in Fig.l and the calculation is stable without pressure oscillation．3.5 The Tracing of the Flow FrontsThe flow of fluid in the cavity is unsteady and the position of the flow fronts values with time．Like in 2.5D model, in this paper, the control volume method is employed to trace the position of the flow fronts after the FAN(Flow Analysis Network)[6]. But 3D control volume is a special volume and more complex than the 2D control volume．It is required that 3D control volumes of all nodes fill the part cavity without gap and hollow space. Two 3D control volumes are shown in Fig．2．4 Results and DiscussionThe test cavity and dimensions are shown in Fig.3(a)．The selected material is ABS780 from Kumbo. The pa rametric constants corresponding to then, γ,B, Tb and β of the five-constant Cross-type Viscosity model are 0．2638, 4．514 ×le4 Pa, 1.3198043×le-7 Pa *S, 1．12236 ×1e4K，0．000 Pa-1．Injection temperature is 45℃，mould temperature is 250℃, injection flow rate is 44．82 cu. cm／s. The meshed 3D model of cavity is shown in Fig. 3(b).“Fountain flow” is a typical flow phenomenon during filling．When the fluid is injected into a relatively colder mould，solid layer is formed in the cavity walls because of the diffusion cooling，so the shear near the walls takes place and is zero in the middle of cavity, and the fluid near the walls deflects to move toward the walls．The fluid near the center moves faster than the average across the thickness an d catches up with the front so the shape of the flow front is round like the fountain．The round shape of the flow front of the example in several filling times predicted by present 3D model and shown in Fig．4(a)，conforms to the theory and experiments．Contrarily, the shape of the flow front predicted by 2.5D model and shown in Fig．4(b) do not reveal the“Fountain flow”．The flow front comparison at the filling stage is illustrated in Fig．5．It shows that the predicted results based on present 3D model agree well with that based on Moldflow 3D mode1．The gate pressure is illustrated in Fig．6，compared with the prediction of Moldflow 3D model．It shows that the predicted gate pressure of present 3D model is mainly in agreement with that based on Moldflow 3D mode1．The major reason for this deviation is difference in dealing with the model an d material parameters．5 ConclusionsA theoretical model and numerical scheme to simulate the filling stage based on a 3D finite element model are presented．A cavity has been employed as example to test the validity. 3D numeral simulation of the filling stage in injection moulding is a development direction in the scope of simulation for plastic injection molding in the future．The long time cost is at present a problem for 3D filling simulation，but with the development of computer hardware andimprovement in simulation technique，the 3D technique will be applied widely．三维注射成型流动模拟的研究摘要:大多数注射成型制品都是具有复杂的几何轮廓和厚壁或薄壁的制品。

涡旋压缩机英文论文

Three-dimension numerical simulation of discharge flow in a scroll air compressorSchool of energy and power engineeringAbstractScroll compressor is being recognized by industry as being high competitive with conventional compressors. Plenty of publications on this subject prove an interest of the researchers as well. Further increases in efficiency may be realized if the flow losses, particularly in the final compression and discharge region are reduced. Detailed understandings of the flow processes occurring in the discharge region are necessary to analysis and reduce the discharge flow losses, which become more serious with operation at large discharge. Due to the complexity of the processes, the only one way to get the results is solving the equations of continuity and momentum using the numerical method. During the past decade, a number of investigations have been conducted on the performance of the scroll compressor. However, relatively little information are available on the details of the fluid flow characteristics within the scroll compressor chamber. In the paper, in the light of the characteristics of a discharge process, reasonable simplification of actual physical model is made and the three-dimension quasi-steady turbulent flow numerical simulation is carried out to study the flow field in the discharge region in a scroll air compressor. Three dimensionaldistributions of velocity and pressure and typical flow patterns that exits in the discharge region are presented, which gives good understanding about the physical processes in the scroll air compressor.1.INTRODUCTIONScroll compressors are applied widely in the refrigeration, air conditioning and power field as being competitive advantages in terms of high efficiency, reduced part requirement, lower noise, and reduced vibration levels. Three exist various losses when a scroll compressor is running, such as moving resistance losses of the orbiting scroll and Oldham, friction losses and flow losses. The discharge flow is the main part of these losses (approximately 3 percent of the input power is consumed due to the flow losses), especially at large discharge . Understanding of the flow processes occurring in the discharge and the final compression region is necessary to reduce these flow losses, which become more pronounced with operation at increasing speed and large discharge. Therefore, three dimension numerical simulation of discharge flow in scroll air compressor with modified top profile is carried out. The important flow patterns that exist in the discharge and final compression region are presented. The analysis results supply the theory basis for finding the sources caused discharge losses and designing the discharge port of scroll compressor, particularly at large discharge.A scroll air compressor of discharge is studied in this paper. The topprofile is modified with symmetrical arcs and the discharge port is kidney-shape port. The basic parameters and modified parameters of scroll tips are shown in the table 1.Figure 1 shows the schematic region of the scroll compressor.Table 1: The basic parameters and modified parameters of scroll tipsFigure 1: Schematic of scroll compressor discharge region.2.PHYSICAL MODELAND AND NUMERICAL METHOD2.1 Physical modelThe gas is driven and compressed by “squish motion” of the orbiting scroll wrap, and this results that an unsteady compressible viscous flow occurs within the scroll compressor working chamber. Due to high rotating speed and steep velocity gradient near the wrap wall, the turbulence characteristics have to be considered. But the orbiting wall speed is small compared to the gas flow velocities, for example, the wall speed is approximately 5 percent of the average velocity of the discharge flow in a scroll air compressor at discharge studied in this paper, so it appears justified that the quasi-steady approach is made to treat the flow field with stationary wall. That is , to ignore the moving of orbiting scroll wall is justified. Therefore, three dimension steady-state turbulence calculations are performed to predict the flow field in the final compressor and discharge region. Air is injected from two sides of thecentral chamber with the instantaneous flow rate at various crank angles. The volume flow rate at various crank angles during the discharge process is shown in figure 2.The figure 3 shows a computational model at a certain crank angle after onset of discharge.Figure 2: V olume flow rate with orbiting discharge crank angleFigure 3: Three dimensional computation model2.2 Numerical methodTurbulent flow exists in the scroll configurations considered and was treated using a normal k- turbulence model. The governing equations were discretized using finite volume method. The SIMPLE algorithm was employed in order to correct the pressure filed. Near the wall, the improved wall function method was employed. The discretization scheme of convection item and diffusion item are respectively the second-order upwind scheme and the central difference scheme. Tao (2001) shows the details of discretization method. In the light of the geometrical characteristics of computational domain, the geometry scale of different parts of the whole domain differs greatly; the block structure gird method was employed to generate grids of the whole domain being separated into several parts, in which grids were generated by the body-fitted coordinate grid system. Grids are so fine that the numerical results are grid-independent. The computational domains at different crank angles are different, so the grids were generated separately. The boundaryconditions are as the followings:(a) InletThe mass flow rate on each of two inlets is the same and equal to the instantaneous volume change rate multiplied by the density.(b)The outlet is set on the location far away as 5 times of height of discharge port in order to guarantee the constant pressure. The discharge pressure is provided on outlet.(c)Non-slip boundary condition for velocity is provided on walls. Advanced wall function method is employed to tread the near wall domain.3. NUMERRICAL RESULTSIn this paper, 0 is defined as the orbiting discharge crank angle. At the discharge moment, that is the crank angle y=45(x is the discharge crank angle), yis taken as zero. Then, y is changing from 0 to 360 degree during the whole process of discharge. According to this definition, for example, at crank angle of 45 degree after the onset of discharge is described as y=45.In this paper, for the convenience of description, location of the z coordinate equal to zero is define as the inlet of discharge port and is named as the surface of the fixed scroll. Location of the z coordinateequal to h (the height of scroll wrap) is named as the top surface of the fixed scroll.The flow field and its discharge from the central chamber region at several crank angles that correspond to 45, 90,180 degree after the onset of discharge is studied. Flow velocity vectors in different axial sections and three dimensional velocity vectors are detailedly analyzed.3.1 y=45The calculated velocity fields in different axial sections are shown in figure 4 (a)-(c) at orbiting discharge crank angle of 45 degree. The flow velocity in fig.4 indicate that flow being injected in the rear of each half central chamber, being turned as it impinges on the opposing wall of orbiting scroll of fixed scroll and proceeding towards the central region of the central chamber. In the central region, flow enters from both half central chamber, passing through throat region formed by the orbiting and fixed scroll tips and proceeds driven by the inertia. Two large scale vortexes develops in the central region near the scroll tips and some small scale vortexes develops in the rear of central chamber near the outer surface of scroll tips. Compared fig 4 (a), (b) with (c), it is shown that vortex flow develops in all different axial sections and number and scale and location of vortex are different in different axial section. That is to say this basic vortex flow pattern persists in this region throughout the entire axial extent of central chamber. Three dimensional velocity vectorsshown in fig 5 indicate clearly the distribution of axial velocity component. The three dimensional flow tends to move vertically downwards as it approaches the central region of the central chamber which is directly upon the discharge port. The axial velocity component is very large at a small axial distance of 0-10mm from the discharge port (when the height of the profile is 52mm). The axial velocity by the order of magnitude is greater than the radial velocity. In contrast, within the rear region of the central chamber, the flow is essentially two dimensional.From the fig 4 and fig 5, it can be seen that the velocity vectors in the mid axial section characterize the general nature of the flow within the entire central chamber. The flow vectors indicate both the two dimensional and the three dimensional nature of the flow depending upon the location. So, only the velocity vectors in the mid plane are analyzed below.Figure 4 : Velocity fields in different axial sectionsFigure 5: Three dimensional velocity vectors3.2 y=90Similar type of flow calculations have been performed at an intermediate crank angle (2=90). It is shown in fig 6. As the discharge process continues in an actual scroll compressor, the orbiting scroll continues to move away from the fixed scroll. This action is associatedwith a progressively increased opening of the central region to the discharge port. This implies a less occluded opening of the discharge port compared with the throat region at y=45.The velocity vectors in axial sections of mid plane and discharge are different from those at y=45 and the magnitude of velocity reduced. A double vortex was predicted to form at the mid axial section and the scale of the vortexes increased to trend to become a large vortex.Figure 6 : Velocity fields in different axial sections3.3 y=180Figure 7 (a)-(b) shows the velocity vectors in the axial sections at orbiting discharge crank angel of 180 degree. From the figure, it is shown that the velocity vectors field is obviously different from those shown in fig .4 and fig.6. A large scale vortex was developed in the discharge region as the discharge port is opened fully. In addition, a less constrictive flow passage exits on the region of the scroll tips, the velocity magnitude reduces further. The velocity vector field shows the occurrence of some small scale vortexes at the rear region of the central chamber.Figure 7: Velocity field in different axial sections4. NONDIMENSIONAL PRESSURE LOSSES COEFFICIENTTo obtain quantitative data characterizing the pressure losses of the final compression and discharge region, nondimensional pressure losses coefficient was define as below:P is the average pressure in the central chamber, pa; pd is the designed discharge pressure, pa.The variation of pressure losses coefficient * with orbiting discharge crank angel for the whole discharge process under different operation conditions is shown in fig 8. the pressure losses coefficient is very large at orbiting discharge crank angel of 0-60 degree. For example, the losses coefficient at 45 degree of orbiting discharge crank angle is approximately ten times larger than the loss coefficient at 180 degree, indicating that the flow losses are largest at the onset of discharge. This result is not surprising, since this is also the point of maximum constriction of the flow area. Furthermore, the high rotating speed and discharge pressure corroborate that significant flow losses would exist. With increasing the opening discharge port, losses coefficient is decreasing rapidly. The results indicate that discharge flow losses concentrate at the onset of discharge and reduce quickly with increasing opening discharge port.In addition, these results imply that the open-close characteristic of discharge port should be stressed to consider when designing a discharge port, particularly for compressor at large discharge. The easier to open, the better the characteristic of discharge port is. Maximum area of discharge port is possibly not the best.Figure 8: Nondimensional pressure losses coefficient with orbitingdischarge crank angle5: CONCLUSIONSInternational Compressor Engineering Conference at Purdue, July 12-15, 2004Three dimension numerical simulation of the discharge flow in a scroll air compressor was conducted to provide the characteristic of flow field in the final compression and discharge region. Detailed analysis is made of the flow velocity vectors in different axial sections. The numerical results show that complex vortex flow patterns exist in the discharge region, not only in axial sections. On the basis of numerical results, the dismensionless pressure losses coefficient is defined and the pressure losses at various crank angles after onset of discharge is analyzed. It is shown that the discharge flow losses greatly large shortly after the onset of discharge. The results shows that, the easier to open, the better the characteristic of discharge port is. Maximum area of discharge port is possibly not the best.REFFRENCES1.Hirano. T., et al., 1989, Development of High Efficiency ScrollCompressor for Heat Pump Air Conditioners, Mitsubishi Heavy Industries, Ltd., Tech. Rev. V ol. 26, No. 3, p: 512-519.2.Patankar S V, Spalding D B., 1972, A calculation procedure forheat、mass and momentum transfer in three-dimensional parabolicflows, Int. J. Heat Transfer, V ol. 15, No.11, p:1787-1806.3.Wang Yunliang, X u zhong, Miao Yongmiao, 1993, Influence ofDifferent Wall Function Methods on turbulent flow fields, Fluid Engineering, V ol. 21, No. 12, : 26-29.4.Tao Wenquan, 2001, Numrical Heat Transfer (second version),Xi’an Jiaotong University Press, Xi’an, 152p.5.Tao Wenquan, 2001, Advanced Numerical Heat Transfer, SciencePublishing Company, Beijing, 41p.6.Thompson J.F., Warsi Z.U.A., Mastin C.W., 1985, Numerical GridGeneration, Foundation and Application, North-Holland New York.。

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沈青等，《可压缩湍流数值计算研究进展概述》131文章编号: (2009)-13可压缩湍流数值计算研究进展概述沈清1张涵信2庄逢甘31中国航天空气动力技术研究院，北京，1000722中国空气动力研究与发展中心，四川绵阳 6210003中国航天科技集团公司，北京，100037摘要本文简单介绍了可压缩湍流的三种主要数值计算方法DNS、LES、RANS。

然后，介绍了我国近年来可压缩湍流数值计算研究的最新进展。

采用DNS方法，分别计算了Mc=0.5、0.8和1.5的超声速混合层失稳过程。

对于Mc=0.5的超声速混合层，获得了二次失稳的演化过程。

对于Mc=0.8的超声速混合层，模拟了涡结构与小激波的相互作用与三维结构的演化过程。

对于Mc=1.5的超声速混合层，模拟了不同频率下出现的三种声辐射涡模态。

对于圆锥小攻角高超声速边界层的稳定性问题，采用DNS方法模拟了边界层失稳的攻角效应，发现了多波干涉失稳现象。

采用LES方法，模拟了超燃冲压发动机进气道内的激波-边界层干扰流动。

采用新型转捩/湍流一体模型，模拟了圆锥高超声速边界层转捩和完全发展湍流流动。

针对高超声速湍流中假设湍流Pr数等于0.9的疑问，探索了一种修正思路，取得了对B-L湍流模式在气动热计算精度上提高的结果。

关键词：可压缩湍流；数值计算；边界层；混合层0 引言可压缩湍流问题来源于航天飞行器的高超声速边界层和超声速混合层流动，具有多尺度、高频脉动、强非线性等特点，实验和计算都十分困难。

面对不同时期航天飞行器发展的需要，自上世纪六十年代起，国外先后在常规风洞、静风洞中开展了圆锥、球钝锥和平板高超声速边界层稳定性和转捩研究，在双喷管试验设备上开展了超声速混合层稳定性的研究。

通过大量的研究，人们对这些问题取得了丰富的认识，但是并没有完全解决这些可压缩湍流问题。

随着计算理论、计算方法和计算机技术的发展，数值计算已成为解决湍流问题的重要研究手段。

直接数值模拟（DNS）、大涡模拟（LES）和基于雷诺平均NS方程的湍流模式计算（RANS）是三种主要的湍流流动计算方法。

鱼类群体运动的元胞自动机模型中的最小势能原理

生物的群体运动是一种个体间协同相互作用的结果, 群体中个体的信息传递对群体运动状态起到重要作用[10]. Gueron 和 Couzin 等研究发现, 群体信息在群体间是通过逐层传递的, 个体的行为决策
6期
陆兴远等: 鱼类群体运动的元胞自动机模型中的最小势能原理
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会受到相邻个体的影响[11−12]. 群体中个体间交互协同的思想为智能机器人集群的自动控制提供了理论基础. 例如, Li 等受到生物系统的启发, 发明了群体颗粒机器人. 虽然每个个体的运动是单一随机的运动, 但通过整个群体的协同, 机器人群体可以朝着指定的激励源方向移动[13], 雷斌受生物群体行为启发. 应用仿生方法研究群体机器人的编队控制, 目标搜索, 实现群体机器人间的协同控制[14].
视觉是动物的共性, 其对生物的群体行为和个体决策有着重要的影响. 视觉影响个体感知周围环境, 是个体获取信息的重要方式. 研究表明, 环境变化、邻居数量和邻居行为等都会影响个体行为决策[19]. Ballerini 等研究发现个体在群体中与其他个体交流时并不是与整个群体交流, 而是与其中的 6~7 个邻居交流[20]. 本研究假设个体的视觉为有限且不变的常值. 如图 1 所示, Ri 为个体的视觉距离; 以 θi 为圆锥半角的圆锥体区域为个体的视角范围, 圆锥体以外的区域为个体的盲区. 在本模型中, 个体只会把在其视觉范围之内距离其最近的 N 个邻居作为参考邻居, 而不是整个鱼群. 个体在选择参考邻居
在之前的研究中, 研究人员大多在二维的假设条件下对群体运动进行研究, 鲜有在三维的条件下研究群体运动, 这与真实的群体状态不符, 并且之前的研究者提出的模型大多比较复杂. 本研究构建了一个基于元胞自动机方法和最小势能原理的简洁三维模型, 并通过数值模拟研究势能在鱼类群体中运动决策和个体间相互协同的作用以及对鱼群在有限空间中形成旋转运动状态的群体机制的影响.

基于涡环栅格法的三体船斜拖水动力数值分析

基于涡环栅格法的三体船斜拖水动力数值分析王鸿东;易宏;余平【摘要】以三体船的操纵性能预报为背景,基于势流理论的三维面元法,对三体船的斜拖运动进行数值模拟,并求得相应的水动力系数.将传统的运用于机翼升力计算的涡环栅格法(VLM)运用于三体船斜拖运动的数值模拟,船体表面被离散成四边形的网格,网格及尾涡面上布置一个涡环,利用船体表面不可穿透条件以及尾缘处的库塔条件对各单元涡强进行求解,求得各个分布点压强以及船体表面压力分布,并根据压力分布积分求得在不同漂角下三体船舶所受的横向力以及转首力矩.最终由计算结果,求得与漂角相关的水动力系数,并与软件计算结果进行对比分析.%The maneuverability of trimaran is set as the background of this paper. Based on the 3D panel method of po-tential flow theory, the oblique towing motion of trimaran is stimulated, and the hydrodynamic derivatives is calculated. Vor-tex lattice method (VLM), which is traditionally used to calculate the lift force of wings, is used for the numerical stimula-tion of trimaran oblique towing motion. Ship hull is derived into many quadrilateral panels, and vortex lattice is placed in every panels and trailing vortex plane. By unpenetrated condition of the hull and Kutta Condition in the trailing edge, the vorticity of every panel could be calculated, and the displacement of pressure on the hull surface could be obtained. Then the lateral force and moment around Z direction could be obtained. By the obtained result, the hydrodynamic derivatives which is related with the drift angle could be calculated, and be used for comparison with the hydrodynamic derivatives which is cal-culated by software.【期刊名称】《舰船科学技术》【年(卷),期】2018(040)004【总页数】5页(P22-26)【关键词】三体船;操纵性;涡环栅格法;横向力;转首力矩【作者】王鸿东;易宏;余平【作者单位】上海交通大学海洋工程国家重点实验室,上海 200240;上海交通大学海洋工程国家重点实验室,上海 200240;上海交通大学海洋工程国家重点实验室,上海 200240【正文语种】中文【中图分类】U661.10 引言三体船是近年来发展迅猛的船型，它是一种高性能船，由1个中体和2个片体组成，相比于普通船型，拥有优良的阻力性能和耐波性能，优秀的稳性，较大的甲板面积，以及可以大型化的特点。

数值模拟方法范文

数值模拟方法范文数值模拟方法（Numerical simulation methods）是指通过数学模型和计算机技术，将实际问题转化为数值计算问题来进行模拟和分析的方法。

数值模拟方法在科学研究、工程设计、天气预报、地震预警、流体力学等领域都有广泛的应用。

下面将详细介绍数值模拟方法的基本原理和常见的应用案例。

首先，建立数学模型是数值模拟的基础。

通过对所研究问题的物理规律进行数学表达，得到偏微分方程或者代数方程组。

常见的数学模型有常微分方程、偏微分方程、代数方程等。

其次，对数学模型进行离散化处理。

将连续问题转化为离散问题，通过将求解区域划分成若干网格节点，确定离散点的坐标和相应的求解函数。

常见的离散化方法有有限差分法、有限元法、谱方法等。

然后，求解数值解是数值模拟的核心。

使用数值计算方法，将离散化得到的方程组转化为代数方程组，通过迭代求解方法得到数值解。

常见的求解方法有迭代法、直接法、迭代与直接法结合的方法等。

最后，分析和验证数值解。

对得到的数值解进行误差分析、收敛性分析等，验证数值解的可靠性和精确性。

常见的分析和验证方法有误差估计、收敛性证明、边界效应分析等。

数值模拟方法在科学研究和工程设计中有着广泛的应用。

例如在天气预报中，通过建立大气数学模型，离散化处理并求解方程组，可以得到未来一段时间的天气预报结果。

在地震预警中，通过对地壳运动和地震波传播的数学建模，可以模拟和分析地震过程，预测地震后的影响和灾害程度，为地震预警提供依据。

在工程设计中，数值模拟方法可以帮助优化设计参数，减少实验成本和时间。

例如在飞机设计中，通过对流体力学问题进行数值模拟，可以优化机身外形，降低阻力，提高飞行性能。

在汽车设计中，通过对车辆的碰撞过程进行数值模拟，可以预测并减少碰撞所造成的伤害。

此外，数值模拟方法还在材料科学、核能工程、市场预测等方面有广泛的应用。

例如在材料科学中，通过数值模拟方法可以研究材料的力学性能、材料的热传导性能等。

温度场三维模拟,附matlab程序

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Since the ﬁber length is much larger than the ﬁber cross section, the capability of heat dissipation from the ﬁber end facet is a lot lower than that from the ﬁber side. Therefore the transverse temperature distributions in the DCF at room temperature are gov-
© 2010 Elsevier GmbH. All rights reserved.
1. Introduction
high-power ﬁber lasers are now mature products and have numerous applications in medical, military, industrial processing and modern telecommunication because of some unique advantages including high conversion efﬁciency, excellent beam quality, less thermal effect, small volume and weight, etc. [1–3]. In the continuous-wave (cw) regim, Yb-doped double-clad ﬁber laser (DCFL) with an output power of 1.36 kW has been reported by using large mode area (LMA) ﬁbers [3]. Although the thermal effects can be ignored in low-power ﬁber lasers, the heat dissipation is an important feature and affects laser performance in kilowatt power domain [4,5]. So the thermal effect in high-power ﬁber laser attracted much attention recently [6,7]. However, few investigations focus on the evolution of the temperature and the inﬂuence of the inner-clad shape. In this paper, a theoretical and numerical analysis of 3D temperature ﬁeld is investigated by solving the transient heat conduction equation.

Three-dimensional numerical simulation of a mechanized twin tunnels in soft ground

Three-dimensional numerical simulation of a mechanized twin tunnels in softgroundNgoc-Anh Do a ,d ,Daniel Dias b ,⇑,Pierpaolo Oreste c ,Irini Djeran-Maigre aaUniversity of Lyon,INSA of Lyon,Laboratory LGCIE,Villeurbanne,France bGrenoble Alpes University,Laboratory LTHE,Grenoble,France cPolitecnico of Torino,Department of Environmental,Land and Infrastructural Engineering,Italy dHanoi University of Mining and Geology,Department of Underground and Mining Construction,Faculty of Civil Engineering,Hanoi,Viet Nama r t i c l e i n f o Article history:Received 8April 2013Received in revised form 15January 2014Accepted 2February 2014Available online 25February 2014Keywords:Numerical modelling Twin tunnelSegmental lining Lining response Settlementa b s t r a c tThe increase in transportation in large cities makes it necessary to construct of twin tunnels at shallow depths.Thus,the prediction of the inﬂuence of a new tunnel construction on an already existing one plays a key role in the optimal design and construction of close parallel shield tunnels in order to avoid any damage to the existing tunnel during and after excavation of the new tunnel.Most of the reported cases in the literature on parallel mechanized excavation of twin tunnels have focused on the effects of the ground condition,tunnel size,tunnel depth,surface loads,and relative posi-tion between the two tunnels on tunnel behaviour.The numerical investigation performed in this study,using the FLAC 3D ﬁnite difference element programme,has made it possible to include the inﬂuence of the construction process between the two tunnels.The structural forces induced in both tunnels and the development of the displacement ﬁeld in the surrounding ground have been highlighted.The results of the numerical analysis have indicated a great impact of a new tunnel construction on an existing tunnel.The inﬂuence of the lagged distance between the two tunnels faces has also been high-lighted.Generally,the simultaneous excavation of twin tunnels causes smaller structural forces and lin-ing displacements than those induced in the case of twin tunnels excavated at a large lagged distance.However,the simultaneous excavation of twin tunnels could result in a higher settlement above the two tunnels.Ó2014Elsevier Ltd.All rights reserved.1.IntroductionIn recent years,many tunnels have been built in urban environ-ments;this often involves the construction of twin tunnels in close proximity to each other.In addition,in many cases,the new tunnel is often excavated adjacent to an already existing one.Thus,the prediction of the inﬂuence of new shield tunnel construction on the existing tunnel plays a key role in the optimal design and construction of close parallel shield tunnels in order to avoid any damage to the existing tunnel during and after excavation of the new tunnel.Interactions between closely-spaced tunnels were studied in the past using a variety of approaches:physical model testing,ﬁeld observations,empirical/analytical methods and ﬁnite element modelling.Kim et al.(1996,1998)performed physical tests to investigate the response of the ﬁrst tunnel lining on the approaching of the second shield.The results of their model tests showed that the interaction effects are greater in the spring line and crown of the existing tunnel.Chapman et al.(2007)described results from a series of small-scale (1/50)laboratory model tests carried out in a kaolin clay which focused on studying the short-term ground movements associated with closely spaced multiple tunnels.The inﬂuence of tunnel distance,tunnel depth and tunnel number were highlighted.The results showed asymmetrical settlement troughs,greater settlement above the second of the twin tunnels con-structed.Their study also demonstrated that the commonly used semi-empirical method to predict the short-term settlement above twin tunnels,using the summation of Gaussian curves,can give inaccurate results.In the study by Choi and Lee (2010),the inﬂu-ence of the size of an existing tunnel,the distance between tunnel centres and the lateral earth pressure factor on mechanical behav-iour of the existing and new tunnels was investigated by quantify-ing the displacement and crack propagation during the excavation/10.1016/j.tust.2014.02.0010886-7798/Ó2014Elsevier Ltd.All rights reserved.⇑Corresponding author.Tel.:+33476635135;fax:+33476825286.E-mail address:daniel.dias@ujf-grenoble.fr (D.Dias).of a new tunnel constructed near an existing tunnel.A series of experimental model tests was performed and analysed.It was found that the displacements decreased and stabilized as the dis-tance between the tunnel centres increased,depending on the size of the existing tunnel.Suwansawat and Einstein(2007)introduced interestingﬁeld measurement results on ground movements induced by parallel EPB tunnels excavated in soft ground in Bangkok.They showed that the operational parameters,such as face pressure,penetration rate,grouting pressure andﬁlling,have signiﬁcant effects on the maximum settlement and extent of the settlement trough.They also showed that the maximum settlement for twin tunnels is not usually located over the midpoint between the two tunnels and that the settlement trough is often asymmetric.Chen et al.(2011)presentedﬁeld measurements conducted on parallel tunnels using EPB shields in silty soil.Their results showed a great dependence of the ground movements on the distance be-tween the second tunnel face and the monitored section.They also indicated that the two settlement troughs caused by the construc-tion of theﬁrst and the second tunnel had similar shapes.However, the second tunnel trough was shallower and wider than that of the ﬁrst tunnel.Theﬁrst tunnel made the symmetric axis of theﬁnal trough of the parallel tunnels incline towards theﬁrst tunnel.In the study by Ocak(2012),thirty longitudinal monitoring sections, obtained through EPB tunnelling,were used to determine the interactions of the longitudinal surface settlement proﬁles in shal-low twin tunnels.He et al.(2012)carried outﬁeld and model tests, based on Chengdu Metro Line1in China,to study the surface set-tlement caused by twin parallel shield tunnelling in sandy cobble strata.The surface settlement mechanism and the effect of tunnel distance on the surface settlement were also studied using the dis-crete element method(DEM).They showed that when the spacing between two tunnels is higher than twice the tunnel diameter,an independent collapsed arch can form.However,in any of the above studies,the resulting structural forces induced in the tunnel lining were not mentioned.Field observations remain the key to understanding the interac-tion between adjacent tunnels.Unfortunately,however,ﬁeld data are often incomplete.It is clear that model testing can only be used to study limited interaction behaviour.Empirical and analytical methods,using the superposition technique(e.g.Wang et al., 2003;Hunt,2005;Suwansawat and Einstein,2007;Yang and Wang,2011),have been used on the basis of the prediction of each individual excavation in order to obtain theﬁnal accumulated set-tlement trough.Generally,superposition method cannot take into account rigorously the effect of an existing tunnel and the repeated unloading of the ground caused by the previous excavation of the ﬁrst tunnel and,therefore,the settlement curves do not represent theﬁnal displacement very well(Divall et al.,2012).Furthermore, empirical and analytical methods also introduce drawbacks for those cases in which complex geological conditions(e.g.multilayer strata)are expected.The use of aﬁnite element model seems to be a promising way of addressing this issue.Leca(1989),Addenbrooke and Potts(1996),Yamaguchi et al. (1998),Sagaseta et al.(1999),Hefny et al.(2004),Ng et al. (2004),Karakus et al.(2007),Hage Chehade and Shahrour(2008), Aﬁﬁpour et al.(2011),Chakeri et al.(2011),Ercelebi et al.(2011), Mirhabibi and Soroush(2012),Hasanpour et al.(2012)have all car-ried out numerical analysis of this interaction problem.Most of these studies focused on considering the effect of the ground con-dition,tunnel size,tunnel depth,surface loads,and relative posi-tion between two tunnels on the surface settlement.Their results were similar in that the inﬂuence of the second tunnel on the pre-viously installed lining of theﬁrst one has been shown to depend on the relative position of the tunnel and on the spacing between the two tunnels.The literature reviewed above clearly indicates that an exten-sive amount of research has been conducted on tunnel interactions between parallel tunnels.Most of this research has focused on the inﬂuence of twin tunnels on ground deformation.However,less work has been devoted to the inﬂuence of the interaction between tunnels on the structural forces induced in a tunnel lining.Ng et al.(2004)performed a series of three dimensional(3D) numerical simulations to investigate the interactions between two parallel noncircular tunnels constructed using the new Austrian tunnelling method(NATM).Special attention was paid to the inﬂuence of the lagged distance between the excavated faces of the twin tunnels(L F)and the load-transfer mechanism between the two tunnels.It was found that L F has a greater inﬂuence on the horizontal movement than on the vertical movement of each tunnel and that the magnitude of the maximum settlement is inde-pendent of L F.They showed that the distributions of the bending moment induced in the tunnel lining are similar in shape,but different in magnitude in the two tunnels.In the study by Liu et al.(2008),the effect of tunnelling on the existing support system(i.e.shotcrete lining and rock bolts)of an adjacent tunnel was investigated through full3Dﬁnite element calculations,coupled with an elasto-plastic material model.It was concluded that the driving of a new tunnel signiﬁcantly af-fects the existing support system when the advancing tunnel face passes the existing support system and has less effect when the face is far from the system.It was also pointed out that the effects of tunnelling on the existing support system depend to a great extent on the relative position between the existing and new tunnels.In order to investigate the inﬂuence of new shield tunnel exca-vation on the internal forces and deformations in the lining of an existing tunnel,Li et al.(2010)presented a series of3D numerical simulations of the interaction between two parallel shield tunnels and parametric analyses.Unfortunately,the existence of the joints in the segmental lining,the construction loads induced during shield tunnelling,such as face pressure,jacking force, grouting pressure,were not simulated in this numerical model. The impact of the new tunnel excavation on the existing tunnel during the advancement of the new tunnel was not considered either.The purpose of a numerical mechanized tunnelling(TBM) model is to take into consideration the large number of processes that take place during tunnel excavation.In order to conduct a rigorous analysis,a3D numerical model should be used.Obviously, there is not a full3D numerical simulation for mechanized twin tunnels in soft ground that allows both ground displacement and structural lining forces to be taken into consideration.The main purpose of this study was to provide a full3D model which would allow the behaviour of the interaction of mechanized twin tunnels to be evaluated,in terms of structural forces induced in the tunnel lining and ground displacement surrounding the two tunnels.Most of the main elements of a mechanized excavation can be simulated in this model:the conical geometry of the shield, the face pressure,the circumferential pressure acting on the cylin-drical surface of the excavated ground in the working chamber be-hind the tunnel face,the circumferential pressure caused by the migration of the grout acting on the excavated ground at the shield tail,the grouting pressure acting simultaneously on the excavated ground and on the tunnel structure behind the shield tail,progres-sive hardening of the grout,the jacking force,the weight of the shield machine,the weight of the back-up train behind the shield machine and the lining joint pattern,including the segment joints, the ring joints and their connection condition.The CYsoil model, which is a strain hardening constitutive model,has been adopted. The Bologna–Florence high speed railway line has been adopted in this study as a reference case.N.-A.Do et al./Tunnelling and Underground Space Technology42(2014)40–51412.Numerical model2.1.Three-dimensional numerical modelThe numerical model,the 3D simulation procedure of a single tunnel and the parameter calibration of the CY soil model were described in Do et al.(2013a).Therefore,only a short overview is given here.However,the numerical model introduced by Do et al.(2013a)has been improved and some other components of the tunnelling process have been simulated in the present study.It includes the weight of the shield machine and the weight of the back-up train behind the shield machine.The tunnel construction process is modelled using a step-by-step approach.Each excavation step corresponds to an advance-ment of the tunnel face of 1.5m,which is equal to the width of a lining ring.A schematic view of the present model is provided in Fig.1.Face pressure has been estimated depending on the horizontal stress induced in the ground in front of the tunnel face (Mollon et al.,2013).This face pressure has been modelled by applying a pressure distribution to the excavation face using a trapezoidal proﬁle in order to account for the slurry density.Owing a slight overcutting,a possible slurry migration could occur over a short distance behind the cutting wheel.Therefore,in addition to the pressure acting on the tunnel face,a pressure,caused by the slurry solution,has also been applied to the cylindrical surface just be-hind the tunnel face.The shield machine has been simulated using ‘‘ﬁctive’’shield introduced by Mollon et al.(2013),Dias et al.(2000)and Jenck and Dias (2004).The geometrical parameters of the shield are presented in Fig.1.The self-weight of the shield is simulated through the vertical loads acting on the grid points of the ground mesh at the tunnel bottom region over an assumed range of 90°in the cross-section and over the whole shield length,as can be seen in Figs.1and 2.In this study,a shield weight value of 6000kN,which refers to a tunnel diameter of 9.4m (JSCE,1996),has been adopted.The distribution of the jacking force has been assumed to be lin-ear over the height of the tunnel.The jacking forces were set on each segment,considering three plates located at 1/6,1/2,and 5/6of the segment length.A total jacking force of about 40MN was adopted in the present model on the basis of the theoretical method proposed by Rijke (2006).The grouting action is modelled in two phases:(1)the liquid state (state 1)represented by a certain pressure acting on theground surface and on the tunnel lining;(2)the solid state (state 2).The distributional radial pressure has been used to simulate this kind of pressure.The grouting pressure has been estimated depending on the ground overburden pressure at the crown of each tunnel (Mollon et al.,2013).The grout was simulated by adopting a uniform pressure which was applied to both the cylin-drical surface of the excavated ground and the external surface of the tunnel lining.As for the face pressure,the annular void be-tween the outside surface of the shield and the excavated ground made the migration of some grout towards the shield possible.This migration was simulated by means of a triangular pressure over the length of one ring (1.5m).The grout was assumed to harden beyond this length and was simulated by means of volume ele-ments with perfect elastic behaviour,and with the elastic charac-teristics E grout =10MPa and m grout =0.22(Mollon et al.,2013).In the present model,the tunnel segments have been modelled using a linear-elastic embedded liner element.The segment joints have been simulated using double node connections.The stiffness characteristics of the joint connection have been represented by a set composed of a rotational spring (K h ),an axial spring (K A )and a radial spring (K R )(Do et al.,2013a,2013b ).In the same way as for the segment joint,the ring joint has also been simulated using double connections.In this study,the rigidity characteristics of the ring joint connection have been represented by a set composed of a rotational spring (K h R ),an axial spring (K AR )and a radial spring (K RR ).The interaction mechanism of each spring is the same as that applied for a segment joint.Once the TBM back-up train enters the excavated tunnels dur-ing the excavation process,it is necessary to take its self-weight into consideration.In a study performed by Lambrughi et al.F a c e p r e s s u r eShieldCutting wheelSegmental liningFresh groutHardened groutGrouting pressure Jacking force1.5m 1.5m7.5m1.5m1.5m1.5cm2.5cm 12.5cm9.1mShield weightBack-up train weightyout of the proposed TBM model (not scaled).42N.-A.Do et al./Tunnelling and Underground Space Technology 42(2014)40–51(2012),this weight was simulated by artiﬁcially increasing the density value of the concrete lining.Kasper and Meschke(2004, 2006)instead modelled the back-up train using an assumed load-ing scheme along the tunnel axis.In the present study,a total weight of3980kN for the back-up train has been simulated through the distribution loads which act on the lining elements at the tunnel bottom region over an assumed angle of90°in the cross-section and over a tunnel length of72m behind the shield tail(Kasper and Meschke,2004)(see Fig.1).2.2.Simulation procedure of mechanized twin tunnelsThe twin tunnel excavation sequence was modelled as follows: (i)excavation of theﬁrst tunnel(left);(ii)excavation of the second tunnel(right)with a lagged distance L F behind the face of theﬁrst tunnel.The plan view and typical cross section of the twin tunnel excavation procedure is illustrated in Figs.3and4.In this work,two different lagged distances(i.e.,L F=0D and 10D)that correspond to L F=0and7.875L S,in which L S is the shield length(L S=12m in the present model),between the tunnel on the left and the one on the right have been adopted and analysed.The case of L F=0D corresponds to the situation in which two tunnel faces are excavated simultaneously in parallel.The case of L F=10D means that the second(new)tunnel is excavated when the lining structure behaviour and ground displacement caused by theﬁrst(existing)tunnel excavation appear to have reached a steady state.The latter case usually occurs in reality.The twin tun-nels in the Bologna–Florence railway line project presented in this paper is a typical example.In fact,the distance between the two tunnels in the Bologna–Florence railway line project is15m (Croce,2011).However,in order to highlight the inﬂuence of the excavation process of a new tunnel on an existing tunnel,a dis-tance from centre to centre of11.75m(1.25D)has been adopted in this study.A full model of the twin tunnels considering a height of60m and a width of131.75m has been adopted.The mesh length of the model is equal to120m.The nodes at all the sides of the model wereﬁxed in the horizontal directions on the x–z and y–z planes (i.e.y=0,y=120,x=À71.75and x=60),while the nodes at the base of the model(z=À40)wereﬁxed in the vertical(z)direction. The perspective view of the developed numerical model,which is composed of around1,100,000grid points and900,000zones,is presented in Fig.5.The positions of the segment joints in each ring are presented in Table1.Finally,it should be mentioned that the average time nec-essary for one calculation is approximately340h when a2.67GHz core i7CPU ram24G computer is used.3.Numerical results and discussionIn order to understand the behaviour of twin tunnels during the excavation process of the new tunnel(right),this section presents variations in the structural lining forces induced in the existingMeasured ring (30) First tunnel (left)Second tunnel (right)Tunnel faceY MSTunnelling directionyx ShieldSegmental lining BL FL SL S ShieldFig.3.Plan view of the twin tunnels(not scaled).Fig.5.Perspective view of the developed numerical model introduced into FLAC3D.N.-A.Do et al./Tunnelling and Underground Space Technology42(2014)40–5143the ground displacement duringstructural forces in the newbeen extracted at the sectionwhich hereafter is called the measured negligible at this section.In Figs.7–9,11and13,and Table2,the Y MS value presents the distance from the new tunnel face(right) to the measured section.In Figs.10,12and14,and Table3,the Y FT value presents the distance from the faces of the two tunnels, which are excavated simultaneously,to the measured section.In Tables2–4,the R values present the ratios between the results ob-tained in the case of twin tunnels with L F=0D or10D and the cor-responding one obtained in the case of a single tunnel.The inﬂuence of the tunnel length advancement on the mea-sured lining ring(ring30)has been evaluated for a single tunnel, which corresponds to the tunnel construction on the left before interacting with the tunnel on the right,considering the instanta-neous variation in structural forces between two successive steps (Do et al.,2013a).The numerical results show that the instanta-neous variation in the structural force induced in the measured lin-ing ring between two excavation steps,which correspond to the installation of rings54and55,is approximately zero.This means that the structural forces determined at this excavation step canRing 1Ring 2Fig.6.Considered lining models.Table1Location of the segment joints in a ring h(degree)(measured counter clockwise fromthe right spring line)(see Fig.6).Joint location0;60;120;30;90;Fig.7.Surface settlements above the twin tunnels.44N.-A.Do et al./Tunnelling and Underground Space Technology42(2014)40–51Fig.7a shows the development of the surface settlement trough in the transverse section during the face advancement of the new tunnel on the right in the case of L F =10D.This ﬁgure shows that the twin tunnels cause an increase in the surface settlement.This could be explained by the accumulated loss of the ground in both two tunnels.In the considered case,the maximum settlementmeasured above the twin tunnels is 47.4%higher than that devel-oped above a single tunnel.In addition,the settlement proﬁle is asymmetric.This means that the maximum settlement is not located over the mid-point between the two tunnels.During the new tunnel advancement (right),the settlement trough shifts gradually from the left to the right.An asymmetric proﬁle of the settlement trough has also been observed through ﬁeld measure-ments obtained at shield tunnelling sites (Suwansawat and Einstein,2007;Chen et al.,2011),analytical results using the superposition technique (Suwansawat and Einstein,2007)and laboratory model tests (Chapman et al.,2006;2007).Fig.7b shows that the two settlement troughs caused by the construction of the tunnels on the left and right have a similar shape.The settlement trough above the new tunnel (right)is deter-mined on the basic of the ﬁnal settlement trough of the twin tun-nels minus the one developed above the existing tunnel (left)before it interacts with the new tunnel.However,the settlement trough caused by the excavation of the new tunnel is shallower and wider than the one caused by the existing tunnel.These con-clusions are in good agreement with ﬁeld observations made by Chen et al.(2011),and He et al.(2012)during the excavation of twin tunnels through respectively silty and sandy soil.The volume loss ratios,determined at the ﬁnal state as the ratio of settlement trough area developed on the ground surface to the cross-section area of the tunnel,of the existing tunnel and new tunnel are sim-ilar and equal to about 0.92%and 0.79%,respectively,and the total volume loss above the twin tunnels is equal to 1.71%.Above result are however different from the laboratory results obtained from the work of Chapman et al.(2007)conducted in clay.Their work showed a greater settlement above the second tunnel.This differ-ence could be attributed to the inﬂuence of the soil type or due to the undrained behaviour of soils.Fig.7b also presents a comparison of the ﬁnal settlement troughs for the different construction procedures (L F =0D and 10D).The maximum settlement above the twin tunnels of about 43.8mm (0.47%D)(Table 4)and the volume loss ratio of 1.81%are observed in the L F =0D case.These results are 109%and 106%higher than the corresponding ones for the L F =10D case.However,the widths of the settlement troughs are similar in both cases.InFig.8.Horizontal displacements between the twin tunnels,for the L F =10D case.Fig.9.Normal displacement in measured lining ring 30of the existing (left)tunnel,for the L F =10D case.displacement in measured lining ring 30of the tunnel case.Space Technology 42(2014)40–5145addition,as expected for the L F=0D case,the settlement troughs that develop during tunnel face advancement are always symmet-rical over the two tunnels.3.2.Horizontal ground displacementThe variations in the horizontal displacement along the PC axis, which is located at the centreline of the two tunnels,during the advancement of the single tunnel on the left are shown in Fig.8a.First,the soil mass between the tunnel crown and the in-vert moves outwards due to the thrust effects of the face pressure in the working chamber.Then,the ground moves toward the tun-nel,due to the convergence displacement over the length of shield. The ground again moves outward at the shield tail,due to the ac-tion of the grouting pressure.These outward movements continue until the steady state is reached because of the grout consolidation and the low value of lateral earth pressure factor(K0=0.5).The maximum horizontal displacement is about6.0mm(0.064%D)at the ground surface.Fig.8b presents the effect of the advancement of the new tunnel on the right on the lateral displacement of the ground between the two tunnels.When the face of the new tunnel approaches theNormal force and longitudinal force of the existing(left)tunnel lining during the advancement of the new(right)tunnel,for force and longitudinal force of the tunnel lining on the left during the simultaneous advancement of the double tunnel faces, 46N.-A.Do et al./Tunnelling and Underground Space Technology42(2014)40–51measured section,a soil mass movement towards the new tunnel caused by the convergence displacement along the length of the shield of the new tunnel is observed.These movements,whichreach a peak value towards the new tunnel,correspond to the mo-ment in which the shield tail of the new tunnel passes over the measured section (see line Y MS =1.3D from the measured section in Fig.8b).When the shield in the new tunnel passes over the mea-sured section,a ground movement towards the existing tunnel on the left can be observed due to the action of the grouting pressure,the grout consolidation,and the low lateral earth pressure factor value (K 0=0.5).The horizontal displacements at the measured sec-tion appear to have reached a steady state when the face of the new tunnel passes over the measured section at about 49.5m,which corresponds to an Y MS value of 5.3D.It is necessary to mentioned that,compared to a corresponding 8.05mm (0.86%D)inward movement at the spring line of a single tunnel (see the ‘‘single tunnel on the left’’line in Fig.8b),the twin tunnel construction results in a 42%reduction in lateral movement at the PC axis between the two tunnels.At the ﬁnal state,the dis-placement of the soil mass zone below the tunnel base is almost zero.On the basis of the above analyses on the surface settlement and lateral displacement,it is reasonable to conclude that,in the region between the two tunnels,the soil mass is subject to more vertical settlements and less horizontal displacements than a sin-gle tunnel.The same conclusion can be found through ﬁeld obser-vations obtained at a shield tunnelling site (see for example,Chen et al.,2011).For the case of the faces of two tunnels advancing simulta-neously (L F =0D),as expected,the lateral displacements between the two tunnels are equal to zero.Bending moment in measured lining ring 30of the existing 10D case.Table 2Development of the structural forces and deformation in measured ring 30of the existing tunnel (left)and surface settlement during the new tunnel advancement (right)(for the L F =10D case).ParametersSingle tunnel Distance Y MS (m)Tunnel on the right –À1D 0 1.3D 3D 4.5D 5.3D –Max.pos.bending moment (kN m/m)71.982.2162.8348.1343.9347.2348.165.8R M+(%)100.0114.2226.2483.8478.0482.5483.891.5Min.neg.bending moment (kN m/m)À93.8À107.4À279.5À498.1À481.6À481.2À480.6À89.9R M À(%)100.0114.5297.8530.7513.1512.8512.095.8Max.normal force (kN/m)14901598209618591948193119271491R N (%)100.0107.2140.7124.8130.8129.6129.3100.1Max.longitudinal force (kN/m)17451966186117191736180917981667R LN (%)100.0112.7106.698.599.5103.6103.095.5Max.normal displacement (mm) 5.69 6.729.2813.1814.3315.0915.42 5.24R disp+(%)100.0118.2163.1231.8252.0265.3271.292.1Min.normal displacement (mm)À2.78À3.40À5.80À9.86À9.00À8.70À8.65À2.51R disp À(%)100.0122.2208.6354.5323.8312.9310.890.1Max.settlement (mm)À27.4À28.6À31.3À36.4À39.0À39.9À40.3–R set (%)100.0104.4114.5133.0142.6145.9147.4–Table 3Development of the structural forces and deformation in measured ring 30of the tunnel on the left and surface settlement during the simultaneous advancement of twin tunnels (for the L F =0D case).ParametersSingle tunnel Distance Y FT (m)–1.3D2.55D3.8D 5.3D Max.pos.bending moment (kN m/m)71.919.1101.3108.9109.9R M+(%)100.026.5140.8151.3152.7Min.neg.bending moment (kN m/m)À93.8À15.0À85.1À95.6À97.4R M À(%)100.016.090.6101.8103.8Max.normal force (kN/m)14901669171517261730R N (%)100.0112.0115.1115.9116.1Max.longitudinal force (kN/m)17452081165219132057R LN (%)100.0119.294.7109.6117.8Max.normal displacement (mm) 5.69 1.77 6.428.649.39R disp+(%)100.031.2112.9151.9165.1Min.normal displacement (mm)À2.78À0.22À3.34À4.41À4.74R disp À(%)100.08.1120.0158.4170.6Max.settlement (mm)À27.4À33.4À40.4À42.8À43.8R set (%)100121.9147.4156.2159.9N.-A.Do et al./Tunnelling and Underground Space Technology 42(2014)40–5147。

空冷汽轮机末两级变工况三维流动的数值模拟_綦蕾

第25卷第5期 2005年10月动力工程Vol.25No.5 Oc t.2005文章编号:1000 6761(2005)05 0647 05空冷汽轮机末两级变工况三维流动的数值模拟綦蕾1, 邹正平1, 陆宏志2, 于尔亮3, 田东强3, 师黎明3(1.北京航空航天大学气动热力重点实验室,北京100083;2.香港理工大学机械学系,香港;3.北京北重汽轮电机有限责任公司,北京100040)摘要:采用三维粘性数值模拟方法对变工况下空冷汽轮机末两级流动进行了模拟,研究了效率和脱流高度等重要参数的变化规律,着重分析了设计点和小容积流量工况时的三维流场。

通过分析了解了机组在变工况运行时末级流动的特点,为空冷汽轮机末级叫片的设计和优化提供了依据。

图8参5关键词:动力机械工程;空冷汽轮机;末级叶片;变工况;数值模拟中图分类号:V221 文献标识码:ANumerical Simulation of 3 Dimensional Flow in Last TwoStages of Air cooled Steam TurbinesQI Lei , ZOU Zhen ping 1, LU Hong zhi 2, YU Er liang 3, TI AN Dong qiang 3, SHI Li ming 3(1.National Key Lab.Of Aero Thermodynamics,Beijing University of Aeronautics and Astronautics,Beijing 100083,China;2.Department of Mechanical Engineering,Hongkong Polytechnic University,Hongkong,China;3.Beijing Beizhong Steam Turbine Generator Co.Ltd.,Beijing 100040,China)Abstract :Flow in last two stages of air cooled stea m turbines under varying load conditions is being studied with the help of numerical 3 dimensional viscous flow simulation methods.The laws that govern variations,like efficiency and blade s height,at which flow separation occurs,are being studied;specially analyzed in detail were the 3 dimensional flo w fields under design and low volume flow c onditions.Understanding of the particularities of flow conditions in the last stages under varying turbine load conditions are gained by an analysis,whic h may serve as a reference for design and optimization of the last stage blades of air cooled steam turbines.Figs 8and refs 5.Key words :power and machanical engineering;air cooled steam turbine;last stage blade;varying load;numerical simulation收稿日期:2005 01 10 修订日期:2005 04 31作者简介:綦蕾(1981 ),女,湖南株洲人,北京航空航天大学能源与动力工程学院博士生,从事叶轮机内部非定常流动研究。

结构与非结构网格之间的转换及应用

Applications Of Transformation Of Structured ToUnstructured MeshesLiu Jing1, 2，Zhang Min1，John C. Chai2，Xu Bin11School of Power Eng.，Nanjing University of Science & Technology，Nanjing (210094)2School of Mechanical and Aero spacing Eng.，Nanyang Tech. University，Singapore (639798)E-mail：mz2455@AbstractThe transformation of structured meshes to unstructured meshes is a branch of mesh generation technology. We can obtain the advantages of both grids that structure grids have the characteristics of convergence quickly and unstructured grids have the characteristics of matching sophisticated calculating domains well from this conversion. Meanwhile, it is expanding the widespread useful application of unstructured mesh codes. This paper gave the models of the transformations of the orthogonal meshes and body-fitted meshes. And, the heat conduction equation was solved using the based cell finite volume method and the secondary order accuracy. Finally, a couple of three dimension examples of heat transfer that included different geometries and boundary conditions were given. Therefore, the procedure was validated exactly and actually.Keywords：structured grids/meshes，unstructured grids/meshes，heat conduction1.IntroductionThe first step of numerical simulation is mesh generation that is cutting the continuous computational space into subdomains and identifying each node. The accuracy and efficiency of engineering numerical simulation mainly defend on the meshes and algorisms. In generally, all kind of mesh has its advantages and disadvantages; also the every numerical method has its constraints. Therefore, successful numerical simulation can only be done on the conditions that meshes and algorisms match perfectly [1].Two commonly kinds of mesh are structured and unstructured mesh/grid. The former characteristic is that the relationship between nodes is fixed and implied in the mesh. Thus, no special action is needed to ensure the relationship. But there don’t exists the property in unstructured mesh, so we must store the information about nodes such as volume nodes number, interfaces nodes number, and neighbor volume number[2-4] .It is stubborn to compare structured grid and unstructured grid exactly, besides considering the numerical algorism. In the brief, structured mesh has the good feature, simplex in generating, converging fast, and steady etc, while unstructured mesh can be more applicable for irregular domain, decomposing and encrypting in whole or part domain and used widely in later computation[4] . The paper takes advantage of two kinds of mesh to get fine results by the transformation between them.2.Transformation Between Both MeshesRegular structured mesh in orthogonal coordination is the oldest, most basic and simplex generation technique, including rectangle mesh of Cartesian coordinates and curve mesh in cylindrical coordinates or spherical coordinates. No detail about this kind of mesh, but the paper based on orthogonal mesh and body-fitted grid.First, we have to get the grid nodes of coordination in three dimensions, and then transform them to unstructured grid nodes number. Finally, numerical simulation will be done based on the unstructured mesh. For the transformation, at first, select cells shape and nodes NCTYPE(I) and NCNODE(J,I), here they are vertex number and coordination value (X(I),Y(J),Z(K)) of cell, respectively. Secondly, get the surface information NFTYPE (I) and NFNODE (J, I) of the cells. Where, the node order conform right hand rule, which is, ensuring the direction of surface normal is outside the cells.At the end, storing all neighbor cells information and their boundary property by KBCC (I).Ultimately, we can obtain the six data files. It is exactly these files comprise surfaces and nodes number for every cell and surface. The key of transformation is rearranging the I/J/K order of structured grid nodes to cell series data structure. Although the program is easy to do, the technique proved to be a handicap. Next part program is given in two dimensions.C**************************************************COME HERE FOR THE NODES OF CELL (cell_node.dat)LM=L2*M2 I0=0 J0=0DO 30 I=1,NCV NCTYPE(I)=8 NCNODE(1,I)=I+I0+J0NCNODE(2,I)=I+1 +I0+J0 NCNODE(3,I)=I+L1+I0+J0 NCNODE(4,I)=I+L2+I0+J0 NCNODE(5,I)=I+I0+J0+LMNCNODE(6,I)=I+1 +I0+J0+LM NCNODE(7,I)=I+L1+I0+J0+LM NCNODE(8,I)=I+L2+I0+J0+LM IF(MOD(I,L3).EQ.0) I0=I0+1IF(MOD(I,L3*M3).EQ.0) J0=J0+L230 CONTINUEC**************************************************The particular examples and their results analysis are provided in following paragraphs.3. Heat Conduction ExamplsProblem 1: We have heat transfer conduction without heat source in cubic region. Geometry and computational grids are showed in figure1, and governing equation is heat conduct equation with constant property in three Cartesian coordinates. The left surface has higher temperature T 2, and the left five ones have lower temperature T 1. Arithmetic formula of governing function and boundary conditions are:0=⎟⎠⎞⎜⎝⎛∂∂∂∂+⎟⎟⎠⎞⎜⎜⎝⎛∂∂∂∂+⎟⎠⎞⎜⎝⎛∂∂∂∂z T k z y T k y x T k x(1.1) 0.1,0.1,0.0,0.121======k T T c b a(1.2)(a) Cubic V olume (b) Orthogonal meshes (c) Body-fitted meshesFigure 1 Geometry and structured/unstructured meshesWe can obtain the exact solution of (1.1) and (1.2) (Kakac and Yener, 1993)[5]，[][]∑∑∞=∞=−−−−−=−−=11121sinh )(sinh )sin()sin(])1(1[])1(1[4),(),(m n mn mn m n m mn nb y b z x ac T T T y x T y x ααβλβλθ(1.3)Where,n λa n π=(n = 1, 2,…,i ) =m βcm π (m = 1, 2, …,i )22mn mn βλα+=(1.4)In Figure 2, the results of temperature distributions were from the transformation of orthogonalmeshes to unstructured grids. The same one was from the transformation of body-fitted meshes to unstructured grids in Figure 3. The solid lines stand for the exact solution. The dashed lines represent numerical solution. The numbers of grid are 10*10*10. There are agreements of temperature fields in both meshes.(a) X =0.5 (b) Y =0.2 (c) Z =0.5Figure 2. The temperature field of orthogonal meshes(————Exact Solution - - - - - -Numerical Solution)(a) X =0.5 (b) Y =0.2 (c) Z =0.5Figure 3. The temperature field of body-fitted meshesProblem 2: We have heat transfer conduction within heat source in cubic region. Geometry and computational grids are showed in figure1, and governing equation is heat conduct equation with constant property in three Cartesian coordinates as following. The all surfaces maintain the constant temperature (T 1 =0) same as the first kind of boundary condition. Mathematical formula of governing function and boundary conditions are:=∂∂+∂∂+∂∂222222zT y T x T )sin()sin()(1c z a x b y y k ππ−− (2.1)The exact solution of this problem is [6]，)sin()sin()sin(]1()()1[(1π8),,,5,3,1222352c z b y n a x cb n a n kb z y x T n πππ⋅++−=∑∞=L （ (2.2)The results of temperature distributions were from the transformation of body-fitted meshes tounstructured grids in Figure 4. The solid lines stand for the exact solution. The dashed lines represent numerical solution. The numbers of grid are 10*10*10. There are agreements of temperature fields in both meshes. There are the symmetrical temperature distribution basic of the boundary conditions and geometry.(a) X =0.5 (b) Y =0.5 (c) Z =0.5Figure 4. The temperature field of body-fitted meshesProblem 3: We have heat transfer conduction without heat source in cylindrical region. Geometry and computational grids are showed in figure 5a, and governing equation is heat conduct equation with constant property in three cylindrical coordinates as following. The outside surface has higher temperature T 2, and the inside surface has lower temperature T 1. Mathematical formula of governing function and boundary conditions are:0112=⎟⎠⎞⎜⎝⎛∂∂∂∂+⎟⎟⎠⎞⎜⎜⎝⎛∂∂∂∂+⎟⎠⎞⎜⎝⎛∂∂∂∂z T k z T k r r T kr r r ϕϕ(3.1) 0.1,0.8,0.4,0.2,0.12121=====k T T r r r r(3.2)The exact solution of this problem is [7-8]，)/ln()/ln()/ln()(122211r r r r T r r T r T r r −=(3.3)In Figure 5, the results of temperature distributions were from the transformation of body-fittedmeshes to unstructured grids. The solid lines stand for the exact solution. The dashed lines represent numerical solution. The numbers of grid are 10*10*10. There are agreements of temperature fields in both meshes. There are the symmetrical temperature distribution basic of the boundary conditions and geometry.(a) Meshes (b)Temperature fields in Z=0.5 (c) The flood picture of temperatureFigure 5. The temperature field of cylindrical coordinates4.Closure RemarkThe produces, which the heat conduction equations were solved, was presente d using the unstructured meshes that were transformed from structured grids. There are two kinds of meshes including orthogonal and body-fitted meshes. We show three examples for evaluating and proving this processor accruable and reasonable. The problem one and two are in the Cantinas coordinate and the problem three is in cylindrical coordinate. All results of numerical simulation were compared with the exact solutions. As a result, there is a perfect agreement between them.References[1] 陶文铨. 计算传热学的近代发展[M] 北京: 科学出版社, 2001.[2] PA TANKAR S V. Computation of Conduction and Duct Flow Heat Transfer [M].USA: Innovative Research Inc, 1991.[3] PA TANKAR S V. Numerical Heat Transfer and Fluid Flow [M]. New York: Hemisphere Publishing, 1981.[4] ZHANG M. Modeling of Radiative Heat Transfer and Diffusion Processes Using Unstructured Grid [D]. USA: Tennessee Technological University; 2000.[5] KAKAC S, YENER Y. Heat Conduction (Third edition) [M]. Taylor & Francis, Publisher, 1993.[6] 马信山. 电磁场基础[M]. 北京: 清华大学出版社, 1995.[7] M. N. 奥齐西克. 热传导[M]. 俞昌铭, 译. 北京: 高等教育出版社, 1984.[8] 南京工学院数学教研组. 数学物理方程和特殊函数[M]. 北京: 人民教育出版社, 1982.。

大直径直拉硅单晶炉热场的改造及数值模拟(1)

第29卷第4期人　工　晶　体　学　报 V ol.29　N o.4　2000年11月 JOURNA L OF SY NTHETIC CRY ST A LS N ovember,2000大直径直拉硅单晶炉热场的改造及数值模拟任丙彦,刘彩池,张志成,郝秋艳(河北工业大学半导体材料研究所,天津300130)摘要:为了降低大直径硅单晶生长过程中氧的引入,对常规的406mm(16英寸)热场进行了改造。

设计了以矮加热器为核心的复合式加热器系统,使晶体生长过程中熔体热对流减小。

通过对热场的数值模拟计算,分析了热场的温度分布,发现熔体的纵向温度梯度下降,熔体热对流减小,硅单晶中氧含量降低。

关键词:直拉硅单晶;热场;加热器;热对流;氧含量;数值模拟中图分类号:O78 文献标识码:A 文章编号:10002985X(2000)0420381205 Improvement and Numeric Simulation for H eat Zone inLarge2diameter Si Single Crystals FurnaceREN Bing2yan,LIU Cai2chi,ZH ANG Zhi2cheng,H AO Qiu2yan(Institute of Sem iconductor M aterials,Hebei University of T echnology,T ianjin300130,China)(Received10March2000,accepted15June2000)Abstract:In order to reduce oxygen content in large2diameter C zochralski Si single crystal(CZSi),we have m odified the heat zone in406mm(16in.)system.Thermal convection of melthas been suppressed by our new heat system with com posite heater.Distribution of tem perature filed was calculated by numeric simulation.The result indicated that axial tem perature gradient was decreased due to the decrease of thermal convection in the melt.The concentration of oxygen in CZSi has been reduced.K ey w ords:CZSi;heat zone;heater thermal convection;oxygen concentration;numericsimulation1　引言传统的直拉(CZ)法生长硅单晶时,氧是主要的非故意掺入的杂质[1]。

2004) Three-Dimensional Dynamic Fracture Analysis

Abstract: This paper describes algorithms for threedimensional dynamic stress and fracture analysis using the material point method (MPM). By allowing dual velocity ﬁelds at background grid nodes, the method provides exact numerical implementation of explicit cracks in a predominantly meshless method. Crack contact schemes were included for automatically preventing crack surfaces from interpenetration. Crack-tip parameters, dynamic J -integral vector and mode I, II, and III stress intensity factor, were calculated from the dynamic stress analysis solution. Comparisons to ﬁnite difference method (FDM), ﬁnite element method (FEM), and boundary element method (BEM), as well as to static theories have shown that MPM can efﬁciently and accurately solve three-dimensional dynamic fracture problems. Since the crack description is independent of the object description, MPM could be useful for simulation of three-dimensional dynamic crack propagation in arbitrary directions. keyword: Material point method, MPM. threedimensional dynamic fracture, cracks, dynamic J-integral, dynamic stress intensity, contact, mode I, mode II, mode III. 1 Introduction

虚拟现实中的三维建模与数学算法

虚拟现实中的三维建模与数学算法Three-dimensional Modeling and MathematicalAlgorithms in Virtual RealityIn the magical world of virtual reality, three-dimensional modeling stands as a cornerstone, framing our digital landscapes with precision and beauty. It's an art form that intersects seamlessly with the realm of mathematics, relying on intricate algorithms to breathe life into these digital creations.Imagine a painter meticulously shaping their canvas with brushes dipped in mathematical formulas. Each stroke, each curve, is carefully calculated to bring out the desired shape and texture. This is precisely what happens when creating three-dimensional models for VR—every detail must be perfectly crafted using mathematical principles.The core of this craft lies in geometry and trigonometry. Lines, planes, angles, and curves all come together harmoniously under the guidance of mathematical laws. These laws govern how objects are positioned within the virtual space, ensuring they maintain realistic proportions and perspectives.Moreover, matrices play a pivotal role in VR modeling. Think of them like invisible threads connecting every point in a model, allowing for transformations such as rotation, scaling, and translation. Without matrices, it would beimpossible to manipulate these objects effectively within the virtual environment.Beyond geometry and matrix manipulation, there's also a need for algorithms that can handle complex shapes and textures. Texture mapping, for instance, involves wrapping images onto 3D surfaces in a seamless manner. This requires sophisticated algorithms capable of calculating how the image should distort or stretch across irregular geometries.And let's not forget about animation—another vital aspect of VR modeling. Mathematical techniques like interpolation and keyframing enable smooth transitions between poses and movements, bringing characters and creatures to life with believable motions.As we delve deeper into the mysteries of virtual reality, we realize that mathematics isn't just some abstract theory; it's the language that brings our imaginations into existence. From simple geometric forms to complex animated sequences, every bit of magic within VR owes its existence to these mathematical algorithms and principles.。

小长径比张开式尾翼弹气动力三维数值模拟

小长径比张开式尾翼弹气动力三维数值模拟张涪;王浩;王帅【摘要】基于有限体积法计算了一种具有小长径比、大展弦比张开式尾翼弹在有攻角超声速粘性流动时的气动特性,分析了该弹周围的流场特性.研究结果表明,该尾翼弹的阻力系数和升力系数均随着马赫数增大而减少,随攻角增大而增大,且呈线性变化;当马赫数从2增大到4时,攻角从4°增大到12°,压心位置变化范围占全弹长的10.3％.【期刊名称】《南京理工大学学报（自然科学版）》【年(卷),期】2014(038)005【总页数】5页(P597-601)【关键词】小长径比;大展弦比;尾翼弹;攻角;气动特性【作者】张涪;王浩;王帅【作者单位】南京理工大学能源与动力工程学院,江苏南京210094;南京理工大学能源与动力工程学院,江苏南京210094;南京理工大学能源与动力工程学院,江苏南京210094【正文语种】中文【中图分类】V11小长径比弹丸常用作子母弹的子弹。

在超声速抛撒后的飞行中,由于条件的约束它很难通过高速旋转产生的陀螺力矩达到稳定飞行。

因此,为了使弹丸达到一定的静稳定裕度,该类弹丸需要安装大展弦比的张开式尾翼,然而尾翼翼展的增大势必会增加弹丸飞行时的阻力。

因此工程设计人员十分关心小长径比大展弦比尾翼弹气动特性的变化规律。

关于高马赫数下小长径比、大展弦比张开式尾翼弹的研究并不多见。

文献[1]使用,CFD结合动网格技术研究了长径比、展弦比适中的某类常规尾翼弹超声速下的气动力特性,分析了动导数随马赫数的变化规律。

文献[2]对某类大长径比尾翼弹流场进行了数值模拟,通过对比分析揭示了卷弧翼对大长径比尾翼弹气动特性的影响。

文献[3]利用风洞试验分析了极小展弦比背鳍对弹丸的气动力特性的影响,通过数值模拟揭示了该影响产生的原因。

文献[4]对某类具有较小展弦比尾翼的迫击炮弹进行了数值模拟,分析了其在跨音速阶段气动特性随马赫数攻角的变化规律。

本文研究的尾翼弹长径比仅为4.96,展弦比达到了8.6,其头部是由风帽和引信部分构成,弹身由较短的3段不同直径圆柱构成,弹尾由船尾部构成。

Numerical control machining simulation a comprehensive survey

This article was downloaded by: [Tsinghua University]On: 19 July 2011, At: 17:06Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UKInternational Journal of Computer IntegratedManufacturingPublication details, including instructions for authors and subscription information:/loi/tcim20Numerical control machining simulation: acomprehensive surveyYu Zhang a , Xun Xu b & Yongxian Liu aa School of Mechanical Engineering and Automation, Northeastern University, Shenyang,110004, PRCb Department of Mechanical Engineering, School of Engineering, University of Auckland,Auckland, 1010, New ZealandAvailable online: 31 May 2011PLEASE SCROLL DOWN FOR ARTICLENumerical control machining simulation:a comprehensive surveyYu Zhang a,b *,Xun Xu b and Yongxian Liu aaSchool of Mechanical Engineering and Automation,Northeastern University,Shenyang 110004,PRC;b Department of MechanicalEngineering,School of Engineering,University of Auckland,Auckland 1010,New Zealand(Received 20July 2010;ﬁnal version received 22February 2011)Since the ﬁrst numerical control (NC)machine tool was created at Massachusetts Institute of Technology in the 1950s,productivity and quality of machined parts have been increased through using NC and later computer numerical control (CNC)machine tools.Like other computer programs,errors may occur in a CNC program,which may lead to scraps or even accidents.Therefore,NC programs need to be veriﬁed before actual machining puter-based NC machining simulation is an economic and safe veriﬁcation method.So far,much research eﬀort concerning NC machining simulation has been made.This paper aims to provide a comprehensive review of such research work and a clear understanding of the direction in the ﬁeld.First,the deﬁnition,common errors,programming approaches and veriﬁcation methods of NC programs are introduced.Then,the deﬁnitions of geometric and physical NC machining simulation are presented.Four categories of NC machining simulation methods are discussed.They are solid-based,object space-based,image space-based and Web-based NC machining simulations.Finally,future trends and concluding remarks are presented.Keywords:computer numerical control;CNC machining;machining simulation;NC program1.IntroductionOver the years,technologies such as numerical control (NC),computer numerical control (CNC)and virtual manufacturing (VM)have changed the way products are made.These developments have improved machine tools and forever changed manufacturing processes,so that today it is possible to automatically produce high-quality products quickly,accurately and at lower cost than ever before (Krar et al.2002).As one of these developments,VM technology refers broadly to the modelling of manufacturing systems and components with an eﬀective use of audiovisual and/or other sensory features to simulate or design alternatives for a real manufacturing environment,mainly through computers.The motivation is to enhance our ability to predict potential problems and ineﬃciencies in product functionality and manufacturability before real manu-facturing occurs (Banerjee and Zetu 2001).NC machin-ing simulation constitutes an important part of VM technology.Since the development of the ﬁrst NC machine tools in 1952at Massachusetts Institute of Technology,NC machining has become a dominant manufacturing mode.NC machining denotes that the coded numerical information is used to control most of the machining actions such as spindle speed,feed rate and tool path while making the ﬁnal workpiece.The variousapproaches used to generate these NC codes may be classiﬁed into three groups:manual part programming,computer-assisted part programming and computer aided design (CAD)part programming.Simple pro-grams can be created manually,perhaps with the aid of a calculator,while more complex programs are usually created using a computer or an automatically pro-grammed tool.The manual method,while adequate for many simple point-to-point processes,requires the programmer to perform all calculations required to deﬁne the cutter-path geometry and can be time consuming.Errors made by the programmer are often not discovered until the program is tested graphically or on the machine tool.Error correction is cumber-some at a machine tool.In addition,because most machine tools have their own languages,the program-mer is required to work with diﬀerent instruction sets,which further complicates part-program creation.The computer-assisted part-programming language ap-proach simpliﬁes the process because the programmer uses the same language for each program,regardless the target machine tool.Moreover,translation of the program to NC code is made by a post-processor needed for each and every machine tool.These post-processors may not guarantee the correctness of a part program.Although the computer-assisted approach oﬀers advantages over the manual approach,both approaches require the programmer to translate*Corresponding author.Email:yzha540@International Journal of Computer Integrated Manufacturing Vol.24,No.7,July 2011,593–609ISSN 0951-192X print/ISSN 1362-3052online Ó2011Taylor &FrancisDOI:10.1080/0951192X.2011.566283D o w n l o a d e d b y [T s i n g h u a U n i v e r s i t y ] a t 17:06 19 J u l y 2011geometric information from one form (usually an engineering drawing)into another,which can be error prone.Creation of NC programs from a CAD model provides yet another option by allowing the part programmer to access the computational capabilities of a computer via an interactive graphics display console.This allows geometry to be described in the form of points,lines,arcs,and so on,just as it is on an engineering drawing,rather than requiring a transla-tion to a text-oriented e of a graphics display terminal also allows the system to display the resulting cutter-path geometry,allowing earlier veriﬁ-cation of a program,which can avoid costly machine setups for program testing (Chang et al.2006).NC program errors are mainly those related to NC language grammar and machining parameters.Because an NC machining program is used to control NC machine tools,NC program errors may cause workpiece undercut and overcut;collision between the workpiece and a cutter,ﬁxture,and/or machine tool;and even machine damage and personnel injury.Hence,after an NC program is generated,it must be carefully veriﬁed before used in real machining.In general,there are three veriﬁcation methods for an NC program,namely manual veriﬁcation procedures,shop-ﬂoor veriﬁcation on NC machine tools and NC computer-based machin-ing simulation.Manual veriﬁcation involves reading and checking an NC program by an operator.This method can only be used to check simple and short NC programs or to correct some easy-to-ﬁnd errors such as functional errors,grammatical errors and spindle speed errors.With the shop-ﬂoor veriﬁcation method,NC programs are veriﬁed by the process of machining wooden,plastic,wax or soft metal workpieces instead of an actual workpiece on a machine tool.Although it is a reliable veriﬁcation approach and a physical object can be obtained through the veriﬁcation process,this approach is expensive and time consuming.In addition,it was reported more than a decade ago that the US industry spent $1.8billion each year to prove or verify NC machining programs (Meister 1988).Another veriﬁcation method is computer-based machining simu-lation.Without consumption of actual material and occupation of machine tools,it can graphically reveal the real machining process,check collisions,evaluate machining parameters,and reveal and iron out the bugs in a computer aided manufacturing (CAM)system.Therefore,it is more intuitive,faster,safer and more cost-eﬀective.In addition,it can also be used for training machine tool operators.NC simulation started to make inroads into commercial systems some 20years ago.They come in three styles.Most of the current commercial CAD/CAM systems have their own NC simulation modules,e.g.Catia’s DELMIA NC machine tool simulationtool,NX’s CAM Integrated Simulation and Veriﬁca-tion software and Pro/E Wildﬁre’s Vericut.Most of the CAM tools (e.g.MasterCAM,GibbCAM and Smart-CAM)are also equipped with simulation options.The third type of NC simulation tools are more or less standalone tools,such as ICAM’s Virtual Machine,MachineWorks and ModuleWorks.All of these commercial simulation tools have limited functional-ities.This is the reason why research in the ﬁeld of NC machining simulation is still ongoing.The objective of this paper is to provide a technical review of the computer-based NC machining simula-tion,categorised as geometric and physical simulations.The remainder of this paper is organised as follows.Section 2,the main section,describes diﬀerent methods of machining simulation,i.e.solid-based NC machining simulation,object space-based NC machining simula-tion,image space-based NC machining simulation and Web-based NC machining simulation.Discussions and future trends are presented in Sections 3and 4,respectively.Concluding remarks are given at the end.2.Research of NC machining simulationIn this paper,machining simulations are divided into two categories,i.e.geometric simulation and physical simulation.As shown in Figure 1,geometric simulation is used to graphically check whether the cutters interfere with ﬁxture,workpiece and machine tools,gouge the part,or leave excess stock behind.In addition,it can provide geometric information such as the entry and exit angle of the cutter to physical simulation.As the name implies,physical simulation of an NC machining process aims to reveal the physical aspects of a machining process,such as cutting force,vibration,surface rough-ness,machining temperature and tool wear.It is based on geometric simulation and conventional metal cutting research (Lorong et al.2006).Considering diﬀerent methods of realising geometric and physical simulation,this section consists of ﬁve subsections,i.e.wireframe-based NC machining simulation,solid-based NC machining simulation,object space-based NC machin-ing simulation,image space-based NC machining simulation and Web-based NC machining simulation.Solid-based NC machining simulation is further classi-ﬁed into constructive solid geometry (CSG)-based and boundary representation (B-rep)-based NC machining simulation.Object space-based NC machining simula-tion is categorised into Z-map-based,vector-based and octree-based NC machining simulation.2.1.Wireframe-based NC machining simulationIn wireframe-based NC machining simulation,tool path and the shape of the machined workpiece are594Y.Zhang et al.D o w n l o a d e d b y [T s i n g h u a U n i v e r s i t y ] a t 17:06 19 J u l y 2011displayed in the form of wireframe.Because wireframe model has a simple data structure and fast data operation,it was widely applied to early NC machining simulations.However,this representation makes com-plex three-dimensional (3D)objects ambiguous and it does not provide actual solid geometric model and information.Hence,wireframe-based NC machining simulation can only be applied to a simple workpiece and produce simple geometric simulation.EMC2(2010)is such free software,which is a descendent of the original EMC software.2.2.Solid-based NC machining simulationSolid modelling is a much more complete 3D model-ling representation.They are useful for the geometric as well as physical simulation of machining process in which in-process workpiece,cutter and chip geometries can be accurately represented.This section discusses two types of solid-based machining simulations,CSG-based machining simulation and B-rep-based machin-ing simulation.2.2.1.CSG-based NC machining simulationIn CSG-based NC machining simulation,parts are represented by a CSG model.An early piece of work was done by Hunt and Voelcker (1982),who used the Part and Assembly Description Language (PADL)modelling system for 2.5-axis machining ter on,through considering the physical aspects of machining operation,Spence et al.(1990)and Spence and Altintas (1994)developed a CSG-based process simulation system for 2.5-axis milling,which consisted of a geometric simulator and physical simulator.In this system,parts were described using a CSG solid model at ﬁrst.Then along each path,after the cutter representedby a semicircle was intersected with the individual geometric primitives describing the part,the cutter/part immersion geometry was generated.Finally,the cutter-part intersection data from cutter/part immersion geometry were abstracted.The physical simulator used the cutter-part intersection data and mechanistic models (Tlusty and MacNeil 1975)to carry out the cutting-force prediction.Applications in predicting cutting force in face-milling and end-milling operations conﬁrmed the validity of the technique.However,this study is limited to 2.5-axis milling.In addition,based on CSG,two methods on collision detection were proposed (Su et al.1999,Ho et al.2001).Taking advantages of the CSG ‘divide-and-conquer’paradigm and distance-aided collision detection for convex bounding volumes,one of the methods realised eﬃcient and precise collision detection.The other method adopted a heterogeneous representation in that CSG was used to represent the tool,and a cloud of over 10,000points was used to represent the workpiece for rapidly detecting collision and penetration depth.However,this method tends to lose eﬃciency and requires a substantial amount of memory as the number of sampled points increases.Furthermore,collisions between the tool and other static parts of the NC machine are not handled by the two above-mentioned methods.2.2.2.B-rep-based NC machining simulationThe B-rep technique for solid modelling,where the surfaces,edges and vertices of an object are explicitly represented,has found wide applications in design and manufacturing (Requicha and Rossignac 1992).In an earlier work done by O’Connell and Jabolkow (1993),B-rep solid models of the machined part were constructed from NC programs in a Cutter Location (CL)data format for 3-axis millingsimulation.Figure 1.General architecture of NC machining simulation.International Journal of Computer Integrated Manufacturing 595D o w n l o a d e d b y [T s i n g h u a U n i v e r s i t y ] a t 17:06 19 J u l y 2011A limitation in this study is that there is no considera-tion for physical simulation.To solve this limitation,El-Mounayri et al.(1997,1998,2002),Imani et al.(1998),Imani and Elbestawi (2001)and Bailey et al.(2002a,2002b)integrated geometric simulation with physical simulation.A good agreement between the simulated and experimentally measured results was obtained.El-Mounayri et al.(1997,1998)developed a generic solid modeller-based ball-end milling process simulation system for 3-axis milling.First,a part was described using a B-rep solid model,and the cutting edges of a cutter were ﬁtted with cubic Bezier curves.Second,for every completed tool path,i.e.one NC block,the tool swept volume was generated and intersected with the part to give the corresponding removed volume,in-process parts and ﬁnal part.Third,the tool cutting edges were intersected with removed volume to produce the tool-part immersion geometry.Finally,after the geometric information was extracted from the tool-part immersion geometry,cutting force was predicted through the cutting-force model for ball-end mills developed by Abrari et al.(1998).This model is based on the concept of equivalent orthogonal cutting conditions and empirical equations for computing shear angle,friction angle,and shear strength of ter on,El-Mounayri et al.(2002)improved this physical simulation using Artiﬁcial Neural Network (ANN)technology and realised an integration of prediction and optimisation uses the same ANN model (El-Mounayri and Deng 2010).Imani et al.(1998)did similar research.In contrast with El-Mounayri’s work mentioned above,they represented the cutting edge by the B-spline curves,which can also be used for the representation of any shape of a cutting edge and is better than cubic Bezier curves.In addition,a new three-component mechanistic force model was developed to calculate instantaneous ball-end milling cutting forces.This force model not only takes into account the geometry of cutting edge (i.e.rake and helix angles)but also considers the variations of the chip-ﬂow angle and cutting coeﬃcients in the axial direction.And then the geometric simulation module was extended to simulate the parts with free-form surfaces by using advanced sweeping/skinning techniques,and the phy-sical simulation module was extended to surface roughness prediction (Imani and Elbestawi 2001).Subsequently,Bailey et al.(2002a,2002b)extended Imani’s work by representing an arbitrary cutting edge design using non-uniform rational B-spline curves,which is better than B-spline curves.In addition,to further guard against process planning errors or unexpected factory ﬂoor events,geometric simulation and physical simulation were integrated with factory ﬂoor monitoring and control (Saturley and Spence 2000,Spence et al.2000).Since B-rep-based machining simulation becomes more time consuming with increased part complexity,parallel processing techniques were used (Fleisig and Spence 2005).To solve the partial limitation and to improve computation eﬃciency,Spence et al.(1990),Spence and Altintas (1994),Yip-Hoi and Huang (2006)used a semi-cylinder to represent the cutter instead of a semicircle;the B-rep to model the part instead of CSG;and cutter engagement features to characterise cutter/workpiece engagement ter,Aras and Yip-Hoi (2008)and Ferry and Yip-Hoi (2008)extended Yip-Hoi and Huang’s work to 3-axis machining and 5-axis machining,respectively.B-rep-based collision detection for 5-axis NC machining was also reported by Ilushin et al.(2005)and Wein et al.(2005).2.3.Object space-based NC machining simulationIn an object space-based machining simulation,parts are represented by a collection of discrete points (with vectors)or surfaces with vectors or certain volume elements.Since objects are discretised,Boolean operations between objects are two-dimensional,even one-dimensional so that simulation computation is improved.Up to now,there are three major decom-position methods for the models in object space-based NC machining simulation,which are Z-map method,vector method and octree method,respectively.These methods are described below.2.3.1.Z-map methodThe Z-map method is used to decompose the model of a part into many 3D histograms.Each 3D histogram starts with the value of the height of the stock.During the simulation process,each tool movement updates the heights of the 3D histograms it passes over if it cuts lower than the currently stored height.Therefore,Boolean operation in this kind of simulation is one dimensional,which means simulation speed is very fast.Anderson (1978)used a 3D histogram to approximate the billet and cutter assembly shape to detect collisions in NC machining.However,no provision is allowed for 4-or 5-axis machining when the cutter is not orthogonal to the cubes.Subsequently,this representation was called Z-map.To get better geometric accuracy,computation eﬃciency and gra-phical quality,many researchers have used diﬀerent technologies to enhance the traditional Z-map model.For example,Hsu and Yang (1993)used isometric projection and raster display to enhance Z-map model for 3-axis milling processes.In 2002,Lee and Ko (2002)and Kang et al.(2002)used the inclined sampling method to enhance the Z-map model.In the same year,Lee and Lee (2002)596Y.Zhang et al.D o w n l o a d e d b y [T s i n g h u a U n i v e r s i t y ] a t 17:06 19 J u l y 2011developed a local mesh decimation method to achieve a smoother rendering as well as a dynamic viewing capability of the Z-map model in a 3-axis milling simulation.The overall algorithm for the periodic local mesh decimation is as follows.(1)The Z-map data of the workpiece are dividedinto small regions,and meshes for each region are generated,decimated and stored;(2)A tool movement command of the NCprogram is read and the Z-map data are updated accordingly.The display mode of a region cut by the tool is set as the Z-map rendering mode;(3)Meshes for regions are rendered by calling therendering functions of a graphics library,such as OpenGL.If a region is set in the Z-map rendering mode,a mesh is generated from the Z-coordinates of the grids in the region,and is passed to the rendering functions.Otherwise,the decimated mesh for the region is passed to the rendering functions;(4)If the current iteration is coincident with thedecimation period,the meshes are generated and decimated for the regions in the Z-map rendering mode,then go to step (2).Otherwise,go to (3)directly.Because of its simple data structure and computa-tion eﬃciency,the Z-map method has been employed for physical simulation such as cutting-force prediction and surface roughness prediction.It was shown that the method could eﬀectively predict cutting force and surface roughness.The cutting force in ball-end milling of sculptured surfaces was predicted by Kim et al.(2000).In this study,the cutter contact area could be obtained by comparing the Z-map data of the cutter with that of the machined surface.Then,after the cutting edge elements were calculated,the 3D contact area and the cutting edge elements were projected to the cutter plane,which was deﬁned as a circular plane that was perpendicular to the cutter axis.By comparing cutting edge element positions with cutter contact area data on the cutter plane,the cutting edge elements that engaged in cutting process could be identiﬁed.Finally,cutting forces acting on the engaged cutting edge elements were calculated using a cutting-force ter,based on the cutting force,cutter deﬂection and form error was predicted accurately (Kim et al.2003).Instead of the semi-spherical surface used in the research by Kim et al.,Jung et al.(2001)proposed an exact chip engagement surface from cutting edge geometry to more accurately update the workpiece model and predict the cutting force.However,a simple cutting-force model with no consideration of the sizeeﬀect of the workpiece material was developed and used in this study so that the accuracy of cutting force was ter,Zhu et al.(2001)extended cutting-force prediction to a 5-axis ball-end milling process.In the above research,average cutting coeﬃcients depend-ing on the cutting condition and traditional Z-map model were used to predict the cutting forces in transient cuts,which resulted in inaccurate and ineﬃcient prediction for instantaneous cutting force,in particular at peak or valley points.To overcome these limitations,Ko et al.(2002)and Yun et al.(2002a,2002b)proposed a new method of calculating cutting-condition-independent coeﬃcient considering the size eﬀect and developed the moving edge node Z-map (ME Z-map).As shown in Figure 2,the fundamental idea in the ME Z-map is that the edge node,which refers to the node closest to the cutting edge,is moved towards the boundary of the cutter movement.Subsequently,physical simulation was extended to surface roughness prediction based on the traditional Z-map model (Liu et al.2006).2.3.2.Vector methodThe vector method means that surfaces of a part are approximated by a set of points with direction vectors that are normal and/or vertical to the surface at each point.A vector extends until it reaches the boundary of the original stock or intersects with another surface of the part.To simulate the cutting process,the intersec-tion of each vector with each tool movement’s envelope is calculated.The length of a vector is reduced if it intersects the envelope.An analogy can be made to mowing a ﬁeld of grass.Each vector in the simulation corresponds to a blade of grass ‘growing’from the desired object.As the simulation progresses,the blades are ‘mowed down’.The lengths of the ﬁnal vectors correspond to the amount of excess material (if above the surface)or the depth of the gouge (if below the surface)at that point (Jerard et al.1989).Figure 2.Fundamental notions for ME Z-map (Adapted from Yun et al.2002b).International Journal of Computer Integrated Manufacturing597D o w n l o a d e d b y [T s i n g h u a U n i v e r s i t y ] a t 17:06 19 J u l y 2011Therefore,this method is usually used to judge whether the part is undercut or overcut.As shown in Figure 3,Chappel (1983)proposed the ‘point-vector’method in which part surface was approximated by a set of points with vector to simulate the material removal process.However,he did not mention how to select the ter,Oliver and Goodman (1986)developed a system similar to Chappel’s,which used a computer graphics image of the desired surface to select the points (Figure 4).This system was considered as the ﬁrst module of an NC veriﬁcation technique.Subsequently,another two modules of this NC veriﬁcation technique were developed to get an eﬃcient simulation.The second module provided a means of extracting a subset of eligible points (Oliver and Goodman 1990).The third module realised the intersection of normal vectors with swept-volume models (Oliver 1992).Later on,as Figure 5illustrates,Jerard et al.(1989)proposed an object-based surface discretisation modelling method that not only shared the characteristics of the methods of Chappel (1983)and Oliver and Goodman (1986)but also contained features that improved simulation eﬃciency.To implement highly accurate NCmachining simulation for mould and die parts,Park et al.(2005)divided discrete vector model into discrete normal vector (DNV)and discrete vertical vector (DVV),and hybridly used DNV and DVV in the machining simulation.As shown in Figure 6,the strategy for modelling a shape that consists of the ‘features’and the ‘others’(i.e.smooth and non-steep areas)can be described as follows:(1)Vertical wall,sharp edge and overhang featureson the input design surfaces are identiﬁed,as shown Figure 6(a);(2)As shown in Figure 6(b),all feature areas areconverted into a set of DNV elements;(3)As shown in Figure 6(c),the whole surface areais converted into a single DVV model;(4)DNV and DVV models are hybridly used tocompensate for each other’s shortcomings.Figure 6(d)shows the conceptual hybrid model,where the DNV and DVV models are super-imposed for better understanding.2.3.3.Octree-based methodAs illustrated in Figure 7,octree schema represents parts in a tree structure.The nodes of a tree are cuboids and are recursively subdivided into eight mutually disjoint child nodes until all nodes contain no parts of the modelled object,or the desired accuracy to the object is reached.That is,each node is checked to see whether it is fully,partially or not (empty)occupied.If a node is empty or full occupied,it does not need to be subdivided.If it is partially occupied,the node is subdivided further.The subdivision process is repeated until all nodes are either full or not occupied,or until geometric accuracy has been reached (Dyllong and Grimm2008).Figure 3.Point-vector model (Adapted from Chappel1983).Figure 4.Image-based point-vector model (Adapted from Karunakaran et al.2010).(a)Discrete model with outward vectors,(b)discrete model with vertical vectors.598Y.Zhang et al.D o w n l o a d e d b y [T s i n g h u a U n i v e r s i t y ] a t 17:06 19 J u l y 2011Hierarchical octree representations oﬀer an attrac-tive alternative for NC machining simulation because its Boolean operation is simple,and the spatial ordering of the data structure maintains this simplicity even when the local cutting region becomes complex.Karunakaran and Shringi (2007)developed a machin-ing simulation system in which the part was repre-sented by a traditional octree for model creation and modiﬁcation,and then was represented by B-rep for those downstream applications such as animated display,veriﬁcation and optimisation.To this end,an algorithm to convert the octree model of the instanta-neous workpiece into B-rep model was presented.This algorithm essentially decomposed the octree model into three quadtree models that store the geometry along the three principal directions (Karunakaran and Shringi 2007).Subsequently,this system was extended to physical simulation for cutting-force prediction using the material removal rate-based average cut-ting-force model (Karunakaran and Shringi 2008).However,using the cutting-force model is inherently incapable of determining the instantaneous cutting force that is essential for optimised cutting and for arriving at optimal values of machining parameters such as feed rate.Therefore,a general instantaneous cutting-force model developed by Altintas and Lee (1996)was used to predict the cutting force (Karuna-karan et al.2010).It was shown that the estimated cutting force agreed well with the experimental results.Traditional octree-based machining simulation demands a large memory and often results in inexact geometric representations.It has been shown that maintenance of a tolerance of 0.01mm over a volume in the order of 100mm per side requires 108octree nodes (Liu et al.1996).Therefore,to decrease memory and improve geometric representation,a number of methods have been proposed.Brunet and Navazo (1990)developed an extended octree model to more accurately represent 3D objects.In the extended octree model,boundary nodes containadditionalFigure 5.Discrete models with vectors (Adapted from Jerard et al.1989).Figure 6.Feature shapes and conceptual hybrid models.(a)Feature shapes,(b)DNV model,(c)DVV model,(d)conceptualhybrid model (Adapted from Park et al.2005).International Journal of Computer Integrated Manufacturing599D o w n l o a d e d b y [T s i n g h u a U n i v e r s i t y ] a t 17:06 19 J u l y 2011。

螺旋桨无人机三维流场数值模拟-红外技术

螺旋桨无人机三维流场数值模拟汪卫华1，李晋岭1，王充1，吕艳梅2，王格芳2，刘光猛1（1. 陆军军官学院，安徽合肥 230031；2. 军械技术研究所，河北石家庄 050000）摘要：采用流体动力学数值模拟方法对无人机及其螺旋桨发动机三维流场进行数值计算，获取了飞机的整体温度分布、螺旋桨发动机高温排气温度、浓度三维分布，为无人机红外辐射特性、空气动力学特性的计算与分析提供数据支撑。

关键词：无人机；数值模拟；红外辐射；温度场中图分类号：TJ85;TP391.9 文献标识码：A 文章编号：1001-8891(2012)05-0292-05Three Dimension Flow Field Numerical Simulationfor Airscrew Unmanned Aircraft VehicleWANG Wei-hua1，LI Jin-ling1，WANG Chong1，LV Yan-mei2，WANG Ge-Fang2，LIU Guang-meng1(1. Artillery officer Academy, Anhui 230031, China; 2. Institute of Ordnance Technology, Shijiazhuang 050000, China)Abstract：The flow field of unmanned aircraft vehicle (UA V) and piston engine airscrew has been calculated using hydrodynamics numerical simulation method. The three dimension temperature distribution of the aircraft, the three dimension temperature distribution and the consistence distribution of high-temperature exhaust gas has been presented, to support for the optimize and improve the infrared radiation characteristics of UA V, and to supply more robust database for the aerodynamics characteristics analysis of UA V, and make a significant joint contribution to the future infrared counterwork capability for the active service UA V.Key words：UA V，numerical simulation，infrared radiation，temperature field0引言信息化战争无人机的地位和作用越来越重要，但战场生存能力弱、反侦察能力差也是其致命的弱点。

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COMPUTATIONAL MECHANICS
ISCM2007,July 30-August 1, 2007, Beijing, China
©2007 Tsinghua University Press & Springer
Nu m erical Si m ulation of Three Di m ensional Turbulent Flow in Double-Suction Centrifugal Pu m ps
Min Yang*, Fujun Wang, Guohui Cong
Department of Fluid machinery, College of Water Conservancy & Civil Engineering, China Agricultural University, Beijing, 100083 China
E mail: yangmin0113@
Abstract
Double-suction centrifugal pumps are widely used in various fields because the flow rate of those is two times as much as single suction pump with the same diameter impeller and it is theoretically in axial balance. Along with the construction of many large projects, such as Water Transfer Project from South to North in China, the size and capacity of double-suction pump is constantly increasing. The design of those machines is mainly based on experience, and can not fully guarantee the performance of the pump. From the operation of large pump stations, there are general phenomena such as vibration and cavitation. Therefore, it is very imperative to study the internal flow within a double-suction centrifugal pump and provide scientific reference for its structure design and stable operation.
This paper describes a numerical study in a double-suction centrifugal pump by using the Reynolds Averaged Navier–Stokes (RANS) approach with the Shear Stress Transport turbulent model (SST) at the different conditions (rated, small and large flow rate). A symmetry condition is employed to provide an easier handling of the geometry. The hydraulic performance is predicted and it is in very good agreement with experimental data. The velocity and pressure distribution in pump are analyzed at the design point and off-design points. Changes of the velocity and the pressure with flow rate are investigated at impeller eye and impeller exit.
Figure: A 3D model with double-suction centrifugal pump
REFERENCES
1.Wang Hong, Tsukamoto Hiroki. E xperimental and numerical study of unsteady flow in a diffuser
pump at off design conditions. J. J ournal of Fluids E ngineering, 2003; 125(6): 767- 778.
2.Chen Hongxun. Research on turbulent flow within the vortex pump. J. J ournal of Hydrodyn. Ser. B,
2004; 16(6): 701-707.
3.Ferreira VG et al. Numerical simulation of turbulent free surface flow with two-equation k-ε
eddy-viscosity models. J. I nternational J ournal for Numerical Methods in Fluids, 2004; 44(4): 347-375.
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