Vortex Generation in a Liquid Metal Duct Flow near a Magnetic Dipole

The generation of vortical structures by a strong magnetic dipole field in a liquid metal duct flow is studied by means of three-dimensional direct numerical simulations. The dipole is considered as the paradigm for a magnetic obstacle which will deviate the streamlines due to Lorentz forces which act on the fluid elements. Our model uses the quasi-static approximation applicable in the limit of small magnetic Reynolds numbers. The analysis covers the stationary flow regime at smaller flow Reynolds numbers Re as well as the fully time-dependent regimes at higher values with a turbulent flow in the wake of the magnetic obstacle. We present a systematic study of these two basic flow regimes on Re and the Hartmann number Ha, a measure of the strength of the magnetic dipole field. Furthermore, three orientations of the dipole are compared, the streamwise, spanwise and wall-normal ones. The most efficient generation of turbulence at a fixed distance above the duct occurs for the spanwise orientation in which we can observe the formation of Hartmann layers at the top plate. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electromagnetic interaction of a conducting cylinder with a magnetic dipole caused by steady rotation

The motion of a conductor in a magnetic field induces eddy currents whose interaction with the field produces Lorentz forces opposing the motion. One can determine the velocity of the conductor from the force on the magnet system since the latter is equal but opposite to the Lorentz force on the conductor. This contactless method is known as Lorentz force velocimetry (LFV). We study an idealized configuration of LFV, i.e. a rotating solid cylinder interacting with a point dipole. The understanding of parameter influences in this setup can be helpful for more realistic configurations. We use a purely kinematic approach appropriate for low magnetic Reynolds numbers. Numerical results for small and large distances between dipole and cylinder have been obtained with the commercial software COMSOL Multiphysics. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Distortion of liquid metal flow in a square duct due to the influence of a magnetic point dipole

We consider liquid metal flow in a square duct with electrically insulating walls under the influence of a magnetic point dipole using three-dimensional direct numerical simulations with a finite-difference method. The dipole acts as a magnetic obstacle. The Lorentz force on the magnet is sensitive to the velocity distribution that is influenced by the magnetic field. The flow transformation by an inhomogeneous local magnetic field is essential for obtaining velocity information from the measured forces. In this paper we present a numerical simulation of a spatially developing flow in a duct with laminar inflow and periodic boundary conditions. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Flow rate measurements in turbulent liquid metal channel flow using Time-of-Flight Lorentz force velocimetry

Non-contact flow control and flow measurements in hot and aggressive metal melts are big challenges in metallurgical applications. Time-of-Flight Lorentz force velocimetry (ToF LFV) is an electromagnetic measurement technique to meet these challenges. Our experimental results demonstrate that this method is well suited to measure flow rate in turbulent liquid metal channel flow without knowledge of both melt and magnetic field properties. Moreover, the measured flow profiles are in very good agreement with predictions of numerical simulations using the commercial program Package FLUENT MHD. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical Study of Creeping Liquid Metal Flow in the Presence of a Permanent Magnet

In this paper, we present the numerical study of interaction of a liquid metal flow with a small permanent magnet. Such an analysis is of fundamental interest for applications involving Lorentz Force Velocimetry (LFV). As a canonical problem, we consider the flow of liquid metal in the creeping flow regime (Re=0.01) through a square duct with electrically insulating walls. For this setup, we perform magnetohydrodynamic (MHD) simulations by coupling the commercial finite volume solver FLUENT and finite element solver COMSOL Multiphysics. Parametric analyses are performed at different relative positions of the permanent magnet with respect to the duct and with different magnetisation directions. The analyses provide good reference results for qualitative understanding of MHD flows exposed to non-uniform magnetic fields. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electromagnetic flow control in liquid metals using Lorentz force techniques

Flow measurement and flow control in opaque and aggressive liquids such as metal melts are challenging tasks in industrial fluid mechanics. Optical measurement techniques as well as submerging probes or control units cannot be applied in case of highly severe environment; hence, contactless electromagnetic methods are of interest for practical flow control because of relatively high electrical conductivity of investigated materials. In this paper we present working principle and experimental results of two such contactless techniques. First, time-of-flight Lorentz force velocimetry (LFV), which allows to determine the flow rate of liquid metal without information about any fluid properties or magnetic field magnitude by cross-correlation of two Lorentz force signals. Secondly, Lorentz torque velocimetry (LTV) - a technique, which uses an electromagnetic pump with a torque sensor connected to the pump's shaft. In the methods so-called Lorentz force [1] is measured, which has electromagnetic nature and is proportional to velocity and flow rate of conductive liquid. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

MHD turbulence in a channel with spanwise field

We study turbulent channel flow of an electrically conducting liquid with a homogeneous magnetic field imposed in the spanwise direction. The Lorentz force is modelled using the quasistatic approximation. Direct and large–eddy simulations are performed for hydrodynamic Reynolds numbers Re=10000 and Re=20000 and the Hartmann number varying in a wide range. The main effect of the magnetic field is the suppression of turbulent velocity fluctuations and momentum transfer in the wall–normal direction. Comparing the results from direct and large–edddy simulations we show that the dynamic Smagorinsky model accurately reproduces the flow transformation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electromagnetic interaction of moving conductors with magnets: kinematic solutions for infinitely long square and cylindrical geometries

The electromagnetic drag force on a point dipole near a moving conductor caused by the induced electric currents is investigated by numerical and analytical computations. Our focus is on prototypical configurations for Lorentz force velocimetry, i.e. velocity measurement from the electromagnetic drag force on the dipole. We examine the particular cases of conducting infinite bars of square or round cross-section, which are moving with constant velocity in the field of arbitrary oriented magnetic dipole. In addition, we study the laminar liquid-metal flow in a square duct. The motion of the conductor is prescribed. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The numerical modelling of DC electromagnetic pump and brake flow

The interaction of an externally imposed magnetic and electric field on the laminar flow of a conducting fluid in a channel is studied using computational techniques. The Navier-Stokes equations and the equations describing the electromagnetic field are solved simultaneously in a single control volume-type computational fluid dynamic code, in a moderate Hartmann number and interaction parameter regime. The flow considered is two-dimensional, with an imposed magnetic field acting in the third dimension over the central region of the channel and decaying exponentially in the remainder. A pair of electrodes placed at right angles to the magnetic field exercises control over the resultant Lorentz force and hence the velocity profile shape. This configuration has application in direct-current electromagnetic pumps or, conversely, electromagnetic brakes. The initial parabolic flow profile acquires an M-shape / W-shape mode in the magnetic field fringe regions, corresponding to a pump / brake. A novel coupled procedure is described to model magnetohydrodynamic phenomena and is used to explore the effects of the Reynolds number, interaction parameter, and applied voltage on the pump / brake configuration.     

Hartmann duct flow at moderate magnetic Reynolds numbers

The application of a uniform external magnetic field on the turbulent duct flow of an electrically conducting fluid leads to several interesting changes in the structure and the mean charateristics of the flow. This is fairly well understood from the existing studies of duct flows in the low magnetic Reynolds number (R_m) limit. In this paper, we present the results for magnetohydrodynamic duct flow at moderate R_m obtained from direct numerical simulations (DNS). Several differences are observed to occur in this case as compared to low R_m flows, such as increased Hartmann layer thickness and enhanced large scale turbulence in the core region of the duct cross-section due to partial expulsion of magnetic flux. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A numerical study of flows driven by a rotating magnetic field in a square container

The influence of the geometry on the magnetically driven flow is studied by means of numerical simulations. Low–frequency, low–induction and low–interaction conditions are assumed. The rotating magnetic field (RMF) gives rise to a time–independent magnetic body force, computed via the electrical potential equation and Ohm's law and a time–dependent part that is neglected due to the low interaction parameter. Flow results of the cylindrical and square container are compared with respect to the magnetic body force, time–averaged velocity fields, first flow instabilities and Reynolds stress tensors. The dependency of the maximal velocity magnitude and the intensity of the magnetic induction is identical in axisymmetric and non–axisymmetric containers and in good agreement with Davidson's theory. However, significant differences are recognized, for instance, in the distribution of the Reynolds stress tensors. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of Infinitely Short MHD Journal Bearings with Toroidal Magnetic Field

Using the approximation of short journal bearings, analytical solutions of the magnetohydrodynamic form of Reynold's bearing equation are derived. The basis of the approach are the MHD basic equations. The ordinary hydrodynamic assumptions of lubrication are applied. The flow is assumed to be isothermal. Induced magnetic fields are neglected. The Lorentz force is the only body force acting on the fluid. A constant and uniform magnetic field is applied in circumferential direction. The electric field is oriented in radial direction.     

MHD free convective flow through porous medium in the presence of hall current, radiation and thermal diffusion

An unsteady free convective flow through porous media of viscous, incompressible, electrically conducting fluid through a vertical porous channel with thermal radiation is studied. A magnetic field of uniform strength is applied perpendicular to the vertical channel. The magnetic Reynolds number is assumed very small so that the induced magnetic field effect is negligible. The injection and suction velocity at both plates is constant and is given by v ₀. The pressure gradient in the channel varies periodically with time along the axis of the channel. The temperature difference of the plates is high enough to induce the radiative heat. Taking Hall current and Soret effect into account, equations of motion, energy, and concentration are solved. The effects of the various parameters, entering into the problem, on velocity, temperature and concentration field are shown graphically.     

Eddy-current braking of a translating solid bar by a magnetic dipole

The paper addresses the problem of a conducting rectangular bar of square cross-section which is moving with constant velocity in the field of an arbitrarily oriented magnetic dipole. The braking Lorentz force on the bar is obtained by FEM and compared with the analytical solution for a moving infinite plate in the field of a magnetic dipole [2]. The computation of the induced currents requires solution of a Laplace equation with mixed boundary conditions for the electric potential inside the moving bar. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of aligned magnetic field on the steady viscous flow past a circular cylinder

The steady viscous incompressible and slightly conducting fluid flow around a circular cylinder with an aligned magnetic field is simulated for the range of Reynolds numbers 100 ? Re ? 500 using the Hartmann number, M. The multigrid method with defect correction technique is used to achieve the second order accurate solution of complete non-linear Navier–Stokes equations. The magnetic Reynolds number is assumed to be small. It is observed that volume of the separation bubble decreases and drag coefficient increases as M is increased. We noticed that the upstream base pressure increases slightly with increase of M whereas downstream base pressure decreases with increase of M. The effect of the magnetic field on the flow is discussed with contours of streamlines, vorticity, plots of surface pressure and surface vorticity.     

Viscous dissipation and Joule heating effects on MHD-free convection from a vertical plate with power-law variation in surface temperature in the presence of Hall and ion-slip currents

An analysis is presented to study the effects of viscous dissipation and Joule heating on MHD-free convection flow past a semi-infinite vertical flat plate in the presence of the combined effect of Hall and ion-slip currents for the case of power-law variation of the wall temperature. The fluid is permeated by a strong transverse magnetic field imposed perpendicularly to the plate on the assumption of a small magnetic Reynolds number. The governing differential equations are transformed by introducing proper non-similarity variables and solved numerically. The effects of various parameters on the velocity and temperature profiles as well as the local wall shear stresses and the local Nusselt number are presented graphically and in tabular form. It is found that the magnetic field acts as a retarding force on the tangential flow but has a propelling effect on the induced lateral flow. The skin-friction factor for the tangential flow and the local Nusselt number decrease but the skin-friction factor for the lateral flow increases as the magnetic field increases. The skin-friction factor for the tangential and lateral flows are increased while the local Nusselt number is decreased if the effect of viscous dissipation, Joule heating and heat generation are considered. The opposite trend was observed as the temperature power coefficient n is increased. Also, the skin-friction factor for the tangential flow and the local Nusselt number are increased due to the Hall and ion-slip currents, whereas the skin-friction factor for the tangential flow increases when Hall values increase to one and decreases for values of Hall greater than one, but reduces by rising ion-slip values.     

Solitary fluid transients in rectangular ducts with transverse magnetic fields

Summary This paper treats a fluid hammer wave which is propagating into a fully developed MHD duct flow and which is produced by suddenly closing a valve at some cross section of a rectangular, insulating duct with a uniform transverse, applied magnetic field. The Mach and magnetic Reynolds numbers are assumed to be small, while the Hartmann number is assumed to be large. For a small interaction parameter, the electromagnetic effects on the fluid hammer wave are small and consist of both dispersion and dissipation. The dispersion is cumulative and becomes larger for large time, while the dissipation remains small for all time.Résumé Cet article traite de l'onde de choc produite par la fermeture subite d'une vanne et qui se propage dans un fluide conducteur d'electricité s'écoulant dans une conduite isolante de section rectangulaire à laquelle est appliqué un champ magnétique transversal et homogène. On admet que le nombre de Reynold magné tique et le nombre de Mach sont petits, alors que le nombre de Hartmann est grand. Pour des faibles valeurs du paramètre d'interaction, les effets électromagnétiques sur l'onde de choc sont petits et comprennent une dispersion et une dissipation. La dispersion est cummulative et augmente avec le temps, alors que la dissipation reste toujours petite.     

A Lorentz force flow meter for application at blast furnaces: design and calibration

A reference Lorentz force flow meter (LFF) has been developed to measure molten steel mass flow at the end of the runner of an experimental blast furnace. It works according to the principles of Lorentz force velocimetry [1] in which a static magnetic field interacts with a liquid metal stream. The magnetic field lines are generated by an arrangement of permanent magnets and penetrate the entire cross-section of the flow generating eddy currents and a total Lorentz force inside the melt. This force is proportional to the mass flow of the liquid metal and owing Newton's third law, there is a counter force of the same magnitude acting on the magnet system which is connected to a load cell. For accurate flow rate measurements, a “dry and wet calibration” of the LFF needs to be performed [2]. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Solitary fluid transients in rectangular ducts with transverse magnetic fields,II

Summary This paper treats a fluid hammer wave which is propagating into a fully devloped MHD duct flow. The wave is produced by suddenly closing a valve at some cross section of a rectangular duct with a uniform, transverse, applied magnetic field, with perfectly conducting walls parallel to the field and with either insulating or perfectly conducting walls perpendicular to the field. The Mach and magnetic Reynolds numbers are assumed to be small, while the Hartmann number is assumed to be large. The jump in velocity and pressure across the wave decreases exponentially in time. The fully developed flow ahead of the wave is undisturbed, and solutions for the velocity and pressure between the valve and the wave are presented.

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Résumé Cet article traite de l'onde de choc produite par la fermeture subite d'une vanne et qui se propage dans un fluide conducteur d'électricité s'écoulant dans une conduite de section rectangulaire à laquelle est appliquée un champ magnétique transversal et homogène. Deux parois de la conduite sont parfaitement conductrices et parallèles au champ magnétique, les deux autres étant parfaitement conductrices ou isolantes. On admet que le nombre de Mach et le nombre magnétique de Reynolds sont petits et que le nombre de Hartmann est grand. Les changements de la vitesse et de la pression à travers l'onde diminuent exponentiellement à temps. L'écoulement à la tête de l'onde n'est pas perturbée. Des solutions pour la vitesse et la pression entre la vanne et l'onde sont presentées.

     

Hydromagnetic flow near an accelerated plate with suction

The two-dimensional unsteady flow of a conducting viscous incompressible fluid past, an infinite flat plate with uniform suction, is considered in the presence of a uniform magnetic field. For a constant time, it is shown that for a given Hartmann numbera, as the cross Reynolds number β (corresponding to the suction velocity of the plate) increases, the velocity at any point of the fluid decreases and the skin friction at the plate increases. The results also hold good for a given β, asa increases if the magnetic lines of force are fixed relative to the fluid and are just opposite for the magnetic lines of force fixed relative to the plate.