ISSN 0967�0912, Steel in Translation, 2011, Vol. 41, No. 12, pp. 992–995. © Allerton Press, Inc., 2011.Original Russian Text © P.S. Kharlashin, A.N. Yatsenko, V.Ya. Bakst, V.G. Gavrilova, O.I. Romanov, 2011, published in “Izvestiya VUZ. Chernaya Metallurgiya,” 2011, No. 12,pp. 55–58.

992

1 Around the world and in most countries within theCommonwealth of Independent States, energy andresource conservation is a pressing problem today. Themetallurgical industry is a major consumer of electricpower, and consequently resource� and energy�con�serving ladle treatment of steel is of great interest [1, 2].

Research suggests that efficient degassing of liquidmetal by inert�gas injection depends not on the inten�sity of injection but on the number of gas bubblesintroduced in the melt per unit time. At high injectionrates, the individual bubbles coalesce, with conse�quent reduction in the gas–metal contact area and inthe efficiency of degassing. In boosting the efficiency,the development of the phase interface is significantlymore important than increase in turbulization of thebath. Accordingly, the injection of preheated inert gas(argon) through a special heat exchanger in the liningof the steel�casting ladle is of interest. The heatexchanger is expedient since much of the heat in theladle is not utilized but rather scattered to the atmo�sphere.

Preheating of the argon tends to produce smallerbubbles from the argon jet in the liquid metal. Theresult is to increase the mixing of the liquid steel onaccount of the significant increase in the number ofascending bubbles; distribute the bubbling zone over alarger melt volume within the ladle; and reduce thecontent of hydrogen and nonmetallic oxide inclusionsin the steel.

In the present work, we assess the potential foreffective use of the casting ladle’s lining as a means ofheating the inert gas and develop a mathematicalmodel of the processes in the multilayer ladle lining.

For that purpose, we need to predict the thermalstate of the ladle lining in the cycle from heating tocooling after metal intake and we need to know thetemperature distribution over the lining layers withinthe ladle’s working run. Therefore, we must considerall the thermal processes in the casting ladle from the

1 This paper was presented at the Eighth International Confer�ence on Heat and Mass Transfer in Metallurgical Systems,Mariupol, September 2010.

onset of heating to the end of casting. The usual cycleof casting�ladle motion in the converter shop is shownin Fig. 1.

The lined casting ladle is sent to the drying andheating system 1 and to the gate�application system 2.The drying and heating time is at least 24 h. The sur�face temperature of the lining’s working layer is 800–900°C. (Heating to 1100–1200°C. is possible.) Afterdrying and heating, gates are fitted to the ladle. Then,using a crane, the ladle is taken to the steel car 3 toawait smelter discharge. After discharge, the ladle,filled with liquid metal, is sent to the ladle–furnaceunit 4 for refining of the steel. Refining takes 12–45 min, depending on the composition and tempera�ture of the steel and its required mechanical proper�ties. Then the ladle is sent to the continuous�castingmachine 5; continuous casting takes 1–2 h. After cast�ing, the slag is removed from the ladle 6. Where neces�sary, the ladle is sent to the repair or lining�replace�ment department 7 or sent to unit 2 for replacement ofa gate. Then the ladle is replaced in the steel car 3 toawait the next smelter discharge. The cycle thenrepeats.

Calculation of the thermophysical state of refracto�ries in the casting ladle must include calculation of thetemperature field in ladle drying and heating, during

Utilizing Heat from the Hot Casting�Ladle Lining in Argon Injection1

P. S. Kharlashin, A. N. Yatsenko, V. Ya. Bakst, V. G. Gavrilova, and O. I. RomanovPriazovsk State Technical University

Received April 5, 2011

DOI: 10.3103/S0967091211120084

1 2 3 4

56

7

SR

Fig. 1. Cycle of casting�ladle motion in the converter shop:SR, steel refining.

STEEL IN TRANSLATION Vol. 41 No. 12 2011

UTILIZING HEAT FROM THE HOT CASTING�LADLE LINING IN ARGON INJECTION 993

the wait for smelter discharge, during steel transporta�tion in the ladle, and in continuous casting of the steel.

The casting ladle is represented as a hollow cylinder.In a linear formulation, we obtain the following equa�tion for the lining, in cylindrical coordinates [3, 4]

(1)

where c is the mean specific heat, kJ/(kg K); ρ is thedensity, kg/m3; t is the temperature, °C.; x, r, ϕ arecylindrical coordinates in which the position of anypoint is determined by the coordinates along the X andR axes and the angle of rotation ϕ (ϕ = 0°–180°); τ isthe time, s; λ is the thermal conductivity, W/(m K).

To calculate the temperature field in the lining dur�ing preliminary ladle heating, we obtain an axisym�metric one�dimensional problem, for which Eq. (1)takes the form

In preliminary ladle heating, the temperature dis�tribution within the lining is initially

The initial temperature field within the ladle liningmay be determined in this case by preliminary calcula�tion or calculation of the ladle cooling during the wait�ing period. Since ladle cooling in the waiting periodand especially the casting period is characterized byconsiderable temperature difference of the lining overthe ladle height, we calculate the cooling of the liningon the basis of an axisymmetric two�dimensionalproblem and write Eq. (1) in the form [4, 5]

(2)

To calculate the cooling of the casting ladle in thewaiting period, we may write the initial temperaturedistribution within the lining in the form

In that case, the initial temperature field within theladle lining may be determined by several methods: bycalculation of the preliminary ladle heating or calcula�tion of the metal discharge in the ladle.

The boundary condition at the lower end of theladle walls is a heat�insulation condition

cρ∂t x r ϕ τ, , ,( )∂τ

������������������������ λ ∂2t x r ϕ τ, , ,( )

∂x2�������������������������� ∂2t x r ϕ τ, , ,( )

∂r2��������������������������+=

+ 1r��∂t x r ϕ τ, , ,( )

∂r������������������������ 1

r2���∂

2t x r ϕ τ, , ,( )∂ϕ

�������������������������� ,+

cρ∂t r τ,( )∂τ

�������������� λ ∂2t r τ,( )

∂r2���������������� 1

r��∂t r τ,( )

∂r��������������+ .=

t r 0,( ) f r( ).=

cρ∂t x r ϕ τ, , ,( )∂τ

������������������������ λ ∂2t x r ϕ τ, , ,( )

∂x2��������������������������=

+ ∂2t x r ϕ τ, , ,( )

∂r2�������������������������� 1

r��∂t x r ϕ τ, , ,( )

∂r������������������������ .+

t x r 0, ,( ) f x r,( ).=

∂t 0 r τ, ,( )/∂x 0.=

An analogous boundary condition is adopted forthe liquid steel when r = 0

For contact of the liquid steel and the lining’sworking surface (r = R0), the boundary condition ofthe fourth kind takes the form

For the other surfaces, we adopt boundary condi�tions of the third kind

where α1Σ, α2Σ, α3Σ are the total heat�transfer coeffi�cients; αΣ = αco + αr; αco and αr are the convective andradiant heat�transfer coefficients, J/(m2 s K); H is thewall height, m; tA is the air temperature, °C.

We use Eq. (2) to calculate the temperature fields inthe steel and the ladle lining during steel casting. Theinitial temperature distribution within the ladle liningtakes the form

In that case, the initial temperature field within theladle lining may be determined by calculation of thesteel transportation in the ladle. The proposed analyt�ical method is relatively complex. Therefore, for engi�neering calculations of the temperature distributionwithin the lining layers, we may use predictive meth�ods for steady thermal operation.

The thermal conductivity of the layers is deter�mined from the standard formula [6]

(3)

where i is the layer number; tmei is the mean tempera�ture of layer i, °C; a, b are empirical constants.

In steady conditions, the heat flux Q through a wallof any form is determined by the Fourier law

(4)

where dt/dr is the temperature gradient, K/m; F(r) isthe isothermal surface area of the layer, m2.

∂tst x 0 τ, ,( )/∂r 0.=

tst x R0 τ, ,( ) t x R0 τ, ,( );=

tst x R0 τ, ,( )/∂r t x R0,( )/∂r.=

λ∂t x Rla τ, ,( )

∂r�����������������������– α1Σ t x Rla τ, ,( ) tA–[ ];=

λ∂t H r τ, ,( )∂r

��������������������– α2Σ t H r τ, ,( ) tA–[ ];=

λ∂tst H r τ, ,( )

∂x�����������������������– α3Σ tst H r τ, ,( ) tA–[ ].=

t x r 0, ,( ) f x r,( ).=

λi ai bi10 5– tmei,+=

Q λ t( )dtdr����F r( ),–=

994

STEEL IN TRANSLATION Vol. 41 No. 12 2011

KHARLASHIN et al.

By variable separation, we obtain

(5)

where SF is the component of the flux per unit area, m–2;k is the form factor (k = 1, 2, 3 for a plate, a cylinder,and a sphere, respectively); Fk is the constant compo�nent of the surface area, m2, while

L is the length of the flat wall, m; ϕ is the apertureangle, deg.

The next step is computer calculation of the inte�grand E by the trapezium method

(6)

where hi = δi/N is the thickness of sublayer i, m; δi isthe thickness of layer i, m; N is the number of sublayersinto which the layer is divided; ri is the layer radius, m.

Boundary conditions of the first kind are assumedon the working side of the lining (tli = const is the tem�

Q drF r( )�������� λ t( )dt;–=

SFdr

F r( )��������

ri 1–

ri

∫1Fk

���� dr

rk 1–��������,

ri 1–

ri

∫= =

Fk 1= LH; Fk 2=πHϕ180

����������;= =

Fk 3= 2π 1 ϕ2���cos–⎝ ⎠

⎛ ⎞ ;=

E dr

rk 1–��������

rl 1–

rl

∫=

= 0.5hi1

rk 1–�������� 2

r1k 1–

�������� 2

r2k 1–

�������� … 2

ri 1–k 1–

�������� 1

ri 1–k 1–

��������+ + + + +⎝ ⎠⎛ ⎞ ,

perature of the liquid steel); boundary conditions of thethird kind are assumed on the outside of the housing

(7)

where tw is the wall temperature and tf is the final walltemperature.

The heat flux through a curvilinear multilayer wallis calculated as

(8)

After solution of Eq. (3), taking account ofEqs. (5)–(8), we may write the temperature at theboundary of the sublayers in the form

To calculate the temperature distribution over cur�vilinear lining layers, we write a program for computercalculation of the temperature fields and heat lossesthrough the lining of a 160�t casting ladle. The workinglayer of the lining consists of KUMAL�5CE refractorypieces (thickness 230 mm), a reinforcing layer ofShKU�37 fireclay brick (thickness 100 mm), quartzitemass (thickness 40 mm), and a housing of carbon steelsheet (thickness 22 mm). The mean liquid�steel tem�perature is 1604°C; an ambient temperature of 20°C isassumed.

Computer calculations indicate that the tempera�ture of a heat exchanger in the ladle lining for inert�gasheating at the beginning of the run is 510–530°C.With lining wear, the temperature of the heatexchanger steadily increases, reaching 655–665°C atthe end of the ladle run (with practically completedestruction of the lining’s working layer), as we see inFig. 2. Thus, the temperature of the heat exchangerincreases by a factor of 1.25. For the future, improve�ment in heat�exchanger design is planned, with trialindustrial runs in the oxygen�converter shop.

CONCLUSIONS

For practical purposes, engineering methods ofassessing the temperature fields within the lining of asteel�casting ladle are adequate. The proposed mathe�matical model permits calculation of the temperaturefields within the ladle lining in industrial processes.Preheating of the ladle lining by inert gas to enhancedegassing and purification of the steel is shown to bepossible in principle.

λ t( )dtdr����– αf tf tw–( ),=

Qtli tw–

hi

λi

���Ei

Fk

����i 1=

M

∑1

αcoFkrmk 1–

�������������������+

����������������������������������������.=

ti N,1

bi N,

������� ai N, λi N,2

2bi N, QSF––( ).–=

700

660

620

580

540

500321

Stage of ladle run

Tem

pera

ture

, °C

Fig. 2. Temperature variation of heat exchanger (—) andmean temperature (� � �) of refractory layer adjacent to theheat exchanger, at the beginning (1), middle (2), and end(3) of the ladle run.

STEEL IN TRANSLATION Vol. 41 No. 12 2011

UTILIZING HEAT FROM THE HOT CASTING�LADLE LINING IN ARGON INJECTION 995

REFERENCES

1. Boichenko, B.M., Okhots’kii, V.B., and Kharlashin, P.S.,Konverterne virobnitstvo stali (teoriya, tekhnologiya,yakist’ stali, konstruktsiya agregativ, retsirkulyatsiyamaterialiv i ekologiya) (Converter Smelting of Steel:Theory, Technology, Purity of Steel, EquipmentDesign, Recycling of Materials, and EnvironmentalImpact), Kiev: Dnipro�VAL, 2004.

2. Kharlashin, P.S. and Yatsenko, A.N., Vestn. Priazovsk.Gos. Tekhn. Univ., 2010, no. 20, pp. 57–61.

3. Kharlashin, P.S., Yatsenko, A.N., and Bakst, V.Ya., inNaukovi pratsi Donets’kogo natsional’nogo tekhnichnogo

universitetu. Seriya: metalurgiina (Proceedings ofDonetsk National Technical University: MetallurgySeries), Donetsk: Izd DonNTU, 2010, issue 12(160),pp. 99–104.

4. Lykov, A.V., Teoriya teploprovodnosti (Theory of HeatConduction), Moscow: Vysshaya Shkola, 1967.

5. Frank�Kamenetskii, D.A., Diffuziya i teploperedacha vkhimicheskoi kinetike (Diffusion and Heat Transfer inChemical Kinetics), Moscow: Nauka, 1967.

6. Levich, V.G., Fiziko�khimicheskaya gidrodinamika(Physicochemical Hydrodynamics), Moscow:AN SSSR, 1952.