# Mathematical modeling of flows in large tundish systems in steelmaking

- Received:

DOI: 10.1007/BF02670209

- Cite this article as:
- Lai, K.Y.M., Salcudean, M., Tanaka, S. et al. MTB (1986) 17: 449. doi:10.1007/BF02670209

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## Abstract

Numerical solutions of the three-dimensional turbulent Navier-Stokes equations, incorporating the*k-ε* turbulence model, are presented for the turbulent flow of liquid within a tundish of high aspect ratio. Experimental results, obtained*via* 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

*E*empirical constant in logarithmic law of wall

*G*generation of turbulent energy: kg/(m - s

_{3})*g*acceleration due to gravity: m/s

_{2}*H*height of tundish: m

*K*_{3}empirical constants in the

*k−ε*turbulence model*k*turbulence kinetic energy: m

^{2}/s^{2}*L*total length of tundish: m

*P*pressure: kg/(m s

^{2})*U*_{t}mean velocity in

*i = x, y*, or z directions (tensor notation: m/s)*U*_{j}mean velocity in

*j*direction,*(j = i)*(tensor notation: m s^{−1})*W*total width of the tundish

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

*X*_{i}direction in tensorial form

*i =*1,2,3 corresponding toX,y,Z,...*ε*turbulence energy dissipation: m

^{2}/s^{3}*μ*dynamic viscosity: kg/(m - s)

*ρ*density of liquid: kg m

^{−3}*σ*_{k}, σ_{v}Schmidt number for

*k*and ε