5th International DAAAM Baltic Conference
“Industrial engineering – Adding innovation capacity of labour force and entrepreneurs”
20-22 April 2006, Tallinn, Estonia
Investigation of the shell solidification in horizontal continuous casting process
Bockus, S.
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Abstract: Horizontal continuous casting is one of the prominent methods of production of cast iron billets. Effective creation of continuous casting technological process needs complete analysis of the continuous casting process. In this paper the influence of basic technological parameters on the shell solidification using the numerical analysis of heat transfer is presented. The results show that the billet shell thickness an increase mainly depends on the billet cooling conditions, the temperature of molten metal in a crucible and a casting rate. A nomograph to calculate shell thickness is developed.
Key words: Continuous casting, cast iron, solidification, heat transfer, mathematical modelling.
1. introduction
The horizontal continuous casting is very productive and economic method and has a lot of advantages in comparison with traditional casting methods: few operations, no waste, stable dimensions of the billet, better operation service characteristics and personal work conditions. All these factors force to be find possibilities to wider implementation of the method.
In the horizontal continuous casting process the liquid metal issues from crucible into a water cooled crystallizer. The liquid metal solidifies in the crystallizer, and a solid shell is formed. The solid shell is then withdrawn periodically in successive strokes [1, 2]. Continuous casting has its peculiarities [3, 4]. This especially can be seen in the cross-sections of the billets, where anomalous, intermediate and normal structural zones can be obtained. This is the result of specific billet cooling and solidification conditions [5]. The quality of the castings and productivity of process depend mainly on the processing conditions. In this respect, the position and the shape of the solidification front plays a significant role. The key to an increase in productivity remains often in the control of all operational parameters. Simulation is convenient and accurate method to understand and analyse the importance of each casting parameter [6].
The main aim of the investigation was to examine the effect of technological, design and heat physics parameters on the process of shell solidification in the crystallizer.
2. formulation of the Solidification model
Billet solidification in the crystallizer is investigated by mathematical modelling of the casting process.
Formation of the billet in continuous casting process mainly is affected by the cooling conditions, which predetermine the parameters of it crystallization (temperature field, crystallization rate, etc.). The cooling conditions vary along the billet length and influence its solidification character. Solidification of the molten metal, being supplied into the crystallizer, is not uniform in the whole volume. Intense cooling of the peripheral zone of the billet results higher solidification rate than in the central zone. Therefore the following three different zones can be distinguished: hard shell zone where the temperature drops below the solidus temperature; intermediate zone where heat of phase transformation occurs, and zone of liquid metal, where heat is transferred by conductivity and convection. In common case, in order to describe mathematically billet solidification during the continuous casting process, system of differential equations should be derived, which consists of: Fourier heat transfer equations for the solidified part of billet; convection heat transfer equation, evolving crystallization heat occurrence in the intermediate zone, for the liquid part of the billet; convectional diffusion equation; molten metal motion equation and continuity equation. To overcome difficulties related to the molten metal hydrodynamics, heat transfer process of the liquid phase is described by the same type equation as that for solidified shell, and the convection effect is evaluated by the heat conductivity coefficient. It is assumed, that heat capacity of the half-solidified zone equals to the effective heat capacity, which is the sum of both actual heat capacity and spectral crystallization heat together with the crystallization heat, occurring in the given temperature. Taking into account these assumptions, the problem of both heat distribution and location of the border between liquid and solidified phases, during the billet solidification process, is solved as heat conductivity differential equation with the corresponding conditions of singularity.
In the all three billet zones, the temperature field is described by one differential heat conductivity equation:
(1)
where c(T) is a billet specific heat capacity as a function of the temperature T; r is a density of the billet; l(T) is an effective heat transfer coefficient; t is a time; Lcr is a specific crystallization heat; y is the amount of solid phase in the given billet element; wheny = 0 the metal is liquid; when y = 1 it is completely solid. Suppose that initial temperature of the billet is uniformly distributed, i.e.
(2)
where Tcb is the temperature of metal coming from the crucible into the crystallizer. Heat transfer on a surface of the billet is going according to the following law:
(3)
where Tsf is the billet surface temperature; a is a heat transfer coefficient; Ten is an environment temperature. Continuous cylindrical billet condition of symmetry is written in the form:
(4)
Presented problems can not be solved analytically. It is solved applying approximate numerical methods. The following heat physics values were used in the calculations:
if TS£T£TL;
Lcr = 268000 J/kg;
r(T) = 8590 - 1.4T, kg/m3;
if TS £ T £ TL;
Stability of the horizontal continuous casting most strongly is affected by the shell thickness at the moment, when billet gets out of the crystallizer. Therefore, values of casting parameters, first of all, must ensure sufficient duration of the billet location in the crystallizer tc, which is related to the drawing regimes by the relationship:
(5)
where L is length of the crystallizer cooling part; vt is pulling velocity of the billet; tp is pause duration, and td is drawing duration. This equation can be rewritten in the form:
(6)
where vac is average casting speed. This equation shows that average continuous casting speed depends on vt and ratio tp/td. Increasing this ratio, average casting velocity decrease and vice versa. If vt is constant, proportional increase or decrease of the values tp and td do not change the average casting velocity. Thus, when tp and td values are a few times decreased, time tc stays constant, and the drawing step decreases too. A decrease of the ratio tp/td results an increase of the casting process productivity. It is recommended to decrease this ratio by decrease of the pause duration, because increase of the drawing time results increment of the drawing step, which has a negative effect on the billet quality. At present the tendency is higher to use drawing frequency and small drawing step. An average casting speed can be increased by an increase of the crystallizer length. The drawing velocity of the billet can be increased both by a decrease of the molten metal in the crucible temperature or by an intensification heat transfer in the crystallizer.
3. the influence of design and technological parameters on the casting process
Aiming to find out the best cooling conditions of the continuously casting billets, the influence of the following parameters on the continuously cast cylindrical iron billets solidified shell thickness have been investigated: cooling intensity of the billet; molten metal temperature in the crucible; molten metal liquidus temperature; billet diameter and casting speed. Simulation of the shell solidification was performed under the following initial technological casting parameters and cooling conditions of a billet: Tc = 1240 oC, a = 1000 W/(m2.K), TL = 1190 oC, R = 0.055 m, a = 3.28.10-6, TS = 1150 oC, tc = 30 s.
The cooling intensity is determined by the heat transfer coefficient. The results of this investigation show that the heat transfer coefficient has a significant effect on the shell thickness which is formed at the end of crystalliser (Fig. 1).
The effect of liquidus temperature of cast iron on the shell thickness is negligible (Fig. 2). Therefore it is possible to use the same value of liquidus temperature of cast iron for the shell thickness calculations.
Fig. 1. Effect of heat transfer coefficient α on the shell thickness x.
A temperature of the molten metal in a crucible has a strong effect on the shell thickness (Fig.3).
Fig. 2. The effect of liquidus temperature of cast iron TL on the shell thickness x.
Fig. 3. Shell thickness x as a function of the temperature Tc of molten metal in the crucible.
Figure 4 shows that the shell thickness which is formed at the end of crystalliser x = 10 mm at Tc = 1210 oC and tc = 24 s. But if Tc = 1270 oC then x = 10 mm only at tc = 35 s.
Fig. 4. Shell thickness x as a function of a temperature Tc and a time tc: 1 – Tc = 1180oC; 2 – Tc = 1210 oC; 3 – Tc = 1270oC.
This Figure shows the effect of the time tc during which the billet is in the crystallizer on the shell thickness also. Because the time tc is related to the average casting speed vac (see Eq. 2) therefore an increase this speed results the decrease of shell thickness.
The influence of a billet diameter on the shell thickness is illustrated in Figure 5, where it is shown that effect of the billet diameter is strong in the case of small values only.
4. determination of the shell thickness
For graphical interpretation of the solutions of the heat conductivity equation the smallest number of criteria and simplexes characterising the heat transfer process at certain boundary conditions, was find out. Method of integral analogs of the theory of similarity had been used for the analysis. At constant molten metal temperature in the holder Equation (1) may be written in the form:
; (7)
where is relative thickness of the shell; is Bio criterion; is Fourier criterion. Figure 6 shows a net nomograph for this equation at molten metal in the crusible temperatures Tc = 1270 0C are developed.
Fig. 5. The influence of billet diameter d on the shell thickness x (tc = 5 s).
Fig.6. Nomograph for the shell thickness determination at Tc =12700 C.
In this nomograph any of variables F0, d or Bi can be unknown value. It is possible to define relative thickness d of the solidified in the crystallizer metal shell, which corresponds to given Bi and F0, values, or choose such technological regime, which results the given shell thickness.
5. Conclusions
Differential equation describing heat transfer during the ingot solidification in the crystallizer was established and solved. Effect of technological, constructional and heat physics parameters on the ingot solidification in the crystallizer rate was investigated. Tests showed that the billet shell thickness an increase mainly depend on the billet cooling conditions, the temperature of the molten metal in crucible and casting speed. Liquidus temperature influence is not strong. Effect of billet diameter is strong at small values of the diameter only. The nomograph to calculate shell thickness was developed.
6. References
1. Huespe, A.E., Cardona, A., Fachinotti, V. Thermomechanical model of a continuous casting process. Computer Methods in Applied Mechanics and Engineering, 182, 2000, 439-455.
2. Beeley,P. Foundry Technology. Butterworth-Heinemann, Oxford, 2001.
3. Noshadi, V., Schneider, W., Kuznetsov, A.V. Internal flow and shell solidification in horizontal continuous casting processes. In Modeling of Casting, Welding, and Advanced Solidification Processes (Thomas, B.G. and Beckermann, C., eds.). The Minerals, Metals & Materials Society, San Diego, California, 1998, 655-662.
4. Das, S.K. Evaluation of solid-liquid interface profile during continuous casting by a spline based formalism. Bull. Mater. Sci., 2001, 24, 373-378.
5. Cicutti, C., Boeri, R. On the relationship between primary and secondary dendrite arm spacing in continuous casting products. Scripta Materialia, 2001, 45, 1455-1460.
6. Modelling for casting and solidification processing (Kuang-O (Oscar) Yu., ed.) Marcel Dekker, Inc., New York, 2002.
7. corresponding address
Prof. Dr. Habil. Stasys Bockus
Kaunas University of Technology,
Department of Metals Technology
Kestucio g. 27, 44025 Kaunas, Lithuania
Phone: +370 37 323758,
Fax: +370 37 323461,
E-mail:
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