基于mixed Lagrangian/Eulerian方法的轮轨滚动接触特性分析

为了缩短有限元方法显式计算轮轨滚动接触的时间,采用mixed Lagrangian/Eulerian方法建立了轮轨滚动接触有限元模型.应用该模型对轮轨接触区的单元进行细化,计算了列车在启动、运行和制动工况下轮轨的接触特性.计算结果表明:不同工况下,轮轨滚动接触区最大Mises应力、最大接触应力和接触斑面积等法向特性变化幅度均在2%以内,但接触区纵向截面中Mises应力分布及纵向剪切应力分布有较大变化;启动和制动工况下,最大Mises应力和最大纵向剪切应力位置均比自由滚动时更接近于轮轨表面;不同工况下,摩擦力大小和方向发生变化,在列车牵引和制动工况中,摩擦力达到极限时轮轨间出现完全滑动,摩擦力方向与滑动方向相反,且不同速度等级下的纵向摩擦力变化幅度也在2%以内.

基于level set的Eulerian-Lagrangian耦合方法及其应用

提出了一种基于水平集的Eulerian-Lagrangian耦合方法,其中Lagrangian方法采用相容显式有限元拉氏方法,Eulerian方法采用基于近似Riemann解的有限体积Eulerian方法,多介质界面处理采用新的水平集和Ghost方法计算.给出了若干数值算例,包括激波管问题以及金属和气体的运动界面及其大变形问题,并分别与精确解和相容显式有限元拉氏方法的计算结果进行了对比.数值结果表明,该方法计算结果正确,精度较高,能够准确捕捉物质界面,适用于处理大变形问题.

高温气流内顺/逆流喷雾的Eulerian-Lagrangian数值仿真(英文)

用Eulerian-Lagrangian方法对高温气流内顺/逆流喷雾过程进行了数值仿真。气相方程用Eulerian方法建立,用k-ε模型封闭;液滴相方程用Lagrangian方法建立,采用了随机轨道模型;考虑了气体和液滴间的双向耦合。结果表明,高温气流内喷雾后,气相流场内产生了速度亏损和温度亏损,气体出口压力变化不大,液滴运动决定于气流湍流强度和自身惯性力,液滴在气道内的停留时间决定于液滴运动特性和气流湍流强度;逆流喷雾对气流的影响比顺流喷雾时大。仿真结果与文献结果基本一致。

基于ε-约束方法的增广Lagrangian多目标协同进化算法

介绍了一种利用协同进化算法求解多目标优化问题的算法。这种算法首先采用ε- 约束方法对多目标优化问题进行处理 ,使其转化为一个单目标带约束的优化问题 ;然后 ,采用增广Lagrangian方法把这个单目标约束优化问题转化成一个存在鞍点的二人零和博弈问题 ;最后 ,利用协同进化的思想 ,用两个种群分别表示目标函数和约束这两个局中人 ,对这个二人零和博弈问题求解。进化过程中的选择、重组和变异算子均采用简单遗传算法(SGA)的机制。通过对两个实验测试问题的研究可以看出 ,这种算法比其它同类进化算法所得的结果要精确、稳定。

二维Lagrangian坐标系下可压气动方程组的间断Petrov-Galerkin方法（英文）

构造矩形网格下求解Lagrangian坐标系下气动方程组的单元中心型格式.空间离散采用控制体积间断Petrov-Galerkin方法,时间离散采用二阶TVD Runge-Kutta方法.利用限制器来抑制非物理震荡并保证RKCV算法的稳定性.构造的算法可以保证物理量的局部守恒.与Runge-Kutta间断Galerkin(RKDG)方法相比较,RKCV方法的计算公式少一项积分项使得计算较简单.给出一些数值算例验证了算法的可靠性及效率.

矩阵不等式约束下矩阵方程最小二乘问题的增广Lagrangian方法

称X∈R^(m×n)为实(R,S)对称矩阵,若满足X=RXS,其中R∈R^(m×m)和S∈R^(n×n)为非平凡实对合矩阵,即R=R^(-1)≠±I_m,S=S^(-1)≠±I_n.该文将优化理论中求凸集上光滑函数最小值的增广Lagrangian方法应用于求解矩阵不等式约束下实(R,S)对称矩阵最小二乘问题,即给定正整数m,n,p,t,q和矩阵A_i∈R^(m×m),B_i∈R^(n×n)(i=1,2,…,q),C∈R^(m×m),E∈R^(p×m),F∈R^(n×t)和D∈R^(p×t),求实(R,S)对称矩阵X∈R^(m×m)且在满足相容矩阵不等式EXF≥D约束下极小化‖∑_(i=1)~qA_iXB_i-C‖,其中EXF≥D表示矩阵EXF-D非负,‖·‖为Frobenius范数.该文给出求解问题的矩阵形式增广Lagrangian方法的迭代格式,并用数值算例验证该方法是可行且高效的.

基于CEL方法的带结构物溃坝流数值模拟

随着全球气温的不断升高,极端天气现象增多,溃坝现象成为水工结构方向需要重点防范的自然灾害。溃坝流的发展会对下游结构物产生巨大的破坏作用,因此深入探究溃坝流现象的水动力学特性以及溃坝流下游结构物所受到的冲击力影响势在必行。本文针对带有结构物的溃坝流动问题现象,采用CEL方法(Coupled Eulerian-Lagrangian analysis,耦合欧拉-拉格朗日方法),对于溃坝流的发展、演化进行了数值模拟。研究结果表明,模拟结果中溃坝流自由表面及流体尖端时程变化与文献试验结果拟合较好,CEL方法可应用在溃坝流现象的模拟,并且具有较好的准确性和精度。结构物材料性能、高度及与结构物与溃坝流间的位置,均会影响溃坝流的运动状态以及结构物的受力变形状态,在不考虑结构物破坏的情况下,提高结构物弹性模量,增加结构物高度,以及减小结构物与溃坝流间的距离均可提高结构物对于溃坝流的阻挡作用。

基于Lagrangian-Eulerian耦合的放射性物质大气扩散模型研究

针对中尺度扩散下拉格朗日模型和欧拉模型在计算效率和准确度方面的矛盾,建立了适用于模拟核事故下放射性物质大气扩散的基于拉格朗日模型与欧拉模型耦合的预测模型,以国内某核电站为例进行了放射性物质扩散的虚拟算例模拟,对模型进行验证和分析。结果表明:拉格朗日-欧拉耦合模型可以较好地模拟放射性物质在大气中的扩散,不仅可以提升中尺度和大尺度下的计算效率,还可以有效减小欧拉模型初始条件所带来的系统误差。

A hybrid Lagrangian-Eulerian numerical model for sea-ice dynamics

A hybrid Lagrangian - Eulerian （HLE） method is developed for sea ice dynamics, which combines the high computational efficiency of finite difference method （FDM） with the high numerical accuracy of smoothed particle hydrodynamics （SPH）. In this HLE model, the sea ice cover is represented by a group of Lagrangian ice particles with their own thicknesses and concentrations. These ice variables are interpolated to the Eularian gird nodes using the Gaussian interpolation function. The FDM is used to determine the ice velocities at Eulerian grid nodes, and the velocities of Lagrangian ice particles are interpolated from these grid velocities with the Gaussian function also. The thicknesses and concentrations of ice particles are determined based on their new locations. With the HLE numerical model, the ice ridging process in a rectangular basin is simulated, and the simulated results are validated with the analytical solution. This method is also applied to the simulation of sea ice dynamics in a vortex wind field. At last, this HLE model is applied to the Bohai Sea, and the simulated concentration, thickness and velocity match the satellite images and the field observed data well.

适用欧拉-拉格朗日方法模拟气液泡状流的气泡破碎模型

欧拉-拉格朗日方法已被广泛应用于模拟鼓泡塔等气-液反应器内的流型、气泡尺寸(或气含率)及其分布。文献中该方法主要基于临界Weber数观点来描述气泡破碎行为,且破碎后的子气泡尺寸由随机数确定。但现有实验和理论研究表明,临界Weber数约束不能体现气体密度等物性参数和泡内气体重分布对气泡破碎行为的影响。针对这些不足,提出了适用欧拉-拉格朗日框架且考虑泡内气体重分布贡献的气泡破碎机理模型,并利用开源软件OpenFOAM开发了基于新破碎模型的求解器。新模型预测结果能较好地吻合实验测量的时均轴向液速、气泡尺寸及其分布等实验数据。特别地,考虑泡内气体重分布现象的破碎机理模型成功预测了实验观测的气泡尺寸双峰分布特征。

Hybrid N-order Lagrangian Interpolation Eulerian-Lagrangian Method for Salinity Calculation

The Eulerian？Lagrangian method（ELM） has been used by many ocean models as the solution of the advection equation,but the numerical error caused by interpolation imposes restriction on its accuracy.In the present study,hybrid N-order Lagrangian interpolation ELM（Li ELM） is put forward in which the N-order Lagrangian interpolation is used at first,then the lower order Lagrangian interpolation is applied in the points where the interpolation results are abnormally higher or lower.The calculation results of a step-shaped salinity advection model are analyzed,which show that higher order（N=3？8） Li ELM can reduce the mean numerical error of salinity calculation,but the numerical oscillation error is still significant.Even number order Li ELM makes larger numerical oscillation error than its adjacent odd number order Li ELM.Hybrid N-order Li ELM can remove numerical oscillation,and it significantly reduces the mean numerical error when N is even and the current is in fixed direction,while it makes less effect on mean numerical error when N is odd or the current direction changes periodically.Hybrid odd number order Li ELM makes less mean numerical error than its adjacent even number order Li ELM when the current is in the fixed direction,while the mean numerical error decreases as N increases when the current direction changes periodically,so odd number of N may be better for application.Among various types of Hybrid N-order Li ELM,the scheme reducing N-order directly to 1st-order may be the optimal for synthetic selection of accuracy and computational efficiency.

New Eulerian-Lagrangian Method for Salinity Calculation

A difference scheme in curvilinear coordinates is put forward for calculation of salinity in estuaries and coastal waters, which is based on Eulerian-Lagrangian method. It combines first-order and second-order Lagrangian interpolation to reduce numerical dispersion and oscillation. And the length of the curvilinear grid is also considered in the interpolation. Then the scheme is used in estuary, coast and ocean model, and several numerical experiments for the Yangtze Estuary and the Hangzhou Bay are conducted to test it. These experiments show that it is suitable for simulations of salinity in estuaries and coastal waters with the models using curvilinear coordinates.

Comparisons of some difference forms for compressible flow in cylindrical geometry on arbitrary Lagrangian and Eulerian framework

The study of cylindrically symmetric compressible fluid is interesting from both theoretical and numerical points of view. In this paper, the typical spherical sym- metry properties of the numerical schemes are discussed, and an area weighted scheme is extended from a Lagrangian method to an arbitrary Lagrangian and Eulerian （ALE） method. Numerical results are presented to compare three discrete configurations, i.e., the control volume scheme, the area weighted scheme, and the plane scheme with the addition of a geometrical source. The fact that the singularity arises from the geometri- cal source term in the plane scheme is illustrated. A suggestion for choosing the discrete formulation is given when the strong shock wave problems are simulated.

Efficient modeling of cable-pulley system with friction based on arbitrary-Lagrangian-Eulerian approach

In conventional modeling of a cable-pulley system, the cable must be finely meshed with Lagrangian elements for valid contact detections with pulleys, leading to extremely low efficiency. The sliding joint method based on the arbitrary-Lagrangian- Eulerian （ALE） formulation still lacks an efficient cable element, and in particular, modeling of friction between a sliding joint and the cable has not been studied. This paper presents efficient multi-body modeling of a cable-pulley system with friction. A variable- length cable element with a node movable along the cable, which is described with ALE, is developed to mesh the cable. A transitional cable element is then proposed to model the contact part of the cable by fixing its two nodes to the two corresponding locations of the pulley. Friction of the cable-pulley is derived as a simple law of tension decay and embedded in the multi-body system modeling. It is simplified as a generalized friction force acting only on the arc-length coordinate. This approach can use a rough mesh on the cable, and is free of contact detections, thus significantly saving computation time. Several examples are presented to validate the proposed method, and show its effectiveness in real engineering applications.

FINITE ELEMENT ANALYSIS FOR CHIP FORMATION IN HIGH SPEED TURNING OPERATIONS BY ARBITRARY LAGRANGIAN EULERIAN METHOD

A two-dimensional finite element （FE） model for the high speed turning operations when orthogonally machining AISI H13 tool steel at 49HRC using poly crystalline cubic boron nitride （PCBN） is described. An arbitrary Lagrangian Eulerian （ALE） method has been adopted which does not need any chip separation criteria as opposed to the traditional Lagrangian approach. Through FE simulations temperature and stresses distributions are presented that could be helpful in predicting tool life and improving process parameters. The results show that high temperatures are generated along the tool rake face as compared to the shear zone temperatures due to high thermal conductivity of PCBN tools.

COMPARISON OF THE EULERIAN AND LAGRANGIAN TIDAL RESIDUALS IN THE BOHAI SEA

Tidal residual is very important to the transport of water particles, nutrients, plankton, etc. in the coastal sea. Eulerian scheme and Lagrangian scheme are two different ways to get the time averaged residual. Solution of the Bohai Sea’s hydrodynamic system using a semi implicit layer averaged numerical model yielded different direction Eulerian and Lagrangian tidal residuals. The latter were stronger than the former in most sea areas. Their different directions produced different circulation pattern in some areas. Compared with the Eulerian residual, the Lagrangian residual seemed to be more in accord with the observation.

A multifractal model for linking Lagrangian and Eulerian velocity structure functions

A multifractal model is developed to connect the Lagrangian multifractal dimensions with their Eulerian counterparts. We propose that the characteristic time scale of a Lagrangian quantity should be the Lagrangian time scale, and it should not be the Eulerian time scale which was widely used in previous studies on Lagrangian statistics. Using the present model, we can obtain the scaling exponents of Lagrangian velocity structure functions from the existing data or models of scaling exponents of Eulerian velocity structure functions. This model is validated by comparing its prediction with the results of experiments, direct numerical simulations, and the previous theoretical models. The comparison shows that the proposed model can better predict the scaling exponents of Lagrangian velocity structure functions, especially for orders larger than 6.

Simulation of sheet metal extrusion processes with Arbitrary Lagrangian-Eulerian method

An Arbitrary Lagrangian-Eulerian(ALE) method was employed to simulate the sheet metal extrusion process,aiming at avoiding mesh distortion and improving the computational accuracy.The method was implemented based on MSC/MARC by using a fractional step method,i.e.a Lagrangian step followed by an Euler step.The Lagrangian step was a pure updated Lagrangian calculation and the Euler step was performed using mesh smoothing and remapping scheme.Due to the extreme distortion of deformation domain,it was almost impossible to complete the whole simulation with only one mesh topology.Therefore,global remeshing combined with the ALE method was used in the simulation work.Based on the numerical model of the process,some deformation features of the sheet metal extrusion process,such as distribution of localized equivalent plastic strain,and shrinkage cavity,were revealed.Furthermore,the differences between conventional extrusion and sheet metal extrusion process were also analyzed.

Coupling of 3D Eulerian and Lagrangian Spray Approaches in Industrial Combustion Engine Simulations

The Lagrangian DDM （discrete droplet model） is state-of-the-art for CFD （computational fluid dynamics） simulations of mixture formation and combustion in industrial engines. A commonly known drawback of the DDM approach is the attenuated validity in the dense spray, where the bulk liquid disintegrates into droplets. There the assumption of single droplets surrounded by a homogenous gas field is not reasonable. In this region, the Eulerian-Eulerian multi-phase approach performs better because instead of parcels the spray is represented by the volume fractions of one bulk liquid and several droplet size class phases. A further drawback of the DDM approach is that increasing the spatial resolution of the computational grid leads to a reduced statistical convergence, since the number of spray parcels per computational cell becomes smaller. It is desirable to combine the benefits of both spray approaches in coupled CFD simulations. Therefore, the dense spray region is simulated separately with the Eulerian spray approach on a highly resolved mesh covering only the region close to the nozzle orifice. The entire engine domain with combustion and emission models is simulated with the Eulerian-Lagrangian spray approach for the dilute spray region. The two simulations are coupled through exchange of boundary conditions and model source terms. An on-line coupling interface manages the data transfer between the two simulation clients, i.e., Eulerian spray and engine client. The aim of this work is to extend the coupled spray approach in terms of exchanging combustion related heat and species sources, and consequently creating the link between Eulerian spray and combustion models. The results show mixture formation and combustion in real-case engine simulations, and demonstrate the feasibility of spray model combination in engineering applications.

Lagrangian time scales and its relationship to Eulerian equivalents in turbulent channel flow

Lagrangian and Eulerian time scales were obtained from the direct numerical simulation of turbulent channel flow at two Reynolds numbers based on the friction velocity and channel half-height, Rer= 80, 100. The Lagrangian integral time scales and time microscales were compared to their Eulerian equivalents. It is found that the ratio of Lagrangian to TL Eulerian integral time scales is given by TE/TiE= 1 ＋ 0.1y＋ for y＋ ≤ 10, and that the ratios between the Lagrangian to theEulerian time microscales are almost the same irrespective of the components. Those increase with y＋ are approximated by ≈ 2.75 - 1.75 exp （-v＋/a） . These results also show that these expressions are independent of the Reynolds number.