Simulation of heat transfer in steel billets during continuous casting

This work is focused on the development of computational algorithms to create a simulator for solving the heat transfer during the continuous casting process of steel. The temperatures and the solid shell thickness profiles were calculated and displayed on the screen for a billet through a defined continuous casting plant （CCP）. The algorithms developed to calculate billet temperatures, involve the solutions of the corresponding equations for the heat removal conditions such as radiation, forced convection, and conduction according to the billet posi- tion through the CCP. This is done by a simultaneous comparison with the kinematics model previously developed. A finite difference method known as Cmnk-Nicholson is applied to solve the two-dimensional computational array （2D model）. Enthalpy （HIJ） and temperature （TIL） in every node are updated at each step time. The routines to display the results have been developed using a graphical user interface （GUI） in the programming language C＋＋. Finally, the results obtained are compared with those of industrial trials for the surface temperature of three steel casters with different plant configurations in different casting conditions.

Simulation factors of steel continuous casting

The factors involved in simulating the continuous casting process of steel and the effects of the factors on the thermal behavior were investigated. The numerical methods and the influence of some assumptions were also analyzed, such as nodes used to discretize the steel in array size and computing time to obtain good approaches. The results show that some of these factors are related with the design of the continuous casting plant （CCP）, such as geometrical configuration, and the operating conditions, such as water flow rate, heat removal coefficient in the mold, casting times, and casting speed in the strand, which affect the heat removal conditions over the temperature and solidification profiles.

A cellular automata model for simulating grain structures with straight and hyperbolic interfaces

A description of a mathematical algorithm for simulating grain structures with straight and hyperbolic interfaces is shown. The presence of straight and hyperbolic interfaces in many grain structures of metallic materials is due to different solidification conditions, in- eluding different solidification speeds, growth directions, and delaying on the nucleation times of each nucleated node. Grain growth is a complex problem to be simulated; therefore, computational methods based on the chaos theory have been developed for this purpose. Straight and hyperbolic interfaces are between columnar and equiaxed grain structures or in transition zones. The algorithm developed in this work involves random distributions of temperature to assign preferential probabilities to each node of the simulated sample for nucleation according to previously defined boundary conditions. Moreover, more than one single nucleation process can be established in order to gen- erate hyperbolic interfaces between the grains. The appearance of new nucleated nodes is declared in sequences with a particular number of nucleated nodes and a number of steps for execution. This input information influences directly on the final grain structure （grain size and dislribution）. Preferential growth directions are also established to obtain equiaxed and columnar grains. The simulation is done using rou- tines for nucleation and growth nested inside the main function. Here, random numbers are generated to place the coordinates of each new nucleated node at each nucleation sequence according to a solidification probability. Nucleation and growth routines are executed as a func- tion of nodal availability in order to know if a node will be part of a grain. Finally, this information is saved in a two-dimensional computa- tional array and displayed on the computer screen placing color pixels on the corresponding position forming an image as is done in cellular automaton.