Motion of a magnetizable liquid in a rotating magnetic field

Moskowitz and Rosensweig [1] describe the drag of a magnetic liquid — a colloidal suspension of ferromagnetic single-domain particles in a liquid carrier — by a rotating magnetic field. Various hydrodynamic models have been proposed [2, 3] to describe the macroscopic behavior of magnetic suspensions. In the model constructed in [2] it was assumed that the intensity of magnetization is always directed along the field so that the body torque is zero. Therefore, this model cannot account for the phenomenon under consideration. We make a number of simplifying assumptions to discuss the steady laminar flow of an incompressible viscous magnetizable liquid with internal rotation of particles moving in an infinitely long cylindrical container in a rotating magnetic field. The physical mechanism setting the liquid in motion is discussed. The importance of unsymmetric stresses and the phenomenon of relaxation of magnetization are emphasized. The solution obtained below is also a solution of the problem of the rotation of a polarizable liquid in a rotating electric field according to the model in [3].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 40–43, July–August, 1970.     

Interaction of a magnetic liquid with a conductor containing current and a permanent magnet

The present study investigates the force exerted by a magnetic liquid on a conductor with a current or a permanent magnet located near its infinite free surface. It is shown that this force is equal to the weight of the liquid raised by the magnetic field above the original horizontal level. The force is found for the cases when the liquid is weakly magnetic and when the shape of its surface differs little from plane. Consideration is given to the equilibrium of a magnet suspended on a small spring near the surface of the magnetic liquid. The critical height is found at which the magnet ceases to be held by the spring and is torn off into the liquid. The experimentally obtained values of the magnitude of of the force acting on the magnet and the height of collapse of the magnet into the liquid are in good agreement with the theoretical results.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 176–181, March–April, 1988.The authors are grateful to V. V. Gogosov for valuable discussion of the study.     

基于永磁环阵列的磁流体支撑及润滑特性研究

在本文中初步探讨了一种永磁环阵列的磁流体支撑及润滑特性,以期获得一种对固定目标区域精准支撑与润滑的方法,并实现低摩擦. 以3D打印树脂材料为基底,在其表面嵌入正方形点阵排布的永磁环阵列,分别在各磁体表面注入特定体积的磁流体,使其在各永磁环表面形成封闭的液体结构. 采用自行设计的支撑力测试系统及往复式摩擦磨损试验机分别对该液体结构支撑及润滑性能进行测试. 结果表明:在磁场作用下的磁流体,除自身磁化和内聚产生液体支撑力外,被磁流体密封于其液体结构内的气体将进一步提升支撑能力;而对于该磁环阵列结构而言,被吸附于其表面的磁流体支撑能力随着磁铁间距的增加而减小,并逐渐趋于稳定,同时磁极排布方式对支撑力也会有所影响;当磁流体密封结构的支撑能力大于外载荷时,即摩擦对偶完全被磁流体支撑,此时可获得0.005的低摩擦系数. 可见该磁流体液环密封结构所形成的液-气混合支撑力显著高于单一液体支撑,而磁环阵列结构可进一步提升总体支撑能力,当该支撑力高于负载时可避免摩擦副间的直接接触,在静止或低速状态下实现低摩擦. 该研究结果对于解决精密低速滑动机构中常出现的“冷焊”及“爬行”现象具有一定应用价值.      

Hydrodynamics of a liquid with deformable and interacting particles

Interest in the hydrodynamics of a liquid with particle rotations and microdeformations has recently intensified [1–9] in connection with the technical applications of different artificially synthesized structured media. A model of a liquid with deformable microstructure was first proposed in [4] and was thermodynamically analyzed in [6], in which a model of a liquid was constructed by means of methods from the thermodynamics of irreversible processes. A model of a macro- and microincompressible liquid with particle rotations and deformations has been proposed [7, 8] based on constitutive equations from [6]. Below we will solve the sphere rotation problem in an infinite liquid given different boundary conditions on the rates of particle rotation and microdeformation within the context of the system of equations presented in [7]. The solution of an analogous problem for a micropolar liquid simulating a suspension with solid particles has been obtained [9] and the solution for a viscous liquid was found by Stokes in [10].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnieheskoi Fiziki, No. 1, pp. 79–87, January–February, 1976.     

Analytic expression of magnetic field distribution of rectangular permanent magnets

From the molecular current viewpoint, an analytic expression exactly describing magnetic field distribution of rectangular permanent magnets magnetized sufficiently in one direction was derived from the Biot-Savart’s law. This expression is useful not only for the case of one rectangular permanent magnet bulk, but also for that of several rectangular permanent magnet bulks. By using this expression, the relations between magnetic field distribution and the size of rectangular permanent magnets as well as the magnitude of magnetic field and the distance from the point in the space to the top ( or bottom ) surface of rectangular permanent magnets were discussed in detail. All the calculating results are consistent with experimental ones. For transverse magnetic field which is a main magnetic field of rectangular permanent magnets, in order to describe its distribution, two quantities, one is the uniformity in magnitude and the other is the uniformity in distribution of magnetic field, were defined. Furthermore, the relations between them and the geometric size of the magnet as well as the distance from the surface of permanent magnets were investigated by these formulas. The numerical results show that the geometric size and the distance have a visible influence on the uniformity in magnitude and the uniformity in distribution of the magnetic field.     

偏置磁场对磁致伸缩纵向导波换能器效能的影响研究

为提高磁致伸缩导波换能器的激励效能,本文研究了磁场结构参数对偏置磁场空间分布的影响。基于COMSOL有限元仿真平台,对磁致伸缩换能器磁场分布特性进行了数值计算,研究了磁路结构形式、磁路和永磁铁数量等对偏置磁场分布的影响,最后优化出适合纵向导波激励的磁场结构参数。检测实验结果表明,随着偏置磁场磁路数量的增加,偏置磁场强度增大,磁场径向均匀性更好,磁致伸缩换能器的效能也相应提高;在相同磁路数量的条件下,永磁体数量的改变对换能器效能影响较小,四磁路偏置磁场最优;轭铁中部增加永磁铁后的磁路结构的偏置磁场的轴向均匀性更高,其激励效能更好。     

新型断路器操作机构的力学测试

为了实现一种结构简单、成本低廉、耗能较低的高压断路器的操作机构,在分析典型永磁电动操作机构的基础上,提出了一种采用永磁驱动的新型操作机构。利用MTS809材料试验系统测得断路器真空室的触头反力,使用Maxwell软件对断路器操作机构的磁力进行仿真与优化。在此基础上,确定操作机构的整体结构并做出10kV真空断路器原理样机。再利用MTS809系统对原理样机的驱动力进行测试验证。驱动力测试结果表明,新型永磁驱动操作机构原理可行,10kV真空断路器原理样机达到预期的设计目标。     

MHD equations for paramagnetic media

The conservation laws are used to obtain phenomenologically the complete system of equations of motion of a conductive paramagnetic fluid in a magnetic field. In addition to the usual MHD equations (with additional terms accounting for the magnetization of the medium), this system includes the equation for the rate of change of the magnetic moment.The hydrodynamic equations for a fluid with internal rotation have been obtained in [1] and extended in [2] to the case of the paramagnetic properties resulting from this rotation: here the fluid was considered nonconducting. The analysis of [2] is extended to the case of a fluid with nonzero electrical conductivity. This will be the same extension of MHD as the theory of [1, 2] is for conventional hydrodynamics.     

Velocity profile measurement of the Taylor vortex flow of a magnetic fluid using the ultrasonic Doppler method

 A successful application of the ultrasound velocity profile (UVP) measuring technique to investigations on the flow of magnetic fluids is described. The flow structure of a magnetic fluid in a concentric annular geometry with a large aspect ratio of 20 and a radius ratio of 0.65 was investigated for a inner cylinder rotation. Axial velocity distributions were measured using the UVP measuring technique. A non-uniform magnetic field was applied to the flow field using a permanent magnet located on the outside of the cylinders. The energy spectral density was calculated from the periodic axial velocity profiles. The critical Reynolds number was obtained for various magnetic field strengths, and the apparent viscosity caused by the applied magnetic field was estimated. The UVP method was demonstrated to provide useful information on the structure of Taylor vortex flow in a magnetic fluid. Received: 27 May 1997/Accepted: 21 July 1998     

Fluid flow in a rotating channel of square section

Laminar flow in a channel rotating about a transverse axis has been studied numerically [1–3] and analytically [4–7] at small Reynolds numbers. The drag coefficient of rotating channels with straight and curvilinear axes has been measured [4, 8, 9]. The present paper gives the results of an experimental investigation into the kinematics of water flow in a channel rotating with different intensities. The flow was visualized by means of hydrogen bubbles and a dye. A study was made of the process of flow separation in a rapidly rotating channel into a core with homogeneous velocity distribution in the direction parallel to the rotation axis and thin shear layers on the walls normal to this axis. The values of the dimensionless numbers were found that correspond to flow rearrangement accompanied by formation of longitudinally oriented vortex structures in the region of higher pressure, and also the values of the rotation parameter needed for the almost complete suppression of turbulence in the region of lower pressure. A general analysis is made of the forms of instability in the different regions of the flow and of the possible flow regimes in a rotating channel.     

爆炸式电磁感应脉冲发生器

为了探索脉冲发生器新的技术方法,在传统脉冲发生器的基础上,提出了一种依靠爆炸驱动的电磁感应脉冲发生器。介绍了发生器的工作过程,对发生器中炸药的爆炸和冲击过程进行了计算和数值模拟,建立了带有初始电压和初始静磁场的发生器的工作电路模型,得出了感应电压的计算方法。设计了一种通过永磁体提供初始静磁场的脉冲发生器,并分别对装有两种不同炸药的发生器进行了实验。实验表明:爆速较高的炸药驱动发生器可产生峰值更高的电压脉冲。实验结果偏低于计算结果,原因是理论计算中简化了磁芯磁场和冲击波速度。     

On the origin of super-rotating layers in magnetohydrodynamic flows

An asymptotic analysis has been performed for the magnetohydrodynamic flow between perfectly conducting concentric cylindrical shells. The flow in the model geometry exhibits all the features which had been discovered in the past for the case of differentially rotating spherical shells considered in the context of geophysical analyses. For strong magnetic fields, the flow domain splits into distinct subregions and exhibits two different types of cores which are separated from each other by a tangent shear layer. The fluid in the inner core flows similar to a solid-body rotation and the outer core is entirely stagnant. With increasing magnetic fields the shear layer becomes thinner and, since the flow rate carried by the layer asymptotes to a finite value, the velocity in the layer increases as the layer thickness decreases. Moreover, the flux carried by the layer rotates in opposite direction compared with the rotation of the body. It is shown that the rotating jet is driven by the electric potential difference between the edges of the inner and the outer core.     

Flow stability of viscous liquid layer with moment stresses on an inclined plane

The flow stability of a liquid layer on an inclined plane with account for molecular spin [1, 2] has been considered in [3] in the absence of moment stresses within the liquid. It was shown in [3] that molecular spin has a destabilizing effect on the flow. In the following we study the combined effect of molecular spin and internal moment stresses on the behavior of three-dimensional disturbances. The validity of Squire's theorem is established. The flow stability of a layer of relatively long-wave disturbances is studied by the method of sequential approximations [4, 5] under the assumption that the rotational viscosity coefficient _r is significantly smaller than the Newtonian viscosity coefficient .     

Magnetohydrodynamic lubrication theory for a cylindrical bearing

Liquid metal, which is a conductor of electric current, may be used as a lubricant at high temperatures. In recent years considerable attention has been devoted to various problems on the motion of an electrically conducting liquid lubricant in magnetic and electric fields (magnetohydrodynamic theory of lubrication), Thus, for example, references [1–3] study the flow of a conducting lubricating fluid between two plane walls located in a magnetic field. An electrically conducting lubricating layer in a magnetohydrodynamic bearing with cylindrical surfaces is considered in [4–8] and elsewhere.The present work is concerned with the solution of the plane magnetohydrodynamic problem on the pressure distribution of a viscous eletrically conducting liquid in the lubricating layer of a cylindrical bearing along whose axis there is directed a constant magnetic field, while a potential difference from an external source is applied between the journal and the bearing. The radial gap in the bearing is not assumed small, and the problem reduces to two-dimensional system of magnetohydrodynamic equations.An expression is obtained for the additional pressure in the lubricating layer resulting from the electromagnetic forces. In the particular case of a very thin layer the result reported in [4–8] is obtained. SI units are used.     

An analytical design method of thin,isotropic press-fit retention sleeve for surface-mounted permanent magnet drives

Electric drives with surface-mounted permanent magnets feature magnet retention sleeves found in the air gap between the rotor and the stator. The design of these components, whose thickness affects the size of the magnetic air gap, has thus significant implications for the overall drive performance. The present work proposes a systematic analytical method for the mechanical design of press-fit retention sleeves for surface-mounted permanent magnet drives. The model relies on the premise that the sleeve is thin and mounted on a much stiffer rotor-magnet assembly. This leads to the assumption of constant thickness before and after the interference fit, as well as the only significant deformation being the hoop extension of the sleeve induced by the press fit. The proposed design method allows for rapid estimations of such sleeve parameters as the thickness and effective overlap, providing critical design points to be verified by subsequent high fidelity approaches. Accordingly, finite-element analysis results are provided as verification of the analytical approach, demonstrating very good agreement between the two approaches.     

Boundary layer on a rotating disk with account for the Hall effect

The steady rotation of a disk of infinite radius in a conducting incompressible fluid in the presence of an axial magnetic field leads to the formation on the disk of a three-dimensional axisymmetric boundary layer in which all quantities, in view of the symmetry, depend only on two coordinates. Since the characteristic dimension is missing in this problem, the problem is self-similar and, consequently, reduces to the solution of ordinary differential equations.Several studies have been made of the steady rotation of a disk in an isotropically conductive fluid. In [1] a study was made of the asymptotic behavior of the solution at a large distance from the disk. In [2] the problem is linearized under the assumption of small Alfven numbers, and the solution is constructed with the aid of the method of integral relations. In the case of small magnetic Reynolds numbers the problem has been solved by numerical methods [3,4]. In [5] the method of integral relations was used to study translational flow past a disk. The rotation of a weakly conductive fluid above a fixed base was studied in [6,7], The effect of conductivity anisotropy on a flow of a similar sort was studied approximately in [8], In the following we present a numerical solution of the boundary-layer problem on a disk with account for the Hall effect.     

磷酸酯类双离子液体的合成及摩擦学性能研究

以咪唑、1,6-二溴代己烷和磷酸三乙酯合成1,6-二(3-乙基-1-咪唑基)己烷二乙基磷酸盐双离子液体,采用核磁共振谱仪(NMR)和傅立叶变换红外光谱仪(FTIR)等对其结构及理化性能进行了分析;用SRV摩擦磨损试验机考察了其作为钢/钢体系润滑剂的减摩抗磨作用;用SEM和XPS对磨痕表面的形貌和元素组成进行了表征,并分析了其润滑机制.结果表明,该类双离子液体具有较好的低温流动性,作为润滑剂对钢/钢摩擦副具有优异的减摩抗磨性能.XPS分析结果表明,该离子液体在钢磨损表面形成了含FePO4和Fe4(P2O7)3等物质的边界润滑膜,从而有效地提高了摩擦副的承载能力和抗磨损性能.     

Numerical Simulation of Ferrofluid Flow for Subsurface Environmental Engineering Applications

Ferrofluids are suspensions of magnetic particles of diameter approximately 10nm stabilized by surfactants in carrier liquids. The large magnetic susceptibility of ferrofluids allows the mobilization of ferrofluid through permeable rock and soil by the application of strong external magnetic fields. We have developed simulation capabilities for both miscible and immiscible conceptualizations of ferrofluid flow through porous media in response to magnetic forces arising from the magnetic field of a rectangular permanent magnet. The flow of ferrofluid is caused by the magnetization of the particles and their attraction toward a magnet, regardless of the orientation of the magnet. The steps involved in calculating the flow of ferrofluid are (1) calculation of the external magnetic field, (2) calculation of the gradient of the external magnetic field, (3) calculation of the magnetization of the ferrofluid, and (4) assembly of the magnetic body force term and addition of this term to the standard pressure gradient and gravity force terms. We compare numerical simulations to laboratory measurements of the magnetic field, fluid pressures, and the twodimensional flow of ferrofluid to demonstrate the applicability of the methods coded in the numerical simulators. We present an example of the use of the simulator for a fieldscale application of ferrofluids for barrier verification.     

Motion of an incompressible conducting liquid in a strong self-consistent magnetic field

One of the common regimes of operation of many laboratory and industrial magnetohydrodynamic (MHD) devices using liquid metals as working medium is the regime for which the Alfvén number A, the ratio of the magnetic and kinetic energy densities, appreciably exceeds unity. For example, for a typical MHD device [1] with characteristic length 0.1 m of the working region, velocity 1 m/sec of the medium, and magnetic induction 1 T (the medium is molten sodium at temperature 330°C) the Alfvén number is A - 900. To simplify the investigation of the processes in such devices, one can use the approximation of a strong magnetic field proposed by Somov and Syrovatskii [2] to describe certain types of hydrodynamic flows of a dissipationless plasma in a magnetic field. In the present paper, the approach to the analysis of the self-consistent magnetohydrodynamic problem in this asymptotic approximation is extended to the case of an incompressible liquid with finite conductivity. A study is made of the closed reduced system of MHD equations obtained from the complete model in the zeroth order in the small parameter A^–1, in which the magnetic field is a force-free field. An investigation is made of the free diffusion of force-free magnetic field with constant coefficient a of proportionality between the current density and the magnetic induction in a spatially unbounded liquid, and the kinematic properties of a velocity field of the liquid in which the force-free nature of the magnetic field is maintained during the damping process are determined. It is shown that the complete class of such velocity fields is represented by the group of rigid-body motions of the liquid.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–9, January–February, 1991.