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Investigation of macrosegregation for different dendritic arm spacing, casting temperature, and thermal boundary conditions in a direct-chill casting

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Abstract

The study of macrosegregation for different dendritic arm spacing, casting temperature, and cooling conditions in a Direct-Chill (DC) casting was investigated in the present study. The velocity variance-elliptic relaxation (\( \overline{{v^{2} }} - f \)) turbulence model was used to account for the turbulence effect in the bulk liquid and slurry region. The thermosolutal effect was implemented in the bulk liquid and slurry flow. The Scheil’s solute redistribution model was used to account for solute partitioning at the solidification interfaces. The pressure-based segregated time-dependent solver was used in the solution method to solve the flow equations. The model validation indicates loawer transition thickness due to: (1) efficient damping of the flow in the slurry zone by the turbulence viscous forces, (2) effective handling of the kinematic wall blocking effects in the vicinity of the slurry zone, and (3) strong mixing of the turbulent fluid motion that tends to decrease the distance between the solidus and liquidus isotherm. In all the cases investigated, it was evident that the thermal boundary condition at the secondary cooling zone, casting inlet temperature and secondary Dendritic Arm Spacing (DAS) affect the segregation ratio both at the centerline and the billet surface.

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Abbreviations

\({A}_\text{mush}\) :

Mushy zone parameter

a:

Discretization coefficient

abs:

Absolute value

\(c\) :

Species concentration

c:

Specific heat capacity J/Kg/K

d :

Is the secondary dendritic arm spacing (μm)

\({D}\) :

Ass diffusivity (m2/s)

\({D}_{t}\) :

Eddy mass diffusivity (m2/s)

f :

Mass fraction

f :

Elliptic relaxation

\({f}_{\mu }\) :

Viscous damping function

\({F}_{\mu }\) :

Switching function

\({f}_{k}\) :

Another switching function

\(g\) :

Fraction

g :

Acceleration due to gravity (m2/s)

\({g}\) :

Volume fraction

h :

Heat transfer coefficient W/\({\mathrm{m}}^{2}/K\)

k :

Turbulent kinetic energy (m2/s2

\({k}_\text{Eff}\) :

Effective thermal conductivity

k :

Thermal conductivity W /m2/K

\({k}_{o}\) :

Partition coefficient

L:

Latent heat of fusion J/Kg

\({L}_{t}\) :

Turbulence length scale

\({m}_{l}\) :

Liquidus slope

P :

Pressure in (pascal

\(\frac{q}{A}\) :

Heat flux

\({\mathrm{Re}}_{T}\) :

Turbulent Reynolds

r:

Radial distance

T :

Temperature, K

\({T}_{t}\) :

Turbulence time scale

t:

Time (seconds)

\(\overline{{v}^{2}}\) :

velocity variance (m2/s2)

\(\overline{v}\) :

Average y-velocity (m/s)

\(\overline{u}\) :

Average r-velocity (m/s)

V :

Velocity vector

\({v}^{^{\prime}}\) :

Fluctuating velocity in the j-direction

x :

Directional vector

x, y:

Cartesian coordinates

\({\alpha }_{t}\) :

Eddy thermal diffusivity

\({\beta }_{T}\) :

Thermal expansion coefficient

\({\beta }_{C}\) :

Solutal expansion coefficient

\(\varepsilon \) :

Turbulence dissipation rate (m2/s3)

ω:

Number to avoid zero division (0.001

\(\mu \) :

Relative viscosity

\({\mu }_{d}\) :

Dynamic laminar viscosity

\({\mu }_{t}\) :

Turbulent viscosity

ρ:

Density Kg\({\mathrm{m}}^{3}\)

\({\sigma }_{C}\) :

The turbulent Schmidt number

\({\sigma }_{t}\) :

Turbulent Prandtl number

\({\tau }\) :

Reynolds stresses

c:

Contact

cr :

Critical

gap:

Air gap in the mold

i :

Index in i-direction

j :

Index in j-direction

l :

Liquid

m :

Melting

r :

Relative

ref:

Reference

s :

Solid

sat:

Saturation

t :

Turbulent

w :

Water

α :

Free stream

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Acknowledgements

This work is accomplished by the support of the Tertiary Education Trust Fund (TETFUND) (www.tetfund.gov.ng).

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Authors and Affiliations

  1. Department of Mechanical Engineering, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria

    M. A. Waheed

  2. Department of Mechatronics Engineering, Federal University of Technology, Owerri, Imo State, Nigeria

    G. C. Nzebuka

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Waheed, M.A., Nzebuka, G.C. Investigation of macrosegregation for different dendritic arm spacing, casting temperature, and thermal boundary conditions in a direct-chill casting. Appl. Phys. A 126, 725 (2020). https://doi.org/10.1007/s00339-020-03920-9

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