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A two-dimensional heat and fluid-flow model of single-roll continuous-sheet casting process

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Abstract

Single-roll continuous-sheet casting process has been simulated using a mathematical model based on considerations of fluid flow, heat transfer, and solidification. The principal model equations include momentum and energy balances which are written for various zones comprising the process. The flow of liquid metal in the pool is taken to be a two-dimensional recirculatory flow. The concepts of vorticity and stream function are used to reduce the number of equations and number of unknowns, respectively. Model equations and boundary conditions are written in terms of dimensionless variables and are solved, using an implicit finite difference technique, to give stream functions and velocity fields in the metal pool, temperature fields in the metal pool, sheet, and caster drum, and the final sheet thickness for various operating parameters. The parameters examined are: (1) rotational speed of the caster drum, (2) liquid metal head in the tundish, (3) superheat of the melt, (4) caster drum material, and (5) cooling conditions prevailing at the inner surface of the caster drum. The final sheet thickness decreases with increasing rotational speed of the caster drum and melt superheat, but it increases with increasing standoff distance and metal head in the tundish.

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Abbreviations

C p :

heat capacity, J Kg−1 K−1

C pd , C pl :

heat capacities of caster drum, liquid steel

C p5 :

and solidified sheet, respectively, J Kg−1 K−1

d :

distance of the solidified sheet from the center of the drum, m

g r , g θ :

radial and angular components of acceleration due to gravity, respectively, ms−2

h ω :

heat-transfer coefficient at the inner surface of the caster drum, W m−2 K−1

i :

grid number in radial direction

j :

grid number in angular direction

K :

thermal conductivity, W m−1 K−1

K d , K l K s :

thermal conductivities of caster drum, liquid steel, and solidified sheet, respectively, W m−1 K−1

l :

axial length of the caster drum, m

L :

latent heat of solidification, J Kg−1

P :

pressure at a point, Kg m−2

Pe l , Pe s :

Peclet numbers of liquid metal, sheet, and

Pe d :

caster drum, respectively

r :

pertaining to the radial direction, m

r 1 , r 2 :

radial distance related to sheet and caster drum, respectively, m

R d :

outer diameter of caster drum, m

R i :

inner diameter of caster drum, m

R I :

radial distance of the tundish wall from the caster drum central axis, m

Re:

Reynolds number as defined by Eq. [12]

Ste:

Stefan number as defined by Eq. [65]

t i :

thickness of the sheet formed at the entry point, m

t θ :

thickness of the solidified sheet at angular position θ, m

t β 2 :

final sheet thickness, m

T :

temperature, K

T f :

constant freezing temperature of liquid steel, K

T l :

temperature of the liquid steel at nozzle exit region, K

T ω :

temperature of the cooling water, K

υ r , υ θ :

velocity components in radial and angular directions, respectively, ms−1

υθ :

average angular sheet velocity at angular position θ, ms−1

υθ max :

maximum angular velocity as defined by Eq. [9], ms−1

α l ,α s :

thermal diffusivities of melt and sheet, respectively, m2 s−1

β1 :

angular position of the caster drum when it comes in contact with the liquid pool of steel, deg

β2 :

angular position at which the solidifying sheet leaves the liquid pool, deg

βnoz :

angular position of upper part of nozzle opening, deg

δ:

standoff distance, mm

η:

dimensionless distance as defined by Eq. (58)

υ :

kinematic viscosity of liquid steel, m2 s−1

ρ d , ρ l , ρ s :

densities of caster drum material, liquid steel, and solidifying sheet, respectively, kg m−3

θ:

pertaining to the angular direction of the cylindrical coordinate system

ω:

vorticity of liquid steel, s−1

ω0 :

speed of rotation of the caster drum, radians/s

ω0 :

speed of rotation of the caster drum, rpm

ψ :

stream function, m2 s−1

ψnmax :

stream function at the sheet/melt interface, m2s−1

ψnmax-1 :

stream function just adjacent the sheet/melt interface toward the liquid side, m2 s−1

†r :

finite difference grid size in radial direction, m

†θ:

finite difference grid size in angular direction, radian

Subscriptd :

is replaced by Cu or SS depending on whether the caster drum is made of copper or stainless steel

Subscript *:

means related variables are in dimensionless form

References

  1. W. Reichelt and K. Warner:Met. Plant Technol., 1988, vol. 11, p. 18.

    Google Scholar 

  2. A.W. Cramb:Iron and Steelmaker, 1988, July, p. 45.

  3. L.L. Teoh:Iron and Steel Engineer, 1988, December, p. 34.

  4. S.P. Mehrotra:Indian Steel Annual, 1991, vol. 133, pp. 97–103.

    Google Scholar 

  5. M.K. Aryan Kumar and S.P. Mehrotra:Steel Res., 1991, vol. 62, pp. 164–70.

    Article  Google Scholar 

  6. M.K. Anjan Kumar and S.P. Mehrotra:Ironmaking and Steelmaking, 1992, vol. 19, pp. 55–63.

    Google Scholar 

  7. R.K. Mallik and S.P. Mehrotra: ISIJ International, 1993, vol. 33, pp. 595–604.

    Article  Google Scholar 

  8. O. Chopra and P. Niessan:Z. Metallkd. 1975, vol. 66, pp. 10–16.

    Google Scholar 

  9. S.M. Pimputkar, R.S. Carbonara, J.J. Rayment, J.L. Me Call, and A. H. Clauer: inRapidly Quenched Metals, S.S. Warimont, ed., Elsevier Publ., New York, NY, 1985, pp. 95–100.

    Chapter  Google Scholar 

  10. J.P. Papal and C.E. Mobley: Proc. Conf. on Casting of Near Net Shape Products, Honolulu, HI, TMS/AIME, Warrendale, PA, 1988, pp. 51–62.

    Google Scholar 

  11. J.K. Brimacombe and I.V. Samarasekera: Proc. Conf. on Casting of Near Net Shape Products, Honolulu, HI TMS/AIME, Warrendale, PA, 1988, pp. 3–24.

    Google Scholar 

  12. Y. Sahai and R.C. Sussman: Proc. Conf. on Casting of Near Net Shape Products. Honolulu, HI, TMS/AIME, Warrendale, PA, 1988, pp. 741–53.

    Google Scholar 

  13. E. Gutierrez-Miravete: Proc. Conf. on Casting of Near Net Shape Products, Honolulu, HI, TMS/AIME, Warrendale, PA, 1988, pp. 31–38.

    Google Scholar 

  14. R.S. Carbonara: Proc. Conf. on Casting of Near Net Shape Products, Honolulu, HI, TMS/AIME, Warrendale, PA, 1988, pp. 169–76.

    Google Scholar 

  15. J.T. Berry: Proc. Conf. Casting of Near Net Shape Products, Honolulu, HI, TMS/AIME, Warrendale, PA, 1988, pp. 41–50.

    Google Scholar 

  16. S.P. Mehrotra and R. Tondon:Steel Res., 1992, vol. 63, pp. 205–11.

    Article  Google Scholar 

  17. M.K. Anjan Kumar and S.P. Mehrotra: Proc. 1st Eur. Conf. on Continuous Casting, Publ. Associzione, Italiana Di Metallurgia, 1991, vol. 2, pp. 367–76.

    Google Scholar 

  18. R.B. Bird, W.E. Stewart, and E.W. Lightfoot:Transport Phenomena, Wiley International Edition, New York, NY, 1960, pp. 85, 96, 319.

    Google Scholar 

  19. V. Gupta and S.K. Gupta:Fluid Mechanics and Its Applications, Wiley Eastern Limited, New Delhi, India, 1985, p. 511.

    Google Scholar 

  20. R.L. Panton:Incompressible Flow, John Wiley and Sons, New York, NY, 1984, pp. 307 and 753.

    Google Scholar 

  21. G.K. Batchelor:An Introduction to Fluid Dynamics, University Printing House, Cambridge, United Kingdom, 1970, pp. 266–69.

    Google Scholar 

  22. Y. Jaluria and K.E. Torrance:Computational Heat Transfer, Hemisphere Publishing Corporation, New York, NY, 1986, pp. 155–82 and 335–36.

    Google Scholar 

  23. A.J. Baker:Finite Element Computational Fluid Mechanics, Hemisphere Publishing Corporation, New York, NY, 1985, pp. 238–39.

    Google Scholar 

  24. P.J. Roache:Computational Fluid Dynamics, Hermosa Publishers, Albuquerque, NM, 1980, p. 141.

    Google Scholar 

  25. F.B. Cheung and S.W. Cha:Numerical Heat Transfer, 1987, vol. 12, pp. 41–56.

    Article  Google Scholar 

  26. R. Peyret and T.D. Taylor:Computational Method for Fluid Flow, Springer Verlag, New York, NY, 1986, p. 27.

    Google Scholar 

  27. B. Carnahan, HA. Luther, and J.O. Wilkes:Applied Numerical Methods, John Wiley & Sons Inc., New York, NY, 1969, pp. 429–508.

    Google Scholar 

  28. D.A. Anderson, J.C. Tannehill, and R.H. Pletcher:Computational Fluid Mechanics and Heat Transfer, Hemisphere Publishing Corp., Washington, DC, 1984, pp. 549–50.

    Google Scholar 

  29. S.S. Sastry:Introductory Methods of Numerical Analysis, Prentice-Hall of India, New Delhi, 1989, pp. 188–89.

    Google Scholar 

  30. R.H. Bogaard:Thermal Conductivity 18, Plenum, New York, NY, 1985, pp. 175–85.

    Book  Google Scholar 

  31. Smithell’ss Metals Reference Book, 6th ed., E.A. Brandes, ed., Butterworth’ss, London, 1983.

    Google Scholar 

  32. E.I. Kazantsev:Industrial Furnaces, Mir Publication, Moscow, 1977.

    Google Scholar 

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Authors and Affiliations

  1. Department of Metallurgical Engineering, Indian Institute of Technology, 208016, Kanpur, India

    M. R. R. I. Shamsi (Graduate Student) & S. P. Mehrotra (Professor and Head)

Authors
  1. M. R. R. I. Shamsi
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  2. S. P. Mehrotra
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Shamsi, M.R.R.I., Mehrotra, S.P. A two-dimensional heat and fluid-flow model of single-roll continuous-sheet casting process. Metall Trans B 24, 521–535 (1993). https://doi.org/10.1007/BF02666435

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