in heating contrél the use of steeltemp®...

1. INTRODUCTION

The STEELTEMP® software for heating comes intwo main editions, edition 1 for fiat and roundproducts, using a finite-difference 2D technique,and edition III for fiat products, using a finiteelement (FEM) 3D technique.

The 3D code is capable of taking into accountnon-uniform heating of stocks caused byradiation shadowing from the skid pipes, thecontact between the wearer bars and the stocksand end effects in the stocks. The 3D temperaturecalcuiations have been verified against trialsmade in slab pusher furnace No. 2 at SSABOxelösund’s heavy plate mill and siab walkingbeam furnace No. 302 at SSAB Tunnplåt’s hotstrip miii.

* Subject of a presentation at the 1998 ATS International SteelmakingConference (Paris, December 1-2, 1998, Session 16).

The authors would like to acknowledge the financial support fromTechnical Field 51 of the Swedish Steel Producers ‘Association, the NordicIndustrial Funds and The Nordic Steel Industiy.

In 1976, the development of a finite-difference program,STEELTEMP®, for temperature and heat transfer analysisin steelworks, commenced. Initially, the program was developed for teeming, cooling, stripping and heating operations in the ingot process. Later, mathematical models forfiat rolling and open-die forging were incorporated.

In the early eighties, very sophisticated mathematicalmodels describing the heating of stocks and oxide scale formation in fuel-fired furnaces were included. Models forinduction heating of stocks for rolling were also madeavailable. Combustion calculations can now also be performed using the program. Moreover, new software forcalibration of the heating models in FOCS systems hasbeen implemented. During the simulation, STEELTEMP®reads and interprets the log files created by the FOCSsystem during the trial.

In the middle of the nineties, a new three-dimensionalfinite-element (FEM) code was developed which was ableto take into consideration non-uniform heating of stockscaused by radiation shadowing from the skid pipes, thecontact between the wearer bars and the stocks, baffies inthe furnace and end effects in the stocks. Verifications ofthe heating models, implemented in the 3D code ofSTEELTEMP®, have been made against analytical solutions and numerical solutions obtained from the 2DSTEELTEMP® code. The three-dimensional temperaturecalculations have also been verified against trials made inslab pusher furnace No. 2 at SSAB Oxelösund’s heavyplate mill and slab walking beam furnace No. 302 at SSABTunnplåt’s hot strip mill.

The mathematical furnace models described are compatiblewith the on-line mathematical models in the FurnaceOptimizing Control System for Reheating Furnaces,FOCS-RF (1), developed by MEFOS and sold worldwideon a license basis by ABB Industrial Systems AB. Carpetdiagrams can be caiculated and calibration of the heatingmodel can be done for FOCS systems using STEELTEMP®.

• MATHEMATICAL MODELS

The STEELTEMP® software for heating comes in twomain editions, edition 1 for fiat and round products, usinga finite-difference 2D technique, and edition III for fiatproducts, using a finite-element (FEM) 3D technique.

The use of STEELTEMP® softwarein heating contrél ..: .

B. Leden (M~F®S, Li~jIeå, Swéden),D. Lindholm, E:’ Nitteberg (lnstit.ute for EnergyTechnology, Kjeller, Norway) : .~

La Revue de Métallurgie-CIT Mars 1999 367

Le logiciel STEELTEMP® de réchauffage des demiproduits au four existe en deux versions: 1 ‘une en différences finies 2D pour produits plats et pour billettesrondes et l’autre aux élémentsfinis 3D pour les produitsplats. C’est un des constituants du logiciel ge’néraid’échange thermique STEELTEMP-IE.

Mod~les mathdmatiques

Depuis 1976, ce logiciel a évolué Ilpermet de caiculerles courbes de chauffage et la formation de calaminedans le cas des demi-produits soit & partir des températures mesurées dans les fours — c ‘est le mod~ie simple —

soit en partant des caractéristiques aéro-thermiques desfours, de la géométrie, des caractéristiques thermiques,de i’écoulement des fluides. C’est un mod~le de contröledynamique complexe. Il est adapté au traitement destransitoires. Ce mod~le est aussi adapté au chauffageinductif Il permet enfin d’effectuer des caiculs relat~fs &la combustion.

Sa version IllA permet de prendre en compte l’effet desglissi~res refroidissantes, les effets d’extrémité des demiproduits et d’apprécier l’homogénéite’ du chauffage. Ona développé un logiciel d’étaionnage des conditions dechauffage FOCS (Furnace Optimization ControiSystem) qui dépouille et prend en compte les mesureseffectudes pendant un essai. On peut ainsi comparer lesdonnées expérimentales et les résultats des calculs effectués par STEELTEMP en temps réel et effectuer desajustements. Le premier niveau de comparaison repérétest-99, est effectué pour s ‘assurer que 1 ‘on prend encompte les m~mes para&tres dans STEELTEMP etdans FOCS, puis on étalonne FOCS.

Applications

Lefourpoussant n° 2 de 80 t/h de SSAB Oxelösund comporte des glissi&es refroidies par un mélange eauvapeur & 245 °C. La disposition de ce four est représentée sur lafigure 3 avec les différents points de mesurede température. La brame d’essais a e<té équipée de thermocouples & trois épaisseurs et les mesures enregistrées.Les calculs suivant 2D STEELTEMP et RCCF200FOCSrendent correctement compte des écarts de températureobservés en relation avec les glissi&es refroidies. Deméme pour les autres parties des brames, 1 ‘accord estsatisfaisant.

Des calculs de répartition de températures dans le four& longerons n° 302 de SSAB Tunnplåt AB ont été effec

tuds avec le logiciel 3D. Les longerons sont maintenus &220 °C. Les 12 thermocouples de la brame d’essais permettent de rendre compte des hétdrogéne’ités de température suivant sept sections. Les conditions d’écoulement des fluides dans le four, modelisé en zoneschauffées et non chauffées, ont été décrites gråce & uneinstrumentation adéquate (fig. 8). Les pas de calculs ontété choisis pour rendre compte des conditions thermiques locales en relation avec la gdomdtrie du four

Le logiciel FOCS a été utilisé pour modéliser le chauffage de la brame d’essai dans les conditions représentées sur la figure 1. Les re’sultats pour la section A,section au droit du longeronfixe n° 6, sontprésentés surla figure 10. L’accord entre caicul et mesure est bonpour les zones 1 & 5; au passage de 1/5 & 2/6, la bramed’essais n’est pas chauffée aussi vite que le mod~le leprévoit. La position des couplesfait penser que le mod~lere~oit des indications non représentatives. L’accord est& nouveau bon dans la zone d’égalisation et les prévisions de conditions globales de chauffage sont satisfaisantes.

Ainsi, le mod~le mathématique décrit est compatibleavec le logiciel Furnace Optimization Control Systemfor Rehating Furnaces (FOCS-RF) développé parMEFOS et maintenant commercialisé dans le mondeentier par ABB Industrial Systems. On peut calculer descartes de température et étalonner des mod~les dechauffage pour le logiciel FOCS en utilisant STEELTEMP

L’utilisation du programmeSTEELTEMP® pour la maitrisedu réchauffage des brames

B. Leden (MEFOS, Luleå, Sweden),D. Lindholm, E. Nitteberg (Institute for EnergyTechnology, Kjeller, Norway)

368 La Revue de Métallurgie-CIT Mars 1999

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Notations:

z length coordinate (m)df distarice between stock and fixed skid pipe (m)dm distance between stock and moveable skid pipe (m)L distance between skid pipes (m)

R radius of skid pipe (m)c~1, cx3, a5 angles determining view factor between stock and

furnace (~)a2, a4 angles determining view factor between stock and skid

pipes (°)

Fig. 1 — Illustration of radiation shadowing of a stock by fixed and moveable skid pipes.

Fig. 1 — Géométrie utilisée dans le modéle de calcul d’effet des longerons de four.

General 2D models

STEELTEMP®-IE (2) is a general program for temperatureand heat-transfer analysis during:

— teeming or continuous casting,

— cooling,

— stripping,

— heating,

— fiat rolling,

— open-die forging,

— water spraying.

The very essence of the mathematical modelling is thespecification of time-dependent boundary conditions,which are an integral part of the specifications for the abovecases. These boundary conditions are:

— radiation,

— gas and walllroof radiation,

— natural convection,

— forced convection,

— given boundary temperature,

— given heat-transfer coefficient and boundary temperature,

— syrnmetry axis.

Besides these single codes, codes in pairs can be used tospecify the boundary conditions of a problem. For instance,the codes 13 and 31 correspond to the composite heattransfer mechanism by radiation plus natural convection.

2D and 3D reheating furnace models

In the reheating furnace models (3), the heating curve of thestocks and oxide scale formation (4) can be caiculated,either from the measured furnace temperatures — thesimple heating model — or from the geometrical and thermal description of the furnace, fuel and air fiows, etc.,using the complex heating model or the dynamicalheating model.

In using the dynamical heating model (5), non-steady-stateheating problems can be analysed, e.g., variations of:

— stock dimensions,

— steel grades,

— first positions of stocks,


— initial temperatures of stocks,

— points of time for charging, transfer and discharging ofstocks,

— transfers of stocks,

— fuel and air flows,

— fuel and air temperatures.

3D reheating furnace models

Non-uniform heating of stocks caused by radiation shadowing effects from the skid pipes, the contact between thewearer bars and the stocks, baffies in the furnace and endeffects in the stocks can be analysed using STEELTEMP®~IllA. In particular, it is possible to determine

— magnitudes of skid marks,

— head and tail end uniformity of stocks,

— cross-sectional uniformity of stocks.

:~i~jiii~i

- 1400-(J0

1 120-w

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uj860-

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On the bottom side of the stock, the density of heat flowrate to the stock varies with the position of the consideredslice on the stock according to figure 1. Those parts of thestock situated close to the skids will be much cooler (up to100 °C) than those paris halfway between skids, wherevirtually no shadowing occurs. The radiation shadowing ofthe stock by skid pipes are calculated from the angles ct.~,

a5 used to determine the view factors between stockand skid pipes (fig. 1).

Verifications of the simple and complex heating models,implemented in the 3D STEELTEMP® code, have beendone against analytical solutions and numerical solutionsobtained from the 2D STEELTEMP®-IE code (6) (7). Thespace discretization of the Fourier heat equation is done differently for the 2D and 3D codes. While the 2D codeemploys a finite-difference method, the box integrationmethod, the 3D code uses a finite-element formulation.The equation solver is however the same for the two codes.In the application case for billet heating in MEFOS’s pilotplant furnace, only minor deviations are obtained between

Fig. 2 — The results of the STEELTEMP®-IE 99-test of the heating model of the RFC200FOCS systemfor the new walking beam furnace at AB Sandvik Steel, Sandviken.

Fig. 2 — Résultat des essais STEELTEMP-IE 99 pour le modéle de chauffage RFC200FOCSinstallé sur le nouveau four å longerons de AB Sandvik ~ Sandviken.

THE FLJF~NACEC :‘~TLTMP 1-.~A7\~GG 1 12 IF .DA.7

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TEMPERATUPES (DC)

100 B.B~1 I~.D62 28.124 ~2..6SSLENOTH ~nJ

~ 100- ~TOCI~ T~M~EPArLJP~ DIFF~P~NC~ LOCJ~ 60-~LII 0-I

-Bo.

-100O000 S.B~1 1~.D82 l9.B~ 26.124 ~2..8SB

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caiculated stock temperatures with the simple heatingmodel for the two codes (6). This hoids as weil for the gasand wall temperatures calculated with the complex heatingmodel for this application (7). The main objective of theverification is to confirm that the 3D code manages toreproduce the resuits obtained from the 2D code.

Combustion caiculations

When modelling the heating of stocks in reheatingfurnaces, it is necessary to know the composition of the fluegases in the furnace atmosphere, the amounts of combustion air required and of the flue gases formed during thecombustion process, the flue gas losses and the thermalefficiency of the combustion process. These quantities arenot easily calculated by hand, so a program for thosecaiculations, FgCalc, has been implemented in the mainmenu bars of STEELTEMP®-IE and IllA.

The user provides the following input:

— the fuel composition,

— the combustion air and flue gas temperature,

— oxygen enrichment,

— fuel/air ratio or oxygen contents of flue gases.

Based on these input values, the program caiculates thecomposition of flue gases, the amounts of required combustion air and formed flue gases, the flue gas losses andthe thermal efficiency of the combustion process. The netcalorific value of the fuel could either be given or calculated from the given composition of the ou or LP gas. Ifthe NO~ emission in ppm is provided, the program will alsocalculate the amount of NO2 in mg/MJ with and withoutrespect to air preheating.

Software for calibration of the heatingmodels in FOCS systems

Special software has been deveioped for caiibration of theheating models in the following FOCS systems:

- FOCS-RF [DEC VAX/Alpha (Open VMS) and PC(Windows NT)];

- FOCS-BNF [DEC VAX/Alpha (Open VMS) and PC(Windows NT)];

— AF200FOCS [ABB Master Piece 2001;

— RFC200FOCS [ABB Advant Controller].

During the simulation, STEELTEMP® reads and interpretsthe log files created by the FOCS system during the trial.The gas and wall biases of the thermocouples used to calculate the fumace temperature above the test stock arestored in a calibration file. These biases can be changedinteractively during the calibration procedure to obtain an

optimal fit between the measured and caiculated heatingcurves of the test stock. The temperatures recorded from thetest stock are converted and stored in a measured data file.

The temperatures calculated with STEELTEMP® can becompared either with corresponding temperatures calculated on-line by the heating model of the FOCS system, orwith measured temperatures in a test stock. The first comparison, the so-called 99-test, is done to ensure that thesame parameters are used both in STEELTEMP® and theFOCS system. The second comparison is used when calibrating the FOCS system.

In January 1996, a new 80 t/h walking beam furnace capableof heating different grades of stainless steeis, Cr steels andlow-alloy steels was commissioned at AB Sandvik Steel,Sandviken. The heating of the stocks is optimized using aRFC200FOCS system installed by ABB Industrial SystemsAB. In collaboration with ABB Industrial Systems AB,MEFOS has performed the 99-test of the heating model ofthe RFC200FOCS system. The resuits of the test are showninfigure 2. According to this figure, the deviations betweenthe temperatures calculated by STEELTEMP®-IE andRFC200FOCS are less than 1 °C for all logged temperatures except in two instances, where logging problems hadoccurred in the RFC200FOCS system.

• APPLICATIONS

Three-dimensional temperaturecaiculations of skid marks on slabsheated in pusher furnace No. 2 atSSAB Oxelösund AB

Pusher furnace

In the plate mili at SSAB Oxelösund AB, traditional steelgrades, weldable extra-high strength steel and abrasionresistant steel are heated in the two 80 t/h pusher fumaces.Furnace No. 2 consists of a top and bottom fired heatingzone, and a top-fired soaking zone with plane hearth. Theheating zones are equipped with six front burners in the topzone and five front bumers in the bottom zone, while thesoaking zone is equipped with six side burners, three oneach side wall of the fumace. The furnace can be fired bothwith coke oven gas and heavy oil. The supplier of the furnace is Didier-Werke AG, Germany.

The slabs are pushed forward in the furnace on two parallelslab rows by two charger pushers on the charging table.When a charger pusher makes a stroke, all slabs are pushedforward on the fixed water-cooled skids. The skid pipes arecooled by a closed evaporative system which circulates a245 °C mixture of 95 % water and 5 % saturated steam.Steam is separated in a drum and fed to the vapour networkof the plant at a pressure of 37 bar.


Control zone 2 Control zone 1

Fig. 3 — Instrumentation and modelling of slab pusher furnace No. 2 at the heavy plate miii at SSAB Oxelösund AB.

Fig. 3 — Représentation schématique et instrumentation du four n° 2 de la tölerie de SSAB Oxelösund.

The instrumentation and mathematical modelling of thefurnace are shown infigure 3. The upper and lower heatingzones are each divided into two dark zones and two burnerzones. In the figure, these zones are identified as zones 1 to4 and 7 to 10, respectively. The soaking zone consists ofone dark zone and one bumer zone, zones 5-6. From acontrol point of view, the furnace is divided into three controlzones. The walllroof temperatures are measured withconventional thermocouples in all zones. In dark zone 7,the gas temperature is measured with a conventionalthermocouple in the waste-gas flue.

Experimental procedure

The test slab was charged on the first row of furnace No. 2.After the test slab had been charged, the production wasrunning at normal rate for ca. 1 h 30 min. When the test slabreached the position 7.552 m and was situated in the middieof dark zone 2/8, problems occurred on one cooling bed forplates situated after the rolling mill. Due to theseproblems, no slabs were discharged from the furnace, andthe test slab remained in the same position for ca. 1 h26 min. When the production started up again, slabs wereonly discharged from furnace No. 2 for ca. 1 h 9 min. Afterthat, the production was then running normally until thetest slab was discharged 5 h 45 min after that it had beencharged into the fumace.

The test slab was fitted with six thermocouples applied totwo different cross-sections, one above the skid positioned

farthest off the fumace wall and one halfway between theskids. Holes of depths 25, 50 and 75 % of the slab thickness, measured from the top surface, were drilled in the testslab. The thermocouples were connected to a recording unitstored in an isolated box with a water reservoir and watervapour outlet. The box was fastened to the test slab andfollowed with it through the furnace. The test slab waspushed stepwise through the fumace together with the otherslabs on the row.

The test conditions are summarized below:

• test slab dimensions and type : 218 x 1695 x 2980 mm3,type S1S1312;

• initial slab temperature : 20 °C;

• fuel : coke oven gas (during the whole trial);

• furnace pressure : 0.7 mm vp;

• drop-out temperature: 1250-1270 Oj:;

• residence time in furnace of test slab: 5 h 45 min.

During the experiments, logging files were created by theFurnace Optimizing Control System for ReheatingFurnaces (FOCS-RF). Slabs and tracking data were storedin an event file. The measured gas and walllroof temperatures, the fuel and air flows to the control zones, etc., werestored in a signal file. Both files can be retrieved in a mathematical model used for calibration to recreate the fumaceoperations during the trial.

Notations: TI = Indicating thermocoupleTC Controlling thermocouple1WG Waste-gas thermocouple


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Resuits

The mesh employed for the test slab, as weil as the positionof the measurement points, are shown in figure 4. Verticalelement rows situated above the skids are shaded. Thewidth of both skid regions is 0.2 m. The cooling of the siabbottom surface from the skids and the radiation shadowingof this surface from the skid pipes were modelled accordingtofigure 1. A heat-transfer coefficient of 20 W1m2•°C and awater vapour temperature of 245 °C were applied to modelthe contact between the skids and the bottom surface of theslab. The partial pressure of the flue gas components CO2and H20 were assumed to be uniform in the furnace andequal to 0.068 and 0.225 atm, respectively. An emissivityequal to 0.9 and 0.8 was used for the furnace walls and thetest slab, respectively.

The time step size was adjusted according to the maximumpermitted relative error of the frequencies of the nodaltemperature changes. During the calculation, the time stepsize was not permitted to exceed 20.0 s. An initial time stepsize of 0.01 s was used. The caiculations were repeatedwith a conjugate gradient soiver, but without any visiblechanges from the solution based on the default equationsolver, commonly referred to as the frequency split algorithm (6).

Figure 5 displays caiculated temperatures in the middle xzplane and in the bottom surface yz-plane, respectively, atthe discharge position of the slab. They clearly demonstratethe influence of the skids. The temperature field isaffected not only on the bottom surface of the slab, but alsothroughout the whole slab thickness. As expected, the

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Skid 1

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Skid 2

No. of nodal points 1x-direction : 9y-direction 33z-direction 41

Measurement poin~J

Fig. 4— The geometricaldimensions, the applied mesh

and the measurement pointlocations of the test slab.

Fig. 4— Géométrie, maillage etpoints de mesure de la brame

d’essais.

0.0

View from bottom surfacez-position [m]

1.0 2.0 3.0

Geometrical dimensions]

x-direction 0.2 18 my-direction : 1.695 mz-direction 2.980 m

00

View from back surfacez-position {m]

1.0 3.0

x-coord. y-coord. z-coord.

z

Ml 0.164m 0.9lOm 0.600mM2 0.109m 0.848m 0.600mM3 0.055 m 0.785 m 0.600 mM4 0.055m 0.910m 1.200mM5 0.109m 0.848m 1.2ØOmM6 0.164m 0.785m 1.200m

La Revue de MétaIIurg~e-CIT Mars 1999

[~Z_PLANE 1= 0.848 Lm]

lINE POIN1I

20505. L~econd~1

x 0.218 Lm)

Fig. 5 — Isotherm plots for the middie xz-plane (y = 0.848 m) and the bottom surface yz-plane (x = 0.218 m) of the testslab at the discharge position of furnace No. 2 at SSAB Oxelösund AB for the trial performed in May 1997.

Fig. 5— Isothermes du plan médian x-z (y = 0,848 m) et de la surface inférieure y-z (x = 0,218 m) de la brame d’essaisau point de défournement du four n° 2 de SSAB Oxelösund lors de l’essai de maj 1997.

effect is more pronounced on the bottom surface comparedto the top surface. The temperature difference between thetop and bottom surface above the skids is about 36 °C. Onthe bottom surface, the temperature ranges from about1223 °C to 1260 °C, where the lowest temperatures areobtained in the centre of the slab above the two fixed skids.The overall temperature distribution seems reasonable, andagrees weil with observations and experiences from thefumace.

The upper part of figure 6 displays the history plot of thecaiculated slab temperatures at the measurement pointslocated above the skid farthest off the furnace wall of slabrow No. 1, as weil as measuredlcalculated furnace tempe

ratures. Temperature deviations between the caiculated andmeasured slab temperatures at the positions 25, 50 and75 % below the top surface are shown in the lower part offigure 6. At the end of the heating zone, the measuredbottom slab temperature (position 75 % below top surface)fluctuates due to measurement errors. This gives rise tolarge temperature deviations between the calculated andmeasured temperatures in this part of the fumace. In theother parts of the furnace, there is relatively good agreement between the caiculated and measured slab temperatures. At the moment of extraction of the test slab from thefurnace, the agreement between the calculated and measured temperatures is good.

~-D~s 1~0

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374 La Revue de Métallurgie-CIT Mars 1999

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1400

1200

1000

0

800

600

400

It

150

100

500

0

-50

-100

-150

Fig. 6 — Upper part: caiculated slab temperatures at the measurement points locatedabove the skid farthest off the furnace wall of slab row No. 1, and measured/caiculated

furnace temperatures of pusher furnace No. 2 at SSAB Oxelösund AB. Lower part:deviations between calculated and measured slab temperatures.

Fig. 6 — Partie supérleure : températures calculées aux points de mesure situés au droit dela glissiére située le plus bin du mur, rangée de brames n° 1 et températures mesurées et

caiculées pour le tour n° 2 de SSAB Oxelösund AB. Partie inférieure : écart entretempératures de brame mesurées et calculées.

slab(25%)— slab(50%)

slab(75%)gas(upper)walI(upper)gas(lower)wall(lower)

5000 10000 15000 20000

Time [si

Time [sj


Three-dimensional temperaturecaiculations of skid marks on slabsheated in the hot strip miii furnaceNo. 302 at SSAB Tunnplåt AB

Walking beam furnace

In the hot strip miii at SSAB Tunnpiåt AB, Borlänge slabsof high-strength, low-ailoy, ULC, C-Mn and Si steel with athickness of 220 mm and lengths of 3600 to 11,000 mm arereheated in two 300 tfh walking beam furnaces. FumaceNo. 302 consists of a large furnace chamber divided into9 control zones, as shown infigure 8. The preheating zones,lower heating and soaking zones are equipped with side andfront burners, while the upper heating and soaking zonesare equipped with radiant roof burners. The fumace has119 bumers and is fired with heavy ou. The upper soakingzone has separate temperature controls for the two sides ofthe furnace. The supplier of the furnace is TechintItalimpianti SpA., Italy.

Forward transfer of slabs in the fumace occurs in one ortwo rows by means of ten beams, four movable and sixfixed, as illustrated in figure 7. The beams are cooled by aclosed evaporative system which circulates a 220 °C mix-ture of 95 % water and 5 % saturated steam. Steam is separated in a drum and fed into a network at a rate of 10-12 t/hat 22 bar. The extensive heat recovery system in the stacksproduces another 10-12 t/h steam. The system is describedin(8).

During 1988 a new furnace (furnace No. 301) was erectednext to fumace No. 302. In the new furnace, baffies separate the preheating, heating and soaking zones. This furnace is fired with LP gas with air preheating temperaturesup to 680 °C. The supplier of this fumace is Chugai Ro Co.,Ltd., Japan.

Experimental procedure

Before the test slab was charged, the fumace had been fihledwith slabs from rolling lot 324, a F-lot with a targetdrop-out temperature of 1280 °C. In front of the full lengthtest slab, two short slabs had been charged and behindthe test slab, one short slab was charged. Almost all slabscharged into the furnace during the trial were of fulllength. During the whole experiment, the production wasrunning at normal rate.

The test slab was fitted with 12 thermocouples applied tofive different cross-sections according to figure 7. A possible non-uniform temperature distribution in width direction of the fumace can be recorded by means of the measurement in cross-section 4 in the middie of the test slab andthe measurements in cross-sections 3 and 7 on each side ofthe test slab. The skid marks are recorded from the measurements in cross-sections A and C above the fixed skids 6and 8, respectively. Holes in the test slab were drilled at anangle of 40° to depths of 25, 50 and 75 % of the slab thickness. The thermocouples were connected to a STOR, type4503, Thermophil recording unit, stored in an isolated boxwith a water reservoir and water vapour outlet. The box was

Fig. 7— Test slab above fixed and moveable beams of walking beam furnace No. 302 at SSAB Tunnplåt AB, Borlänge.

Fig. 7 — Brame d’essais positionnée sur les longerons fixes et mobiles du four n° 302 de SSAB Tunnplåt AB, Borlänge.

Notations: F = Fixed skid pipeM = Moveable skid pipe


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Notations: TI = Indicating thermocoupleTC = Controlling thermocoupleTWG = Waste-gas thermocouple

fastened to the test slab and followed with it through thefurnace.

The test conditions are summarized below

• test slab dimensions and type : 220 x 1100 x 9775 mm3,type S1S1312;

• initial slab temperature: 10 °C;

• fuel : heavy ou E05 (0.37 wt-% S);

• furnace pressure : 0.7 mm vp;

• drop-out temperature of F-lot: 1280 °C;

• residence time in furnace of test slab : 2 h 56 min.

During the experiment, logging files were created by theFurnace Optimizing Control System for ReheatingFurnaces (FOCS-RF) (9). Slabs and tracking data werestored in an event file. The measured gas and wall/rooftemperatures, the fuel and air flows to the control zones,etc., were stored in a signal file. These two files can be usedby STEELTEMP® to recreate the furnace operation duringthe trials.

Furnace modelling

In the mathematical model of the fumace, the upper andlower preheating zones are each divided into two darkzones and two burner zones, zones 1 to 4 and 9 to 12,respectively. The two upper and lower heating zonescorrespond each to two bumer zones, zones 5-6 and 13-14,respectively. The upper soaking zone is divided into twoburner zones, zones 7-8. The lower soaking zone consistsof one burner zone (zone 15). The wall/roof temperaturesare measured with conventional thermocouples in all zones.In dark zone 1, the gas temperature is measured witha conventional thermocouple in the waste-gas flue. The

Fig. 8— Instrumentation and modelling of walking beam furnace No. 302of the hot strip miii at SSAB Tunnplåt AB, Borlänge.

Fig. 8 — Instrumentation et modélisation du four n° 302 du train ä bandede SSAB Tunnplåt AB Borlänge.

view of the furnace infigure 8.

Resuits from 3D temperature caiculations

In the caiculations, the cross-section of the test slab (xyplane) was divided into three regions, each with two elements in the outer regions and four elements in the centerregion. To be able to accurately model the cooling from theskid buttons and radiation shadowing from the skid pipesand end effects, the test slab has been divided into21 regions in length direction (z-direction). The size of theregions above the skid pipes was chosen to be equal to thewidth of the skid buttons (50 mm) on which the slabs rest.

The software for calibration of the heating models of FOCSsystems was used to caiculate the heating curve of the testslab from the log files created by the FOCS system duringthe trial. The cooling of the test slab bottom surface fromthe skid buttons and the radiation shadowing of this surfacefrom the skid pipes were modelled according to figure 1. Aheat-transfer coefficient of 20 W/m2.°C and a water vapourtemperature of 220 °C were applied to model the contactbetween the skids and the bottom surface of the slab. Thepartial pressure of the flue gas components CO2 and H20were assumed to be uniform in the furnace and equal to0.109 atm and 0.093 atm, respectively. An emissivity equalto 0.9 and 0.8 was used for the furnace walls and the testslab, respectively.

Figure 9 shows the isotherms in the middie xz-plane andthe bottom surface yz-plane of the test slab, when this slabis in the discharge position. From this figure, it can be seenthat the lowest temperature is obtained above the fixedskids in the centre of the test slab. This should be comparedwith SSAB Oxelösund’s pusher fumace No. 2 with soakinghearth, where the lowest temperature was obtained just

Cantrol Controlzonel —...—-..I....Contralzone2._...I.——wne3-—..1 ~

8_L~C0ntrOi CentralControl zone 5 —J—ControI zone 1 ~ 7 —1--—— ~.

furnace instrumentation and modelling are shown in a side


= 0.555 [in]

above the fixed skids on the bottom surface of the test slab(fig. 5). The temperature above the moveable skids in thecentre of the test slab is ca. 10 °C higher. The temperaturedifference between the top and bottom surface of the testslab above the moveable skids is ca. 30 °C.

On the bottom surface of the test slab the temperaturesrange from about 1228 °C to 1333 °C, where the lowesttemperatures are obtained in the centre of the slab abovethe fixed skids.

The upper part offigure 10 displays the history plot of thecaiculated slab temperatures at the measurement points in

cross-section A, located above the fixed skid 6. In thiscross-section, a good agreement is obtained between thecalculated and measured slab temperatures in control zones1 to 5. In the changeover area between control zones 1 to 5and 2 to 6, the test slab is not heated as fast during the trialas the mode! predicts. In this changeover area, there are noburners and the lack of an indicating/fictitious thermocouple here implies that the model will receive incorrectinformation about the furnace temperature (linear interpolation is used between the wall thermocouples, TC4-TC5and TC12-TC13, to determine the fumace temperatureabove the test slab). In the soaking zone, a good agreementis obtained between the calculated and measured slab tem

2 6 8

Hr1’~fLH-~r ‘H’

Z0x is

lp

~-j

IIME POINTI

10456. L~econds]01

ci

ci

Ii,

0

ciC1J -

ci

LI)r%J -

0

01

‘00

1228.0 [C]1555.7 [Ci

1240.0 [Ci1260.0 [Ci1270.0 [Ci12&).0 [Ci1290.0 [C]15tX~.0 [CJ1550.0 [C]

1 ISDTHERMS~Mtr-i volue :Mox vcikje :iso~herm :iso~herrn :isoLherm :Lso~hera :130 IhermL30 I~herm150 Iherm

YZ-PL~”NE

0 27-ox is

6 8 10

0.220 [in]

lillE POINTI

10456. [seconds]

ISOTHERMS

hin votue : 1228.0 [Cihl~x votun : 1552.6 [C]i~o1herm : 1240.0 [C]isolherm 1250.0 [C]isolherm : 1280.0 [C]isolherm : 1290.0 [Ciisolherm 1500.0 [C]Lsolherm 1550.0 [C]

Fig. 9 — Isotherms in the middie xz-plane (y = 0.555 m) and the bottom yz-plane (x = 0.210 m) of the test slabat discharge position of furnace No. 302 at SSAB Tunnplåt AB for the trial performed in November 1997.

Fig. 9 — Isothermes du plan médian xz (y = 0,555 m) et du plan inférieur yz (x = 0,210 m) de la brame d’essaiau moment du déchargement du four n° 302 de SSAB Tunnplåt AB lors de l’essai de novembre 1997.


FOURS

1400

1200

1000

800

1..

400

200

0

Time Is]

150

100

~-50

.4-

0

~ -50 ____________

-100

-150

Time LsjFig. 10 — Upper part: Caiculated slab temperatures at the measurement points located above skid 6

(z 6.200 m), and measureWcalculated furnace temperatures of furnace No. 302 at SSAB Tunnplåt AB.Lower part: Deviations between caiculated and measured slab temperatures

Fig. 10— Partie supérieure : températures de brame caiculées aux points de mesure situés au-dessusdu longeron 6 (z = 6,200 m) et températures de four mesurées et calculées pour le four fl° 302 de

SSAB Tunnplåt AB. Partie inférieure : écart entre les températures de brame calculées et mesurées.

0 2000 4000 6000 8000 10000

~0080~00~

— slab(25%)

— slab(50%)

slab(75%)


peratures. Hence the caiculated slab temperatures in thedischarge position should be reliable.

• REFERENCES

(1) LEDEN (B.). A control system for fuel optimization ofreheating fumaces. Scand. J. Metallurgy, 15, n° 10 (1986),p. 16-24.

(2) LEDEN (B.). STEELTEMP® : a program for temperatureanalysis in steel plants. Scand. J. Metallurgy, 15 (1986),p. 215-223.

(3) LEDEN (B.). Mathematical reheating furnace models inSTEELTEMP®. Proceedings of the International Conference Scanheating’85, MEFOS, Luleå (June 1985).

(4) JARL (M.), LEDEN (B.). Oxide scale formation on steel rnfuel fired reheating furnaces. Proceedings InternationalConference Scanheating’85, Paper No. 22, MEFOS, Luleå(June 1985).

(5) LEDEN (B.), RENSGARD (A.), KORTENIEMI (M.).Analysis of hot charging process for slabs by advancedsimulation program STEELTEMP® at Outokumpu Polarit’shot strip mill in Tomio, Finland. La Revue de MetallurgieCIT, n° 4 (1994), p. 541-548.

(6) LINDHOLM (D.), LEDEN (B.). A finite-element methodfor solution of the three-dimensional time - dependent heat- conduction equation with application for heating of steelsin reheating fumaces. Numerical heat transfer, Part AApplication, Vol. 35, n° 1 (January 1999).

(7) LINDHOLM (D.). Verification of the complex heatingmodel implemented in the three-dimensional finite-elementcode of STEELTEMP®. PROSIM-note 017/1997, Institutefor Energy Technology, Kjeller (September 1997).

(8) BOCCI (G.), SORESINA (R.), KLEVSJO (K.H.). New300-tlh reheat furnace at SSAB, Domnarvet. Iron and SteelEngineer, 52 (1985), p. 23-28.

(9) NORBERG (P.O.), LEDEN (B.). New developments of thecomputer control system FOCS-RF. Application to the hotstrip mill at SSAB Domnarvet. Proceedings of theInternational Conference Scanheating II, MEFOS, Luleå(June 1988).

Bo LEDEN was bom on the lOth of April 1944 in Lund,Sweden. He obtained his Master of Science in ElectricalEngineering 1967, Licentiate of Science 1971 and Dr. ofScience 1975 in Automatic Control, all at the Lund Instituteof Technology, Lund, Sweden. Since 1975, he has beenemployed at MEFOS and has been the project leader of thedevelopment of STEELTEMP® and the Furnace OptimizingControl Systems, named FOCS systems, for different typesof fumaces. Today, the FOCS systems are sold worldwideon a license basis by ABB Industrial Systems AB.

Dag LINDHOLM and Edvin NITTEBERG, Institute forEnergy Technology, Kjeller, Norway.


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