J. Mater. Sci. Technol. ›› 2022, Vol. 102: 204-212.DOI: 10.1016/j.jmst.2021.06.025
• Research Article • Previous Articles Next Articles
Binqiang Wang, Long Zeng*(), Neng Ren, Mingxu Xia*(
), Jianguo Li
Received:
2021-02-28
Revised:
2021-05-23
Accepted:
2021-06-08
Published:
2022-03-10
Online:
2021-08-27
Contact:
Long Zeng,Mingxu Xia
About author:
mingxu.xia@sjtu.edu.cn (M. Xia).Binqiang Wang, Long Zeng, Neng Ren, Mingxu Xia, Jianguo Li. A comprehensive understanding of grain selection in spiral grain selector during directional solidification[J]. J. Mater. Sci. Technol., 2022, 102: 204-212.
dw (mm) | DS (mm) | D (mm) | θ (°) | H (mm) |
---|---|---|---|---|
4 | 15 | 10 | 30 | 10 |
Table 1 Geometry parameters of spiral grain selector.
dw (mm) | DS (mm) | D (mm) | θ (°) | H (mm) |
---|---|---|---|---|
4 | 15 | 10 | 30 | 10 |
Governing equations |
---|
Radiation transfer:$\nabla \left( I\left( \vec{r},\vec{s} \right)\vec{s} \right)+\left( a+{{\sigma }_{s}} \right)I\left( \vec{r},\vec{s} \right)=a{{n}^{2}}\frac{\sigma {{T}^{4}}}{\pi }+\frac{{{\sigma }_{s}}}{4\pi }\underset{0}{\overset{4\pi }{\mathop \int }}\,I\left( \vec{r},{{{\vec{s}}}^{\prime }} \right)\text{ }\!\!\Phi\!\!\text{ }\left( \vec{s},{{{\vec{s}}}^{\prime }} \right)\text{d}{{\text{ }\!\!\Omega\!\!\text{ }}^{\prime }}$ (1)Enthalpy equations:$\frac{\partial \left( \rho H \right)}{\partial t}=\nabla \cdot \left( \lambda \nabla T \right)+S$(2)$H={{h}_{\text{ref}}}+\underset{{{T}_{\text{ref}}}}{\overset{T}{\mathop \int }}\,{{c}_{\text{p}}}\left( T \right)dT+{{f}_{\text{l}}}L$(3)Solidification:$={{f}_{1}}=\left\{ \begin{matrix} 1 & {} & {{T}_{liquidus}}-T \\ \frac{T-{{T}_{solidus}}}{{{T}_{liquidus}}<{{T}_{solidus}}} & {} & {{T}_{liquidus}}\le T\le {{T}_{solidus}} \\ 0 & {} & T<{{T}_{solidus}} \\ \end{matrix} \right.$(4) |
Table 2 List of governing equations.
Governing equations |
---|
Radiation transfer:$\nabla \left( I\left( \vec{r},\vec{s} \right)\vec{s} \right)+\left( a+{{\sigma }_{s}} \right)I\left( \vec{r},\vec{s} \right)=a{{n}^{2}}\frac{\sigma {{T}^{4}}}{\pi }+\frac{{{\sigma }_{s}}}{4\pi }\underset{0}{\overset{4\pi }{\mathop \int }}\,I\left( \vec{r},{{{\vec{s}}}^{\prime }} \right)\text{ }\!\!\Phi\!\!\text{ }\left( \vec{s},{{{\vec{s}}}^{\prime }} \right)\text{d}{{\text{ }\!\!\Omega\!\!\text{ }}^{\prime }}$ (1)Enthalpy equations:$\frac{\partial \left( \rho H \right)}{\partial t}=\nabla \cdot \left( \lambda \nabla T \right)+S$(2)$H={{h}_{\text{ref}}}+\underset{{{T}_{\text{ref}}}}{\overset{T}{\mathop \int }}\,{{c}_{\text{p}}}\left( T \right)dT+{{f}_{\text{l}}}L$(3)Solidification:$={{f}_{1}}=\left\{ \begin{matrix} 1 & {} & {{T}_{liquidus}}-T \\ \frac{T-{{T}_{solidus}}}{{{T}_{liquidus}}<{{T}_{solidus}}} & {} & {{T}_{liquidus}}\le T\le {{T}_{solidus}} \\ 0 & {} & T<{{T}_{solidus}} \\ \end{matrix} \right.$(4) |
Fig. 2. The EBSD orientation image maps at different heights of grain selector A (a1-a6), grain selector B (b1-b6) and grain selector C (c1-c6); Corresponding IPFs of grain selector A (a1*-a6*), grain selector B (b1*-b6*) and grain selector C (c1*-c6*).
Fig. 3. Relationship between grain density and growth distance (a), and relationship between area percentage of corresponding grains and grow distance (b).
Fig. 4. The orientation image maps (a1-c1), IPFs (a2-c2) and optical micrographs (a3-b3) of corresponding slices between positions 3 and 4 for spiral selector A.
Fig. 5. The orientation image maps (a1-c1), IPFs (a2-b2) and optical micrographs (a3-b3) of corresponding slices between positions 3 and 4 for spiral selector B.
Fig. 6. The orientation image map (a1-c1), IPFs (a2-b2) and optical micrographs (a3-b3) of corresponding slices between positions 3 and 4 for spiral selector C.
Fig. 8. Solidification sequence of liquid metal at the solidification time of (a) 46 s; (b) 62 s; (c), 78 s; (d) 126 s; and corresponding thermal gradient vector G in the spiral grain selector (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.).
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