Acta Metallurgica Sinica (English Letters) ›› 2019, Vol. 32 ›› Issue (11): 1396-1406.DOI: 10.1007/s40195-019-00897-0
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Kang-Xin Chen1, Hou-Fa Shen1()
Received:
2018-12-05
Revised:
2019-03-19
Online:
2019-11-10
Published:
2019-11-10
Kang-Xin Chen, Hou-Fa Shen. Numerical Simulation of Macrosegregation Caused by Thermal-Solutal Convection and Solidification Shrinkage Using ALE Model[J]. Acta Metallurgica Sinica (English Letters), 2019, 32(11): 1396-1406.
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Properties | Units | Value |
---|---|---|
Liquid density, ρl | kg m-3 | 10,000 |
Solid density, ρs | kg m-3 | 10,800 |
Specific heat in liquid, cl | J kg-1 K-1 | 154.7 |
Specific heat in solid, cs | J kg-1 K-1 | 177.9 |
Thermal conductivity in liquid, kl | W m-1 K-1 | 22.9 |
Thermal conductivity in solid, ks | W m-1 K-1 | 39.7 |
Latent heat, L | J kg-1 | 30,162 |
Liquid dynamic viscosity, μl | kg m-1 s-1 | 2.3?×?10-3 |
Thermal expansion coefficient, βT | K-1 | 1.09?×?10-4 |
Solutal expansion coefficient, βw | (wt%)-1 | 3.54?×?10-3 |
Secondary dendrite arm spacing, λ2 | m | 71?×?10-6 |
Melting point of the pure metal, Tf | °C | 327.5 |
Liquidus slope, m | K(wt%)-1 | -?2.334 |
Partition coefficient, kP | 0.31 | |
Eutectic temperature, Teut | °C | 183.0 |
Eutectic composition, weut | wt% | 61.9 |
Nominal concentration, w0 | wt% | 19.2 |
Initial temperature, T0 | °C | 287 |
Heat transfer coefficient | W m-2 K-1 | 1000 |
External temperature | °C | 20 |
Diffusion coefficient in liquid, Dl | m2 s-1 | 1.05?×?10-9 |
Table 1 Thermal-physical properties and computational parameters used in calculations
Properties | Units | Value |
---|---|---|
Liquid density, ρl | kg m-3 | 10,000 |
Solid density, ρs | kg m-3 | 10,800 |
Specific heat in liquid, cl | J kg-1 K-1 | 154.7 |
Specific heat in solid, cs | J kg-1 K-1 | 177.9 |
Thermal conductivity in liquid, kl | W m-1 K-1 | 22.9 |
Thermal conductivity in solid, ks | W m-1 K-1 | 39.7 |
Latent heat, L | J kg-1 | 30,162 |
Liquid dynamic viscosity, μl | kg m-1 s-1 | 2.3?×?10-3 |
Thermal expansion coefficient, βT | K-1 | 1.09?×?10-4 |
Solutal expansion coefficient, βw | (wt%)-1 | 3.54?×?10-3 |
Secondary dendrite arm spacing, λ2 | m | 71?×?10-6 |
Melting point of the pure metal, Tf | °C | 327.5 |
Liquidus slope, m | K(wt%)-1 | -?2.334 |
Partition coefficient, kP | 0.31 | |
Eutectic temperature, Teut | °C | 183.0 |
Eutectic composition, weut | wt% | 61.9 |
Nominal concentration, w0 | wt% | 19.2 |
Initial temperature, T0 | °C | 287 |
Heat transfer coefficient | W m-2 K-1 | 1000 |
External temperature | °C | 20 |
Diffusion coefficient in liquid, Dl | m2 s-1 | 1.05?×?10-9 |
Solidification time (s) | wmax (wt%) | wmin (wt%) | ||||||
---|---|---|---|---|---|---|---|---|
Mesh I | Mesh II | Mesh III | Ref [ | Mesh I | Mesh II | Mesh III | Ref [ | |
50 | 20.27 | 20.26 | 20.27 | 20.0 | 18.86 | 18.61 | 17.83 | 18.8 |
100 | 20.27 | 20.26 | 20.27 | 20.1 | 18.62 | 18.48 | 17.66 | 18.6 |
200 | 20.27 | 20.26 | 20.50 | 20.2 | 18.36 | 18.26 | 17.74 | 18.3 |
400 | 20.27 | 20.26 | 20.73 | 20.2 | 17.90 | 17.88 | 17.48 | 17.4 |
Table 2 Comparison of maximum and minimum concentrations in midplane of casting for the three meshes
Solidification time (s) | wmax (wt%) | wmin (wt%) | ||||||
---|---|---|---|---|---|---|---|---|
Mesh I | Mesh II | Mesh III | Ref [ | Mesh I | Mesh II | Mesh III | Ref [ | |
50 | 20.27 | 20.26 | 20.27 | 20.0 | 18.86 | 18.61 | 17.83 | 18.8 |
100 | 20.27 | 20.26 | 20.27 | 20.1 | 18.62 | 18.48 | 17.66 | 18.6 |
200 | 20.27 | 20.26 | 20.50 | 20.2 | 18.36 | 18.26 | 17.74 | 18.3 |
400 | 20.27 | 20.26 | 20.73 | 20.2 | 17.90 | 17.88 | 17.48 | 17.4 |
Fig. 3 Solidification sequence and fluid flow of Pb-19.2 wt%Sn alloy at different times a-d correspond to the ALE shrinkage model, e-h correspond to the simplified model without shrinkage: a, e 50 s, b, f 100 s, c, g 200 s, d, h 1000 s
Fig. 4 Evolution of temperature field of Pb-19.2%Sn alloy at different times a-d corresponds to the ALE shrinkage model, e-h corresponds to the simplified model without shrinkage: a, e 200 s, b, f 400 s, c, g 600 s, d, h 800 s
Fig. 5 Evolution of Sn concentration distribution of Pb-19.2%Sn alloy at different times a-d corresponds to the ALE shrinkage model, e-h corresponds to the simplified model without shrinkage: a, e 200 s, b, f 400 s, c, g 600 s, d, h 800 s
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