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Acta Metall Sin  2016, Vol. 52 Issue (9): 1096-1104    DOI: 10.11900/0412.1961.2015.00627
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A COLUMNAR & NON-GLOBULAR EQUIAXED MIXED THREE-PHASE MODEL BASED ON THERMOSOLUTAL CONVECTION AND GRAIN MOVEMENT
Jun LI1,Honghao GE1,Menghuai WU2,3(),Andreas LUDWIG2,Jianguo LI1
1 School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
2 Simulation and Modeling of Metallurgical Processes, University of Leoben, A-8700, Austria
3 Christian-Doppler Lab for Advanced Process Simulation of Solidification and Melting, University of Leoben, A-8700, Austria
Cite this article: 

Jun LI,Honghao GE,Menghuai WU,Andreas LUDWIG,Jianguo LI. A COLUMNAR & NON-GLOBULAR EQUIAXED MIXED THREE-PHASE MODEL BASED ON THERMOSOLUTAL CONVECTION AND GRAIN MOVEMENT. Acta Metall Sin, 2016, 52(9): 1096-1104.

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Abstract  

The prediction of the macrosegregation in large ingot is a challenging issue due to the size of the ingots and the variety of the phenomena to be accounted for, such as thermal-solutal convection of the liquid, equiaxed grain motion, evolution of grain morphology by suitably considering a coupled grain growth model in the macroscopic solidification model, the columnar-to-equiaxed transition (CET), and shrinkage, etc.. Each of these phenomena is very important to the solidification pattern, while it is impossible for one model to consider all the phenomena together until now due to the computation power limited. Thus, the model capability and computational cost should be counterpoised for the simulation of large ingot. In this work, a mixed three-phase (simplified dendritic-equiaxed, columnar and liquid) solidification model is described based on Eulerian-Eulerian approach and volume average method. The model considers the thermosolutal buoyancy flow, the movement of equiaxed crystal, and the capture of the equiaxed crystals by growing columnar tree trunks. The mechanical interaction and impingement between columnar and equiaxed crystals are considered which give the capability to predict CET. In order to enhance the model capability without increasing the computational cost significantly, a simplified method is proposed to consider the dendritic of equiaxed crystal. This model is employed to simulate the formation process of macrosegregation for two different steel ingots (3.25 and 25 t). The general macrosegregation pattern predicted by this model includes the cone of negative segregation in the bottom of ingot, quasi-A-segregation in the columnar zone, and positive segregation in the top region, which are quite similar to the classic knowledge. The CET zones are also predicted. Although there is still some quantitative discrepancy, the macrosegregation distribution predicted by this model is quite similar to the experimental measurements. The non-globular equiaxed three-phase mixed model results are compared with the globular-equiaxed mixed three-phase model ones, which indicated that for large ingots the equiaxed dendritic structure plays an important role in liquid flow and it affects final characteristic of macrosegregation. It is predicted successfully that a negative segregation zone would be formed in the upper region due to the formation of a local mini-ingot and the subsequent sedimentation and piling up of equiaxed grains within the mini-ingot.

Key words:  numerical simulation      macrosegregation      steel ingot      grain movement      CET     
Received:  07 December 2015     
Fund: Support by Christian-Doppler Lab for Advanced Process Simulation of Solidification and Melting (Austria), National Natural Science Foundation of China (No.51404152), National Basic Research Program of China (No.2011CB012900), Shanghai Pujiang Program (No.14PJ1404800) and Shanghai International Cooperation Project (No.14140711-000)

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https://www.ams.org.cn/EN/10.11900/0412.1961.2015.00627     OR     https://www.ams.org.cn/EN/Y2016/V52/I9/1096

Fig.1  Schematic of equiaxed dendritic structure and envelope[28] (vtip—dendritic tip growth velocity; denv—equiaxed envelope diameter; de—equiaxed solid diameter; vRs—growth velocity of solid)
Fig.2  Boundary and initial conditions of 3.25 t steel ingot
Fig.3  Predicted solidification sequence of the 3.25 t ingot at 100 s (a), 500 s (b), 2000 s (c) and 6000 s (d) (The volume fraction of each phase is shown in color map with 20 levels from 0 to 1. The left half of each graphic shows the evolution of the columnar volume fraction (fc) and the melt velocity (ul) vectors. The right half of each graphic shows the evolution of the equiaxed volume fraction (fe) and the equiaxed sedimentation velocity (ue) vectors. The position of the columnar dendrite tip was marked with a black solid line) (CET—columnar to equiaxed transition)
Fig.4  Final macrosegregation color maps of 3.25 t steel ingot predicted by simplified dendritic model (a), globular model (b), and the comparison between simulated and experimental macrosegregation distributions along the central line for different models (c)
Property Symbol Unit Value
Melting point of pure iron Tf K 1805.15
Liquidus slope m K%-1 -80.45
Equilibrium partition coefficient k - 0.36
Reference density ρl, ρe, ρc kgm-3 6990
Solid-liquid density difference Δρ kgm-3 150
Specific heat cpl, cpc, cpe Jkg-1K-1 500
Thermal conductivity kl, ke, kc Wm-1K-1 34.0
Latent heat L Jkg-1 2.71×105
Viscosity μ kgm-1s-1 4.2×10-3
Thermal expansion coefficient βT K-1 1.07×10-4
Solutal expansion coefficient βc %-1 1.4×10-2
Dendritic arm spacing λ1 m 5×10-4
Diffusion coefficient (liquid) Dl m2s-1 2.0×10-8
Diffusion coefficient (solid) De, Dc m2s-1 1.0×10-9
Table 1  Thermodynamic and physical properties of model for 3.25 t steel ingot
Fig.5  Boundary and initial conditions for simulation, simulated and experimental results of 25 t steel ingot(a) boundary and initial conditions for simulation(b) experimentally etched surface(c) experimentally measured macrosegregation map(d) simulated macrosegregation pattern(e) comparison between simulated and experimental central line macrosegregation distributions
Fig.6  Formation of negative segregation zone in the upper of ingot(a) the macrosegregation distribution(b) the local equiaxed distribution(c) the formation schematic of equiaxed zone in upper of ingot
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