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Mathematical modeling of flow field in slab continuous casting mold considering mold powder and solidified shell with high temperature quantitative measurement

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Abstract

Optimization of mathematical model of flow field in slab continuous casting mold was performed by means of industrial measurement and mathematical modeling. The rod deflection method was used to quantitatively measure the velocities near the mold surface at high temperature. The measurement results were compared with the simulation results of three mathematical models at different argon gas flow rates of 6, 10 and 14 L min−1. The model 1 neglects the mold powder layer, thermal effect and solidified shell. The model 2 only considers the influence of mold powder layer. The model 3 considers the influence of mold powder layer, thermal effect and solidified shell on the flow field. In all three models, the diameter of argon bubbles obeys Rosin–Rammler distribution fitted according to the experimental data of others’ previous work. With increasing the argon gas flow rate, the velocity of liquid steel near the mold surface decreases. The model 1 seriously underestimates the shear stress of liquid steel near the mold surface, and its calculation results show higher velocity near the mold surface, lower turbulent kinetic energy and wider distribution of argon gas bubbles in the mold. The simulation results of model 2 only considering the viscous resistance of the mold powder layer to liquid steel makes the velocity near the surface lower than the measurement results obviously. The calculated velocities near the mold surface with model 3 are in best agreement with the measured results, showing the reasonable spatial distribution range of argon bubbles in the mold and the moderate turbulent kinetic energy. In the present conditions, the best argon gas flow rate is 10 L min−1 due to the moderate velocity near the mold surface, the appropriate distribution of argon gas bubbles in the mold and the smallest fluctuation amplitude on the mold surface.

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Abbreviations

A mush :

Mushy zone constant

c W :

Specific heat capacity of cooling water, J kg−1 K−1

D :

Width or thickness of mold, mm

d :

Distance to meniscus, m

d b :

Bubble diameter, m

d m :

Effective length of mold, m

F mom :

Momentum exchange caused by interphase force traction, N m−3

F D :

Drag force, N

F f :

Buoyancy, N

F g :

Gravity force, N

F i :

Flow rate of cooling water on a certain face of mold, L min−1

F L :

Lift force, N

F P :

Pressure gradient force, N

F V :

Virtual mass force, N

F vol :

Interface tension volume force, N m−3

g(g i, g j, g k):

Gravity acceleration vector, m s−2

h :

Equivalent heat transfer coefficient between solidified shell and cooling water, kJ m−2 h−1 °C−1

k :

Interface curvature, m−2

m :

Cooling water flow rate of mold, kg s−1

m b :

Bubble mass, kg

M eff :

Effective cooling area of mold, m2

n :

Normal vector of interface, m−1

\(\hat{\varvec{n}}\) :

Unit normal vector of interface, m−1

p :

Pressure, Pa

p 1, p 2 :

Pressure on both sides of two-phase interface, Pa

\(\stackrel{\mathrm{-}}{\text{\it q}}\) :

Average heat flux in mold area, W m−2

q s :

Heat flux between solidified shell and cooling water, W m−2

R 1, R 2 :

Principal radii of curvature at two-phase interface in orthogonal directions, m

S :

Additional momentum source caused by solidification, N m−3

t :

Time, s

∆T :

Temperature rise of cooling water flowing through mold, K

T :

Temperature, K

T liquidus :

Liquidus temperature, K

T solidus :

Solidus temperature, K

T w :

Cooling water temperature, °C

u(u i, u j, u k):

Velocity of continuous phase, m s−1

u b :

Bubble velocity, m s−1

u i , j :

Velocity perpendicular to i, j plane, m s−1

u p :

Casting speed, m s−1

W :

Cooling intensity, L m−2 s−1

X :

Distance from meniscus to bottom of mold, cm

x(x i, x j, x k):

Location vector, m

α slag :

Volume fraction of liquid mold powder

α steel :

Volume fraction of liquid steel

β :

Liquid fraction of steel

ε :

Turbulent energy dissipation rate, m2 s−3

κ :

Turbulent kinetic energy, m2 s−2

λ 2 :

Secondary dendrite spacing, m

μ l :

Liquid viscosity, Pa s

μ slag :

Viscosity of liquid mold powder, Pa s

μ steel :

Viscosity of liquid steel, Pa s

μ t :

Turbulent viscosity, Pa s

ξ :

Small constant to avoid a zero denominator

ρ :

Density of continuous phase, kg m−3

ρ b :

Bubble density, kg m−3

ρ slag :

Density of liquid mold powder, kg m−3

ρ steel :

Density of liquid steel, kg m−3

σ :

Interface tension coefficient, N m−1

i, j, k :

Indices for different spatial coordinate directions

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (U1960202) and HBIS Handan Iron and Steel Group Co., Ltd.

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Authors and Affiliations

  1. State Key Laboratory of Advanced Special Steel, School of Materials Science and Engineering, Shanghai University, Shanghai, 200444, China

    Yi-bo Liu, Jian Yang & Chao Ma

  2. Technology Center, HBIS Handan Iron and Steel Group Co., Ltd., Handan, 56015, Hebei, China

    Tao Zhang, Fu-bin Gao, Tai-quan Li & Jun-li Chen

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  1. Yi-bo Liu
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Correspondence to Jian Yang.

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Liu, Yb., Yang, J., Ma, C. et al. Mathematical modeling of flow field in slab continuous casting mold considering mold powder and solidified shell with high temperature quantitative measurement. J. Iron Steel Res. Int. 29, 445–461 (2022). https://doi.org/10.1007/s42243-021-00654-7

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