基于无网格Galerkin法求解矩形绝缘管道内的磁流体流动

无量纲磁流体流动控制方程中的哈特曼数较大将导致数值计算发散或误差过大。将无网格Galerkin法引入绝缘管道内的稳定磁流体流动计算中,针对磁流体控制方程中大哈特曼数导致计算误差大的情况,对无网格Galerkin法添加了稳定项。计算结果表明,同等条件下,添加了稳定项的无网格Galerkin法总体相对误差远小于标准无网格Galerkin法的结果,且可以计算哈特曼数最大达50000绝缘管道内的磁流体流动。     

无网格MLPG法求解轴对称弹性体扭转问题

应用无网格局部彼得洛夫-伽辽金法(MLPG)研究轴对称弹性体扭转问题,给出了矩阵形式的控制方程,发展了MLPG求解轴对称体弹性扭转问题的数值计算方法。算例分析表明:此方法对求解此类问题具有良好的适应性,数值解能达到理想的计算精度。     

无网格局部Petrov-Galerkin方法中本质边界条件的处理

鉴于无网格局部Petrov-Galerkin方法(MLPG)形函数的非插值性质,将一种新的本质边界处理方案——完全变换法与MLPG结合,通过变换矩阵修正形函数,使其满足Kronecker-δ条件,实现了本质边界的精确实施。进一步与MLPG中通常处理边界的罚方法作了比较研究,数值结果表明新方法的可靠性与精确度。     

无网格局部强弱法求解不规则域问题

无网格局部彼得洛夫-伽辽金(meshless local Petrov-Galerkin,MLPG)法是一种具有代表性的无网格方法,在计算力学领域得到广泛应用.然而,这种方法在边界上需执行积分运算,通常很难处理不规则求解域问题.为了克服MLPG法的这种局限性,提出了无网格局部强弱(meshless local strong-weak,MLSW)法.MLSW法采用MLPG法离散内部求解域,采用无网格介点(meshless intervention-point,MIP)法施加自然边界条件,并采用配点法施加本质边界条件,避免执行边界积分运算,可适用于求解各类复杂的不规则域问题.从理论上讲,这种结合式方法,既保持了MLPG法稳定而精确计算的优势,同时兼备配点型方法在处理复杂结构问题时简洁而灵活的优势,实现了弱式法和强式法的优势互补.此外,MLSW法采用移动最小二乘核(moving least squares core,MLSc)近似法来构造形函数,是对传统移动最小二乘(moving least squares,MLS)近似法的一种改进.MLSc使用核基函数代替通常的基函数,有利于数值求解的精确性和稳定性,而且其导数近似计算变得更为简单.数值算例结果初步表明:这种新方法实施简单,求解稳定、精确,表现出适合工程运用的潜力.     

高超声速MHD球头激波脱体距离理论求解

高超声速飞行器强激波后高温气体形成具有导电性的等离子体流场, 电离气体为磁场应用提供了直接工作环境, 磁流体流动控制技术利用外加磁场影响激波后的离子或电子运动规律, 这可以有效改善高超声速飞行器气动特性. 激波脱体距离作为高超声速磁流体流动控制较为直观的气动现象, 受到研究者重点关注; 磁场添加后激波脱体距离发生变化, 其变化幅度直接反映磁控效果, 然而基于高超声速磁流体流动控制的相关理论模型较少, 需要进一步发展. 本文基于低磁雷诺数假设和偶极子磁场分布的条件, 通过对连续方程沿径向积分以及对动量方程采用分离变量的方法, 推导了高超声速磁流体流动控制下的球头激波脱体距离解析表达式. 理论分析结果表明, 激波脱体距离随着磁相互作用系数的增加而变大; 随着来流速度的增加, 磁相互作用系数变为影响激波脱体距离大小的主要因素. 本文理论模型可以达到快速评估磁控效果的目的, 对高超声速磁流体流动控制实验方案设计和结果分析具有一定的指导意义.      

局部彼得洛夫-伽辽金法分析各向异性板屈曲

基于Kirchhoff板理论和对挠度函数采用移动最小二乘近似函数进行插值，进一步研究无网格局部Petrov-Galerkin(MLPG)方法在各向异性板稳定问题中的应用．分析中，本质边界条件采用罚因子法施加，离散的特征值方程由板稳定控制方程的局部积分对称弱形式中得到．通过数值算例并与其他方法的结果进行比较，表明MLPG法求解各向异性薄板稳定问题具有收敛性好、精度高等一系列优点．     

求解一维理想磁流体方程的移动网格熵稳定格式

磁流体方程的数值求解在等离子体物理学、天体物理研究以及流动控制等领域具有重要意义,本文构造了用于求解理想磁流体动力学方程的基于移动网格的熵稳定格式,此方法将Roe型熵稳定格式与自适应移动网格算法结合,空间方向采用熵稳定格式对磁流体动力学方程进行离散,利用变分法构造网格演化方程并通过Gauss-Seidel迭代法对其迭代求解实现网格的自适应分布,在此基础上采用守恒型插值公式实现新旧节点上的量值传递,利用三阶强稳定Runge-Kutta方法将数值解推进到下一时间层。数值实验表明,该算法能有效捕捉解的结构(特别是激波和稀疏波),分辨率高,通用性好,具有强鲁棒性。     

计算二维粘性流动的流线迭代法

本文提出一种利用流线迭代法来计算任意形状流道中定常粘性层流流动的数值方法。通过任意非正交曲线网格中的压力梯度方程、能量方程和熵方程之间的迭代计算,可以得到整个流道中定常粘性可压缩(或不可压缩)流动的数值解。本文导出了二维(包括轴对称)流道中的基本方程,并详细地叙述了本方法的计算步骤。利用本方法对一些流道进行了数值计算,计算结果与其他巳知的数值解符合得很好。     

非结构混合网格高超声速绕流与磁场干扰数值模拟

对均匀磁场干扰下的二维钝头体无粘高超声速流场进行了基于非结构混合网格的数值模拟.受磁流体力学方程组高度非线性的影响及考虑到数值模拟格式的精度,目前在此类流场的数值模拟中大多使用结构网格及有限差分方法,因而在三维复杂外形及复杂流场方面的研究受到限制.本文主要探索使用非结构网格(含混合网格)技术时的数值模拟方法.控制方程为耦合了Maxwell方程及无粘流体力学方程的磁流体力学方程组,数值离散格式采用Jameson有限体积格心格式,5步Runge-Kutta显式时间推进.计算模型为二维钝头体,初始磁场均匀分布.对不同磁感应强度影响下的高超声速流场进行了数值模拟,并与有限的资料进行了对比,得到了较符合的结果.     

基于制造解的非结构二阶有限体积离散格式的精度测试与验证

随着计算机技术的飞速进步,计算流体力学得到迅猛发展,数值计算虽能够快速得到离散结果,但是数值结果的正确性与精度则需要通过严谨的方法来进行验证和确认.制造解方法和网格收敛性研究作为验证与确认的重要手段已经广泛应用于计算流体力学代码验证、精度分析、边界条件验证等方面.本文在实现标量制造解和分量制造解方法的基础上,通过将制造解方法精度测试结果与经典精确解(二维无黏等熵涡)精度测试结果进行对比,进一步证实了制造解精度测试方法的有效性,并将两种制造解方法应用于非结构网格二阶精度有限体积离散格式的精度测试与验证,对各种常用的梯度重构方法、对流通量格式、扩散通量格式进行了网格收敛性精度测试.结果显示,基于Green-Gauss公式的梯度重构方法在不规则网格上会出现精度降阶的情况,导致流动模拟精度严重下降,而基于最小二乘(least squares)的梯度重构方法对网格是否规则并不敏感.对流通量格式的精度测试显示,所测试的各种对流通量格式均能达到二阶精度,且各方法精度几乎相同;而扩散通量离散中界面梯度求解方法的选择对流动模拟精度有显著影响.     

Two‐level finite element method with a stabilizing subgrid for the incompressible MHD equations

We consider the Galerkin finite element method (FEM) for the incompressible magnetohydrodynamic (MHD) equations in two dimension. The domain is discretized into a set of regular triangular elements and the finite‐dimensional spaces employed consist of piecewise continuous linear interpolants enriched with the residual‐free bubble functions. To find the bubble part of the solution, a two‐level FEM with a stabilizing subgrid of a single node is described and its application to the MHD equations is displayed. Numerical approximations employing the proposed algorithm are presented for three benchmark problems including the MHD cavity flow and the MHD flow over a step. The results show that the proper choice of the subgrid node is crucial to get stable and accurate numerical approximations consistent with the physical configuration of the problem at a cheap computational cost. Furthermore, the approximate solutions obtained show the well‐known characteristics of the MHD flow. Copyright © 2009 John Wiley & Sons, Ltd.     

MHD flow of a viscous fluid on a nonlinear porous shrinking sheet with homotopy analysis method

The present paper investigates the magnetohydrodynamic（MHD） flow of a viscous fluid towards a nonlinear porous shrinking sheet.The governing equations are simplified by similarity transformations.The reduced problem is then solved by the homotopy analysis method.The pertinent parameters appearing in the problem are discussed graphically and presented in tables.It is found that the shrinking solutions exist in the presence of MHD.It is also observed from the tables that the solutions for f（0） with different values of parameters are convergent.     

An extensive numerical benchmark of the various magnetohydrodynamic flows

There is a continuous need for an updated series of numerical benchmarks dealing with various aspects of the magnetohydrodynamics (MHD) phenomena (i.e. interactions of the flow of an electrically conducting fluid and an externally imposed magnetic field). The focus of the present study is numerical magnetohydrodynamics (MHD) where we have performed an extensive series of simulations for generic configurations, including: (i) a laminar conjugate MHD flow in a duct with varied electrical conductivity of the walls, (ii) a back-step flow, (iii) a multiphase cavity flow, (iv) a rising bubble in liquid metal and (v) a turbulent conjugate MHD flow in a duct with varied electrical conductivity of surrounding walls. All considered benchmark situations are for the one-way coupled MHD approach, where the induced magnetic field is negligible. The governing equations describing the one-way coupled MHD phenomena are numerically implemented in the open-source code OpenFOAM. The novel elements of the numerical algorithm include fully-conservative forms of the discretized Lorentz force in the momentum equation and divergence-free current density, the conjugate MHD (coupling of the wall/fluid domains), the multi-phase MHD, and, finally, the MHD turbulence. The multi-phase phenomena are simulated with the Volume of Fluid (VOF) approach, whereas the MHD turbulence is simulated with the dynamic Large-Eddy Simulation (LES) method. For all considered benchmark cases, a very good agreement is obtained with available analytical solutions and other numerical results in the literature. The presented extensive numerical benchmarks are expected to be potentially useful for developers of the numerical codes used to simulate various types of the complex MHD phenomena.     

Solution of magnetohydrodynamic flow in a rectangular duct by Chebyshev collocation method

In this study, matrix representation of the Chebyshev collocation method for partial differential equation has been represented and applied to solve magnetohydrodynamic (MHD) flow equations in a rectangular duct in the presence of transverse external oblique magnetic field. Numerical solution of velocity and induced magnetic field is obtained for steady‐state, fully developed, incompressible flow for a conducting fluid inside the duct. The Chebyshev collocation method is used with a reasonable number of collocations points, which gives accurate numerical solutions of the MHD flow problem. The results for velocity and induced magnetic field are visualized in terms of graphics for values of Hartmann number H≤1000. Copyright © 2010 John Wiley & Sons, Ltd.     

Multirail electromagnetic launcher powered from a pulsed magnetohydrodynamic generator

The operation of an electromagnetic multirail launcher of solids powered from a pulsed magnetohydrodynamic (MHD) generator is studied. The plasma flow in the channel of the pulsed MHD generator and the possibility of launching solids in a rapid-fire mode of launcher operation are considered. It is shown that this mode of launcher operation can be implemented by matching the plasma flow dynamics in the channel of the pulsed MHD generator and the launching conditions. It is also shown that powerful pulsed MHD generators can be used as a source of electrical energy for rapid-fire electromagnetic rail launchers operating in a burst mode.     

Hypersonic Flow Past the Spherical Nose of a Body in the Presence of a Magnetic Field

The hypersonic flow past the nose of a spherical body containing current sources generating a magnetic field is investigated theoretically and numerically. The magnetohydrodynamic (MHD) flow is analyzed on the basis of the complete system of Navier-Stokes equations containing the force and thermal MHD terms and the electrodynamic equations. Local and integral thermal and aerodynamic characteristics of the body are found. It is shown that the presence of a magnetic field makes it possible to reduce the heat flow to the body in the neighborhood of the stagnation point by several times. However, in this case the total body drag increases.     

Review on the application and prospect of magnetohydrodynamics in aeronautical engineering

介绍了磁流体动力学在航空工程中的主要应用方式,主要包括：磁流体冲压组合发动机、磁流体涡轮组合发动机、燃烧室后磁流体发电、表面磁流体发电、磁流体加速风洞、磁流体推力矢量、进气道大尺寸磁流体流动控制、边界层分离流动控制、边界层转捩控制、飞行器头部热流控制等;探讨了磁流体技术在应用中存在的关键科学与技术问题,对导电流体的产生、磁流体实验设备与实验技术、多场耦合机理及数值模拟方法等进行了分析;最后对磁流体技术在航空工程上的应用与发展进行了总结与展望.     

进气道等离子体/磁流体流动控制研究进展

为实现高速飞行器的宽速域飞行,如何保证进气道在非设计状态下的性能至关重要。相比于传统被动控制方式,等离子体/磁流体流动控制技术作为新概念主动流动控制技术,由于其具有结构简单,快速响应,并可根据实际飞行条件进行反馈控制等优势,在国内外上得到了广泛关注。本文介绍了等离子体/磁流体在高超/超声速进气道的主要应用方式与等离子体/磁流体建模方法。当进气道处于超临界状态时,等离子体/磁流体流动控制主要通过热阻塞效应产生虚拟型面,从而将激波系推回至唇口,该技术有望在需要短时间流动控制的高马赫数导弹上走向工程应用;由于等离子体/磁流体激励器与壁面平齐安装,对于高超声速飞行条件,相比于粗糙元其对热防护的要求较低,并且通过超声速风洞实验初步证明了通过高频激励对边界层施加扰动的可行性,需要从稳定性理论的角度对其物理机制进行研究。在后续发展中需要进一步创新等离子体产生技术及激励方式,发展等离子体与流的全耦合计算模型等离子体与流的全耦合计算模型与高效算法 ,为指导工程应用提供依据.      

基于高温气体效应的磁流体流动控制研究进展

高超声速飞行器强激波后高温气体形成具有导电性的等离子体流场,电离气体为磁场应用提供了直接工作环境.磁流体控制技术利用外加磁场影响激波后的离子或电子运动规律,可有效地改善高超声速飞行器气动特性,在飞行器气动力操控和热环境管理等方面均具有广阔的应用前景; 同时,超导材料及电磁技术的发展又重新推动了这一领域的研究热潮.虽然国内外在高超声速磁流体流动控制领域已开展了一些研究工作,但其实验研究依然极具挑战, 且由于实验条件及测量技术等限制,其压力、热流等参数的测量并没有得出较为系统的结论,因此需要对影响脱体激波距离、热流、压力变化的规律及机理进行深入研究; 同时,数值模拟方法和理论分析也亟待可靠的实验数据来对其进行验证.本综述调研和讨论了基于高温真实气体效应的磁流体流动控制技术研究,主要针对磁流体流动控制的试验技术、数值模拟、理论方法以及流动控制的主要研究方向等进行了总结,并对其发展趋势进行了讨论和展望.