Metallurgical and Materials Transactions B

, Volume 49, Issue 4, pp 1925–1944 | Cite as

Multiphase Model of Semisolid Slurry Generation and Isothermal Holding During Cooling Slope Rheoprocessing of A356 Al Alloy

  • Prosenjit Das
  • Sudip K. Samanta
  • Biswanath Mondal
  • Pradip DuttaEmail author


In the present paper, we present an experimentally validated 3D multiphase and multiscale solidification model to understand the transport processes involved during slurry generation with a cooling slope. In this process, superheated liquid alloy is poured at the top of the cooling slope and allowed to flow along the slope under the influence of gravity. As the melt flows down the slope, it progressively loses its superheat, starts solidifying at the melt/slope interface with formation of solid crystals, and eventually exits the slope as semisolid slurry. In the present simulation, the three phases considered are the parent melt as the primary phase, and the solid grains and air as secondary phases. The air phase forms a definable air/liquid melt interface as the free surface. After exiting the slope, the slurry fills an isothermal holding bath maintained at the slope exit temperature, which promotes further globularization of microstructure. The outcomes of the present model include prediction of volume fractions of the three different phases considered, grain evolution, grain growth, size, sphericity and distribution of solid grains, temperature field, velocity field, macrosegregation and microsegregation. In addition, the model is found to be capable of making predictions of morphological evolution of primary grains at the onset of isothermal coarsening. The results obtained from the present simulations are validated by performing quantitative image analysis of micrographs of the rapidly oil-quenched semisolid slurry samples, collected from strategic locations along the slope and from the isothermal slurry holding bath.



Drag coefficient


Diameter, m


Maximum solids fraction


Gravity acceleration, m s−2


Momentum exchange coefficient, kg m−3 s−1


Momentum exchange, kg m−2s−2


Prandlt number


Pressure, Pa


Reynolds number


Temperature, K


Solidus temperature of alloy, K


Melting temperature of pure Al, K


Density, kg m−3


Viscosity, kg m−1 s−1

\( {\vec{\mathbf{u}}} \)

Velocity vector, m s−1


Diffusion coefficient, m2 s−1


Grain production rate, m−3 s−1


Species exchange rate, kg m−3 s−1


Mixture concentration


Time, s


Surface tension of untreated melt


Specific heat, J kg−1 K−1


Fraction of liquid


Volume fraction


Enthalpy, KJ kg−1


Thermal conductivity, W m−1 K−1


Heat-transfer coefficient, W m−2 K−1


Latent heat, KJ/kg


Energy exchange by heat transfer, J m−3 s−1


Nusselt number


Partition coefficient


Liquidus temperature of alloy, K


Temperature at point K, K


Temperature at point G, K

\( \bar{\bar{\tau }} \)

Stress tensors, kg m−1 s−2

\( {\vec{\mathbf{u}}}^{*} \)

Interface velocity, m/s


Mass-transfer rate, kg s−1 m−3


Grain density, m−3


Interface species concentration


Time step, s


Grain growth rate

\( \sigma_{\bmod } \)

Surface tension of modified melt



Stands for drag-related part


Stands for phase-transfer-related part


l, s, a

Stands for liquid metal, solid α-Al grain and air



The authors would like to thank DST, New Delhi and CSIR-CMERI for their financial support to this study and all the members of NNMT group for their cooperation and cordial help toward successful completion of this research study.


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Copyright information

© The Minerals, Metals & Materials Society and ASM International 2018

Authors and Affiliations

  • Prosenjit Das
    • 1
    • 2
  • Sudip K. Samanta
    • 2
  • Biswanath Mondal
    • 1
  • Pradip Dutta
    • 3
    Email author
  1. 1.Center for Advanced Materials ProcessingCSIR-Central Mechanical Engineering Research InstituteDurgapurIndia
  2. 2.NNMT GroupCSIR-Central Mechanical Engineering Research InstituteDurgapurIndia
  3. 3.Department of Mechanical EngineeringIndian Institute of ScienceBangaloreIndia

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