Abstract
The formation of macrosegregation in a rectangular ingot with reduced cross section from the riser to the casting, chilled from the bottom, has been studied numerically. In addition to positive inverse segregation occurring near the chilled surface, very severe negative segregation around the under-riser region and moderate positive segregation near the top corners of the casting were found. Although large circulating vortexes are created by natural convection in the under-riser region during the early stage of solidification, the fluid flow in the mushy zone is dominated by solidification shrinkage. As a result, the final solute distribution in the casting is determined by the flow of solute-rich liquid in the mushy zone owing to the combined effects of solidification shrinkage and change of cross section from casting to riser. Detailed explanations regarding the effect of different flow phenomena on the formation of the segregations are provided. The effects of riser size and cooling condition at the bottom of the ingot on the formation of macrosegregation also were studied. The predicted negative and positive macrosegregations in the casting compared very well with the available experimental data.
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Abbreviations
- c :
-
specific heat
- C :
-
coefficient in Eqs. [2] through [3], defined in Eq. [9]
- C 1 :
-
permeability coefficient, defined in Eq. [8]
- d :
-
dendrite arm spacing
- D :
-
mass-diffusion coefficient
- f :
-
mass fraction
- g :
-
volume fraction or gravitational acceleration
- h :
-
enthalpy
- h c :
-
effective convection heat transfer coefficient between casting and chill
- H :
-
latent heat
- k :
-
thermal conductivity
- k p :
-
equilibrium partition ratio
- K :
-
permeability function, defined in Eq. [8]
- p :
-
pressure
- t :
-
time
- T :
-
temperature
- T m :
-
fusion temperature at zero solute concentrationu velocity component in thex-direction v velocity component in they-direction V velocity vectorx, y Cartesian coordinates
- β s :
-
solutal expansion coefficient
- β T :
-
thermal expansion coefficient
- μ :
-
dynamic viscosity
- ρ :
-
density
- 0 :
-
initial value
- c :
-
chill
- e :
-
eutectic
- l :
-
liquid phase
- m :
-
fusion
- r :
-
relative to solid phase
- s :
-
solid phase
- α :
-
constituent of alloy
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Diao, Q.Z., Tsai, H.L. Modeling of the formation of under-riser macrosegregation during solidification of binary alloys. Metall Mater Trans A 25, 1051–1062 (1994). https://doi.org/10.1007/BF02652280
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DOI: https://doi.org/10.1007/BF02652280