The Temperature Field Measurement of Billet Based on Multi-Information Fusion

Ma Jiaocheng1,+, Liu Jun2, Yang Qiang1 and Chen Liangyu1

1School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110004, China2School of Nuclear Engineering and Geophysics, East China Institute of Technology, Nanchang 330013, China

In the continuous casting process, the internal temperature of billet is difficult to be measured and the surface temperature of billet is alsodifficult to be measured accurately. The steady-state heat transfer models can only be used for simulating the steady-state casting operations inoff-line. For better control over the whole continuous casting cycle, recently more attention have been paid to developing real-time heat transfermodels which are valid under casting condition varying frequently. Considering the heat transfer coefficient is the precondition of solving themodel, and it is difficult to be measured directly. An identification method of heat transfer coefficient based on genetic algorithm was developed.According to the measured temperature and shell thickness, the heat transfer coefficient of each spray zone was determined. In order to test thedynamic performance of the real-time heat transfer model, the surface temperature was measured using the CCD (charge coupled device)temperature measurement system, which can effectively eliminate the impact of the scales on the billet surface and keep the fluctuation of themeasured surface temperature within the range of «10°C. The temperature field measurement of billet was realized by the multi-informationfusion of CCD temperature measurement system, measured shell thickness and data acquisition system. This provides the possibility to improvethe existing cooling system based on the feed-back control considering the measured surface temperature. [doi:10.2320/matertrans.M2014055]

(Received February 18, 2014; Accepted May 19, 2014; Published July 25, 2014)

Keywords: continuous casting, heat transfer coefficient, charge coupled device, measured temperature

1. Introduction

In the continuous casting process, the internal defectswhich can be formed in cast material are due to inappropriatecasting operation and improper secondary cooling waterdistribution.1) In order to eliminate these defects, the billetsolidification process must be controlled.2­4) The presence ofsteam within the spray chamber and the formation of scalesrandomly on the billet surface render the impracticable ofcontinuous direct temperature measurements.5,6) Many heattransfer models have been developed and used to optimizethe secondary cooling process.2,7) But these heat transfermodels can only be used for simulating the steady-statecasting operation in off-line. In the actual production, due tothe impact of equipments, processes and actual productionconditions, etc., the process parameters are fluctuantfrequently, such as superheat, casting speed and secondarycooling water,8) more attention have been paid to developingreal-time heat transfer models which are valid under dynamiccasting conditions. However, the heat transfer coefficient ofeach spray zone as the precondition to solve the models isdifficult to be measured directly. The empirical heat transfercoefficient to be obtained in specific conditions will lead tothe large deviation in the application. Therefore, the heattransfer coefficient must be identified before the modelapplication. In order to identify the heat transfer coefficient,the shell thicknesses and surface temperatures of billet underdifferent conditions were measured and the optimizationalgorithm of identification the heat transfer coefficient wasdeveloped. The surface temperatures of billet were measuredusing CCD measurement system. The high-resolution CCDcamera can eliminate the effect of scales on the billet surface.The temperature field measurement of billet was realized bythe multi-information fusion of CCD temperature measure-ment system, measured shell thickness and data acquisitionsystem, which provides the possibility to improve the

existing cooling system based on the feed-back controlconsidering the measured surface temperature.

2. Real-Time Heat Transfer Model

The mathematical heat transfer model is used to describethe heat transfer and solidification process of billetcontinuous casting. Compared to the heat transfer in thelateral direction, the heat transfer in the casting direction canbe ignored due to high energy, low conductivity and highcasting speed of the steel. Thus it can be described by thetwo-dimensional non-steady state solidification equation asfollows:2,3,7)

µc@T

@¸¼ @

@xk@T

@x

� �þ @

@yk@T

@y

� �þ S ð1Þ

where T, ¸, k, c, µ and S represent billet temperature, time,thermal conductivity of steel, specific heat capacity of steel,density of steel, latent heat, respectively.

To solve the model, taking into account the billetsymmetry, only a quarter of the billet section is calculated.The grid division and boundary conditions for the cross-section of the billet are shown in Fig. 1. The P is the controlvolume, and w, e, n, s are the correspondence interfaces. Inthe time interval (t, t + "t), eq. (2) is obtained by finitevolume method and the discrete equation group of completeimplied format is formulated.9)Z n

s

Z e

w

Z tþ�t

t

µc@T

@tdtdxdy

¼Z tþ�t

t

Z n

s

Z e

w

@

@xk@T

@x

� �dxdydt

þZ tþ�t

t

Z e

w

Z n

s

@

@yk@T

@y

� �dydxdt

þZ tþ�t

t

Z e

w

Z n

s

Sdxdydt ð2Þ+Corresponding author, E-mail: majiaocheng@163.com

Materials Transactions, Vol. 55, No. 8 (2014) pp. 1319 to 1323©2014 The Japan Institute of Metals and Materials

(1) Initial condition:

T ¼ T0 ð3Þ(2) Boundary condition:

Mould zone:

� k@T

@n¼ a� b

ffiffit

pð4Þ

Secondary cooling zone:

� k@T

@n¼ hðT � TwarÞ þ ¾·ðT 4 � T 4

airÞ ð5Þ

Air cooling zone:

� k@T

@n¼ ¾·ðT 4 � T 4

airÞ ð6Þ

where T is the billet temperature, T0 is the pouringtemperature, a and b are the constants, t is the residencetime of liquid steel in the mould, Twar is the cooling watertemperature, Tair is the air temperature, ¾ is the emissivity, · isthe Stefan-Boltzman constant, S is the latent heat, n is theexterior normal of cooling boundary.

The heat transfer coefficient h is calculated by thefollowing equation:10)

h ¼ 1570w0:55ð1� 0:0075TwarÞ¡

ð7Þ

where h is the heat transfer coefficient (W/m2/K), w is thewater flow density (L/m2/s), Twar is the cooling watertemperature, ¡ is the machine-dependent calibration factor ofeach spray zone.

In order to calculate the real-time temperature field of billetin actual casting process, the casting process parameters mustbe gathered in real-time. The time interval of sampling mustbe very short enough so that the data can be updated in atimely to accurately reflect the transient variation of the billettemperature field. At the same time, the interval time must belonger than the model calculation time and has certainmargin. Therefore, the acquisition time of process parametersmust be determined according to the caster machine.

3. Surface Temperature Measurement and HeatTransfer Coefficient Identification

The accuracy of real-time heat transfer model is critical tooptimize secondary cooling water dynamically to control theshell thickness, the liquid pool depth, and the temperatureof straightening point, therefore the real-time heat transfermodel must be revised and validated before application. Thedevelopers validated the model by measuring the shellthickness or surface temperature in different locations of thebillet, but the thickness measurement cannot realize the real-time measurement for the billet. Therefore, in this paper, themodel correction was carried out by means of measured billetsurface temperatures, as well as a few measured shellthicknesses under steady-state condition.

The temperature measured by traditional infrared ther-mometer which is single-point measurement fluctuates up to100°C under the impact of scales generated randomly, whilethe average filter used to eliminate temperature fluctuationcauses the measurement lag and deviations.11) In this study,the CCD measurement system was developed to measure thesurface temperature of billet. Figure 2 shows the systemstructure of the CCD measurement system. With the high-resolution CCD camera,12,13) subtle change within the rangeof 1mm diameter on the billet surface can be detected, andthe surface temperature of billet can be detected from the gapbetween the scales, effectively overcoming the effect ofscales.

Model correction is important to ensure the accuracy oftemperature field. The heat transfer coefficient of each sprayzone is difficulty to be measured directly. The empirical heat

X

Y

= 0x

Tk

0=y

Tk

x

Tk = −q

qy

Tk −=

Axis of symmetry

Pw en

s

Fig. 1 The grid division and the boundary conditions for the cross-sectionof the billet.

Bill

et

CCD camera

Infrared thermometerSoft measurement of billet

temperature field

Real-time heat transfer model

Heat

Am

plitu

de

corr

ectio

n

Pos

ition

ig

Com

bine

d

measured shell thickness

Fig. 2 Structure of the CCD measurement system.

M. Jiaocheng, L. Jun, Y. Qiang and C. Liangyu1320

transfer coefficient to be obtained in specific conditions willlead to the large deviation in the application. Therefore, forthe application of model, the calculation results of modelmust be consistent with the measured ones by identificationthe heat transfer coefficient. In this paper, the heat transfercoefficients were identified with genetic algorithm. Theparameter ¡ of each spray zone was identified by themeasured surface temperature and shell thickness of billet.

Considering the measurement error of shell thickness andsurface temperature, the constraint conditions were as follows:

(1) The error of measured and calculated shell thicknessmust be limited to within the range of 2mm.

jHcal �Hmeasj � 2 ð8Þ(2) The error of measured and calculated temperature

must be limited to within the range of 10°C.

jT cal � Tmeasj � 10 ð9ÞThe objective was to minimize deviation of the measured

and calculated values as a function of the heat transfercoefficients and two constraints of measured shell thicknessand temperatures, and the F(¡) was the objective function.This is achieved by carrying out a series of simulationsperformed by the heat transfer model. The optimizationprocess using the penalty function method:

Fð¡Þ ¼Xni¼1

jHcali �Hmeas

i jHmeas

i

wHi

þXmi¼1

jT cali � Tmeas

i jTmeasi

wTi þ Pð¡Þ ð10Þ

where wiH, wi

T is the weight of the criterion. P(¡) is thepenalty function.The genetic algorithm2) applied for the parameter identi-

fication in continuous casting consists of:Step 1: generation an initial population of results simu-

lated with input parameters of process (nominal);Step 2: compute the billet surface temperature and shell

thickness of setting points and the objectivefunction;

Step 3: modify heat transfer parameters in each regionwhere the constraint was violated;

Step 4: the generation of new results;Step 5: compute the billet surface temperature and shell

thickness of setting points and the objectivefunction;

Step 6: if objective function decreased, then the result isF(¡);

Step 7: if F(¡) ¼ 0 end, and output the parameters ofeach sprays zone; otherwise go to step 2.

4. Results and Discussion

The real-time model was based on an actual caster in asteel plant. The caster radius is 10m. The secondary coolingis spread over three zones, and each zone is independentlycontrolled through control valves to regulate the flow ofwater to the spray nozzles. The parameters of caster andthermal physical properties of Q235 steel used in calculationwere shown in Tables 1 and 2, respectively.

In the casting process, the fluctuation of superheat ofmolten steel causes frequently change of the casting speedand secondary cooling water. In order to research thedynamic temperature field of billet under varying castingconditions, the surface temperature was measured continu-ously at the secondary cooling zones. Figures 3, 4 and 5show the field application of CCD temperature measurementsystem, the CCD image of billet surface and surfacetemperature distribution of billet, respectively. It can be seenfrom Fig. 4 that the scales generated randomly on the surfaceof billet lead to measured temperature fluctuation. In order toreduce or even eliminate the temperature fluctuation, therectangle area at the measured point was divided intomany small grids (the size of each small grid size is1mm © 1mm). The average temperature of each grid wasregarded as the center point of grid. The surface temperaturegradient of billet is very little in the withdrawal direction, soit was assumed that the temperature at measured pointneighborhood doesn’t change in the withdrawal direction andthe max temperature of grid of each column was near theactual temperature of correspondence grid of measured pointtransverse. The temperature of measured point can beobtained by the curve fitting of max temperature of eachcolumn. This peak filtering method can effectively reduce oreliminate the impact of scales on the temperature measure-ment and keep the measured surface temperature fluctuationwithin the range of «10°C. Figure 6 shows the comparisonof measured temperatures between CCD measurementsystem and infrared single-point measurement system.Traditional temperature measurement method which adoptsinfrared single-point measurement technique can cause thefluctuation of measured temperature up to 100°C. The newCCD measurement system and its peak filter method used in

Table 1 Geometry of the billet caster.

Parameter Value

Section size (mm) 150 © 150

Mold length (m) 0.85

Spray zone lengths (m)

zone 1 0.32

zone 2 1.95

zone 3 5.69

Table 2 Thermal physical properties of Q235 steel.

Parameter Value

Liquidus temperature (°C) 1515

Solidus temperature (°C) 1485

Specific heat of liquid steel (kJ/kg/K) 0.84

Specific heat of solid steel (kJ/kg/K) 0.67

Density of liquid steel (kg/m3) 7000

Density of solid steel (kg/m3) 7600

Heat conductivity of liquid steel (W/m/K) 34.0

Heat conductivity of solid steel (W/m/K) 29.4

Heat of fusion (kJ/kg) 270

Emissivity 0.8

The Temperature Field Measurement of Billet Based on Multi-Information Fusion 1321

this study can effectively eliminate the impact of scales andkeep the small temperature fluctuation.

The real-time heat transfer model was revised by measur-ing the shell thicknesses and surface temperatures in differentlocations of the billet. The shell thickness was measured byusing shooting nails, which include FeS, whose solutedistribution has a very significant difference when sulfurelement diffuses between liquid and solid.14) So the shellthickness can be gained at the shooting nails position by thesulfur print. The shell thicknesses and temperatures wereshown in Tables 3 and 4 between the measured andcalculated values after the identification of the heat transfercoefficient. The parameters ¡ of heat transfer of each sprayzone were 3.73, 4.15 and 4.57, respectively. From the

Table 3, the consistency of shell thickness between exper-imental data and numerical results was obtained. As shownin Table 4, the test error was within the range of «10°Cbetween the measured and calculated temperatures of eachsecondary cooling zone under steady condition, and thecalculated result was basically consistent with the measureddata.

In order to test the dynamic performance and responseto operation conditions of the real-time transfer model, thesurface temperatures calculated by the real-time model andmeasured by the CCD temperature measurement system werecompared at 12.51m distance from meniscus in the actualcasting process. As seen in Fig. 7, the calculated surfacetemperatures were agreement well with the measured ones.

Fig. 4 The CCD image and grid division of billet surface at measuredpoint.

Fig. 5 Billet surface temperature distribution captured by CCD temper-ature measurement system.

0 10 20 30900

920

940

960

980

1000

1020

1040

1060

2

3

infrared measurement system

Mea

sure

men

t tem

pera

ture

(°C

)

Casting time, t/min

CCD measurement system

Cas

ting

spe

ed (

m/m

in)

casting speed

Fig. 6 Comparison between CCD measurement system and infraredsingle-point measurement system.

Table 3 Comparison between calculated and measured shell thickness at 3.07 and 8.71m distance from meniscus.

No.Casting

temperature (°C)Casting

speed (m/min)

Secondary coolingwater flow (Mg/h)

Shell thickness (mm)

3.07 8.71

Zone1 Zone2 Zone3 measured calculated measured calculated

1 1560 2.10 9.39 9.22 2.76 27 28 50 49

2 1547 2.63 10.85 20.25 4.55 24 23 47 48

Fig. 3 Field application of CCD temperature measurement system.

M. Jiaocheng, L. Jun, Y. Qiang and C. Liangyu1322

The temperature field measurement of billet was realized bythe multi-information fusion of CCD temperature measure-ment system, measured shell thickness and data acquisitionsystem, which provides the possibility to improve theexisting cooling system based on the feed-back controlconsidering the measured surface temperature.

5. Conclusion

The real-time heat transfer model and heat transfercoefficient identification method were developed. The surfacetemperatures were measured by CCD measurement system,

which can effectively eliminate the impact of scales on thetemperature measurement and keep the measured surfacetemperature fluctuation within the range of «10°C. Thetemperature field measurement of billet was realized by themulti-information fusion of CCD temperature measurementsystem, measured shell thickness and data acquisition system,which provides the possibility to improve the existingcooling system based on the feed-back control consideringthe measured surface temperature.

Acknowledgements

The authors would like to gratefully acknowledge thefinancial support of National Natural Science Foundation ofChina (61004135, 51304050).

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0 20 40 60 80 100 120 140950

1000

1050

1100

1

2

3

4

5

Tem

pera

ture

(°C

)

Casting time, t/min

calculated

measured

Cas

ting

spee

d (m

/min

)

Fig. 7 Comparison between calculated and measured temperature atchanging the casting speed.

Table 4 Comparison between measured and calculated temperatures ofsecondary cooling zones.

Distance frommeniscus (m)

1.17 3.12 8.81 7.28 10.56 12.51

Calculated (°C) 982 989 992 995 1056 1052

Measured (°C) 980 979 1001 1003 1049 1045

The Temperature Field Measurement of Billet Based on Multi-Information Fusion 1323