A numerical benchmark test for continuous casting of steel III

This paper represents a continuation of numerical results regarding the recently proposed industrial benchmark test [1], obtained by a meshless method. A part of the benchmark test, involving turbulent fluid flow with solidification in two dimensions, was elaborated in [2]. A preliminary macrosegregation upgrade was presented in [3], and in [4], a first three dimensional test was performed. Previous tests were bound to calculations in mold and sub-moldregions only. In the present paper, reference calculations in two dimensions are presented for the entire strand. The physical model is established on a set of macroscopic equations for mass, energy, momentum, species, turbulent kinetic energy, and dissipation rate. The mixture continuum model is used to treat the solidification system. The mushy zone is modeled as a Darcy porous media with Kozeny-Karman permeability relation, where the morphology of the porous media is modeled by a constant value. The incompressible turbulent flow of the molten steel is described by the Low-Reynolds-Number k-ε turbulence model, closed by the Abe-Kondoh-Nagano closure coefficients and damping functions. Lever microsegregation model is used. The numerical method is established on explicit time-stepping, collocation with scaled multiquadrics radial basis functions with adaptive selection of its shape on non-uniform five-nodded influence domains. The velocity-pressure coupling of the incompressible flow is resolved by the explicit Chorin'sfractional step method. 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. (paper)