A cellular automaton-lattice Boltzmann method for modeling growth and settlement of the dendrites for Al-4.7%Cu solidification

Liu, L.; Pian, Song; Zhang, Zhao; Bao, Y.; Li, R.; Chen, H.

doi:10.1016/j.commatsci.2018.01.015

Cited by 25 publications

(16 citation statements)

References 20 publications

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“…Then, it will settle downward in the stagnant fluid under the action of gravity force. In order to capture the particle settlement in a relative small domain and save computation time, a moving mesh technique, which has been successfully used in the simulation of particle movement and dendritic growth [52,53] is adopted in the present study. The main characteristics of this technique is that when the particle settles downward by one mesh unit, one layer of mesh is added to the bottom of the simulation domain, and one layer of mesh is removed at the top of the simulation domain.…”

Section: Settlement Of a Round Particle In A Stagnant Fluidmentioning

confidence: 99%

“…Thus, when the preferential growth direction of the equiaxed dendrite is 0°, no horizontal translation and no rotation occur with the dendrite settlement, which has also been pointed out by the other researchers. [52] Figure 13 shows the variation of dendrite settling velocity with time. It is notable that at the initial stage of dendrite settlement, the settling velocity increases rapidly, because the growth velocity of dendrite is very high, and the gravity, which is the driving force for the dendrite settlement, increases rapidly.…”

Section: B Simulation Of Dendrite Settlement In a Terrestrial Conditionmentioning

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: Settlement Of a Round Particle In A Stagnant Fluidmentioning

confidence: 99%

Section: B Simulation Of Dendrite Settlement In a Terrestrial Conditionmentioning

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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“…phase-field/level set/cellular automaton models. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] While the majority of the earlier studies refer to solidification of static particles in fluid flow, the motion of growing solid particles in the melt was addressed by more recent investigations. Solutions for the latter problem were presented by Do-Quang and Amberg, 21 Steinbach,22,23 Qi et al, 25 and Takaki and coworkers, 24,26,27 who coupled the phase-field approach to the Navier-Stokes equations 21,25 or to lattice Boltzmann hydrodynamics.…”

Section: Introductionmentioning

confidence: 99%

Phase-field lattice Boltzmann model for dendrites growing and moving in melt flow

2019

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The phase-field and lattice Boltzmann methods have been combined to simulate the growth of solid particles moving in melt flow. To handle mobile particles, an overlapping multigrid scheme was developed, in which each individual particle has its own moving grid, with local fields attached to it. Using this approach we were able to simulate simultaneous binary solidification, solute diffusion, melt flow, solid motion, the effect of gravity, and collision of the particles. The method has been applied for describing two possible modes of columnar to equiaxed transition in the Al-Ti system.npj Computational Materials (2019) 5:113 ; https://doi.

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“…Numerical simulations make it possible to trace the formation and development of first and higher order arms in dendrites or the coupled phase growth during eutectic solidification, taking the interaction of growing crystallites into account. Information on the topology of the modelled structures and on the microsegregation of alloy components in the liquid and solid phases is obtained [ 3 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ].…”

Section: Introductionmentioning

confidence: 99%

CA Modeling of Microsegregation and Growth of Equiaxed Dendrites in the Binary Al-Mg Alloy

Zyska

2021

Materials

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A two-dimensional model based on the Cellular Automaton (CA) technique for simulating free dendritic growth in the binary Al + 5 wt.% alloy was presented. In the model, the local increment of the solid fraction was calculated using a methodology that takes into account changes in the concentration of the liquid and solid phase component in the interface cells during the solidification transition. The procedure of discarding the alloy component to the cells in the immediate vicinity was used to describe the initial, unstable dendrite growth phase under transient diffusion conditions. Numerical simulations of solidification were performed for a single dendrite using cooling rates of 5, 25 and 45 K/s and for many crystals assuming the boundary condition of the third kind (Newton). The formation and growth of primary and secondary branches as well as the development of component microsegregation in the liquid and solid phase during solidification of the investigated alloy were analysed. It was found that with an increase in the cooling rate, the dendrite morphology changes, its cross-section and the distance between the secondary arms decrease, while the degree of component microsegregation and temperature recalescence in the initial stage of solidification increase. In order to determine the potential of the numerical model, the simulation results were compared with the predictions of the Lipton–Glicksman–Kurz (LGK) analytical model and the experimental solidification tests. It was demonstrated that the variability of the dendrite tip diameter and the growth rate determined in the Cellular Automaton (CA) model are similar to the values obtained in the LGK model. As part of the solidification tests carried out using the Derivative Differential Thermal Analysis (DDTA) method, a good fit of the CA model was established in terms of the shape of the solidification curves as well as the location of the characteristic phase transition temperatures and transformation time. Comparative tests of the real structure of the Al + 5 wt.% Mg alloy with the simulated structure were also carried out, and the compliance of the Secondary Dendrite Arm Spacing (SDAS) parameter and magnesium concentration profiles on the cross-section of the secondary dendrites arms was assessed.

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A cellular automaton-lattice Boltzmann method for modeling growth and settlement of the dendrites for Al-4.7%Cu solidification

Cited by 25 publications

References 20 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

Phase-field lattice Boltzmann model for dendrites growing and moving in melt flow

CA Modeling of Microsegregation and Growth of Equiaxed Dendrites in the Binary Al-Mg Alloy

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