Three dimensional simulation of macrosegregation in steel billets by a meshless method

There is a continuously developing need for benchmarking of solidification simulations - from the theoretical as well as from the applied points of view. The history of related benchmarking shows differences of the results between different numerical methods, and differences in comparison with the experiments when solving even quite simple solidification situations. The present benchmark test proposes a three dimensional version of the recently developed two dimensional solidification benchmark of the continuous casting with turbulent fluid flow and solidification with macrosegregation. The macroscopic transport equations for mass, momentum, energy, species, turbulent kinetic energy and dissipation rate are considered. Turbulent effects are incorporated through the solution of a low-Re turbulence model. The solidification system is treated by the mixture-continuum model, where the mushy zone is modeled as a Darcy porous media with Kozeny-Karman permeability relation and columnar solid phase moving with the casting velocity. The Fe-C binary phase diagram and the lever rule microsegregation model are used to obtain the carbon segregation in the billet. The transport equations are solved by our newly developed and efficient meshless numerical technique, based on local collocation with radial basis functions and fractional step velocity- pressure coupling. The presented results represent first simulations of a three-dimensional solidification problem by a meshless method. (paper)