heat transfer in steelmaking ladle refractories and steel

$: Heat transfer in steelmaking ladle refractories and steel$
Scandinavian Journal of Metallurgy 2000; 29: 232–258 Copyright C Munksgaard 2000Printed in Denmark. All rights reserved

SCANDINAVIANJOURNAL OF METALLURGY

ISSN 0371-0459

Review Article

Heat transfer in steelmaking ladle refractories and steeltemperature

A literature review

Tom P. FredmanHeat Engineering Laboratory, Åbo Akademi University, Biskopsgatan 8, FIN-20500 Åbo, Finland*

Key words: ladle, refractory, lining, steel, heat transfer

c Munksgaard, 2000

Introduction

The word ‘‘ladle’’ has been used in the English lan-guage since the 12th century to denote ‘‘a deep-bowl-ed, long-handled spoon designed to convey liquids’’,or a resembling instrument [1]. Although this type ofdevice has been present in metallurgical operationssince the discovery of iron, functioning as a means oftransporting molten metal in the casting procedure, itis only recently that attention has turned towards theloss of heat from the molten contents of the ladle. Thisis due to the rapid development of contemporarysteelmaking and new ladle designs.

The purpose of this paper is to review some of theliterature dealing with heat transfer in steelmakingladle refractories and mathematical models thereof.The reviewed works are classified into experimentally-and theoretically-focused investigations. Relatedtopics, e.g., measurement and modeling of steel tem-perature in the ladle or tundish and temperature con-trol in casting, are included. Most contributions to thefield are conference papers and plant-specific studies,although there are a small number of refereed journalpapers and some scientific theses and course material.

In most steelmaking facilities, the temperature evo-lution of the heat during casting is determined by thetapping temperature of the converter. Therefore, in or-

* e-mail: tfredman/abo.fi

232

der to control the casting temperature properly, it isvery important to predict the loss of energy from theheat at all process steps from the converter to the cast-ing machine. This requirement can be relaxed and theoperating conditions of the converter can be standard-ized by introduction of melt reheating equipmentalong the process route to ensure a sufficiently highcasting temperature. Reheating should be done asclose to the caster as possible (e.g., by plasma or in-duction heating in the tundish), to minimize tempera-ture variation during casting. However, as reheatingfacilities tend to be energy and space consuming aswell as expensive, it is still adopted practice to usetapping temperature as a control variable for the tem-perature trajectory at casting.

Traditionally, the estimation of heat losses wasdone by the caster foreman on the basis of long-termprofessional experience. Recent developments in con-tinuous casting practice, multiple ladle operationswith limited transfer facilities, new steel grades, newrefractory materials and ladle/tundish designs andman-power reduction due to automation of the pro-cesses have led to a need for more accurate heat lossestimation. The molten metal looses heat during hold-ing, transportation, pouring and stirring stages be-tween the converter and casting machine. Cooling isalso performed, when necessary, by scrap additionsand at ladle treatment when adding alloying elementsto the melt. Modeling the influence of stirring, pour-ing and alloying on heat temperature is mostly done

Heat transfer in steelmaking ladle refractories

using empirical expressions formed on the basis ofpreviously obtained measurement data. First prin-ciples have mainly been employed to describe theheat losses due to holding and transportation.

It is evident that more refined methods of heat lossestimation will be required in future steelmaking asladle treatment processes will become more important[2] and the casting temperature window for most steelqualities will be narrower. Process logistics is alsolikely to become more complex with higher demandson productivity and energy economy.

There are a number of frequently-used decisionvariables in temperature control, for cooling; idlingthe heat, stirring and scrap addition, for heating; re-heating if equipment for this is available, either chem-ically or electrically. If the temperature of a heat de-clines too rapidly during casting, the casting speedcan be increased. On the other hand, casting speedcan be lowered if there is insufficient shell thickness.In severe cases, when it is anticipated that the heat islikely to be interrupted, despite high casting speed,the heat can be partly or entirely rejected and recycledto the process as scrap. For the heat loss to the ladlerefractory, the most important factors for temperaturecontrol are the thermal state of the lining at tappingfrom the converter and the thermal properties of therefractory. Continuous measurement of the thermalstate being inconvenient and difficult, estimation ap-pears a possible application for first-principlesmodeling. Other variables affecting heat loss are theextent of refractory wear and scull (solidified metalresidue in the ladle). Heat loss is also a function of theladle holding time, stirring time, nature and extent ofladle treatment (alloying etc.), slag amount and com-position as well as casting time [3, 4].

Strategies for improving temperature control can bedivided into 2 approaches; the hardware and the soft-ware approach. Hardware improvement of tempera-ture control includes use of insulating cover agents onfree slag surfaces to inhibit radiation and convectionheat transfer, ladle lids for the same purpose and fordecreasing radiation heat transfer from the free innerwall surfaces of ladle lining. Another frequently-usedmeasure at revamping of steel plants is to increaseladle capacity, reducing the heat loss per mass ofmetal. Recently, new refractory materials have ap-peared on the market, giving improved mechanicalstability and improved wear resistance. Thus, moreheats can be cast with the same refractory and energysavings due to fewer preheatings and ‘‘thermal start-ups’’ of newly assembled ladle refractories can beachieved. Unfortunately, most of these new materialsstore more energy and conduct heat better. This will

233

surely present a challenge to heat loss estimation andis, in fact, the background to much of recent work inthis area. As mentioned, an effective but expensiveroute to improved temperature control is installationof reheating facilities. Since this requires reliable on-line temperature measurement for control of the heat-ing input and major investments as well as increasedenergy input it has not been very popular.

Software improvement of temperature control in-cludes systematic heat loss estimation and processscheduling, e.g., through use of expert systems, simula-tion and tuning caster operation for coherence to con-verter output. Attempting to estimate the heat lossesalong the route between converter and casting machineand to correct the influence of these on the casting tem-perature by altering the converter tapping temperatureresembles the feedforward approach of control engin-eering. However, there is also feedback represented bythe thermal state of the ladle brought to tapping.

Thermal control in continuous casting

In a series of articles, [5–7], Cramb outlines differentcontrol strategies for continuous casting. Emphasis ison time and temperature control. The author defines timecontrol as the problem of targeting each operationalstep on a specified time plus or minus an acceptablevariation. Time control, in continuous casting, is de-pendent upon temperature control. To improve timecontrol, the temperature can be manipulated if the rightprocess hardware is available. There are 2 operatingstrategies for achieving high productivity on castingmachines. One is to maintain steady state operationthrough process consistency, reproducibility, statisticalanalysis and research to deepen the understanding ofeach process step. The alternative is biasing the oper-ation to deal with poor coordination. An example ofthis approach is use of ladle metallurgy as a buffer be-tween steelmaking and the caster when synchroniza-tion between these is poor. Whereas the consistencystrategy requires extended research and developmentof the process, the latter coordination approach empha-sizes quick decisions. In this strategy, optimization ofsteelmaking tends to become more important than thatof continuous casting. Temperature control in casteroperation has 3 objectives. Tundish superheat is to becontrolled, a sufficiently high heat content of the liquidsteel must be ensured to allow for the intermediate op-erations before the tundish and, finally, slab enthalpy isto be maximized. These can be met by proper controlof liquid steel temperature, of which Cramb notes threemain strategies.

Fredman

O Tap every heat at the highest possible superheat,allowing for delays etc., correct the temperature of(cool) the heat at the ladle metallurgy station

O Tap every heat with the minimum possible super-heat, which will enable meeting the aim tundishtemperature without correcting actions

O Tap every heat at a predetermined temperature, re-heat or cool in the ladle or tundish if necessary.

The 1st strategy is typical for coordination time con-trol, resulting in long ladle heat times and frequentladle cooling. Furnace and ladle refractory life is gen-erally poor due to high tapping temperatures. More-over, the use of scrap in the BOF is minimized, whichlimits production. In the 2nd approach, energy cost isminimal but extended knowledge of heat loss mech-anisms is fundamental. No room for process irregular-ities can be allowed and the strategy is not very flex-ible. Successful implementation of this approach re-quires an on-line computer program for calculation offurnace tap temperature based upon the caster sched-uling. Strategy no. 3 maximizes furnace and refractorylife as well as simplicity of operation, however, cost-ing more in installation and operation of special ladleand tundish heating devices. Depending on the com-position of the specific grade to be cast, optimal oper-ation can be achieved with a mixture of the 2nd and3rd strategy or, if reheating facilities are there, withstrategy no. 3. Relying completely on the 2nd strategyis possible only with an advanced on-line computersimulation system, properly tuned to the actual cast-ing operation and accounting for all heat loss mechan-isms of the molten metal during its residence in theladle and tundish. Accurate modeling of the pre-heating and waiting empty phases is also essential. Inany case, calculation of the temperature at tapping oron exit from the ladle station must be done. This isthe topic of [7], where a simple flowsheet for the cal-culation is presented. As a starting point, the liquidustemperature for the specific steel grade to be cast istaken. To this the desired superheat in the tundish isadded, giving the aim tundish temperature. If the cal-culated heat losses during residence in the tundishand at draining the ladle are added, the aim tempera-ture on departure from ladle treatment is obtained.Adding the standard loss during ladle treatment anda calculated loss due to holding will give the aim steeltemperature on arrival at ladle treatment station. Fi-nally, adding the tapping losses brings us to the pre-dicted tapping temperature. Reliable estimation of thedifferent heat losses generally requires statisticalanalysis of measurement data from the specific caster.Some empirical knowledge can be omitted if relevant

234

theoretical knowledge is incorporated into models fordifferent heat losses. However, no matter how ad-vanced a model, tuning to the actual process will al-ways be needed. This is understandable consideringthe large number of variables influencing the steeltemperature. Tap temperature estimation should bebased on timing, ladle and tundish lining status, pro-jected ladle metallurgy operations and projected cast-ing time. Furthermore, if the steelmaking shop isclosely synchronized to the caster, tap temperaturescan be lower than if there are bottlenecks in the pro-cess logistics. If so, steel reheating might be necessarywhich, apart from easing temperature control, givesthe steelmaker the ability to recover cold heats andallows for extended degassing and ladle metallurgy.

Experimental studies of steelmakingladle systems

OverviewMany of the reviewed articles with an experimentalapproach to temperature control feature temperaturemeasurements in steelmaking ladles in circulation.The most common method is to insert thermocouplesinto the refractory lining at different distances fromthe ladle bottom and hot face to monitor the tempera-ture of the lining during the ladle cycle [8–16]. In anearly work, [17], the temperature of ladle hot face wasrecorded by immersion of a thermocouple, in contactwith the refractory, into the molten metal. A non-con-tact method, use of a radiation pyrometer, is describedby Ettwig [18]. This method was used by various in-vestigators [14, 15, 19]. In a few works [13, 14, 19] thethermal stratification of the molten metal was investi-gated by immersion of a lance fitted with thermo-couples at different heights. Other experimental tech-niques include tracer experiments to determine theresidence time distribution of the steel in the tundish[12]. The tare weight of ladles can also be measuredsystematically [19] to track sculling and refractorywear, and tundish steel temperature may be measuredby thermocouple immersion [13, 14, 17]. A physicalmodeling approach was adopted by Hlinka & Miller[20], who simulated the filled ladle using a vesselmade from acrylic plastic containing hot water.

Reviewed investigationsSamways & Dancy [17] measured steel temperatureduring normal operation of a 285 t open hearth andan 84 t basic oxygen furnace in an ingot casting pro-cess. These measurements were done with Pt-Pt 10%Rh thermocouples, calibrated against the meltingpoint of pure iron. Tap temperatures were recorded


Fig. 1. Schematic of the ladle-tundish model. Experimental apparatusused by Hlinka & Miller [20]. Courtesy of the Association of Iron andSteel Engineers.

within 1 min of tap and teeming (casting) tempera-tures were taken by immersing a silica sheath slowlyinto the teeming stream as close to the nozzle as poss-ible. Ladle temperatures were monitored with a con-tact chromel-alumel thermocouple to give an indi-cation of ladle brick temperature. Ladle additions,tapping, holding and teeming times were also re-corded in an effort to formulate a statistical model forthe overall drop in steel temperature between tappingand teeming. The tapping time and temperature, steel

235

grade chemical composition, refractory thermal state,holding and casting time and temperature were iden-tified as the most important variables affecting thetemperature drop.

Data were gathered from 73 open hearth heats and25 basic oxygen heats and a computer program basedon expressions linear in tapping, holding and teemingtimes was designed. The effect of ladle additions wasestimated by considering different reaction mechan-isms and their consequences for the temperaturedrop. Ladle heat losses from conduction through thewalls and radiation as well as convection from themelt surface were correlated with tapping, holdingand teeming times. Surface losses were consideredonly during tapping because of the insulating effectof the slag, reducing convection losses. An interestingobservation is the accelerated temperature drop at thefinal stages of teeming, as the relative importance ofconduction losses through the bottom increased. Al-though the results may not be valid as such for mod-ern continuous casting processes, the work is a goodexample of how empirical models can be formulatedand evaluated.

Hlinka & Miller [20] developed a method formodeling liquid steel-refractory systems by means ofhot water and acrylic plastic, see Fig. 1 for their ex-perimental setup. This physical modeling approachwas tested at the Homer Research Laboratories ofBethlehem Steel. The method allows both heat andfluid flow phenomena to be studied simultaneouslyand the observations can, with certain preconditions,be scaled up to the ladle-tundish system used instrand casting. The purpose of the work was to studythe effect of ladle and tundish preheat and castingspeed on steel temperature. As mathematical calcu-lations gave misleading results, assumed due to ther-mal stratification in the molten steel, physicalmodeling was adopted. Through dimensional analy-sis of the heat transfer from the steel to the refractoryit was found that containers made from acrylic plasticcontaining hot water with a layer of mineral oil tosimulate slag could model the ladle and tundish. Themelt surface, of the model as well as the real system,was considered completely insulated by the slag.Temperatures were recorded at three positions in themodel system; by the ladle stopper rod on the bottom,in the tundish and near the surface of the water inthe ladle. Tracer dyes were injected into the ladle tovisualize the convection currents. A marked differ-ence was found between the fluid flow in a ladle withthick and a ladle with thin slag, see Fig. 2. The tem-perature in a tundish teemed from a ladle with thickslag leveled off and stayed almost constant during

Fredman

Fig. 2. Convection currents during teeming. Impact of slag layer onstratification, according to the results of Hlinka & Miller [20]. Cour-tesy of the Association of Iron and Steel Engineers.

casting. Moreover, it was observed that stratificationin the ladle actually serves to even out the tempera-ture trajectory of the teeming stream as the colder pe-ripheral streams descend towards the nozzle and arereplaced by hotter steel from the bulk zone. This phe-nomenon was pronounced especially during pro-longed casts and was attributed to the insulating ef-fect of the slag layer. When water model observationswere scaled up and compared with measurements ona 7.5 t heat made in the lab melt shop, agreement waswithin 12æC. The effect of preheat of ladle and tundishwas investigated by keeping hot water in the vesselsprior to the experiments and the results were scaledup to 7.5 t and 75 t heats, respectively. Tundish level-off temperature as fuction of casting rate was also ob-tained from the model trials and a slight increase intundish temperature was detected for high castingspeeds. A probable cause was thought to be the stor-age of heat in tundish walls/refractory at the initialstages of casting. As a higher level-off temperature,which occurred for higher casting rates, allows alower tap temperature, the model experiments con-firmed that casting speed can be increased to managecold heats. Finally, scale factors were calculated fromsimilarity considerations of material properties, tem-perature, time, heat and fluid flow and geometry.

Ameling et al. [8] outline temperature control of‘‘die Hamburger Stahlwerke GmbH’’. After the ladlefleet had been revamped from schamotte to dolomitelinings with tighter requirements on temperature con-trol, it was necessary to obtain more accurate on-lineprocess information. The ladles were permanently fit-ted with two thermocouples each, one measuring thetemperature of the steel shell – safety lining interfaceand one the temperature at the interface between theworking and safety linings. The difference betweenthese readings was used to quantify the thermal state

236

of the lining and fed to the process computer togetherwith other important variables, such as estimatedtime to start of casting and amounts of ladle ad-ditions, to calculate the required tapping temperature.Portable ladle covers were in continuous use and inte-grated lids were on trial. A prototype ladle had liningbricks laid in a spiral – like manner to prevent jointopening and cracking. Although the response of thetemperature measurements to irregularities in theladle cycle can be questioned, the initial results fromthe trials were characterized as promising.

Widdowson [21] presents a summary of methodsand aims for control of temperature and chemicalcomposition in the ladle. An assessment of existingprocedures and future prospects is given, with em-phasis on composition chemistry. The benefits of inertgas bubbling as a means of avoiding thermal stratifi-cation and minimizing idle time between gas stirringand tapping from the converter are outlined on basisof previous reports. As key variables for temperaturecontrol Widdowson lists tapping time and tempera-ture, ladle additions, scull, slag load, lining and meltsurface properties, holding and stirring times and tun-dish state.

Kitamura et al. [10] briefly report on a measurementcampaign with six thermocouples in a ladle lined withroseki firebrick. The ladle was monitored during ladletreatment, degassing and teeming. From the data, cor-relations were obtained for the temperature drop ofthe molten steel as a function of time elapsed fromend of tap. Covered as well as uncovered ladles wereincluded in the study.

Saunders [16] gives guidelines for preheating andthermal control developed after switching from fire-clay to high-alumina ladle linings. The studied planthad ingot as well as continuous casting processroutes. Considering the 25% increase in density andthe doubling of lining thermal conductivity, a meas-urement campaign spanning 80 heats for a ladle with70% alumina lining was implemented. It was foundthat to avoid excessive sculling and refractory damagea revision of practice would be necessary. Preheat ef-ficiency was described by considering waste gas tem-perature, excess combustion air and existence of heatrecovery. Saunders recommends that preheat facilitiesbe specified so as to deliver around 70% of the ther-mal energy to the lining required for steady state inthe nominal preheat time. The initial thermal state ofthe lining was discovered to be a major factor affect-ing heat loss during the ladle cycle. Measurements in-dicated that the lining reached thermal quasi steadystate in five regular ladle cycles. A computer modelfor the refractory thermal state was developed for use


Fig. 3. Calculated and measured temperatures, by Saunders [16], asfunctions of preheat time at different positions in the ladle lining.Courtesy of the Iron & Steel Society.

in preheating control and estimation of steel heat lossbetween tapping and casting. In Fig. 3, the tempera-tures at various monitored positions in the lining of aladle are compared with calculated results obtainedwith the model. When the ladle cycle was regular,both preheat and tap-teem simulations agreed wellwith the measurements. The model was also used fordesign purposes, to compare thermal efficiency of dif-ferent refractory materials and to calculate the re-quired thickness of insulating linings. Insulatinglinings were found to be cost-effective in rapid con-tinuous casting cycles where there is risk of exceedingthe recommended maximum ladle shell temperatureof 370æC.

Rieche et al. [14] studied heat losses from the 220 tladles of plant no. 1 of Mannesmannrohren-WerkeAG. In particular, it was desired to determine the in-fluence of thermal state at tapping and use of insulat-ing covers on the steel temperature drop. The ladlefleet had dolomite working linings and schamottesafety linings with insulation bricks between thesafety lining and ladle shell. The ladle lining and steeltemperatures were monitored with thermocouples,tundish steel temperature was measured with an im-mersion probe and the exposed hot face temperatureswith a radiation pyrometer. The measurements com-pared reasonably well with calculations of steadystate heat conduction through the ladle wall, despitevariation of thermal conductivity with temperaturenot considered in the model and irregularities in the

237

ladle cycle. In Fig. 5, a comparison of the measuredand calculated temperature profiles is presented. Aspreheating capacity was inadequate, the resultsshowed clear benefits of using ladle lids and insulat-ing agents on the slag surface. After a disturbance,such as prolonged waiting, it took at least two ladlecycles to re-establish quasi steady state. When a newlylined ladle went into service, approximately four ladlecycles were needed to arrive at steady conditions.This is illustrated in Fig. 6. The time from end of castto begin of tap and casting time were detrimental forsteel temperature drop in the next cycle. An interest-ing detail is the jump downwards in temperature atthe safety lining – shell interface indicated by themeasurements (cf. Fig. 5). A possible cause of this islining separation caused by thermal expansion of theshell. It was also observed how the temperature con-tinued to decrease for a short while after tapping ofsteel into the ladle had begun, (see Fig. 6 stage d) inthe ladle cycles. From measurement data, it was esti-mated that the steel cooling rate reached a stablevalue of about 0.42æC/min 50 min after end of tap-ping. The temperature measurements of stratificationin the molten steel gave a maximum difference be-tween top and bottom of 14æC, diminishing after gasflushing for 1 min. When stratification re-occurred,the temperature difference between top and bottomwas only 4æC. Results from lance measurements in-tended for examination of stratification should, how-ever, be viewed critically as immersion of the lancealways more or less disturbs the flow field, which inthis type of system is strongly coupled with the tem-perature field.

Cardouat [22] reports on how tighter requirementson temperature control and lack of reheating equip-ment initiated investigation of heat losses at the Solm-er works. Thermal development during ladle treat-ment, alloying, waiting periods and pouring werestudied. A model dependent on idle time of the heatprior to casting, ladle treatment time and nature ofadditions and tare weight of ladle before tap was for-mulated. No measurement results are given, neitheris the mathematics behind the model described. Acomputerized system for ladle management, includ-ing facilities for follow-up on the use of ladle preheatand maintenance, is reported to be under develop-ment.

Minion & Leckie [11] investigated the impact of anovel ladle lid system on temperature control, usingthermocouple measurements from the ladle linings. Anew lid handling system was developed at the StelcoHamilton plant, featuring attachment of the lid to theladle with hinges, making overhead cranes for this

Fredman

purpose obsolete and bringing down uncovered timeto a minimum. The lids were removed from the ladlesonly at tapping from the converter. Measurements in-dicated that the safety lining and shell reached ther-mal quasi steady state in a few cycles, the maximumshell temperatures being 220æC for a ladle with alu-mina working lining. An alternative cycling practicewith preheating instead of ladle lids was evaluatedand compared with the lid practice with respect to hotface temperature, steel temperature drop, amount ofcooling scrap and refractory wear and durability. Byall of these criteria, the strategy using the novel lidsystem was clearly superior to preheating. The vari-ation in hot face temperatures after casting decreasedto 30æC with the lids and this helped to reduce slagline refractory joint opening and spalling. Thus, goodtemperature control and ladle practice, apart from de-livering ladles to tap in a sufficiently hot state andusing suitable lining materials, must also include useand rational handling of ladle lids. The measuredsteel temperature drops during the campaign werecompared with simulations done at the University ofToronto and the calculations proved that lid use con-sistently lowered tapping temperatures. Moreover, aflatter temperature trajectory of the steel during cast-ing could be achieved.

Perkins et al. [12] summarizes temperature controlat the Lackenby works of British Steel plc. A varietyof experimental techniques were used, including ther-mocouple monitoring of ladle linings, tracer experi-ments to investigate tundish residence times andphysical scale modeling with mercury and water tostudy thermal effects of gas flushing. The concepts‘‘mean working lining temperature’’ and ‘‘cooling rateof working lining’’ were used for classification of thethermal state of ladle linings into 7 disjoint classes.Preheating rules for the different classes were formu-lated and a computer code for ladle scheduling wasdeveloped. The computer program keeps track ofladle availability, thermal status and identifies theones suitable for tapping. Results from the residencetime experiments were scaled up and an empiricalmodel for tundish output temperature was set upwith the help of calculated wall and surface heatlosses and a simplified model of ladle fluid dynamics.Steel heat loss in the tundish was considered a func-tion of residence time only. Unfortunately, initial dif-ficulties blocked on-line use of the model in the pro-cess computer. The ultimate aim of the project wasdesign of an on-line system for temperature control.It was discovered that improvements would beneeded in modeling heat losses during gas flushingand in temperature measurement prior to tapping be-

238

fore the model could become reliable enough for on-line operation.

Thermal behavior of the refractories of the 300 tandalusite-schamotte ladles in the Rheinhausenworks of Krupp Stahl AG was studied by Hoppmannet al. [9]. The usual observation method, with thermo-couple measurements over a campaign consisting ofseveral ladle cycles, was employed. The safety liningand shell reached quasi steady state in four ladlecycles after a newly lined ladle was taken from pre-heating into operation. As the working lining woredown toward the end of the campaign, the heat lossfrom the steel increased. Shell temperature never ex-ceeded 250æC when ladle lids were used periodicallyduring waiting times. Theoretical results for the re-fractory thermal state prior to tapping were obtainedby solution of the dynamic heat conduction equation.Radiation losses from the slag surface of the steel werecalculated and partial solidification of the slag as wellas re-melting on stirring of the heat were considered.The greatest discrepancy between theoretical esti-mates and measurements was observed at the ther-mocouple positions in the vicinity of the hot face, i.e.,where the dynamics are most important, and the errorwas estimated to be equivalent to a temperature dif-ference in the steel of 0.8æC. For preheating, it wasfound that only 23% of the input energy to the gasburner increased the energy content of the refractory,0.3% was stored in the ladle lid, 6% was conductedthrough the refractory walls and 70.5% was lost withthe combustion exhaust gases. Thermal behavior ofthe andalusite-lined ladles was compared with the re-sults from a similar study of 100 t dolomite linedladles. In a 60 min waiting period, when the steel inthe larger ladle cooled 72æC (0.65æC/min), the steel co-oled 95æC (0.85æC/min) in the smaller one.

Christensen [23] assessed heat losses for two differ-ent ladle configurations, a tapping ladle lined withcarbon paste and fireclay brick and one lined solelywith fireclay brick. The distribution of the heat loss tothe surroundings between the slag surface (and coverwhen in use), ladle bottom and sidewall is outlinedfor these two systems, as well as losses at tapping,refining, pouring and while the ladles stood empty.Here, heat radiating from the top of the ladleamounted to most of the overall heat loss. The tem-perature drop of the molten metal arising from con-duction to the lining is not indicated. Only shell tem-peratures were measured and, from these, experimen-tal correlations yielded estimates of the heat flux tothe ambient. Radiation losses were studied using aninteresting measurement setup consisting of a smallcopper plate water-cooled on one side. Maintaining


water flow through the cooling circuit at a constantrate and measuring the in- and output temperaturesfor the water gave a hint of the absorbed radiationheat flux.

Petegnief et al. [13] report on experiments carriedout at the Hagondange and Neuves-Maisons plants ofthe French steel industry. Although these plants hadladle furnaces there was a need for improved tem-perature control. Temperatures were measured in therefractory of a 135 t ladle over a campaign of 30 heats,ladle stratification and tundish temperatures weremeasured with lance and immersion thermocouples.For comparison, one-dimensional temperature pro-files were obtaine by solving the heat conductionequation using a finite difference method. Agreementwith measurements was within 50æC. When steel tem-peratures in the ladle were estimated from the tundishmeasurements and the temperature drop was calcu-lated, the heat balance model relying on calculatedtemperature profiles failed. A probable cause of thiswas temperature stratification and sculling. To studystratification, the two-dimensional Navier-Stokesequations were solved numerically for the flow field,which was combined with the energy balance equa-tion for the molten steel. Based on the theoretical cal-culations, minor adjustments could be made to theheat balance model for steel in the tundish. When thethermal effects of ladle lid use were studied, it ap-peared that lid practice would reduce preheating timeby 1 h 40 min for a natural gas burner consuming180 normal m3/h of fuel. The information from theexperiments and modeling was used in an operator’sguide for the ladle furnace at Hagondange. As a resultof the introduction of the new decision support, stan-dard deviation in tundish steel temperature was re-duced by 50%. It was concluded that good tempera-ture control can be achieved with relatively simplemodels, provided the ladle cycle is sufficiently reg-ular.

Rutqvist et al. [15] found that the most importantfactor influencing casting temperature is ladle thermalstate prior to tapping, provided the ladle cycle is suf-ficiently regular and rapid. For quantification of thethermal state, measurement of the hot face tempera-ture of the empty ladle was proposed. Remote meas-urement of this temperature was possible through theuse of a radiation thermometer (pyrometer). To inves-tigate whether this type of measurement could beused to unambiguously classify the possible internalthermal states of the refractory, a thermocouple meas-urement campaign was undertaken. It turned out thatif, in addition to the temperature, its time derivativewould be known, the character of the internal thermal

239

state could be determined. Formally, this can be ex-plained by considering the boundary condition at thehot face; the heat flux is proportional to the surfacetemperature. Hence, the temperature and its time de-rivative determine the heat flux and its rate of change,characterizing the thermal state of the dynamic partof the lining. The internal profiles of the refractorywere simulated for a set of disjoint classes made upof different temperature and time derivative valuesfor the hot face. The simulations were verified by thethermocouple measurements. For each class, an em-pirical model for the steel temperature drop wasformed on the basis of campaign data.

The main topic of Grip [19] is radiation pyrometermeasurement of ladle hot face temperature on transferfrom continuous casting and during preheating. Briefsummaries are also given of thermal stratificationstudies with thermocouple lance, impact of gas stir-ring on stratification, development of a thermal modelfor molten steel in the ladle cycle and preheat burnercontrol. Interpretation of measurement data was simi-lar to [15] and the main objective was to control con-verter tapping temperature so as to minimize scrapcooling and deviation from aim casting temperature.The positions of the pyrometers were at the sandingstation in ladle maintenance, at the ladle track beforethe converter and at the ladle burners. Hot face physi-cal properties could vary substantially within thesame ladle. This was due to slag residue, sculls, wear,refractory cracks etc., and could give a dispersion ofup to 50æC in the measurements. The sanding pro-cedure resulted in sand clouds interfering opticallywith pyrometer operation, which could be avoided byextending the period of measurement beyond thesanding time and retaining the maximum tempera-ture value. Problems with pyrometer overheating atthe ladle burners also occurred. Ladle sculling was es-timated by monitoring the tare weights of the ladles.However, inconsistent results were obtained due tocalibration differences between the overhead cranes.It was decided to use the same overhead crane everytime when weighing a specific ladle, if possible.

Ettwig [18] discusses non-contact measurement oftemperatures on hot surfaces using a polarization py-rometer for wavelengths shorter than 700 nm (visiblelight lies between 390 nm and 770 nm). Temperaturemeasurement with this method is possible to an accu-racy of 10 K above 800 K. The greatest error source isbackground (reflected) radiation from the examinedsurface. There are a number of methods to suppressthe reflected radiation, such as water cooled deflectiondevices or polarization of the measurement beam.Water cooling has some drawbacks: energy is needed

Fredman

Fig. 4. Reflectances for radiation incident on a metal.

Fig. 5. Temperature profiles in the ladle lining calculated and measuredby Rieche et al. Adapted from data in [14].

to sustain the cooling, measurement errors are in-troduced due to cooling of the studied surface, reflec-tion from the water cooling equipment onto the sur-face and lower reliability of the measurement. For re-flection and absorption of incident radiation at a met-allic surface, the reflectances for the parallelly andperpendicularly polarized components behave dif-ferently. In fact, the reflectance of the parallelly polar-

240

Fig. 6. Temperature trajectories at the measurement points in the ladlelining during various process stages, by Rieche et al. [14]. Calculationsare indicated by broken lines and measurements by full lines. Adaptedfrom data in [14].

ized component goes through a minimum at an inci-dence angle (measured from the surface normal vec-tor) of approximately 1.2 rad. This result of Ettwig[18] will be derived here by considering the Maxwellequations for the electromagnetic field, [24], fromwhich the reflectances for the polarization compo-nents of the incident radiation on the surface can beobtained. Expressed as functions of incident andtransmitted angles (qi, qt), real (nR) and imaginary (nI)parts of the index of refraction (n), it is seen that

Ri (qi, qt) Ω|n|2 cos2qiª2nR cosqi cosqtπcos2qt

|n|2 cos2qiπ2nR cosqi cosqtπcos2qt, (1)

for the parallelly polarized component, and

R' (qi, qt) Ω|n|2 cos2qtª2nR cosqi cosqtπcos2qi

|n|2 cos2qtπ2nR cosqi cosqtπcos2qi, (2)

for the perpendicularly polarized one. For the indexof refraction, obviously

|n| Ω !n2Rπn2

I . (3)

The relation between incident and transmitted angles,considering air as the surrounding medium, is Snellslaw of ray optics

sin (qi) Ω |n|sin (qt) . (4)

Combination of (1), (2) with Snells law (4) yields thereflectances as functions of the incident angle qi. Plot-ting gives (for nR Ω 2.5 and nI Ω 0.5) the result in Fig.4, which is similar to that of [18].

As Ettwig [18] points out, obviously, the measure-ment angle for the pyrometer should be kept as closeas possible to the minimum point of (1) in order tominimize errors due to background radiation. An-other useful recommendation, given by [25], is thatcare should be taken to maintain the same location of


Table 1. Reviewed experimental works relating to ladle thermal state

Corresponding Measurements Featuresauthor thermocouples pyrometer steel temp. special supporting remark

techniques theor. model

Samways [17] hot face yesHlinka [20] phys. mod., fluid-flow

scale-up studyAmeling [8] lining calc. of tap temp.,

from meas.Kitamura [10] liningSaunders [16] lining lining aid design,

thermal state preheat eval.Rieche [14] lining hot face ladle, thermal

tundish steady stateMinion [11] lining yes eval. lid vs.

preheatingPerkins [12] lining phys. mod., thermal state,

tracer exp. schedulingHoppmann [9] lining lining

thermal stateChristensen [23] shell radiation loss

measurementPetegnief [13] lining ladle, coupled heat 1-D thermal, aid decision-

tundish mass transfer flow field makingRutqvist [15] lining hot faceGrip [19] hot face ladle monitor ladle steel temp.

tare weight modelEttwig [18] general measurement optics minimize

hot surface focusing meas. errors

the measurement point on the hot face of each ladle,in order to minimize errors due to differences in sur-face conditions.

Summary of the experimental studies

The reviewed experimentally focused works relatingto thermal state of ladle systems have been summar-ized in Table 1. In the classification of the investi-gations, experimental setup (type of measurements)and special features have been used as criteria. Asspecial features are considered both novel experimen-tal methods and supporting theory, such as tracer ex-periments or a flow field model for the molten steel.Further characterization of the work, such as its prin-cipal aim or an emphasized sub-topic, is included inthe remark entry.

From Table 1, it is observed that a large part ofthe research is focused very much on applications andresults specific to one particular plant. Basic researchis only represented through [18] and [20]. This isunderstandable, keeping in mind the high cost of ob-taining extensive measurement data from which moregeneral conclusions can be derived. Producing resultsfor one specific plant is, however, fairly straightfor-ward. A downside with this approach is the need forrenewed research effort in case of a major overhaul of

241

the equipment, e.g., the ladle fleet or tundishes. Onthe other hand, since good temperature control makessteel production more cost-effective, it is often not de-sired to generalize the knowledge to the benefit ofcompetitors.

Lining temperature measurement having become awell-established technique, research into fluid dynam-ics and thermal stratification of the molten steel hasgained popularity in recent years. The problems ofthis area are related to the aggressive environmentand the fact that the measurement easily disturbs theflow field. Furthermore, in some cases thermal strati-fication has been observed to be beneficial for steeltemperature control, giving a flatter temperature tra-jectory at the tundish exit valve. Possible areas stillopen to research might be the change of thermal prop-erties of lining materials and ladle scheduling. Theformer topic would require integration of basic re-search of lining material chemistry with applied workin the plant. For the latter, it has been known for sometime that optimal ladle scheduling is characterized byregularity and good process flow. Frequently, though,ladle scheduling is overridden by other factors in theplant logistics and temperature control suffers due tobottlenecks, e.g., in crane capacity. Consequently, im-proving process integration improves temperaturecontrol.

Fredman

Theoretical modeling of steelmakingladle systems

OverviewWhen continuous casting processes were introduced,estimation of temperature drop between tapping andpouring (casting) by traditional methods, i.e., on thebasis of long-term foundryman experience, becamemuch more difficult. This motivated research to ident-ify factors behind heat losses from ladles and tundish-es and later to formulate theoretical models of thesesystems for simulation purposes. Several theoreticalinvestigations of steelmaking ladle thermal state havebeen done in the last five decades. Early contributionsinclude simulation of heat losses and refractory tem-perature profiles on an analog computer [26, 27]. Later[28–33], the heat conduction through the refractorywas calculated numerically. Some workers [28, 30, 34–36] used thermocouple measurements from the refrac-tory and molten steel to validate theoretical resultsand ‘‘tune’’ their models to consistency with empiricaldata. Since all mathematical models for thermal con-duction and convection contain a multitude of physi-cal parameters, some of which are temperature de-pendent, model performance strongly depends onchoosing correct values. Tuning model output tomatch thermocouple samples of refractory tempera-ture profile is a multidimensional optimization prob-lem. Frequently, this problem is ill-posed, and aunique solution may not always exist.

Reviewed investigationsPaschkis [26] and Paschkis & Hlinka [27] investigatedtemperature drop of steel in ladles between tappingand pouring with the simulation model ‘‘The Heatand Mass Flow Analyzer’’ implemented on an analogcomputer. Two ladle sizes, of capacities roughlyequivalent to 70 kg and 7300 kg with thicknesses ofthe firebrick lining of 2.5 or 7.5 cm and 15 or 25 cm,respectively, were investigated. In the first study [26],the metal in the ladle was assumed completely stag-nant and only conduction of heat occurred in the bulk.In the second [27], the molten steel was perfectlymixed. It is argued that these two constitute limitingcases for the temperature drop of the steel as the for-mer gives an underestimate and the latter an overesti-mate of the cooling of the steel. For the completelystagnant model case, part of the steel solidifies on thehot face of the ladle, releasing its heat of fusion to therefractory. This would imply that if ladle scullingtakes place, it is favorable to wait longer before cast-ing, a conclusion that would be deemed absurd in anysteel shop. Consequently, the limit model results have

242

to be judged with reservation. It was also found thatproper preheating is essential and that for a ladle tobe well preheated not only the hot face temperaturebut also the temperature profile in the refractory mustreach a high enough level. The thicker the lining, themore can be gained by preheating as the storage ofheat increases. The same argument applies to lid use;higher preheat and a thicker lid enable more energy tobe stored. There is a critical lining thickness, though,beyond which no improvement in thermal economycan be expected. On basis of the temperature drop forboth limiting cases, the prospects of estimating thereal temperature drop are discussed and it is con-cluded that this must be done ‘‘on the floor’’ based onobservations of the, admittedly, vague concept ‘‘de-gree of agitation’’ of the molten steel.

Alberny & Leclercq [37] developed a mathematicalmodel for the temperature evolution of steel in thetundish. Insufficient thermal control at casting causesproblems when the superheat (difference between thetemperature of the molten metal and solidificationtemperature) drops too low, as clogging of the teem-ing nozzles and sculling in the casting mold are thenlikely. Furthermore, at low superheats the shape of theteeming stream becomes incoherent, leading to in-crease in re-oxidation from the atmosphere and qual-ity problems in the final product. Too high a super-heat will cause break-out of liquid steel from the sol-idified shell after the strand has passed through themold in the casting machine. The solidification speedwas found to be proportional to the negative super-heat. Thus, as the superheat increases, the solidifi-cation is retarded, increasing the risk of a break-out.Another negative effect of high superheat is the result-ing inferior structure of the solidified product, withtypical formation of internal cracks and axial porositygiving poor product quality. The events in the tundishbeing highly dependent on previous stages, such asladle initial thermal and physical state, holding time,ladle metallurgy etc., the ladle was included in themodel. The model estimates the variation in steel tem-perature, through energy balance equations, at theexit valves of both the ladle and tundish. Heat lossesthrough the overhead slag and refractory walls werecalculated by a finite difference method. For the slagemissivity a value of 0.8 was used and thermal diffu-sivity of the refractory was approximated as constant.From the appropriate balance equation an averagetemperature of the steel could be obtained, consider-ing a time dependence of the heat flux from the meltto the hot face proportional to the inverse square rootof time.

The same time dependence for the heat flux is ex-


hibited by a semi-infinite solid with prescribed sur-face temperature equal to one and uniform initial tem-perature equal to zero:

T(x,t) Ω2

!pE¬

x/(2!atexp (ªh2) dh , (5)

where the thermal diffusivity, a Ω k/rcp, was intro-duced. The integral in (5) is customarily termed thecomplementary error function at the position indicatedby the lower integration limit. Taking the spatial de-rivative to calculate the heat flux across the hot face,yields

q(x0,t)ΩªFk–T(x,t)–x

Gx Ω x0

Ω1

!p

k

!atexp Sª

x20

4atD .

(6)

Assuming that the entire heat loss of the melt occursthrough conduction to the refractory and convectionfrom the slag surface, described by a constant termQconv, a simple energy balance for the steel has theform

CpdTsteel (t)

dtπ q(x0,t)S0πQconv Ω 0 , (7)

where S0 denotes the area of contact between steeland refractory. Integration leads to the form, (disre-garding the exponential factor in (6))

Tsteel(t) Ω Tsteel(0)ªA!tªBt . (8)

This equation, with empirically determined coef-ficients A, B, has frequently been used in the industryfor statistical modeling of temperature drop of steelin the ladle cycle, and is occasionally referred to as theYngve Sundberg equation.

Alberny & Leclercq [37] introduced the differencebetween the mean steel temperature and that of thepouring stream exiting the ladle in order to describestratification. Consideration of the convection currentsin the ladle in combination with tests gave an estimateof the rate of decrease of the stratification temperaturedifference. A number of simulations were carried outwith the model to set guidelines for good temperaturecontrol. Here, the importance of preheating and sup-pressing stratification was illustrated.

Chone & Teyssier [38] outline a mathematicalmodel for ladle heat loss estimation developed at IR-SID, Maizieres-les-Metz in France. The main objectiveof the model is to aid evaluation of lining design alter-natives and changes to practice, such as adding insu-lation layers to the refractory or the effect of pro-longed holding times between consecutive heats. Thecore of the model is the energy balance equation for

243

the liquid steel in the ladle. The different stages of theladle cycle, such as preheating, waiting prior to tap,tapping, loaded waiting, casting and cooling can allbe described by altering terms and boundary con-ditions in the energy balance. Thermal impact of ladlelid, covering substance and slag can also be simu-lated. The model simulates the temperature profiles inthe lining, lid and slag/surface layer, heat loss fromthe tapping jet, metal/slag surface or through the lin-ing and the metal temperature as functions of time.Mathematically, the model is straightforward, the ge-ometry is one-dimensional and the metal is assumedto be perfectly mixed. Arising differential equationswere solved numerically. Heat losses due to morecomplex phenomena, such as use of lid, coveringagents and argon stirring are simulated by alteringthe waiting time so as to adjust the heat loss. Severalother factors are considered; convection boundarylayers, tapping jet shape, slag and metal surface prop-erties as well as lining, slag and steel initial tempera-tures. To evaluate the model, temperatures at preheat,end of tap and after 7–9 min of waiting were deter-mined for a 7.5 t ladle. Good agreement was obtainedduring waiting and casting, but discrepancies wereobserved for the preheating and tapping stages. Poss-ible reasons were incoherent tapping stream shapeand melt splashing. Model output was also comparedwith measurements from a 60 t and a 240 t ladle. Forthe former, agreement was satisfactory but for the lat-ter the results were somewhat inconsistent. In thiscase, the cause was thought to be melt stratification,inevitable with the ladle capacity and residence timesinvolved. Finally, the authors remark that accurateknowledge of lining thermophysical properties waslacking, especially for the heat conductivity. It wasfound that the best surface heat loss protection wasprovided by a 10 cm thick slag layer (for casting timesshorter than 1 h). Conduction is most significant forcold ladles and the heat flow is inversely proportionalto the square root of time, see eq. (6). Insulation ma-terials in the lining were judged interesting if holdingtimes are long in comparison with empty times and ifthe lining is thin or has high thermal conductivity. Itwas noted that, for good performance, the insulationmust be installed within the dynamic part of thelining.

Omotani et al. [39] adopted a similar function forthe heat conduction to the refractory as in [37], butwith a convection boundary condition at the hot face.A model for steel temperature was formulatedthrough the heat balance equation, which was solvednumerically. Customary idealizations, such as uni-form preheat state, no stratification and instant tap-

Fredman

ping were introduced. The ladle lining was thickenough to keep the thermal field of the outermostlayers at quasi steady state, which was confirmed bycalculations. Heat loss from the slag surface was as-sumed to be directly proportional to the temperaturedifference between slag and metal, when the slagcover was thicker than 12 cm and consisted of carried-over furnace slag. The heat balance can be expressedin terms of the first-order ordinary differential equa-tion

dTsteel(t)dt

πP(t)Tsteel(t) Ω Q(t) , (9)

with general functions of time P(t), Q(t). This equationcan be integrated after multiplication by an integrat-ing factor of the form exp (etP(s)ds), yielding

Tsteel(t) ΩetQ(h) exp (ehP (s) ds) dh

exp (etP (s) ds). (10)

A number of examples were worked out with the heatbalance model. Typically, in a billet or slab continuouscasting operation, 55–60% of the total heat lost isstored in the ladle wall refractory, 15–20% in the ladlebottom and 25–30% is lost through the slag. Smallerladles are generally more sensitive to changes in taptemperature, preheating practice and type of refrac-tory brick. It was demonstrated how the loss throughthe slag layer increases slightly before commencing toa very slow decline. Increasing tap temperature wasshown to be advantageous in emergencies with riskof excessive sculling or nozzle clogging, but not as aroutine temperature control measure.

Pfeifer et al. [31] developed a thermal model for theoverhead (above the melt surface) part of the ladle.In particular, the effects of changes to slag thickness,stirring practice, ladle opening and lid geometry wereinvestigated. The mathematical model includes par-tial solidification of the slag, transient heat conductionthrough the wall and lid as well as different practicesof gas stirring and two alternative designs of the ladleupper section. Simulations for different ladle sizesand geometries were carried out in order to comparetheir energy economy. The temperature dependenceof the thermophysical properties was considered forthe wall but not for the lid and slag. The boundaryconditions on the (isothermal and grey) hot surfacesare functions of the radiation from the slag surface.After calculation of the view factors for the surfacesand surface temperatures using the heat conductionmodel with known surface heat flux, the surface heatflux was updated using the radiation model by solv-ing a system of linear equations. The conduction

244

Fig. 7. Steel temperature drop as a function of time for different ladleopening configurations. Adapted from data in [31].

equations were solved numerically by the Euler dif-ference scheme. Two ladle designs with no stirringand different slag thickness were compared, one hadthe conventional cylindrical shape and the other hada conical upper section, making the ladle narrower atthe lid than in the middle. The design alternatives didnot differ much in performance whereas a thicker slaglayer could reduce temperature drop by more than10æC for an 80 t ladle. On the other hand, when stir-ring with argon or nitrogen, use of a lid may be im-possible, making the difference in thermal perform-ance more significant. It was found that the largestreduction of temperature drop is obtained with coni-cal ladle head in combination with a lid, when poss-ible. The steel temperature drop as a function of timefor the conventional and conical ladle heads are de-picted in Fig. 7, from which a final difference of over10æC in favor of the conical form can be observed. Incomparison with a conventional ladle, the conical con-cept reduced heat loss from the steel by 16%. Espe-cially with prolonged gas stirring and ladles ofsmaller capacity, the conical ladle head was foundbeneficial for thermal control.

In [32] Pfeifer et al. combined the model in [31]with thermal models for the tapping stream, alloyingadditions and transient conduction through the side-wall and bottom of the ladle in order to estimate cast-ing stream temperature. The thermal model of thetapping stream consists of an energy balance equationfor an infinitesimal length element of the stream, to-gether with simple expressions for the average massflow and velocity of the steel exiting the ladle. Irregu-


larity in the stream shape (deviation from circularcross section) was considered through a correctionfactor. When the ladle was filled, calculations weredone using the model in [31] as well as numericallysolved equations for transient heat conduction belowthe slag surface. Alloying was considered by a simpleempirical expression. The thermal properties of thelining materials were functions of temperature in theexplicit finite difference equations. The heat balancewas solved for the steel temperature by Euler’smethod at tapping, holding and casting, consideringrelevant loss terms for each stage. When the ladle wasempty, the thermal status was obtained using a pro-cedure similar to that of [31]. Performance of themodel was tested for a 100 t ladle during a measure-ment campaign. In order to minimize temperaturedrop, a low tapping height and short duration wereimportant as well as maintaining circular cross sectionof the stream. A typical temperature drop in favorableconditions was around 5æC. Model temperature pro-files in the lining agreed reasonably with measure-ments. Steel temperature measurements immediatelyafter tapping agreed with an average deviation of 7æCwith model output over a campaign of 20 heats. Abetter indicator of model accuracy is the overall tem-perature drop for a heat compared with measure-ments. The measurements averaged over 38 heatsgave a value of 70æC as model predictions spread be-tween 20æC and 100æC, the larger deviations corre-sponding to heats with greater amounts of alloyingadditions. Finally, the authors outline a tuning pro-cedure for the model on basis of measurements beforeand after vacuum treatment subsequent to tapping.Model steel temperature is here corrected by takingover the measurement value. The average deviationof model predictions from measurements at this stagewas 5.9æC.

In [40] Pfeifer et al. report a model for preheating.The work supports their previous work in [31, 32].The mathematical model consists of an energy balancebetween net energy per time released from combus-tion and energy flow to the lining sidewall, bottom,the ladle lid and losses. The combustion gases wereassumed to be well mixed and uniform in tempera-ture, all surfaces inside the ladle were isothermal andcombustion was complete, i.e., no combustible com-pounds remained in the exhaust gases. The balancewas solved numerically for the combustion gas tem-perature after having obtained the gas volume flowfrom combustion chemistry calculations. Possible re-cuperation (preheating of the input air to the burner)was also considered. Heat exchange between the com-bustion gases and inner surfaces of the ladle was de-

245

scribed by radiation and convection heat transfer.Model calculations were done to compare perform-ance of different fuels, such as blast furnace exhaustgas, coke oven gas and natural gas. The influence ofcombustion parameters like temperature and oxygencontent of combustion air and preheating time wasalso investigated. For instance, high fuel supply andshort preheating time resulted in larger temperaturegradients in the lining as compared to preheatingusing lower fuel supply and longer times. For a con-stant input of fuel, the steel temperature drop as afunction of preheating time exhibited a minimum.This was because losses from ladle and lid shells in-crease with time when the overall temperature levelof the lining goes up. Combustion with excess of airgave rise to a larger steel temperature drop than stoi-chiometric air supply, while combustion with pureoxygen gave the lowest temperature drop. Using a re-cuperator could also be recommended. To validate thecomplete model, consisting of the preheating modelcoupled with heat conduction through the lining,simulations were compared with thermocouple meas-urements from a ladle during drying of a fresh liningassembly. Three thermocouples were mounted in thebottom of the ladle, one in the safety and two in theworking lining. For the measurement point in theworking lining, the model estimates were consistentwith the results, but for the others an offset was ob-served. The simulated temperatures during dryingwere consistently lower than the measured, whichmight be due to a systematic measurement error, mis-judgement of thermocouple positions or incorrectvalues of thermal properties in the model.

Morrow & Russell [30] describe a thermal modelfor ladle refractories and steel temperature. The basisof the model is a finite difference solution of the one-dimensional heat conduction equation at the bottom,sidewall intermediate level and slag line of the refrac-tory. Variation of thermal conductivity and specificheat with temperature was considered in the calcu-lations by fitting curves to data on these propertiesand using the obtained equations in the finite differ-ence procedure. To verify the model, a degassing ladlewas fitted with thermocouples in the refractory andtemperatures were monitored during preheat andduring the second and third heats on the lining. Thethermocouples were mounted 64 mm from the hotface into the working lining and at each material in-terface for three height positions. For the steel tem-perature, considered uniform throughout the melt, themodel vs. measurement exhibited good agreementand the largest discrepancy occurred at end of teem-ing when the mass of steel in the ladle was small. The

Fredman

lining temperatures, on the other hand, showed onlypartial agreement. At the bottom the consistency wasfairly good during preheat, but deteriorated for aperiod at start of the second heat. At the slag line,consistency during the first heat was poor but im-proved on the third heat, whereas in the sidewall thesituation resembled that of the bottom. A possibleerror source in the measurement procedure could beheat transfer resistances at the material interfaces aris-ing from imperfect contact, such as gaps, mortar resi-due etc. Morrow & Russell [30] used their model toinvestigate whether insulation layers of different con-figurations could bring down shell temperatures of aningot teeming ladle (lined with 70% alumina brickand a direct-bonded basic slag line) and compared theresults with those of a similar evaluation using asteady state model. The steady state calculationsyielded higher temperatures throughout and particu-larly the slag line area was much cooler in the calcu-lations with the dynamic model. Thus, when studyingdifferent design alternatives for reducing safety liningand shell temperatures, conclusions drawn fromsteady state calculations remain valid if the dynamicsis considered. An exception is that steady state calcu-lation indicates an advantage of placing the insulationbetween the shell and safety linings over placementbetween working and safety linings, due to lower heatloss. This advantage is enhanced if a higher qualitysafety lining material is used, permitting operationover multiple campaigns on the working lining. Thedynamic model showed that the insulating layer wasmore effective in reducing steel heat loss when placedbetween the working and safety linings, which is inagreement with [38]. However, costly replacement ofthe insulation is then necessary whenever the work-ing lining is renewed. As further applications of themodel, studies were done of the effects on steel tem-perature of lining material and wear, preheat time anduse of refractory lid versus insulating slag cover. Thegreatest impact of preheating was observed duringthe first hour. In a continuous casting operation, useof insulating slag cover was found to decrease steelheat loss especially during initial heats. However,when the ladle was cycled, a refractory lid was moreadvantageous.

Hlinka et al. [29] report a thermal model for ladlelinings and steel temperature drop, developed atBethlehem Steel. A previously developed computercode for solution of the dynamic heat conductionequation for a one-dimensional geometry was takenas starting point. The ladle geometry is reduced to onedimension by replacement with a slab, by consideringthe ratio of the mass of steel to the contacting surface

246

area on the bottom and sidewall. The slab concept in-volves multiple layers, consisting of all refractory ma-terial layers, the ladle shell and the liquid steel. Onteeming, the ladle is drained layer by layer from thebottom. This is modeled by reducing the thermaldiffusivity of the slab according to a scheme de-veloped from experiments. If desired, stratification inthe liquid steel can be considered for by altering theconductivity of the corresponding ‘‘liquid steel layer’’of the slab. Material properties were chosen accordingto the various events in the ladle cycle. For instance,tapping was simulated by introducing real coefficientvalues in place of the infinite thermal conductivityand zero specific heat used for the empty ladle. Onsurfaces exposed to the ambient, the heat transfer co-efficient included both radiation and convection, theemissivity was 0.8 throughout and a view factor ofunity was used for the ladle shell and cover/slag sur-face. Integration of elemental view factors for the in-side of the empty ladle yielded the average 0.5. Ineach heat, the model is updated with the liquidus andsolidus temperatures, from which sculling is esti-mated. For the slag, the heat conductivity was ma-nipulated in order to simulate heat transport acrossthe slag layer. No heat of solidification is liberated tothe system on freezing of the upper slag layer. Refrac-tory lining materials are handled using their commer-cial trade names and relevant temperature dependentproperties are imported from a data base incorporatedinto the model. The same applies to ladle geometry,referenced through plant names. Cover use can alsobe modeled and the initial temperature profile of thecover can be saved for future use. A number of eventsin the ladle cycle can be simulated after initializationof the temperature field, including preheat/recon-ditioning, tapping with possible additions (consideredthrough their entalphies), stirring, teeming and slagremoval. Stirring is considered by increasing the in-ternodal thermal diffusivity within the steel as a func-tion of stirring time and intensity. The model wasused to investigate when quasi steady state is reachedafter introduction of a cold ladle into the cycle andwhat preheat level this state corresponds to. The out-come was that three cycles were sufficient to establishsteady conditions in most of the lining and that thesame state would be reached with 6 h of preheat witha 980æC gas flame. In addition, the benefits of slag ver-sus ladle cover use were studied and company policywas changed to use of both ladle covers and surfaceinsulation to improve temperature control.

Tomazin et al. [25] investigated alternative ladle re-fractories and cycle practice. In two plants of LTVSteel in Aliquippa, PA and East Chicago, IN, ingot


casting processes were revamped to continuous cast-ing. As a result, the conventional firebrick ladlelinings could not withstand the higher temperatures,more aggressive slags, ladle metallurgy and pro-longed holding times. Steel cleanliness and desul-phurization also suffered when firebrick was in use.Thus, it was decided to phase out the firebrick liningsin favor of 70% Al2O3 linings with MgO slag lines forboth plants. Considering the higher thermal conduc-tivity and specific heat as compared with firebrick, itwas necessary to study the thermal behavior of theladle and its impact on temperature control. Pre-heating facilities were installed at both works. Oneladle at Aliquippa was monitored during preheatingand cycle with 30 thermocouples, yielding data for thedevelopment of a preheating practice and tuning of amathematical model. The mathematical model was anumerical solution of the heat conduction through theladle wall based on an explicit finite difference pro-cedure with temperature dependent refractory ther-mal properties. Steel temperature was assumed uni-form throughout the melt and axial heat transfer inthe refractory was disregarded. Radial temperatureprofiles were calculated at a number of heights in thewall in order to consider the steel surface position ateach point of the ladle cycle. The bottom and slaglayer temperature variations were assumed to bepurely axial. Above the steel surface, view factors forall surfaces were calculated for the radiative heattransfer. The model was also used to evaluate meas-urement variables for observation of the heat content.Apart from hot and cold face temperatures, the wait-ing time between heats was important for determin-ing required corrections at tapping. Covers werejudged most important during casting and emptywaiting time, when the radiative heat loss is most sig-nificant. In some simulations worn ladles, when mod-erately preheated from cold, actually reduced heatloss due to smaller heat storage. However, a wornladle in cycle (at thermal quasi steady state) hadlarger heat loss than a freshly lined one.

Hoppmann et al. [41] present a process model forcalculation of the converter tapping temperaturewhen considering estimated heat losses in the ladleand tundish as well as initial thermal state of the ves-sels and thermal efficiency of the previous heat.Model input can be divided into two categories; theprecharge and the postcharge data. As precharge vari-ables were considered the waiting and preheat timesbefore tapping, lid use, sculling extent and durationof the previous heat as well as the age of the lining(from which the remaining thickness was estimated).Postcharge input consisted of the planned stirring

247

time and alloy weight, planned transfer and waitingtimes and the casting time. In the output are indicatedthe estimated temperatures at tapping and start ofcasting, starting and ending times for tapping andcasting and the predicted stirring time. In addition,the temperature profile across the lining and tempera-ture drop in the ladle can be obtained at any time.The heat loss calculations were based on experimentaldata together with energy and mass balance compu-tations. The temperature trajectory during casting wasestimated on the basis of initial cooling rate, durationof cast, tundish preheat and number of heats cast. Theslag thickness in the ladle was estimated from data onthe oxidation and mean transferred weight of con-verter slag, heat loss through the slag was dependenton thickness only. After charging the converter, thetapping temperature was calculated iteratively withthe desired superheat at end of casting as an end cri-terion. Finally, a comparison between the estimatedtapping temperature and real process data was done,showing an average difference of 5æC with a standarddeviation of 8.3æC.

In [35], Hoppmann et al. describe an on-line pro-cess model for the steel temperature during secondarymetallurgy integrated with estimation of the castingtemperature. The system consists of mass and energybalance equations for the ladle, ladle furnace and vac-uum degassing process. A numerical solution of theheat conduction equation is incorporated into themodel. The state of the slag and heat loss due to al-loying were considered using cooling coefficients anddeoxidation factors. At casting, the net heat flux outof the homogeneous molten steel was expressed in theform

q(t) Ω oi

ai exp (bit), (11)

where the ai, bi were determined by fitting the heatflux (11) to numerically calculated values from the on-line model. Eq. (11) was also used for extrapolation,i.e., heat fluxes were calculated for times outside thetime range of the coefficients ai, bi. Expressing the netheat flux as above leads to an energy balance equationfor the molten steel in the form

dTsteel

dtΩ o

i

ci exp (bit) , (12)

which can be readily integrated to yield an expressionfor the average temperature of the molten steel in theladle during casting

Fredman

Tsteel (t) Ω Tsteel (0)πoi

ci

bi[exp (bit)ª1] . (13)

In addition to estimation of the casting temperature,the model was used for optimization of ladle furnaceoperation. Tuning the on-line model was done off-lineand the outputs were compared with actual processmeasurements. At casting, an accuracy of 4.7æC couldbe achieved, an excellent result in view of the meas-urement accuracy of approximately 5æC.

Chapellier [42] describes temperature control at theSollac plant of Florange, France. The converter tap-ping temperature is calculated on basis of chargingparameters, aim temperature for oxygen blowing, slagoxidation level etc. Because the plant has a ladle fur-nace facility, tapping temperature management is sep-arated from temperature control in the ladle and atcasting. The tapping temperature is kept as low aspossible for a given steelgrade and ladle furnace oper-ation is determined by the desired casting tempera-ture trajectory. The casting operator gives the pro-jected casting start time as input to a computer pro-gram which calculates a series of aim temperaturesfor different points in time for the ladle furnace. Thecode uses simple empirical linear expressions depend-ent on liquidus temperature, maximum superheat inthe ladle, foreseen casting duration and time elapsedbetween the last temperature measurement in the fur-nace and start of casting. Cooling of the steel duringholding is estimated using a constant cooling rate de-pendent on ladle treatment time and length of the pre-vious empty period. Raising the heat by 1æC is equiva-lent to an energy input of approximately 100 kWh.The practice used is designed to give a tundish super-heat of 26æC for a fresh ladle and 23æC for a cycledone. At a production rate of 32 heats a day, 6 ladleswere in cycle. It was estimated that holding acoverless ladle for one hour costs 0.6 kWh/ton of steelmore than for a covered one and that insulationlinings save 2.0 kWh/ton. Ideal ladle cycle lengths inthe plant were 2.3–3.0 h and the actual lengths 3.7–5.0h. Temperature control in the plant is reported to beaccurate to within the measurement accuracy, typic-ally smaller than 4æC.

Koo et al. [43] investigated stratification in the steelduring holding and the impact of Ar gas bubbling.The heat loss from the steel to the lining was esti-mated by numerical solution of the heat conductionequation under the assumptions of perfect mixing anduniform temperature of the molten steel. Stratificationwas modeled by setting up the necessary equations ofchange; the continuity equation and the equations ofmotion and energy, all with the radius r and the

248

height z (from the bottom) as independent variables.Hence, all equations were axisymmetric. Turbulencewas considered with a k–e model featuring equationsof turbulent kinetic energy and dissipation rate of tur-bulent energy. In the equation of motion, buoyancydue to temperature gradients as well as Ar injectionwere included. The boundary conditions were zeroheat flux at the steel-slag boundary, no slip and transi-ent heat conduction (from the mentioned numericalsolution) at the hot face. The solution of this systemwas carried out using the PHOENICS program pack-age for computational fluid dynamics. For verificationof the heat conduction model, thermocouples werefitted into the lining of a trial ladle. The measure-ments, however, appear to be lagged with respect tothe simulations, suggesting that the time constant ofthe thermocouples has been disregarded. Simulationswere done to evaluate effects of holding duration, re-fractory wear and stratification during holding as wellas restratification after gas stirring. Each heat wascompared with a standard case, with respect to steelresidence time and waiting time. Corrections to thestandard case were handled by temperature compen-sating factors, introduced before tapping or duringladle metallurgy. The most interesting results, how-ever, were the stratification simulations, where a tem-perature difference between top and bottom of theladle amounting to 24æC was obtained for a holdingtime of 20 min. Bubbling the melt with Ar reducedthe maximal temperature difference to 3æC, indicatingthe advantages of mixing prior to casting. In Fig. 8,the temperature and velocity fields as well as the dis-tributions of kinetic energy are shown for a stratifiedmelt and an Ar-bubbled one. Supporting the work bya heat balance for the steel would have given a niceillustration of temperature trajectory in the tundishand impact of gas bubbling on it.

Gaston et al. [44] present a model for predictingsteel temperature and thermal state of the tundishduring continuous casting. The theory and methodsare applicable also to the ladle, which is a similar sys-tem. The model consists of the usual heat balanceequations for the steel in the tundish while it is beingfilled and while casting is in progress, including heatlosses due to radiation and conduction heat transfer.Steel level variation in the tundish was assumed to belinear with time during the filling stage. Heat lossesto the walls were calculated under the idealizationthat the wall be a semi-infinite solid. Solution of thecoupled steel heat balance and heat conduction modelwas carried out numerically. In order to test the sensi-tivity of the model to stratification, simulations werecompared with available experimental data, confirm-


Fig. 8. Results of Koo et al. [43] on the influence ofmixing with Ar gas on stratification in the ladle.Courtesy of the Iron & Steel Society.

ing the model results. Furthermore, to describe thetemperature of steel entering the tundish, a heat bal-ance for the steel in the ladle was formulated. In thiscase, thermal state of the ladle refractory was re-garded stationary and the radiative heat losses wereignored assuming that the top surface of the moltensteel was insulated. Experimental results from the

Fig. 9. Estimated steel temperature trajectories and measurements ofGaston et al. [44]. Courtesy of the Institute of Materials.

249

plant General Savio, Aceria LD-SOMISA in Rosario,Argentina were used for model validation. The steeltemperature was measured in the ladle before castingand in the tundish with an interval of 10 min duringcasting of two consecutive heats. The tundish wascold before the first heat. Agreement between simula-tions and measurements in the tundish was within10æC, with overestimation in the beginning andunderestimation at the end of casting, cf. Fig. 9. Ther-mal stratification in the ladle was not considered: Ifthis had been done, the model would have producedlower temperature estimates in the beginning, whenthe colder bottom layers of steel are teemed from theladle.

Shklyar et al. [45] present a thermal model conceptfor a steelmaking ladle. Dynamic heat conductionthrough the ladle lining, heat transfer above the slagsurface (or in an empty ladle) and heat transferthrough the slag layer are considered in the model.Other features include temperature dependent ther-mal properties, variation in the steel level, thermal ef-fects of metallurgical additives, lid use and efficiency,refractory wear and preheating. The ladle cycle is di-vided into stages: tapping, ladle metallurgy, teeming,empty waiting time and ladle preheating. The liningis divided into regions of constant surface tempera-ture, where radial (sidewall) or axial (bottom) tem-

Fredman

perature profiles are computed. Moreover, perfectthermal contact is assumed at the boundaries betweenthe lining layers and at the hot face. For the slag layer,a conduction-convection equation with a constantheat transfer coefficient is included. At the slag line,the difference between average slag temperature andthe hot face temperature is used as driving force forheat transfer. Preheating is also modeled, fuel energycontent and input as well as moisture ratio of the lin-ing, combustion parameters and exhaust temperatureare considered in the heat balance. A few examplesimulations are presented in the form of graphs de-picting calculated hot face temperature as a functionof time for situations with lid use/no lid and gap be-tween lid and ladle/absence of gap. In addition, thecalculated and set point fuel flowrate together withcalculated and set point hot face lining temperatureare given for simulated preheating of a 370 t ladlelined with magnesia-spinel clay. No experimentaldata, in support of the model, is presented.

Mucciardi & Grandillo [46] used a general-purposesoftware application called FASTP (Facility for theAnalysis of Systems in Transport Phenomena) forthermal analysis of a steelmaking ladle in cycle. Thissoftware package has been developed at the MetalsProcessing Centre of McGill University for simulationof dynamic heat and mass transfer processes. Thecode is based on an explicit finite difference method.Simulation was carried out for two alternative refrac-tory configurations, one of which had a layer of insu-lating tiles between the ladle shell and safety lining.In order to consider the cooling of the upper hot faceduring casting, the ladle was sectioned into 5 seg-ments each with a capacity of 16 t, each requiring 20min to empty. Hence, the uppermost segment had anaverage contact time with the steel of 50 min and thelowermost segment 130 min. As might be expected,the temperature profile in the lining was clearlyhigher for the insulated lining, where the boundarybetween the safety and insulating linings reached aquasi steady state temperature of almost 800æC. Whenthe energy content of the lining was examined at dif-ferent stages of the ladle cycle, significant drops wereobserved during preparation and waiting. Equivalenttemperature drops for the steel arising from liningstorage and losses to the surroundings were calcu-lated for the 2 lining types. The conclusion was thatthe insulation had impact on only the losses to thesurroundings and none on the storage of heat in therefractory.

Saha et al. [33] developed a mathematical model forscheduling preheating of fresh dolomite refractorylinings. The authors recommend basic refractories,

250

such as dolomite, magnesite and chrome-magnesiteover conventional fire clay/high grog–high alumina re-fractories. Ladle linings in modern steelmaking mustwithstand high tapping temperatures, aggressive slagsand injectants, extensive stirring by gas injection, ther-mal cycling, vacuum conditions and prolonged hold-ing times. Basic bricks, having better thermodynamicstability than aluminosilicate materials, are thus moresuitable for ladle linings. However, basic bricks requiredifferent handling and preheating. Being hygroscopic,these have to be handled dry throughout and the safetylining must be heated to remove all moisture before theworking lining is assembled. Prolonged preheating isnot advisable, since this will cause bond degradation inthe working lining. Hence, the hot face temperaturemust be increased to 950–1100æC during the first 2 h ofpreheating and kept at this level for no longer than 12h. Shell temperature should be kept below 250æC ascompared to 350æC for high alumina refractories. Tomeet these specifications, a dynamic heat flow modelwas formulated and solved using finite differences.The temperature evolution of the ladle lining can besimulated for various fuels, fuel rates and refractoryconfigurations. A number of simplifications weremade, first of all the geometry was reduced to one di-mension and the tar dolo ramming mass used to bondthe dolomite bricks and the safety lining was con-sidered an integral part of the dolomite brick lining. Inaddition, specific heat and thermal conductivity wereregarded as constant within each lining layer. At thehot face, the radiation emissivity was taken dependentof both combustion gas composition and the tempera-ture of the gas. A scheme for computing the radiationheat flux as a function of temperature is outlined. Fi-nally, a number of example simulations were studiedwith the purpose of investigating suitable fuels andfuel rates for a specified preheating task both for freshand circulated ladles. The advantage of preheating thecombustion air was also noted here. In a comparison ofmeasured lining temperatures with simulated ones,agreement was satisfactory.

Austin et al. [28] outline a thermal model for steel-making ladles developed at the BHP steelworks inAustralia. The model was used in an extensive para-metric study of the various stages in the ladle cycle.Mathematically, the model is based on a numericalsolution of the transient two-dimensional heat con-duction equation. An energy balance for the moltensteel was included in order to simulate the tempera-ture drop. Stage data, ladle geometry, refractory prop-erties and results can all be accessed through a userinterface. Refractory configurations can be easily ma-nipulated and temperature dependence of the thermal


Fig. 10. Temperature profiles in the ladle lining for different preheatingand empty times. By Austin et al. [28]. Courtesy of the Iron & SteelSociety.

properties can be considered. The arising non-linearsystem of equations is solved using the alternating di-rection implicit method with adaptive time stepping.A few examples featuring temperature profiles in thelining are presented. Tuning of the model was doneby adjusting convection coefficients, emissivities etc.in stages by comparing simulations with measure-ments. The procedure is illustrated by results for thepreheat and first four cycles of a 275 t test ladle moni-tored with thermocouples in the lining. With the tun-ed model, thermal effects of preheating, slag thick-ness, holding time, lid use, empty time, refractorytype and wear were investigated.

In the parametric study, a well-cycled ladle (definedarbitrarily as the state occurring after 10 heats) waskept as reference. During preheating, the ratio of mo-mentary to final heat content was considered a func-tion of time only and quasi steady state for a freshlylined ladle was established after four to six heats, de-pending on preheating time. The most important fac-tor for steel chilling during the ladle cycle was work-ing lining heat content, influenced mainly by thelength of waiting time between consecutive heats.Long empty periods were compensated by pre-heating, however, for short periods preheating turnedout to be counterproductive. Consider an empty timeof 30 min, after which the hot face temperature hasfallen significantly but the temperature profile in theworking lining still is high. Applying preheat willnow only serve to increase the hot face temperatureto the flame temperature, after which the temperaturegradient between the flame and lining becomes small,resulting in low heat flux. Since the heat content ofthe working and safety linings then remains virtually

251

unaffected, heat is lost to the surroundings throughthe steel shell. This was confirmed by the model cal-culation results for different preheating times after anidle period, illustrated in Fig. 10. Overhead heat lossfrom the molten steel was found to be mainly due toradiation with no slag layer and conduction throughthe slag when one was present. Conduction losseswere one order of magnitude smaller than radiativelosses. Increasing slag layer thickness did not reducethe heat loss significantly, neither did lid use duringperiods with the ladle filled, if a slag layer was pres-ent. Lid use was found significant mainly when thehot face was exposed, like during casting and emptyperiods. When the ladle was filled, much larger im-pact on steel heat loss was observed for the lining heatcontent in comparison with lid use. In the BHP plant,high alumina linings were used predominantly. Tocompare this lining configuration with zirconia brickrefractories, the transient steel temperature was simu-lated for a well-cycled ladle in both cases. As ex-pected, the simulations predicted larger heat loss forhigh alumina than for zirconia although the initialchill during tapping was slightly larger for zirconiathan for high alumina. Finally, the effect of liningwear on heat loss was studied with the model. It wasfound that a ladle which is only slightly worn deliversmetal at almost the same temperature as a new ladle,whereas for a heavily worn one the delivery tempera-ture is substantially lower, suggesting nonlinearity inthe impact of wear on heat loss.

Gaston et al. [47] estimated the temperature drop ofmolten steel during tapping into the ladle. The workis a part of a larger thermal model for the ladle cycle,implemented as a computer code package. Heat lossesboth due to exposure of the tapping stream to the am-bient air and due to radiation from the steel head inthe ladle and to conduction into the ladle working lin-ing were studied. In order to model the heat loss fromthe tapping stream, stationary mass and momentumbalance equations were set up together with the dif-ferential energy balance for an infinitesimal heightelement of the stream. Combination of these and inte-gration of the energy balance yielded an estimate ofthe temperature drop of the metal stream for a givenstream height. In agreement with experiments, the ex-ample calculation using realistic plant data shows atemperature drop of about 0.5æC for a constant tap-ping height of 2 m. For the steel in the ladle, the heatbalance equation for a linearly time dependent steellevel is integrated after substitution of loss terms aris-ing from conduction to the refractory working liningand radiation from the steel surface. Radiation heatloss is assumed constant and a function of the steel

Fredman

tapping and ambient air temperatures. Losses due toconduction are approximated inversely proportionalto the square root of time. The approximations for theheat losses are valid for short tapping/filling timesand small overall temperature drops for the steel. Thetemperature drop of the steel exhibits the same formof time dependence as the Yngve Sundberg equation(8) with the prefactor of the linear term describingradiation from the melt surface of constant area andthe prefactor of the square root term describing con-duction to the working lining. Finally, an example cal-culation for a 2 min tapping is carried out for twodifferent ladle preheat levels (800æC and 1200æC).After an elapsed time of 6 min the total temperaturedrops of the molten steel in the ladle are 33æC and25æC, respectively. An advantage of the outlined ap-

Fig. 11. Ladle thermal tracking model display of Zoryk & Reid [48].Courtesy of the Iron & Steel Society.

Fig. 12. Display for the steel temperature flight path model of Zoryk &Reid [48]. Courtesy of the Iron & Steel Society.

252

proach is that it is not necessary to know the tempera-ture profile in the ladle refractory.

Zoryk & Reid [48] describe an integrated systemfor on-line estimation of liquid steel temperature inthe ladle and tundish, developed at the ScunthorpeWorks of British Steel plc. The system consists of twoseparate models, one for uninterrupted calculation ofrefractory lining temperatures for all operationalladles and one for calculation and visualization ofliquid steel temperature in the ladle and tundish (thetemperature ‘‘flight path’’). The former is called TheLadle Thermal Tracking Model and the latter The FlightPath Model. An example display of the Ladle ThermalTracking Model is depicted in Fig. 11 and an exampleof the Flight Path Model display in Fig. 12. Bothmodels are based on finite difference methods to solvethe one-dimensional heat conduction equation andliquid steel energy balance, respectively. Temperatureprofiles in the lining are computed at two positions,at the center of the ladle bottom and halfway up theladle wall. Boundary conditions for the lining tem-perature profile model during periods of cooling, dry-ing, preheating and casting were studied by thermo-couple monitoring of 3 different depths within the lin-ing at the bottom and in the sidewall. The perform-ance of the simulations with regard to matching meas-ured thermocouple temperatures is demonstrated,showing an average difference between measuredand calculated temperatures of approximately 25æC.In the calculation of the steel temperature trajectory,the heat balance includes conduction to refractories,convection and radiation from lining and slag surface,tapping and teeming losses as well as chilling due toalloying. When using the ladle arc furnace, the modelis fed with data on power inputs, heating times andinduction stirring.

The ladle thermal tracking model calculates thethermal states of all ladles in use, considering the cur-rent status of the ladle, i.e., cooling, preheating, dry-ing or in cycle. For the two profile positions, refrac-tory types and thicknesses are kept in a data base andrefractory wear is modeled with an average wear rateobtained from the current campaign lining life andinspections. Model output is available in a variety ofways, as history of ladle use in the plant, as tempera-ture profiles for a specific ladle and as a table rankingthe operational ladles with respect to thermal state.Additional features are prediction of thermal state fora number of ladles based on planned process routes,access to data bases containing ladle fleet parametersand initialization of thermal state.

The ‘‘flight path’’ calculations start right after tap-ping, an initial steel temperature trajectory prediction


is obtained on basis of the ladle thermal state, finalBOF temperature measurement, planned processroute and parameters (including casting speed evalu-ated from the section size to be cast and recommenda-tions for the particular steel grade). Subsequently, asdata from actual events, e.g., argon stirring, degas-sing, reheating, alloying or even unexpected delaysbecome available to the flight path model, updates ofthe predicted process routes are made and the steeltemperature flight path for the remainder of the castis revised. From this, the plant operators can takenecessary corrective action to ensure that the aim tem-perature for the steel at start of casting is met. Thesecorrections can amount to ladle arc furnace reheating,additional/reduced argon stirring, scrap cooling or al-tering the process route. When casting is in progress,ladle and tundish dip temperature measurement iscarried out routinely enabling revision of steel tem-perature flight path.

The performance of the on-line system was review-ed on basis of ability to predict measured ladle andtundish dip temperatures. The standard measurementerror for the ladle dip was ∫5æC and on average 86%of all ladle dip temperatures were calculated to withinmeasurement error bounds by the flight path model.For some reason the error for tundish dips was larger(∫7æC) and for the slab caster 92% of the dip tempera-tures were estimated by the model to within errorbounds. The bloom and billet casting routes of theplant showed almost 25% lower figures, due to theirsignificantly longer residence times for the steel in thetundish, resulting in stratification.

Sistilli & Erny [49] describe a ladle tracking systemimplemented at the Steubenville, OH plant of Wheel-ing-Pittsburgh Steel Corp. After conversion to con-tinuous casting in 1991, a need for improvement inladle status tracking became evident. More stringentquality requirements and the dramatic increase in theamount of secondary refinement performed in ladlesthreatened to substantially increase the number of re-jected heats and ladle refractory failures (‘‘burn-throughs’’). For each ladle, a database was created,containing variables critical for refractory perform-ance, such as event times, stirring and reheating data.When a heat is tapped, a new record is added to thedata base and the furnace crew enters the ladle num-ber along with alloy and desulphurization materialadditions. The rest of the data are automaticallyadded to the database, and it is possible to view thestatistics of any ladle in the fleet. An analysis of theinfluence of key operating variables on refractory per-formance was carried out. One particular lining speci-fication was evaluated over a campaign of 63 ladle

253

cycles. The most important variables were identifiedto be average steel contact time, number of reheats,number of desulphurizations and average stirringtime, the last two exhibiting the strongest negative ef-fect on ladle lining life. Finally, a heuristic method ofpredicting ladle life is outlined, where the results ofthe study are used to relate the current mode of oper-ation (values of the ‘‘key variables’’) to an average ex-pected ladle life for the entire plant. Over a referencetime of three months, the ladle life forecasting accu-racy was 80% ∫3 heats.

Olika & Bjorkman [36] used temperature measure-ments from the ladle wall and molten steel to evaluatea commercial computer program package, TempSim,for simulation of ladle thermal state and steel heatloss. The main component of TempSim is an energybalance for the molten steel. The program features cal-culation of lining temperatures during ladle mainten-ance and preheating as well as heat loss and steel tem-perature during alloying, heating and vacuum treat-ment. Temperature drop during tapping and deoxi-dation, effects of melting and solidification of slag andvariations in steel level in the ladle can also be studiedusing TempSim. The ladle lining is divided into foursections for which the material, thickness and heightare specified. One section consists of the ladle bottom,while the remaining regions make up the sidewall.Each section can be divided into a maximum of tensubsections. The tapping stage can be divided intothree temporal subintervals, where 1/4, 1/2 and 1/4of the molten steel leaves the converter, respectively.A simple linear regression model, with separate coef-ficients for different temperature intervals, is used forestimation of the temperature drop between in-con-verter temperature measurement and end of tapping.

A measurement campaign was implemented atSSAB Tunnplåt AB of Luleå, Sweden in order to moni-tor lining temperature profile, hot face, steel and slagtemperatures. Slag thickness and chemical compo-sition were also investigated. 2 thermocouples wereplaced at the bottom and 12 in the sidewall of a ladle.Hot face temperatures were measured, using a py-rometer, at the end of casting just after slag-off, before

Table 2. Boundary conditions for the ladle thermal model in [34]

Parameter Ladle cooling Ladle preheating

wall bottom wall and bottom

convection coefficient, 12.6 8.4 12.0[h]ΩW/(m2K)

view factor, ( ) 0.12 0.06 0.0gas temperature (æC) 1900

Fredman

and after ladle cleaning and about 2–3 min prior totapping. Steel temperature in the ladle was measuredevery 5 min throughout ladle metallurgy and immedi-ately before casting. With TempSim, steel temperatureon arrival to the caster could be estimated with a stan-dard deviation from measurements of 3æC. The simu-lations underestimated temperature drop during ladlemetallurgy and overestimated it during transfer tocasting. This was explained by overestimation of ini-tial thermal state and poor understanding of the radi-ative heat transfer. Other reasons were insufficientknowledge of parameters, such as slag weight fromthe converter, waiting time in the converter, tappingtime, extent of stratification and lining wear. Disagree-ment of measurements with simulated lining tem-perature profiles was thought due to sculling and theresulting reduction in emissivity.

Barber et al. [34] investigated how an existing ladlefleet could be modified to withstand the prolongedsteel residence times and higher superheats of thenew horizontal continuous caster put into operationat the Avesta Panteg plant of Sheffield, UK. It wasdecided that some form of additional insulationwould be necessary to reduce steel heat loss and shelltemperature. Insulation had been retrofitted pre-viously at other plants, mainly to prevent shell tem-peratures from exceeding safety recommendations.The insulation had to be sufficiently thin, since ladlecapacity otherwise would have decreased. In order tostudy various refractory configurations, thermalmodels for the ladle and tundish were developed.These were based on finite difference solution of theheat conduction equation with parameters tuned soas to match the model output with thermocouplemeasurements in the ladle lining (Table 2). 5 thermo-couples were installed in the sidewall and 5 in thebottom lining of the monitored ladle. A total of 24ingot casts over a period of 5 days were logged withthe thermocouples.

Further calculations were done on heat lossthrough slag and insulating powder covers, liquidsteel exposure on stirring and melting and the effectof alloy additions. Initial trials were carried out witha commercially available material in the form ofthin, flexible sheets with a quoted thermal conduc-tivity of 0.035 W/mK, capable of withstanding tem-peratures up to 1025æC. Measurements were doneon an ingot casting ladle insulated with 5 mm of thesuggested material, where the effective thermal con-ductivity of the material was found to be approxi-mately twice that of the quoted value. After 65heats the lining was inspected and a compression ofthe insulation roughly equivalent to 20% could be

254

observed. In view of these results and further modelcalculations, the ladles intended for operation withthe new horizontal continuous caster were equippedwith 5 mm of the insulation in the sidewall and 12.5mm at the bottom. The final design went through athird measurement campaign, where hot face tem-peratures for the insulation were observed to besafely below the recommended limit. An operatingpractice for the continuous casting was also estab-lished and ladle dip temperature measurementswere taken, where the total temperature drop nowturned out to be 46æC. Moreover, it was decided thatthe ladle be kept idle for 1.5–2 h in order to soakthe lining thermally before start of casting. An alter-native practice is to make the cycle as consistentand regular as possible without long waitingperiods. Finally, it was observed that insulation re-sulted in hotter linings, a potential threat to refrac-tory integrity. However, working lining life for themodified ladle fleet reached 3000 min of steel con-tact time, which was roughly the same as for theold ingot casting ladles. The insulation lifetime inthe new fleet was three working linings.

Grip [50] outlines simple methods for calculationof steel temperature drop in the ladle. Elementaryprinciples of conduction heat transfer and use of theYngve Sundberg equation (8) are discussed. The com-mercial code TempSim is briefly described and it isdemonstrated how the result from TempSim conformsto equation (8) with suitable coefficients. Through aseries of measurement results, Grip illustrates thequasi-stationary nature of lining temperature profilesand the importance of thermal history (e.g., pre-heating) and regularity in the ladle cycle. The fre-quently overestimated chilling effect of gas stirring isindicated in a simple manual calculation, showing amuch smaller temperature drop than the measuredone. Grip claims that this is a result of stratificationand that stirring is not an effective means of tempera-ture adjustment. Finally, a temperature control systembased on simple regression expressions of the form(8), developed using TempSim, is described.

Fredman & Saxen [51] developed an analyticalmodel for estimation of temperature profiles in ladlerefractories. The model is based on local solution, byseparation of variables, of the one-dimensional tran-sient heat conduction equation within the lininglayers. Using the local solutions, an overall tempera-ture profile can be formed after computation of thematerial boundary temperatures. Model dynamicsare considered in the working lining only, the outerlayers of the refractory are at steady state. This ap-proach of simplifying the dynamics and geometry


Table 3. Reviewed theoretical works relating to ladle thermal state

Ref. Model structure Features

independent steel temp. tundish type of purpose remarkvariables, solution included included measurement of model

method

Paschkis [26] (,t) yes, stagnant no estimate steel analog comp.melt temp. drop implementation

Paschkis [27] (,t) yes, stirred no estimate steel analog comp.melt temp. drop implementation

Alberny [37] (r,t),FDE stirred yes, steel improve stratificationtemperature temp. control considered

Chone [38] (r,t) stirred no steel aid design, whole cycletemperature decisions considered

Omotani [39] (r,t) stirred no decision steel heatsupport balance

Pfeifer [31] (r,t),FDE stirred no design of stirring,ladle head slag th. inv.

Pfeifer [32] (r,t),FDE yes,also no lining improve mod. tuningtap stream temp. control described

Pfeifer [40] (r,t) stirred no lining simulate preh. strat.preheating investigated

Morrow [30] (r,t),FDE stirred no lining lining variabledesign therm. props.

Hlinka [29] (r,t),FDE variable no decision whole cyclestirring support considered

Tomazin [25] (r,t),FDE yes lining design, variabletherm. practice therm. props

Hoppmann [41] (,t) yes yes steel calc. converter part. statist.temperature tap. temp. model

Hoppmann [35] (,t) yes no steel calc. casting part. analyt.temperature temperature model

Chapellier [42] (,t) yes no calc. converter statisticaltap. temp. model

Koo [43] (,t) yes, no lining study eff. CFD-calc. ofstratified of stirring stirring

Gaston [44] (r,t) yes yes steel estim. strat. steel heattemperature in tundish balance

Shklyar [45] (r,t) yes no simulate steel heatpreheating balance

Mucciardi [46] (r,t),FDE no no lining used avail.design software

Saha [33] (r,t),FDE no no lining simulate studiedpreheating recuperative preh.

Austin [28] (r,z,t),ADI yes no lining improve used adaptivetemp. control time step

Gaston [47] (r,t) yes, also no est. tapping ladle loadtap stream temp. drop linear in t

Zoryk [48] (r,t),FDE yes yes lining on-line est. of th. state ofsteel temp. steel temp. in ladle fleet

ladle, tundishSistilli [49] (,) no no scheduling analyze statistical

data scheduling investigationOlika [36] (r,t) yes no lining, hot calc. casting part. statist.

face, steel temp. temperature modelBarber [34] (r,t),FDE yes yes lining aid redesign inv. various

of ladle fleet heat lossesGrip [50] (r,t) yes no lining, develop simple studied regularity,

steel temp. temp. models preheatingFredman [51] (r,t) no no lining, rapid est. of rapid

steel temp. th. state computationFredman [52] (r,z,t),FEM yes no lining aid design, dynamics after

steel temp. decisions preheating

ensures rapid computation and maximum flexibilityin boundary conditions, beneficial for, e.g., on-line

255

simulation. Apart from computational issues, suchas efficient solution of eigenvalue spectra, cooling of

Fredman

the exposed hot face is discussed. To illustrate thefeasibility of the approach, simulations were com-pared with data from a measurement campaign im-plemented at the facilities of a Finnish steel pro-ducer. A ladle with a two-layer refractory was fittedwith 6 thermocouples in the lining and the readingslogged over some 26 heats. The simulations were inacceptable agreement with the measured tempera-tures.

Fredman et al. [52] present a two-dimensionalmathematical model for simulation of thermal state ofladle linings and steel temperature during casting. Forthe lining geometry, the two-dimensional dynamicheat conduction equation is solved, using the FiniteElement Method (FEM), simultaneously with the en-ergy balance equation for the perfectly mixed steel.Radiation heat transfer above the slag surface iscoupled with both the thermal state of the lining andthe energy balance. Hence, radiation, convection aswell as conduction in the lining are considered at eachtime step in the solution of the energy balance for themolten steel. As the computations become ratherheavy, the model is suitable mainly for off-line simu-lation. Lining design, scheduling and decision sup-port are feasible application areas for the model,which also features a user-friendly interface for inputdata specification. To validate the model, a measure-ment campaign was carried out at the facilities of aFinnish steel producer. A 3-layer refractory lining wasfitted with 16 thermocouples at 2 heights in the side-wall and one position at the bottom. The campaignwas more extensive as compared to [51], and tempera-tures were recorded for a total of 82 heats. To test thedynamics of the model and study the gradual increasein heat content of the lining, simulations were doneover some ten initial heats for a fresh ladle. Apartfrom minor technical problems with the thermo-couples, due to overheating, the campaign was suc-cessful in demonstrating the feasibility and usefulnessof the model.

Summary of the theoretical models

The reviewed theoretically focused works relating tothermal state of ladle systems have been summarizedin Table 3. In the classification of the investigationsthe model structure and special features of the workhave been used as criteria. Model structure is de-scribed through the dimensionality (set of indepen-dent variables), the solution method used in the simu-lation and the output. Possible output might be oneor several of the lining thermal state, steel tempera-ture in(to) the ladle and thermal state/steel tempera-

256

ture in the tundish. Assumptions pertaining to the de-gree of agitation in the steel are indicated for someworks. For the set of independent variables, (r, z, t)denotes a two-dimensional, dynamic model where ris the radial coordinate, z is the height coordinate andt is time. When the height is omitted, the model isessentially one-dimensional, although temperatureprofiles may have been computed both at several po-sitions on the ladle sidewall as well as on the bottom.In cases where all of the variables have been omittedit was not possible to establish the exact structure ofthe model on basis of the text. The same applies tothe solution method used. Where indicated, the ab-breviations FDE, FEM and ADI have been used forfinite difference equations, finite element method andalternating direction implicit, respectively. These areexplained in the numerical mathematics literature, see[53]. As features are considered supporting measure-ments (in some cases used for validation and tuningof the model) as well as the purpose of the model andspecial methods or details indicated under ‘‘remark’’.

From Table 3, it is seen that the objectives of theinvestigations have been quite varying. Nevertheless,the basis of the works is in many cases a one-dimen-sional model for the temperature profile across the lin-ing of the ladle and/or the tundish. In most cases, thestraightforward and simple finite difference schemewas chosen for a method of solution. Only a fewmodels, [28] and [52], were 2-dimensional and usedspecial solution methods. Austin et al. [28] used theADI-method, based on finite differences, and Fred-man et al. [52] used FEM. One work, [48], was primar-ily concerned with on-line simulation. Thus, in mostcases, except [48] and [51], the computation time wasprobably not critical for the choice of model. It alsoappears that the one-dimensional approach has be-come a commonly accepted method among theworkers in the field. Another reason for its popularityis perhaps the increased complexity in boundary con-ditions for two-dimensional models, resulting in moreparameters open to assumption and more difficulttuning of the model. A fact, however, is that none ofthe reviewed one-dimensional studies address theissue of axial (in the z-direction) heat transfer in thelining quantitatively. On the other hand, for the mol-ten steel, thermal uniformity is a reasonable assump-tion in light of the measurements and CFD (compu-tational fluid dynamics) studies included in a numberof the reviewed works. As was noted in the summaryof the experimental investigations, the slight thermalstratification occurring in the ladle evens out the tem-perature of the steel exiting the tundish. Hence, as-suming the melt to be perfectly stirred causes the heat


balance to give a lower steel temperature at start andin the end of casting a heat. Making some suitableapproximation of the stratification might make itpossible to consider this phenomenon through theheat balance, without expensive fluid dynamics com-putations. In a few works, the variation of the thermo-physical properties with temperature was considered.Apparently, the functions for thermal conductivityand specific heat had been supplied by the refractoryvendor or manufacturer. A potential problem here isthe change taking place in the material over the liningcampaign. Consequently, the used functions may nothave been even close to the real temperature depend-encies after the first five heats on the lining.

The performance of the steel temperature modelssummarized in Table 3, when compared with meas-urement data in the investigations, was varying. Goodagreement, e.g., in [48], was obtained when sufficientmeasurement data was available, making it possibleto tune the model through adjusting its parametersso as to produce lining temperature profiles and steeltemperature trajectories agreeing with campaignmeasurements. Clearly, this applies to the presentedlining thermal models as well.

Conclusions

A literature review dealing with topics related tomonitoring and modeling the heat loss from ladles insteel production has been presented. A wide range ofworks were covered, including issues from processscheduling in continuous casting to optics and physi-cal modeling. Scheduling and process control have adirect impact on the heat loss from the steel-ladle sys-tem and can be combined with design of processequipment to reduce heat loss. Studying these sys-tems experimentally is fundamental not only forunderstanding the involved mechanisms of heat andmass transfer but also for formulation of theoreticalmodels describing the thermal state of the system. Inthe part dealing with theoretical modeling, focus hasnot been as strongly on results in the form of agree-ment with measurements as on model structure andcentral ideas implemented in the model formulation.The reason was that comparison of different modelsdescribing different plants and validated against ex-perimental data obtained under different circum-stances was difficult. Looking back at the reviewedworks awakes some thoughts on modeling this typeof system. Design evaluation and on-line simulationseem so require completely different model structuresin order to address key issues, such as model realismand computation speed. Therefore, a more complex,

257

perhaps two-dimensional dynamic model is suitablefor design purposes and a simpler one-dimensionalmodel for on-line simulation. The simpler model doesnot have to be merely a regression equation for thedrop in steel temperature as a function of time in aparticular plant, but it could be a combination of ana-lytical and numerical results for the heat conductionand energy balance in the system. In a situation whereboth model types would be required, it might also bepossible to validate the on-line model against the de-sign model if necessary. Naturally, this would be feas-ible only after thorough validation of the more com-plex design model.

Acknowledgements

Permissions to reproduce previously published fig-ures, granted by The Association of Iron and SteelEngineers, The Iron & Steel Society and The Insti-tute of Materials are gratefully acknowledged. Theauthor also wishes to express his gratitude for thefinancial support received from Liikesivistysrahasto,Finland.

References

1. Mish FC. Webster’s 9th New Collegiate Dictionary. Merri-am-Webster Inc., Springfield, Mass. USA, 1988.

2. Fruehan R. Iron & Steelmaker 1996: July: 25–33.3. Kivela E, Sipola M. Teraksen lampotilahallinta senkkakasit-

telyjen ja jatkuvavalun aikana. Technical course print, in Fin-nish, Jun. 1994. Taydennyskoulutuskurssi Tulenkestavat Ter-asteollisuudessa, PohTo, Oulu Finland.

4. Sillanpaa M. Model for predicting the evolution of steel tem-perature in a continuous casting tundish on the basis of ex-pert knowledge. Report 91-1, Åbo Akademi University, HeatEngineering Laboratory, Biskopsgatan 8, FIN-20500 ÅboFinland, 1991.

5. Cramb AW. Trends in caster operation, part 1. Iron & Steel-maker Sep. 1989: 45.

6. Cramb AW. Trends in caster operation, part 2. Iron & Steel-maker Oct. 1989: 56.

7. Cramb AW. Trends in caster operation, part 3. Iron & Steel-maker Nov. 1989: 47–48.

8. Ameling D, Walden K, Wethkamp H. Stahl und Eisen 1981:101 (15): 35–39.

9. Hoppmann W, Pfeifer H, Fett FN, Fiege L. Stahl und Eisen1987: 107 (1): 49–54.

10. Kitamura M, Kawasaki S, Kawai S, Kawai K, Miyake K.Transactions ISIJ 1983: 23: B–165.

11. Minion RL, Leckie CF. Steel temperature control in the ladlein a high productivity BOF shop. In: 5th International Ironand Steel Congress. Proc the 69th Steelmaking Conf. Iron &Steel Society 1986: 69: 335–343.

12. Perkins A, Robertson T, Smith D. Fachberichte HuttenpraxisMetallweiterverarbeitung 1986: 24 (8): 649–656.

13. Petegnief J, Birat JP, Larrecq M, Bobrie M, Lemiere F, Fautrel-le Y. Revue de Metallurgie – CIT 1989: Jan: 47–54.

Fredman

14. Rieche K, Kohn W, Wunnenberg K. Stahl und Eisen 1985:105 (19): 41–46.

15. Rutqvist S, Bergman D, Olika B. Scandinavian Journal ofMetallurgy 1990: 19: 146–152.

16. Saunders LM. Preheating and controlled thermal cycling ofsteel handling ladles. In: 66th Steelmaking Conf Proc. Iron &Steel Society 1983: 66: 69–75.

17. Samways NL, Dancy TE. Journal of Metals 1960: 331–337.18. Ettwig HH. Stahl und Eisen 1995: 115 (6): 67–70.19. Grip C-E. Measurement of ladle wall temperature to im-

prove control of steel temperature in BOF plant. In: 77thSteelmaking Conference Proceedings, Iron & Steel Society1994: 77: March.

20. Hlinka JW, Miller TW. Temperature loss in liquid steel-re-fractory systems. Iron and Steel Engineer, Aug. 1970.

21. Widdowson R. Ironmaking and Steelmaking 1981: 8 (5): 195–200.

22. Cardouat JM. Revue de Metallurgie – CIT 1986: 203–210.23. Christensen KW. Heat losses and scull formation in Fe-Si

and Si-metal ladles. In: Electric Furnace Conference Proc.Iron & Steel Society 1988: 195–199.

24. Hecht E. Optics, 4. Addison-Wesley, 2nd edition, 1987.25. Tomazin CE, Upton EA, Wallis RA. The effect of ladle refrac-

tories and practices on steel temperature control. Iron &Steelmaker 1986: Jun. 28–34.

26. Paschkis V. Temperature drop in pouring ladles. AFS Trans-actions 1956: 64: 565–576.

27. Paschkis V, Hlinka JW. Temperature drop in pouring ladles,part two. AFS Transactions 1957: 65: 276–281.

28. Austin PR, O’Rourke SL, He QL, Rex AJ. Thermal modellingof steel ladles. In: 75th Steelmaking Conference Proceedings,vol. 75, pp. 317–323. Iron & Steel Society, 1992.

29. Hlinka JW, Cramb AW, Bright DH. A model for predictingthe thermal history of a ladle of steel. In: 68th SteelmakingConference Proc. Iron & Steel Society 1985: 68: 35–46.

30. Morrow GD, Russell RO. Thermal modeling in melt shopapplications. Am Ceram Soc Bull 1985: 64 (7): 1007–1012.

31. Pfeifer H, Fett FN, Schafer H, Heinen K-H. Stahl und Eisen1983: 103 (25–26): 1321–1326.

32. Pfeifer H, Fett FN, Schafer H, Heinen K-H. Modell zur ther-mischen Simulation von Stahlgiesspfannen. Stahl und Eisen1984: 104 (24): 1279–1287.

33. Saha JK, Ajmani SK, Chatterjee A. Ironmaking and Steel-making 1991: 18 (6): 417–422.

34. Barber B, Watson G, Bowden L. Ironmaking and Steelmak-ing 1994: 21: 150–153.

35. Hoppmann W, Fett FN, Hsu G, Fiege L. Stahl und Eisen1989: 109 (23): 1177–1186.

258

36. Olika B, Bjorkman B. Scandinavian Journal of Metallurgy1993: 22: 213–219.

37. Alberny R, Leclercq A. Heat losses from liquid steel in theladle and in the tundish of a continuous-casting installation.In: Mathematical process models in iron and steelmaking,Proceedings, Amsterdam, pp. 151–156. The Metals Society,1973.

38. Chone MJ, Teyssier F. Senkan lampohavioiden laskeminen.Technical Report RE 137, IRSID, Maizieres-les-Metz, Oct.1973. Translated from French at Rautaruukki Oy, Finland.

39. Omotani MA, Heaslip LJ, Maclean A. Ladle temperaturecontrol during continuous casting. Iron & Steelmaker 1983:Oct: 29–35.

40. Pfeifer H, Fett FN, Schafer H, Heinen K-H. Stahl und Eisen1985: 105 (14/15): 759–764.

41. Hoppmann W, Fett FN, Fiege L, Bachmann R. Stahl undEisen 1988: 108 (2): 61–66.

42. Chapellier P. Revue de Metallurgie – CIT 1989: 687–692.43. Koo YS, Kang T, Lee IR, Shin YK, Gal HY. Thermal cycle

model of ladle for steel temperature control in melt shopand its application. In: 72nd Steelmaking Conf Proc. Iron &Steel Society, Apr 1989: vol. 72.

44. Gaston A, Laura R, Medina M. Ironmaking and Steelmaking1991: 18 (5): 370–373.

45. Shklyar FR, Malkin VM, Korshunov VA, Sovetkin VL. Math-ematical model of thermal performance of steel pouringladle. Steel in the USSR Feb. 1991: 21: 68–70.

46. Mucciardi F, Grandillo A. Optimizing ladle cycling strat-egies. In: 74th Steelmaking Conf Proc. Iron & Steel Society1991: 74: 757–760.

47. Gaston A, Laura R, Medina M. Thermal cycle of continuoussteel casting ladles: a mathematical model for predicting thesteel temperature during the tapping and the filling period.Latin American Applied Research 1993: 195–200.

48. Zoryk A, Reid PM. On-line liquid steel temperature control.Iron & Steelmaker 1993: June: 21–27.

49. Sistilli FR, Erny EL. Computerized steel ladle tracking.Iron & Steelmaker 1993: Oct: 63–66.

50. Grip C-E. Calculation of the ladle temperature. Technicalcourse print, Feb. 1995. Metallurgisten prosessien mallin-tamisen perusteet ja tyokalut, PohTO, Oulu Finland.

51. Fredman TP, Saxen H. Metallurgical and Materials Trans-actions B 1998: 29B: 651–659.

52. Fredman TP, Torrkulla J, Saxen H. Metallurgical and Ma-terials Transactions B 1999: 30B: 323–329.

53. Vemuri V, Karplus WJ. Digital computer treatment of partialdifferential equations. Prentice-Hall Series in ComputationalMathematics. Prentice-Hall, Englewood Cliffs, NJ, 1981.

本文献由“学霸图书馆-文献云下载”收集自网络，仅供学习交流使用。

学霸图书馆（www.xuebalib.com）是一个“整合众多图书馆数据库资源，

提供一站式文献检索和下载服务”的24 小时在线不限IP

图书馆。

图书馆致力于便利、促进学习与科研，提供最强文献下载服务。

图书馆导航：

图书馆首页文献云下载图书馆入口外文数据库大全疑难文献辅助工具

http://www.xuebalib.com/cloud/

http://www.xuebalib.com/

http://www.xuebalib.com/cloud/


http://www.xuebalib.com/vip.html

http://www.xuebalib.com/db.php

http://www.xuebalib.com/zixun/2014-08-15/44.html


heat transfer in steelmaking ladle refractories and steel

Documents