Skip to main content
SpringerLink
Log in

A model of a casting

  • Published:
Applied Scientific Research Aims and scope Submit manuscript

Abstract

A model of a casting is presented which describes the freezing of a mushy zone, growing with a dynamically calculated undercooling at the dendrite tips. Equiaxed grains are introduced ahead of a columnar front. The model resembles a combination of the Stefan and mushy zone problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

Symbol:

Meaning

c 0 :

composition

C :

heat capacity per unit volume

C 1, C 2, C 3 :

parameters

D :

solutal diffusion coefficient

g :

weight fraction

G :

temperature gradient

h :

heat transfer coefficient

H :

heat content or enthalpy per unit volume

I :

nucleation rate per unit volume

k :

distribution coefficient

k i :

thermal conductivity (i=s or l)

K i :

thermal conductivity of a single phase (i=s or l)

L :

latent heat per unit volume evolved at the front

m :

liquidus slope

N :

number of grain per unit volume

N 0 :

number of substrate particles per unit volume

r :

extended radius of a grain

t :

time

T :

temperature at time t

v :

velocity

x :

distance

α :

width of control volume immediately ahead of the columnar front

β :

width of control volume immediately behind the columnar front

δ :

boundary layer thickness

δt :

time discretisation interval

δx :

spatial discretisation interval

ΔH :

latent heat per unit volume

ΔT :

undercooling

κ :

pseudo heat transfer coefficient

ω :

extended volume fraction of grains

Ω :

volume fraction of grains

Subscript:

Meaning

e :

east face of the control volume

E :

centre of the control volume to the east

ex :

of the mould

L :

liquidus

l :

liquid

0:

Centre of the control volume

s :

solid

w :

west face of the control volume

W :

centre of the control volume to the west

Superscript:

Meaning

B :

bulk

I :

columnar front

m :

modified

p :

pure

*:

equiaxed

′:

at time t+δt

-:

average

References

  1. J. Stefan: Ann. Phys. u. Chem. (ed. by Wiedemann) N.F., 42 (1891) 269–281.

    Google Scholar 

  2. N. Shamsundar: In: Moving Boundary Problems, ed. by D.G. Wilson, A.D. Solomon and P.T. Buggs (1981) 165–185. Pubd by Academic Press Inc., New York, U.S.A.

    Google Scholar 

  3. P.N. Hansen: In: Solidification and Casting of Metals (1979) 350–356. Pubd by Metals Society, London, U.K.

    Google Scholar 

  4. R.E. Marrone, J.O. Wilkes and R.D. Pehlke: Cast Metals Research J. 9 (1970) 184.

    Google Scholar 

  5. S.C. Flood and J.D. Hunt: In: Proc. Conf. on Modeling of Casting and Welding Processes, Henniker, New Hampshire, U.S.A. (1983) 207–218.

    Google Scholar 

  6. S.C. Flood: D. Phil Thesis, University of Oxford (1985).

  7. T.W. Clyne: In: Proc. 2nd Intern. Conf. on Numerical Methods in Thermal Problems, Venice, Italy (1981) 240–256.

  8. T.W. Clyne: Metallurgical Transactions 15B (1984) 369–381.

    Google Scholar 

  9. M.H. Burden and J.D. Hunt: J. Crystal Growth 22 (1974) Part I: 99–108, Part II: 109–116.

    Google Scholar 

  10. M. Tassa and J.D. Hunt: J. Crystal Growth 34 (1976) 38–48.

    Google Scholar 

  11. I. Jin and J.G. Sutherland: In: Solidification and Casting of Metals (1979) 256–259. Pubd by Metals Society, London, U.K.

    Google Scholar 

  12. R. Elliot: In: Eutectic Solidification Processing (1983) 247–251. Pubd by Butterworths & Co., London, U.K.

    Google Scholar 

  13. T.W. Clyne and W. Kurz: Metallurgical Transactions 12A (1981) 965–971.

    Google Scholar 

  14. J.D. Hunt: In: Solidification and Casting of Metals (1979) 3–9. Pubd by Metals Society, London, U.K.

    Google Scholar 

  15. J.W. Christian: In: The Theory of Transformations in Metals and Alloys. Part I (1975) 17–18. Pubd by Pergamon Press, Oxford, U.K.

    Google Scholar 

  16. J.W. Christian: ibid., In:

    Google Scholar 

  17. J.D. Hunt: Mat. Sci. Eng. 65 (1984) 75–83.

    Google Scholar 

  18. B. Carnahan, H.A. Luther and J.O. Wilkes: In: Applied Numerical Methods (1969) 449–450. Pubd by John Wiley, New York, U.S.A.

    Google Scholar 

  19. B. Chalmers: In: Principles of Solidification (1964) 257–259, 265–268. Pubd by John Wiley, New York, U.S.A.

    Google Scholar 

  20. R. Morando, H. Biloni, G.S. Cole and G.F. Bolling: Metallurgical Transactions 1 (1970) 1407–1412.

    Google Scholar 

  21. I. Maxwell and A. Hellawell: Acta Metallurgica 23 (1975) 901–909.

    Google Scholar 

Download references

Author information

Author notes

  1. S. C. Flood

    Present address: Banbury Laboratories, Alcan International Ltd., Southam Road, OX16 7SP, Banbury, Oxon, UK

Authors and Affiliations

  1. Dept. of Metallurgy and Science of Materials, University of Oxford, Parks Road, OX1 3PH, Oxford, UK

    S. C. Flood & J. D. Hunt

Authors
  1. S. C. Flood
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. D. Hunt
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Flood, S.C., Hunt, J.D. A model of a casting. Applied Scientific Research 44, 27–42 (1987). https://doi.org/10.1007/BF00412004

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00412004

Keywords

Search

Navigation