MEFOSMetallurgical Research PlantMeta! Working Research P!ant Date Our reference

1985-03-28 BTF85019Attended to by Your date Your reference

Revised 1993-02-08

MATHEMATICAL REHEATINGFURNACE MODELS IN STEELTEMP®

by

Tekn. Dr. Bo LedenMEFOS, Metal Working Research Plant

Box 812, S-95 1 28 Luleå, SwedenInternational Conference SCANHEATING ‘85, Luleå, June 1985

ASTRACT

STEELTEMP® is a finite-difference program for temperature and heat-transfer analysis duringteeming or continuous casting, cooling, stripping, heating, fiat rolling and open die forging.Temperatures and densities of heat fiow rate are caiculated in a cross section of the steel. Thisis assumed to be rectangular or circular. Composite structures as liquid steel in an ingot mould,billet on a ceramic hearth, ingot standing against a wall in a soaking pit, etc. can be analysed.Various heat balances, time and isothermal plots can be printed Out.

In the reheating furnace models the heating curve of the stocks and the oxide scale formationcan either be caiculated from the measured furnace temperatures or from the geometrical andthermal description of the furnace, fuel and air fiows, fuel and air temperatures, etc. Models forinduction heating of stocks for rolling are also available. The reheating furnace models havebeen evaluated against piot plant experiments made in the walking beam furnace at MEFOS,Metal Working Research Plant.

The program is used by a number of Scandinavian steelworks for production planning, processoptimization and process analysis in their own PC, workstations or main frame computers.

Mailing address Visitors’ address Phone Telex Fas Postal giro Bank accountMEFOS Arontorpsvagen 1 0920-55640 80482 MEFOS S +46-920 558 32 6 1800-9 758-6555Box 812 Luleå Int. +46-920 55640S-951 28 Luleå (Sweden)

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TABLE OF CONTENTS

NOMENCLATURE

1 INTRODUCTION 1

2 PROGRAM DESCRIPTION 12.1 General description 12.2 Input data 2

2.2.1 Group 0 22.2.2 Group 1 22.2.3 Group 2 22.2.4 Group 3 32.2.5 Group 4 32.2.6 Group 5 32.2.7 Group 6 42.2.8 Group 7 42.2.9 Group 8 4

3 MATHEMATICAL MODELS 53.1 Time dependant boundary conditions for stock 5

with neighbours (simple heating model)3.2 Stock heating in fuel fired furnaces (complex and 8

dynamical heating model)3.3 Induction heating of stocks for rolling 103.4 Oxide scale formation in fuel fired furnaces [4] 10

4 APPLICATION - BILLET HEATING IN THE WALKING 11BEAM FURNACE AT MEFOS, METAL WORKINGRESEARCH PLANT

4.1 Experiment 114.2 Pilot plant walldng beam fumace 124.3 Region and mesh division 144.4 Results from simple heating model 144.5 Results from complex heating model 16

5 ACKNOWLEDGEMENT 19

6 REFERENCES 20

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NOMENCLATURE

L~ inner length of zone k (m)

L~ inner width of zone k (m)

s gas layer thickness (average mean beam length (m)for gas-surface radiation exchange)

A area (m2)total envelope surface of stock (m2)

A~ total area of upper stock surfaces in zone k (m2)

A~ total area of inner walls and roof surface in zone k (ni2)

t time (s)

O temperature (°C)O temperature (K)

Am amount of fonned oxide scale on stock (kg)

ii~ mass flow rate (kg/s)

mass flow rate to control zone k (kg/s)= ~p / A density of heat flow rate (W/m2)

heat flow rate (W)

partial pressure of gas component x (atm)

p density (kg/m3)Cp specific heat capacity (JIkg°C)

mean specific heat capacity (0-0 °C) (J/kgoc)

h=c~~ 0 specific enthalpy (J/kg)

thermal conductivity (W/m0C)hscaie specific latent heat of oxide scale formation (JIkg)Hf net calorific value of fuel (J/kg)

Es emissivity of stock (-)emissivity of walls/roof (-)

Eg Eg (Og ~~Px~) emissivity of gas (-)Ags Ags (Og~ Os, 5Px~) gas absorptivity for radiation (-)

from stock

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Agw = Agw (Og~ O~, SP~~) gas absorptivity for (-)radiation from walls/roof

Agm = ½ (Ags+Agw) mean gas absorptivity for radiation (-)from stock and walls/roof

= 1-A~ mean gas transmissivity for radiation (-)between stock and walls/roofview factor between walls, (-)roof and stock respectively

Esw E [0,1] direct-exchange factor between (-)walls, roof and stock respectivelycorrection factor for flame radiation (-)mass leakage factor (-)(no leakage corresponds to 1=1)

Constants:

a = 5.6697.10-8 Stefan-Boltzmann’s constant (W/m2K4)linear constant in scale (kg/m2s)growth modelparabolic constant in scale (kg2/m4s)growth model

Indices:

a ambients surfaceg gasw wall

f fuel£ air

cw conduction through fumace wallcgs convection gas-stockleak leakage

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1 INTRODUCTION

In 1976 the development of a finite-difference program STEELTEMP® for temperature andheat-transfer analysis in steelworks commenced. It was realized that a tool was needed tosimulate several consecutive steel process operations accurately in order to be able to optimizethe total production in the work. First the program was developed for the teeming, cooling,stripping and heating operations in the ingot process. Later mathematical models for fiat rollingand open die forging were incorporated.

In the early eighties very sophisticated mathematical models describing the heating of stocksand oxide scale formation in fuel fired furnaces have been inciuded. Models for induction heating of stocks for rolling are also available. Using the program optimum stripping time, tracktime and heating practice can be achieved for the ingot process. Moreover, the interactionbetween the furnace and the rolling mill in, e.g. a hot strip mil can be analysed. Novel designconcepts as hot direct charging (HDC) and hot direct rolling (HDR) can also be analysedquantitatively.

The program can simpiy be implemented in the customers own PC, workstations or main framecomputers using the available input and output devices, including colour text and graphicsapplications. STEELTEMP® is today used by most Scandinavian steelworks for productionplanning, process optimization and process analysis.

The mathematical furnace models described are compatible to the on-line mathematical modelsin the fuel optimization control system for reheating furnaces FOCS-RF [1], installed all overthe world. Using these models carpet diagrams and delay strategy multiplier tables can becaiculated for different types of furnaces.

2 PROGRAM DESCRIPTION

2.1 General description

STEELTEMP® is a finite-difference program for temperature and heat-transfer analysis during:

• teeming or continuous casting• cooling• stripping• heating• fiat rolling• open die forging• water spraying.

Temperatures and densities of heat fiow rate are calculated in a cross section of the steel. Thisis assumed to be rectangular or circular. Composite structures as liquid steel in an ingot mould,billet on a ceramic hearth, ingot standing against a wall in a soaking pit, etc. can be analysed.Various heat balances, time and isothermal piots can be printed out.

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The numerical method used to solve the Fourier heat conduction equation is based on box integration and a frequency triangular split (F~S) method for space discretization and time integration respectively. Thermal data, (P’ Cp and ~), and other material quantities are assumed tobe piecewise linear functions of temperature given in tables stored in the material data base ofthe program. The latent heat of solidification H is included in the specific heat capacity Cp. Theprogram automatically adjusts the size of the time step up and down as the nonlinearities inboundary conditions and material parameters vary in order to optimize COmputatiOn time andcosts. A detailed description of the numerical method is given by Madsen [2].

STEELTEMP® is practical oriented and simple to use compared to general programs fortemperature and stress analysis.

2.2 Input data

Input data are divided into the following 9 groups:

Group 0 - Identification of jobGroup 1 - Production planGroup 2 - Geometrical descriptionGroup 3 - Material data descriptionGroup 4- Starting conditionsGroup 5 - Boundary conditionsGroup 6 - Integration and output dataGroup 7 - End of sub-caseGroup 8 - End of job.

Several cases can be run in one job. After specifying input data for group 0-7 of the first case,it is only necessary to specify input data for the groups in cases succeeding, where some para-meters should be changed. For the other groups input data already specified are used. If datagroup 4 is not specified, then the latest caiculated temperatures are used as initial temperaturesfor the next case. Each case is finished with data group 7, which starts the computations.

2.2.1 Group 0

This group is used for identification of the job.

2.2.2 Group 1

An event file of the stocks to be processed is given here.

2.2.3 Group 2

In this group the geometry of the structure, the region and mesh division are specified. Different materials can be used in the different parts of the structure, a doser mesh division can begenerated near the surface of the structure, etc.

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2.2.4 Group 3

Using a neat overlay technique the types of material are specified for the different regions ofthe structure. The emissivities of the used materials are also specified.

In the material data base of the program thermal data, (P’ Cp and ?~.), of steels, moulds, ceramicmaterials, oxide scale, air, fiue gases are stored. Moreover, yield stresses, resistivities, relativepermeabiities and oxide scale growth parameters are available for the steels, volume coefficient of expansion and thermal diffusivity for air, viscosities, etc. for air and the fiue gases.

The user can introduce his own material data for the structure and list out the whole materialdata base.

2.2.5 Group 4

This group is used to specify the initial temperatures of the structure. These can be read froman input or a permanent file. A neat overlay technique is used to specify the temperatures in thedifferent materials and/or regions of the structure.

This group can also be used to remove certain paris of the structure at a given time, e.g. whenstripping the ingot mould.

2.2.6 Group 5

In this group the boundary conditions of the structure are specified. In order to simplify theinput data specification the following cases are distinguished:

• time dependant boundary conditions for stock with neighbours• heating in rectangular top-fired furnaces, rectangular top- and bottom-fired furnaces, circu

lar top-fired furnaces, heating in induction furnaces with power concentrated to the surfaceof the stock or distributed over the power penetration depth

• oxide scale formation in fuel fired fumaces• fiat rolling and open die forging.

The very essence of the input data specification is the specification of the time dependantboundary conditions, which are an integral part of the specification for all other cases.

An overlay technique analogous to the one for the material data group can be used to specifythe boundary conditions of the different sides or parts of sides for the structure.

It is also possible to copy the boundary condition specification from one time interval toanother. Using the overlay technique the boundary condition description can be modified afterthe copying. The procedure is illustrated in Fig. 2.1.

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Time interval 1 2 3 NALFASide 1 2 341234123 4 1 2 3 4Region 1—3 1—3 1—3 1—3

Boundary condition copying

[J Modification of boundaryconditions on side 3, regions 1-3

Figure 2.1 - Illustration of boundary condition copying and overlay technique inSTEELTEMP®.

2.2.7 Group 6

In this group integration and output data are specified. The user specifies desired computational accuracy, minimum and maximum integration step, stripping and integration time.

The user is recommended to print out the temperature distribution in the whole structuretogether with an isothermal and a time plot.

Moreover, the user can print:

• physical constants and the material data base• frequencies of the temperature change• intemal and external densities of heat flow rate• bo dary condition parameters for each mesh on the sides of the structure• various heat balances.

2.2.8 Group 7

This group is used to specify the end of the sub-case and to start the computations.

2.2.9 Group 8

This group is used to specify the end of the job.

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3 MATHEMATICAL MODELS

3.1 Time dependant boundarv conditions for stock with nei~hbours (simple heating model)

Time dependant boundary conditions for stock with neighbours are specified according to:

• number of time intervals• points of time for changes in the boundary conditions• indices for distances to surrounding objects in the time intervals• distances from stock to surrounding objects in the time intervals• boundary conditions in the time intervals• flue gas compositions in the time intervals• radiation with time dependant flue gas bias in the time intervals• free-stream velocities and characteristic length of forced convection heat-transfer process

in the time intervals• linear variation of boundary temperature, heat-transfer coefficient and/or gas layer

thickness in the time intervals.

In the program the following boundary conditions are implemented:

1 = radiation2 = gas and wall/roof radiation3 = natural convection4= forced convection6 = given boundary temperature7 = given heat-transfer coefficient and boundary temperature8 = stock in a fumace9= symmetry axis.

Besides these single codes 1-9 codes in pair can be used. For instance, the codes 13 and 31correspond to the composite heat-transfer mechanism radiation plus natural convection.

The fact that simple codes can be used to specify the boundary conditions essentially simplifiesthe input data specification. This is illustrated with an example dealing with stock heating in arotary hearth furnace. In order to be able to accurately model the heat conduction from the hothearth to the cold stock just after the stock has been charged into the furnace, the ceramichearth is included in the structure. In this example view factors, gas layer thicknesses andradiation exchange factors are automatically calculated for the different sides of the stock fromthe specification of the geometrical location of the stock, the flue gas composition andwall/roof temperatures along the furnace. These data are readily available to the user. Structureand boundary conditions for the case are shown in Fig. 3.1.

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Side 4

Gas, wall androof radiation.

Side 1

Notations: 09 gas temperature= wall temperature

0a = ambient temperature

Legrit 135

Figure 3.1 - Structure and boundary conditions for a stock on a ceramic hearth heated in arotary hearth furnace.

For caiculation of the density of heat flow rate to the stock from the flue gases (CO2, H20 andS02), walls and roof the following mathematical models are used:

aes~Pg,s = 1— (lEs)(1—Ags) (eg €~ Ags

and

c~e~ ft3~~ — ~4’)“ w

(3.1)

(3.2)

The caiculation of the gas emissivity Eg Eg (eg~ SP~~) and absorptivityAgs Ags (Og~ O~, spx~) as a function of the gas temperature eg. the stock surface temperaturee5, the gas layer thickness s and partial pressures p,~ of CO2, H20 and S02 is based on analytical expressions given by Schack [3]. The gas radiation from S02 is inciuded in the C02-ra-diation by adding the partial pressure of S02 to the one for CO2.

Y

Steel

Oxide

Resistit 80K Side 3

Code 13(Oa shouldbe given).

RGO.6

X Side2

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The direct-exchange factor between the walls, roof and stock respectively is given by

Esw EsEw~gmP5~+I~sw (3.3)

where &~ is a correction factor for flame radiation.

The mean transmissivity of the gas is caiculated from

iitgmlAgm, Agm~ji~Ags+Agw) (3.4)

where A~ is the mean gas absorptivity for radiation from the stock and walls respectively.

The view factor ~ is obtained from

N 1E.E3~, f3~=—(sinF3~—sin~3k) (3.5)

k=1 2

For blooms on a plane hearth the caiculation of the angle ~3j~ and ~k is illustrated in Fig. 3.2.

In the program the view factor ~ is automatically caiculated from the geometrical locationof the stocks and the shape of the furnace.

= = = 900

_900

~!rTFigure 3.2 - Blooms on a plane hearth illustrating the caiculation of view factors (N=1).

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3.2 Stock heating in fuel fired furnaces (complex and dvnamical heating model)

Input data to the mathematical model are:

• number of top, bottom and control zones and rows of stock in the furnace• position of first and last stock in the furnace• mean thicknesses of the different linings of the furnace walls• material codes for the refractory linings• ambient temperature and emissivity for the outer furnace walls• mass and gas leakage factors and other heat losses in the zones• types and dimensions of the different fumace zones, (dark or burner zone, plug flow or

weil stired zone, top- or top- and bottom-fired zone, etc.)• initial temperatures for the inner linings of the furnace walls in the zones• number of stocks, stock dimensions, pitch between stocks, material code and initial

temperature of stocks and drop-out interval of the lot (only complex heating model)• an event file of the stocks to be heated given in input data group 1 (only dynamical heating

model)• net calorific values and mean specific heat capacities for the fuels to the control zones• number of table values for storage of time dependant fuel inputs (only dynamical heating

model)• points of time for changes in the fuel inputs (only dynamical heating model)• fuel and air flows to the control zones in the time intervals• do. for the fuel and air temperatures in the time intervals.

Using input data for time dependant boundary conditions the distances to neighbouring stocks,boundary condition codes, flue gas composition, emissivity of inner furnace walls, the freestream velocity of the flue gases and the characteristic length of the stocks are specified foreach zone. In input data group 3 the emissivity of the stocks is specified.

In the mathematical model the furnace is divided into dark and burner zones. By definition nofuel is supplied to a dark zone. In a weil stirred zone the gas temperature is assumed to beconstant. Each furnace zone is in its tum divided into a number of isothermal subzones. Thestocks and the furnace walls are assumed to be grey and diffuse bodies. Moreover, the heatconduction in the fumace wall is presupposed to be stationary.

Using the mathematical models for radiation heat exchange between gas-stock (3.1), gas-wall(3.12) and wall-stock (3.2), the prevaiing mass transport and mass leakage, etc. in the furnaceand supplied fuel and air flows, etc., the following heat balance is obtained for each subzone

Øf + ~ + ~Pg~ + ~sca1e + l~ieaic 4~s ~ ~Pw + (3.6)

where

~Pg,s + øw,s + øcgs (3.7)

~Pg,w ~ øs,w ~Pcw (3.8)

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= Hf rnf + cpføfrnf (3.9)

= h~rh~ (3.10)

(Pg = hglilg, mg0~~ = rng~~+ Ifif + ‘~‘e +(‘q —i)~(ii4~ + ii~). (3.11)

The density of heat flow rate to the walls from the gas is given by:

— ( 4 4•~ A~+(1—ew)(L~L’~—A~) /(i—e~)~Pg,w — G~Eg9g AgwGw~ + a Ak

r~W

(eg(1_Es)(1 — Agm)G~ — Agw(1 . — Agm)O~j) (3.12)

To account for gases leaking in or out from the furnace a mass leakage factor ~ is used. Thisfactor gives the mass flow rate of leaking gas relative to the total amount of fuel and air flowsupplied to the furnace. The gas leaking in and out from the furnace is assumed to have thesame temperature as the environment 0a and the flue gas eg respectively. The heat flow ratesupplied or disposed in each zone is given by

~ r1≥1

øleak = (3.13)

(111)~p øg~(ii4(+ii4), T1<1g k

From the heat balance (3.6) the gas temperature is solved iteratively and from it the heat flowrates ~Pg,w and ~ and then by a new iterative procedure the wall temperature fulfilling(3.8) is obtained for each subzone.

During this procedure the stock temperatures along the furnace are kept constant. Integrationbackwards and forwards along the furnace finally gives the stock, gas and wall/roof temperatures.

A method to solve the so-called inverse heating problem is inciuded in the model. The methodmakes it possible to caiculate the required furnace temperatures and fuel flows to the controlzones from the given stock heating curve, fuel-air ratios and the input data given above. Fromthe given stock heating curve and estimated values of the fuel flows the gas and wall/rooftemperatures are solved from the heat balances (3.6) and wall balances (3.8) for the controlzones. By an iterative procedure the furnace temperatures and fuel flows satysfying the heatbalances (3.6) and wall balances (3.8) for the control zones are finally obtained.

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3.3 Induction heating of stocks for rolling

Input data to the mathematical model are given below:

• number of control zones in the furnace• stock intake times in the control zones• numbers of coils and coil turns per coil in the control zones• effective lengths and center-center distances between coils, etc. in the control zones• coil currents, coil frequencies, coil thermal efficiencies and magnetic flux leakages between

coils in the control zones.

In the mathematical model the supplied power can be concentrated to the surface of the stockor exponentially distributed within the power penetration depth. To describe the radiation exchange between the stock and the ceramic lining the time dependant boundary conditions forstock with neighbours are used, (cf. section 3.1).

3.4 Oxide scale formation in fuel fired furnaces [41

Separately or simultaneously with the computation of the stock heating curve in a fuel firedfumace the amount of formed oxide scale can be caiculated as a function of time by specifyingthe following (additional) input data:

• type of steel• type of furnace atmosphere• velocity of gas flow near the stock• characteristic length of the stock• partial pressure of oxygen in the flue gases.

A mathematical mode! which describes a combination of linear and parabolic scale growth isused in STEELTEMP®. The model contains a linear constant Ke , which describes the diffusion of oxygen through the atmosphere boundary layer surrounding the stock and the oxidationwith CO2 and H20, and a parabolic constant K~ , which describes the diffusion of the Fe2~iron ions through the growing wilstite layer in Ihe scale, according to

1 (Am2~ 1 (Am~—I I+—I — I~t (3.14)K~l~ A~ ) K~~A~)

The oxide scale formation gives rise to the heat flow rate

A(Am)øscale — hsc~e At (3.15)

where hscale is the specific latent heat of oxide scale formation.

The model has been adjusted to experimental data from 8 different steels in two differentfumace atmospheres, (propan and heavy ou).

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4 APPLICATEON - BILLET HEATING IN THE WALKING BEAMFURNACE AT MEFOS, METAL WORKING RESEARCH PLANT

4.1 Experiment

In order to achieve steady-state fumace conditions two fumace fillings of stocks were firstfeeded through the furnace. Thereafter the test billet supplied with a trailing thermocouple wascharged. The thermocouple was applied in a hole, driled from below to 30 mm depth from thetop surface, and nailed along one side of the billet. The test bilet was followed by 2 accuratelyweighed bilets. Then an additional 5 bilets were charged after which 2 accurately weighedbilets were charged again. Bilets were then charged into the furnace until the last chargedweighed billet was discharged.

The test conditions are summarized below:

Steel: lOOxlOOxl500 mm, type St 37Pitch: 163 mmInitial stock temperature: 20 °CFuel: Heavy ou Eo5 (1.30 weight % S)Drop-out interval: 2 min 00 sFurnace atmosphere: 3 vol % 02Control zone temperatures: 1040 - 1235 - 1235 °C.

In Table 4.1 the recorded wall and roof temperatures, waste gas temperature and the amountof oxide scale formed during the trial are shown.

Table 4.1 - Wall and roof temperatures, waste gas temperature and amount of formed oxidescale during the trial (No. 14).

Zone 1 Zone 2 Zone 3 Zone 4

Wall temperature [ °q -- 1040 1234 1234Roof temperature [ °Cj 828 1061 1245 1258

Waste gas temperature: 692 °CAmount of formed oxide scale: 1.5 kg or 1.33 %

During the trial the furnace was fired with heavy oil Eo5 with 1.30 weight % sulphur. The netcalorific value and the mean specific heat of the fuel are

Hf = 42 200 kJ/kg

Cpf = 1 840 J/kg °C

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The flue gas composition used in the caiculations is

(CO2) = 12.4 vol % , (02) = 3.0 vol %(H20) = 9.9 vol % , (N2) = 74.55 vol %(S02) = 0.15 vol %

In Table 4.2 the recorded fuel flows and fuel temperature, combustion air flows and combustion air temperature and atomizing air flows and atomizing air temperature are put togetherfor the trial.

Table 4.2 - Fuel and air flows, fuel and air temperature recorded during the trial (No. 14).

Control Control Controlzone 1 zone 2 zone 3

Fuelfiow [kg/hl 36.0 48.6 31.3Combustion air flow [m3n/h] 581 650 405Atomizing air flow [m3n/h] 7 7 7

Fuel temperature: 106 °CCombustion air temperature: 250 °CAtomizing air temperature: 45 °C

A considerable air infiltration occurs through the charge door, (T11=1.01), and the dischargedoor, (r14=1.12), despite the fact that the furnace pressure is as high as 1.0 mm H20. Theemissivities of the stock and walls/roof are assumed to be a~ =0.8 and ew =0.9 respectively.

4.2 Pilot plant walking beam furnace

The design of the furnace body is such that 3 weil defined temperature control zones have beenobtained. Each control zone has two side fired burners. The zones are thermally separated bybaffels. The furnace is made up of 1 dark zone and 3 burner zones.

The fixed hearth is equipped with two 200 mm high ridges, one on each side of the walkingbeam. In this way, the heating of the biliets occurs from all sides.

For accurate control of the temperature and the atmosphere (02-content) in each control zonethe furnace is equipped with a local Honeyweii TDC 2000 burner control system with loggingfacilities. In Fig. 4.1 a longitudinal cross section of the fumace, indicating geometrical data andlocations of the indicating and controlling thermocouples for temperatures, is shown.

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Side view of the walking beam furnace

Figure 4.1 - Side view of the walldng beam furnace, showing geometrical data and locationof indicating and controlling thermocouples for temperatures, at MEFOS, MetalWorking Research Plant.

A schematic figure of the furnace wall lining, indicating thicknesses and thermal data at a fixedtemperature for the different ceramic materials, is shown in Fig. 4.2. The caiculations are madeunder the assumption that the wall and roof linings in the whole furnace are identical and equalto the lining in Fig. 4.2.

Outer side of furnace wall Thermal data

[°C] [kg/m31 [J/kg °C] [W/m °C]

135 Block-Mix (90 mm) 400 310 950 0.09mm Insblock-19 (45 mm)

100 G-20 (50 mm) 870 670 1 290 0.33mm G-23 (50 mm)

210 Kast-O-Lite 30 1 1 0 1 3 0 1 4 0 0.50mm

Figure 4.2 - Schematic figure of furnace wall lining, indicating thicknesses and thermaldata at a fixed temperature, for the different ceramic materials.

•Control zone 3—..-[.-Control zone 2—.~ -~ Control zone 1Bumer zone 4 Bumer zone 3 Burner zone 2 Dark zone 1

2.450 2.100 1.750 2.700

TC

Notations: TI = indicating thermocouple (roof and waste gas llue temperature)TC = controlling thermocouple (wall temperature)

5 mm plate casing

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4.3 Region and mesh division

During the heating the largest temperature gradients occur near the stock top surface. Therefore, a doser mesh division should be used here. In this case, since the cross section of thestock is relatively small, it suffices to divide each region into one or two meshes. Region andmesh division is given in Fig. 4.3.

0.Symmetryaxis

0.030

Side 4

0.070

0.100

x

Side 1

0.030 0.050

Figure 4.3 - Region and mesh division for a lOOx 100 mm stock.

4.4 Results from simple heating model

In the simple heating model the heating curve of the stocks is caiculated from the recordedthermocouple signals for the wall and roof temperatures and waste gas temperature. For simplicity the wau/roof temperature is assumed to vary linearly between the waste gas flue and thethermocouple recording the roof temperature in the dark z’one and, further onto burner zone 2,and to be constant and equal to the measured wall temperature in the burner zones. The gastemperature is assumed to vary in the same way as the wall/roof temperature.

The caiculated heating curve is in good agreement with the measured one of the test billet ascan be seen from Fig. 4.4. The maximum temperature deviation between these curves is 49°Cand occurs in burner zone 3. The assumption made on the temperature profile in the zonesstrongly affects the heating curve of the stocks.

Y

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Drop-out interval 2 min 00 s

~—____

~ ~~

:::z_1’_

1 2 3

z

4 5 6 7 8 9[m]1 1 1

0 20 40 60 80 100

Figure 4.4 - Caiculated and measured temperatures when heating lOOxlOOxl500 mmSt 37 low carbon steel to 1235°C in the wallcing beam furnace at MEFOS,Metal Working Research Plant using the simple heating model.

[Cj 0

1 200

1 000~

800 -

fl

0-

—0-- /1 1~-z

7

/

/fp

200

Gas and wall temperatures:Ø measured waste gas flue temperatureØ measured wall temperature

—~— gas temperature—o— wall temperatureStock temperatures:—+— measured temperature

(30 mm below the top surtace)—X— calculated temperature

(I~ 0~’0calculated 0measured)

/1J

01~0 [min]

2.700 4.450 .55 9.000[m]

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In the fuel optiniization control system for reheating fumaces FOCS-RF [1] the furnace temperature profile can be automatically generated from the recorded thermocoupie signais in thedifferent zones using a simple specification for the type of furnace profile (constant or linearcontinuous profile) for the zones.

4.5 Resuits from complex heating model

In the complex heating model the heating curve of the stocks, the gas and wall/roof temperatures in the furnace are caiculated from the geometrical and thermal description of the furnace,fuel and air flows, fuel and air temperatures to the control zones, etc. The gas temperature isassumed to be constant in the burner zones (weil stirred) in this particular example. The heat ofoxidation from the scale formation is inciuded in the caiculations.

The caiculated temperatures are in good agreement with the measured heating curve of the testbilet, the measured inner wall temperatures in the burner zones, the measured roof temperature in the dark zone as shown in Fig. 4.5. The maximum furnace temperature deviationappears in burner zone 4 and reaches 39 °C. The maximum deviation between the measuredand caiculated billet temperatures reaches 37°C and appears in the beginning of burner zone 3.

The scale loss for the different positions aiong the furnace, caiculated from the measured stockheating curve using the modei (3.14), can be found in Jarl and Leden [4].

In Table 4.3 the heat flow rates involved can be studied in detail for the furnace. This tableshows that the major part of the heat flow rate generated in burner zone 4 is transported withthe flue gases to bumer zone 3 and 2 and further onto dark zone 1. The air infiltration, occuring through the discharge door, significantly contributes in this heat transportation. Only aminor part of the heat flow rate in burner zone 4 can be absorbed by the stocks, since theyhave almost reached their final temperature as they enter this zone. In dark zone 1, burner zone2 and 3 approximately the same amount of heat flow rates are absorbed by the stocks.

From Table 4.3 the total heat flow rate balance for the furnace, shown in Fig. 4.6, can be abtained. From this figure it can be seen that the heat of oxidation corresponds to 4 % of the totalfuel heat input. In the recuperator 23 % of the heat flow rate in the waste gases is recovered,corresponding to a combustion air temperature of 250 °C. The efficiency (ratio between heatto steel and heat supplied with the fuel) of the furnace is 63 %.

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Drop-outinterval2minOOs

.0 [m]

[mg/cm2]

Figure 4.5 - Caiculated and measured temperatures when heating lOOxlOOxl500 mmSt 37 low carbon steel to 1235 °C in the wallcing beam furnace at MEFOS,Metal Working Research Plant using the complex heating model.

1

1

2.700 4.450 6.550

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Table 4.3 - Heat flow rates in the zones of the walking beam furnace at MEFOS,Metal Working Research Plant (trial no. 14).

Heat flow rate Zone 1 Zone 2 Zone 3 Zone 4 Disposed heatflow rate

Ø~j~ [kW] 667 754 366 0

øgout [kW] 666 936 754 366 666

~g,s [kW] 151 170 142 28

øg,w [kW] 115 121 120 31

~ [kW] 111 116 112 23

cp~ [kW] 3 5 8 8 24

øloss [kW] 5 5 5 5 20Subtotal [kW] 674 12 15 17 710

cp’ [kW] 124 127 115 24 390cp2 [kW] 20 16 15 3 54cp3 [kW] 53 70 65 13 201cp4 [kW] 59 67 56 13 195cp5+6 [kW] 6 6 6 1 19cptot [kW] 262 286 257 54 859

Total disposedheatflowrate [kW] 936 298 272 71 1569

Supplied heatflow rate

cpf [kW] 0 424 572 369 1365~e [kW] 0 53 60 38 151

~leak [kW] 0 0 0 2 2øscale [kw] 0 1 26 24 51

Total suppliedheat flow rate [kw] 0 478 658 432 1569

-19- BTF85019

Oxidation heat andair infiltration heat

Heat lossesthroughfurnace wallsand other heatlosses

Heat of ou Heat of combustion air

Figure 4.6 - Total heat flow rate balance (kW) for the wallcing beam furnace atMEFOS, Metal Working Research Plant (trial No. 14).

5 ACKNOWLEDGEMENT

The financial support by the National Swedish Board for Technical Development (STU) undercontract 78-5264 is appreciated.

The work has been performed in collaboration with the Institute of Energy Technology (IFE)in Norway. In particular E. Madsen and E. Nitteberg have been involved in the project.

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6 REFERENCES

[1] Leden, B.: “A control system for fuel optimization of reheating furnacesu, Scand. JMetallurgy 15(1986), No. 1, pp. 16-24.

[2] Madsen, E. E.: “Some frequence exponential methods for numerical solution of heatconduction problems”, Proceedings Conference Numerical Methods in Heat Transfer,University of Wales, Swansea, John Wiley & Sons, pp. 8 1-89, July 1979.

[3] Schack, K.: “Berechnung der Strahlung von Wasserdampf und Kohlendioxid”, ChemieIng. Techn., Vol. 42, No. 2, Jan. 1970, pp. 53-58(also in VDI-Wärmeatlas, Berechnungsblätter fUr den W~rmetibergang, 2:nd ed.,VDI-Verlag GmbH, Dtisseldorf, 1974, pp. Kc3-Kc4).

[4] Jarl, M. and Leden, B.: “Oxide scale formation on steel in fuel fired reheating furnaces”,Proceedings International Conference SCANHEATING ‘85, Paper No. 22, MEFOS,Luleå, June 1985.