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Computer modeling of a temperature field and a solid phase fraction in casted billets is the base of any numerical simulation of the continuous casting technology. Temperature distribution in an ingot longitudinal and cross section for the same technological parameters is a function of solidification rate and rate of the solidification heat release. Nucleation rate and solid grain growth velocity depend on a melt undercooling below the liquidus temperature, and consequently depend on a temperature value. The results of the primary grain growth and temperature distribution modeling are presented for the square steel continuous casting 160×160 mm produced by CELSA Steel Works in Ostrowiec. For the modeling the ProCAST R software was used. Virtual structure of primary grains in the continuous ingot cross section was compared with a structure of a real ingot.Keywords: ProCAST, structure, solidification, continuous casting, modelingPodstawą modelowania matematycznego procesu ciągłego odlewania stali (COS) jest symulacja komputerowa pola temperatury i składu fazowego w obszarze wlewka. Rozkład temperatury wzdłuż wlewka i w jego przekroju przy zadanych parametrach odlewania zależy m.in. od intensywności przemiany fazowej, której towarzyszy wydzielanie się ciepła krystalizacji. Szybkości zarodkowania i wzrostu ziaren fazy stałej z ciekłej stali są uzależnione od jej przechłodzenia poniżej temperatury likwidus, a więc, w sposób pośredni od wartości temperatury. W pracy przedstawiono wyniki modelowania pola temperatury i procesu tworzenia się struktury pierwotnej stali B500 SP podczas krzepnięcia wlewka ciągłego o przekroju 160×160 mm, odlewanego w warunkach CELSA HUTA OSTROWIEC. Do celów modelowania wykorzystano oprogramowanie ProCAST. Uzyskaną w symulacji strukturę ziaren pierwotnych w przekroju poprzecznym skonfrontowano z wynikami badań struktury rzeczywistej przekroju poprzecznego wlewków kwadratowych. Mathematical modeling of the continuous casting solidificationIn the earlier papers about the heat transfer in a continuous casting ingot the numerical solutions of the Fourier (or Fourier-Kirchhoff) partial differential equations were used [1][2][3][4][5][6][7][8][9][10][11]. For the numerical solution the Euler meshes were used. This kind of computational mesh is fixed in space. That is why additional calculations are needed to describe quantitatively the convectional heat transport generated by the movement of an ingot solid part in a stationary coordinate system connected with an installation. The phenomena of the grain nucleation and growth in the aforementioned publications are not taken into account.The attempts of the microstructure formation modeling in the continuous casting as results of the grains nucleation and growth are shown in [12,13]. The so-called micro-macro model was used in these papers. In the micro-macro modeling the heat transfer process was analyzed in scale of an ingot (macro). Mathematical model of the nucleation and growth of solid grains in the micro-scale make it possible to predict the s...

The paper presents the analysis of numerical simulation of the Bridgman directional solidification process performed on CMSX-4 rods. The numerical simulation was studied applying the ProCAST software. The constitutive law parameters of the normal Gaussian distribution were used to describe the nucleation process. The coefficients of the equation were determined and used to calculate the growth rate of dendrite tip. The analysis of the as-cast microstructure was carried out with the use of Aphelion software in order to determine the average area of grains and their quantity. The experimental verification of both nucleation and grain growth coefficients used for the simulation of the directional solidification process confirmed that the model was correct and described well the investigated process of directional solidification using the Bridgman method.

The mathematical model of the globular eutectic solidification in 2D was designed. Pro¬posed model is based on the Cellular Automaton Finite Differences (CA-FD) calculation method. Model has been used for studies of the primary and of globular eutectic grains growth during the ductile iron (DI) solidification. A hyper-eutectic composition has been analyzed but this model can be used in the solidification modeling of hypo- and eutectic DI. The proposed model makes possible to trace the unrestricted growth of primary grains of two phases from the liq¬uid, transition from free to cooperative solidification, and cooperative growth of globular eutectic.

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