Numerical and experimental study of the traveling magnetic field effect on the horizontal solidification in a rectangular cavity part 2: Acting forces ratio and solidification parameters

In recent decades, many phase change processes in metals have been optimized using traveling magnetic fields due to a better understanding of their electromagnetic impact in such applications. In this paper, numerical and experimental study of the effect of traveling magnetic field on the solidification process was evaluated. A three-dimensional numerical model based on the multi-domain method was used to analyze the process of gallium horizontal solidification under the electromagnetic impact in a laboratory-size rectangular cavity. A linear inductor creating traveling magnetic field was designed and built for appropriate measurements and validation the calculations. The analysis was focused on the influence of the ratio between the applied electromagnetic forces and natural convective forces on the solidification front location and shape and on the velocity field. Since the overall electromagnetic force impact on the melt reduced during the solidification, when the melt area was converting into a solid, a new approach to control the solidification parameters was analyzed. In this approach, the value of electromagnetic force acting on the remaining melt during the process was maintained. The main result is the development and improvement of an effective tool for the analysis of direct solidification parameters.The experimental setup included an ultrasonic Doppler velocimeter (UDV) for noninvasive measurements of the velocities in the liquid part of the metal and the liquid-solid interface position, its profile and displacement. All important characteristics of the process were measured, and the results of computations agreed well enough with experimentally obtained data.     

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.      

磁悬浮隔振器动态电磁力实验与建模

磁悬浮隔振器的核心部件是电磁作动器,得到其输出电磁力与线圈电流及气隙之间的模型对实现磁悬浮隔振器的主动隔振有着重要的意义.实际系统中,磁悬浮隔振器运动频率对电磁力模型参数有较大影响,为了得到比较精确的符合实际的电磁力模型,对原有模型进行了修正,给出了新的考虑频率因素的修正模型;并且设计了基于MTS809的动态电磁力实验建模方案,直接根据电磁力实时测量数据辨识得到动态电磁力修正模型,而不需要对磁路进行任何假设.实验结果表明,该方法建立的电磁力修正模型更符合实际情况.     

Modelling impingement of hollow metal droplets onto a flat surface

Despite many theoretical and experimental works dealing with the impact of dense melt droplets on the substrate during the process of thermal spray coating, the dynamics of the impingement of hollow melt droplet and the subsequent splat formation are not well addressed. In this paper a model study for the dynamic impingement of hollow droplet is presented. The hollow droplet is modelled such that it consists of a liquid shell enclosing a gas cavity. The impingement model considers the transient flow dynamics during impact, spreading and solidification of the droplet using the volume of fluid surface tracking method (VOF) coupled with a solidification model within a one-domain continuum formulation. The results for spreading, solidification and formation of splats clearly show that the impingement process of hollow droplet is distinctly different from the dense droplet. Study with different droplet void fractions and void distribution indicates that void fraction and void distribution have a significant influence on the flow dynamics during impact and on the final splat shape. The results are likely to provide insights for the less-explored behaviour of hollow melt droplets in thermal spray coating processes.     

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.     

Influence of velocity profile on calibration function of Lorentz force flowmeter

A Lorentz force flowmeter is a noncontact electromagnetic flow-measuring device based on exposing a flowing electrically conducting liquid to a magnetic field and measuring the force acting on the magnet system. The measured Lorentz force is proportional to the flow rate via a calibration coefficient which depends on the velocity distribution and magnetic field in liquid. In this paper, the influence of different velocity profiles on the calibration coefficient is investigated by using numerical simulations. The Lorentz forces are computed for laminar flows in closed and open rectangular channels, and the results are compared with the simplified case of a solid conductor moving at a constant velocity. The numerical computations demonstrate that calibration coefficients for solid bodies are always higher than for liquid metals. Moreover, it can be found that for some parameters the solid-body calibration coefficient is almost twice as high as for a liquid metal. These differences are explained by analyzing the patterns of the induced eddy currents and the spatial distributions of the Lorentz force density. The result provides a first step for evaluating the influence of the laminar velocity profiles on the calibration function of a Lorentz force flowmeter.     

Electromagnetically generated vortex streets in a narrow channel

The understanding of fluid wakes is of fundamental importance in several technological applications. In this paper, we present an experimental and numerical study of vortex wakes produced by a traveling localized Lorentz force in a thin layer of electrolyte contained in a narrow channel. The experimental set up consists of an open rectangular container with two parallel electrodes placed along its longest walls and connected to a power source that supplies a uniform DC current to the fluid layer. A permanent magnet located underneath the container is moved with a constant velocity so that the interplay of the moving magnetic field and the applied transversal current generates a traveling Lorentz force that stirs the electrolyte and creates different vortex wakes according to the flow conditions. Attention is focused on the effect of lateral walls on the flow patterns, therefore, two containers of different width and magnets of different sizes were used to vary the blockage parameter. Numerical simulations using a quasi-two-dimensional model agree qualitatively with experimental visualizations. Further, flow transition maps built from experimental and numerical results are presented.     

Ultrasonic Doppler velocimetry in liquid gallium

For the first time, flow velocity is measured in a vortex of liquid gallium, using the pulsed Doppler shift ultrasonic method. At the top of a copper cylinder filled with liquid gallium, we spin a disk and create a turbulent vortex with a dominant nearly axisymmetric velocity field with little variation in the axial direction. The velocity profiles are shown to be well resolved and in quantitative agreement with earlier observations. Reliable velocity measurements in liquid gallium could be obtained only after serious problems due to the formation of oxides were solved. This work opens the way to performing accurate velocity measurements in other liquid metals; preliminary results for liquid sodium are shown. Received: 14 January 2000 / Accepted: 12 January 2001     

Simulation and experimental studies of a vibro-impact capsule system driven by an external magnetic field

This paper studies the electromagnetic field used for driving a vibro-impact capsule prototype for small bowel endoscopy. Mathematical models of the electromagnetic field and the capsule system are introduced, and analytical solution of the magnetic force applied on the capsule is derived and verified by experiment. The impact force between the inner mass of the capsule and the capsule body is also compared via numerical simulation and experimental testing. By comparing the capsule’s progressions under different control parameters (e.g. the excitation frequency and duty cycle), the merits of using the vibro-impact propulsion are revealed. Based on the experimental results, the optimised speed of the prototype can achieve up to 3.85 mm/s. It is therefore that the potential feasibility of using the external electromagnetic field for propelling the vibro-impact capsule system is validated.

     

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.      

强脉冲电磁力驱动的冲击载荷

冲击载荷在材料科学与工程领域具有一定的应用。随着研究的深入, 对冲击速度、冲击能量提出了更高的需求, 是落锤所无法达到的。强脉冲磁场可由脉冲大电流产生, 通过合适的装置可产生强脉冲电磁力, 进而可转换为冲击载荷。通过数值模拟, 给出了强脉冲磁场、电磁力及冲头运动过程的数值模拟结果。采用高速摄像对该压缩冲击装置的运动过程进行记录, 通过对影像数据处理获得了冲击速度及冲击能量, 验证了模拟结果。     

Stability of conducting liquid flowing down an inclined plane at moderate Reynolds number in the presence of constant electromagnetic field

The stability of a conducting viscous film flowing down an inclined plane at moderate Reynolds number in the presence of electromagnetic field is investigated under induction-free approximation. Using momentum integral method a non-linear evolution equation for the development of the free surface is derived. The linear stability analysis of the evolution equation shows that the magnetic field stabilizes the flow whereas the electric field stabilizes or destabilizes the flow depending on its orientation with the flow. The weakly non-linear study reveals that both the supercritical stability and subcritical instability are possible for this type of thin film flow. The influence of magnetic field on the different zones is very significant, while the impact of electric field is very feeble in comparison.     

Two-layer flow of magnetic fluids

The plane two-layer flow of viscous incompressible fluids with differentmagnetic properties between two horizontal rigid planes in a nonuniform traveling magnetic field is investigated. An arbitrary nonuniform periodic traveling magnetic field generates wavelike changes in the interface between the media and fluid flows with nonzero flow rates. From the given magnetic field the interface shape and the velocities, pressures and mean flow rates of the fluids are calculated. The cases of a cosine magnetic force and of the magnetic field created by ferromagnetic cylinders moving in a uniform magnetic field are considered. The effect of various parameters on the mean flow rates of the fluids is investigated.     

On the Electric Potential Induced by a Homogeneous Magnetic Field in a Turbulent Pipe Flow

In this paper we study a turbulent pipe flow of a weakly electrical conducting fluid subjected to a homogeneous magnetic field which is applied perpendicular to the flow. This configuration forms the basis of a so-called electromagnetic induction flow meter. When the Hartmann number is small so that modification of flow by the Lorenz force can be neglected, the influence of the magnetic field results only in a spatially and temporally varying electric potential. The magnitude of the potential difference across the pipe is then proportional to the flow rate and this constitutes the principle of the flow meter. In this study the flow and electric potential are computed with help of a numerical flow simulation called Large-Eddy Simulation (LES) to which we have added an equation for the electrical potential. The results of the LES have been compared with experiments in which the electric potential is measured as a function of time at several positions on the circumference of the pipe. Both the experimental and numerical results for the mean potential at the pipe wall agree very well with an exact solution that can be obtained in this particular case of a homogeneous magnetic field. Furthermore, it is found that fluctuations in the electric potential due to the turbulence, are small compared to the velocity fluctuations. Based on the results we conclude that electrical-magnetic effects in pipe flow can be accurately computed with LES.     

电磁极宽度对圆柱绕流场影响的数值分析

在雷诺数Re=200的情况,利用Maxwell方程直接数值计算表面包覆电极与磁极圆柱体产生的电磁力分布,将其加入到动量方程中,在各种电磁力作用参数和电磁极宽度的组合下,对表面覆盖电磁极圆柱体在弱电解质中的绕流场结构及其升阻力特性进行了数值模拟与分析.结果表明,当电磁极宽度较小时,圆柱体绕流场的分离点越容易接近后驻点,而电磁力对总阻力的影响并不明显,但对压差和摩擦阻力均有明显影响.当电磁极宽度较大时,圆柱体尾部区域越容易产生射流现象,而且总阻力随电磁力作用参数和电磁极宽度增大而减小.在电磁力尚不足以完全抑制周期性涡脱落的情况下,升力幅值随电磁力作用参数增大而减小,但随电磁极宽度则先减小后略有增加,升力脉动频率则均随电磁力作用参数和电磁极宽度增大而增加.研究表明,电磁力可以有效地改善圆柱体绕流场结构,达到减小圆柱体阻力并抑制其脉动升力之目的,因此是圆柱型结构的一种有效流动控制手段.     

Numerical simulation of heat,mass and momentum transport behaviours in directionally solidifying alloy castings under electromagnetic fields using an extended Direct‐SIMPLE scheme

A Direct‐SIMPLE scheme is further extended for numerical simulations of heat and species mass transfer, and liquid flow behaviours in solidification processes of shaped alloy castings under various electromagnetic (EM) fields, based on a binary continuum model (a solidification transport phenomena/processes (STP)‐based dendrite solidification model). Unlike in a SIMPLE scheme, no iterative computations are needed to achieve the final pressure and velocity corrections in the extended Direct‐SIMPLE procedure, therefore extremely high computational efforts can be avoided. Using three different types of model alloys, pseudo‐binary In718 base‐4.85 wt% Nb, γ(TiAl)‐55 at% Al and Al‐4.5 wt% Cu systems, sample computations for solving strongly coupled solidification transport phenomena in directionally solidifying shaped castings under static and harmonic EM‐fields of different strengths are carried out, to demonstrate the feasibility and efficient calculation performance of the present model and numerical methods. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical Investigation on Marginal Stability and Convection with and without Magnetic Field in a Mushy Layer

In this article, an investigation is conducted to analyze the marginal stability with and without magnetic field in a mushy layer. During alloy solidification, such mushy layer, which is adjacent to the solidification front and composed of solid dendrites and liquid, is known to produce vertical chimneys. Here, we carry out numerical investigation for particular range of parameter values, which cover those of available experimental studies, to determine the convective flow at the onset of motion. The governing coupled non-linear partial differential equations are non-dimensionalised and solved to get the steady basic-state solution. The thickness of the mushy layer is determined as a part of the solution. Using multiple shooting technique, we determine the steady-state solutions in a range of critical Rayleigh number. We analyse the effect of several parameters, Chandrasekhar number Q, and Robert’s number τ on the problem. It was found that an increase in Q has a stabilizing effect on solidification and the critical Rayleigh number increases on increasing Q. It was also found that for moderate or small values of Robert’s number τ the critical Rayleigh number is mostly insensitive.     

Magnetovibrational flows in a magnetic fluid

A new type of flow in a magnetic fluid has been experimentally detected and investigated. The interaction between an alternating nonuniform magnetic field and a magnetic fluid leads to the parametric excitation of traveling capillary-gravitational waves which are the direct cause of the average flow. A necessary condition of formation of hydrodynamic flows in an alternating field is also the presence of time-dependent harmonics with multiple frequencies synchronized with the first harmonic, so that the time dependence of the ponderomotive force is generally pulsed. It is shown that for plane vibrational flows the classical theory cannot explain the high intensity of the average flows observed. It is suggested that the high intensity of magnetovibrational flows is related to the violation of the cylindrical symmetry of the traveling capillary-gravitational waves and the transition to a three-dimensional motion. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 124–133, January–February, 1998.     

Influence of shear and orthogonal vibration on semisolid aluminum flow properties

Understanding flow properties and flow effects of liquid and semisolid aluminum became a key solution for know-how of the casting processes. It is essential to find and study a new solution of interactive and efficient structure control of processed aluminum suspension. This task was solved by an adaptation of an electromagnetic actuator and high-resolution tempering unit to a conventional rotational rheometer. Initially, the research reveals a precise detection of transition temperatures in steady and transient shear flow. It was found that superposition of mechanical vibration orthogonal to the shear flow radically decreases shear viscosity of semisolid slurry. However, liquid state rheological properties show structural behavior, but stayed insensitive to mechanical oscillations. Analysis of boundary conditions before fundamental experiment shows that no considerable side effects were present during the experiment under vibration. The study reveals transition of strongly shear-thinning concentrated aluminum suspension to almost Newtonian fluid under vibration in shear flow. It is recommended to relate such phenomenon to non-equilibrium between structure formation and structure break-up under vibration and hydrodynamic forces of shear flow. The results illustrate how sensitive the structure of slurry is to vibration in general and in particular during the solidification phase. The revealed results provide a solid basis for further fundamental investigations.