多层复合壳体三维振动分析的谱——微分求积混合法

对于较厚的多层复合壳体,其振动位移沿厚度方向呈锯齿形变化且层间剪切和拉、压应力呈三维耦合状态,采用传统的等效单层理论分析已不能满足精度要求. 建立不受结构厚度、铺层材料性质和铺层方式限制的三维分析方法具有重要的研究价值. 本文以独立铺层为建模对象,结合广义谱方法与微分求积技术建立了一种适用一般边界条件和铺层方式的多层复合壳体三维分析新方法——谱--微分求积混合法. 该方法应用三维弹性理论对独立铺层进行精确建模,有效克服了二维简化理论对横向变形以及层间应力估计不确切的缺点;引入微分求积技术对铺层进行数值离散,将三维偏微分问题转化为二维偏微分问题,降低了求解维度和难度;应用广义谱方法近似地表述离散计算面上的场变量,将获取的二维偏微分方程转化为以场变量谱展开系数为未知量的线性代数方程组,避免了对超越方程的求解. 数值验证结果表明该方法收敛性好,计算精度高.      

多层复合壳体三维振动分析的谱-微分求积混合法

对于较厚的多层复合壳体,其振动位移沿厚度方向呈锯齿形变化且层间剪切和拉、压应力呈三维耦合状态,采用传统的等效单层理论分析已不能满足精度要求.建立不受结构厚度、铺层材料性质和铺层方式限制的三维分析方法具有重要的研究价值.本文以独立铺层为建模对象,结合广义谱方法与微分求积技术建立了一种适用一般边界条件和铺层方式的多层复合壳体三维分析新方法——谱-微分求积混合法.该方法应用三维弹性理论对独立铺层进行精确建模,有效克服了二维简化理论对横向变形以及层间应力估计不确切的缺点;引入微分求积技术对铺层进行数值离散,将三维偏微分问题转化为二维偏微分问题,降低了求解维度和难度;应用广义谱方法近似地表述离散计算面上的场变量,将获取的二维偏微分方程转化为以场变量谱展开系数为未知量的线性代数方程组,避免了对超越方程的求解.数值验证结果表明该方法收敛性好,计算精度高.     

用微分求积方法计算二维薄板在超音速流中的非线性颤振

采用了一种微分求积方法将二维薄板在超音速气流作用下的非线性动力学方程离散为常微分方程,并用Runge-Kutta数值方法进行了计算.为验证微分求积方法的结果,与伽辽金方法计算结果进行了比较,取得了一致的结果.微分求积法的计算结果用分叉图、相平面、时域曲线以及功率谱进行了描述,结果表明在特定的参数区间存在混沌运动,而通向混沌的道路是经过一系列周期倍化分叉产生的.     

岩体渗透结构类型的划分及其渗透特性研究

提出了一种计算二维有限变形弹塑性摩擦接触问题形状设计灵敏度的算法. 采用主动 集策略和mortar方法处理接触边线上的约束条件. 在mortar接触边线的切线和法线方向上 采用相同的名义罚函数，提出基于名义罚函数的移动摩擦锥算法来正则化接触约束条件，发 展了一种新的二维多体有限变形摩擦接触算法. 在此基础上, 通过将离散形式的摩擦接触问题 控制方程对形状设计变量微分，得到了该路径相关问题的直接微分法解析设计灵敏度 计算格式, 其节点位移灵敏度方程在每个增量步不用迭代、直接求解. 与国际上现有 的二维多体有限变形摩擦接触问题的解析设计灵敏度算法相比，本算法不需分 解为法向和切向推导，表达式较简洁，便于编程实现. 数值算例验证了算法的精度 和有效性.     

弹塑性摩擦接触问题形状设计灵敏度分析

提出了一种计算二维有限变形弹塑性摩擦接触问题形状设计灵敏度的算法.采用主动集策略和mortar方法处理接触边线上的约束条件.在mortar接触边线的切线和法线方向上采用相同的名义罚函数,提出基于名义罚函数的移动摩擦锥算法来正则化接触约束条件,发展了一种新的二维多体有限变形摩擦接触算法.在此基础上,通过将离散形式的摩擦接触问题控制方程对形状设计变量微分,得到了该路径相关问题的直接微分法解析设计灵敏度计算格式,其节点位移灵敏度方程在每个增量步不用迭代、直接求解.与国际上现有的二维多体有限变形摩擦接触问题的解析设计灵敏度算法相比,本算法不需分解为法向和切向推导,表达式较简洁,便于编程实现.数值算例验证了算法的精度和有效性.     

有限谱ENO格式及其应用

首先对王健平提出的有限谱法^[1-3]做了进一步的理论研究，发现了一些新的有限谱法的插值基函数组，并互将有限谱法应用在ENO格式中，构造了有限谱ENO计算格式，然后通过对一维Euler方程的几个经典的模型问题和二维湍流与弱激波相互作用问题的数值计算，并且与理论解或准精确解进行比较分析，从而表明了此格式对于激波和其他间断具有较高的分辨率，在激波附近基本上没有明显的数值振荡，而且对于流场中的细致结构也具有相当高的精度。     

基于非结构化同位网格的SIMPLE算法

通过基于非结构化网格的有限体积法对二维稳态Navier—Stokes方程进行了数值求解。其中对流项采用延迟修正的二阶格式进行离散；扩散项的离散采用二阶中心差分格式；对于压力-速度耦合利用SIMPLE算法进行处理；计算节点的布置采用同位网格技术，界面流速通过动量插值确定。本文对方腔驱动流、倾斜腔驱动流和圆柱外部绕流问题进行了计算，讨论了非结构化同位网格有限体积法在实现SIMPLE算法时，迭代次数与欠松弛系数的关系、不同网格情况的收敛性、同结构化网格的对比以及流场尾迹结构。通过和以往结果比较可知，本文的方法是准确和可信的。     

动脉中脉动流的准二维分析与数值计算

本文考虑了血液的菲牛顿流动特性,对血液在动脉管系中的脉动流建立了准二维流动模型。利用有限差分方法得到了动脉管系内非牛顿流体的准二维不定常流动的数值解。并以人体五根主要动脉所组成的动脉管系为例,进行了详细的数值计算。计算结果表明,在动脉的某些典型位置上。计算所得的理论波形与实测波形是相似的。     

求解固体力学问题的强?弱耦合形式单元微分法

单元微分法是一种新型强形式有限单元法. 与弱形式算法相比, 该算法直接对控制方程进行离散, 不需要用到数值积分. 因此该算法有较简单的形式, 并且其在计算系数矩阵时具有极高的效率. 但作为一种强形式算法, 单元微分法往往需要较多网格或者更高阶单元才能达到满意的计算精度. 与此同时, 对于一些包含奇异点的模型, 如在多材料界面、间断边界条件、裂纹尖端等处, 传统单元微分法往往得不到较精确的计算结果. 为了克服这些缺点, 本文提出了将伽辽金有限元法与单元微分法相结合的强?弱耦合算法, 即整体模型采用单元微分法的同时, 在奇异点附近或某些关键部件采用有限元法. 该策略在保留单元微分法高效率与简洁形式等优点的同时, 确保了求解奇异问题的精度. 在处理大规模问题时, 针对关键部件采用有限元法, 其他部件采用单元微分法, 可以在得到较精确结果的同时, 极大提高整体计算效率. 在本文中, 给出了两个典型算例, 一个是具有切口的二维问题, 一个是复杂的三维发动机问题. 针对这两个问题, 分析了该耦合算法在求二维奇异问题和三维大规模问题时的精度与效率.      

谱体积方法单元分割与问题单元标记方法的改进研究

谱体积方法是一种本质上解决网格依赖性的高精度CFD计算方法,本文研究了二维Euler方程的谱体积方法,提出一种基于切比雪夫多项式的单元分割方法,建立了基于WENO的变量限制器方法,并发展了结合谱体积和控制体的问题单元标记方法.采用15°超声速压缩拐角和NACA0012跨声速流动两个典型算例进行验证,结果表明,该分区方法具有更好的计算精度,标记方法可有效识别不连续区域,在较少的网格下即可获得与密网格传统有限体积法相当的计算精度.     

Measurement of spectrum with particle image velocimetry

The purpose of this paper is to show that the measurement of turbulent spectrum using wholefield velocity techniques such as particle image velocimetry (PIV) is possible. Toward this end, data from the axial plane of a self-similar turbulent axisymmetric jet, at a Reynolds number, based on Taylor microscale of 30 has been analyzed. The two-dimensional velocity data are first high-pass filtered, which educes the vortices. An automated method is then used to identify the vortices and measure their properties. By directly measuring the energy of the vortices, it is possible to plot the turbulence spectrum. The spectrum presented here shows the presence of energy containing and inertial regimes. However, the smallest scales have not been resolved in the measurements. The slope of the spectrum in the inertial subrange is about −1.6. The number of vortices in the two regimes have also been measured. The number of vortices in the energy containing regime is substantially smaller than those in the inertial subrange. The technique has been verified by analyzing another dataset. These results show that the direct measurement of vortex properties with reasonable confidence is possible using PIV and an appropriate vortex eduction technique.     

Flow structure in a flat vortex chamber

We investigate a flow in a flat vortex chamber in which the distance between the end walls is smaller than the radius of the chamber. The study was mainly performed by optical methods: a Töpler device was employed, with the Foucault knife replaced by a diaphragm. It is shown that the flow in the chamber has a complicated spatial structure. In addition to the basic helical flow, an intense “transverse” rotation of the type of Taylor-Görtler vortices occurs. In contrast to previously studied flows, where these vortices were observed near a concave surface, in the motion considered transverse vortices occur in the entire working volume of the chamber. In this case, four parallel vortex filaments are formed. The high intensity of the vortices has allowed one to visualize them by the Töpler method and by “tinting” the flow by highly disperse particles. Quantitative dependences of the dimensions of the vortex cells on the flow regime, i.e., on the pressure of gas deceleration, were obtained.     

Spiral and Wavy Vortex Flows in Short Counter-Rotating Taylor–Couette Cells

Differentially rotating cylinders result in a rich variety of vortical flows for cylindrical Couette flow. In this study we investigate the case of a short, finite-length cavity with counter-rotating cylinders via direct numerical simulation using a three-dimensional spectral method. We consider aspect ratios ranging from 5 to 6. Two complex flow regimes, wavy vortices and interpenetrating spirals, occur with similar appearance to those found experimentally for much larger aspect ratios. For wavy vortices the wave speed is similar to that found for counter-rotating systems and systems in which the outer cylinder is stationary. For the interpenetrating spiral structure, the vortices are largely confined to the unstable region near the inner cylinder. The endwalls appear to damp and stabilize the flow as the aspect ratio is reduced to the point that in some cases the vortical flow is suppressed. At higher inner cylinder speeds, the interpenetrating spirals acquire a waviness and the vortices, while generally near the inner cylinder, can extend all of the way to the outer cylinder. Received 5 November 2001 and accepted 29 March 2002 Published online 2 October 2002 Communicated by H.J.S. Fernando     

不可压缩机翼绕流的有限谱法计算

结合有限谱QUICK格式求解不可压缩粘性流问题。这一格式用于模拟不同攻角下的NACA1200机翼绕流问题。利用体积力，提出了将流场速度从0加速到来流速度的方法。区别于传统的压力梯度为零的边界条件，推导出一个更精确的压力边界条件。为使速度散度保持为零，在泊松方程中给速度散度一个特殊的处理。这一成果说明了有限谱法不但具有很高的精度，而且能灵活地和其他格式一起构造出新的格式，从而成功地应用到复杂流场不可压缩流动的数值计算中。     

Eulerian spectrum of finite-time Lyapunov exponents in compound channels

Fluid flows reveal a wealth of structures, such as vortices and barriers to transport. Usually, either an Eulerian or a Lagrangian frame of reference is employed in order to detect such features of the flow. However, the two frameworks detect structures that have different properties. Indeed, common Eulerian diagnostics (Hua-Klein and Okubo-Weiss criterion) employed in order to detect vortices do not always agree with Lagrangian diagnostics such as finite-time Lyapunov exponents. Besides, the former are Galilean-invariant whereas the latter is objective. However, both the Lagrangian and the Eulerian approaches to coherent structure detection must show some links under any inertial-frame. Compound channels flows have been accurately studied in the past, both from a Lagrangian and an Eulerian point of view. The features detected do not superimpose: Eulerian vortices do not coincide with barriers to transport. The missing link between the two approaches is here recovered thanks to a spectral analysis.

     

Multiscale block spectral solution for unsteady flows

Many problems of interest are characterized by 2 distinctive and disparate scales and a huge multiplicity of similar small‐scale elements. The corresponding scale‐dependent solvability manifests itself in the high gradient flow around each element needing a fine mesh locally and the similar flow patterns among all elements globally. In a block spectral approach making use of the scale‐dependent solvability, the global domain is decomposed into a large number of similar small blocks. The mesh‐pointwise block spectra will establish the block‐block variation, for which only a small set of blocks need to be solved with a fine mesh resolution. The solution can then be very efficiently obtained by coupling the local fine mesh solution and the global coarse mesh solution through a block spectral mapping. Previously, the block spectral method has only been developed for steady flows. The present work extends the methodology to unsteady flows of short temporal and spatial scales (eg, those due to self‐excited unsteady vortices and turbulence disturbances). A source term–based approach is adopted to facilitate a two‐way coupling in terms of time‐averaged flow solutions. The global coarse base mesh solution provides an appropriate environment and boundary condition to the local fine mesh blocks, while the local fine mesh solution provides the source terms (propagated through the block spectral mapping) to the global coarse mesh domain. The computational method will be presented with several numerical examples and sensitivity studies. The results consistently demonstrate the validity and potential of the proposed approach.     

Numerical simulation on evolution of subharmonic low-speed streaks in minimal channel turbulent flow

The evolution of low-speed streaks in the turbulent boundary layer of the minimum channel flow unit at a low Reynolds number is simulated by the direct numer- ical simulation （DNS） based on the standard Fourier-Chebyshev spectral method. The subharmonic sinuous （SS） mode for two spanwise-aligned low-speed streaks is excited by imposing the initial perturbations. The possibilities and the physical realities of the turbulent sustaining in the minimal channel unit are examined. Based on such a flow field environment, the evolution of the low-speed streaks during a cycle of turbulent sus- taining, including lift-up, oscillation, and breakdown, is investigated. The development of streamwise vortices and the dynamics of vortex structures are examined. The results show that the vortices generated from the same streak are staggered along the streamwise direction, while the vortices induced by different streaks tilt toward the normal direction due to the mutual induction effect. It is the spatial variations of the streamwise vortices that cause the lift-up of the streaks. By resolving the transport dynamics of enstrophy, the strength of the vortices is found to continuously grow in the logarithmic layer through the vortex stretching mechanism during the evolution of streaks. The enhancement of the vortices contributes to the spanwise oscillation and the following breakdown of the low-speed streaks.     

A high‐order element‐based Galerkin method for the barotropic vorticity equation

A high‐order element‐based Galerkin method is developed to solve the non‐divergent barotropic vorticity equation (BVE). The solution process involves solving a conservative transport equation for the vorticity fields and a Poisson equation for the stream function fields. The discontinuous Galerkin method is employed for solving the transport equation and a spectral element method (continuous Galerkin) is used for the Poisson equation. A third‐order strong stability preserving explicit Runge–Kutta scheme is used for time integration. A series of tests have been performed to validate the model, which include the evolution of an idealized tropical cyclone and interaction of dual vortices in close proximity. The numerical convergence study is performed by solving the BVE on the sphere where the analytic solution is known. The test results are consistent with physical observations, and the model exhibits exponential convergence. Copyright © 2008 John Wiley & Sons, Ltd.     

石崆山Ⅱ段岩质高边坡稳定性的工程地质系统分析研究

岩质高边坡稳定性的分析评价涉及工程地质学、岩体力学、计算科学等多学科交汇的问题,是一较为复杂的系统工程问题。在系统分析岩质高边坡赋存的地质背景和环境条件的基础上,采用系统分析评价、综合集成的方法应是研究分析和解决该问题的有效和最佳方法。针对漳—龙高速公路石崆山Ⅱ段岩质高边坡工程,在系统分析边坡工程地质特性的基础上,采用赤平极射投影法和有限单元(FEM)法等,进行综合评价和系统分析,获得的稳定性结论,已正常运营使用若干年,反映了系统分析,综合评价方法是成功和有效的。它表明,综合评价、系统分析应是岩质高边坡稳定性评价分析的重要途径;它的综合内容和集成方式及其完善与工程实用性,有待进一步深入的研究和工程实践的运用及其经验的积累。     

Analysis of tornado and near-ground turbulence using a hybrid meteorological model/engineering LES method

A new hybrid meteorological model/engineering LES method was used to analyze a tornado and near-ground turbulence under realistic conditions. The hybrid method estimates high frequency turbulence regeneration in an actual severe storm that has complex thermal conditions in order to alleviate the problem of high frequency component dissipation in meteorological models and generate appropriate field data to investigate near-ground flow and wind loading on buildings. The high frequency regeneration method was validated in the convective boundary layer and the energy spectrum of the velocity field was successfully extended to higher frequency region in good agreement with −5/3 Kolmogorov law.Multi-scale simulations of a tornado were conducted based on meteorological model outputs with three different terrain conditions, including an actual urban building geometry and terrain, and the changes in the main tornado vortex and the interactions with near-ground turbulent field were examined. On roughened surfaces with uniform blocks and buildings, the main tornado vortex was connected to near-ground vertical vortices arising due to the urban geometry. The structure was significantly deformed, splitting into numerous finer vortices below several times the building height. These near-ground vortices create localized sharp pressure drop patterns and also affect the movement of the tornado. These effects of low pressure on buildings were quantitatively analyzed.