Flow of a Weakly Conducting Fluid in a Channel Filled with a Darcy–Brinkman–Forchheimer Porous Medium

We investigate in this article, the fully developed flow in a fluid-saturated channel filled with a Darcy–Brinkman–Forchheimer porous medium, which is conducted with an electrically varying parallel Lorentz force. The Lorentz force varies exponentially in the vertical direction due to low fluid electrical conductivity and the special arrangement of the magnetic and electric fields at the lower plate. With the homotopy analysis method (HAM), a particularly effective technique in solving nonlinear problems, analytical approximation series solutions with high accuracy are derived for fluid velocity and the results are illustrated in form of figures. All these flows are new and are presented for the first time in the literature.     

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.     

The influences of wall Lorentz force and field Lorentz force on the cylinder drag reduction

In this paper,the effects of Lorentz force on drag reduction for a circular cylinder have been studied experimentally and numerically.Based on its effects on drag reduction,the Lorentz force is found to be classified into two parts:one acts directly on the cylinder,named as the wall Lorentz force,and the other called the field Lorentz force acts on the fluid inside the boundary layer.The wall Lorentz force leads to the generation of a thrust,whereas the field Lorentz force results in drag increase.Since the former dominates the drag variation,the drag would reduce accordingly and even turn into negative (thrust) with the application of Lorentz force.     

Instability of cylinder wake under open-loop active control

Instability of a wake controlled by a streamwise Lorentz force is investigated through a Floquet stability analysis. The streamwise Lorentz force, which is a two-dimensional control input created by an electromagnetic actuator located on the cylinder surface,adjusts the base flow to affect the three-dimensional wake instability and achieve wake stabilization and transition delay. The instability mode at a Reynolds number Re = 300 can be transformed from B to A with N = 1.0, where N is an interaction number representing the strength of the Lorentz force relative to the inertial force in the fluid. The wake flow is Floquet stable when N increases to 1.3. The spanwise perturbation wavelengths are 3.926 D and 0.822 D in the modes A and B, respectively, where D is the cylinder diameter. In addition, the oscillating amplitudes of drag and lift are reduced with the increase in the interaction number. Particle tracing is used to explore the essential physical mechanism for mode transformation. The path lines show that suppression of flow separation hinders the fluid deformation and rotation, leading to the decrease in elliptic and hyperbolic instability regions, which is the material cause of mode transformation.All of the results indicate that wake stabilization and transition delay can be achieved under open-loop active control via the streamwise Lorentz force.     

Magneto-thermo-elastic stresses in an infinitely long cylindrical conductor carrying a uniformly distributed axial current

A formulation of two-dimensional magneto-thermo-elastostatic boundary value problems is presented in this paper. It is found that since the Lorentz pondermotive body force is conservative in this case, a nonhomogeneous biharmonic equation for the stress function can be derived. The effects of the Lorentz body force and Joule heating on the elastic deformation can thus be easily examined. As an illustrative example, stresses induced in an infinitely long cylindrical conductor carrying a uniformly distributed axial current is analysed.     

电磁力控制翼型绕流分离的增升减阻效率研究

电磁力可有效对流体流动进行控制,增升减阻,抑制流动分离,制约其推广应用的瓶颈为控制效率问题.为提高其控制效率,基于翼型绕流的电磁力控制,对电磁力增升减阻的控制效率问题进行数值研究. 根据能量守恒定律,推导电磁力控制能耗的比,基于升力和阻力计算节省能量. 定义电磁力的控制效率为能量节省与电磁力控制所需能耗的比值,研究不同工况下电磁力增升减阻的控制效率. 发现在控制开始阶段,电磁力能量主要消耗在增加边界层流体的动能上,电磁力控制效率非常低,但电磁力控制效率会随着电磁力工作时间的增长而增加;电磁力控制效率随着来流速度的增加呈指数下降;通过增加电磁力激活板的输入能量可增强电磁力的控制效果,但无法明显增加其控制效率.      

翼型绕流的电磁力控制

将表面包覆电磁激活板的翼型,按一定的攻角,置于流动的弱电介质溶液中,电磁激活板可产生作用于流体的切向电磁力(Lorentz力),从而改变流体边界层的结构. 在转动水槽中,对翼型绕流及电磁力控制下的绕流形态进行了实验研究. 结果表明,未加电磁力时,前缘涡的脱落点是不确定的,与流场具体条件有关,而后缘涡仅在尖角处脱落. 前缘涡与后缘涡相互影响,并周期性的脱体,在尾部形成涡街. 施加电磁力后,当力的方向与流动方向相同时,可以在一定程度上抑制分离,消除涡街,其效果与减小攻角类似. 加反向电磁力时,则相当于加大攻角,在翼型体的背风面形成涡街.      

Investigation of the flow around a circular cylinder under the influence of an electromagnetic force

An investigation of the effect of the local electromagnetic body force on the flow behavior around a circular cylinder is conducted. The electromagnetic force is applied locally on the cylinder surface in the range of 70–130° from the stagnation point along the cylinder circumference in both clockwise and counterclockwise directions. The numerical results predict that the Lorentz force applied in the circumferential direction on the cylinder moves the separation point rearward, and reduces the drag. To validate the numerical results, an experiment is conducted with a circular cylinder of 5 cm diameter. The electrodes and permanent magnets are flush mounted on the cylinder in such a way that the Lorentz force is generated in the circumferential direction. Flow visualization with polystyrene particles and direct drag measurement using strain gages are made. The fluid used is natural sea water of electric conductivity of about 4 (Ω m)^-1. Induction effect can be neglected in the present investigation due to the low flow speed and the Lorentz force is proportional to E×B where E is an applied electric field and B is a magnetic field. Received: 7 June 1998/Accepted: 28 April 1999     

Performance enhancement of a DC-operated micropump with electroosmosis in a hybrid nanofluid: fractional Cattaneo heat flux problem

The purpose of this investigation is to theoretically shed some light on the effect of the unsteady electroosmotic flow (EOF) of an incompressible fractional second-grade fluid with low-dense mixtures of two spherical nanoparticles, copper, and titanium. The flow of the hybrid nanofluid takes place through a vertical micro-channel. A fractional Cattaneo model with heat conduction is considered. For the DC-operated micropump, the Lorentz force is responsible for the pressure difference through the microchannel. The Debye-Hükel approximation is utilized to linearize the charge density. The semi-analytical solutions for the velocity and heat equations are obtained with the Laplace and finite Fourier sine transforms and their numerical inverses. In addition to the analytical procedures, a numerical algorithm based on the finite difference method is introduced for the given domain. A comparison between the two solutions is presented. The variations of the velocity heat transfer against the enhancements in the pertinent parameters are thoroughly investigated graphically. It is noticed that the fractional-order parameter provides a crucial memory effect on the fluid and temperature fields. The present work has theoretical implications for biofluid-based microfluidic transport systems.

     

Control of Flow Separation Using Electromagnetic Forces

If a fluid is electrically conductive, its flow may be controlled using electromagnetic forces. Meanwhile, this technique is a recognized tool even on an industrial scale for handling highly conductive materials like liquid metals. However, also fluids of low electrical conductivity as considered in the present study, like sea-water and other electrolytes, permit electromagnetic flow control. Experimental results on the prevention of flow separation by means of a streamwise, wall parallel Lorentz force acting on the suction side of inclined flat plates and hydrofoils will be presented.     

Numerical and experimental study of electromagnetically driven vortical flows

The paper reports on numerical and experimental investigations of electromagnetically driven vortical flows of an electrically conductive fluid in a generic setup. Two different configurations of permanent magnets are considered: a 3-magnet configuration in which the resulting Lorentz force is focused in the wall-boundary layers, and a 2-magnet configuration which creates a centrally located intensive swirling motion. For both configurations the intensity of the Lorentz force could be varied by variation of the electrode DC current between 0.5 and 10 A.A comparative assessment of measured (PIV) and numerically calculated (LES with electromagnetically extended subgrid closure) velocity fields showed good agreement for both configurations. It is demonstrated that the newly designed setup can be used for fundamental studies of the interactions between fluid flow, turbulence and electromagnetic fields and provide detailed insights into the underlying physics of these interactions. This in turn can be used to optimise magnetic control of flow, turbulence and heat transfer in various configurations of practical relevance.     

Electromagnetic control of seawater flow around circular cylinders

We investigate numerically the electromagnetic control of seawater flows over an infinitely long circular cylinder. Stripes of electrodes and magnets, wrapped around the cylinder surface, produce a tangential body force (Lorentz force) that stabilizes the flow. This mechanism delays flow separation, reduces drag and lift, and finally suppresses the von Kármán vortex street. Results from two-dimensional simulations of the Navier–Stokes equations in a range 10<Re<300 and Lorentz force calculations are presented. Emphasis is placed on the disclosure of physical phenomena as well as a quantitative detection of the flow field and forces. It is shown that the drag strongly depends on the geometry of the electromagnetic actuator and on its location at the cylinder surface. The effect of flow control increases with larger Reynolds numbers, since the boundary layer thickness and the penetration depth of the Lorentz force are closely connected.     

Transport and deposition of neutral particles in magnetohydrodynamic turbulent channel flows at low magnetic Reynolds numbers

The effect of Lorentz force on particle transport and deposition is studied by using direct numerical simulation of turbulent channel flow of electrically conducting fluids combined with discrete particle simulation of the trajectories of uncharged, spherical particles. The magnetohydrodynamic equations for fluid flows at low magnetic Reynolds numbers are adopted. The particle motion is determined by the drag, added mass, and pressure gradient forces. Results are obtained for flows with particle ensembles of various densities and diameters in the presence of streamwise, wall-normal or spanwise magnetic fields. It is found that the particle dispersion in the wall-normal and spanwise directions is decreased due to the changes of the underlying fluid turbulence by the Lorentz force, while it is increased in the streamwise direction. The particle accumulation in the near-wall region is diminished in the magnetohydrodynamic flows. In addition, the tendency of small inertia particles to concentrate preferentially in the low-speed streaks near the walls is strengthened with increasing Hartmann number. The particle transport by turbophoretic drift and turbulent diffusion is damped by the magnetic field and, consequently, particle deposition is reduced.     

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.     

Specific features of propagation of unsteady waves in a rotating spherical layer of an ideal incompressible stratified electroconducting fluid in the equatorial latitude belt

Three-dimensional large-scale motions of a rotating inviscid incompressible stratified ideal electroconducting fluid in a spherical equatorial latitude belt are studied. The mathematical model of this physical process is a closed system of partial differential equations consisting of hydrodynamic equations, which take into account the Earth rotation and the Lorentz force, and corresponding equations of magnetic dynamics with appropriate boundary conditions. An analytical solution of the system is constructed in the approximation of an equatorial β-plane, which describes propagation of lowamplitude waves.     

Stationary cylindrical vortex in a viscous electrically conducting fluid

An exact solution of the magnetohydrodynamic equations is constructed which describes steady vortex flow in a stationary cylinder on the axis of which a conductor carrying a known current is located. The solution is obtained under the assumption that the fluid is viscous and has finite electrical conductivity and that the magnetic field has only the axial and azimuthal components in a cylindrical coordinate system. It is found that the action of the Lorentz force is compensated by changing the pressure. Fluid flow occurs from the periphery to the axis of the cylinder under a pressure gradient, with flow rotation and swirling. The fluid flow causes a concentration of the magnetic lines near the axis of the cylinder, providing an exponential decrease in the magnetic field strength with distance from the axis. This flow can be considered as a model of a local increase in the magnetic field strength due to the transfer of its force lines by the flow of the electrically conducting fluid.     

An axisymmetric Stokes flow: application to linear induction pumps

One of the main problems in theoretical analyses of linear induction pumps is the derivation of the induced flow profiles. We consider the steady-state incompressible flow of a viscous fluid due to an assumed axisymmetric body force. The Stokes solutions obtained may be employed to discuss some of the design points for those linear induction pumps where this force approximates the exact induced Lorentz body force. The neglected inertia terms indicate that the linear solutions remain valid for sufficiently small source currents.     

电磁流变效应微磨头抛光加工电磁协同作用机理

将磨料混入以Fe3O4为分散粒子的电磁流变液作为抛光液,在电磁场耦合作用下形成电磁流变效应微磨头对玻璃材料进行抛光加工试验,通过考察不同电磁场耦合条件下玻璃材料的去除量,揭示了电磁流变效应微磨头抛光规律,建立了分散粒子的力学模型,深入研究了电磁流变效应微磨头抛光的电磁协同作用机理.结果表明:励磁电压为5V、电场电压3kV时,电磁流变效应微磨头材料去除量达到电流变效应微磨头的1.74倍和磁流变效应微磨头的5.71倍,产生了显著的电磁流变协同效应;电磁流变液分散粒子所受的电场力、磁场力和洛伦兹力产生的自旋力偶的综合作用决定了电磁流变效应微磨头链串的稳定性及其加工性能,在适当的电场和磁场耦合状态下能获得良好的电磁流变协同效应.     

Some two-dimensional flows at finite magnetic reynolds numbers

Flows at finite magnetic Reynolds numbers are characterized by a strong effect of the induced magnetic fields on the stream. In the present paper we determine the current distribution and estimate the influence of the Lorentz force component perpendicular to the stream in a two-dimensional channel with electrodes. We also estimate the influence of nonuniformities of the velocity in the stream path of an incompressible fluid when the characteristic magnetic Reynolds numbers     

Evolution of global enstrophy in cylinder wake controlled by Lorentz force

The Okubo-Weiss function is correlated with the fluid particle compression, deformation and vorticity, which provides a simple way to characterize different regions of a flow-field. In the present paper, it shows mathematically that the global integration of Okubo-Weiss function is always equal to zero for a two dimensional incompressible flow with no-slip boundaries. To validate the conclusion, a flow passing a circular cylinder con- trolled by the electromagnetic force is calculated numerically as an example. Distributions of global enstrophy, total squared strain and Okubo-Weiss function in the controlled flow field are discussed. The influence of Lorentz force on the distribution is analyzed.