### Developing continuous-casting-process control based on advanced mathematical modelling Uporaba naprednega matematičnega modeliranja za razvoj kontrole postopka kontinuirnega ulivanja

Jan Falkus, Katarzyna Miłkowska-Piszczek
2015 Materiali in Tehnologije
The method of continuous casting of steel -due to its ability to maximize the yield of liquid steel, along with substantially reducing the energy consumption of the production process -has become the fundamental method for obtaining steel semi-products. Nowadays, over 90 % of the global steel is cast with the continuous method. In recent years the ability to numerically model metallurgical processes -including the continuous process of steel casting -has been very important for creating new
more » ... or creating new technologies, along with modifying those that already exist. The mathematical modelling of solidification processes with numerical methods allowed a full comprehensive reconstruction of the complex physical and chemical nature of the solidification processes. However, having to formulate a numerical model of the continuous-casting process is an extremely complex task because the requirements stipulate that a correct set of material parameters, along with the process data, have to be implemented. As regards the formulation of a mathematical model of the steel continuous-casting process, a comprehensive description of the heat transfer during the continuous casting is an important item. The complexity of this issue requires that conscious simplifications are made when formulating mathematical models for the calculation of the cast-strand solidification process. The number and type of the simplifications -which are necessary in this case -are the keys to the correctness of the results obtained, and they also influence the scope and accuracy when it comes to verifying the model. It is crucial to define the problem on the basis of the finite-element theory, and the elimination of numerical errors is obviously a necessary condition to ensure the correctness of the analysis performed. This paper contains a description of a number of solutions that are based on the finite-element method (FEM) for the models using the Euler, Lagrange and MiLE meshes. All the model concepts are illustrated with the examples of the calculations that were completed using the actual industrial data, along with the properties of the materials as determined by laboratory tests. The pivot of the considerations conducted is related to the verification of the correctness of the calculations, together with the sensitivity analysis of individual model types. The conclusions present an assessment of the progress of the current numerical models of the continuous-casting process, along with the directions for their further development. Metoda kontinuirnega ulivanja jekla je postala osnovna metoda za pridobivanje jeklenih polproizvodov zaradi mo'nosti maksimalnega izkoristka staljenega jekla ter zmanj{anja porabe energije za proizvodni proces. Danes je okrog 90 % svetovne proizvodnje jekla ulitega z metodo kontinuirnega ulivanja. V preteklih letih je bila mo'nost modeliranja postopka ulivanja jekla zelo pomembna pri nastajanju novih tehnologij vklju~no z modificiranjem'e obstoje~ih. Matemati~no modeliranje procesa strjevanja z numeri~nimi metodami je omogo~ilo celovito rekonstrukcijo kompleksne fizikalne in kemijske narave procesa strjevanja. Vendar pa je postavitev numeri~nega modela postopka kontinuirnega ulivanja zelo zahtevna naloga, ker zahteve dolo~ajo, da je treba uporabiti pravilne parametre materiala vklju~no s podatki procesa. Glede na postavitev matemati~nega modela postopka kontinuirnega ulivanja je pomembna postavka celovit opis prenosa toplote med kontinuirnim ulivanjem. Kompleksnost tega vpra{anja zahteva zavestne poenostavitve pri postavitvi matemati~nih modelov za izra~un procesa strjevanjà ile. [tevilo in vrsta poenostavitve, ki so v tem primeru nujne, sta klju~za pravilnost dobljenih rezultatov, vplivajo pa tudi na obseg in natan~nost, ko pride do preverjanja modela. Klju~nega pomena je definiranje problema, ki temelji na teoriji metode kon~nih elementov, odprava numeri~nih napak pa je o~itno potrebni pogoj za zagotovitev pravilnosti izvr{enih analiz.^lanek vsebuje opis {tevilnih re{itev, ki temeljijo na metodi kon~nih elementov (FEM), za modele, ki uporabljajo Euler-jevo, Lagrange-jevo in MiLE-mre'o. Prikazani so vsi koncepti modelov z izra~uni, ki so bili dopolnjeni z uporabo pravih industrijskih podatkov, skupaj z lastnostmi materialov, kot je bilo dolo~eno v laboratorijskih preizkusih. Te'i{~e izvr{enih obravnav je povezano s preverjanjem pravilnosti izra~unov, skupaj z ob~utljivo analizo posameznih vrst modelov. V sklepih je predstavljena ocena glede napredovanja sedanjih numeri~nih modelov postopka kontinuirnega ulivanja vklju~no z napotki za njihov nadaljnji razvoj. Figure 1: Structure of the layer between the mould and the shell Slika 1: Zgradba podro~ja med kokilo in strjeno skorjo