Green’s function solution for transient heat conduction in annular fin during solidification of phase change material

The Green’s function method is applied for the transient temperature of an annular fin when a phase change material (PCM) solidifies on it. The solidification of the PCMs takes place in a cylindrical shell storage. The thickness of the solid PCM on the fin varies with time and is obtained by the Megerlin method. The models are found with the Bessel equation to form an analytical solution. Three different kinds of boundary conditions are investigated. The comparison between analytical and numerical solutions is given. The results demonstrate that the significant accuracy is obtained for the temperature distribution for the fin in all cases.     

The matric algorithm of Lyapunov exponent for the experimental data obtained in dynamic analysis

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基于基因表达式编程的数据驱动湍流建模

计算流体动力学是湍流研究的重要手段, 其中雷诺平均模拟在航空航天等实际工程中得到了广泛应用. 雷诺平均模拟的结果很大程度上依赖于湍流模型的预测精度, 而实际工程应用中常用的模型往往精度有限. 近年来, 数据驱动的湍流建模方法得到越来越多的关注. 本文介绍了基于基因表达式编程 (gene-expression programming, GEP) 方法的湍流建模相关进展. 本文首先讨论基因表达式编程应用于湍流建模的具体方法, 包括基本算法、显式代数应力模型和湍流传热两种建模框架、模型测试方法以及损失函数设置等. 在此基础上, 基因表达式编程方法被应用于涡轮叶栅尾流混合、竖直平板间自然对流、三维横向流中的射流等问题. 结果表明, GEP可以有效提升常用模型对于尾流混合损失、壁面热通量等关键参数的预测精度. 基因表达式编程方法可以显式给出模型方程, 因此模型具有可解释性强等特点. 基于双向耦合方法得到的模型还被证明具有较好的后验测试精度和鲁棒性. 基因表达式编程方法还被初步应用于大涡模拟亚格子应力和边界层转捩等问题的建模, 在不同湍流建模领域表现出很大的潜力.      

Local discontinuous Galerkin method for a nonlocal viscous conservation laws

The purpose of this article is to investigate high‐order numerical approximations of scalar conservation laws with nonlocal viscous term. The viscous term is given in the form of convolution in space variable. With the help of the characteristic of viscous term, we design a semidiscrete local discontinuous Galerkin (LDG) method to solve the nonlocal model. We prove stability and convergence of semidiscrete LDG method in L² norm. The theoretical analysis reveals that the present numerical scheme is stable with optimal convergence order for the linear case, and it is stable with sub‐optimal convergence order for nonlinear case. To demonstrate the validity and accuracy of our scheme, we test the Burgers equation with two typical nonlocal fractional viscous terms. The numerical results show the convergence order accuracy in space for both linear and nonlinear cases. Some numerical simulations are provided to show the robustness and effectiveness of the present numerical scheme.     

A representative volume element based on translational symmetries for FE analysis of cracked laminates with two arrays of cracks

A methodology is proposed for the construction of a representative volume element (RVE) for analysis of laminated composites containing two arrays of ply cracks running in different directions. The only requirement is that the cracks in any ply are uniformly spaced, and if more than one ply of a given orientation is cracked, then the crack spacing of individual plies must only be in exact multiples of each other. The spacing of cracks in the two directions can be fully independent. The RVE is constructed through a systematic consideration of translational symmetries present in the cracked laminate. As a result, the boundary conditions on the RVE can be imposed without compromising accuracy. Examples of the application of the RVE methodology are given to illustrate its broad capability and a finite element (FE) stress analysis is performed for these cases to illustrate results such as the crack surface displacements, local stress fields and RVE-averaged elastic properties. For one case, the average properties are compared with experimental results, showing good agreement.     

A comparative study of the MQD method and several correlation-based PIV evaluation algorithms

 The Minimum Quadratic Difference (MQD) method is compared with methods conventionally used for the evaluation of PIV recordings, i.e. correlation-based evaluation with fixed interrogation windows (auto- or cross-correlation) and correlation-based tracking. The comparison is performed by studying the evaluation accuracy achieved when applying these methods to pairs of synthetic PIV recordings for which the true displacements are known. The influence of the magnitude of the particle image displacement, evaluation window size, density of particle image distribution, and particle image size on the accuracy are investigated. In all these cases the best results in terms of a statistical error are obtained with the MQD method. The superiority of the MQD method can be explained with its potential of accounting for non-uniformities in the particle image distribution and a non-uniform illumination. It is also shown that the conventional correlation-based methods may produce principal errors that are non-existent for the MQD method. The evaluation speed achievable for the MQD method by making use of the FFT is comparable to that common for the generally used auto- or cross-correlation algorithm. Finally, a quantitative explanation is given for the often observed phenomenon that PIV velocity results tend to be smaller than the true values. Received: 15 May 1998/Accepted: 24 April 1999     

Comparison of hybrid and standard discontinuous Galerkin methods in a mesh-optimisation setting

This paper assesses the benefits of hybridization on the accuracy and efficiency of high-order discontinuous Galerkin (DG) discretizations. Two hybridized methods are considered in addition to DG: hybridized DG (HDG) and embedded DG (EDG). These methods offer memory and computational time savings by introducing trace degrees of freedom on faces that become the only globally-coupled unknowns. To mitigate the effects of solution singularities on accuracy, the methods are compared in an adaptive setting on meshes optimised for the accurate prediction of chosen scalar outputs. Compressible flow results for the Euler and Reynolds-averaged Navier-Stokes equations demonstrate that the hybridized methods offer cost savings relative to DG in memory and computational time. In addition, for the cases tested, EDG yields the lowest error levels for a given number of degrees of freedom. These benefits disappear on uniformly-refined meshes, indicating the importance of using order-optimised meshes when comparing the discretizations.     

Some further results of the boundary element method for plate bending

Some further results of the boundary element method for the Kirchhoff type plate bending problems are given. The direct boundary integral equation-boundary element scheme with higher conforming properties is used for several computation examples. The results of computation show that the numerical scheme seems to be more economical in computer time and with better accuracy in comparison with some previous results.     

On the characterization of grid density in grid refinement studies for discretization error estimation

This paper discusses the estimation of discretization errors on the basis of power series expansions for grid sets that are not geometrically similar, that is, grids not exhibiting a constant grid refinement ratio for the entire computational domain. Simple test cases with structured and unstructured grids are used to demonstrate that reliable error estimates on the basis of power series expansions can be made if the grids are refined systematically. However, if the grid refinement ratio is not constant in the complete domain, the definition of the typical cell size is not obvious, and the observed order of accuracy may not be equal to the expected theoretical order of the discretization. Some alternatives for the definition of the typical cell size are tested. In these tests, the error estimation does not show a significant effect of the definition of the typical cell size even for some cases with data sets clearly outside the ‘asymptotic range’. For non‐geometrically similar grids, the best estimates of the observed order of accuracy are obtained with the typical cell size on the basis of the mode of the cell size (the cell size that occurs more often in a given grid). Copyright © 2012 John Wiley & Sons, Ltd.     

Natural frequencies of longitudinal oscillations for a nonuniform variable cross-section rod

The natural frequencies of longitudinal oscillations of a rod such that its Young’s modulus, the density, and the cross-sectional area are functions of the longitudinal coordinate are analyzed. For solving the corresponding problem, an integral formula is used to represent the general solution to the original Helmholtz equation with variable coefficients in terms of the general solution to the accompanying equation with constant coefficients. Frequency equations are derived in the form of rapidly converging Leibniz series for three types of boundary conditions. For these cases the frequency zerothapproximation equations are given to quickly find the lowest natural frequencies with an adequate accuracy.     

结构参数大修改时的特征值重分析方法

就结构参数发生大修改的情况提出了两种高精度的特征值重分析方法：Ｐａｄｅ　逼近法和推广的Ｋｉｒｓｃｈ混合法．利用这两种方法,计算了一个具有２０２个结点,３５７个梁单元的平面框架的近似特征值．计算结果表明,所提出的方法是结构参数修改时的特征值重分析的有效方法．     

一个基于塑性的损伤本构模型的参数辨识

研究了一个用于混凝土的基于塑性的损伤模型本构参数辨识问题。把从实验获得的应力-应变曲线与数值计算中获得的应力-应变曲线的差别,作为局部水平上最小二乘法的目标函数。为了求解这个反问题,局部水平上求解损伤弹塑性正问题的子程序被嵌入到本文的反问题的迭代格式之中。灵敏度系数矩阵是通过有限差分方法近似计算得到的。给出的数值计算例子计算了单轴压缩试验结果的参数辨识问题。采用反分析得到的模型参数值,对单向拉伸及三种不同侧压作用下的压缩试验进行了数值模拟。数值结果表明:本文采用的应力反分析计算格式稳定,且具有合理的准确性,数值计算得到的应力-应变结果可以较准确地拟合实验曲线。     

Capturing the baroclinic effect in non-Boussinesq gravity currents

Direct numerical simulations of two-dimensional gravity currents with small and medium density variations are performed using different non-Boussinesq buoyancy approximations. Taking the full low-Machnumber approximation as the reference, the accuracy of several buoyancy terms are examined. It is found that all considered buoyancy terms performed well in the cases with small density variation. In the cases with medium density variation, the classical gravitational Boussinesq’s buoyancy term showed the lack of accuracy, and a simple correction did not make any improvement. In contrast, the recently introduced second-order buoyancy term showed a significantly higher accuracy. The present results and our previous derivations indicate that simple algebraic buoyancy approximations extended from the Boussinesq’s gravitational buoyancy are unlikely to achieve an accuracy beyond first order. Instead, it seems necessary to solve at least one extra Poisson equation for buoyancy terms to capture the higher-order baroclinic effect. An approximate analysis is also provided to show the leading term of the non-Boussinesq effect corresponding to gravity.     

A quadratic-element formulation of the complex variable boundary element method

The complex variable boundary element method (CVBEM) for simply connected domains is extended to include the use of quadratic elements and interpolating functions. The derivation follows the format for linear elements given in the literature, with second-degree Lagrange polynomials taken as the interpolating functions. The quadratic-element CVBEM nodal- and interior-point equations are given in detail, and the resulting formulation is successfully tested by solving example problems with available analytical solutions. Comparisons of computational efficiency and accuracy are made between the solutions obtained using linear and quadratic elements. Additional comparisons are made using published results from other boundary element methods.     

Some results of testing simple structures under constant and variable loading during creep

The design of two rigs for room-temperature creep testing is described. One is for testing beams in pure bending and the other for testing circular plates simply supported at the outer edge and loaded through a rigid central boss. A system for giving reproducible step-loading cycles is also described. Typical creep-deformation curves for commercially pure aluminum beams and plates under steady and variable loading are given. These test results are compared with predictions based on the tensile-creep behavior. The repeatability and accuracy of these results are also discussed.     

AN APPROXIMATE SOLUTION OF EIGEN－FREQUENCIES OF TRANSVERSE VIBRATION OF RECTANGULAR PLATES WITH ELASTICAL RESTRAINTS

ＡＮＡＰＰＲＯＸＩＭＡＴＥＳＯＬＵＴＩＯＮＯＦＥＩＧＥＮ－ＦＲＥＱＵＥＮＣＩＥＳＯＦＴＲＡＮＳＶＥＲＳＥＶＩＢＲＡＴＩＯＮＯＦＲＥＣＴＡＮＧＵＬＡＲＰＬＡＴＥＳＷＩＴＨＥＬＡＳＴＩＣＡＬＲＥＳＴＲＡＩＮＴＳ（周叮）ＡＮＡＰＰＲＯＸＩＭＡＴＥＳＯＬＵＴ...     

PRECISE INTEGRAL ALGORITHM BASED SOLUTION FOR TRANSIENT INVERSE HEAT CONDUCTION PROBLEMS WITH MULTI-VARIABLES

IntroductionIHCPs (InverseHeatConductionProblems)arecloselyassociatedwithmanyengineeringaspects,andwelldocumentedintheliteratures,coveringtheidentificationsofthermalparameters[1,2 ],boundaryshapes[3],boundaryconditions[4 ]andsource_relatedterms[5 ,6 ]etc .Howeveritseemsthatonlylittleworkisdirectlyconcernedwithmulti_variablesidentificationsbyauthors’knowledge.Tsengetal.presentedanapproachtodeterminingtwokindsofvariables[7],butonlygavefewnumericalexamplestodeterminethemsimultaneously .Thesol…     

Numerical scheme for accurately capturing gas migration described by 1D multiphase drift flux model

A numerical scheme is designed and implemented to solve a simplified set of equations modeling 1-D multi-phase flow based on drift flux model in an isothermal setup with phase dissolution. The difficulty in obtaining the analytical Jacobian of the fluxes leads to the difficulty in obtaining an efficient linearized Riemann solver which in turn affects the accuracy in capturing the contact wavefront/gas migration. To address this issue a fully explicit second order finite volume solver based on flux corrected transport (FCT) is implemented. The choice of variables used for limiting the fluxes affects the amount of numerical diffusion and an appropriate choice of the gradient in volume fraction is used. Practical test cases while drilling in the oil and gas industry, of gas injection inside a well annulus and shut-in of the vertical well are presented. The results conclude that the FCT solver is better and efficient for accurately capturing gas migration for multi-phase models with phase behaviour involving slip velocities given by algebraic relations.     

多传感器多尺度融合估计在组合导航系统中的应用

基于某一给定尺度上的动态系统和不同尺度上的观测系统建立了多传感器的多尺度融合估计模型及算法，并将此算法应用于GPS／INS组合导航系统中，获得了比仅在单一尺度上进行估计更好的结果，有效地提高了组合导航系统的精度。