Influence of external flows on pattern growth

Медведев, Д. А.; Fischaleck, Thomas; Kassner, Klaus

doi:10.1016/j.jcrysgro.2006.10.227

Cited by 25 publications

(14 citation statements)

References 25 publications

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“…Phase-field models have been developed [223][224][225] and widely used to simulate solidification in the presence of fluid flow [226][227][228][229][230][231][232][233][234][235][236]. Other methods, such as the sharp-interface tracking technique [237][238][239], lattice Boltzmann models [240][241][242][243], cellular automaton techniques [244][245][246] and Monte Carlo simulations [247], have also become available.…”

Section: Dendrite Tip Growthmentioning

confidence: 99%

Solidification microstructures and solid-state parallels: Recent developments, future directions

et al. 2009

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Rapid advances in atomistic and phase-field modeling techniques as well as new experiments have led to major progress in solidification science during the first years of this century. Here we review the most important findings in this technologically important area that impact our quantitative understanding of: (i) key anisotropic properties of the solid-liquid interface that govern solidification pattern evolution, including the solid-liquid interface free energy and the kinetic coefficient; (ii) dendritic solidification at small and large growth rates, with particular emphasis on orientation selection; (iii) regular and irregular eutectic and peritectic microstructures; (iv) effects of convection on microstructure formation; (v) solidification at a high volume fraction of solid and the related formation of pores and hot cracks; and (vi) solid-state transformations as far as they relate to solidification models and techniques. In light of this progress, critical issues that point to directions for future research in both solidification and solid-state transformations are identified.

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Section: Dendrite Tip Growthmentioning

confidence: 99%

Solidification microstructures and solid-state parallels: Recent developments, future directions

et al. 2009

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“…where Df s is the solid fraction increment of the interface cell at one time step, which is evaluated by equation (15), and C Ã,s l and C Ã,s s are the interface liquid and solid compositions of solute element s respectively. The rejected DC s is added to the remaining liquid in the same cell and its surrounding neighbour cells.…”

Section: Solution Of Phase Fraction Evolutionmentioning

confidence: 99%

“…Since LBM describes fluid motion at the level of the distribution functions, it can be naturally incorporated with the related simulation techniques for crystal growth in a fluid flow. Miller et al 14 and Medvedev et al 15 developed phase field LBM coupled models for the simulation of convective dendritic growth in pure substances. Recently, some of the present authors suggested a CA based approach coupled to an LBM solver for simulating the dendrite growth of binary alloys in the presence of forced convection.…”

Section: Introductionmentioning

confidence: 99%

Modelling of dendritic growth in ternary alloy solidification with melt convection

Sun¹,

Zhu²,

Taguchi³

et al. 2011

International Journal of Cast Metals Research

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A two-dimensional lattice Boltzmann-cellular automaton model is coupled with the CALPHAD (Calculation of Phase Diagrams) method for simulating dendritic growth during ternary alloy solidification with convection. In the model, the kinetics of dendritic growth is determined by the difference between the equilibrium liquidus temperature and the actual temperature at the solid/liquid interface, incorporating the effects of the interface curvature and the preferred dendritic growth orientation. The lattice Boltzmann method is used for evaluating the local liquid compositions of the two solutes impacted by diffusion and convection. Based on the local liquid compositions, the equilibrium liquidus temperature and the solid concentrations of the two solutes are obtained by the CALPHAD method. The model is applied to simulate dendritic growth of an Al-4?0 wt-%Cu-1?0 wt-%Mg ternary alloy with melt convection. The results demonstrate the high numerical convergence and stability, as well as computational efficiency, of the proposed model. Melt convection is found to influence the dendritic morphologies and microsegregation patterns in the solidification of ternary alloys.

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“…Since LBM describes fluid motion at the level of the distribution functions, it can be incorporated naturally with the related simulation techniques for crystal growth in a fluid flow. Miller et al [9] and Medvedev et al [10] introduced phase field (PF) based models into the framework of LBM for the simulation of convective dendritic growth in a pure substance where the driving force for the phase transformation is thermal undercooling. However, few studies have been reported about applying LBM to simulate the dendritic growth in the presence of melt flow during alloy solidification.…”

Section: Introductionmentioning

confidence: 99%

Lattice Boltzmann modeling of dendritic growth in forced and natural convection

Sun

Zhu

Pan

et al. 2011

Computers & Mathematics with Applications

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a b s t r a c tA two-dimensional (2D) coupled model is developed for the simulation of dendritic growth during alloy solidification in the presence of forced and natural convection. Instead of conventional continuum-based Navier-Stokes (NS) solvers, the present model adopts a kinetic-based lattice Boltzmann method (LBM), which describes flow dynamics by the evolution of distribution functions of moving pseudo-particles, for the numerical computations of flow dynamics as well as thermal and solutal transport. The dendritic growth is modeled using a solutal equilibrium approach previously proposed by Zhu and Stefanescu (ZS), in which the evolution of the solid/liquid interface is driven by the difference between the local equilibrium composition and the local actual liquid composition. The local equilibrium composition is calculated from the local temperature and curvature. The local temperature and actual liquid composition, controlled by both diffusion and convection, are obtained by solving the LB equations using the lattice Bhatnagar-Gross-Krook (LBGK) scheme. Detailed model validation is performed by comparing the simulations with analytical predictions, which demonstrates the quantitative capability of the proposed model. Furthermore, the convective dendritic growth features predicted by the present model are compared with those obtained from the Zhu-Stefanescu and Navier-Stokes (ZS-NS) model, in which the fluid flow is calculated using an NS solver. It is found that the evolution of the solid fraction of dendritic growth calculated by both models coincides well. However, the present model has the significant advantages of numerical stability and computational efficiency for the simulation of dendritic growth with melt convection.

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Influence of external flows on pattern growth

Cited by 25 publications

References 25 publications

Solidification microstructures and solid-state parallels: Recent developments, future directions

Solidification microstructures and solid-state parallels: Recent developments, future directions

Modelling of dendritic growth in ternary alloy solidification with melt convection

Lattice Boltzmann modeling of dendritic growth in forced and natural convection

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