Papers by Author: Božidar Šarler

Abstract: A two dimensional model was developed to predict the grain structure (Equiaxed to Columnar Transformation (ECT) and Columnar to Equiaxed Transformation (CET) in the continuous casting of steel. The processes of nucleation, growth and impingement of the grains are modelled as follows: (I) the nucleation is modeled through a continuous dependency of the nucleation density on temperature by the Gaussian distribution. Different nucleation parameters are used at the boundary and in the bulk region. (II) The growth and impingement are modeled by the Kurz, Giovanola, Trivedi (KGT) model. The Cellular Automata (CA) technique is used to solve the model. The CA method is based on the Nastac’s and simplified neighborhoods. Calculations are shown for square billets of the dimension 140 mm. Fixed input parameter of the model represents the macroscopic temperature field obtained from the Štore Steel billet simulation system [1]. All other grain structure physical model parameters are varied, such as: the surface and the bulk area, mean nucleation undercooling, standard deviation of undercooling, maximum density of nuclei. The computational parameters, such as the micro mesh size and the time step are varied as well. The influence of the variation of different parameters on calculated grain structure is shown. Finally, the model parameters are adjusted in order to obtain the experimentally determined actual billet ECT and CET positions for 51CrV4+Mo spring steel (Al: 0.02, Cr: 1.05, Cu: 0.125, Mn: 0.9,Mo: 0.025, Ni: 0.1, Si: 0.275, V: 0.155, C: 0.51, P: 0.0125, S: 0.0275 wt%). A systematic procedure is outlined for adjusting of the model data with the experiment.

Abstract: This paper for the first time explores the application of the meshless approach, structured on the Local Radial Basis Function Collocation Method (LRBFCM), for solving the freezing process with convection in the liquid phase for a metals-like material in a closed rectangular cavity. The enthalpy one-domain formulation is used to avoid inclusion of additional boundary conditions at the fluid-solid interface. To avoid numerical instabilities, the freezing of a pure substance is modeled by a narrow phase change interval. The fluid flow is solved by a local pressure-velocity coupling, based on the mass continuity violation [1-3], and the explicit time stepping is used to drive the system to the free boundary solution. The results are presented through temperature and streamfunction contours and the liquid-solid interface position at the steady state, as well as the time development of the average Nusselt number and the time development of the cavity average liquid fraction. Results are validated with already benchmarked melting example [3]. The paper represents first steps in solution of the Hebdich and Hunt experiment by an alternative numerical technique, different from the classical finite volume or finite element methods [4].

Abstract: This paper describes an overview of a new meshless solution procedure for calculation of one-domain coupled macroscopic heat, mass, momentum and species transfer problems as well as phase-field concepts of grain evolution. The solution procedure is defined on the macro [1] as well as on the micro levels [2] by a set of nodes which can be non-uniformly distributed. The domain and boundary of interest are divided into overlapping influence areas. On each of them, the fields are represented by the multiquadrics radial basis functions (RBF) collocation on a related sub-set of nodes. The time-stepping is performed in an explicit way. All governing equations are solved in their strong form, i.e. no integrations are performed. The polygonisation is not present and the formulation of the method is practically independent of the problem dimension. The solution can be easily and efficiently adapted in node redistribution and/or refinement sense, which is of utmost importance when coping with fields exhibiting sharp gradients. The concept and the results of the multiscale solidification modeling with the new approach are compared with the classical mesh-based [3] approach. The method turns out to be extremely simple to code and accurate, inclusion of the complicated physics can easily be looked over. The coding in 2D or 3D is almost identical.

Abstract: A model for solving isothermal solid-solid phase transformations in multicomponent aluminium alloys is presented. A multiphase-field model for the dissolutions of various phases in an aluminium matrix during homogenization is presented. Driving forces for phase transformations are calculated using data obtained from the commercial software JMatPro and an aluminium database. An integrated concept of the multiphase-field model with solute diffusion is used. A onedimensional model for the simultaneous dissolution of the Mg2Si and Si phases in the aluminium matrix of ternary Al-Mg-Si alloys is introduced. An explicit central finite difference numerical scheme is used for the solution of the time transient phase-field equations and the solute diffusion equations.

Abstract: This paper introduces a general numerical scheme for solving convective-diffusive problems that appear in the solution of microscopic and macroscopic transport phenomena in continuous castings and the heat treatment of aluminium alloys. The numerical scheme is based on spatial discretisation that involves pointisation only. The solution is based on diffuse collocation with multi-quadric radial basis functions. The application of the method is demonstrated in a simplified model of a billet DC casting and verified by a comparison with the classical finite volume method.