基于OpenFOAM的投影法磁流体求解器开发与验证

在开源计算流体力学C++工具包OpenFOAM环境下开发了低磁雷诺数条件下的磁流体求解器,并进行了验证。采用投影算法求解动量方程和压力泊松方程;采用非结构网格同位相容守恒算法求解电势泊松方程、感应电流和洛伦兹力;采用边界耦合方法求解流固耦合电势场。通过对均匀磁场下导电方管和导电圆管内的完全发展磁流体层流的数值模拟和解析解的对比,对求解器进行了验证。进一步对非均匀强磁场作用下导电方管和导电圆管内完全发展磁流体层流进行了数值模拟,并与ALEX实验结果进行了比较。数值解和实验结果吻合良好。所开发的求解器可用于复杂结构强磁场作用下磁流体的数值模拟研究。     

平行壁变形导电管磁流体层流数值模拟

采用自主开发的基于 OpenFOAM 环境下的磁流体求解器,对外加横向均匀磁场的导电方管、平行 壁内凹导电管以及平行壁外凸导电管内的磁流体进行了层流数值模拟。在壁面电导率为 0.01、流体雷诺数为 500、 哈特曼数为 500~2000 的条件下,研究了三种导电管中液态金属磁流体速度分布和压降。结果表明：平行壁内凹 和外凸对速度分布具有显著影响;在相同参数条件下,平行壁内凹管的压降大于方管,而平行壁外凸管的压降小 于方管。     

带引流条导电矩形管磁流体湍流大涡数值模拟

为研究引流条对磁流体湍流的影响，采用自主开发的低磁雷诺数流固耦合磁流体相干结构模型大涡模拟求解器，对均匀磁场作用下平行层内带引流条导电矩形管和标准导电矩形管中液态金属湍流进行了数值模拟研究。结果表明，外加垂直流动方向的均匀磁场与流动的导电流体相互作用产生与流动方向相反的洛伦兹力，能够抑制磁流体的湍流脉动，这种抑制作用随着哈特曼数增大而增强。在弱导电率条件下，当Re=16350、Ha=212 时，两种管道中的流动均转换为层流流动状态。管道内壁面摩擦系数随着哈特曼数的增大而增大。引流条能在其近壁局部区域增强横向速度，有效激发湍流，但在弱壁面导电率条件下，带引流条导电矩形管壁面摩擦系数较标准矩形管大。     

径向线内电子束的空间极限电流

为了对径向线内电子束的空间极限电流及相关物理参量进行分析, 在径向方向无穷长与束流密度轴向均匀的假设条件下, 对电势满足的线性泊松方程进行了解析求解, 得到了空间极限电流的解析表达式, 接下来对束流密度轴向非均匀分析条件下电势满足的非线性方程进行了数值求解, 并与解析结果进行了对比。研究表明径向电子束具有较高的空间极限电流且当束流接近于极限电流传输时, 束密度的非均匀性明显增加, 相关结论可以为径向高功率微波器件的设计提供指导。     

带FCI液态包层的MHD效应及热变形模拟

本文结合CFD与FEM方法,对国际热核聚变实验堆(ITER)的双冷锂铅(DCLL)包层进行了"磁-热-流-固"多物理耦合场的三维数值模拟.基于电势方法,采用PISO算法和相容守恒格式求解了包含Lorentz力的不可压Navier-Stokes方程。应用有限元方法分析了DCLL包层关键部件流道插件(FCI)在热场和磁场耦合作用下的热应力.利用多物理场的顺序耦合算法获得了在强磁场作用下,包层内金属流体的压力、速度和温度分布,研究了各种厚度和导电率的FCI对于包层内MHD效应和传热性能的影响。     

矩形管道载氚热磁流体输运特性的数值模拟研究

聚变堆液态金属包层矩形管道中的氚输运过程与磁流体动力学(MHD)流动传热过程耦合在一起，形成了复杂的载氚热磁流体输运特性。基于开发的MHD流动与传热数值模拟程序对矩形管道中液态金属MHD流动传热特性及其氚输运的影响进行了数值模拟。该程序首先求解了动量守恒方程，并与理论解进行了对比验证，然后与能量守恒方程耦合求解，得到了温度影响下矩形管道中的液态金属流场分布，在此基础上对强磁场高核热梯度影响下的氚浓度分布进行了数值模拟，得到了氚浓度在管道中的分布特性。结果显示，液态金属在矩形管道中的流动传热对氚输运过程产生了显著影响。     

交错网格下MHD相容守恒格式的发展

在低磁场雷诺数条件下,基于电势泊松方程,发展了交错网格下可以精确计算电流和洛伦兹力(电磁力)的相容守恒格式。采用压力为变量的原始变量法求解不可压缩Navier-Stokes方程,所计算的电流满足电荷守恒定律,所计算的电磁力满足动量守恒定律。对金属流体在Hartmann数50~5000范围内验证了格式的精确性。交错网格下相容守恒格式的发展为后续MHD稳定性分析、湍流的大涡模拟及直接数值模拟提供很好的选择。     

基于格子Boltzmann方法的超声速非平衡流模拟

基于D1Q4可压缩格子Boltzmann模型,按照流通矢量分裂方法的思路,采用坐标旋转技术构造求解三维带化学反应Navier-Stokes方程对流通量求解器.结合有限体积法求解三维化学非平衡流Navier-Stokes方程,采用时间算子分裂算法解决化学反应刚性问题,数值模拟超声速化学非平衡流的三个经典算例.数值结果表明:在高马赫数下,采用D1Q4可压缩格子Boltzmann模型构造的三维对流通量求解器数值模拟中没有出现非物理解,同时在超声速化学非平衡流场中正确分辨激波、燃烧波等物理现象,精度和分辨率均较高,验证了本文构造的三维对流通量求解器的可靠性,拓宽了D1Q4可压缩格子Boltzmann模型的应用范围,为计算超声速化学非平衡流提供一种新方法.     

基于非结构网格的不可压流动耦合求解器

采用非结构化网格有限容积法求解了不可压N-S方程组,对流项采用GAMMA格式,扩散项采用二阶中心差分格式建立离散方程,用SOAR算法处理压力与速度的耦合关系,得到了一种求解不可压N-S方程的非结构网格耦合求解器。通过方腔顶盖驱动流、后台阶绕流以及方腔自然对流等几个典型的算例,考察了求解器的计算精度及收敛特性,并与SIMPLE算法进行了比较,结果表明该求解器是有效可行的。     

三维立方体内辐射磁流体流动与传热研究

采用配置点谱方法求解了在存在壁面温差的立体方腔内有外加磁场作用下热辐射对磁流体流动与传热的影响。采用谱投影算法处理速度和压力的耦合,辐射传递方程的角向离散采用球带等差数列微元等分离散坐标(SRAPN)法进行离散,最后在相同的节点下采用配置点谱方法进行求解。在验证数值方法之后,分析了Ha数、介质光学厚度、以及导热辐射参数对等温面、流线投影等的详细影响规律。     

导电突扩管中磁流体管流的数值模拟

采用基于OpenFOAM环境自主开发的低磁雷诺数磁流体求解器,对45°和90°突扩矩形管中液态金属流体在受到垂直流向的外加磁场作用时的速度、感应电流、压力的分布及突扩位置处的MHD三维现象进行数值模拟.结果表明：磁场沿突扩方向时,由于无回流涡,45°比90°突扩管在肩部位置速度分布更优.哈特曼数增大,强射流和突扩结构,在突扩肩部位置引发流动的不稳定性.伴随感应电流的不稳定,流动不稳定发展到突扩位置上游.磁场沿垂直突扩方向时感应电流的三维效应显著.哈特曼数增大,MHD压降显著增大.同方向磁场和相同哈特曼数,不同突扩角度的三维无量纲压力梯度无明显差异.     

Induced electric current-based formulation in computations of low magnetic Reynolds number magnetohydrodynamic flows

We use the induced electric current as the main electromagnetic variable to compute low magnetic Reynolds number magnetohydrodynamic (MHD) flows. The equation for the induced electric current is derived by taking the curl of the induction equation and using Ampère’s law. Boundary conditions on the induced electric current are derived at the interface between the liquid and the thin conducting wall by considering the current loop closing in the wall and the adjacent liquid. These boundary conditions at the liquid–solid interface include the Robin boundary condition for the wall-normal component of the current and an additional equation for the wall potential to compute the tangential current component. The suggested formulation (denominated j-formulation) is applied to three common types of MHD wall-bounded flows by implementing the finite-difference technique: (i) high Hartmann number fully developed flows in a rectangular duct with conducting walls; (ii) quasi-two-dimensional duct flow in the entry into a magnet; and (iii) flow past a magnetic obstacle. Comparisons have been performed against the traditional formulation based on the induced magnetic field (B-formulation), demonstrating very good agreement.     

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基于感应电磁场方程发展了低磁雷诺数条件下充分发展液态金属管道流的数值模拟程序。为了校正程序,分别计算了两种工况：液态金属在全绝缘管道和部分绝缘管道中的流动,数值结果与Hunt和Shercliff的解析解吻合的很好,表明该程序具有很高的精度。最后利用发展的程序对液态金属钠钾合金在管壁材料为304不锈钢的全导电管道中的流动进行了数值模拟,并对流速分布和MHD压降结果与实验结果进行了比较,结果表明数值与实验结果吻合较好。     

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在开源的CFD工具包OpenFOAM环境下开发了基于低磁雷诺数的磁流体湍流数值模拟求解器,对2π×1×1的方管中无磁场湍流和磁流体湍流进行直接数值模拟研究,给出了截面瞬时速度、平均速度的分布,截面对称中心线上的脉动速度的均方根值、湍动能的分布。计算结果表明,外加磁场对磁流体湍流具有抑制作用和并且这种抑制作用具有各向异性。     

磁流体管流的直接数值模拟研究

在开源的CFD 工具包OpenFOAM 环境下开发了基于低磁雷诺数的磁流体湍流数值模拟求解器,对 2π ×1×1的方管中无磁场湍流和磁流体湍流进行直接数值模拟研究,给出了截面瞬时速度、平均速度的分布,截面对称中心线上的脉动速度的均方根值、湍动能的分布。计算结果表明,外加磁场对磁流体湍流具有抑制作用和并且这种抑制作用具有各向异性。     

Effects of hall current on MHD Couette flow in a rotating system with arbitrary magnetic field

Author has studied the MHD Couette flow in a rotating environment with non- conducting walls in the presence of an arbitrary magnetic field. The solution in dimensionless form contains four pertinent flow parameters, viz. the Hartmann number, the rotation parameter which is the reciprocal of the Ekman number, the Hall current parameter, and the angle of inclination of the magnetic field to the positive direction of the axis of rotation. An interplay of hydromagnetic force and Coriolis force with an inclusion of Hall current plays a significant role in determining the MHD flow behaviour. The velocity and induced magnetic field distributions are depicted graphically. Also, the numerical results of shear stresses and the rate of mass flows are presented graphically.     

A consistent and conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part III: On a staggered mesh

The consistent and conservative scheme developed on a rectangular collocated mesh [M.-J. Ni, R. Munipalli, N.B. Morley, P. Huang, M.A. Abdou, A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part I: on a rectangular collocated grid system, Journal of Computational Physics 227 (2007) 174–204] and on an arbitrary collocated mesh [M.-J. Ni, R. Munipalli, P. Huang, N.B. Morley, M.A. Abdou, A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part II: on an arbitrary collocated mesh, Journal of Computational Physics 227 (2007) 205–228] has been extended and specially designed for calculation of the Lorentz force on a staggered grid system (Part III) by solving the electrical potential equation for magnetohydrodynamics (MHD) at a low magnetic Reynolds number. In a staggered mesh, pressure (p) and electrical potential (φ) are located in the cell center, while velocities and current fluxes are located on the cell faces of a main control volume. The scheme numerically meets the physical conservation laws, charge conservation law and momentum conservation law. Physically, the Lorentz force conserves the momentum when the magnetic field is constant or spatial coordinate independent. The calculation of current density fluxes on cell faces is conducted using a scheme consistent with the discretization for solution of the electrical potential Poisson equation, which can ensure the calculated current density conserves the charge. A divergence formula of the Lorentz force is used to calculate the Lorentz force at the cell center of a main control volume, which can numerically conserve the momentum at constant or spatial coordinate independent magnetic field. The calculated cell-center Lorentz forces are then interpolated to the cell faces, which are used to obtain the corresponding velocity fluxes by solving the momentum equations. The “conservative” is an important property of the scheme, which can guarantee computational accuracy of MHD flows at high Hartmann number with a strongly non-uniform mesh employed to resolve the Hartmann layers and side layers. 2D fully developed MHD flows with analytical solutions available have been conducted to validate the scheme at a staggered mesh. 3D MHD flows, with the experimental data available, at a constant magnetic field in a rectangular duct with sudden expansion and at a varying magnetic field in a rectangular duct are conducted on a staggered mesh to verify the computational accuracy of the scheme. It is expected that the scheme for the Lorentz force can be employed together with a fully conservative scheme for the convective term and the pressure term [Y. Morinishi, T.S. Lund, O.V. Vasilyev, P. Moin, Fully conservative higher order finite difference schemes for incompressible flow, Journal of Computational Physics 143 (1998) 90–124] for direct simulation of MHD turbulence and MHD instability with good accuracy at a staggered mesh.     

Characterization of the three-dimensional supersonic flow for the MHD generator

A numerical procedure based on a five-wave MHD model associated with non-ideal, low magnetic Reynolds number MHD flows was developed in the present study for analyzing the flow fields in the MHD generator of a MHD bypass scramjet. The numerical procedure is composed of an entropy conditioned scheme for solving the non-homogeneous Navier-Stokes equations, in conjunction with an SOR method for solving the elliptic equation governing the electrical potential. It was found that a separation would take place near the downstream edge of the second electrode, where the local adverse pressure gradient is large, and the core of the flow field is characterized as a 2-D flow due to the Hartmann effects along the direction of the magnetic field. The electric current lines would be increasingly distorted as the magnetic interactive parameter increases, and even induce an eddy current. Induced eddy current was also found in the different cross-sections along the axial direction, all of these would definitely deteriorate the performance of the MHD generator. The cross-sectional M-shape velocity profile found along the axial direction between the insulating walls is responsible for the formation of the vortex flow at the corner of the insulator cross-section, which, in turn, induces the corner eddy current at the corner. A numerical parametric study was also performed, and the computed performance parameters for the MHD generator suggest that, in order to enhance the performance of MHD generator, the magnetic interaction parameter should be elevated.