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Convection in the two-phase zone of solidifying alloys

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Abstract

The analysis is applicable to alloy solidification which proceeds horizontally to the center of a mold. The model follows the growth of the solid-liquid zone adjacent to the chill face (the initial transient), the movement of the zone across the mold, and the region of final solidification adjacent to the centerline (the final transient). During solidification the density of the liquid varies across the twophase zone. Consequently, there is natural convection which is treated as flow through a porous medium. The equations for convection are coupled with the equation of solute redistribution between the phases in order to calculate macrosegregation after solidification is complete. Results were computed for alloys which show: (1) “inverse segregation≓ at a cooled-surface; (2) macrosegregation resulting from solidification with the initial transient, a period with a complete two-phase zone, and a final transient; and (3) macrosegregation when the width of the two-phase zone exceeds the semi-width of the mold.

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Abbreviations

A:

coefficient in the pressure equation, Eq. [5]

A x,Ay :

components of A

α E :

constant to describe temperature field, Eq. [6b]

B :

parameter in the pressure equation, Eq. [5]

B :

parameter in the pressure equation in the form of Eq. [18]

b E, bE :

constants to describe temperature field, Eqs. [6a, b]

C E :

eutectic composition

C L :

composition of the interdendritic liquid vC0 composition of the bulk liquid

C p :

heat capacity

C s :

local average composition of the solid after solidification, Eq. [13] or [14]

C*/s :

composition of the solid at the solid-liquid interface

g :

gravitational constant

g:

acceleration due to gravity

g E :

volume fraction of eutectic liquid

g L :

local volume fraction of liquid

g s :

local volume fraction of solid

H :

enthalpy

K :

permeability

k :

equilibrium partition ratio,Cf/CL

L :

height of the ingot

n :

unit vector

p :

pressure

p :

modified pressure, Eq. [17]

p 0 :

ambient pressure

q :

constant to describe temperature field, Eqs. [6a, b]

T :

temperature

T E :

eutectic temperature

T L :

liquidus temperature

t :

time

t E, ti :

time at the passage of eutectic isotherm and liquidus isotherm, respectively

U E :

velocity of the eutectic isotherm

V :

velocity of the interdendritic liquid

V x, Vy :

components of V

W :

width of the solid-liquid zone

x :

distance from the chill-surface

xc :

semiwidth of the ingot

x E,xL :

positions of the eutectic isotherm and liquidus isotherm, respectively

x p :

distance to the liquid/porosity surface

x′ x :

distance to the location of the final solidification of the entire ingot

y :

distance from the bottom of the ingot

γ :

permeability coefficient, Eq. [3]

η:

vertical coordinate in the computational domain

k :

thermal conductivity

Ώ :

viscosity

ξ:

horizontal coordinate in the computational domain

ρ:

density

ρL,ρS :

density of the interdendritic liquid and primary solid, respectively

ρLE, ρSE :

density of the eutectic liquid and the eutectic solid, respectively

ρ LO :

density of the liquid at the liquidus isotherm

Τ:

time in the computational domain

References

  1. A. L. Maples and D. R. Poirier: Report No. 80HV007, vol. I, General Electric Company, Huntsville, AL, 1980.

    Google Scholar 

  2. A. L. Maples and D. R. Poirier: Report No. 80HV007, General Electric Company, Huntsville, AL, 1980, vol. II.

    Google Scholar 

  3. A. L. Maples and D. R. Poirier: Report No. 80HV007, General Electric Company, Huntsville, AL, 1980, vol. III.

    Google Scholar 

  4. A. L. Maples and D. R. Poirier: Report No. 81HV001, vol. I, General Electric Company, Huntsville, AL, 1981.

    Google Scholar 

  5. A. L. Maples and D. R. Poirier: Report No. 81HV001, General Electric Company, Huntsville, AL, 1981., vol. II.

    Google Scholar 

  6. R. Mehrabian, M. Keane, and M. C. Flemings:Metall. Trans., 1970, vol. 1, pp. 1209–20.

    CAS  Google Scholar 

  7. T. Fujii, D.R. Poirier, and M.C. Flemings:Metall. Trans. B, 1979, vol. 10B, pp. 331–39.

    Article  CAS  Google Scholar 

  8. M. C. Flemings and G. E. Nereo:Trans. TMS-A1ME, 1967, vol. 239, pp. 1449–61.

    CAS  Google Scholar 

  9. M.C. Flemings: Solidification Processing, McGraw-Hill Book Co., New York, NY, 1974, pp. 134-76.

  10. S. Kou, D.R. Poirier, and M.C. Flemings:Electric Furnace Proceedings, Iron and Steel Society of AIME, New York, NY, 1977, vol. 35, pp. 221–28.

    Google Scholar 

  11. S. Kou, D. R. Poirier, and M. C. Flemings:Metall. Trans. B, 1978, vol. 9B, pp. 711–19.

    CAS  Google Scholar 

  12. S.D. Ridder, F. C. Reyes, S. Chakravorty, R. Mehrabian, J.D. Nauman, J. H. Chen, and H. J. Klein:Metall. Trans. B, 1978, vol. 9B, pp. 415–25.

    CAS  Google Scholar 

  13. S.D. Ridder, S. Kou, and R. Mehrabian,Metall. Trans. B, 1981, vol. 12B, pp. 435–47.

    CAS  Google Scholar 

  14. C. L. Jeanfils, J. H. Chen, and H. J. Klein:Modeling of Casting and Welding Processes, TMS-AIME, Warrendale, PA, 1981, pp. 313–32.

    Google Scholar 

  15. D. N. Petrakis, M. C. Flemings, and D. R. Poirier:Modeling of Casting and Welding Processes, TMS-AIME, Warrendale, PA, 1981, pp. 285-312.

    Google Scholar 

  16. J.F. Thompson, FC. Thames, and C.W. Mastin:J. Comp. Phys., 1974, vol. 15, p. 299.

    Article  Google Scholar 

  17. B. A. Carre:Computer J., 1961, vol. 4, p. 73.

    Article  Google Scholar 

  18. E. Isaacson and H. B. Keller:Analysis of Numerical Methods, John Wiley, New York, NY, 1966, p. 468.

    Google Scholar 

  19. R. Mehrabian, M. Keane, and M. C. Flemings:Metall. Trans., 1970, vol. 1, pp. 3238–41.

    CAS  Google Scholar 

  20. D.R. Poirier, M.C. Flemings, R. Mehrabian, and H.J. Klein:Advances in Metal Processing, Plenum Press, New York, NY, 1981, pp. 277–318.

    Google Scholar 

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Authors and Affiliations

  1. General Electric Company, 35807, Huntsville, AL

    A. L. Maples (Systems Analyst)

  2. Department of Metallurgical Engineering, The University of Arizona, 85721, Tucson, AZ

    D. R. Poirier (Professor)

Authors
  1. A. L. Maples
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  2. D. R. Poirier
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Maples, A.L., Poirier, D.R. Convection in the two-phase zone of solidifying alloys. Metall Trans B 15, 163–172 (1984). https://doi.org/10.1007/BF02661075

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