Numerical simulation of polyhedral crystal growth based on a mathematical model arising from non–local thermomechanics

In this work we present some results of the numerical simulation of the growth of a crystal from its melt, taking into account faceting. The simulation is based on a numerical solution of a three–dimensional generalized Stefan problem. That problem arises from a non–local thermomechanical theory applied to a continuous system with an interface and embodies ideas from the dislocation theory of crystal growth. In the model, the crystal surface is an isotherm and the growth velocity of a crystal face depends on the velocities of the other faces and on the whole crystal configuration as well as on the temperature gradient. A front fixing formulation of the model is considered. This is a conservative form of the Isotherm Migration Method [6, 7, 8, 9, 10, 11] in spherical coordinates. The numerical solution is based on an explicit finite difference discretization of the resulting non–linear equations. We develop a theoretical analysis of the interface equations that drive the crystal face motion. Numerical results, showing evolution of complex crystals with configuration changing during the growth, are in accord with experimental results. Furthermore, numerical experiments offer useful information on the influence of certain parameters in the model on the growth process. Received: March 21, 1996     

磁场对双扩散液层热毛细对流的影响

通过数值模拟的方法对磁场作用下的双扩散液层热毛细对流进行了研究, 模型中同时考虑了热毛细效应和溶质毛细效应的存在. 研究结果显示, 外部磁场能够有效削弱液层内热毛细对流的强度, 改变热毛细对流的对流结构; 随着磁场强度的增大, 液层内热毛细对流的对流强度逐渐减小, 热质传递过程中扩散效应逐渐得到增强; 最终, 溶质浓度沿水平方向呈梯度分布. 因此, 当磁场强度足够大时能够实现晶体生长中所需的纯扩散条件.     

Modeling of the dynamics of diffusion crystal growth from a cooling magmatic melt

The process of diffusion growth of a single crystal of plagioclase (consisting of two components: albite and anorthite) from a cooling magma melt is considered. Crystallization starts when the temperature becomes lower than the melting (liquidus) temperature and occurs as a result of the diffusion of melt components to the boundary of the growing crystal. The crystallization process is simulated by solving a system of nonlinear, linked by cross terms, nonstationary diffusion equations for albite, anorthite, and residual melt in the coordinate system moving with the growing crystal boundary. The dependence of the crystal growth rate on undercooling and temperature and of its composition on temperature and pressure is taken into account. Both quantities substantially depend on the component concentration ratio in the melt on the crystal-melt interface. The competition between the diffusion and crystal growth processes and the complex dependence of these processes on the current melt and crystal compositions and the system temperature lead to a strong nonlinearity of the problem. As a result of numerical simulation, it is established that with a linear decrease in temperature the growing crystal composition changes nonmonotonically. This makes it possible to propose a novel interpretation of the crystal zoning typical of natural magmatic systems.     

楔形罩线型聚能装药侵彻钢锭

为了获得楔形罩线型聚能装药射流侵彻钢锭的特点和规律,利用ANSYS/LS-DYNA软件建立了三维数值计算模型,并进行了数值模拟。在此基础上,进行了实际的切割实验:对于某一炸高条件,切割深度随时间的增加先快速增加,后缓慢增加;对于不同的炸高,切割深度随炸高的增加而缓慢增加,当炸高为40~60 mm和70~120 mm时,侵彻深度表现出对炸高的不敏感性;同时,获得了不同炸高条件下不同时刻的钢锭切口断面形状。结果表明,数值模拟和切割实验结果有很好的一致性,可以用该三维数值计算模型模拟实际切割器侵彻钢靶的过程,并获得其特点和规律。     

基于相移干涉技术的晶体溶解及生长边界层实时监测

晶体在溶解及生长过程中边界层的信息直接影响晶体生长速度和物质输运过程,进而影响晶体质量和生长机制。本文利用相移干涉技术建立了晶体生长过程实时监测系统,对无机盐晶体溶解及生长过程中的边界层信息及物质输运过程进行了实时监测,获得了整个实验过程中的晶体生长速度。实验表明:在溶解过程中,边界层内浓度分布与晶体界面距离呈指数下降关系,边界层内浓度差与晶体溶解速度随时间呈指数减小关系;在结晶过程中,边界层内浓度分布规律与溶解过程相反;边界层内浓度差和晶体生长速度曲线则呈现出先上升再下降最后趋于稳定的规律,且在重力场和物质输运过程的共同作用下,晶体表面会产生浮力对流现象。     

周期激励下单搭接接头强度与振动特性研究

主要研究汽车轻量化粘接结构在周期性振动载荷激励下强度与振动属性的改变。首先,利用实验手段,研究了振动载荷对单搭接接头疲劳特性的影响,分析了疲劳后接头的强度及模态频率的变化;其次,通过仿真分析方法,建立了基于经典双线性内聚力模型(Cohesive Zone Model)的单搭接接头静态及动态仿真模型,对胶接接头的模态频率、振型及加载开裂过程中胶层单元失效扩展进行模拟,与此同时,探讨了疲劳载荷对胶层内聚力模型的弱化效应。最后,利用SEM电镜分析手段,从微观上分析了粘接接头疲劳损伤及断裂机理。     

Dynamic model of crop growth system and numerical simulation of crop growth process under the multi-environment external force action

IntroductionAccordingtobiomechanics,thegrowthsystemoffarmlandcropistheartificiallyecologicalsystemthatchangestheenvironmentalresourcefactors(light,temperature,soilwaterandcarbondioxideetc .)intothefarmlandprimaryproductivity .Thesystemisactedbytheexternalforcevariablesofenvironment,inabroadsense,whichincludeslightintensity ,thetemperaturemaintenanceaction ,soilwater,andtheeffectiveuserateofnutrientsetc.Withinsystemisalsoactedbybiologicalvariableswhichincludethecropleafindex ,rootvolume ,biomas…     

基于近场动力学的单晶冰弹性各向异性数值模拟方法

天然冰材料在变形与破坏行为上的各向异性特征是冰与结构相互作用中产生复杂载荷过程的关键诱因, 而天然冰各向异性的根源则在于单晶冰的各向异性. 目前, 学术界针对单晶冰各向异性的数值模拟方法研究仍较为缺乏. 为了准确再现天然冰材料的特殊力学性质, 本文基于近场动力学理论, 提出了一种单晶冰弹性各向异性的数值模拟方法. 该方法的核心思想是将单晶冰杨氏模量沿不同加载方向的变化规律引入到近场动力学力密度向量的影响函数中. 以前人实验测试得到的杨氏模量值为参考, 通过开展与C轴呈0°, 45°和90°三个加载方向的单晶冰单轴压缩数值模拟实验, 提出了针对该影响函数的修正和辅助参数标定方法, 最终在15°, 30°, 60°和75°等其他四个加载方向进行了验证. 结果表明: 本文提出的针对影响函数的修正与参数标定方法, 能够较为便捷地找到数值模型杨氏模量与参考杨氏模量相一致的影响函数最优解, 即本文提出的基于影响函数的近场动力学数值模拟方法, 能够合理、准确地模拟单晶冰的弹性各向异性行为. 本文研究成果可为后续多晶冰各向异性数值模拟方法的建立提供基础性参考.      

高能炸药摩擦感度的数值模拟

为了研究炸药摩擦安全性,利用熔化摩擦模型对几种高能炸药的摩擦感度进行了数值模拟,结果符合实验,并根据热分解反应速率分析了感度规律。由于炸药熔点一般低于点火温度,所以基于一个考虑熔化现象的炸药摩擦模型,在炸药感度实验条件下进行了一维数值模拟,给出了炸药熔化结果和摩擦点火的时间:4种摩擦感度较弱的炸药包括DATB、NQ、TATB和TNT的点火时间的顺序即感度顺序符合实验结果,说明摩擦点火模型适应性。进一步结合炸药热分解反应速率的大小顺序,数值模拟证明,在一定摩擦强度下,点火顺序会发生交换,说明摩擦感度实验不能完全说明炸药摩擦感度强弱顺序。     

飞机风挡结构抗鸟撞一体化设计技术研究

结合大型非线性有限元分析软件,实践了飞机风挡结构由初步设计、数值仿真以及实验验证的一体化设计过程,建立了适于风挡结构材料的非线性黏弹性本构计算接口程序,对合理选取单元类型、材料模型、边界条件影响以及试验设计等工作细节进行了深入研究,通过实验与仿真计算结果的对比,验证了数值仿真计算模型的精度．为飞机风挡的抗鸟撞结构设计-数值仿真-实验验证一体化技术提供了支持论证．     

Hybrid lattice Boltzmann finite‐difference simulation of axisymmetric swirling and rotating flows

The axisymmetric flows with swirl or rotation were solved by a hybrid scheme with lattice Boltzmann method for the axial and radial velocities and finite‐difference method for the azimuthal (or swirl) velocity and the temperature. An incompressible axisymmetric lattice Boltzmann D2Q9 model was proposed to solve the axial and radial velocities through inserting source terms into the two‐dimensional lattice Boltzmann equation. Present hybrid scheme was firstly validated by simulations of Taylor–Couette flows between two concentric cylinders. Then the benchmark problems of melt flow in Czochralski crystal growth were studied and accurate results were obtained. Numerical experiment demonstrated that present axisymmetric D2Q9 model is more stable than the previous axisymmetric D2Q9 model (J. Comp. Phys. 2003; 186 (1):295–307). Hence, compared with the previous model, present numerical method provides a significant advantage in simulation melt flow cases with high Reynolds number and high Grashof number. Copyright © 2006 John Wiley & Sons, Ltd.     

晶体生长过程实时监测系统

实时监测晶体生长过程对研究晶体生长动力学以及调控晶体生长过程有着很重要的意义。结合干涉技术、相移技术以及时间序列位相提取技术,建立了一个晶体生长过程实时监测系统。该系统主要由三条光束组成,通过设定快门参数组成不同的Mach-Zehnder干涉光路,可同时用于无机盐晶体和蛋白质晶体生长过程的实时定量监测。利用该系统及时间序列位相提取方法,对NaCl晶体在自然蒸发情况下的生长过程以及溶菌酶蛋白悬滴法结晶过程进行了研究,对该系统和方法在研究晶体结晶过程中的可行性及优势进行了验证。结果表明,该系统不仅可以获得晶体结晶过程中的实时绝对浓度、过饱和度等晶体生长动力学参数;而且对于蛋白质结晶过程,快门系统的引入解决了蛋白溶液多浓度场叠加的分离问题,在一个实验周期内获得了溶菌酶蛋白结晶过程中的实时蛋白浓度演变、实时沉淀剂浓度变化等结晶动力学参数。这些关键参数为下一步探索结晶条件对晶体质量的影响、分析蛋白结晶相图以及优化蛋白质晶体质量提供了定量数据基础。     

Controlling the growth interface shape in the growth of CdTe single crystals by the traveling heater method

This article presents the results of a numerical simulation study carried out for controlling the growth interface shape in the THM (Traveling Heater Method) growth of CdTe single crystals. Applying different thermal boundary conditions and a crucible rotation, the optimum growth conditions for a desired interface shape were obtained. The simulation results show that by controlling the heat removal at the bottom of the crucible, a flatter (or slightly concave towards the crystal) growth interface can be maintained throughout the growth process. A crucible rotation rate of 5 rpm seems optimal for a favorable growth interface shape. To cite this article: S. Dost, Y.C. Liu, C. R. Mecanique 335 (2007).     

数值模拟油井射孔器作用过程方法研究及应用

提高射孔器性能是射孔弹厂家面临的和油田用户关心的主要问题。油井聚能射孔器的作用过程涉及爆轰波的形成、传播、爆轰波与其他介质的相互作用等爆轰问题,射流的形成、延展等界面碰撞问题,射流对靶的侵彻、靶的成坑和动态响应等侵彻问题,作用过程复杂。为了研究油井聚能射孔器的作用过程和机理,降低设计成本,缩短研制周期,本文介绍了模拟石油射孔器从炸药起爆,射流形成,射流侵彻钢靶、井液、混凝土靶的整个作用过程的欧拉数值方法,包括数学模型、离散方法、相应的本构模型,以及为节省计算机时采用的计算和理论分析耦合的模拟方法,并将数值模拟结果与实验进行了比较。研究结果表明,数值模拟结果与实验结果符合的较好,说明方法是有效的和可行的。     

浅埋高压输气管道爆炸地面振动的原型试验与数值模拟研究

针对浅埋高压输气管道爆炸产生的地面振动效应,采用现场试验结合数值模拟的方法展开研究。组织实施了全尺寸天然气管道爆炸试验,掌握了高压输气管道爆炸地面振动的量级范围以及衰减规律。经试验数据分析得到,埋地高压天然气管道爆炸造成的地面振动主要产生于物理爆炸过程中,随后发生的天然气爆燃过程并未产生明显的地面振动。基于非线性有限元程序 LS-Dyna建立了高压输气管道爆炸试验计算模型,计算结果与试验现象吻合较好,验证了模型参数设计的合理性。进一步分析了管道爆炸瞬间管内气体-管壁-土体的相互作用机理、应力分布以及裂纹扩展规律。由计算结果分析得到,管道开裂是由于内部高压气体推动管壁向两侧扩展在裂纹尖端处形成了应力集中,管壁冲击土体的速度可达50 m/s,冲击产生的塑性状态向远处传播逐渐衰减为弹性应力波,即形成了地面振动效应。研究成果揭示了高压气体管道爆炸地面振动的主要成因,可为爆炸事故振动预防提供理论参考和技术支持。     

The target wave patterns of a reaction-diffusion process in an immobilized enzyme

In this paper, the target wave patterns of a reaction-diffusion process were discovered by numerical simulation of an immobilized enzyme mathematical model. The substrate concentration periodically diffuses from initial state to all around, and the product concentration also periodically increases with target wave patterns, and finally they reach the equilibrium states.     

RDX(210)单晶准等熵压缩实验的数值分析

基于准等熵压缩实验,建立了考虑线弹塑性效应的反积分数学模型,并针对Sandia的含能材料RDX(210)的无反应准等熵压缩实验数据,进行了数值模拟和分析.结果表明,本文模型可以恰当地描述该含能材料的准等熵压缩实验过程,可以得到与文献结果吻合较好的样品加载速度历史;计算得到了样品内部任意位置直至加载面上的信息、应力应变和...     

Numerical simulation of particle migration in asymmetric bifurcation channel

In this work we provide numerical validation of the particle migration during flow of concentrated suspension in asymmetric T-junction bifurcation channel observed in a recent experiment [1]. The mathematical models developed to explain particle migration phenomenon basically fall into two categories, namely, suspension balance model and diffusive flux model. These models have been successfully applied to explain migration behavior in several two-dimensional flows. However, many processes often involve flow in complex 3D geometries. In this work we have carried out numerical simulation of concentrated suspension flow in 3D bifurcation geometry using the diffusive flux model. The simulation method was validated with available experimental and theoretical results for channel flow. After validation of the method we have applied the simulation technique to study the flow of concentrated suspensions through an asymmetric T-junction bifurcation composed of rectangular channels. It is observed that in the span-wise direction inhomogeneous concentration distribution that develops upstream persists throughout the inlet and downstream channels. Due to the migration of particles near the bifurcation section there is almost equal partitioning of flow in the two downstream branches. The detailed comparison of numerical simulation results is made with the experimental data.     

A New Unsteady Three Dimensional Model for Macromolecular Transport and Water Filtration Across the Arterial Wall

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爆炸加工洞内自然通风三维数值模拟和模型实验研究

为减少对环境污染而建造全球最大爆炸加工场地,建造之前需要对其进行深入研究,特别是自然通风问题。为此,本文对实际结构的1/6模型进行实验研究,同时采用三维瞬态数值模拟方法,对实际结构和1/6实验模型在自然通风条件下有害气体浓度衰减情况进行详细研究。通过数值模拟可以推导出1/6实验模型与实际结构有害气体衰减时间比例常数;并依据1/6模型实验结果,推测出实际结构有害气体排出时间,为实际结构设计提供理论支持。