The mathematical and numerical simulation model of the liquid steel flow in a tundish is presented in this paper. The problem was treated

as a complex and solved by the finite element method. The single-strand slab tundish is used to continuous casting slabs. The internal work

space of the tundish was modified by the following flow control devices. The first device was a striker pad situated in the pouring tundish

zone. The second device was a baffle with three holes and the third device was a baffle without hole. The main purpose of using these

devices was to cause a quiet liquid mixing as well as give directional metal flow upwards which facilitated inclusion floatation. The

interaction of flow control devices on hydrodynamic conditions was received from numerical simulation. As a result of the computations

carried out, the liquid steel flow and steel temperature fields were obtained. The influence of the tundish modification on velocity fields in

the liquid phase of steel was estimated, because these have an essential influence on high quality of a continuous steel cast slab.

The paper presents an approach of numerical modelling of alloy solidification in permanent mold and transient heat transport between the casting and the mold in two-dimensional space. The gap of time-dependent width called "air gap", filled with heat conducting gaseous medium is included in the model. The coefficient of thermal conductivity of the gas filling the space between the casting and the mold is small enough to introduce significant thermal resistance into the heat transport process. The mathematical model of heat transport is based on the partial differential equation of heat conduction written independently for the solidifying region and the mold. Appropriate solidification model based on the latent heat of solidification is also included in the mathematical description. These equations are supplemented by appropriate initial and boundary conditions. The formation process of air gap depends on the thermal deformations of the mold and the casting. The numerical model is based on the finite element method (FEM) with independent spatial discretization of interacting regions. It results in multi-mesh problem because the considered regions are disconnected.

Presented paper shows the mathematical and numerical approaches for modelling of binary alloy solidification solved by the Finite Element Method (FEM). The phenomenon of shrinkage cavities formation process is included in the numerical model. Multiple macroscopic cavities can be modelled within the single casting volume. Solid, liquid and gaseous phases with different material properties are taken into account during solidification process. Mathematical model uses the differential equation of heat diffusion. Modification of specific heat is used to describe the heat releasing during liquid-solid phase change. Numerical procedure of shrinkage cavities evolution is based on the recognition of non-connected liquid volumes and local shrinkage computation in the each of them. The recognition is done by the selection of sets of interconnected nodes containing liquid phase in the finite element mesh. Original computer program was developed to perform calculation process. Obtained results of temperature and shrinkage cavities distributions are presented and discussed in details.

In this paper, the mathematical model and numerical simulations of the molten steel flow by the submerged entry nozzle and the filling process of the continuous casting mould cavity are presented. In the mathematical model, the temperature fields were obtained by solving the energy equation, while the velocity fields were calculated by solving the momentum equations and the continuity equation. These equations contain the turbulent viscosity which is found by solving two additional transport equations for the turbulent kinetic energy and its rate of dissipation. In the numerical simulations, coupling of the thermal and fluid flow phenomena by changes in the thermophysical parameters of alloy depending on the temperature has been taken into consideration. This problem (2D) was solved by using the finite element method. Numerical simulations of filling the continuous casting mould cavity were performed for two variants of liquid metal pouring. The effect of the cases of pouring the continuous casting mould on the velocity fields and the solid phase growth kinetics in the process of filling the continuous casting mould was evaluated as these magnitudes have an influence on the high quality of the continuous cast steel slab.

The work concerns of modeling the process of manufacturing machine parts by casting method. Making a casting without internal defects is a difficult task and usually requires numerous computer simulations and their experimental verification at the prototyping stage. Numerical simulations are then of priority importance in determining the appropriate parameters of the casting process and in selecting the shape of the riser for the casting fed with it. These actions are aimed at leading shrinkage defects to the riser, so that the casting remains free from this type of defects. Since shrinkage defects usually disqualify the casting from its further use, this type of research is still valid and requires further work. The paper presents the mathematical model and the results of numerical simulations of the casting solidification process obtained by using the Finite Element Method (FEM). A partial differential equation describing the course of thermal phenomena in the process of 3D casting creating was applied. This equation was supplemented with appropriate boundary and initial conditions that define the physical problem under consideration. In numerical simulations, by selecting the appropriate shape riser, an attempt was made to obtain a casting without internal defects, using a simple method of identifying their location. This is the main aim of the research as such defects in the casting disqualify it from use.

The mathematical model and numerical simulations of the solidification of a cylindrical shaped casting, which take into account the process of filling the mould cavity by liquid metal and feeding the casting through the riser during its solidification, are presented in the paper. Mutual dependence of thermal and flow phenomena were taken into account because have an essential influence on solidification process. The effect of the riser shape on the effectiveness of feeding of the solidifying casting was determined. In order to obtain the casting without shrinkage defects, an appropriate selection of riser shape was made, which is important for foundry practice. Numerical calculations of the solidification process of system consisting of the casting and the conical or cylindrical riser were carried out. The velocity fields have been obtained from the solution of momentum equations and continuity equation, while temperature fields from solving the equation of heat conductivity containing the convection term. Changes in thermo-physical parameters as a function of temperature were considered. The finite element method (FEM) was used to solve the problem.

The mathematical model and numerical simulations of the solidification of a cylindrical casting, which take into account the process of the mould cavity filling by liquid metal and the feeding of the casting through the conical riser during its solidification, are proposed in the paper. The interdependence of thermal and flow phenomena were taken into account because they have an essential influence on solidification process. The effect of the pouring temperature and pouring velocity of the metal on the solidification kinetics of the casting was determined. In order to obtain the casting without shrinkage defects, an appropriate selection of these parameters was tried, which is important for foundry practice. The velocity fields have been obtained from the solution of Navier-Stokes equations and continuity equation, while temperature fields from solving the equation of heat conductivity containing the convection term. In the solidification modelling the changes in thermo-physical parameters as a function of temperature were considered. The finite element method (FEM) was used to solve the problem.

Knowledge about complex physical phenomena used in the casting process simulation requires continuous complementary research and improvement in mathematical modeling. The basic mathematical model taking into account only thermal phenomena often becomes insufficient to analyze the process of metal solidification, therefore more complex models are formulated, which include coupled heat-flow phenomena, mechanical or shrinkage phenomena. However, such models significantly complicate and lengthen numerical simulations; therefore the work is limited only to the analysis of coupled thermal and flow phenomena. The mathematical description consists then of a system of Navier-Stokes differential equations, flow continuity and energy. The finite element method was used to numerically modeling this problem. In computer simulations, the impact of liquid metal movements on the alloy solidification process in the casting-riser system was assessed, which was the purpose of this work, and the locations of possible shrinkage defects were pointed out, trying to ensure the right supply conditions for the casting to be free from these defects.