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Mathematical and numerical basis of binary alloy solidification models with substitute thermal capacity. Part 2

Węgrzyn-Skrzypczak E., Skrzypczak T.

Journal of Applied Mathematics and Computational Mechanics

2014

Vol. 13, nr 2

141--147

In this paper, the results obtained from five models of the solidification with substitute thermal capacity were compared. The calculations were carried out for steel containing 0.35% carbon with using an in-home solver based on the finite element method (FEM). A comparison was made on the base of analysis of the cooling curves at selected nodes.

Numerical procedure of solving some inverse problem in solidification of the binary alloy

Hetmaniok E., Słota D.

Computer Assisted Methods in Engineering and Science

2012

Vol. 19, no. 4

393--402

The paper presents a solution of an inverse problem consisting in determination of boundary conditions in the process of binary alloy solidification when temperature measurements in selected points of the cast are known. In the investigated model the distribution of temperature is described using the Stefan model with the liquidus temperature varying in dependance on concentration of the alloy component. For description of the concentration we apply the model in which the immediate equalization of chemical composition of the alloy is assumed (lever arm model). Experimental verifcation of the developed algorithm is also presented.

Front tracking based macroscopic modeling of equiaxed and columnar zones in a binary alloy solidification

Seredyński M., Banaszek J.

Journal of Power Technologies

2011

Vol. 91, nr 2

77-81

The Front Tracking based computer simulation model of solid-liquid phase transition driven by diffusion and thermo-solutal natural convection is presented, and its predictions are verified and validated by comparison with the data obtained from the other available numerical solution and the experimental study. The front tracking approach, based on local dendrite tip kinetics, is capable of distinguishing zones of columnar mush and of equiaxed grains and, thus, provides means for more precise modeling of binary alloy solidification.

A phase-field model for the isothermal solidification process of a binary alloy

Kessler D., Krüger O., Rappaz J.

Computer Assisted Mechanics and Engineering Sciences

2000

Vol. 7, No. 3

279-288

We study a phase-field model for the isothermal solidification of a binary alloy which involves the relative concentration and the order parameter. We prove the existence of weak solutions as well as regularity and uniqueness results under Lipschitz and boundeness assumptions for the nonlinearities. A maximum principle holds that justifies these assumptions. A numerical approximation and some numerical results are also presented