倾斜非均匀磁场下导电方管磁流体管流的数值模拟研究

热核聚变反应堆液态金属包层应用中的一个重要问题是液态金属在导电管中流动和强磁场相互作用产生的额外的磁流体动力学压降.这种磁流体动力学压降远远大于普通水力学压降.美国阿贡国家实验室ALEX研究小组,对非均匀磁场下导电管中液态金属磁流体动力学效应进行了实验研究,其实验结果成为液态金属包层数值验证的标准模型之一.液态金属包层在应用中会受到不同方向的磁场作用,本文以ALEX的非均匀磁场下导电方管中液态金属管流实验中的一组参数为基础,保持哈特曼数、雷诺数和壁面电导率不变,采用三维直接数值模拟的方法,研究了外加磁场与侧壁之间的倾角对导电方管内液态金属流动的速度、电流和压降分布的影响.研究结果表明:沿流向相同横截面上的速度、电流以及压力分布均随磁场的倾斜而同向旋转.倾斜磁场均匀段,横截面上的高速区位于平行磁场方向的哈特曼层和平行层交叉位置,压力梯度随磁场倾角的增大先增大后减小.倾斜磁场递减段,在三维磁流体动力学效应作用下,横截面上的高速射流位置向垂直磁场方向偏移.磁场递减段的三维磁流体动力学压降随磁场倾角的增大而增大.随磁场倾斜,截面上的射流峰值逐渐减小,二次流增强,引发层流向湍流的转捩.     

聚变堆相关的液态金属膜流初步实验研究

在磁约束核聚变堆的面对等离子部件设计中,液态金属锂膜流因具有带走杂质、保护面对等离子固壁等优点而被认为是优选方案之一.然而,如何克服聚变堆中强磁场环境下产生的磁流体力学效应并形成大面积均匀铺展锂膜流动是目前亟需解决的问题.本文通过搭建室温液态镓铟锡回路和高温液态锂回路,开展了两种不同特性的液态金属膜流实验,并采用传统可视化方法获得了展向磁场存在时镓铟锡和锂在导电底板形成的液膜流动表面特征.实验结果表明:无磁场时,两种液态金属膜流流动表面波动特性与常规流体膜流均一致,即随着流动雷诺数的增加表面波动变得更为混乱;而展向磁场存在时,镓铟锡膜流表面波动变得更为规则,且沿着磁场方向平行排列,表现为拟二维波动的特征;而锂膜流却产生了明显的磁流体力学阻力效应,表现为在流动方向局部产生锂滞留现象,且滞留点随雷诺数增大向下游移动.最后通过膜流受力分析,进一步阐述了锂膜流受到比镓铟锡膜流更为严重磁流体力学效应影响的原因.     

聚变堆相关的液态金属膜流初步实验研究

在磁约束核聚变堆的面对等离子部件设计中,液态金属锂膜流因具有带走杂质、保护面对等离子固壁等优点而被认为是优选方案之一. 然而,如何克服聚变堆中强磁场环境下产生的磁流体力学效应并形成大面积均匀铺展锂膜流动是目前亟需解决的问题.本文通过搭建室温液 态镓铟锡回路和高温液态锂回路,开展了两种不同特性的液态金属膜流实验, 并采用传统可视化方法获得了展向磁场存在时镓铟锡和锂在导电底板形成的液膜流动表面特征.实验结果 表明: 无磁场时,两种液态金属膜流流动表面波动特性与常规流体膜流均一致, 即随着流动雷诺数的增加表面波动变得更为混乱; 而展向磁场存在时,镓铟锡膜流表面波动变得更为规则, 且沿着磁场方向平行排列,表现为拟二维波动的特征; 而锂膜流却产生了明显的磁流体 力学阻力效应,表现为在流动方向局部产生锂滞留现象, 且滞留点随雷诺数增大向下游移动. 最后通过膜流受力分析,进一步阐述了锂膜流受到比镓铟锡膜流更为严重磁流体力学效应影响的原因.      

流向磁场作用下圆柱绕流的直接数值模拟

绕流是托卡马克装置中液态包层内常见的流动形态,对流场与热量分布有着重要的影响.本文通过直接数值模拟(DNS),研究了不同磁场强度下$Re=3900$的圆柱绕流,分析了磁场强度对于湍流尾迹的影响.无磁场情况下,直接数值模拟的结果与前人的实验及模拟结果吻合很好.圆柱下游的尾迹中,随着流向距离的增大, 流向速度剖面逐渐从U型进化呈V型, 并慢慢趋于平缓,这表明尾迹中的流动结构受圆柱影响逐渐减小.圆柱后方两侧的剪切层中,由于Kelvin-Helmholtz不稳定性的影响,可以清晰地看到小尺度剪切层涡的脱落.通过对无磁场的计算结果施加流向磁场,本文计算了哈特曼数($Ha$)分别为20, 40和80的工况,以研究磁场效应对于湍流的影响.结果表明磁场较弱时,流动依然呈三维湍流状态.随着磁场增强, 近圆柱尾流区受磁场抑制明显,回流区被拉长,剪切层失稳位置向下游转移.圆柱后方的涡结构由于受到竖直方向洛伦兹力的挤压作用,随着哈特曼数的增加尾迹区域逐渐变窄.相比于无磁场情况的涡结构,由于磁场的耗散作用,相应的涡结构尺度变小.该研究不仅扩展了现有磁场下湍流运动的参数范围,对于液态包层的设计及安全运行同样具有重要的理论指导意义和工程应用价值.      

DIRECT NUMERICAL SIMULATIONS ON THE TURBULENT FLOW PAST A CONFINED CIRCULAR CYLINDER WITH THE INFLUENCE OF THE STREAMWISE MAGNETIC FIELDS1)

绕流是托卡马克装置中液态包层内常见的流动形态,对流场与热量分布有着重要的影响.本文通过直接数值模拟(DNS),研究了不同磁场强度下$Re=3900$的圆柱绕流,分析了磁场强度对于湍流尾迹的影响.无磁场情况下,直接数值模拟的结果与前人的实验及模拟结果吻合很好.圆柱下游的尾迹中,随着流向距离的增大, 流向速度剖面逐渐从U型进化呈V型, 并慢慢趋于平缓,这表明尾迹中的流动结构受圆柱影响逐渐减小.圆柱后方两侧的剪切层中,由于Kelvin-Helmholtz不稳定性的影响,可以清晰地看到小尺度剪切层涡的脱落.通过对无磁场的计算结果施加流向磁场,本文计算了哈特曼数($Ha$)分别为20, 40和80的工况,以研究磁场效应对于湍流的影响.结果表明磁场较弱时,流动依然呈三维湍流状态.随着磁场增强, 近圆柱尾流区受磁场抑制明显,回流区被拉长,剪切层失稳位置向下游转移.圆柱后方的涡结构由于受到竖直方向洛伦兹力的挤压作用,随着哈特曼数的增加尾迹区域逐渐变窄.相比于无磁场情况的涡结构,由于磁场的耗散作用,相应的涡结构尺度变小.该研究不仅扩展了现有磁场下湍流运动的参数范围,对于液态包层的设计及安全运行同样具有重要的理论指导意义和工程应用价值.     

强磁场影响下镓液滴撞击固壁的实验研究

在材料的电磁冶金过程及磁约束核聚变装置中, 金属液滴在磁场和壁面温度影响下的撞击过程表现出复杂的动力学特性. 本文对水平磁场作用下液态镓(Ga)液滴撞击等温和过冷壁面的铺展和回弹特性进行了实验研究. 采用高速相机拍摄液滴撞击过程中轮廓的变化, 通过图像处理获得不同磁场强度、不同撞击速度和不同底板温度下的最大铺展因子、回弹过程中的最大高度以及产生的二次液滴的半径和速度. 碰撞速度由0.45 ~ 1.8 m/s, 磁场强度从0 ~ 1.6 T, 底板温度为30 °C, ?20 °C和?10 °C. 基于实验结果分析了磁场和壁面温度对液滴铺展和回弹的影响规律. 实验结果表明, 液滴撞击等温壁面和过冷壁面的最大铺展因子随We的变化均与理论预测关系式一致. 液滴撞击等温壁面的情况下, 不同的We下, 出现不同的回弹现象. 磁场抑制了平行于磁场方向的液滴铺展和回弹过程中二次液滴的产生, 而对回弹过程中的液滴在平行磁场方向上有拉伸作用. 液滴撞击过冷壁面时, 在一定的We值范围内, 同样会出现二次液滴分离现象, 此时产生的二次液滴的速度较小. 磁场的增强和We的增大都会导致液滴在高度方向的振荡减弱, 加速凝固过程.      

磁流体动力学斜激波控制数值模拟分析

高超声速飞行器MHD(磁流体动力学)斜激波控制应用的关键在于理解等离子体斜激波流场与磁场的相互作用规律,这里发展了全MHD数值模拟方法对其进行研究,数值方法基于八波方程附加源项形式,进行有限体积离散,采用了Roe求解器、OC-TVD空间格式和LU-SGS方法,且采用投影方法降低磁场伪散度误差.考察外加均匀磁场的马赫10无粘导电拐角流动,压缩角为10°.结果中散度误差较低,并且通过激波参数验证了结果的准确性.流场显示,磁场使得激波角增大,部分情况下出现了快、慢激波结构,其中快激波变化更明显;壁面压强根据磁场的不同出现了不同程度的降低.最后采用群速度图方法进行了快慢激波形式分析,解释了磁场影响下流场形式变化机理.     

哈特曼边界层的初级稳定性分析

导电流体在法向外置磁场的作用下,在贴近壁面处会形成哈特曼边界层.哈特曼边界层的稳定性研究对电磁冶金过程和热核聚变反应冷却系统等相关设备的设计和运行都有着十分重要的意义.本文采用非正则模态稳定性分析方法,对两无限大绝缘平行平板内导电流体流动的稳定性进行了研究.通过在时间上迭代求解扰动变量的控制方程组和伴随控制方程组,获得了在磁场作用下初级扰动的增长情况及其空间分布形式,分析了磁场强度对最优扰动增长倍数G_max、最优展向波数β_opt和最优时刻t_opt的影响,并考察了上下两个哈特曼边界层之间的相互作用.结果表明,最优初始扰动的空间分布形式为沿着流场方向的漩涡,关于法向方向对称或者反对称.当哈特曼数Ha较大时(Ha>10),对称漩涡和反对称漩涡形式的初始扰动增长倍数基本相等;上下两个哈特曼边界层可以认为是彼此独立的,不会相互影响,此时最优扰动增长倍数G_max与局部雷诺数R的平方成正比,相应的最优展向波数β_opt和最优时刻t_opt均正比于哈特曼数Ha.当哈特曼数Ha较小时(Ha<10),反对称漩涡形式的初始扰动更为不稳定,其增长倍数大于对称漩涡的增长倍数,且上下两个边界层之间存在着一定的相互作用,并对整个流场的稳定性产生一定的影响.      

几何非线性软铁磁导电梁式板在磁场中的动力响应

本文提出一套描述静磁场中软铁磁导电梁式板大挠度自由振动的基本方程,在这组方程中,磁化、涡电流和几何非线性梁式板的力学行为之间的相互耦合被考虑。对两端铰支（不可移）的梁式板,详细讨论了电导率、磁导率、外加磁场的大小和倾角以及板的几何非线性对其自由振动的周期（或频率）和振幅的影响,数值结果显示,板的几何非线性引起的面内张力使板的固有频率上升,导电性和磁化则使频率下降。在磁弱性失稳临界磁场值两侧,板的频率随磁场变化的规律明显不同。另外,随着磁场倾角的增加或者磁导率的增大,电磁阻尼效应明显增强,振动被显著抑制。     

载流线圈非均匀感应磁场中圆板的磁弹性固有振动

针对处于载流圆线圈平面内非均匀感应磁场中的导电圆板,基于Kirchhoff薄板理论,给出了磁场中圆板的磁弹性横向振动基本方程。根据电磁理论,推得载流线圈感应非均匀磁场强度的椭圆积分表达式,并导出了圆板所受电磁力计算式。通过位移函数的设定并应用伽辽金法,得到了圆板的磁弹性轴对称振动微分方程及固有频率的表达式。通过算例,绘制了周边夹支和简支两种边界条件下圆板的磁弹性固有振动特性曲线图,分析了两种边界条件下固有频率、阻尼比、电磁力矩随线圈载流强度、圆板半径、板厚等参数的变化规律。结果表明,线圈的载流强度对圆板的振动和电磁特性有显著影响,即电流增大,磁感应强度及阻尼比随之显著增大,圆板固有频率随之显著减小。     

The effect of magnetic field on two-phase liquid metal flow

In this paper, the basic equations of two-phase liquid metal flow in a magnetic field are derived, and specifically, two-phase liquid metal MHD flow in a rectangular channel is studied, and the expressions of velocity distribution of liquid and gas phases and the ratioK ₀ of the pressure drop in two-phase MHD flow to that in single-phase are derived. Results of calculation show that the ratioK ₀ is smaller than unity and decreases with increasing void fraction and Hartmann number because the effective electrical conductivity in the two-phase case decreases. The Project is supported by the National Natural Science Foundation of China.     

Direct simulation of MHD flows in dual-coolant liquid metal fusion blanket using a consistent and conservative scheme

Direct simulation of 3-D MHD (magnetohydrodynamics) flows in liquid metal fusion blanket with flow channel insert (FCI) has been conducted. Two kinds of pressure equilibrium slot (PES) in FCI, which are used to balance the pressure difference between the inside and outside of FCI, are considered with a slot in Hartmann wall or a slot in side wall, respectively. The velocity and pressure distribution of FCI made of SiC/SiC_f are numerically studied to illustrate the 3-D MHD flow effects, which clearly show that the flows in fusion blanket with FCI are typical three-dimensional issues and the assumption of 2-D fully developed flows is not the real physical problem of the MHD flows in dual-coolant liquid metal fusion blanket. The optimum opening location of PES has been analyzed based on the 3-D pressure and velocity distributions.     

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.     

MHD Couette two-fluid flow and heat transfer in presence of uniform inclined magnetic field

The MHD Couette flow of two immiscible fluids in a parallel plate channel in the presence of an applied electric and inclined magnetic field is investigated in the paper. One of the fluids is assumed to be electrically conducting, while the other fluid and the channel plates are assumed to be electrically insulating. Separate solutions with appropriate boundary conditions for each fluid are obtained and these solutions are matched at the interface using suitable matching conditions. The partial differential equations governing the flow and heat transfer are transformed to ordinary differential equations and closed-form solutions are obtained in both fluid regions of the channel. The results for various values of the Hartmann number, the angle of magnetic field inclination, the loading parameter and the ratio of the heights of the fluids are presented graphically to show their effect on the flow and heat transfer characteristics.     

Wall functions for numerical modeling of laminar MHD flows

A general wall function treatment is presented for the numerical modeling of laminar magnetohydrodynamic (MHD) flows. The wall function expressions are derived analytically from the steady-state momentum and electric potential equations, making use only of local variables of the numerical solution. No assumptions are made regarding the orientation of the magnetic field relative to the wall, nor of the magnitude of the Hartmann number, or the wall conductivity. The wall functions are used for defining implicit boundary conditions for velocity and electric potential, and for computing mass flow and electrical currents in near wall-cells. The wall function treatment was validated in a finite volume formulation, and compared with an analytic solution for a fully developed channel flow in a transverse magnetic field. For the case with insulating walls, a uniform 20×20 grid, and Hartmann numbers Ha={10,30,100}, the accuracy of pressure drop and wall shear stress predictions was {1.1%,1.6%,0.5%}, respectively. Comparable results were obtained also with conducting Hartmann walls. The accuracy of predicted pressure drop and wall shear stress was essentially independent of the resolution of the Hartmann layers. When applied also to the parallel walls, the wall functions reduced the errors by a factor two to three. The wall functions can be implemented in any general flow solver, to allow accurate predictions at reasonable cost even for complex geometries and nonuniform magnetic fields.     

磁场对液态金属流的制动效应

研究在静磁场作用下；连铸坯中液态金属的流动，建立了二维数学模型并考虑了湍流的影响．采用数值分析方法分析了磁场对液态金属流股的制动效应．计算结果说明静磁场可以有效地减小流股速度并使其分散，同时使上升到液态金属液面的反转流减弱．随着哈特曼数增高和雷诺数的减小，磁场的制动效应增强．     

Natural convection flow under a magnetic field in an inclined square enclosure differentialy heated on adjacent walls

Steady, laminar, natural-convection flow in the presence of a magnetic field in an inclined square enclosure differentially heated along the bottom and left vertical walls while the other walls are kept isothermal was considered. The governing equations were solved numerically for the stream function, vorticity and temperature ratio using the differential quadrature method for various Grashof and Hartmann numbers, inclination angle of the enclosure and direction of the magnetic field. The orientation of the enclosure changes the temperature gradient inside and has a significant effect on the flow pattern. Magnetic field suppresses the convective flow and its direction also influences the flow pattern, causing the appearance of inner loops and multiple eddies. The surface heat flux along the bottom wall is slightly increased by clockwise inclination and reduced by half by the counterclockwise inclination. The surface heat flux along the upper portion of the left side wall is reversed by the rise of warmer fluids due to the convection currents for no inclination and clockwise inclination of the enclosure.     

Numerical modeling of bubble-driven liquid metal flows with external static magnetic field

Three-dimensional numerical simulations are presented considering the impact of a steady magnetic field on a bubble-driven liquid metal flow inside a cylinder. The injection of moderate gas flow rates through a single orifice at the bottom of the fluid vessel results in the formation of a bubble plume. The magnetic field is applied in either vertical or horizontal direction. The calculations were performed by means of the commercial software package CFX using the Euler–Euler multiphase model and the RANS–SST turbulence model. The non-isotropic nature of MHD turbulence was taken into account by specific modifications of the turbulence model. The numerical models are validated with recent experimental results. (Zhang, C., Eckert, S., Gerbeth, G., 2007. The flow structure of a bubble-driven liquid–metal jet in a horizontal magnetic field, J. Fluid Mech. 575, 57–82.) The comparison between the numerical simulations and the experimental findings shows a good agreement. The calculations are able to reproduce a striking feature of a horizontal magnetic field found in the range of moderate Hartmann numbers revealing that such a steady transverse magnetic field may destabilize the flow and cause distinct oscillations of the liquid velocity.     

Laminar flow through channels with porous walls and with an applied transverse magnetic field

Summary The problem of two-dimensional steady laminar flow of a viscous incompressible and electrically conducting fluid through a channel with two equally porous walls in the presence of a transverse magnetic field has been extended to include all values of Hartmann number and small suction velocity at the walls. Expressions for the velocity components, the pressure and the wall friction in terms of the Hartmann number and the suction Reynolds number are given. It is found that the pressure drop in the major flow direction and the wall friction decrease with the increase in suction and increase with the increase in the strength of the magnetic field.     

Stability of flow of a thin layer of viscous magnetic liquid

The laminar flow of a thin layer of heavy viscous magnetic liquid down an inclined wall is examined. The stability and control of the flow of an ordinary liquid are affected only by alteration of the angle of inclination of the solid wall and the velocity of the adjacent gas flow. When magnetic liquids are used [1, 2], an effective method of flow control may be control of the magnetic field. By using magnetic fields of various configurations it is possible to control the flow of a thin film of viscous liquid, modify the stability of laminar film flow, and change the shape of the free surface of the laminarly flowing thin film, a factor which plays a role in mass transfer, whose rate depends on the phase contact surface area. The magnetic field significantly affects the shape of the free surface of a magnetic liquid [3, 4]. In this paper the velocity profile of a layer of viscous magnetic liquid adjoining a gas flow and flowing down an inclined solid wall in a uniform magnetic field is found. It is shown that the flow can be controlled by the magnetic field. The problem of stability of the flow is solved in a linear formulation in which perturbations of the magnetic field are taken into account. The stability condition is found. The flow stability is affected by the nonuniform nature of the field and also by its direction.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 59–65, September–October, 1977.