三维双楔面定常激波相互作用

本文通过理论分析,将三维对称双楔面上定常激波相互作用简化到二维截面进行分析,利用二维非定常激波楔面反射理论求解该三维激波相互作用结构。同时,通过采用二阶精度的NND格式求解三维Euler方程,对该理论分析结果做出数值模拟验证。理论分析和数值模拟结果显示,对于三维双楔面超声速定常流动在取定的二维截面上激波结构兼有二维非定常及定常激波反射的性质,即形成了类似于二维非定常激波楔面反射的规则反射、单马赫反射、过渡马赫反射及双马赫反射等结构,同时其规则—马赫反射转变却遵循适用于二维定常激波反射的von Neumann准则。理论分析得出的各种反射结构的存在范围与数值模拟结果吻合良好。同时,探讨了两楔面间夹角以及楔面前缘后掠角对该激波结构的影响。

三维非定常激波双楔面反射的数值研究

本文采用有限体积方法,在非结构自适应网格上求解三维Euler方程,数值研究了三维非定常激波在双楔面上的反射现象。结果显示,三维激波在双楔面上也会反射形成三维马赫反射和规则反射;此外,还会形成一种非典型的三维准马赫反射。由于三维影响,通过二维激波反射理论预测的三维马赫反射区域存在一定的误差,该误差在文中得到了修正。

硝基甲烷热解化学反应流的数值研究

本文对激波管硝基甲烷热解化学反应流进行了研究，给出了一个严格考虑到化学反应流中化学反应、体积和流动效应的一维Euler方程的全解析耦合算法。对硝基甲烷激波管热解进行了模拟，并把耦合算法得到的模拟结果和激波管实验数据进行了对比验证，两者符合较好。此外，本文还对耦合算法与等温、等压和等容三种简化模型的计算结果进行了对比分析，结果表明，当化学反应流热效应显著增强时，等温假设失效，等压和等容简化模型也偏离实际情形，而全解析耦合算法可以有效解决化学反应与流动相互耦合的问题。

用双流体模型模拟超声速气固两相流动

采用了双流体模型对JPL(Jet Propulsion Laboratory)喷管中气固两相流动以及超声速射流两相流动进行了数值模拟,并研究了可压缩两相流动中气相与颗粒的相互作用规律.自主开发的一般曲线坐标系下二维轴对称可压缩双流体程序Solve2D,对气相求解Navier-Stokes(N-S)方程组,采用k-ε湍流模型,颗粒相求解Euler方程组.对JPL喷管内的两相流场和湍流两相射流流场进行了数值模拟,研究了不同颗粒质量百分数以及不同颗粒直径时的气固两相流场的流动规律.

Improvement of FEM's dynamic property

The discretization size is limited by the sampling theorem, and the limit is one half of the wavelength of the highest frequency of the problem. However, one half of the wavelength is an ideal value. In general, the discretization size that can ensure the accuracy of the simulation is much smaller than this value in the traditional finite element method. The possible reason of this phenomenon is analyzed in this paper, and an efficient method is given to improve the simulation accuracy.

Hydroelastic dynamic characteristics of a slender axis-symmetric body

The slender axis-symmetric submarine body moving in the vertical plane is the object of our investigation. A coupling model is developed where displacements of a solid body as a Euler beam (consisting of rigid motions and elastic deformations) and fluid pressures are employed as basic independent variables, including the interaction between hydrodynamic forces and structure dynamic forces. Firstly the hydrodynamic forces, depending on and conversely influencing body motions, are taken into account as the governing equations. The expressions of fluid pressure are derived based on the potential theory. The characteristics of fluid pressure, including its components, distribution and effect on structure dynamics, are analyzed. Then the coupling model is solved numerically by means of a finite element method (FEM). This avoids the complicacy, combining CFD (fluid) and FEM (structure), of direct numerical simulation, and allows the body with a non-strict ideal shape so as to be more suitable for practical engineering. An illustrative example is given in which the hydroelastic dynamic characteristics, natural frequencies and modes of a submarine body are analyzed and compared with experimental results. Satisfactory agreement is observed and the model presented in this paper is shown to be valid.

压电驱动器应变传递模型分析

随着压电材料结构在航空航天结构控制领域的广泛应用, 压电驱动器与主体结构间的应变传递问题的研究日益重要. 该文首先对压电驱动器应用中的应变传递模型----均匀应变模型与Bernoulli-Euler模型进行了优缺点的分析对比; 其次将Bernoulli-Euler模型用于考虑胶层影响情况, 考虑到压电驱动器在航空航天领域的应用, 着重类似于翼面结构的模型分析, 得到了实际应用中压电驱动器沿结构厚度方向的应变传递表达式; 最后通过数值计算的方法确定了所得应变表达式适用的胶粘剂弹性模量及厚度的范围. 结果表明此表达式的有效性, 使 Bernoulli-Euler模型的应用更接近于实际情况, 同时为智能结构实际应变分布的分析提供了一定的依据与基础

细长轴对称体的水弹性振动特性分析

以在水中做纵向平面内运动的细长轴对称体为研究对象.在建立描述流体-结构耦合振动系统的计算模型时,对固体采用位移(包括刚体运动位移和弹性Euler梁振动位移),对流体采用压力作为基本变量,首先建立了考虑流体作用力的结构动力学方程,推导了考虑结构运动的流体压力表达式,分析了水动力载荷的特征:包括水动压力的来源,组成,分布形式与影响范围等.在此基础上给出了描述水中运动物体的位移(结构)-压力(流体)格式的流固耦合系统模型.然后利用有限元数值方法(FEM)对方程进行了求解,克服了解析解对研究对象外形的限制,同时避免了流固耦合直接数值模拟中CFD+FEM的复杂性,对于典型的工程结构非常适用.最后,通过算例给出了水中运动物体的水弹性频率和模态,并将计算结果与试验结果进行了对比,证明了本文计算模型的有效性

不同积分变分原理的统一

依据定量因果原理的数学表示,统一地导出了Lagrange量中含坐标关于时间一阶、二阶导数的积分型的Hamilton原理、Voss原理、Hlder原理和Maupertuis-Lagrange原理等,给出了这些原理的本质联系和统一描述.得出f0=0并不是通常的保持Euler-Lagrange方程不变的结果,而是满足定量因果原理的结果.还得出Lagrange量的所有的积分型变分原理等价地对应于两类满足定量因果原理的不变形式.同时发现所有积分型变分原理的运动方程都是Euler-Lagrange方程,但不同条件的变分原理所对应的不同群G作用下的守恒量是不同的.从而可对过去众多零散的积分型变分原理有一个系统和深入的理解,并使这些变分原理自然地成为定量因果原理的推论.

Unified expressions of all integral variational principles

In terms of the quantitative causal principle, this paper obtains a general variational principle, gives unified expressions of the general, Hamilton, Voss, Holder, Maupertuis-Lagrange variational principles of integral style, the invariant quantities of the general, Voss, Holder, Maupertuis-Lagrange variational principles are given, finally the Noether conservation charges of the general, Voss, Holder, Maupertuis-Lagrange variational principles axe deduced, and the intrinsic relations among the invariant quantities and the Noether conservation charges of all the integral variational principles axe achieved.

Calculating the equation of state parameters and predicting the spinodal curve of isotactic polypropylene/poly(ethylene-co-octene) blend by molecular dynamics simulations combined with Sanchez-Lacombe lattice fluid theory

Molecular dynamics simulations are adopted to calculate the equation of state characteristic parameters P*, rho*, and T* of isotactic polypropylene (iPP) and poly(ethylene-co-octene) (PEOC), which can be further used in the Sanchez-Lacombe lattice fluid theory (SLLFT) to describe the respective physical properties. The calculated T* is a function of the temperature, which was also found in the literature. To solve this problem, we propose a Boltzmann fitting of the data and obtain T* at the high-temperature limit. With these characteristic parameters, the pressure-volume-temperature (PVT) data of iPP and PEOC are predicted by the SLLFT equation of state. To justify the correctness of our results, we also obtain the PVT data for iPP and PEOC by experiments. Good agreement is found between the two sets of data. By integrating the Euler-Lagrange equation and the Cahn-Hilliard relation, we predict the density profiles and the surface tensions for iPP and PEOC, respectively. Furthermore, a recursive method is proposed to obtain the characteristic interaction energy parameter between iPP and PEOC. This method, which does not require fitting to the experimental phase equilibrium data, suggests an alternative way to predict the phase diagrams that are not easily obtained in experiments.

高寒草甸生态系统陆地生物圈模式研究及应用

改进了适合于高寒草甸生态系统的陆地生态圈模式，分析了模式中温度变化与水分运动分层的物理原因，说明了气候状况对地表面能量交换的影响，给出了净辐射和蒸散量新的计算方法，提出了有很差分计算中具有二阶精度的Euler隐式格式，介绍了中国科学院海北高寒草甸生态站的气候概况和野外观测情况。最后利用本模式对高寒草甸生态站地区的土壤-植被-大气间水热交换过程进行了数值模拟，模拟值与实测值吻合较好。

轮式仿人机器人的ZMP建模及动态稳定判据

介绍了ZMP的概念,比较常见的几种ZMP建模方法,提出将高效牛顿-欧拉算法(RENA)与ZMP的概念相结合的迭代ZMP建模方法,并利用该方法完成轮式仿人机器人的ZMP建模.通过模型分析,得出该轮式仿人机器人的ZMP简化计算公式.最后得出此类轮式仿人机器人的稳定性判据及稳定度的定义.

Elliptic Object Detection Based on Shape Preserving and Active Contour

本文通过形状约束方程(组)与一般主动轮廓模型结合,将目标形状与主动轮廓模型融合到统一能量泛函模型中,提出了一种形状保持主动轮廓模型即曲线在演化过程中保持为某一类特定形状。模型通过参数化水平集函数的零水平集控制演化曲线形状,不仅达到了分割即目标的目的,而且能够给出特定目标的定量描述。根据形状保持主动轮廓模型,建立了一个用于椭圆状目标检测的统一能量泛函模型,导出了相应的Euler-Lagrange常微分方程并用水平集方法实现了椭圆状目标检测。此模型可以应用于眼底乳头分割,虹膜检测及相机标定。实验结果表明,此模型不仅能够准确的检测出给定图像中的椭圆状目标,而且有很强的抗噪、抗变形及遮挡性能。

仿人机器人腰部机构的动力学建模、控制与仿真

本文介绍的仿人机器人具有差动腰部机构,它除了受自身的动力学影响以外,还受到手臂和车体运动以及外力、外力矩等对腰部机构关节力矩的影响。笔者利用高效牛顿-欧拉算法完成了仿人机器人的整体建模;在不考虑各关节间耦合运动的情况下,对整体动力学模型进行适当简化,得到了腰部机构的动力学模型。简化后的动力学模型既反映了机器人车体、腰部及双臂的动力学关系,又大大地减小了计算量,易于实现基于动力学的控制算法。基于动力学模型,给出了腰部机构PD伺服轨迹跟踪控制算法,并结合计算力矩方法用于补偿腰部机构两关节受到的力矩扰动。仿真分析表明,该控制方法可以明显提高腰部机构的位置跟踪精度,并提高仿人机器人的整体作业精度。