NUMERICAL SIMULATION OF SOLIDIFICATION IN CONTINUOUS CASTING OF ROUNDS

Transcription

1 NUMERICAL SIMULATION OF SOLIDIFICATION IN CONTINUOUS CASTING OF ROUNDS Christian Bernhard *, Markus Lechner *, Markus Forsthuber **, Erich Doringer **, Wolfgang Rauter ** * Christian-Doppler Laboratory for Metallurgical Fundamentals of Continuous Casting, Leoben, Austria ** voestalpine Stahl Donawitz, Leoben, Austria ABSTRACT: voestalpine Stahl Donawitz operates a 5-strand 230 mm round, bowtype continuous casting machine. In a joint research project between voestalpine and the Christian-Doppler Laboratory for Metallurgical Fundamentals of Continuous Casting, based on the commercial software package calcosoft2d, a 2D-FE model of the caster was developed. The model considers mass and heat transport. Some details, for example the mold, have been treated in 3D. The actual model allows the calculation of surface temperature and shell growth dependent on casting parameters such as superheat, casting speed and secondary cooling strategy. This model is the basis for further calculations concerning the formation of centreline segregations in the continuous casting of high carbon steels. The validation of the model is another important part of the presentation. A mold was equipped with 32 thermocouples, which allow the prediction of local heat transfer over the height and circumference of the mold for the most common steel grades, and give a highly reliable boundary condition for the solidification in the mold. Within the scope of the actual work, the surface temperature was measured at different positions below the mold. This allows the adjustment of the heat transfer boundary conditions to the measured temperature. In addition, the calculated shell growth is compared with the position of white bands, induced by final stirring in different positions, and for different steel grades. The careful definition of the boundary conditions and the validation of the model for different steel grades and casting parameters resulted in the development of a highly reliable und useful tool for both, process control and process development. 1 Introduction A comprehensive numerical simulation of the continuous casting process demands a simultaneous analysis of multi-physics and multi-scale aspects. The modelling of at least the following continuum phenomena and their interactions is required: fluid flow heat transfer phase changes solid mechanics electromagnetics

2 The computational modelling of such interacting phenomena, by e.g. Finite Element (FE) or Finite Volume (FV) methods is still a challenge, in spite of the rapid development of hardware and numerical methods. In addition, the physical phenomena are active on various scales in space and time. For instance, macrosegregation will depend on enrichment at the scale of a dendrite and the transport of the segregated melt caused by thermal and solutal buoyancy both at the scale of the mushy zone and at the macroscopic scale of the casting. Compression and expansion of the mushy zone initiated by thermal contraction and process-related distortion of the strand shell have a dominant influence on the transport of segregated melt out of the mushy zone and demand the consideration of thermo-mechanical incidents at different length scales, too. The different dimensions, together with the effects of alloying elements (segregation, precipitation); the phase transformation of steels during and after solidification (shrinkage, porosity); or the deformation of the solidifying shell (bulging, unbending), make the continuous casting process a challenging task to control and optimise. Due to the complexity of the process, numerical simulation is becoming a significant tool for continuous casting engineers, providing a more complete understanding on the entire process. 2 Basic equations 2.1 Mass conservation The mass conservation equation can be expressed as follows: div( f v + f v ) = div( v) = 0 (1) l l s s Where v is the velocity vector and f s and f l are the volumetric mass fractions of the solid and the liquid phases. 2.2 Momentum conservation A general form of the momentum conservation equation is: v ρ + v v = divσ + F V (2) t where ρ is the density, σ the stress tensor and F V the volumetric force. 2.3 Heat conservation The heat conservation equation can be expressed as: H t + div( Hv) div( λ T ) = S (3)

3 where H is the enthalpy, λ is the thermal conductivity, T is the temperature and S is the source term. 2.4 Heat conduction Because of the high heat capacity and low thermal conductivity of steel and the high casting speeds used in steel casting, the heat transferred by conduction in the axial (z) direction is small compared to the heat transferred by the bulk motion of the strand and can be ignored /1/. The thermal conduction equation for the calculation can be mathematically defined as: 2 T 2 x = T cρ t λ (4) where c is the heat capacity 3 Boundary conditions The following boundary conditions were used to model continuous casting machine no. 3 at voestalpine Stahl Donawitz GmbH. The technical data can be taken from Table 1 /2/. Annual Production t Ladle Size 67 t Type of Machine Bow type caster with curved mold Number of Strands 5 Casting Size 283 x 390 mm round 230 mm Radius 12 m Metallurgical Length (max.) 35.5 m Casting Speed m/min (283 x 390 mm) m/min (230 round) Tundish Capacity appr. 29 t EMS Mold-stirrer and movable final stirrer Length of Mold 800 mm, hydraulic oscillation Secondary cooling 5 zones air/mist Table 1: Technical data of the Donawitz bloom caster /2/ 3.1 Mold The most important parameters for heat flux in the mold in addition to the mold geometry are steel grade, mold flux and casting speed. Heat flux is therefore a particularly system-dependent value. Universally valid definitions are rare and imprecise. The determination of the integral heat flux from the temperature increase of primary cooling water gives a quantitative indication of the amount of heat

4 removed in the mold. As the heat flux density is not constant over the height of the mold, use of the integral heat flux as boundary condition for numerical simulation decreases the accuracy of the calculated results. The determination of local heat flux demands a complex instrumentation of the mold with thermocouples. Within the scope of two diploma-theses, the local heat flux for molds with different tapers was investigated /3, 4/. This provides a comprehensive database for the most frequently cast steel grades. Figure 1 shows an example for heat flux in the mold versus distance from the top of the mold for a high carbon prestressed concrete steel at two casting speeds. The maximum heat flux at the meniscus amounts to between 2.0 and 2.1 MW/m², and decreases to between 1.5 and 1.6 MW/m² in the middle of the mold. The high heat removal in the upper part of the mold results in a loss of contact between mold and strand at the mold outlet. The horizontal lines show the integral heat flux calculated from the temperature difference of the cooling water. 2,4 2,2 Heat Flux [MW/m²] 2,0 1,8 1,6 1,4 1,2 1,0 0,8 0,6 1,57 MW/m² (integral heat flux) 1,63 MW/m² (integral heat flux) Prestressed concrete steel: v c =1,60 m/min v c =1,35 m/min Distance from the mold top [mm] Figure 1: Distribution of heat flux in the mold versus distance from the top of the mold 3.2 Secondary cooling zone: The total heat transfer coefficient can be written as follows /5, 6/: h sec n = m GI FP + σ sec 3 ε T (5) 0 where: h sec n m sec GI FP ε σ T 0 = total heat transfer coefficient in the secondary cooling zone = specific cooling water in the secondary cooling zone = impulse of the cooling media = fit parameter = emission ratio = Boltzmann s constant = surface temperature

5 Equation 5 considers that both pure water and air/mist nozzles are in use and yields steady results for a wide range of steel grades. The secondary cooling zone of the Donawitz caster is divided into five cooling zones with separately adjustable water flow rates. For a first approach the heat transfer coefficient (convective and radiation) was assumed to be only a function of the water flow rate and thus constant for every cooling zone. The results were sufficient to predict solidification, but correspondence with the measured surface temperature was poor. Therefore, in a second step, the initial boundary condition was replaced by a more complex one, considering the position of spray nozzles. In continuous casting of rounds the contact between strand and rolls plays no role, and is therefore neglected. Figure 2 shows a schematic distribution of the heat transfer coefficient at the surface of the strand. The heat transfer coefficient is composed of radiation (dependent on surface temperature) and convection (dependent on cooling water impulse and temperature). Figure 2: Schematic distribution of the heat transfer coefficient in a part of the secondary cooling 3.3 Steel grades The product mix of the Donawitz steel plant covers a wide range of carbon steels. Although the actual project focuses mainly on higher carbon steels, the reliability of the results also had to be proved for low carbon and medium carbon steels, and thus for a wide range of cooling strategies and casting parameters.

6 For six steel grades with a carbon content of between 0.07 wt.-% and 0.82 wt.-% the solidification was calculated at casting speeds of 1.5, 1.6 and 1.75 m/min, with varying superheat and three different cooling patterns. 4 Calculations and results The calculations were performed using calcosoft2d. The modelling of a continuous casting machine with a metallurgical length of more than 15 m in 3D is still too CPUtime costly. Some parts of the machine were therefore modelled in 3D, and the insights incorporated into a cost-saving 2D model. The modelling of the mold region in 3D, shown in figure 3, has proven a relatively small influence of fluid flow in the axial direction on solidification and the surface temperature. A quarter of a cross section of the strand is therefore withdrawn through a time and space dependent field of boundary conditions. Figure 3: Temperature distribution, progress of solidification and heat flux calculated by calcosoft3d The model is based on average conservation equations (equ. 1-4): the mass and heat conservation equations averaged over both the liquid and solid phases and the momentum conservation averaged on the liquid phase only. These equations are solved using a fully implicit time-stepping scheme and a standard Petrov-Galerkin formulation in finite elements. The thermophysical data of the steel grades were calculated using IDS Version

7 The validation of the model was performed by the measurement of surface temperature by optical pyrometer in five different positions within and after the secondary cooling zone, the measurement of solidification isotherms by stirring of white bands in the final stirrer area Figure 4 shows a sulphur print of a white band. According to the literature /7/, the position of the white band corresponds to a solid fraction of around 0.3 at the moment of electromagnetic stirring. The zone of influence of the stirrer has a length of approximately 1 m. The outer diameter therefore marks the running-in of the 0.3- isotherm into the stirrer region, and the inner diameter marks the run-out. The white band allows an accurate determination of the solidification progress. Figure 4: White band produced by the final stirrer As can be seen from figure 4, the white band is not circular but elliptical and displaced from the centre of the bloom. This shape is the result of gravity and nonuniform cooling conditions on the surface. For validation purposes the average value of four diameters, rotated from each other by 45 degrees, is used. Figure 5 shows a comparison of calculated and measured radii of the white bands. Figure 5: Comparison of the calculated and the measured liquid pool

8 Figure 6: Measured surface temperatures at 3 different measuring points The validation of the calculated surface temperature, mainly in the secondary cooling zone, is much more delicate. Optical measurement of the surface temperature is affected by scale formation and the adherence of mold flux residuals at the surface. The high-temperature vapour atmosphere is another element of uncertainty. Near spray nozzles, even small displacements of the optical sensors result in strong variations in the measured temperature. The measured surface temperatures can therefore only be considered as a qualitative indicator for the accuracy of the calculations. Figure 7: Measured and calculated surface temperatures Figure 6 shows the measured surface temperatures in three different positions within the secondary cooling zone for a cold upsetting steel with a carbon content of 0.3%.

9 The wild fluctuations in the temperature of the secondary cooling zone, demonstrate the difficulties of the measurement technique. Figure 7 shows an example of calculated and measured surface temperature for cold upsetting steel. As can be seen, the tendency of the calculated temperatures corresponds with those measured, but the systematic difference of about 90 C demands a further improvement in measurement and the consideration of scale formation in the model. 5 Conclusions A heat transfer model for continuous casting of rounds was developed to calculate the temperature distribution and to study the process of solidification in the continuous casting process. The present paper deals with the first results and the validation of the model for a wide range of steel grades. In further steps, the model will be extended by considering stirring in the mold and during the final stages of solidification. The ultimate objective of the project is to develop a tool for the comparison of different technical approaches for the control of centreline segregation in the continuous casting of rounds. 6 References /1/ Lally, B., Biegler, L. and H. Henein: Finite Difference Heat Transfer Modeling for Continuous Casting, Metall. Trans. B, vol. 21B, 1990, no. 4, pp /2/ Erker, M. Brandl, W., Schöllnhammer, H. and G. Wolf: Experience with the five-strand bloom caster as part of the new integrated compact LD steelmaking plant at voestalpine Stahl Donawitz GmbH, Proceedings of the 4th European Continuous Casting Conference, Birmingham 2002, Vol. 1, pp /3/ Rauter, W.: Influence of selected casting parameters on heat removal in a round continuous casting mold, Diploma-thesis, Institute of Ferrous Metallurgy, University of Leoben, 2001 /4/ Tince, T.: Influence of mold taper on local heat flux density, Diploma-thesis, Institute of Ferrous Metallurgy, University of Leoben, 2003 /5/ Reiners U.: Heat transfer by spray water cooling of hot surfaces in the region of stable film boiling, Ph.-D.-thesis at Technical University of Clausthal, 1987 /6/ Schwerdtfeger, K.: Metallurgy of continuous casting. Verlag Stahleisen, Düsseldorf, 1992 /7/ Oh, K., S.; Chang, Y., W.: Macro and microscopic segregation behavior of center segregations in high carbon steel CC blooms during the final stage of solidification, Proceedings of the 13 th Process Technology Conference, Iron and Steel Society, Inc. (USA), 1995, pp