A mathematical method for the forecast of the type of structure in the steel static ingot has been recently developed. Currently, the method has been applied to structural zones prediction in the brass ingots obtained by the continuous casting. Both the temperature field and thermal gradient field have been calculated in order to predict mathematically the existence of some structural zones in the solidifying brass ingot. Particularly, the velocity of the liquidus isotherm movement and thermal gradient behavior versus solidification time have been considered. The analysis of the mentioned velocity allows the conclusion that the brass ingots can evince: chilled columnar grains-, (CC), fine columnar grains-, (FC), columnar grains-, (C), equiaxed grains zone, (E), and even the single crystal, (SC), situated axially. The role of the mentioned morphologies is analyzed to decide whether the hard particles existing in the brass ingots can be swallowed or rejected by the solid / liquid (s/l) interface of a given type of the growing grains. It is suggested that the columnar grains push the hard particles to the end of a brass ingot during its continuous casting.
An innovative method for determining the structural zones in the large static steel ingots has been described. It is based on the mathematical interpretation of some functions obtained due to simulation of temperature field and thermal gradient field for solidifying massive ingot. The method is associated with the extrema of an analyzed function and with its points of inflection. Particularly, the CET transformation is predicted as a time-consuming transition from the columnar- into equiaxed structure. The equations dealing with heat transfer balance for the continuous casting are presented and used for the simulation of temperature field in the solidifying virtual static brass ingot. The developed method for the prediction of structural zones formation is applied to determine these zones in the solidifying brass static ingot. Some differences / similarities between structure formation during solidification of the steel static ingot and virtual brass static ingot are studied. The developed method allows to predict the following structural zones: fine columnar grains zone, (FC), columnar grains zone, (C), equiaxed grains zone, (E). The FCCT-transformation and CET-transformation are forecast as sharp transitions of the analyzed structures. Similarities between steel static ingot morphology and that predicted for the virtual brass static ingot are described.
The Structural Peclet Number has been estimated experimentally by analyzing the morphology of the continuously cast brass ingots. It allowed to adapt a proper development of the Ivantsov’s series in order to formulate the Growth Law for the columnar structure formation in the brass ingots solidified in stationary condition. Simultaneously, the Thermal Peclet Number together with the Biot, Stefan, and Fourier Numbers is used in the model describing the heat transfer connected with the so-called contact layer (air gap between an ingot and crystallizer). It lead to define the shape and position of the s/l interface in the brass ingot subjected to the vertical continuous displacement within the crystallizer (in gravity). Particularly, a comparison of the shape of the simulated s/l interface at the axis of the continuously cast brass ingot with the real shape revealed at the ingot axis is delivered. Structural zones in the continuously cast brass ingot are revealed: FC – fine columnar grains, C – columnar grains, E – equiaxed grains, SC – single crystal situated axially.
Some metallographic studies performed on the basis of the massive forging steel static ingot, on its cross-section, allowed to reveal the following morphological zones: a/ columnar grains (treated as the austenite single crystals), b/ columnar into equiaxed grains transformation, c/ equiaxed grains at the ingot axis. These zones are reproduced theoretically by the numerical simulation. The simulation was based on the calculation of both temperature field in the solidifying large steel ingot and thermal gradient field obtained for the same boundary conditions. The detailed analysis of the velocity of the liquidus isotherm movement shows that the zone of columnar grains begins to disappear at the first point of inflection and the equiaxed grains are formed exclusively at the second point of inflection of the analyzed curve. In the case of the continuously cast brass ingots three different morphologies are revealed: a/ columnar structure, b/ columnar and equiaxed structure with the CET, and c/ columnar structure with the single crystal formation at the ingot axis. Some forecasts of the temperature field are proposed for these three revealed morphologies. An analysis / forecast of the behavior of the operating point in the mold is delivered for the continuously cast ingot. A characteristic delay between some points of breakage of the temperature profile recorded at the operating point and analogous phenomena in the solidifying alloy is postulated.
The problem of determination of the phase-change boundary position at the mathematical modeling of continuous ingot temperature field is considered. The description of the heat transfer process takes into account the dependence of the thermal physical characteristics on the temperature, so that the mathematical model is based on the nonlinear partial differential equations. The boundary position between liquid and solid phase is given by the temperatures equality condition and the Stefan condition for the two-dimensional case. The new method of calculation of the phase-change boundary position is proposed. This method based on the finite-differences with using explicit schemes and on the iteration method of solving of non-linear system equations. The proposed method of calculation is many times faster than the real time. So that it amenable to be used for model predictive control of continuous semifinished product solidification.
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