Finite Element Method Based on Equivalent Magnetic Energy Method for Computation of 2D Nonlinear Eddy Current Field

In this paper, the finite element method using vector potential in applications to 2D nonlinear eddy current field is discussed. The authors use the equivalent magnetic energy method to deal with magnetization curve of ferromagnetic material,and present the formulation of 2D nonlinear eddy current field.With this method the authors analyze the eddy current field in an induction ladle furnace and the force distribution in the charge (molten metal),and plot the corresponding curves.

An Introductory Note on Finite Element Problems Based on the Eddy Current Testing Approach

The paper addresses the first eddy current benchmark problem proposed by the World Federation of Nondestructive Evaluation Centers (WFNDEC). The problem simulates the eddy current response to the presence of an axisymmetric circumferential defect in an Inconel-600 tube. All simulations employ the axisymmetric code of the electromagnetic field simulator Finite Element Method Magnetics. For three different frequencies of excitation, it is explained how the displacement of the detecting coil inside the tube leads to a variation in the impedance of the eddy current coil. Variations of the resistive and inductive components of the impedance with distance from the defect region are used to build the impedance trajectory for each frequency of analysis.

Eddy Current Analyses by Domain Decomposition Method Using Double-Double Precision

A matrix equation solved in an eddy current analysis,??-??method based on a domain decomposition method becomes a complex symmetric system.In general,iterative method is used as the solver.Convergence of iterative method in an interface problem is improved by increasing an accuracy of a solution of an iterative method of a subdomain problem.However,it is difficult to improve the convergence by using a small convergence criterion in the subdomain problem.Therefore,authors propose a method to introduce double-double precision into the interface problem and the subdomain problem.This proposed method improves the convergence of the interface problem.In this paper,first,we describe proposed method.Second,we confirm validity of the method by using Team Workshop Problem 7,standard model for eddy current analysis.Finally,we show effectiveness of the method from two numerical results.

3D Eddy Current and Temperature Field Analysis of Large Hydro-generators in Leading Phase Operations

As a common practice,a large hydro-generator will operate in leading phase conditions to absorb the reactive power of the power grid.However,the accurate and precise prediction of the leading phase operation capacity of a large hydro-generator has always been a formidable challenge to engineers and academicians because it is extremely hard to compute the eddy currents and losses as well as the local overheating in the pressure plate and finger.To address this problem,a full three dimensional(3D)finite element model and method of the coupled eddy current and temperature fields in the end region of a large hydro-generator are developed.The equivalent medium parameters used in the computations are comprehensively discussed.Moreover,some numerically based solution methodologies for accurate computation of the field and armature currents under different leading phase conditions are proposed.Numerical results on the coupled eddy current and temperature fields in the end regions of a 250 MW hydro-generator confirm positively the feasibility of the present work.

Calculation of Eddy Current Loss and Short-circuit Force in SSZ11-50000/110 Power Transformer

The ?method is used in this paper to calculate the leakage magnetic field of SSZ11-50000/110 Power transformer, and by which the structures’ influences to the main leakage flux are analyzed. Through the combination of the product and TEAM Problem 21B, the surface impedance method shows its great advantage in the calculation of eddy current loss.

Comparison of three formulations for eddy-current problems in a spiral coil electromagnetic acoustic transducer

Three differential equations based on different definitions of current density are compared. Formulation I is based on an incomplete equation for total current density （TCD）. Formulations II and {I1 are based on incomplete and complete equations for source current density （SCD）, respectively. Using the weak form of finite element method （FEM）, three formulations were applied in a spiral coil electromagnetic acoustic transducer （EMAT） example to solve magnetic vector potential （MVP）. The input impedances calculated by Formulation III are in excellent agreement with the experimental measurements. Results show that the errors for Formulations I ＆ II vary with coil diameter, coil spacing, lift-off distance and external excitation frequency, for the existence of eddy-current and skin ＆ proximity effects. And the current distribution across the coil conductor also follows the same trend. It is better to choose Formulation I instead of Formulation Ili to solve MVP when the coil diameter is less than twice the skin depth for Formulation I is a low cost and high efficiency calculation method.

High performance parallel computing of large eddy simulation of the flow in a curved duct with square cross section

Large eddy simulation(LES) cooperated with a high performance parallel computing method is applied to simulate the flow in a curved duct with square cross section in the paper. The method consists of parallel domain decomposition of grids, creation of virtual diagonal bordered matrix, assembling of boundary matrix, parallel LDL^T decomposition, parallel solving of Poisson Equation, parallel estimation of convergence and so on. The parallel computing method can solve the problems that are difficult to solve using traditional serial computing. Furthermore, existing microcomputers can be fully used to resolve some large-scale problems of complex turbulent flow.

Large eddy simulation for wind field analysis based on stabilized finite element method

In this paper,a stabilized finite element technique,actualized by streamline upwind Petrov-Galerkin(SUPG) stabilized method and three-step finite element method(FEM),for large eddy simulation(LES) is developed to predict the wind flow with high Reynolds numbers.Weak form of LES motion equation is combined with the SUPG stabilized term for the spatial finite element discretization.An explicit three-step scheme is implemented for the temporal discretization.For the numerical example of 2D wind flow over a square rib at Re=4.2×105,the Smagorinsky's subgrid-scale(SSGS) model,the DSGS model,and the DSGS model with Cabot near-wall model are applied,and their results are analyzed and compared with experimental results.Furthermore,numerical examples of 3D wind flow around a surface-mounted cube with different Reynolds numbers are performed using DSGS model with Cabot near-wall model based on the present stabilized method to study the wind field and compared with experimental and numerical results.Finally,vortex structures for wind flow around a surface-mounted cube are studied by present numerical method.Stable and satisfactory results are obtained,which are consistent with most of the measurements even under coarse mesh.

Study on the Effect of Magnetic Pole Clipping Angle on the Eddy Current Loss of Permanent Magnets in the Rotor of Magnetically Levitated Permanent Magnet Synchronous High-Speed Electric Spindles

Aiming at the problem of high temperature and even demagnetization failure of permanent magnet (PM) due to PM eddy current loss in PM synchronous high-speed motors, this paper proposes a technique to lessen PM eddy current loss by cutting the angle of PM poles to change the shape of PM structure. Firstly, an analysis is conducted on the mechanism of PM synchronous high-speed motor eddy current loss production, the theoretical analytical model of PM eddy current loss is deduced, and it is theoretically proved that the magnetic pole shaving angle can reduce PM eddy current loss. Then, a 25 KW surface-type PM synchronous high-speed motor as an object, using two-dimensional time-step finite element method (FEM) to model and analyze PM eddy current loss. The results show that the smaller the PM pole shaving angle, the less its eddy current loss will be, it is possible to minimize the pole shaving angle of eddy current loss by 9.8% compared to the unshaved angle. Finally, the temperature field of the PM is calculated using a finite element method, and the outcomes demonstrate that the maximum temperature of the PM with a magnetic pole shaving angle can be reduced by about 5% compared with the unshaved angle.

轮缘推进永磁电机-护套-介质系统建模与仿真

为了降低轮缘推进器永磁电机的涡流损耗,研究护套材料与厚度对永磁电机涡流损耗的影响,基于有限元电磁分析软件ANSYS Electronics Desktop,建立电机-护套-介质系统模型,并通过仿真结果与数值计算结论的对比验证模型准确性;计算永磁电机定转子护套、永磁体涡流密度分布,分析护套材料与厚度对涡流损耗的影响规律。结果表明:护套材料电导率较高时护套中的涡流密度远大于永磁体中的,电导率较低时两者大小相近;采用电导率较低的护套材料时电机产生的涡流损耗远小于采用电导率较高的护套材料;护套材料对护套单位体积涡流损耗影响较大,对永磁体影响较小;定转子护套的厚度比与产生的涡流损耗呈正相关;随着护套厚度比增大,采用电导率较低的护套对永磁体及护套单位体积涡流损耗影响较小,而电导率较高的护套因为屏蔽作用能够通过降低永磁体的涡流密度来降低永磁体涡流损耗;气隙介质在空气、淡水、海水中的变化对电机的磁通密度分布没有显著影响。研究成果可为轮缘推进器永磁电机护套设计提供参考。

基于Riccati传递矩阵法的永磁涡流联轴器固有频率分析

在对永磁涡流联轴器进行模态特性研究时,为了提高对联轴器转子系统的固有频率分析计算的准确度,利用传递矩阵法构建了转子的动力学分析模型。将永磁体的磁力统一化为零质量铰链连接,简化了涡流联轴器的磁电作用力,将复杂的研究模型转化为一个机械强度问题,使用Riccati传递矩阵法对完成等效化处理的转子进行模态分析,得到联轴器的固有频率与对应振型。在此基础上,将分析结果与精细三维有限元仿真结果进行了对比。结果表明,该方法能够较准确地对永磁涡流联轴器进行固有频率分析,与高精度仿真模型分析产生的结果误差不超过8%。通过改进计算数据与有限元分析结果进行对比研究,为永磁涡流联轴器的动力学特性研究提供了理论依据。

表贴式永磁电机在PWM激励下永磁体涡流损耗计算模型

针对现有模型难以计算PWM激励下表贴式永磁电机永磁体涡流损耗问题,提出了一种计算由PWM谐波引起的永磁体内涡流损耗计算模型。该模型通过磁导率分布函数获取气隙径向磁密,能够考虑定子开槽及谐波电流影响。首先,在忽略涡流反作用情况下解析计算了永磁体内磁密变化率;然后,应用有限差分法数值计算了永磁体内电位,综合得到了涡流损耗;最后,用有限元法验证了模型的准确性。研究结果表明:随着永磁体分段数的增大,涡流损耗减小,涡流反作用也随之减弱;永磁体涡流损耗主要由1倍、2倍开关频率附近电流谐波引起。

Adaptive hp-Finite Element Computations for Time-Harmonic Maxwell’s Equations

In this paper,hp-adaptive finite element methods are studied for timeharmonic Maxwell’s equations.We propose the parallel hp-adaptive algorithms on conforming unstructured tetrahedral meshes based on residual-based a posteriori error estimates.Extensive numerical experiments are reported to investigate the efficiency of the hp-adaptive methods for point singularities,edge singularities,and an engineering benchmark problem of Maxwell’s equations.The hp-adaptive methods show much better performance than the h-adaptive method.

90°弯曲圆管内流动数值模拟

为验证数值模拟方法对于边界形状复杂流场的适用性,应用湍流大涡模拟方法对90°弯曲圆管内流动进行了数值模拟．采用Taylor-Galerkin有限元法求解．数值计算的结果与实验结果吻合较好．表明大涡模拟方法适用于边界形状复杂,存在各向异性的大尺度涡的流动仿真．

方形截面弯管二次流数值模拟

应用湍流大涡模拟方法对含有和不含导流叶片的方形截面 90°弯道的二次流动进行了数值模拟 ,同时给出了Taylor-Galerkin有限元离散格式。管道加装叶片后 ,形成了两对二次流 ,其强度较低且沿程变化不大 。

电涡流传感器的有限元仿真研究与分析

电磁场的分布情况是影响电涡流传感器灵敏度和线性度的主要原因。从电涡流传感器的基本原理出发,采用有限元方法,利用ANSYS语言,通过建模、定义材料特性、划分网格、设置边界条件、加载及求解等,对电涡流传感器的电磁场进行仿真研究,并由理论公式验证模型的正确性。通过计算3种尺寸参数不同的线圈,研究分析了线圈的形状结构对传感器灵敏度和线性度的影响,对于电涡流传感器线圈的设计具有指导意义。

有限元–边界元耦合法在运动导体涡流场中的应用

基于A,φ-A法和库伦规范,推导了导体区域和非导体区域的有限元方程及自由空间的边界元方程,通过引入交界面条件,实现了将边界元矩阵等效为有限元矩阵求解的有限元-边界元耦合法(finite element and boundary element coupling method,FE-BECM)。将FE-BECM应用于TEAM-7问题的计算,验证了该方法处理开域涡流问题的有效性。当FE-BECM应用于运动导体涡流场(moving conductor eddy current,MCEC)问题时,用有限元离散源电流区域和运动部件,用边界元离散自由空间并关联相互独立的有限元区域。该方法克服了常规有限元法使用1套网格处理运动问题所遇到的麻烦。使用有限元-边界元耦合法对单级线圈炮问题进行了计算,验证了算法处理运动导体涡流场问题的有效性。

基于COMSOL有限元法的电涡流传感器仿真

为了研究电涡流传感器中电涡流探头线圈的结构参数对检测性能的影响,以电磁场理论为基础,采用有限元分析法,以有限元仿真软件COMSOL为工具,建立电涡流传感器的检测模型,通过仿真研究电涡流传感器探头的电磁特性和影响其性能的探头线圈内径、外径、厚度等结构参数.结果表明:电涡流传感器探头线圈的电阻值与电抗值随线圈内径和外径的增大及厚度的减少而呈上升趋势,当内径和外径越大、厚度越小时,电涡流传感器的灵敏度越高,且线圈厚度对传感器灵敏度的影响更明显.研究结果对研制用于钢闸门缺陷检测的电涡流传感器的优化设计具有一定的参考价值.

弯曲管段内流动的大涡模拟

本文应用湍流大涡模拟方法对三维空间的弯管流进行了数值模拟。计算中使用了隐含流线迎风耗散作用的具有三阶部分展开的 Taylor_ Galerkin离散格式 ,导出了经 Gauss滤波后的基本方程组的有限元列式。数值计算结果与实验结果符合较好 。

线圈形状及几何参数对电涡流传感器性能的影响

针对电涡流传感器探头线圈形状及其参数对传感器灵敏度和线性范围的影响问题,本文以Biot-Savart定律为基础,推导了具有梯形截面的矩形柱线圈和圆形柱线圈对称轴上任一点的磁场分布,确定了在以位移为检测量的电涡流传感器中采用圆柱线圈更合理,并通过有限元法研究和分析了在线圈匝数密度不变和变化2种情况下圆柱线圈内径、外径、厚度、截面形状(矩形、梯形和倒梯形)对传感器灵敏度和线性范围的影响,为合理选择线圈参数和优化传感器性能提供参考。