拉格朗日分析方法研究现状及应用中应注意的问题

拉格朗日分析方法在研究材料的动态力学性能方面具有重要作用。我们对拉格朗日分析方法的产生、发展以及目前的研究现状进行了简要的分析总结,并揭示了在应用中应注意的几个问题。     

拉格朗日反分析方法误差分析

系统地讨论了路径线法及曲面拟合法误差发展。反分析计算误差可分成截断误差及增殖误差两部分,截断误差及增殖误差受测量量计数目及量计间距影响,增加量计数,减小量计间距可以减小截断误差,但不利于控制增殖误差。反分析计算误差发展可分为三个过程：开始,计算误差主要来源于截断误差;其后,误差受截断误差和增殖误差共同影响;最后,增殖误差是主要的。无论是曲面拟合法还是路径线法,各量计线上增殖误差可用时间多项式函数来表示,且多项式最高幂次数与量计线数目有关。     

高能炸药爆轰波反应区流场的拉格朗日分析方法

给出了一种简单的、对高能炸药爆轰反应区流场进行拉格朗日分析的方法。若已知未反应炸药和反应产物的状态方程，采用适当假设，我们可以在不知道反应速率函数的情况下得到爆轰反应区中的关系ｐ（）和ｕ（）等。根据这些关系及爆轰反应区中拉氏量计的实验结果ｐ（ｔ）［或ｕ（ｔ）］，通过插值或数据拟合可以得到爆轰反应区中的反应流场。我们将此方法应用于ＰＢＸ－９４０４炸药，并得到其爆轰反应区中的反应流场。     

曲面拟合在拉格朗日反分析方法中应用的探讨

把一组不同位置的速度(应变)波形构筑的x-t域离散成8节点或9节点单元,每个单元的插值函数为10或12参数多项式,利用拉格朗日反分析可以得到相应的应力(速度)波形。正如路径线法,曲面拟合反分析的某一单元函数值计算需要利用前一单元与该单元交界点的计算值,因而误差生成和发展有时很难预测、控制。文中对不同位置、不同数量量计线情况下,拉格朗日反分析中的曲面拟合法及路径线法误差生成、发展进行了分析,分析结果对材料实验中布置速度(应变)传感器的数量及其间距是有一定帮助的。     

用组合式电磁粒子速度计研究JOB-9003炸药的冲击起爆过程

用组合式电磁粒子速度计研究了JOB-9003炸药在不同冲击压力下的起爆过程。粒子速度计所测波形较好地反映出了炸药中冲击波向爆轰波的转变过程。对冲击波跟踪器所测波形的分析表明,冲击压力为4.9 GPa时,JOB-9003炸药冲击转爆轰的距离和时间分别为xD=6.06 mm和tD=1.13 s,当冲击压力增加到 5.8 GPa时,转爆轰的距离和时间减小为xD=5.66 mm和tD=1.01 s。     

用改进的基于质点速度测量的拉格朗日分析方法研究尼龙动态力学特性

采用改进的基于质点速度波形测量的拉格朗日分析方法,研究了率型材料的动态力学性能.首先用高磁感应强度的钕铁硼强滋材料研制出新型磁电式粒子速度计,其性能高于前人文献所报道的性能.其次,在理论分析和数值模拟的基础上得出,用实测的质点速度波形来求应力波形时,实测的应力边界是不可缺少的.在实际研究中,要同时测得质点速度以及应力量...     

新型二维发散波电磁粒子速度计的设计初探

为探索发散波作用下粒子速度二维电磁测试方法,研究了脉冲电流作用下Helmholtz线圈磁场特性,设计了新型二维发散波电磁粒子速度计构型.通过有机玻璃试验样品中粒子速度的一维和二维电磁测试对比实验,表明新型二维发散波电磁粒子速度计可以为具有分界面、沟槽或节理的非均匀分层介质中的发散波传播规律研究提供有效的测试手段.     

拉格朗日松弛算法在平台罗经多故障诊断技术中的应用研究

最优多故障诊断问题是一个NP-hard问题。针对平台罗经这一复杂系统，采用有向图描述元件与测试点间的因果依赖关系，并建立系统的多信号模型。在考虑元件发生故障的先验概率的前提下，提出一种基于拉格朗日算法（LRA）和子梯度优化算法（SOA）近最优多故障诊断算法，并在某型平台罗经的方位稳定系统多故障诊断中得到应用。结果表明：该方法相对于传统的单故障诊断方法诊断速度快，适用于平台罗经这类大型复杂系统的多故障诊断。     

一种研究炸药反应阈值的新方法

应用火药炮发射飞片产生低冲击压力的加载方法,采用组合式电磁粒子速度计测量不同加载压力情况下的炸药内部粒子速度,发展了一种用粒子速度与加载压力关系分析炸药反应阈值的新方法,获得了低冲击作用下JOB-9003炸药的反应阈值。研究表明,JOB-9003炸药的化学反应阈值和点火阈值分别为1.33GPa和1.87GPa,炸药的反应阈值与厚度无关。该研究方法为炸药安全性的研究提供了一些新的思路,研究结果可以为炸药安全性评估提供有益的参考。     

应用于气炮上测量材料质点速度的恒磁质点速度计的研制

研制了一种应用于气炮上测量质点速度的恒磁质点速度计,此装置操作简单、稳定可靠。     

Fourier analysis of the Eulerian–Lagrangian least squares collocation method

A Fourier analysis was performed in order to study the numerical characteristics of the effective Eulerian–Lagrangian least squares collocation (ELLESCO) method. As applied to the transport equation, ELLESCO requires a C¹-continuous trial space and has two degrees of freedom per node. Two coupled discrete equations are generated for a typical interior node for a one-dimensional problem. Each degree of freedom is expanded separately in a Fourier series and is substituted into the discrete equations to form a homogeneous matrix equation. The required singularity of the system matrix leads to a ‘physical’ amplification factor that characterizes the numerical propagation of the initial conditions and a ‘computational’ one that can affect stability. Unconditional stability for time-stepping weights greater than or equal to 0-5 is demonstrated. With advection only, ELLESCO accurately propagates spatial wavelengths down to 2Δx. As the dimensionless dispersion number becomes large, implicit formulations accurately propagate the phase, but the higher-wave-number components are underdamped. At large dispersion numbers, phase errors combined with underdamping cause oscillations in Crank–Nicolson solutions. These effects lead to limits on the temporal discretization when dispersion is present. Increases in the number of collocation points per element improve the spectral behaviour of ELLESCO.     

考虑颗粒间碰撞的气固两相流拉格朗日模拟

在均匀,稳定的各向同性气固两相紊流场颗粒弥散的拉格朗日模拟计算方法基础上,进一步考虑了流场中颗粒之间的碰撞对于模拟计算结果的影响。与Lavieville用大涡模拟所做的计算结果进行了对比,以对本方法进行验证,并考察了颗粒间的碰撞分别对流体相和颗粒相的影响。     

A new method for the construction of a Lagrangian

In this paper, the necessary condition for the existence of a Lagrangian for the ordered direct analytic representation of a system of second-order ordinary differential equations on a connected domain is given. Under that condition, a new method for the construction of the Lagrangian is proposed. The domain of definition of the constructed Lagrangian might be diminished. Supported by China Doctoral Program Foundation of Institution of Higher Education and National Natural Science Foundation of China     

Experimental Determination of Lagrangian Velocity Statistics in Turbulent Pipe Flow

The calculation of Lagrangian statistics out of experimentally determined data from homogeneously seeded inhomogeneous turbulent flows is far from straightforward since statistical properties are position-dependent, necessitating local sampling. Two solutions for the preferential sampling of faster particles at a certain position in the flow are proposed. The performance of both methods was tested using DNS calculations for turbulent pipe flow. Both methods show a good performance for various statistical properties, thus providing two reliable ways to analyze experimental data from inhomogeneous turbulent flows.     

基于最小二乘法的反应流拉格朗日分析在冲击起爆中的研究

现有反应流拉格朗日分析方法在已知粒子速度情况下,求解方法仍有不足。本文针对这一情况,将反解法与自洽检验法相结合,提出了基于最小二乘法的反应流拉格朗日反解法,该方法的理论精度能够实现应力沿路径线的 M阶导数为零（M为迹线数）,并且该方法能够满足自洽检验法。为了验证该方法的有效性,利用该方法对一组小隔板冲击起爆试验数据进行了处理,对比了本文方法、试验处理以及传统的反解法处理结果,表明该方法不仅可以适当减小迹线上的偶然误差,还能够使得迹线函数更好地反映各物理量沿迹线的变化性态。     

Numerical Study and Lagrangian Modelling of Turbulent Heat Transport

A stochastic Lagrangian model for both fluid velocities and temperature fluctuations is evaluated from Direct Numerical Simulation of heat transport in homogeneous isotropic turbulence submitted to a linear mean temperature gradient. The first stage lies on the study of the Lagrangian fluid turbulence statistics (Lagrangian correlations functions) computed from predictions of DNS. They are crucial for the analysis and the modelling of the fluid turbulent properties along discrete particle trajectories. In the second stage, a velocity-scalar Lagrangian stochastic model is proposed and evaluated from the DNS data. The coefficients of the drift and diffusion terms of the model are determined by only Lagrangian timescales, temperature variance and turbulent flux. The shapes of correlation functions present a good agreement between DNS results and stochastic modelling approach.     

A nodal Godunov method for Lagrangian shock hydrodynamics on unstructured tetrahedral grids

We present a nodal Godunov method for Lagrangian shock hydrodynamics. The method is designed to operate on three‐dimensional unstructured grids composed of tetrahedral cells. A node‐centered finite element formulation avoids mesh stiffness, and an approximate Riemann solver in the fluid reference frame ensures a stable, upwind formulation. This choice leads to a non‐zero mass flux between control volumes, even though the mesh moves at the fluid velocity, but eliminates volume errors that arise due to the difference between the fluid velocity and the contact wave speed. A monotone piecewise linear reconstruction of primitive variables is used to compute interface unknowns and recover second‐order accuracy. The scheme has been tested on a variety of standard test problems and exhibits first‐order accuracy on shock problems and second‐order accuracy on smooth flows using meshes of up to O(10⁶) tetrahedra. Copyright © 2014 John Wiley & Sons, Ltd.     

Lagrangian model on the turbulent motion of small solid particle in turbulent boundary layer flows

.Intr0ductionSurfaceerosionofmaterialbysolid-particleimpactisanimportantprobleminmultiphaseflowindustriaIdevicesandthecharacteristicsoftheparticIe'smotioninaturbulentboundarylayerflowisthebaseofthestudyofthematerialsurfaceerosion.Manycalculationmodelshave…     

An implicit Lagrangian lattice Boltzmann method for the compressible flows

In this paper, we propose a new Lagrangian lattice Boltzmann method (LBM) for simulating the compressible flows. The new scheme simulates fluid flows based on the displacement distribution functions. The compressible flows, such as shock waves and contact discontinuities are modelled by using Lagrangian LBM. In this model, we select the element in the Lagrangian coordinate to satisfy the basic fluid laws. This model is a simpler version than the corresponding Eulerian coordinates, because the convection term of the Euler equations disappears. The numerical simulations conform to classical results. Copyright © 2006 John Wiley & Sons, Ltd.