Metallurgical Transactions B

, Volume 17, Issue 3, pp 449–459 | Cite as

Mathematical modeling of flows in large tundish systems in steelmaking

  • K. Y. M. Lai
  • M. Salcudean
  • S. Tanaka
  • R. I. L. Guthrie
Transport Phenomena


Numerical solutions of the three-dimensional turbulent Navier-Stokes equations, incorporating thek-ε turbulence model, are presented for the turbulent flow of liquid within a tundish of high aspect ratio. Experimental results, obtainedvia Laser-Doppler anemometry and flow visualization techniques, are also reported. Calculated flow fields were shown to be similar to corresponding experimental flow fields. Such results can provide useful technological information regarding the design of tundishes in the steel industry for optimization of steel cleanliness.

List of symbols


empirical constant in logarithmic law of wall


generation of turbulent energy: kg/(m - s3)


acceleration due to gravity: m/s2


height of tundish: m


empirical constants in thek−ε turbulence model


turbulence kinetic energy: m2/s2


total length of tundish: m


pressure: kg/(m s2)


mean velocity ini = x, y, or z directions (tensor notation: m/s)


mean velocity inj direction,(j = i) (tensor notation: m s−1)


total width of the tundish


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


direction in tensorial formi = 1,2,3 corresponding toX,y,Z,...


turbulence energy dissipation: m2/s3


dynamic viscosity: kg/(m - s)


density of liquid: kg m−3

σk, σv

Schmidt number fork and ε


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Copyright information

© The Metallurgical Society of American Institute of Mining 1986

Authors and Affiliations

  • K. Y. M. Lai
    • 1
  • M. Salcudean
    • 2
  • S. Tanaka
    • 3
  • R. I. L. Guthrie
    • 4
  1. 1.Department of Mechanical EngineeringPrinceton UniversityVancouverCanada
  2. 2.Department of Mechanical EngineeringUniversity of British ColumbiaVancouverCanada
  3. 3.Nippon Steel CorporationJapan
  4. 4.Department of Metallurgical EngineeringMcGill UniversityMontrealCanada

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