Advertisement

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 Dutta
Article
  • 158 Downloads

Abstract

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.

Nomenclature

CD

Drag coefficient

D

Diameter, m

fs,max

Maximum solids fraction

g

Gravity acceleration, m s−2

K

Momentum exchange coefficient, kg m−3 s−1

U

Momentum exchange, kg m−2s−2

Pr

Prandlt number

P

Pressure, Pa

Re

Reynolds number

T

Temperature, K

Ts

Solidus temperature of alloy, K

Tm

Melting temperature of pure Al, K

ρ

Density, kg m−3

μ

Viscosity, kg m−1 s−1

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

Velocity vector, m s−1

D

Diffusion coefficient, m2 s−1

N

Grain production rate, m−3 s−1

C

Species exchange rate, kg m−3 s−1

Cmix

Mixture concentration

t

Time, s

σunt

Surface tension of untreated melt

cp

Specific heat, J kg−1 K−1

Φ

Fraction of liquid

f

Volume fraction

h

Enthalpy, KJ kg−1

k

Thermal conductivity, W m−1 K−1

H

Heat-transfer coefficient, W m−2 K−1

L

Latent heat, KJ/kg

Q

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

Nu

Nusselt number

kP

Partition coefficient

Tl

Liquidus temperature of alloy, K

TK

Temperature at point K, K

TG

Temperature at point G, K

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

Stress tensors, kg m−1 s−2

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

Interface velocity, m/s

M

Mass-transfer rate, kg s−1 m−3

n

Grain density, m−3

c*

Interface species concentration

Δt

Time step, s

ν

Grain growth rate

\( \sigma_{\bmod } \)

Surface tension of modified melt

Superscripts

d

Stands for drag-related part

p

Stands for phase-transfer-related part

Subscripts

l, s, a

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

Notes

Acknowledgments

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.

References

  1. 1.
    C. Beckermann and J. Ni: Int. Comm. Heat Mass Transfer, 1996, vol. 23, pp. 315-324.CrossRefGoogle Scholar
  2. 2.
    C. Beckermann and C.Y. Wang: Metall. Mater. Trans. A, 1996, vol. 27A, pp. 2754-2764.Google Scholar
  3. 3.
    C. Beckermann and C.Y. Wang: Metall. Mater. Trans. A, 1996, vol. 27A, pp. 2765-2783.Google Scholar
  4. 4.
    M. Wu, A. Ludwig, A. Buhring-Polaczek, M. Fehlbier, and P.R. Sahm: International journal of heat and mass transfer, 2003, vol. 46, pp. 2819-2832.CrossRefGoogle Scholar
  5. 5.
    M. Wu and A. Ludwig: Metall. Mater. Trans. A, 2006, vol. 37A, pp. 1613-1631.CrossRefGoogle Scholar
  6. 6.
    M. Wu and A. Ludwig: Metall. Mater. Trans. A, 2007, vol. 38A, pp. 1465-1475.CrossRefGoogle Scholar
  7. 7.
    M. Wu and A. Ludwig: Acta Materialia, 2010, vol. 57, pp. 5621-5631.CrossRefGoogle Scholar
  8. 8.
    M. Wu and A. Ludwig: Acta Materialia, 2010, vol. 57, pp. 5632-5644.CrossRefGoogle Scholar
  9. 9.
    P.R. Chakraborty and P. Dutta: Metall. Mater. Trans. B, 2011, vol. 42B, pp. 1075-1079.CrossRefGoogle Scholar
  10. 10.
    T. Wang, B. Pustal, M. Abondano, T. Grimming, A. Buhring-Polaczek, M. Wu, and A. Ludwig: Trans. Nonferrous Met. Soc. China, 2005, vol. 15(2), pp. 389-394.Google Scholar
  11. 11.
    N. K. Kund, P. Dutta: Trans. Nonferrous Met. Soc. China, 2010, vol. 20, pp. s50-s54.CrossRefGoogle Scholar
  12. 12.
    P. Das, S.K. Samanta, H. Chattopadhyay, B.B. Sharma, and P. Dutta: Material Science and Technology, 2013, vol. 29, pp. 83-92.CrossRefGoogle Scholar
  13. 13.
    P. Das, S.K. Samanta, H. Chattopadhyay, and P. Dutta: Acta Metallurgica Sinica (English Letters), 2012, vol. 25, pp. 329-339.Google Scholar
  14. 14.
    M. Rappaz: Int. Mater. Rev., 1989, vol. 34, pp. 93-123.CrossRefGoogle Scholar
  15. 15.
    P. Das, S.K. Samanta, and P. Dutta: Metall. Mater. Trans. B, 2015, vol. 46B, 1302-1313.CrossRefGoogle Scholar
  16. 16.
    A. Ludwig and M. Wu: : Metall. Mater. Trans. A, 2002, vol. 33A, pp. 3673-3683.CrossRefGoogle Scholar
  17. 17.
    R.B. Bird, W.E. Stewart, and E.N. Lightfoot: Transport Phenomena, John Wiley & Sons, New York, NY, 1960.Google Scholar
  18. 18.
    T. Wang, M. Wu, A. Ludwig, M. Abondano, B. Pustal, and A. Buhring-Polaczek: International Journal of Cast metals research, 2005, vol. 18(4), pp. 221-228.CrossRefGoogle Scholar
  19. 19.
    L. Schiller and Z. Naumann: Z. Ver. Deutsch. Ing., 1935, vol. 77, pp 318.Google Scholar
  20. 20.
    D.J. Gun, Int. J. Heat Mass Transfer, 1978, vol. 21, pp. 467–476.CrossRefGoogle Scholar
  21. 21.
    W.E. Ranz, W.R. Marshal: Chem. Eng. Prog., 1952, vol. 48 (3), pp. 141–146.Google Scholar
  22. 22.
    S.K. Samanta, H. Chattopadhyay, B. Pustal, R. Berger, M.M. Godkhindi, and A. Buhrig-Polaczek: International Journal of Heat and Mass Transfer, 2008, vol. 51(3), pp. 672-682.CrossRefGoogle Scholar
  23. 23.
    R. Canyook, S. Petsut, S. Wisutmethangoon, M. C. Flemings, J. Wannasin: Trans Nonferrous Met Soc China, 2010, vol. 20, pp. 1649-1655.CrossRefGoogle Scholar
  24. 24.
    R. Canyook, J. Wannasin, S. Wisutmethangoon, and M. C. Flemings: Acta Mater., 2012, vol. 60, pp. 3501–3510.CrossRefGoogle Scholar
  25. 25.
    P. Das, S. K. Samanta, B.R.K. Venkatpathi, H. Chattopadhyay, and P. Dutta: Trans. Indian Inst. Met., 2012, vol. 65, pp. 669-672.CrossRefGoogle Scholar
  26. 26.
    D. Brabazon, D.J. Browne, and A.J. Carr: Mater. Sci. Eng. A, 2003, vol. 356, pp. 69–80.CrossRefGoogle Scholar
  27. 27.
    A. Blanco, Z. Azpilgain, J. Lozares, P. Kapranos, and I. Hurtado: Trans. Nonferrous Met. Soc. China, 2010, vol. 20, pp. 1638–1642.CrossRefGoogle Scholar
  28. 28.
    E. Tzimas, A. Zavaliangos: Materials Science and Engineering A, 2000, vol. 289, pp. 228–240.CrossRefGoogle Scholar
  29. 29.
    H.V. Atkinson and D. Liu: Materials Science and Engineering A, 2008, vol. 496, pp. 439–446.CrossRefGoogle Scholar
  30. 30.
    E.J. Zoqui, M. Paes, M.H. Robert: Journal of Materials Processing Technology, 2004, vol. 153-154, pp. 300-306.CrossRefGoogle Scholar
  31. 31.
    [31] H.M. Guo, X. Q. Luo, A.S. Zhang, and X. J. Yang: Trans. Nonferrous Met. Soc. China, 2010, vol. 20, pp. 1361-1366.CrossRefGoogle Scholar
  32. 32.
    [32] J. Koke, M. Modigell: Journal of Non-Newtonian Fluid Mech., 2003, vol. 112, pp. 141-160.CrossRefGoogle Scholar
  33. 33.
    [33] M. Modigell, J. Koke, Mechanics of Time-Dependent Materials, 1999, vol. 3, pp. 15–30.CrossRefGoogle Scholar
  34. 34.
    [34] M. Modigell, J. Koke: Journal of Materials Processing Technology, 2001, vol. 111, pp 53-58.CrossRefGoogle Scholar

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
  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

Personalised recommendations