A Phase-Field Lattice-Boltzmann Study on Dendritic Growth of Al-Cu Alloy Under Convection

Zhang, Ang; Du, Jinglian; Guo, Zhipeng; Wang, Qigui; Xiong, Shoumei

doi:10.1007/s11663-018-1418-1

Cited by 56 publications

(13 citation statements)

References 57 publications

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“…Jeong et al [24] developed a high-efficient three dimensional (3D) PF model with an adaptive grid refinement technology to study the effect of fluid flow on dendritic growth and successfully simulated the effect of convection on the static dendritic growth in the melt. In order to further improve the computation efficiency, [32][33][34][35] the Lattice Boltzmann method (LBM) was introduced to calculate the fluid flow in the melt, instead of the traditional computational fluid dynamic method, because of the advantages of simple programming and easy parallel solution. Thus, the LBM method has been widely applied to predict the complicated fluid flow, such as microfluidics, [36] multi-component fluids [37] and multi-phase fluids, [38] and it also has a good prospect in solving the transport phenomenon in the precision machining of materials.…”

Section: Introductionmentioning

confidence: 99%

“…Miller et al [41] proposed the PF model coupled with the LBM to simulate the stationary dendritic growth of binary alloys, and studied the effect of convection on the growth of primary dendritic arms. Zhang et al [35] developed a PF-LBM model with a parallel and adaptive mesh refinement algorithm (Para-AMR) to simulate the dendritic growth under convection, and the results proved that the dendrite growth in the upstream region was promoted, but the dendritic growth in the downstream region was inhibited. Although a significant achievement in the prediction of dendritic growth under convection with improved calculation method has been made, the dendrite was artificially fixed and set as a stationary rigid body in the above mentioned works without taking into consideration the dendrite motion in the melt with convection.…”

Section: Introductionmentioning

confidence: 99%

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PF-LBM Modelling of Dendritic Growth and Motion in an Undercooled Melt of Fe-C Binary Alloy

Luo

Wang

et al. 2020

Metall Mater Trans B

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In the present study, a two-dimensional phase field model coupled with Lattice Boltzmann method (PF-LBM) is proposed to predict the dendritic growth and motion in the melt of Fe-C binary alloy, where the phase field method (PF) is used to calculate the dendritic growth, including the phase field and the concentration field, and the lattice Boltzmann method (LBM) is used to calculate the flow field. The dendrite motion is determined by Newton's Second Law and tracked by Lagrangian point in a Cartesian coordinate system. Later, the model validations were performed with the benchmark of a solid particle settlement in a stagnant fluid and particle motion in a shear flow, and the results show that the present model is capable of predicting the solid particle motion in the fluid flow. Finally, the model is adopted to investigate the dendritic growth and motion in a forced fluid flow (laminar flow or rotational flow), and the dendrite settlement in a terrestrial environment. The results show that when the forced fluid flow is a laminar flow, the free dendrite would be driven to translate, and the relative velocity between the dendrite and flow fluid decreases, resulting in weak influence of fluid flow on the dendritic growth. When the forced fluid flow is a rotational fluid flow, the dendrite would centrifugally rotate on the domain center with a counterclockwise self-spinning, and the rotation radius becomes larger and larger. For the case of dendrite settlement in a terrestrial environment, the relative movement between the dendrite and melt promotes the downward branch growth, but inhibits the upward branch growth, and two vortices form at the wake region of dendrite. Therefore, the settling dendrite shows a significant asymmetrical morphology.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

PF-LBM Modelling of Dendritic Growth and Motion in an Undercooled Melt of Fe-C Binary Alloy

Luo

Wang

et al. 2020

Metall Mater Trans B

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“…For the 2D case, A ( n ) is

A (n) = 1 + ε \cos 4 φ

where ε denotes the anisotropy strength, and φ = arctan( ϕ y / ϕ x ) is the angle between the primary dendrite arm and the x ‐axis. [ 3,24 ] α PF , D PF , v PF , and j at‐PF are

a_{normalPF} = a_{2} λ Le

D_{normalPF} = a_{2} λ

v_{normalPF} = \frac{v}{W_{0} (/) τ_{0}} = \frac{d_{0} a_{2} λ^{2}}{D a_{1}} v

j_{at - PF} = - \frac{1 + (1 - k) U}{2 \sqrt{2}} \frac{\partial ϕ}{\partial t_{normalPF}} \frac{\nabla ϕ}{(||, \nabla ϕ)}

…”

Section: Mathematical Modelmentioning

confidence: 99%

“…[ 21 ] Medvedev et al., [ 22 ] Takaki et al., [ 23 ] and the current authors. [ 24,25 ] But for the fully coupled thermal‐solute‐convection transport, very limited studies are performed. Jelinek et al.…”

Section: Introductionmentioning

confidence: 99%

Solution to Multiscale and Multiphysics Problems: A Phase‐Field Study of Fully Coupled Thermal‐Solute‐Convection Dendrite Growth

Zhang

Jiang

Guo³

et al. 2021

Advcd Theory and Sims

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Solidification process is a complex phase transition problem involving multiscale and multiphysical characteristics. To investigate the complex interaction, a high‐performance numerical scheme is developed to explore the thermal‐solute‐convection interaction during solidification. Al–Cu dendrite growth with the Lewis number ≈104 and Prandtl number ≈10−2 (or Schmidt number ≈102) is simulated and discussed. By constructing a multilevel data structure, this numerical scheme allows the time step magnified by 2–3 orders of magnitude in comparison with that for explicit methods. With the capacity of the acceleration strategy including parallel computing and adaptive mesh refinement, the computing efficiency can be further improved by 2–3 orders of magnitude. The combination of multilevel structure and acceleration strategy makes a problem of up to 109 uniform meshes much easier to handle. The coupled governing equations involving the multiscale and multiphysical characteristics are solved with high efficiency and high numerical stability, even when the solid fraction approaches 100%. Both single and multi‐dendrite growths are discussed to reveal the effect of the thermal‐solute‐convection interaction on the large‐scale 2D and 3D microstructure evolution. The presence of the liquid flow changes the distribution of both domain temperature and solute component, which changes dendrite morphology and growth dynamics.

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“…The governing equations about phase and solute fields (Equations (10) and (11)) were discretized using the finite difference method onto a rectangle computing domain with an equal grid spacing of Δx=Δy and sloved by the robust algorithm. The details about space and time discretization, and parallel computing scheme can be found in reference [28,29]. In this article, a server (Dell, Inc., Roderock, TX, USA) with 416 processors in GRINM (General Research Institute for Nonferrous Metals) was used to solve the cases designed according to the experimental data.…”

Section: Model Descriptionmentioning

confidence: 99%

Effect of Temperature Gradient on the Grain Size Homogeneity of SEED Produced Semi-Solid Slurries by Phase-Field Simulation

Luo

Guo

et al. 2019

Materials

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The distribution homogeneity of grain size affects the fluidity of the semi-solid slurry, which in turn affects the properties of the casting. One key factor affecting grain size uniformity resides in the nucleation number, which has been studied thoroughly, while the other factor is temperature gradient which has not been investigated yet. In this study, the microstructure evolutions under certain temperature gradients are investigated by experiment and simulation using a two-dimensional quantitative phase-field (PF) model. A parallel and adaptive mesh refinement algorithm is adopted to solve the nonlinear phase-field equations. The results indicate that temperature gradient can affect the size distribution of microstructure in the semi-solid slurry prepared by the SEED process. A higher temperature gradient (in the range of 0.230~0.657 °C/mm) along the radial direction is beneficial to the homogeneity of the grain size in a slurry.

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A Phase-Field Lattice-Boltzmann Study on Dendritic Growth of Al-Cu Alloy Under Convection

Cited by 56 publications

References 57 publications

PF-LBM Modelling of Dendritic Growth and Motion in an Undercooled Melt of Fe-C Binary Alloy

PF-LBM Modelling of Dendritic Growth and Motion in an Undercooled Melt of Fe-C Binary Alloy

Solution to Multiscale and Multiphysics Problems: A Phase‐Field Study of Fully Coupled Thermal‐Solute‐Convection Dendrite Growth

Effect of Temperature Gradient on the Grain Size Homogeneity of SEED Produced Semi-Solid Slurries by Phase-Field Simulation

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