Journal of Materials Processing Technology 153–154 (2004) 386–391

Computer simulation of the thermal regime of double-loopchannel induction furnaces

J.I. Ghojel, R.N. Ibrahim∗Department of Mechanical Engineering, Monash University,

Caulfield Campus, 900 Dandenong Road, Caulfield Estate, Vic. 3143, Melbourne, Australia

Abstract

Double-channel induction furnaces are used extensively in many processing industries due, mainly, to their relatively low operating costs.However, thermal stresses in the refractory lining caused by high temperatures during the loading cycle can cause erosion of the lining andpremature inductor failure. Prevention of premature failure by close monitoring of the thermal regime of the inductor is very important tooperators and relatively simple and reliable tools need to be developed to this end. The present work is related to the development of sucha tool using a thermal modelling software and unidirectional axial channel flow speeds of the melt that are estimated from analysis basedon the first-law of thermodynamics. This analysis reduces the cost, complications and uncertainties associated with coupled multiple fieldanalysis approach. The results of the analysis show reasonable correlation with reported flow data and a comprehensive set of scenarioscan be devised on the basis of the developed approach to simulate start-up, transient operation and steady state operation of double-channelinduction furnaces.© 2004 Elsevier B.V. All rights reserved.

Keywords: Computer; Simulation; Channel; Induction; Furnace

1. Introduction

Twin-channel induction furnaces are used extensively formelting and holding metals and alloys in many processingindustries. This is due to their high overall efficiency, gooddegassing and homogenisation of the melt, low oxide andslag formation and low energy cost (as result of the potentialto use preferential electricity rates). A schematic diagramof an induction furnace is shown inFig. 1. Alternatingcurrent in the primary coil wound around two sides of acontinuous iron or steel core induces large current densitiesin the molten metal in the channels which form single-turnsecondary coils. The currents induced in the channels heatthe metal in the inductor, which in its turn mixes via theside channels with the metal held in the melting or holdingpot. The relatively colder metal flows back to the inductorthrough the central channel. Large pots are normally de-signed with several channel induction heaters in order tomeet their high melt rates.

It is generally accepted that the function of the primarycoil is to induce large electric current densities in the chan-nels and heat the metal (Joule heating). The electromagnetic

∗ Corresponding author. Tel.:+61-3-9903-2846; fax:+61-3-9903-2766.E-mail addresses: jamil.ghojel@eng.monash.edu.au (J.I. Ghojel),raafat.ibrahim@eng.monash.edu.au (R.N. Ibrahim).

field in the system acts primarily in the planes perpendicu-lar to the axes of the channels and no significant axial flows,resulting from electromagnetic forces, along the channelsaxes are detected[1,2]. The flow in the cross-sectional areasof the channels exhibit double-vortex flow pattern resultingfrom the interaction of the stray primary magnetic field andthe magnetic field of the induced current in the melt loops[3].

Since relatively vigorous mass and heat transfer from thechannels to the main pot is essential to maintain the tem-perature of the bulk of the metal in the pot, there must besignificant axial flows in the side channels. This is despitethe fact that the axial flow velocities that are observed bycomputation or measurement tend to be small and appearto have random up and down pattern[2,4–6]. This leavesthermal buoyancy forces as the main cause of axial flow.

Heat conduction is believed to be caused by turbulent con-duction across the channels resulting from the strong mixingof the melt by the electromagnetic forces and the convec-tive heat transfer along the axes of the channels caused bythermal buoyancy.

It is evident from above that the 3D-coupled physicalphenomena involved in the function of channel inductionfurnaces are not fully understood, and experimental investi-gations using cold mercury or Woods metal are inadequateand unrealistic. The present work is an attempt to develop

0924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.jmatprotec.2004.04.123

J.I. Ghojel, R.N. Ibrahim / Journal of Materials Processing Technology 153–154 (2004) 386–391 387

Fig. 1. Schematic diagram of AJAX twin-channel inductor and pot com-bination.

simple flow hypothesis based on first-law and thermal anal-ysis of a generic 3D inductor model using general purposethermal analysis software. This analysis is useful for en-gineering purposes where most of the downtime faced byoperators is related to the deterioration of the refractorycomponent of the inductor as a result of thermal relatedproblems, particularly during loading of the melt pot.

2. Thermal modelling

2.1. The software

The channel induction furnace is a good example of cou-pled field engineering system, which explains its complexityand the difficulty in predicting the behaviour of the moltenmetal under normal and abnormal operating conditions. Ininduction furnaces, electrical, electromagnetic, fluid flow,gravitational and heat transfer phenomena are continuouslyinteracting in a non-linear fashion. Computer modelling ofsuch a system will ideally require direct coupling of all thesephenomena, preferably in a single software package. How-ever, this is still impractical for the following reasons:

1. There are no software packages to date capable of si-multaneously coupling all the above-mentioned physicalphenomena. One of the better known packages can cou-ple two or three fields such as electromagnetic-thermalto predict Joule heating or fluid–electromagnetic to sim-ulate induction stirring.

2. Modelling of coupled phenomena is inefficient—compu-ting time could be very long.

3. High software cost.4. Modellers of high level of skill in different fields are

required.

For engineering purposes it might be adequate to modelusing a single field package (thermal analysis package) withcarefully selected boundary conditions. For the current work

Fig. 2. Single field sequential thermal analysis scheme.

a general purpose thermal analysis software is used for theinvestigation of the temperature field in the inductor. Thesoftware is SINDA/G and its graphical modeller SINDA/3D.SINDA/G is a finite difference code based on the lumpedparameter modelling technique and allows FORTRAN codeto be mixed with its own commands for better user controlof boundary conditions. The graphical modeller can be usedas 3D interactive pre- and post-processor (Fig. 2).

2.2. The model

Fig. 3shows one-half of the refractory part of the systemas generated by the graphical modeller. Due to its symmetry,only one-quarter of the model is solved.

2.3. Input data

The input data required for the thermal analysis includethe material properties (thermal conductivity, specific heat,density and resistivity, the latter being required only if theload is given as current density). The boundary conditions(heat losses to the surroundings), input heat rate and masstransport (flow speed) of the molten metal in the channels.Material properties can be found from published data andcan be constant, temperature-dependent or dependent ontemperature difference. In this investigation, the propertieswere taken constant. The heat losses to the surroundings in-clude both convection and radiation heat transfer from theoutside surfaces to the surroundings at ambient temperatureand from the inner surfaces of the duct of the coil–iron coreassembly to the air or water provided to cool the coils. Theestimation of the input heat and mass transport are moreproblematic and the approach used in this investigation isoutlined below.

2.3.1. Mass transportElectromagnetic forces act mainly in the plane perpen-

dicular to the axes of the central and side channels. Theseforces do not seem to have a bearing on the unidirectionalflow of the melt in the direction of the axes of the channels;however, they may contribute to the pinching and cavitation

388 J.I. Ghojel, R.N. Ibrahim / Journal of Materials Processing Technology 153–154 (2004) 386–391

Fig. 3. Inductor model showing the sectioned refractory (a) and the molten metal (b).

in the channels. The circulatory motion caused by theseforces could also cause erosion damage of the lining bythe combined action of melt motion and chemical reac-tion between the lining material and the melt. Estimates ofunidirectional flow speed of the melt have been made bymathematical modelling, physical modelling and computermodelling, but these have been mainly for small scale sys-tems with low energy inputs. Therefore, there is little dataavailable for use in three-dimensional computer modellingof practical inductors. The approach used in this investiga-tion was based on simple first-law analysis of steady statesteady flow (SSSF) process as shown inFig. 4 andEq. (1)

∑mi

(hi + C2

i

2+ gZi

)+∑

Ei

=∑

me

(he + C2

e

2+ gZe

)+∑

Ee (1)

where subscripts i and e denote inlet and exit conditionsfor the control volume. Assuming the inlet velocity at theentrance to the gently narrowing central channel is very

small, and since the elevations at the entrance and exit arethe same, the equation is reduced to

C3e + 2cp�TCe − Q

Aeρ= 0 (2)

Fig. 4. SSSF schematic of twin-channel inductor.

J.I. Ghojel, R.N. Ibrahim / Journal of Materials Processing Technology 153–154 (2004) 386–391 389

Fig. 5. Mass transport as a function of input heatQ and temperaturedifference�T.

whereCe is the flow velocity out of the side channels (m/s),cp the specific heat at constant pressure of the melt (J/kg K),�T the temperature increase between the inlet to the centralchannel and exit from the side channels (◦C), Q the net rateof energy input into the system (W),Ae the cross-sectionalarea of the side channel (m2), ρ the density of the melt(kg/m3).

The relationship betweenCe, Q, and�T can be simplifiedby solving Eq. (2) for a given inductor and melt and atdifferent values of�T. This relationship is approximated byEq. (3)and shown inFig. 5.

Ce = kQ

�T(3)

wherek is the constant for a given system and is dependenton the geometry of the inductor side channel and proper-ties of the melt.Eq. (3) indicates that the mass transport isdirectly proportional to the input heat and inversely to thetemperature difference and this correlation is generally sup-ported by experiments.Fig. 5 shows that for a given�T,Ce changes linearly withQ and the temperature gradientchanges from 50 to 10◦C, at constantQ and accompaniedwith a five-fold increase in the flow velocity in the side chan-nel. Research in the laboratories of the German industrialgroup ABB indicates a four-fold velocity increase for thesame temperature range in a 1500 kW TCIF for aluminium[7].

The lower curve represent data published by Vives andRocou[2]. This data relate to actual measurements of flowrate in a four-tenth stainless steel model of a 1300 kW in-ductor unit using cold mercury. Data presented by Drewakand Muhlbauer[4] for a low load case, relating to a stainlesssteel model filled with Woods metal are shown inFig. 6.This figure is the same asFig. 5 with x and y-axis scalesreduced to 20 kW and 0.1 m/s, respectively. These data andthe ABB data[7] referred to earlier can be considered to beshowing reasonable correlation between the predicted andobserved flow velocities.

2.3.2. Input heatThe electrical energy input and the thermal efficiency

(electrical to Joule heating conversion efficiency) are needed

Fig. 6. Mass transport as a function of input heatQ and temperaturedifference�T.

to estimate the heat input into the molten metal. Analysisshows that for an assumption of electrical current ratio of2:1 between the central channel and any of the side channelsthe volume heat input is almost the same for all channelswith the heat input being dependent on the volume of eachchannel. In the generic model investigated in this study themolten metal was taken as pure zinc and the refractory asalumina. An electrical input energy of 400 kW and a thermalefficiency of 75% were assumed. The corresponding flowvelocity in the side channel for a net heat input of 300 kWand temperature increase of 50◦C from the central chan-nel to the side channel was estimated to be about 0.267 m/s(Fig. 5).

3. Computer simulation

The following scenarios were considered for this study:start-up, high mass transport with and without a thermostatand low mass transport without a thermostat.

3.1. Start-up

For this scenario, it was assumed that the system was firstconditioned by heating it uniformly to 100◦C then allowingthe molten metal in the inductor at a temperature of 50◦Cabove the melting temperature to cool down to a temperature

Fig. 7. Temperature–time histories with a thermostat (fluctuating lines)and without (solid lines) under transient operating conditions.

390 J.I. Ghojel, R.N. Ibrahim / Journal of Materials Processing Technology 153–154 (2004) 386–391

Fig. 8. Temperature contours in the inductor without a thermostat.

Fig. 9. Temperature contours in the inductor with a thermostat.

slightly above the melting temperature. This was then takenas the starting point for all subsequent simulations. Otherstart-up scenarios are also possible with proper assumptions.

3.2. Low mass transport

Fig. 7 show the temperature–time histories at the centrenodes in the central and side channels under transient op-erating conditions with and without a thermostat. The flowvelocity at the side channel in this case was taken to beequal to 0.267 m/s. Without a thermostat (smooth lines), thetemperature tends to increase continuously with continuousheat addition with a higher increase rate in the side chan-nel. However, in a typical operation of a channel inductionfurnace, the temperature of the melt will be maintained ata temperature slightly above the melting temperature witha closed loop control system (fluctuating lines). The tem-

perature of the melt in the central channel is maintained, inthis case, by the software within the range of 715–720◦Cwith an on/off thermostat system. Under these conditions thetemperature difference between the side and central chan-nels approaches 80◦C compared with the predicted 50◦Cby first-law analysis.

Fig. 10. Effect of mass transport on channel temperatures.

J.I. Ghojel, R.N. Ibrahim / Journal of Materials Processing Technology 153–154 (2004) 386–391 391

Figs. 8 and 9show the temperature contours in the induc-tor without and with a thermostat. These results show thatthe molten metal is heated continuously as it moves fromthe central channel to the side channels with the maximumtemperature being reached at the exit from the side chan-nels. The metal jet is then quenched as it interacts with themetal in the upper chamber.

3.3. High mass transport

The temperature contours for this case looks similar tothose for low flow speed inFig. 8 with lower peak temper-ature.Fig. 10 shows the temperature–time histories at thecentre nodes in the central and side channels under transientoperating conditions and constant input heat for three masstransport cases: low (0.236 m/s), intermediate (0.42 m/s) andhigh (0.69 m/s) flow speeds. The temperature at the cen-tral node of the side channel increases with decreasing flowspeed as a result of increased residence time, while the tem-perature at the centre node of the central channel remainsalmost unchanged. This indicates that mass transport playsa critical role in determining the temperature regime of theinductor and further research is required to quantify the op-timum flow speed value for a particular design if durabilityissues of inductors are to be addressed.

4. Conclusions

Estimates of the flow speed from the exit of the sidechannels from first-law analysis seem to correlate reason-ably well with the experimental and analytical publisheddata. These data, with appropriate boundary conditionassumptions can be used to simulate various operatingconditions of inductors using dedicated thermal analysis

software packages. The method developed can be used fordifferent inductor sizes and different metals, both ferrousand non-ferrous. Improvement can be made to the methodby improving the assumptions when data of temperaturemeasurements in actual inductors become available. Furtherwork, both experimental and analytical, is required to quan-tify the flow speed in channel inductors and correlate thatwith the input energy and temperature regime in the induc-tor. As it stands the model is adequate for use by inductordesigners and users to predict the temperature regime ofthe inductor under different loading regimes and use that toprevent premature inductor failure.

References

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[3] R. Drewak, A. Jakovich, A.A. Muhlbauer, B. Nacke, Experimentaland numerical investigations of the melt flow in channel-inductionfurnaces, Magnitnaya Gidrodinamika (Magnetohydrodynamics) 32 (4)(1996) 433–443.

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