Solution of macrosegregation in continuously cast billets by a meshless method

Abstract

The main aim of this paper is to demonstrate the applicability and the advantages of a novel meshless method for simulation of macrosegregation in steel billets. The physical model is established on a set of macroscopic equations for mass, energy, momentum, species, turbulent kinetic energy, and dissipation rate in two dimensions. The mixture continuum model is used to treat the solidification system. The mushy zone is modelled as a Darcy porous media with Kozeny-Karman permeability relation, where the morphology of the porous media is modelled by a constant value. The incompressible turbulent flow of the molten steel is described by the Low-Reynolds-Number (LRN) k-epsilon turbulence model, closed by the Launder and Sharma closure coefficients and damping functions. The microsegregation equations rely on lever rule. The numerical method is established on explicit timestepping, and collocation with multiquadrics radial basis functions on non-uniform five-noded influence domains, and adaptive upwinding technique. The velocity-pressure coupling of the incompressible flow is resolved by the explicit Chorin's fractional step method, with the intermediate velocity field, calculated without the pressure term. A recently proposed standard continuous casting configuration with Fe-C system has been used for verification of the model. The advantages of the method are its simplicity and efficiency, since no polygonisation is involved, easy adaptation of the nodal points in areas with high gradients, almost the same formulation in two and three dimensions, high accuracy and low numerical diffusion.