Modeling dendritic growth of a binary alloy

Zhao, P.; Vénere, Marcelo; Heinrich, J. C.; Poirier, D. R.

doi:10.1016/s0021-9991(03)00185-2

Cited by 43 publications

(50 citation statements)

References 43 publications

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“…In that work, the diffusion equation was solved using a boundary integral approach. Other authors have proposed successful approaches to both the Stefan problem and its extension to the solidification of binary alloys [160,162,151,167,142,164,141,7,52]. In the case of the Stefan problem, the two main ingredients are:…”

Section: A Level-set Approach To the Stefan Problemmentioning

confidence: 99%

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High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

2012

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We present a review of some of the state-of-the-art numerical methods for solving the Stefan problem and the Poisson and the diffusion equations on irregular domains using (i) the level-set method for representing the (possibly moving) irregular domain's boundary, (ii) the ghost-fluid method for imposing the Dirichlet boundary condition at the irregular domain's boundary and (iii) a quadtree/octree nodebased adaptive mesh refinement for capturing small length scales while significantly reducing the memory and CPU footprint. In addition, we highlight common misconceptions and describe how to properly implement these methods. Numerical experiments illustrate quantitative and qualitative results.

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Section: A Level-set Approach To the Stefan Problemmentioning

confidence: 99%

“…However, in the case of free boundary problems, the high cost of regularly reconstructing a boundary fitted mesh is computationally inefficient. Nevertheless, authors have successfully analyzed Stefan-type problems for simulating dendritic growth; see e.g [52,167] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

2012

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“…5,6) In such models, the nucleation and growth of each crystal in the domain of interest is directly simulated, yielding a computed macrostructure. At smaller scales, the growth of individual dendrites has been studied, either by sharp interface tracking, [7][8][9][10] or by phase field methods. [11][12][13] It is beyond the scope of this paper to outline the attributes of these models, but such an appraisal has been completed.…”

Section: Introductionmentioning

confidence: 99%

A New Equiaxed Solidification Predictor from a Model of Columnar Growth

Browne¹

2005

ISIJ Int.

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A new indicator of the potential for the formation of an equiaxed zone during alloy solidification is proposed. The indicator, or equiaxed index, is calculated from the predictions of a numerical model of non-equilibrium columnar solidification. This model uses a front-tracking approach to simulate the nucleation and growth of an undercooled columnar dendritic front into the liquid phase in a 2D casting process. The algorithm for the advancing front is based on expressions developed from considerations of dendrite tip growth. A comparison is made with models in which growth of individual, and competing, columnar crystals are simulated. The equiaxed index is based on numerical integration of an undercooled ravine in front of the advancing columnar front, and changes with time. This proposed metric is a predictor of the relative tendency to form an equiaxed zone. Study of the peak values confirm that equiaxed solidification is more likely in concentrated alloys, and also where the rate of heat extraction to the mould is low. This is in agreement with experimental data from the literature.KEY WORDS: alloy solidification; columnar growth; equiaxed microstructure, front-tracking model. via consideration of non-equilibrium dendrite tip kinetics. The algorithm used was based on expressions developed from analysis of dendrite tip growth where the primary spacing is relatively large, implying that most of the solute is rejected interdendritically. In this case the additional treatment of diffusion of solute through a continuous layer ahead of the growing dendritic front was not necessary. The solidification fronts were represented as boundaries joining discrete computational markers which moved, according to their temperature, in a direction normal to the front. The front could be considered as a line separating liquid from a zone of partially solid alloy. This front was not the liquidus isotherm, but rather was undercooled according to the local thermal and solidification conditions. The kinetics of dendrite tip advance were used to determine the velocity of any computational marker V m , according to its undercooling DT m , as follows: T m , the temperature of the marker, being calculated via interpolation from surrounding nodal temperatures, and T L being the alloy liquidus temperature. C 1 is an alloy-dependent constant which incorporates the effect of solute rejection at the dendrite tip.16) Its value, for a binary alloy, is calculated, 17) using Eq. (1c), in which D is the diffusion coefficient for solute in the liquid, m the liquidus slope, k p the partition coefficient, C o the alloy composition (solute level), and q a curvature undercooling constant (the GibbsThomson parameter). This velocity-undercooling relationship 16) is valid for alloy dendrites for cases where the spacing between primary dendrites is reasonably large. 18,19) Such a situation often arises in casting processes, where the thermal gradient is relatively low. In such cases a continuous layer of solute does not have to be pushed forward into the...

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“…Provatas used adaptive mesh refinement to do research on the computation of dendritic microstructures [10][11][12]. In 2003, Zhao used adaptive finite element method to simulate the growth of directional solidification microstructure [13]. In 2005, Takaki used adaptive quadtree grids to do phase field simulation during directional solidification of binary alloy [14].…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Solidification Microstructure based on Adaptive Octree Grids

Yin¹,

Li²,

Wu³

et al. 2016

Archives of Foundry Engineering

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The main work of this paper focuses on the simulation of binary alloy solidification using the phase field model and adaptive octree grids. Ni-Cu binary alloy is used as an example in this paper to do research on the numerical simulation of isothermal solidification of binary alloy. Firstly, the WBM model, numerical issues and adaptive octree grids have been explained. Secondary, the numerical simulation results of three dimensional morphology of the equiaxed grain and concentration variations are given, taking the efficiency advantage of the adaptive octree grids. The microsegregation of binary alloy has been analysed emphatically. Then, numerical simulation results of the influence of thermo-physical parameters on the growth of the equiaxed grain are also given. At last, a simulation experiment of large scale and long-time has been carried out. It is found that increases of initial temperature and initial concentration will make grain grow along certain directions and adaptive octree grids can effectively be used in simulations of microstructure.

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Modeling dendritic growth of a binary alloy

Cited by 43 publications

References 43 publications

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

A New Equiaxed Solidification Predictor from a Model of Columnar Growth

Numerical Simulation of Solidification Microstructure based on Adaptive Octree Grids

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