Electromagnetic Force Field Research Articles

Finite element analysis of electromagnetic and fluid flow phenomena in rotary electromagnetic stirring of steel

This paper describes a fixed-grid methodology for the numerical simulation of electromagnetically driven flow in three-dimensional inductively stirred systems. It is based on a hybrid differential–integral formulation of the electromagnetic field to limit the finite difference/element solution of the electromagnetic field problem to the fluid flow domain. The electromagnetic field in the system was described using current vector potential ( T) and reduced magnetic scalar potential ( ψ) formulation of the field. The fluid flow problem was represented by turbulent Navier–Stokes equation. The governing equations were discretized using Galerkin method of weighted residual, and the discretized electromagnetic and fluid flow equations were solved simultaneously using an efficient finite element segregated algorithm. This new method was used to simulate sub-mold rotary electromagnetic stirring in continuous casting of steel. The computed results have shown that the electromagnetic force field generates a strong rotational flow within the vertical section covered by the stirrer, and a relatively strong secondary flow beyond the stirrer. It has also been shown that the rotational and secondary flows were driven primarily by the vorticity of the force field at the billet corners. The induced flow in the molten pool was found to be turbulent and the effective mixing region in the molten pool was about three times the length of the stirrer. The principal conclusion emerging form this work is that the secondary flow promotes mixing beyond the region confined by the stirrer, and the extent of mixing depends on the frequency of the applied rotating magnetic field.

Calculation of three-dimensional electromagnetic force field during arc welding

Electromagnetic force is an important driving force for convection in the weld pool during arc welding. Accurate calculation of the electromagnetic force field requires complex numerical calculations of three-dimensional current density and magnetic flux fields. Several simplifying assumptions have been suggested to avoid the complex calculations. The resulting analytical expressions for the electromagnetic force field have been widely used without any critical evaluation of their intrinsic merit, since accurate numerical calculations were difficult in the past because of lack of fast computers. A numerical model has been developed to accurately calculate the current density and magnetic flux fields and the resulting electromagnetic force field in three dimensions in the entire weldment. The model can take into account any current distribution on the work piece surface and evaluate the effects of different arc locations and work piece geometry on the electromagnetic force field. Contributions of the electrode current, arc plasma, and current distribution inside the three-dimensional work piece to the magnetic field and the electromagnetic force field are determined. The electromagnetic force field computed from the model is compared with those obtained from the commonly used simplified expressions of electromagnetic force to examine the accuracy of the commonly used simplifying assumptions. The accuracy of the computed electromagnetic force field can be significantly improved by using the proposed numerical model.

直流電磁力場における非導電性2粒子に作用する電磁泳動力

直流電磁力場における非導電性2粒子に作用する電磁泳動力

Theoretical model for particle behavior at solidifying front in electromagnetic force field

The particle migrating behavior at solidifying front is discussed in theory with the application of electromagnetic force field (EMFF), on the basis of foregone analysis of force upon particle ahead of solidifying front without electromagnetic force field. The critical solidification velocities of particle pushing/engulfment transition ahead of horizontal and vertical interface are derived respectively when a certain EMFF is applied. And the critical electromagnetic forces of particle pushing/engulfment transition ahead of horizontal and vertical interface are also derived separately when a certain solidifying velocity is given.

Electromagnetic field and lifting capacity for longitudinal electromagnetic levitator

Detailed studies of the longitudinal electromagnetic levitator are presented. An appropriate electric current model for the computation of the electromagnetic force field in the levitated specimen is introduced. From this new model, the essential equations for the electromagnetic field and the lifting force field for a cylindrical sample are derived and the current density distribution is studied. Both lifting force and lifting capacity for the longitudinal electromagnetic levitator are analyzed and compared with the experimental data. The results can be used to design longitudinal electromagnetic levitators for different levitation purposes, to select suitable material for levitation, and to provide the framework for further investigation of melting phenomena and materials processing using the longitudinal electromagnetic levitator.

Crystallization of aluminum alloys in the presence of vertical electromagnetic force fields

The influence of vertical and steady electromagnetic force fields applied during the solidification of representative aluminum alloys was investigated. The experiments were performed both in the absence and in the presence of electromagnetic body force fields, oriented either upward or downward, and for various degrees of heat extraction rate. Several physical mechanisms of magnetohydrodynamic origin, acting on the macro- and microstructure of these alloys, have been revealed. It has been established that the stirring and liquid-solid-phase separation phenomena results in a decided grain refinement and, under certain conditions, in the segregation of the most part of the eutectic phase from the primary solid.

Analysis of Velocity and Temperature Fields of Molten Metal in DC Electric Arc Furnace.

Recently some small scale industries have started using DC electric arc furnace to recycle scrap materials, however modelling and simulation data are very limited in the literature. Therefore, it appears that a numerical simulation could provide many important components for predicting suitable operating conditions, better design and efficient control of the process. With this objective, a numerical simulation model is developed under certain simplifying assumptions. A SIMPLER algorithm is used to solve the model equations.Computed results show that the circulating patterns and the patterns of increasing the temperature of the melt are significantly affected by the change in bottom electrode diameter and these calculated results present very important information. For example, a furnace can be designed in such a way that the melt temperature can be increased uniformly throughout the bath which is very important for making homogeneous alloys. It is also found that the effect of natural convection on melt circulation is negligible, that is, circulation is totally controlled by the electromagnetic force field. In addition to the flow field data, data obtained from the electromagnetic field computations are also presented.

Numerical simulation and experimental results of the metal armature acceleration

A numerical model for calculating the contact pressure in EM rail launchers is developed. The calculation code is based on the solution of steady, axis-symmetrical contact springiness problem utilizing the finite element method. An experimental investigation was also carried out with the following parameters: (1) the power supply system was based on 5 MJ capacitor banks charged to 4.3 kV; (2) the rail accelerator had a bore length of 4.2 m and a bore diameter of 30 mm; (3) the rail material was bronze and the insulator material was fiberglass STB-3 (G-10 type); and (4) the preaccelerator was a conventional powder gun. The experimental results agree with the authors' understanding of armature physics at velocities of 2.1 to 2.7 km/s. The results can be improved with correct calculation of balancing forces that provide the necessary contact in the conducting part of the armature, and the normal pressure force, which is responsible for friction. The problem of 2-D and 3-D distribution of nonsteady electromagnetic heat and force fields in the fixed contact zone should then be solved.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Theory of atomic spectral emission intensity

The theoretical derivation of a new spectral line intensity formula for atomic radiative emission is presented. The theory is based on first principles of quantum physics, electrodynamics, and statistical physics. Quantum rules lead to revision of the conventional principle of local thermal equilibrium of matter and radiation. Study of electrodynamics suggests absence of spectral emission from fractions of the numbers of atoms and ions in a plasma due to radiative inhibition caused by electromagnetic force fields. Statistical probability methods are extended by the statement: A macroscopic physical system develops in the most probable of all conceivable ways consistent with the constraining conditions for the system. The crucial role of statistical physics in transforming quantum logic into common sense logic is stressed. The theory is strongly supported by experimental evidence.

The fluid flow aspects of electromagnetic levitation processes

This paper reports an analytical investigation of magnetohydrodynamic phenomena in electromagnetic levitation processes. The flow is treated as a Stokes flow, and the turbulence in the system is accounted for by using a constant eddy viscosity model, which may be derived from the Prandtl mixing length theory. The curl of the electromagnetic force field for flow calculations and the global lifting force for earthbound levitation are derived. The stream function is introduced, and the resultant scalar equation for fluid flow is solved by the method of separation of variables. The analytical solutions obtained are applicable to all applied frequencies and all conducting materials. Both detailed calculations and asymptotic analyses are presented. Calculated results illustrate that the flow field is characterized by two toroidal recirculating loops, and is strongly correlated to the distribution of the curl of the force field, which in turn depends on the coil placement. Compared with sophisticated numerical computations, the analytical solutions predict well the flow pattern, but underestimate the velocity magnitude as a result of overestimating the eddy sizes by the eddy viscosity model. The asymptotic analyses show that, for a high frequency of applied field or a perfect conductor, the global levitational force is proportional to the square of the input current and increases with increasing conductivity or frequency. The characteristic velocity is proportional to the input current, but inversely proportional to the square root of the liquid density, for a turbulent flow, while it is proportional to the square of the input current, but inversely proportional to the molecular viscosity, for a Stokes flow.

Calculations and experiments concerning lifting force and power in TEMPUS

The purpose of this investigation is to perform a critical test of some of the computational algorithms developed for predicting the electromagnetic force fields and the heating rates that may be achieved in the TEMPUS Electromagnetic Levitation device which will be deployed in IML-2 for performing a range of experiments, including the determination of the viscosity of undercooled melts, undercooling studies and high temperature calorimetry. Up to the present time extensive calculations have been carried out to predict the electromagnetic force fields, hence the lifting forces and the power absorption that may be achieved for various sample sizes and property values, but as yet no direct confirmation of these predictions has been available. In the paper we shall report on experiments that were conducted at DLR in Cologne, aimed at directly measuring the lifting force experienced by spherical metal specimens in the EML device and the experimentally determined lifting forces are being compared with the theoretical predictions, for a range of conditions, including coil configuration, sample position, sample conductivity and current levels. Some calculations are also reported regarding the power absorption by the sample. In general the agreement between the theoretical predictions and the experimental measurements has been excellent; furthermore, the theoretical predictions, based on machine computation were found to be in good agreement with analytical solutions as well.

The electrodynamic and hydrodynamic phenomena in magnetically-levitated molten droplets—I. Steady state behavior

A mathematical formulation is given and computed results are presented describing the behavior of electromagnetically-levitated metal droplets under the conditions of microgravity. In the formulation the electromagnetic force field is calculated using a modification of the volume integral method and these results are then combined with the FIDAP code to calculate the steady state melt velocities. The specific computational results are presented for the conditions corresponding to the planned IML-2 Space Shuttle experiment, using the TEMPUS device, which has separate “heating” and “positioning” coils. While the computed results are necessarily specific to the input conditions, some general conclusions may be drawn from this work. These include the fact that for the planned TEMPUS experiments the positioning coils will produce only a very weak melt circulation, while the heating coils are like to produce a mildly turbulent recirculating flow pattern within the samples. The computed results also allow us to assess the effect of sample size, material properties and the applied current on these phenomena.

An improved computational technique for calculating electromagnetic forces and power absorptions generated in spherical and deformed body in levitation melting devices

An improved computational technique for calculating the electromagnetic force field, the power absorption, and the deformation of an electromagnetically levitated metal sample is described. The technique is based on the volume integral method but represents a substantial refinement: the coordinate transformation employed allows the efficient treatment of a broad class of rotationally symmetrical bodies. Compound results are presented to represent the behavior of levitation melted metal samples in a multicoil, multifrequency levitation unit to be used in microgravity experiments. The theoretical predictions are compared with both analytical solutions and the results of previous computational efforts for the spherical samples, and the agreement has been very good. The treatment of problems involving deformed surfaces and actually predicting the deformed shape of the specimens should be the major contribution of the proposed method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Flow Characteristics by Induction and Gas Stirring in ASEA-SKF Ladle.

A numberical study was performed for the three-dimensional turbulent fluid flow in the ASEA-SKF ladle. The recirculatory flows are induced by an electromagnetic force field and/or gas injection. The effect of each stirring method and that of combined stirring on the flow characteristics were examined.Induction stirring was superior to gas stirring for the removal of non-metallic inclusions due to the flow pattern with a less stagnant region. As for the mixing effect, however, gas stirring was more effective than induction stirring. From the numerical results, combined stirring of the induction and gas stirring was suggested, so that it was more effective than each individual stirring method. The numerical results were compared with the data from the field operations, which showed good qualitative agreements.

Magnetohydrodynamic flows in a channel-induction furnace

Experiments performed in a four-tenth scale physical model of a 1300 kW inductor unit are described. The approach was, first, to measure the electromagnetic parameters, namely, the magnetic field and current density components, as well as the phase shift between these periodic vectors; and next, to find the electromagnetic force field from these parts. These results were connected with the experimentally determined liquid-metal flow fields. Both the effects of the time-smoothed electromagnetic forces on solid inclusions in suspension within the melt and the influence of the fluctuating electromagnetic forces on the probable existence of a cavitation phenomenon were also estimated. This present work, which reveals the impact of the magnetic field leaks on the velocity pattern, may be considered as a preliminary investigation, in an attempt to control the magnetoydrodynamic flows in channel-induction furnaces.

On the calculation of the electromagnetic force field in the circular stirring of metallic melts

A mathematical representation has been developed to represent the electromagnetic force field used to impart rotary motion to a cylindrically shaped molten metal pool. Problems of this type arise in the electromagnetic stirring of continuous casting systems. The formulation given here introduces two new facets which have been neglected by previous investigations, namely, an allowance for the nonlinear dependence of the magnetic flux intensity on the radial distance, and the coupling between the melt velocity and the induced field. It is shown that neglecting these factors may involve errors in the 20%–50% range.

Substratum Interpretation of the Sagnac-and the Aharonov-Bohm Effect

Abstract It is shown that a substratum interpretation reveals a close relationship between the Sagnac- and the Aharonov-Bohm-effect. The characteristic peculiarity of the Aharonov-Bohm-effect, to produce a phase shift of the electron wave function even in the absence of any electromagnetic force fields, can be duplicated by a thought experiment for light waves in the gravitational field of a massive rotating cylinder, which demonstrates that the somewhat similar Sagnac-effect is not caused by centrifugal and Corioli’s forces, as it is sometimes claimed. In the substratum interpretation, both the Sagnac and Aharonov-Bohm effect find their explanation in a rotational motion of the substratum. If the substratum flow is irrotational, having the form of a potential vortex, these effects persist even though there are no force fields present.

The moreau-evans hydrodynamic model applied to actual hall-héroult cells

An extension of the Moreau-Evans[1] model for Hall-Heroult cells hydrodynamics is presented. Numerical techniques are used to solve the Moreau-Evans model equations with realistic electromagnetic force fields; the predicted results are compared with those of another model which is the property of Kaiser Aluminum Company and whose results are considered as in fairly good agreement with available measurements (velocity in aluminum, for instance). The main input in this hydrodynamic model,i.e., the electromagnetic force field throughout the two liquids, was previously computed. For a given cell design these data were calculated using the electromagnetic program of Lympany and Evans.[2] For actual cells the forces were deduced from measurements of the magnetic field provided by Kaiser Aluminum Company. As expected, the cryolite flow is found to be governed by the large channels, and to be strongly dependent on the presence of such a channel between the two files of anodes. The use of numerical solution has made possible the analysis of new effects as the interfacial drag and the influence of small channels between anode blocks.

Experimental measurement and numerical computation of velocity and turbulence parameters in a heated liquid metal system

Experimental measurements are reported describing the velocity field and the turbulence parameters in molten Woods metal due to the passage of a DC current between two electrodes immersed into the melt. The measurements were made using a hot film anemometer. A mathematical model has been developed to represent these measurements; in essence, this relied on the solution of Maxwell’s equations to represent the electromagnetic force field and turbulent Navier-Stokes equations to represent the fluid flow field. Three different turbulence models were examined; two were variants of thek-e model, while the third was mixing length model type. In general, the velocities were well predicted by all three of these models, but there were significant discrepancies as far as the turbulence parameters were concerned. In the paper, a new criterion was suggested to predict the onset of turbulence in systems of this type.

Flow fields in electromagnetic stirring of rectangular strands with linear inductors: Part I. theory and experiments with cold models

A model is presented to compute the electromagnetic force fields and fluid flow fields in electromagnetic stirring of continuously cast strands with rectangular cross-section. The model involves the solution of the Maxwell equations, the Navier-Stokes equations, and the transport equations for the turbulence characteristicsk and e. The procedure of depth-averaging is applied in the treatment of several three-dimensional flows. Experiments were performed to check the computations using mercury as fluid. The spatial distribution of the magnetic induction and of the force density was determined for the laboratory inductor used in the stirring experiments. The flow velocity was measured photographically or with a drag probe, respectively. The agreement between experimental and theoretical data was found to be within 25 pct. It is concluded that the theory is sufficiently reliable to predict the flow fields in electromagnetic stirring of steel strands. In Part II of this paper the model is applied to analyze stirring situations in continuous casting of steel.