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Three-dimensional mathematical modeling of fluid flow in slab tundishes and its verification with water model experiments

  • J. -L. Yeh
  • W. -S. Hwang
  • C. -L. Chou
Processing

Abstract

A three-dimensional mathematical model has been developed based on the incorporation of a computational fluid dynamics technique, called SOLA-SURF, and theK-ε turbulence model. Numerical solutions of the three-dimensional turbulent Navier-Stokes equations and theK and ε equations together with the free surface treatment are presented to study the turbulent flow behavior of molten steel in tundishes. Computed results describing the three-dimensional flow field, particle path lines, residence time distribution curve during steady-state operation are presented. The values oftmin,tpeak, andtmean derived from the residence time distribution curve are used to evaluate the effects of using various combinations of flow control devices such as dams, weirs, and dams with a hole in the flow field. The computed results were compared with the experimental data obtained from a full-scale plexiglas/water model of tundish. The comparisons exhibited good consistency.

Keywords

Molten Steel Residence Time Distribution Calculated Velocity Inclusion Removal Residence Time Distribution Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Symbols

C

Concentration of tracer, kg/m3

C1,C2,C3,Cd

Empirical constants in theK-ε turbulence model

di

Width of the inlet nozzle, m

De

Effective diffusivity, m2/sec

Dm

Molecular diffusivity, m2/sec

gi

Gravitational constant in vector notation,i = 1,2,3 corresponding tox, v, z directions, m/sec2

h

Height of the liquid, m

K

Turbulence kinetic energy, m2/sec2

Ki

AT value at the inlet nozzle, m2/sec2

n,n + 1

Old time level and new time level, respectively

P

Pressure, kg/m ⋅ sec2

Rp

Radius of the inclusion particle, m

t

Time, sec

tmean

Mean residence time, min

tmin

Minimum residence time, sec

tpeak

Peak residence time, min

u,v,w

Mean velocity components inx, y, z directions, m/sec

ui,uj

Mean velocity in vector notation,i,j= 1, 2, 3 corresponding tox, y, z directions, m/sec

Ui

Normal inlet velocity, m/sec

Vt

Rising velocity, m/sec

x,y,z

Lateral (length), vertical, and width directed coordinates with respect to a rectangular tundish

Xi,Xj

Coordinate axes in vector notation, i,j = 1, 2, 3 corresponding tox,y, z directions, m

δt

Time step, sec

ε

Dissipation rate of turbulence energy, m2/sec3

εi

e value at the inlet nozzle, nr/sec3

μm

Molecular viscosity, m2/sec

ve

Effective kinematic viscosity, m2/sec

vm

Molecular kinematic viscosity, m2/sec

vt

Turbulent kinematic viscosity, m2/sec

ρl

Density of the liquid, kg/m3

ρp

Density of the inclusion particle, kg/m3

σk σe

Schmidt numbers forK and e

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References

  1. 1.
    Y. Sahaiand, R. Ahuja,Ironmaking and Steelmaking, 13(5), 241–247(1986).Google Scholar
  2. 2.
    T. DebRoy and J.A. Sychterz,Metall. Trans. B, 16, 497–504 (1985).CrossRefGoogle Scholar
  3. 3.
    J. Szekely and N. El-Kaddah,Steelmaking Proceedings, ISS-AIME,69, 761–776(1986).Google Scholar
  4. 4.
    K.H. Tacke and J.C. Ludwig,Steel Res., 58, 262–270 (1987).CrossRefGoogle Scholar
  5. 5.
    K.Y.M. Lai, M. Salcudean, S. Tanaka, and R.l.L. Guthrie,Metall. Trans. B, 17,449–459 (1986).CrossRefGoogle Scholar
  6. 6.
    Y. He and Y. Sahai,Metall. Trans. B, 18, 81–92 (1987).CrossRefGoogle Scholar
  7. 7.
    J.L. Yeh, H.J. Lin, CL. Chou, and W.S. Hwang,J. Mater. Eng., 12(2), 167–175(1990).CrossRefGoogle Scholar
  8. 8.
    C.W. Hirt, B.D. Nichols, and N.C. Romero, Los Alamos Scientific Laboratory Report LA-5852 (1975).Google Scholar
  9. 9.
    B.E. Launder and D.B. Spalding,Mathematical Models of Turbulence, Academic Press, New York (1972).Google Scholar
  10. 10.
    B.E. Launder and D.B. Spalding,Computer Methods in Applied Mechanics and Engineering, Vol 3, 269–289 (1974).CrossRefGoogle Scholar
  11. 11.
    B.D. Nichols and C.W. Hirt,J. Computational Phys., 8,434–448 (1971).CrossRefGoogle Scholar
  12. 12.
    J. Szekely,Fluid Flow Phenomena in Metals Processing, Academic Press, New York (1979).Google Scholar

Copyright information

© ASM International 1992

Authors and Affiliations

  • J. -L. Yeh
    • 1
  • W. -S. Hwang
    • 1
  • C. -L. Chou
    • 2
  1. 1.Metallurgy and Materials ScienceNational Cheng Kung UniversityTainanTaiwan
  2. 2.Steel & Aluminum Research and Development DepartmentChina Steel CorporationKaohsiungTaiwan

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