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．     

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．     

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.      

Analytic models of heterogenous magnetic fields for liquid metal flow simulations

A physically consistent approach is considered for defining an external magnetic field as needed in computational fluid dynamics problems involving magnetohydrodynamics (MHD). The approach results in simple analytical formulae that can be used in numerical studies where an inhomogeneous magnetic field influences a liquid metal flow. The resulting magnetic field is divergence and curl-free, and contains two components and parameters to vary. As an illustration, the following examples are considered: peakwise, stepwise, shelfwise inhomogeneous magnetic fields, and the field induced by a solenoid. Finally, the impact of the streamwise magnetic field component is shown qualitatively to be significant for rapidly changing fields.     

The influence of a magnetic field on the mechanical behavior of a fluid interface

This work focuses on a theoretical investigation of the shape and equilibrium height of a magnetic liquid–liquid interface formed between two vertical flat plates in response to vertical magnetic fields. The formulation is based on an extension of the so called Young–Laplace equation for an incompressible magnetic fluid forming a two-dimensional free interface. A first order dependence of the fluid susceptibility with respect to the magnetic field is considered. The formulation results in a hydrodynamic-magnetic coupled problem governed by a nonlinear second order differential equation that describes the liquid–liquid meniscus shape. According to this formulation, five relevant physical parameters are revealed in this fluid static problem. The standard gravitational Bond number, the contact angle and three new parameters related to magnetic effects in the present study: the magnetic Bond number, the magnetic susceptibility and its derivative with respect to the field. The nonlinear governing equation is integrated numerically using a fourth order Runge-Kutta method with a Newton–Raphson scheme, in order to accelerate the convergence of the solution. The influence of the relevant parameters on the rise and shape of the liquid–liquid interface is examined. The interface shape response in the presence of a magnetic field varying with characteristic wavenumbers is also explored. The numerical results are compared with asymptotic predictions also derived here for small values of the magnetic Bond number and constant susceptibility. A very good agreement is observed. In addition, all the parameters are varied in order to understand how the scales influence the meniscus shape. Finally, we discuss how to control the shape of the meniscus by applying a magnetic field.     

Surface shape of a magnetic liquid drop near the edge of a magnetic wedge

The two-dimensional problem of the shape of the free surface of a magnetic fluid in a gravity field, a uniform external magnetic field and the nonuniform field of a magnetized metal wedge is considered. The results of numerically calculating the shape of the free surface of a magnetic liquid drop retained on an inclined plane by the field of a magnetizing wedge are presented. The changes in the shape of the free surface of an infinite volume of magnetic liquid near the edge of a wedge with increase in the external field are investigated. It is shown that for a certain critical field some of the magnetic liquid separates and adheres to the edge of the wedge. Experimental data on the determination of the maximum cross-sectional area of a drop retained by the magnetic field of a wedge and the critical rise of the magnetic liquid relative to the level outside the field are presented. The experimental and theoretical results are in agreement.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 113–119, July–August, 1992.The authors wish to thank V. V. Gogosov for useful discussions and his interest in the work.     

“Magnetic-ribs” in fully developed laminar liquid–metal channel flow

This paper documents the numerical investigation of the effects of non-uniform magnetic fields, i.e. magnetic-ribs, on a liquid–metal flowing through a two-dimensional channel. The magnetic ribs are physically represented by electric currents flowing underneath the channel walls. The Lorentz forces generated by the magnetic ribs alter the flow field and, as consequence, the convective heat transfer and wall shear stress. The dimensionless numbers characterizing a liquid–metal flow through a magnetic field are the Reynolds (Re) and the Stuart (N) numbers. The latter provides the ratio of the Lorentz forces and the inertial forces. A liquid–metal flow in a laminar regime has been simulated in the absence of a magnetic field (Re_H = 1000, N = 0), and in two different magnetic ribs configurations for increasing values of the Stuart number (Re_H = 1000, N equal to 0.5, 2 and 5). The analysis of the resulting velocity, temperature and force fields has revealed the heat transport phenomena governing these magneto-hydro-dynamic flows. Moreover, it has been noticed that, by increasing the strength of the magnetic field, the convective heat transfer increases with local Nusselt numbers that are as much 27.0% larger if compared to those evaluated in the absence of the magnetic field. Such a convective heat transfer enhancement has been obtained at expenses of the pressure drop, which increases more than twice with respect to the non-magnetic case.     

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.      

Turbulence and transport of passive scalar in magnetohydrodynamic channel flows with different orientations of magnetic field

DNS of turbulent flow and passive scalar transport in a channel are conducted for the situation when the fluid is electrically conducting (for example, a liquid metal) and the flow is affected by an imposed magnetic field. The cases of wall-normal, spanwise, and streamwise orientation of the magnetic field are considered. As main results, we find that the magnetic fields, especially those in the wall-normal and spanwise directions, significantly reduce the turbulent scalar transport and modify the properties of the scalar distribution.     

Velocity measurements in liquid sodium by means of ultrasound Doppler velocimetry

A successful application of ultrasound Doppler velocimetry in liquid sodium flows is described. To obtain sufficient Doppler signals, different problems had to be solved: the transmission of the ultrasonic beam through the channel wall made of stainless steel, the acoustic coupling between the transducer and the channel wall, and the wetting of the inner surface of the wall by the liquid metal, respectively. A sodium flow in a square duct exposed to a transverse magnetic field is investigated. In accordance with the existing knowledge about MHD channel flows, we found that the velocity profiles modified to a M-shape owing to the effect of an inhomogeneous magnetic field. Received: 12 June 2001/Accepted: 27 October 2001     

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.     

Spin-up and spin-down dynamics of a liquid metal driven by a single rotating magnetic field pulse

This paper presents a study concerning the transient dynamics of the flow field inside a liquid metal filling a finite cylindrical container: The flow is created by applying a rotating magnetic field (RMF) in the form of a single pulse. The flow structure is governed by an impulsive spin-up from the rest state which is followed by a spin-down phase, with the fluid in a state of inertia. The pulse length has been found to have a distinct influence on the transient fluid flow. Two cases are considered: an enclosed cavity and a cavity with a free surface, in order to show that in both cases the recirculating flow in the radial-meridional plane displays periodical reversals. This phenomena is especially pronounced if the pulse length of the electromagnetic forcing corresponds to the so-called initial adjustment phase as defined by Nikrityuk, Ungarish, Eckert, Grundmann [P.A. Nikrityuk, M. Ungarish, K. Eckert, R. Grundmann, Spin-up of a liquid metal flow driven by a rotating magnetic field in a finite cylinder. A numerical and analytical study, Phys. Fluids 17 (2005) 067101–0671016].     

Instability of the magnetic fluid shape in the field of a line conductor with current

The static shape of the surface of a finite magnetic fluid volume between horizontal plates is investigated theoretically. The nonuniform magnetic field is generated by a horizontal line conductor with current, which is placed above the upper plate. The variational problem of minimum energy relative to plane surface perturbations is considered for a simply connected magnetic fluid volume. The problem is solved for arbitrary magnetic fields in the noninductive approximation with account for the gravity force and surface tension. Unstable solutions are found. The possibility of stepwise behavior in response to quasi-static changes of the current in the conductor is investigated for the surface shape of a finite magnetic fluid volume.     

Containing liquid metal in a vacuum by circularly polarized magnetic field in the presence of a conducting jacket

In this article we study the possibility of stable containment of a liquid metal in a vacuum by a high-frequency circularly polarized magnetic field. It is considered that the oscillation frequency of the metal, in view of its inertia, is considerably less than the field rotation frequency. The problem is solved in the two-dimensional formulation. In the case of infinite conductivity of the liquid it is shown that by selecting the required distance of the metal from the jacket all possible disturbances may be stabilized. Then we consider the case of finite conductivity, but with high field frequency and with disturbances for which the skin layer oscillates together with the liquid as an elastic film, and it is shown that the stability criterion remains as before. Then the case of shortwave disturbances (small magnetic Reynolds numbers) is considered. These disturbances can be stabilized only by surface tension forces; therefore, for stability, it is necessary that the skin layer depth be sufficiently small.The author thanks Yu. I. Samoilenko for posing the problem and for his helpful discussions.     

Nonlinear waves on the free surface of an electrically conducting liquid

Gravity waves of small but finite amplitude on the free surface of an electrically conducting liquid are examined. For the waves whose propagation is described by the Korteweg-de Vries equation (in the absence of a magnetic field), equations are derived. In addition to nonlinearity and dispersion, these equations include the influence of applied magnetic fields. As an example, the effect of magnetic damping on a solitary wave is presented.     

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.     

Free-surface magnetohydrodynamic flow with solidification

The paper considers an analysis of a liquid metal flow, occurring in the horizontal belt strip casting process. The liquid metal flows over a moving copper belt with a growing solidifying phase beneath the melt. The effect of applying a transverse magnetic field is investigated. A set of three-dimensional shallow water equations is derived. Supercritical flow is assumed and the shallow water equations are solved numerically using a shock-capturing method, which automatically takes care of the possibility of oblique hydraulic jumps.It is shown that non-uniform conditions introduced in the feeding region give a pattern of steady hydraulic jumps, which propagate downstream and are reflected at the sidewalls. The effect of the magnetic field is to brake the flow and damp the standing hydraulic jump pattern. Different feeding methods are compared and it is shown that the magnetic field erases the initial differences in liquid distribution using different feeding techniques.     

Incremental elastic motions superimposed on a finite deformation in the presence of an electromagnetic field

The equations describing the interaction of an electromagnetic sensitive elastic solid with electric and magnetic fields under finite deformations are summarized, both for time-independent deformations and, in the non-relativistic approximation, time-dependent motions. The equations are given in both Eulerian and Lagrangian form, and the latter are then used to derive the equations governing incremental motions and electromagnetic fields superimposed on a configuration with a known static finite deformation and time-independent electromagnetic field. As a first application the equations are specialized to the quasimagnetostatic approximation and in this context the general equations governing time-harmonic plane-wave disturbances of an initial static configuration are derived. For a prototype model of an incompressible isotropic magnetoelastic solid a specific formula for the acoustic shear wave speed is obtained, which allows results for different relative orientations of the underlying magnetic field and the direction of wave propagation to be compared. The general equations are then used to examine two-dimensional motions, and further expressions for the wave speed are obtained for a general incompressible isotropic magnetoelastic solid.