Metallurgical and Materials Transactions A

, Volume 50, Issue 3, pp 1323–1332 | Cite as

Modelling of Inclusion Effects on Macrosegregation in Solidifying Steel Ingot with a Multi-phase Approach

  • Duanxing Cai
  • Fengli Ren
  • Honghao Ge
  • Hee-Soo Kim
  • Jun LiEmail author
  • Jianguo Li


A multi-phase dendritic solidification model coupled with Euler–Lagrange framework has been established to characterize the effect of inclusions on macrosegregation in steel ingots. The present model includes many important solidification phenomena such as columnar growth, nucleation, growth of equiaxed and dendritic structure of equiaxed crystals, crystal sedimentation, and melt thermal-solutal convection. A dense discrete phase is employed to simulate the motion of the inclusions and their interaction with fluid flow. Fractal theory is applied to consider the morphology of the inclusion clusters. Based on this model, the effects of the inclusion size and cluster morphology have been investigated for the solidification of a 55-ton industrial Fe-0.33 wt pct C ingot. The results show that inclusions around 15 to 20 μm enhance the macrosegregation significantly, while neither small (i.e. 5 μm) nor large (i.e. 30 μm) inclusions have any obvious influence on the macrosegregation. It’s shown how the compactness of the inclusion cluster plays a dominant role in macrosegregation. The mechanism of how the inclusions affect macrosegregation is also discussed. This study provides valuable information for the control of casting defects caused by inclusions.



Initial concentration (wt pct)


Reference concentration (wt pct)

Cls, Clc

Species exchange (kg m−3 s−1)


Diffusion coefficient (m2 s−1)

fl, fs, fenv, fc, fp

Volume fraction (1)

\( \overrightarrow {{g_{l} }} \),\( \overrightarrow {{g_{s} }} \)

Reduced gravity (m s−2)


Volume heat transfer coeff. (W m−3 °C−1)


Latent heat (J kg−1)

kl, ks, kc

Thermal conductivity (W m−1 °C−1)


Slope of the liquidius in phase diagram (°C)


Grain number density (m−3)

Qls, Qlc, Qcs,

Energy transfer (J m−3 s−1)


Surface area concentration of envelope (m−1)

\( \dot{T} \)

Cooling rate (°C s−1)

\( \overrightarrow {{u_{l} }} \),\( \overrightarrow {{u_{s} }} \),\( \overrightarrow {{u_{p} }} \)

Velocity (m s−1)


Columnar growth speed in radius direction (m s−1)


Dendrite tip velocity (m s−1)

\( \varGamma_{\text{env}} \)

Envelope transfer rate (kg m−3 s−1)

ρl, ρs, ρc, ρp

Density (kg m−3)

cl, cs, cc

Species concentration (wt pct)


Mix concentration (wt pct)


Specific heat (J kg−1°C−1)

ds, denv

Diameter of solid and envelop (m)


Temperature gradient (K m−1)


Heat transfer coefficient (W m−2 °C−1)

hl, hs, hc

Enthalpy (J kg−1)


Solute partitioning coeff. (1)

Mls, Mlc

Net mass transfer rate (kg m−3 s−1)


Grain production rate by nucleation (m−3 s−1)


Pressure (N m−2)


Surface area concentration of solid and columnar phase (m−1)


Temperature (°C)


Time (s)

Uls, Ulc, Ulp, Ucs,

Momentum exchange rate (kg m−2 s−2)


Solid phase growth speed (m s−1)

μl, μs

Viscosity (kg m−1 s−1)


Columnar grain space (m)



Liquid phase (melt)


Grain envelope


Discrete particle phase


Solid phase (solid skeleton)


Columnar phase





This work is sponsored by National Key Research and Development Program of China (No. 2017YFB0305300) the Joint Funds of the National Natural Science Foundation of China (No. U1660203), National Natural Science Foundation of China (No. 51404152), Shanghai Pujiang Program (No. 14PJ1404800).


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Copyright information

© The Minerals, Metals & Materials Society and ASM International 2019

Authors and Affiliations

  • Duanxing Cai
    • 1
  • Fengli Ren
    • 1
  • Honghao Ge
    • 2
  • Hee-Soo Kim
    • 3
  • Jun Li
    • 1
    • 5
    Email author
  • Jianguo Li
    • 1
    • 4
  1. 1.School of Materials Science and EngineeringShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Institute of Laser Advanced ManufacturingZhejiang University of TechnologyHangzhouChina
  3. 3.Department of Materials Science & EngineeringChosun UniversityGwangjuKorea
  4. 4.Collaborative Innovation Center for Advanced Ship and Deep-Sea ExplorationShanghai Jiao Tong UniversityShanghaiChina
  5. 5.Department of EngineeringUniversity of LeicesterLeicesterUK

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