Abstract:

The project's co-founder is a Slovenian state-of-the-art manufacturer of steel Štore Steel. The company is a global player, renowned for its topmost quality products, used in automotive, aircraft, space, sports and military industries.

The project contents are tied to a sequence of our four previous, successfully completed applied research projects, and the accompanying EU Framework Programmes, projects with USA and China. Based on the gained knowledge, we have digitalised the 2016 installed, continuous casting of steel machine with advanced computational models.

The main aim of this project was to develop further and refine the existing continuous casting on-line and off-line models for prediction and mitigation of casting defects such as macrosegregation, inclusions, shape distortion, porosity, hot tearing, decreased surface quality and both internal and surface cracks.

In the project, an integrated multiscale, multiphysics, and multiobjective model of the mentioned continuous casting processes, has been further established and describes the phenomena from the top of the mould up to the cooling of the billets. It integrates thermomechanics, thermofluids, thermodynamics, transport phenomena, electromagnetic science and technology, and magnetohydrodynamics. The multiscale coupling includes relations between the process parameters, product macrostructure, microstructure and properties. The multiphysics coupling consists of relations between the solution of electromagnetic field and temperature, velocity, concentration, deformation and stress fields. The multiobjective features enable proper setting and optimisation of process parameters concerning productivity, product quality and/or environmental impact.

The coupled equations of mass, energy, momentum, species and turbulent models are solved in the Eulerian system. The microscopic models are based on the Lagrangian movement of the representative part of the microstructure. The microstructure models are based on our original point automata and phase-field methods. The electromagnetic field is solved through Maxwell equations. The models are evaluated in realistic threedimensional settings using our original meshless methods, for which we received numerous awards. The numerical implementation is establishedon a common computational platform, exploiting the parallel computing capabilities of modern supercomputers. The models have been validated  based on in-plant measurements, laboratory materials characterisation and water similarity models. The described modelling aims to predict the product properties as a function of complex process parameters and estimate the possible design changes of the casting device.

The project's outcome is new knowledge for improved quality, enhanced process capabilities and productivity. The results have been implemented in production, published in top journals in the field and presented as invited talks at major international meetings on the project topics.  

 

The phases of the project and their realization:

Work Package 1:Refinement of the physical models

WP1 - Task 1.1: Fluid mechanics part of solidification

Five non-uniformly distributed subdomain points with a scheme of filter width calculation. ●Central subdomain point. ○Four neighbouring sub-domain points.Velocity magnitude field for LES model. a) t = 0 s. b) t = 5 s. c) t=10 s. d) t=50 s. e) t = 100 s. f) t = 500 s. g) t = 1000 s. h) t = 5000 s.

[1.1.1] VERTNIK, Robert, MRAMOR, Katarina, ŠARLER, Božidar. Solution of three-dimensional temperature and turbulent velocity field in continuously cast steel billets with electromagnetic stirring by a meshless method. Engineering analysis with boundary elements. Jul. 2019, vol. 104, str. 347-363, ilustr. ISSN 0955-997. https://www.sciencedirect.com/science/article/pii/S0955799718305010?via%3Dihub, DOI: 10.1016/j.enganabound.2019.03.026. [COBISS.SI-ID 1474474].

[1.1.2] MRAMOR, Katarina, VERTNIK, Robert, ŠARLER, Božidar. Application of the local RBF collocation method to natural convection in a 3D cavity influenced by a magnetic field. Engineering analysis with boundary elements. 2020, vol. 116, str. 1-13, ilustr. ISSN 0955-7997. https://www.sciencedirect.com/science/article/abs/pii/S0955799720300977, DOI: 10.1016/j.enganabound.2020.03.025. [COBISS.SI-ID 17163547].

[1.1.3] Hatić V, Mavrič B, Šarler B. Simulation of a macrosegregation benchmark with a meshless diffuse approximate method. International journal of numerical methods for heat & fluid flow. 2018;28(2):361-380. doi:10.1108/HFF-04-2017-0143.

[1. 1.4] Gregorc J, Kunavar A, Šarler B. RANS versus scale resolved approach for modeling turbulent flow in continuous casting of steel. Metals. 2021;11(7):1-12. doi:10.3390/met11071140.

[1.1.5] MRAMOR, Katarina, VERTNIK, Robert, ŠARLER, Božidar. Meshless approach to the large-eddy simulation of the continuous casting process. Engineering analysis with boundary elements. May 2022, vol. 138, str. 319-338, ilustr. ISSN 0955-7997. https://www.sciencedirect.com/science/article/pii/S0955799722000649, DOI: 10.1016/j.enganabound.2022.03.001. [COBISS.SI-ID 100532739].

[1.1.6] MRAMOR, Katarina, VERTNIK, Robert, ŠARLER, Božidar. Large-eddy simulation of continuous casting process. V: WU, Menghuai (ur.). STEEL SIM 2021 : 9th International Conference on Modeling and Simulation of Metallurgical Processes in Steelmaking, 05-07 October 2021, virtual conference. 9th International Conference on Modeling and Simulation of Metallurgical Processes in Steelmaking, 05-07 October 2021, virtual conference. [S. l.: ASMET, Austrian Society for Metallurgy and Materials, 2021]. F. 310-317, ilustr. ISBN 978-3-200-07994-6. [COBISS.SI-ID 79648003].

[1.1.7] Gregorc J, Kunavar A, Šarler B. Performance of turbulence models for flow prediction in a mould of continuous steel caster. In: MCWASP XV: International Conference on Modelling of Casting, Welding and Advanced Solidification Processes. MCWASP XV: International Conference on Modelling of Casting, Welding and Advanced Solidification Processes. IOP Publishing; 2020:1-8. doi:10.1088/1757-899X/861/1/012019.

[1.1.8] MRAMOR, Katarina, VERTNIK, Robert, ŠARLER, Božidar. Numerical modelling of the effect of electromagnetic stirring direction in continuous casting of steel billets. V: ROÓSZ, A. (ur.). Solidification and Gravity VII : selected, peer reviewed papers from the Seventh International Conference on Solidification and Gravity : Miskolc-Lillafüred, Hungary, September 3-6, 2018. Miskolc: Hungarian Academy of Sciences - University of Miskolc, Materials Science Research Group: Miskolc Committee of Hungarian Academy of Sciences, [2018?]. Str. 167-172, ilustr. ISBN 978-963-508-889-8. [COBISS.SI-ID 1424554].

[1.1.9] Mramor K, Hatić V, Šarler B. A meshless approach for solving binary alloy solidification with moving grains. EUROMAT 2021: European Congress and Exhibition on Advanced Materials and Processes. Published online 2021:1. https://submit.asmet.org/event/53/contributions/3427/.

 

WP1 - Task 1.2: Travelling slice model of solid mechanics

The results of the mechanical model at the exit from the mould cooling area.

[1.2.1] Šarler B, Mavrič B, Dobravec T, Vertnik R. A comprehensive slice model for continuous casting of steel. In: Proceedings: 10th European Conference on Continuous Casting, Bari, Italy, 20-22 October 2021. Proceedings: 10th European Conference on Continuous Casting, Bari, Italy, 20-22 October 2021. s. n.; 2021:1-10.

[1.2.2] Mavrič B, Dobravec T, Vertnik R, Šarler B. A meshless thermomechanical travelling-slice model of continuous casting of steel. In: IOP Conference Series. IOP conference series. ; 2020:1-8. doi:10.1088/1757-899X/861/1/012018.

[1.2.3] Mavrič B, Dobravec T, Vertnik R, Šarler B. Investigation of the effect of asymmetric thermal conditions on stresses during continuous casting of steel with the use of meshless travelling-slice model. In: Roósz A, ed. Solidification and Gravity VII: Selected, Peer Reviewed Papers from the Seventh International Conference on Solidification and Gravity. Solidification and Gravity VII: selected, peer reviewed papers from the Seventh International Conference on Solidification and Gravity. Hungarian Academy of Sciences - University of Miskolc, Materials Science Research Group; Miskolc Committee of Hungarian Academy of Sciences; 2018:197-203.

[1.2.4] Šarler B, Mavrič B, Vertnik R, Dobravec T. A temperature, concentration, stress and grain structure slice model for continuous casting of steel. Book of Abstracts. Published online 2021:36-37. https://submit.asmet.org/event/55/book-of-abstracts.pdf.

[1.2.5] Mramor K, Vertnik R, Šarler B. Simulation of macrosegregation in continuous casting of steel based on large-eddy turbulence model and meshless solution procedure. Book of abstracts. Published online 2022:212.

[1.2.6] Mavrič B, Dobravec T, Vertnik R, Šarler B. Meshless solution of thermomechanical slice model of continuous casting of steel. The 13th World congress on computational mechanics (WCCM XIII) [and] 2nd Pan American congress on computational mechanics (PANACM II) July 22-27, 2018, New York, USA. Published online 2018:1. http://www.wccm2018.org/program.

[1.2.7] Mavrič B, Dobravec T, Vertnik R, Šarler B. Brezmrežni model potujoče rezine za napovedovanje mehanskih deformacij pri kontinuirnem ulivanju jekla. Akademija strojništva 2018: povezovanje in mreženje. 2018;7(3/4):77. http://www.zveza-zsis.si/2018/10/25/svet-strojnistva-akademija-strojnistva-2018/.

WP1 - Task 1.3: 3D Model of solid mechanics

zz-components of stress (left) and plastic strain(right) field of uniaxially loaded cube.

[1.3.1] Mavrič B, Dobravec T, Vertnik R, Šarler B. Brezmrežni model potujoče rezine za napovedovanje mehanskih deformacij pri kontinuirnem ulivanju jekla. Akademija strojništva 2018: povezovanje in mreženje. 2018;7(3/4):77. http://www.zveza-zsis.si/2018/10/25/svet-strojnistva-akademija-strojnistva-2018/.

 

WP1 - Task 1.4: Microstructure modelling

Discretisation-induced anisotropy during the phase-field modelling of dendritic growth in arbitrary preferential growth directions using regular and scattered node distributions.

Poglavitne reference: 

[1.4.1] Dobravec T, Mavrič B, Šarler B. Reduction of discretisation-induced anisotropy in the phase-field modelling of dendritic growth by meshless approach. Computational materials science. 2020;(172):1-12. doi:10.1016/j.commatsci.2019.109166.

[1.4.2]  Dobravec T, Mavrič B, Šarler B. Development of adaptive meshless solution procedure for phase field modelling of dendritic solidification in carbon steel. In: Wu M, ed. STEEL SIM 2021: 9th International Conference on Modeling and Simulation of Metallurgical Processes in Steelmaking, 05-07 October 2021, Virtual Conference. STEEL SIM 2021: 9th International Conference on Modeling and Simulation of Metallurgical Processes in Steelmaking, 05-07 October 2021, virtual conference. ASMET, Austrian Society for Metallurgy and Materials; 2021:291-301.

[1.4.3] Dobravec T, Mavrič B, Šarler B. Phase field modelling of dendritic solidification by using an adaptive meshless solution procedure. In: MCWASP XV: International Conference on Modelling of Casting, Welding and Advanced Solidification Processes. MCWASP XV: International Conference on Modelling of Casting, Welding and Advanced Solidification Processes. IOP Publishing; 2020:1-7. doi:10.1088/1757-899X/861/1/012060.

[1.4.4] Dobravec T, Mavrič B, Šarler B. Meshless phase field modeling of dendritic growth. In: Roósz A, ed. Solidification and Gravity VII: Selected, Peer Reviewed Papers from the Seventh International Conference on Solidification and Gravity. Solidification and Gravity VII: selected, peer reviewed papers from the Seventh International Conference on Solidification and Gravity. Hungarian Academy of Sciences - University of Miskolc, Materials Science Research Group; Miskolc Committee of Hungarian Academy of Sciences; 2018:52-58.

[1.4.5] Dobravec T, Mavrič B, Rek Z, Zahoor R, Šarler B. Development of adaptive-meshless solution procedure for the phase-field modelling of dendritic solidification with melt convection. Book of abstracts. Published online 2022:158.

[1.4.6] Dobravec T, Mavrič B, Šarler B. Analysis of mesh-induced anisotropy in the phase-field modelling of dendritic growth in binary alloys by novel adaptive meshless solution procedure. EUROMAT 2021: European Congress and Exhibition on Advanced Materials and Processes. Published online 2021:1. https://submit.asmet.org/event/53/.

[1.4.7] Dobravec T, Mavrič B, Šarler B. Development of meshless method for an accurate phase-field modelling of dendrites with arbitrary orientations. Godec M, Donik Č, Kocijan A, Paulin I, eds. Program in knjiga povzetkov. Published online 2019:f. 41. http://mit.imt.si/Revija/izvodi/mit194/BookOfAbstracts_27ICM&T.pdf.

 

Work Package 2:Parallelization for use on HPC systems

Computational time as a function of the number of OpenMP threads for simulating natural convection in a 3-D cavity.

[2.1] Šarler B. Meshless modelling of materials and processes: presentation at the PRACE Scientific & Industrial Conference 2018, 29-31 May 2018 University of Ljubljana Ljubljana, Slovenia. [COBISS.SI-ID 16271387].  

 

Work Package 3:Validation and verification

WP3 - Task 3.1: Experiments in continuous casting

WP3 - Task 3.2: Similarity water model of the caster

The velocity field in a water model of a caster for continuous casting of steel.

[3.2.1] Gregorc J, Šarler B. The characteristics of flow field inside water model of an industrial continuous steel caster. Godec M, Donik Č, Kocijan A, Paulin I, eds. Program in knjiga povzetkov. Published online 2019:f. 59. http://mit.imt.si/Revija/izvodi/mit194/BookOfAbstracts_27ICM&T.pdf.

[3.2.2] Gregorc J, Šarler B. Postavitev vodnega modela za raziskavo toka kapljevine pri kontinuiranem ulivanju jekla. Akademija strojništva 2018: povezovanje in mreženje. 2018;7(3/4):79. http://www.zveza-zsis.si/2018/10/25/svet-strojnistva-akademija-strojnistva-2018/.

[3.2.3] Gregorc J, Šarler B. The design of water model experiment for fluid dynamics of continuous casting of steel billets. Godec M, Donik Č, Kocijan A, Paulin I, eds. Program in knjiga povzetkov. Published online 2018:51. http://mit.imt.si/Revija/izvodi/mit184/BookOfAbstracts_26ICM&T.pdf.

 

WP3 - Task 3.3: International benchmark tests

[3.3.1] Hatić V, Cisternas Fernández M, Mavrič B, Založnik M, Combeau H, Šarler B. Simulation of a macrosegregation benchmark in a cylindrical coordinate system with a meshless method. International journal of thermal sciences. 2019;(142):121-133. doi:10.1016/j.ijthermalsci.2019.04.009.

[3.3.2] Abdolahzadeh M, Šarler B, Tayebi A. Numerical simulation of Goblin - Le Quéré melting benchmark by using the meshless smooth particle hydrodynamics method. Book of abstracts. Published online 2022:197.

 

Work Package 4:Use of models in industry

[4.0.1] VERTNIK, Robert, MRAMOR, Katarina, ŠARLER, Božidar. Solution of three-dimensional temperature and turbulent velocity field in continuously cast steel billets with electromagnetic stirring by a meshless method. Engineering analysis with boundary elements. Jul. 2019, vol. 104, str. 347-363, ilustr. ISSN 0955-7997.

https://www.sciencedirect.com/science/article/pii/S0955799718305010?via%3Dihub