VÝPO ET TEPLOTNÍHO POLE PLYNULE LITÉ OCELOVÉ BRAMY T SN P ED PR VALEM

Transcription

1 VÝPO ET TEPLOTNÍHO POLE PLYNULE LITÉ OCELOVÉ BRAMY T SN P ED PR VALEM THE CALCULATION OF THE TEMPERATURE FIELD OF A CONCAST SLAB TIGHTLY BEFORE THE BREAKOUT Franti ek KAVI KA a, Karel STRÁNSKÝ a, Bohumil SEKANINA a, Milo MASARIK b,josef T TINA a, Tomá MAUDER a a) Brno University of Technology, Technická 2, Brno, CR, b) EVRAZ VÍTKOVICE, a.s. Ostrava, CR Abstrakt P vodní numerický model byl aplikován na simulaci teplotního pole plynule lité bramy pro p ípad, e lití oceli o chemickém slo ení A skon ilo a okam it následovalo lití oceli chemického slo ení B. V míst rovnání bramy v sekundární chladicí zón m e zvý ením lokální a teplotní heterogenity oceli dojít k pr valu. Teplotní pole bramy bylo vypo teno pro t i varianty chemického slo ení. První varianta je pro chemické slo ení oceli A, druhá pro chemické slo ení oceli B a t etí pro pr m rné chemického slo ení z A a B. Teplotní model poskytuje teplotní historii ka dého bodu p í ného ezu b hem jeho pohybu celým ZPO od hladiny taveniny v krystalizátoru a po pálicí stroj, pr b h isolikvid, isosolid a dal ích izoterem a dále izoplochy konstantní teploty. Sou initel p enosu tepla pod tryskami je dán sou tem sou initele nucené konvekce a t.zv. redukovaného konvek ního sou initele p enosu od sálání. Výpo et také stanoví metalurgickou délku a rozsah t.zv. mushy zóny, tj. oblasti mezi teplotou izolikvidu a izosolidu. Výpo tem jsou tak získány parametry teplotního pole do bezrozm rných kritérií podobnosti. Tato kriteria budou po vy íslení charakterizovat stupe rizika vzniku nebezpe ného pr valu. Abstract Original numerical model was applied to the simulation of the temperature field of concast steel slab, when melt of steel of quality A finished and immediately the melt of quality B followed. In the secondary-cooling zone in the unbending point, the breakout of the steel can occur in points of increased local chemical and temperature heterogeneity of the steel. The temperature field of the slab was calculated for three variants of the chemical composition. The first variant is for the chemical composition of steel quality A, the second for the chemical composition of steel quality B and the third for the average chemical composition from quality A and quality B. The temperature model was provides the temperature history of every points of a crosssection during its movement through the whole caster from the level of the melt in the crystallizer to the cutting torch, the course of isoliquidus, isosolidus and next isotherms, further temperature isozones. Heat transfer coefficient beneath the jets is given by the sum of the forced convection coefficient and the so-called reduced convection coefficient corresponding to heat transfer by radiation. The calculation also evaluates the metallurgical length and a range of mushy zone, i.e. zone between isosoliquidus and isoliquidus. The calculated parameters from the temperature field to the dimensionless criteria of similarity are obtained. After numeration these criteria will characterize the level of risk of dangerous breakout. Klí ová slova: plynule litá brama, teplotní pole, chemické slo ení, pr val, kriteria podobnosti Key words: concast slab, temperature field, chemical composition, breakout, criteria of similarity

2 1. INTRODUCTION Oscillation marks are transverse grooves forming on the surface of the solidifying shell of a concast slab. The hooks are solidified microscopically thin surface layers of steel [1-3]. They are covered with oxides and slag. Their microstructure is different to that of the base material of the solidifying shell. The formation of the oscillation marks and hooks are related. The depth of the oscillation marks and also the shape, size and the microstructure of the hooks vary irregularly. An increasing extent of these changes leads to a defect in the shape of a crack, which reduces the thickness of the solidified shell of the slab upon its exit from the mould and causes a dangerous notch. In the secondary-cooling zone, where the slab is beginning to straighten out, the breakout of the steel can occur in points of increased local chemical and temperature heterogeneity of the steel. Especially dangerous are the changes in the chemical composition of the steel during the actual concasting. The consequences of this operational immediate change in the chemical composition of the steel, which are not prevented by a breakout system directly inside the mould, could lead to immediate interruption in the concasting and a breakout at a greater distance from the mould than usual. 2. INTERRUPTION OF CONCASTING This case was recorded during the process of concasting of mm steel slabs of quality A and quality B. The change in the chemical compositions of the steels of both qualities was carried out very quickly by changing the tundish. Inside the mould, steel B mixed with steel A of the previous melt. The pouring continued another 20 minutes but then, after, in the unbending point of the slab, at a distance of m away from the level of the melt inside the mould, there occurred a breakout Obr.1. Vzorek oblasti pr valu Fig.1. A sample from the breakout area between the 7th and 8th segments and the caster stopped. The difference in height between the level inside the mould and the breakout point was m. This tear in the shell occurred on the small radius of the caster. A 250 mm thick sample was taken from the breakout area using a longitudinal axial cut (Fig. 1). a 0.41 wt. % carbon content and 9.95 wt. % chromium content (melts 1 to 3) and quality B steel with 0.17 wt. % carbon content and 0.70 wt. % chromium content (melt 4). Detailed chemical composition of both steels is in Fig. 2 and 3. The casting of the first two melts of quality A took place without any significant issues, after the casting of the third melt of quality A, the fourth melt of quality B followed. 3. APPLICATION OF THE NUMERICAL MODEL ON A CONCAST SLAB In the first phase of the analyses, the aim was to determine the material, physical, chemical and technological parameters, which both melts 3 and 4 differed in. Table 1 contains the individual parameters of both melts, entering into off-line version of the numerical model of temperature field in the slab [4].

3 Tab 1. Parametry charakterizující tavbu 3 (ocel A) a tavbu 4 (ocel B) Table 1. The parameters characterizing the melt 3 (steel quality A) and melt 4 (steel quality B) Item # Parameter Symbol Units A melt 3 B melt 4 1 Pouring speed w [m.s -1 ] Dynamic viscosity η [m -1.kg.s -1 ] TL TL η = ρ.ν [m -1.kg.s -1 ] TS TS 3 Density ρ [kg.m -3 ] Latent heat of the phase change L [m 2.kg.s -2 ] Specific heat capacity cp [m 2.s -2.K -1 ] Solidus temperature TS [ C] Liquidus temperature TL [ C] Difference between the liquidus and solidus temperatures TL TS [ C] The numerical model takes into account the temperature field of the entire slab (from the meniscus of the level of the melt in the mould to the cutting torch) using a 3D mesh containing more than a million nodal points. The solidification and cooling of a concast slab is a global problem of 3D transient heat and mass transfer. If heat conduction within the heat transfer in this system is decisive, the process is described by the Fourier- Kirchhoff equation. It describes the temperature field of the solidifying slab in all three of its states: at the temperatures above the liquidus (i.e. the melt), within the interval between the liquidus and solidus (i.e. in the mushy zone) and at the temperatures below the solidus (i.e. the solid state). In order to solve these it is convenient to use the explicit numerical method of finite differences. Numerical simulation of the release of latent heats of phase or structural changes is carried out by introducing the enthalpy function dependent on temperature T. The latent heats are contained here. After the automated generation of the mesh (preprocessing) ties on the entry of the thermophysical material properties of the investigated system, including their dependence on temperature in the form of tables or using polynomials. They are namely the heat conductivity k, the specific heat capacity c and density ρ of the cast metal. The 3D model had first been designed as an off-line version and later as an on-line version so that it could work in real time. After correction and testing, it will be possible to implement it on any caster thanks to the universal nature of the code. Off-line model analyses the temperature field of the actual concasting while it passes through the primary-, secondary- and tertiary-cooling zone, i.e. through the entire caster, as well as through the most important or problematic parts of the caster. Simultaneously, this enables the analysis of the temperature field of the mould and, therefore, the optimisation of its operational parameters, such as cooling, oscillations and the casting flux used. The numerical model fully considers the non-linearity of the task, i.e. the dependence of the thermophysical properties, especially of the concasting material and the mould on the temperature, as it does the dependence of the boundary conditions on surface temperature and other influences (shift rate, cooling intensity, etc.). The numerical model is equipped with an interactive graphics environment for facilitated entry of the input parameters with the successive automatic generation of the mesh (i.e. pre-processing), as well as modern graphics output that displays the temperature field using contour lines in the various sections, time curves, etc. (i.e. post-processing). The software, based on this model must be user-friendly and it is possible to change the parameters by the trained steelworks staff. In this way it is ready for immediate application in the appropriate offices as an off-line system. The model is fully functional and accurately conducts general analyses of the influences of the various technological measures on the formation of the temperature field of the entire concasting. In a similar way, it helps the staff to analyse the failure state of the caster.

4 Off-line version of the temperaturel model was used now to simulate the temperature field of steel slab of melt No.3 (steel quality A), steel slab of melt No. 4 (steel quality B) and a mixture of A and B quality. We consider that each thermophysical property (thermal conductivity, heat capacity, density and enthalpy) of the mixture A + B is the arithmetic average of the properties of steel A and B. The dependence of these parameters on temperature was observed [5]. The model can solve nonlinear problem. The original model solves the temperature history of every point of the cross-section during its movement through the whole caster from the crystallizer to the cutting torch. Fig. 2 shows the temperature curves of the slab cross-section for steel quality A, Fig 3 for steel quality B, Fig. 4 for steel quality A+B. In these graphs a curve shows also the grow of the thickness of a solidified shell. A wt% C 0.95 Cr 0.03 Ni 0.70 Mn 0.28 Si Obr. 2. Teplotní historie bod p í ného ezu bramou (ocel A) Fig. 2. Temperature history of points of the slab cross-section (steel A) B wt% C 0.07 Cr 0.02 Ni 1.46 Mn 0.23 Si Obr. 3. Teplotní historie bod p í ného ezu bramou (ocel B) Fig. 3. Temperature history of points of the slab cross-section (steel B) A+B Obr. 4. Teplotní historie bod p í ného ezu bramou (ocel A+B) Fig. 4. Temperature history of points of the slab cross-section (steel A+B) The model provides also the curves of isoliquidus (red) and isosolidus (blue). The model draws these isotherms in both axial longitudinal sections of the slab for steel A, B and steel mixture A+B to the common Figure to the better compare. The figure 5 shows the comparison in the first axial longitudinal section, the Fig. 6 in the second axial longitudinal section. Areas between isoliquidus and isosolidus, therefore in the solidification interval are the so-called mushy zones.

5 A A B B A+B A+B Obr. 5. ISOSOLIDa A ISOLIkvida V prvním osovém podélném ezu bramou Fig. 5. Isosolidus and isoliquidus in the first axial longitudinal section of the slab. Obr. 6. ISOSOLIDa A ISOLIQUIDa Ve druhém osovém podélném ezu bramou Fig.6. Isosolidus and isoliquidus in the second axial longitudinal section of the slab. For example calculated mushy zone (the area between isoliquidus -red curve and isosolidus- blue curve) in the cross-section of the slab in which the break out has occured (at a distance of m from the level of melt in the mould) for steel A is shown in the Figure 7 for the quality of the A, B and A + B. A B A+B Obr. 7. Mushy zóna v p í ném ezu pr valem Fig. 7. A mushy zone in the cross-section of the breakout 4. THE APPLICATION OF SIMILARITY THEORY. They collected thermophysical parameters of both qualities of steel, technological parameters of the caster (casting speed, mold characteristics, etc.) and data that were obtained by means of off-line model of the temperature field of the both slabs. Mutual dependence of the set of thus stipulated parameters and quantities will be determined. For this an application of theory of physical similarity is assumed. It is expected at the same time that this way based on three basic theorems (π theorem of dimensional independence and theorem of dimensional homogeneity) will make it possible to determine the number or even a kind of dimensionless arguments representing criteria of similarity. It enables also reduction of the number of independent variables, describing individual partial processes accompanying continuous casting of steel slabs and also causal dependencies between these quantities. This is in principle the only possible manner how to described, evaluate and control with use of criteria in extreme cases stability of complex physicalchemical processes, from which the continuous casting is composed. That is to say that the existing findings and experience indicate that it is impossible, at least at present, to realise an absolutely exact mathematical-

6 physical and chemical description of the whole process and control deduced from it from the moment when liquid steel enters the tundish, including inter-mixing of individual heats, till the moment when steel enters the mold, its passage through the whole system of secondary cooling and zones of straightening till the final product. Application of similarity theory will be the subject of a separate article. 5. CONCLUSION A breakout of the concast slab right under the mould is usually detected and indicated by an anti-breakout system. However, breakouts occur at contcasting, i.e. failure of strength of solidified shell even at smooth change of grade of the cast steel, most often on radial CCM at the place of straightening of the slab. This irreparable defect is moreover often initiated by surface defects, the origin of which is already in the mold during the beginning of crystallisation. These are oscillation marks and sub-surface pockets - hooks. Both phenomena, i.e. formation of marks and hooks are related to each other. These defects may also lead under certain conditions, such as change of grade of contcast steel, to interruption of casting and to breakout, as it is demonstrated in the photo of macro-structure of defect, taken directly at the place of breakout of continuously cast slab. Moreover the breakout occured after a quick change in the chemical composition of the concast steel quality A and the quality B. The change in the chemical compositions of the steels of both qualities was carried out very quickly by changing the tundish. The pouring continued another 20 minutes but then, in the unbending point of the slab, there occurred a breakout and the caster stopped. Off-line version of the temperature model was used to simulate of the temperature field of the slab of steel quality A, steel quality B and a mixture of A and B quality. They collected thermophysical parameters of both qualities of steel, technological parameters of the caster (casting speed, mold characteristics, etc.) and data that were obtained by means of off-line temperature model. Mutual dependence of the set of thus stipulated parameters and quantities will be determined. For this an application of theory of physical similarity and the derivation of similarity criteria is assumed. ACKNOWLEDGMENTS This analysis was conducted using a program devised within the framework of the GA CR projects No. 106/08/0606, 106/09/0940, 106/09/0969 and P107/11/1566. REFERENCES [1] BADRI A. et al. A Mold Simulator for Continuous Casting of Steel. Part II. The Formation of Oscillation Marks during the Continuous Casting of Low Carbon Steel. Metallurgical and Materials Transactions B, Volume 36 B, June 2005, pp [2] THOMAS, B.G., J. SENGUPTA, and OJEDA, C. Mechanism of Hook and Oscillation Mark Formation In Ultra-Low Carbon Steel. In Second Baosteel Biennial Conference, Vol. 1, 2006, pp [3] OJEDA, C. et al. Mathematical Modeling of Thermal-Fluid Flow in the Meniscus Region During an Oscillation Cycle. AISTech 2006 Proceedings, Vol. 1, pp [4] STETINA J.et al. Optimization of technology and control of a slab caster. I. Off-line numerical model of temperature field of a slab a parametric studies. Hutnicke listy LXIII, No.1/2010, pp [5] LOUHENKILPI, S., LAITINEN, E., NIEMINEN, R. Real-Time Simulation of Heat Transfer in Continuous Casting. Metallurgical Transactions B, 24B:4, 1993, pp