T (1) Key words: continuous casting, heat transfer model, shell thickness, surface temperature

Transcription

1 Applied Mechanics and Materials Online: ISSN: , Vols , pp doi: / Trans Tech Publications, Switzerland Numerical simulation of billet continuous casting solidification based on the measurement of shell thickness and surface temperature MA Jiao cheng 1,a, SUN Huizhao 2, WANG Xuebin 2, LV Xia 2 1. School of Mechanical Engineering and Automation Northeastern University Shenyang, Liaoning, China 2. Research and Development Center, Laiwu Iron and Steel Inc. Shandong, China a majiaocheng@163.com Key words: continuous casting, heat transfer model, shell thickness, surface temperature Abstract: In order to more accurate simulation the solidification of billet continuous casting. The measured shell thickness and surface temperature have been used to revise the heat transfer model. The calculated results of the model are in excellent agreement with the experimental ones based on an actual casting machine. The revised model can excellent to simulate the billet solidification process. So it provides the possibility for better simulation the dynamic solidification process and optimizing of the secondary cooling water. 1. Introduction In the continuous casting process, the internal defects which can be formed in cast material are due to inappropriate casting operation and improper secondary cooling water distribution, especially the defects of cracks represented by the midway crack and centreline crack which cover over 50% of total quality problems [1,2]. Secondary cooling control is one of the key techniques of influencing the quality of billet. The solidification process in the secondary cooling should be controlled, which is equal to control the temperature field of billet. In order to avoid internal cracks and other defects, it is necessary to analyses the solidification process based on the heat transfer model. Owing to the influence of high-temperature, water vapor, water film and scales on the strand surface, etc in the secondary cooling zone, it is difficult to measure the billet surface temperature accurately, let alone the internal temperature. In order to better control the billet solidification process, many mathematical heat transfer models [3,4] for continuous casting have been developed and the solidification process has been studied. Especially, the dynamic model which can simulate the actual solidification process has been established [5]. However, the solidification heat transfer model for correction and verification of the actual field is very less. The industry experiment has been done according to an actual machine. The thickness combined with surface temperature of measured has been used to correct the model, In view of the present defects which the heat transfer model has been revised by using only measured thickness or measured surface temperature. It provides the possibility for better simulation the dynamic solidification process [5,6] and optimizing of the secondary cooling water [7,8]. 2. Mathematical model and modified method In order to simulate the billet continuous casting process of heat transfer and solidification, some assumptions have been made in the present mathematical models [3-5]. The two-dimensional heat conduction equation and the boundary conditions are shown as follows: ρ c = k + k + q (1) τ x x y y All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-04/03/16,02:23:15)

2 82 Information Engineering for Mechanics and Materials where T is the billet temperature, t is the time, x, y is the rectangular coordinates, k is the thermal conductivity of steel, c is the specific heat capacity of steel, ρ is the density of steel, and q is the latent heat source. (1) Initial condition ( x, y, t) T0 T t = (2) = 0 (2) In mould k = q= a b t (3) n (3) Secondary cooling zone 4 4 k = h( T Twar) + εσ ( T T air ) (4) n (3) Radiation cooling zone 4 4 k = εσ ( T T air ) (5) n where T 0 is casting temperature; a,b are decided by the water flow rate and the difference of water temperature in the mould; h is heat transfer coefficient; k is the thermal conductivity; T is the strand surface temperature; T war is the cooling water temperature;ε is the emissivity; σ is the Stefan-Boltzman constant; T air is the air temperature. h Heat transfer coefficients h are calculated by the following equation [9.10] : w ( T war ) = (6) α Where w is the water flow density (L/m 2 /s), T war is the cooling water temperature, α is a machine-dependent calibration factor. The accuracy and reliability of model is the key of practical. The revised of model is to determine the boundary conditions. The convective heat transfer coefficient of secondary cooling of billet sections is difficult to directly accurately measure because of the impact of the pressure of cooling water, the density of water flow and the billet surface temperature. The modification of the model is to adjust the heat transfer coefficient to make the calculated data good agreement to the measured ones. The modified parameters of model are mainly the billet surface temperature or the shell thickness. As the shell thickness can be well reflected the changes of the casting speed, but it does not reflect the billet surface temperature. The billet shell thickness can be well reflected the changes of the casting speed, and it has very good stability, but it does not reflect the billet surface temperature. The billet surface temperature can be well reflected by the measured temperature. Owing to the influence of high-temperature, water vapor, water film and scales on the strand surface, etc in the secondary cooling zone, it is difficult to measure the billet surface temperature accurately. The surface temperature was measured by the thermal imager in the exit of the secondary cooling. The shell thickness was measured by the nail shooting in secondary cooling zone respectively. The model was revised by the measured data.

3 Applied Mechanics and Materials Vols J Optimization objective function: H H n c m i i min = di (7) m i= 1 Hi Where H, are calculated and measured shell thickness and surface temperature c m i Hi respectively. d i is the weight. 3. Results and discussion The heat transfer and solidification model is based on an actual casting machine in a steel plant. There are three cooling segments: mould, secondary and radiation cooling segment. The secondary cooling segment has three zones with independently controlled water sprays. The computing parameters are shown in Table 1. The shell thickness at the end of each spray zone and the surface temperature at the secondary cooling exit were measured in different pouring process conditions as shown in Table 2. The heat transfer coefficients of secondary cooling zones were revised to make the calculation billet thickness and the surface temperature with the measured results consistent. Table 1 Geometry of the billet caster Parameter Value Section size(m x m) Mold length(m) 0.80 Spray zone lengths(m) zone zone zone Surface temperature measuring point(m) 7.7 Table 2 Comparison between calculated and measured shell thicknesses and surface temperature Casting speed (m/min) Shell thickness (mm) temperature( ) calculated measured calculated measured Shooting nail method is use sulfur distribution different in the different metal phase to define the phase bound. So the shell thickness can be gained at the shooting nails position by the sulfur print, as shown Fig 1.

4 84 Information Engineering for Mechanics and Materials Fig.1 Method of measuring shell thickness There is a great fluctuation on the measured temperature, because of the influence of the scale on the strand surface. Some areas of the strand surface are covered by the scale and some are not, especially the air gap that forms between the scale and the strand surface can cause the fluctuation above 100. The pyrometer is spot measurement, so it s very difficult to reflect the actual surface temperature. In the radiation region, the surface temperature gradient of billet is rather little in the withdrawal direction, so it was assumed that the temperature in a small rectangle area at measured point neighborhood doesn t change and the top temperature are near the actual surface temperature. The effect of the scale has been reduced through multipoint measuring with thermal imager in the rectangle area and selecting the maximal temperature as the measured temperature. Fig 2 show that the measured surface temperature and peak extraction temperature at the secondary cooling exit by changing operation conditions. Fig.2 The measured surface temperature Temperature( ) central temperature shell thickness surface temperature calculated measured Shell thickness(mm) Distance from meniscus(m) Fig.3 Measured and calculated shell thickness and surface temperature

5 Applied Mechanics and Materials Vols The shell thickness and the temperature of billet can be gained by the heat transfer model which was revised by shell thickness and surface temperature of measured. From Fig 3, a consistent result of shell thickness and surface temperature between experimental data and numerical results is obtained. From the results that the revised model can more accurate simulate the billet solidification process. Conclusions The correction method of heat transfer model and the key correction parameters have been studied. The surface temperature and shell thicknesses were measured by the thermal imager in the exit of the secondary cooling and nail shooting in secondary cooling zone respectively and the model was revised by the measured data. The revised model can excellent to simulate the billet solidification process, and it provides the possibility for better optimizing of the second cooling water. Acknowledgment The authors would like to gratefully acknowledge the financial support of National Natural Science Foundation of China ( ). References: [1] J.K. Brimacombe, I.V. Samarasekera, J.E. Lait. Continuous Casting-Heat Flow, Solidification and Crack Formation [J]. Iron and Steel Society, AIME, New York, (1984), 26. [2] T.Nozaki, J.I.Matsuno, K.Murata, H.Ooi, and M.Kodama, A Secondary Cooling Pattern for Preventing Surface Cracks of Continuous Casting Slab, Trans. Iron Steel Inst. Jpn., 1978, Vol.18(6), pp [3] Hongming WANG, Guirong Li, Mathematical Heat Transfer Model Research for the Improvement of Continuous Casting Slab Temperature, ISIJ International, Vol.45(2005), No.9, [4] Bo Rogberg, Testing and Application of a Computer Program for Simulating the Solidification Process of a Continuously Cast Strand, Scandinvian Journal Metallurgy 12(1983), [5] MA Jiao cheng, XIE Zhi, JIA Guang lin. Applying of real-time heat transfer and solidification model on the dynamic control system of billet continuous casting [J]. ISIJ International, 2008, 48(12), [6] Karl Mörwald, Kurt Dittenberger., Gerald Hohenbichler. Improvement of Secondary Cooling Control by On-line Temperature Calculation [J], Steelmaking conference proceedings[c], 1997: [7] C.A.Santos, J.A.Spim, A.Garia, Mathematical modeling and optimization strategies (genetic algorithm, and knowledge base) applied to the continuous casting of steel [J], Engineering Applications of Artificial Intelligence, 16 (2003) [8] Lally. B., Biegler. L.T., Henein, H.,Henein. Optimization and Continuous Casting: Part II. Application to Industrial Caster [J], Metallurgical Transactions B, 1991, Vol.22 (7): [9] Mizikar, E.A. Spray Cooling Investigation for Continuous Casting of Billets and Blooms, Iron and Steel Engineer, 47(1970), 53. [10] Sang-Min LEE, Suk-Yong JANG, Problems in using the Air-mist Spray Cooling and Its Solving Methods at Pohang, No.4 Continuous Casting Machine, ISIJ International,Vol.36 (1996),S208-S210.

6 Information Engineering for Mechanics and Materials / Numerical Simulation of Billet Continuous Casting Solidification Based on the Measurement of Shell Thickness and Surface Temperature /