The Effect of Slab Thickness on the Solidification of Low carbon Steel in Continuous Casting Process: A Simulation Case Study

Document Type : Research Paper

Author

Sharif University off Technology

10.22034/ijissi.2023.562171.1250

Abstract

One of the most important and effective factors of the solidification in the steel continuous casting process is the geometry of the strand. To study the effect of this geometry, the influence of slab thickness will be investigated. To this end, first, a thermal model is proposed such that its reliability is verified by simulating another paper in the literature and comparing the results with that research. In the model of the present work, the thermophysical properties are calculated based on the computational thermodynamics model, CALPHAD technique. Then three different thicknesses are chosen subject to the same cooling conditions and technological parameters. Afterward, the metallurgical length and shell thickness for these thicknesses are compared. As the shell thickness is approximated by a square root function of time, holding the coefficient K, finally, the K factor of the mentioned thicknesses are extracted each and compared with one another such that the higher the thickness, the higher the K coefficient

Keywords


  1. [1] J. Hejazi, Ingot Casting, Irainan Foundarymen Soci-

    ety, 1982, (in Persian).

    [2] B. Petrus, D. Hammon, M. Miller, B. Williams, A.

    Zewe, Z. Chen, J. Bentsman, B. Thomas, Newmethod to

    measure metallurgical length and application to improve

    computational models, Iron and Steel Technology Con-

    ference and 7th International Conference on the Science

    and Technology of Ironmaking, Cleavlad , USA, 2015.

    [3] X. Huang, B. Thomas, Modeling of steel grade tran-

    sition in continuous slab casting processes, Metallur-

    gical Transactions B. 24 (1993) 393-379. https://doi.

    org/10.1007/BF02659140.

    [4] C. Santos, J. Spim, A. Garcia, Mathematical model-

    ing and optimization strategies (genetic algorithm and

    knowledge base) applied to the continuous casting of

    steel, Engineering Applications of Artificial Intelligence.

    16 (2003) 511-527. https://doi.org/10.1016/S0952-

    1976(03)00072-1.

    [5] M. Long, D. Chen, J. Zhang, Q. Ouyang, Novel on-

    line temperature control system with closed feedback

    loop for steel continuous casting, Ironmaking & Steel-

    making. 38 (2011) 620-629. https://doi.org/10.1179/174

    3281211Y.0000000042.

    [6] L. Klimeš, J. Štětina, A rapid GPU-based heat trans-

    fer and solidification model for dynamic computer sim-

    ulations of continuous steel casting, Journal of Materi-

    als Processing Technology. 226 (2015) 1-14. https://doi.

    org/10.1016/j.jmatprotec.2015.06.016.

    [7] S. Louhenkilpi, M. Mäkinen, S. Vapalahti, T. Räisänen,

    1. Laine, 3D steady state and transient simulation tools

    for heat transfer and solidification in continuous casting,

    Materials Science and Engineering: A. 413(2005) 135-

    1. https://doi.org/10.1016/j.msea.2005.08.153.

    [8] K. Zheng, B. Petrus, B. G. Thomas, J. Bentsman,

    Design and implementation of a real-time spray cooling

    control system for continuous casting of thin steel slabs,

    Proceeding AISTech Steelmaking Conference, Indianap-

    olis, 2007.

    [9] J. Yang, Z. Xie, Z. Ji, H. Meng, Real-time heat trans-

    fer model based on variable non-uniform grid for dynam-

    ic control of continuous casting billets, ISIJ international.

    54 (2014) 328-335. https://doi.org/10.2355/isijinterna-

    tional.54.328.

    [10] B. Petrus, K. Zheng, X. Zhou, B. Thomas, J. Bents-

    man, Real-time, model-based spray-cooling control

    system for steel continuous casting, Metallurgical and

    materials transactions B. 42 (2011) 87-103. https://doi.

    org/10.1007/s11663-010-9452-7.

    [11] T. Männikkö, E. Laitinen, P. Neittaanmäki, Re-

    al-time simulation and control system for the continuous

    casting process, in: H.-H. Sebastian, K.Tammer (eds),

    System Modelling and Optimization, Springer-verlag

    Berlin Heidelberg GmbH, 1990, pp.809-817.

    [12] E. Laitinen, P. Neittaanmäki, T. Männikkö, On the Real-time Simulation and Control of the Continuous

    Casting Process, In: J. Manley, S. McKee, D. Owens

    (eds), Proceedings of the Third European Conference on

    Mathematics in Industry, Springer-verlag Berlin Heidel-

    berg GmbH, 1990, pp.401–408.

    [13] L. Guo, Y. Tian, M. Yao, H. Shen, Temperature dis-

    tribution and dynamic control of secondary cooling in

    slab continuous casting, International Journal of Miner-

    als, Metallurgy and Materials. 16 (2009) 626-631. https://

    doi.org/10.1016/S1674-4799(10)60003-9.

    [14] M. Jauhola, E. Kivela, J. Konttinen, E. Laitinen, S.

    Louhenkilpi, Dynamic secondary cooling model for a

    continuous casting machine, Proceeding 6th Internation-

    al Rolling Conference, Dusseldorf, Germany, 1994.

    [15] Y. Zhai, Y. Li, B. Ma, C. Yan, Z. Jiang, The optimi-

    sation of the secondary cooling water distribution with

    improved genetic algorithm in continuous casting of

    steels. 19 (2015) 26-31. https://doi.org/10.1179/143289

    1715Z.0000000001362.

    [16] K. Worapradya, P. Thanakijkasem. Optimum spray

    cooling in continuous slab casting process under produc-

    tivity improvement, IEEE International Conference on

    Industrial Engineering and Engineering Management,

    Hong Kong, 2009.

    [17] D. Słota, Identification of the cooling condition in

    2-D and 3-D continuous casting processes, Numerical

    Heat Transfer Part B: Fundamentals. 2 (2009) 155-176.

    https://doi.org/10.1080/10407790802605232.

    [18] B. Filipic, E. Laitinen, Model-based tuning of pro-

    cess parameters for steady-state steel casting, Informati-

    ca an international journal of computing and informatics.

    29 (2005) 2005 491-496.

    [19] K. Cho, B. Kim, Numerical analysis of secondary

    cooling in continuous slab casting, Journal of Materials

    Science and Technology. 24(2008) 389-390. https://doi.

    org/10.1016/S0924-0136(01)00654-9.

    [20] F. Camisani-Calzolari, I. Craig, P. Pistorius, Specifica-

    tion framework for control of the secondary cooling zone

    in continuous casting, ISIJ international. 38 (1999) 7131-

    1. https://doi.org/10.2355/isijinternational.38.447.

    [21] J. Zhang, D. Chen, C. Zhang, S. Wang, W. Hwang,

    Dynamic spray cooling control model based on the track-

    ing of velocity and superheat for the continuous casting

    steel, Journal of Materials Processing Technology. 229

    (2016) 651-658. https://doi.org/10.1016/j.jmatpro-

    tec.2015.10.015.

    [22] N. Cheung, A. Garcia, The use of a heuristic search

    technique for the optimization of quality of steel bil-

    lets produced by continuous casting, Engineering Ap-

    plications of Artificial Intelligence. 14 (2001) 229-238.

    https://doi.org/10.1016/S0952-1976(00)00075-0.

    [23] D. Van der Spuy, I. Craig, P. Pistorius, An optimi-

    zation procedure for the secondary cooling zone of a

    continuous billet caster, Journal of the Southern African

    Institute of Mining and Metallurgy. 99 (1999) 49-54.

    https://hdl.handle.net/10520/AJA0038223X_2613.

    80

    [24] T. Mauder, C. Sandera, J. Stetina, Optimal control

    algorithm for continuous casting process by using fuzzy

    logic, Steel Research International. 86 (2015) 785-798.

    https://doi.org/10.1002/srin.201400213.

    [25] Y. Wang, X. Luo, Y. Yu, Q. Yin, Evaluation of

    heat transfer coefficients in continuous casting under

    large disturbance by weighted least squares Leven-

    berg-Marquardt method, Applied Thermal Engineering.

    111 (2017) 989-996. https://doi.org/10.1016/j.applther-

    maleng.2016.09.154.

    [26] Y. Yu, X. Luo, Estimation of heat transfer coeffi-

    cients and heat flux on the billet surface by an integrated

    approach, International Journal of Heat and Mass Trans-

    fer. 90 (2015) 645-653. https://doi.org/10.1016/j.ijheat-

    masstransfer.2015.07.008.

    [27] T. Männikkö and M. Mäkelä, Nonsmooth penalty

    techniques in control of the continuous casting process,

    in: P. Neittaanmaki (eds), Numerical Methods for Free

    Boundary Problems, Springer-Basel AG, 1991, pp.297-

    1. https://doi.org/10.1007/978-3-0348-5715-426.

    [28] B. Lally, L. Biegler, H. Henein, Optimization and

    continuous casting: Part II Application to industrial cast-

    ers, Metallurgical Transactions B. 22 (1991) 649-659.

    https://doi.org/10.1007/BF02679020.

    [29] S. Louhenkilpi, E. Laitinen, R. Nieminen, Real-time

    simulation of heat transfer in continuous casting, Metal-

    lurgical Transactions B. 24 (1993) 685-693. https://doi.

    org/10.1007/BF02673184.

    [30] M. Bellet, L. Salazar-Bbetancourt, O. Jaouen, F.

    Costes, Modelling of water spray cooling Impact on ther-

    momechanics of solid shell and automatic monitoring to

    keep metallurgical length constant, European continuous

    casting conference (8th ECCC), Austrian society for met-

    allurgy and materials, 2014.

    [31] R. Tavakoli, Smooth modeling of solidification

    based on the latent heat evolution approach, The Interna-

    tional Journal of Advanced Manufacturing Technology,

    88 (2017) 3041-3052. https://doi.org/10.1007/s00170-

    016-9012-7.

    [32] M. Sadat, A. H. Gheysari, S. Sadat, The effects of

    casting speed on steel continuous casting process, Heat

    and mass transfer. 47 (2011) 1601-1609. https://doi. org/10.1007/s00231-011-0822-8.

    [33] E. Majchrzak, Numerical simulation of continuous

    casting solidification by boundary element method, En-

    gineering Analysis with Boundary Elements. 11 (1993)

    95-99. https://doi.org/10.1016/0955-7997(93)90028-J.

    [34] Z. Han, D. Chen, K. Feng, M. Long, Development

    and application of dynamic soft-reduction control model

    to slab continuous casting process, ISIJ international. 50

    (2010) 1637-1643. https://doi.org/10.2355/isijinterna-

    tional.50.1637.

    [35] M. Alizadeh, A. J. Jahromi, O. Abouali, A new

    semi-analytical model for prediction of the strand surface

    temperature in the continuous casting of steel in the mold

    region, ISIJ international. 48 (2008) 161-169. https://doi.

    org/10.2355/isijinternational.48.161.

    [36] A. Pourfathi, R. Tavakoli, Thermal optimization of

    secondary cooling systems in the continuous steel cast-

    ing process, International Journal of Thermal Sciences.

    183 (2023) 107860. https://doi.org/10.1016/j.ijthermals-

    ci.2022.107860.

    [37] Y. Yu, X. Luo, H. Y. Zhang, Q. Zhang, Dynamic op-

    timization method of secondary cooling water quantity in

    continuous casting based on three-dimensional transient

    nonlinear convective heat transfer equation, Applied

    Thermal Engineering. 160 (2019) 113988. https://doi.

    org/10.1016/j.applthermaleng.2019.113988.

    [38] S. Chaudhuri, R. Singh, K. Patwari, S. Majumdar,

    1. Ray, A. Singh, N. Neogi, Design and implementation

    of an automated secondary cooling system for the contin-

    uous casting of billets, ISA transactions. 49 (2010) 121-

    1. https://doi.org/10.1016/j.isatra.2009.09.005.

    [39] S. Lalitha, S. Chattopadhyay, S. Das, K. Godiwal-

    la, Simulation of heat transfer in the continuous casting

    mold, Transactions of the Indian Institute of Metals. 44

    (1991) 89-92.

    [40] J. Dantzig, Ch. Tucker, Modeling in materials pro-

    cessing, Cambridge university press, 2001.

    [41] K. Spitzer, K. Harste, B. Weber, P. Monheim, K.

    Schwerdtfeger, Mathematical model for thermal tracking

    and on-line control in continuous casting, ISIJ interna-

    tional. 32 (1992) 848-856. https://doi.org/10.2355/isijin-

    ternational.32.848.