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Numerical simulation of macrosegregation in steel ingots using a two-phase model

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Abstract

A two-phase model for the prediction of macrosegregation formed during solidification is presented. This model incorporates the descriptions of heat transfer, melt convection, solute transport, and solid movement on the system scale with microscopic relations for grain nucleation and growth. Then the model is used to simulate the solidification of a benchmark industrial 3.3-t steel ingot. Simulations are performed to investigate the effects of grain motion and pipe shrinkage formation on the final macrosegregation pattern. The model predictions are compared with experimental data and numerical results from literatures. It is demonstrated that the model is able to express the overall macrosegregation patterns in the ingot. Furthermore, the results show that it is essential to consider the motion of equiaxed grains and the formation of pipe shrinkage in modelling. Several issues for future model improvements are identified.

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Abbreviations

c :

Specific heat capacity, J·kg−1·K−1

C :

Concentration of carbon, wt%

d s :

Grain diameter, m

D :

Mass diffusivity, m2·s−1

g :

Volume fraction

g c :

Grain packing limit

g :

Gravity vector, m·s−2

k p :

Partition ratio

k :

Thermal conductivity, W·m−1·K−1

L :

Latent heat, J·kg−1

m l :

Liquidus slope, K·wt%−1

N :

Grain production rate, m−3·s−1

n :

Grain density, m−3

n max :

Maximum grain density, m−3

p :

Pressure, N·m−2

Re :

Reynolds number

S v :

Interfacial area concentration, m−1

t :

Time, s

T :

Temperature, °C

T m :

Melting point of pure iron, °C

u :

Velocity vector, m·s−1

β :

Drag coefficient, kg·m−3·s−1

β sl :

Solidification volume shrinkage

β C :

Solutal expansion coefficient, wt%−1

β T :

Thermal expansion coefficient, K−1

Γ :

Interfacial phase change rate, kg·m−3·s−1

δ :

Solute diffusion length, m

ΔT :

Undercooling, K

ΔT N :

Undercooling for maximum grain production rate, K

ΔT σ :

Gaussian distribution width of the nucleation law, K

μ :

Dynamic viscosity, kg·m−1·s−1

ρ :

Density, kg·m−3.

0:

Initial

b:

Buoyancy

l:

Liquid phase

ref:

Reference

s:

Solid phase

*:

Equilibrium at the solid-liquid interface.

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Authors and Affiliations

  1. The Key Laboratory of the Ministry of Education of China for Advanced Materials Processing Technology, Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, China

    Wen-sheng Li, Hou-fa Shen & Bai-cheng Liu

Authors
  1. Wen-sheng Li
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  2. Hou-fa Shen
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  3. Bai-cheng Liu
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Corresponding author

Correspondence to Hou-fa Shen.

Additional information

This work was financially supported by the National Science and Technology Major Project of China (No.2011ZX04014-052) and the National Basic Research Priorities Program of China (No.2011CB012900).

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Li, Ws., Shen, Hf. & Liu, Bc. Numerical simulation of macrosegregation in steel ingots using a two-phase model. Int J Miner Metall Mater 19, 787–794 (2012). https://doi.org/10.1007/s12613-012-0629-8

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  • DOI: https://doi.org/10.1007/s12613-012-0629-8

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