Numerical Simulation of the Dynamic Contraction of Dendrite Solidification in the Al-4.7%Cu Alloy

doi:10.11900/0412.1961.2024.00406

Acta Metall Sin

2026, Vol. 62

Issue (3): 509-522 DOI: 10.11900/0412.1961.2024.00406

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Numerical Simulation of the Dynamic Contraction of Dendrite Solidification in the Al-4.7%Cu Alloy

ZHU Baofeng, LI Chenyu, ZHANG Shijie, LI Ri(

)

College of Materials Science and Engineering, Hebei University of Technology, Tianjin 300401, China

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ZHU Baofeng, LI Chenyu, ZHANG Shijie, LI Ri. Numerical Simulation of the Dynamic Contraction of Dendrite Solidification in the Al-4.7%Cu Alloy. Acta Metall Sin, 2026, 62(3): 509-522.

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Abstract

The dynamic formation process of microshrinkage pole in alloy castings is directly related to the dendrite solidification process. To simulate dendrite shrinkage in the Al-4.7%Cu (mass fraction) alloy during solidification, we proposed a coupling model combining cellular automata (CA) and the lattice Boltzmann method (LBM), referred to as the CA-LBM model. In this model, CA was used to simulate the formation of shrinkage pores during dendrite growth, whereas LBM was applied to study the diffusion process of shrinkage pores in the liquid phase (fully liquid conditions). First, the accuracy of the proposed CA-LBM numerical model was verified through the numerical simulation of the diffusion homogenization of a vacuum cavity in liquid. Then, the solidification process of a single dendrite—with and without dendrite shrinkage were compared, followed by the calculations of the multi-dendrite solidification contraction process with and without dendrite shrinkage. Simulations of the single-dendrite solidification process indicated that no internal pores were formed in the single dendrites when shrinkage was not considered. However, when shrinkage was considered, uniform microshrinkage pores appeared in the single dendrites. Moreover, the presence of shrinkage pores notably influenced dendrite morphology by promoting secondary branching. The results of the multidendrite contraction simulation also showed that micro-shrinkage pores tended to form at the junctions of the last solidified dendrites. A comparison between the calculated number of shrinkage poles and the theoretical value showed a small error, indicating the effectiveness and reliability of the proposed numerical model.

Key words: Al-Cu alloy solidification dendrite shrinkage CA-LBM numerical model

Received: 28 November 2024

ZTFLH:

TG111.4

Fund: National Natural Science Foundation of China(51975182)

Corresponding Authors: LI Ri, professor, Tel: (022)60202006, E-mail: hbcllr@hebut.edu.cn

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	ZHU Baofeng
	LI Chenyu
	ZHANG Shijie
	LI Ri

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https://www.ams.org.cn/EN/10.11900/0412.1961.2024.00406 OR https://www.ams.org.cn/EN/Y2026/V62/I3/509

Fig.1 A model of the microscopic shrinkage algorithm

Table 1 Thermophysical parameters of Al-4.7%Cu

Fig.2 Model flow chart (CA—cellular automata, LBM—lattice Boltzmann method)

Fig.3 Standard bounce format

Fig.4 Diffusion modeling of vacuum holes under nine grids

Fig.5 Nine-grid validations of initial conditions (a), diffusion process (b, c), and final results of the simulation (d) in vacuum cavity diffusion process (f_emp—shrinkage of a cell)

Fig.6 Twenty-five grid (a1-a4) and one-hundred grid (b1-b4) verifications in vacuum cavity diffusion process
(a1, b1) initial conditions (a2, a3, b2, b3) diffusion process (a4, b4) final results of the simulation

Fig.7 Computational domain of multigrid flow field in vacuum cavity diffusion process
(a) pure liquid phase (b) lateral obstacle (c) vertical-like obstacle

Fig.8 Condensation diffusion (first 3000 steps) in pure liquid phase (The depth of color only represents the concentration of shrinkage holes, the same below)
(a) 230 steps (b-o) continue to output the result of the calculation every 60 steps

Fig.9 Condensation diffusion in pure liquid phase (after 3000 steps)
(a) 3000 steps (b-o) continue to output the result of the calculation every 3000 steps

Fig.10 Schematics of shrinkage diffusion in a multigrid flow field with lateral obstacle (a1-a5) and vertical-like obstacle (b1-b5)
(a1) step = 120 (a2) step = 260 (a3) step = 430 (a4) step = 640 (a5) step = 770
(b1) step = 130 (b2) step = 240 (b3) step = 390 (b4) step = 560 (b5) step = 720

Fig.11 Schematics of two-point spread
(a) step = 90 (b) step = 130 (c) step = 180 (d) step = 240

Fig.12 Simulation results of monodendritic growth without considering shrinkage (a1-a5) and considering shrinkage generation and diffusion (b1-b5) (f_s—solid fraction)
(a1, b1) step = 110 (a2, b2) step = 150 (a3, b3) step = 500 (a4, b4) step = 1321 (a5, b5) step = 1374

Fig.13 Comparisons of the total number of shrinkage holes obtained in single dendrite calculations with theoretical values ( $T ¯$ —average temperature of the universal grid, N—number of grids occupied by the total shrinkage hole volume)

Fig.14 Simulation results of polydendritic grains
(a) locations of 25 nucleation points
(b) polycrystalline grains with different site orientations

Fig.15 Schematics of polydendrite growth
(a) step = 160 (b) step = 340 (c) step = 1010 (d) step = 1328

Fig.16 Comparisons of the total shrinkage porosity obtained from the multi-dendrite calculations with the theoretical values

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