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Effect of strip feeding into mold on fluid flow and heat transfer in continuous casting process

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Abstract

Steel strip feeding into the mold during continuous casting is known as an innovative technology. The newly applied technology is designed to further improve the slab quality. To analyze the complex phase change processes, molten sodium thiosulphate (Na2S2O3·5H2O) was used in the experimental investigation as a transparent analog for metallic alloys. Then, a numerical model incorporating fluid flow, heat transfer and phase change during strip feeding into the mold process was developed. The generalized enthalpy-based method was applied to describe the phase change behavior, and the porous media theory was used to model the blockage of fluid flow by the dendrites in the mushy zone between the strip and melt as well as the solidified shell and melt. The validated model was then used for the simulation of the real strip feeding into the mold process in an industrial scale. The whole shape of the strip under the effect of jet flow from the submerged entry nozzle (SEN) was presented. Results show that the strip will reach a pseudo-steady state after experiencing steel sheath formation, steel sheath melting and strip melting processes. When using the feeding method that is the strip narrow side toward the SEN in the present condition, the strip immersion length can reach 4.5 m below the meniscus and the slab centerline temperature can be decreased by 21 K to a maximum. When the strip feeding speed increased from 0.3 to 0.5 m/s, the minimum temperature of the centerline could be lowered by 4 K or so.

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Abbreviations

\(c_{\text{p}}\) :

Specific heat of mixture, J kg−1 K−1

\(c_{\text{l}}\) :

Specific heat of liquid steel, J kg−1 K−1

\(c_{\text{s}}\) :

Specific heat of solid steel, J kg−1 K−1

\(c_{\text{w}}\) :

Specific heat of water, J kg−1 K−1

\(C_{\mu }\), \(C_{1}\), \(C_{2}\), \(C_{3}\) :

Empirical constants

\(d\) :

Strip thickness, m

\(d_{1}\) :

Primary dendrite arm spacing, μm

\(d_{ 2}\) :

Secondary dendrite arm spacing, μm

\(D_{\text{s}}\) :

Slab thickness, m

\(\vec{g}\) :

Gravity, m s−2

\(G_{k}\) :

Generation of turbulence kinetic energy due to mean velocity gradients, J

\(G_{\text{b}}\) :

Generation of turbulence kinetic energy due to buoyancy, J

\(h\) :

Heat transfer coefficient, W m−2 K−1

\(h_{\text{rad}}\) :

Heat transfer coefficient of radiation, W m−2 K−1

\(h_{\text{spray}}\) :

Surface heat transfer coefficient in the secondary cooling zone, W m−2 K−1

\(H\) :

Total enthalpy, J K−1

\(H_{\text{m} }\) :

Length of mold, m

\(H_{\text{ref}}\) :

Reference enthalpy, J K−1

K :

Turbulence kinetic energy

\(K\) :

Solidification coefficient

\(K_{\text{p}}\) :

Permeability of the mushy zone

\(L\) :

Latent heat, J kg−1

\(L_{\text{c} }\) :

Liquid core depth of cast slab, m

\(L_{\text{m} }\) :

Slab width, m

Nu :

Nusselt number

\(p\) :

Pressure, Pa

\({{Pe}}\) :

Peclet number

\(q\) :

Heat loss along mold zone, J s−1

\(q_{\text{b}}\) :

Heat brought away by cooling boundary, J s−1

\(\bar{q}\) :

Mean heat flux of mold, W m−2

\(Q_{\text{w}}^{\text{c}}\) :

Water flux in spray zones, m3 h−1

\(R_{\varepsilon }\) :

Term response to effects of rapid strain and streamline curvature

\(S\) :

Contact area of strand’s surface, m2

\(s\) :

Solidified shell thickness, mm

\(\vec{S}_{\text{B}}\) :

Momentum source term, N m−3

\(\vec{S}_{\text{p}}\) :

Momentum sink term, N m−3

\(T\) :

Temperature, K

\(T_{0}\) :

Initial temperature, K

\(T_{\text{c}}\) :

Strip temperature, K

\(T_{\text{m}}\) :

Liquid steel temperature, K

\(T_{\text{ref}}\) :

Reference temperature, K

\(T_{\text{l} }\) :

Liquidus temperature, K

\(T_{\text{s}}\) :

Solidus temperature, K

\(T_{\text{amb}}\), \(T_{\text{spray}}\), \(T_{\text{surf}}\) :

Temperature of air, spray cooling water and strand surface, respectively, K

\(\Delta T\) :

Superheat of liquid steel, K

\(\Delta T_{\text{w} }\) :

Cooling water temperature difference, K

\(\vec{u}\) :

Average velocity, m s−1

\(\vec{u}_{\text{l}}\) :

Velocity of liquid phase, m s−1

\(\vec{u}_{\text{s}}\) :

Velocity of solid phase, m s−1

\(v_{\text{a} }\) :

Strip feeding speed, m s−1

\(v_{\text{c}}\) :

Casting speed, m s−1

\(W\) :

Cooling water flux, m3 h−1

\(w\) :

Strip width, m

\(w_{\text{f}}\) :

Forced convection flow velocity, m s−1

x :

Coordinate position along slab width

z :

Distance below meniscus, m

\(\alpha\) :

Temperature conductivity coefficient, m2 s−1

\(\alpha_{k}\)\(\alpha_{\varepsilon }\) :

Inverse effective Prandtl number for k and ε, respectively

β :

Liquid fraction

\(\beta_{\text{T}}\) :

Thermal expansion coefficient, K−1

\(\varepsilon\) :

Turbulence dissipation rate

\(\varepsilon_{\text{b} }\) :

Blackness

\(\mu_{\text{eff}}\) :

Effective viscosity, kg m−1 s−1

\(\mu_{\text{l}}\) :

Laminar viscosity, kg m−1 s−1

\(\mu_{\text{t}}\) :

Turbulent viscosity, kg m−1 s−1

\(\rho_{\text{l}}\) :

Density of liquid steel, kg m−3

\(\rho_{\text{s} }\) :

Density of solid steel, kg m−3

\(\rho_{\text{w} }\) :

Density of water, kg m−3

\(\lambda\) :

Thermal conductivity of steel, W m−1 K−1

\(\lambda_{\text{l}}\) :

Thermal conductivity of liquid phase, W m−1 K−1

\(\lambda_{\text{s}}\) :

Thermal conductivity of solid phase, W m−1 K−1

\(\sigma\) :

Boltzmann’s constant

\(\sigma_{\text{t}}\) :

Turbulent Prandtl number

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Acknowledgements

This work was funded by the National Natural Science Foundation of China (Nos. 51574068 and 51974071) and Yong Elite Scientists Sponsorship Program by China Association for Science and Technology (No. 2018QNRC001).

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Correspondence to Bao-kuan Li.

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Niu, R., Li, B., Liu, Z. et al. Effect of strip feeding into mold on fluid flow and heat transfer in continuous casting process. J. Iron Steel Res. Int. (2020). https://doi.org/10.1007/s42243-019-00341-8

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Keywords

  • Steel strip feeding
  • Generalized enthalpy method
  • Solidification
  • Melting
  • Continuous casting