Abstract
In solidification processes of large industrial castings and ingots, the transport of solid in the liquid has an important effect on the final grain structure and macrosegregation. Modeling is still challenging as complex interactions between heat and mass transfers at microscopic and macroscopic scales are highly coupled. This paper first presents a multi-scale numerical solidification model coupling nucleation, grain growth and solute diffusion at microscopic scales with heat and mass transfer, including transport of liquid and solid phases at macroscopic scales. The resolution consists of a splitting method, which considers the evolution and interaction of quantities during the process with a transport stage and a growth stage. This splitting reduces the nonlinear complexity of the set of considered equations and provides an efficient numerical implementation. It is inspired by the work of Založnik et al. [1,2], which used a finite volume method (FVM). The present work develops the solution based on the finite element method (FEM). Numerical results obtained with this model are presented and simulations without and with grain transport are compared to study the impact of solid-phase transport on the solidification process and on the formation of macrosegregation.
Highlights
Solidification modelling accounting for melt convection and solid movement has been limited
It is worth noticing that these models were based on the finite volume method (FVM), while the use of the finite element method (FEM) has been rarely considered for volume-averaged multiphase multiscale modelling of solidification
Besides ongoing advancements with FVM, the present study aims at developing FEM solvers when solid transport is to be considered
Summary
Solidification modelling accounting for melt convection and solid movement has been limited. The first important works were proposed with a volume-averaged model consistently connecting microscopic phenomena to macroscopic transports [3,4,5,6]. The numerical resolution algorithm proposed by Založnik and Combeau [1] efficiently dealt with the complexity of the strongly coupled problem by using a splitting method. This splitting method was successfully applied to large industrial castings [11]. A numerical FEM solidification model is presented accounting for microscopic phenomena as well as for the motion of solid and liquid. Results demonstrate an efficient FEM resolution scheme implemented for the purely convective transport problem, which is difficult to solve numerically with the FEM in the absence of diffusive effects
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