Fluid flow, solidification and solute transport in billet continuous casting with different stirrer positions

ABSTRACT

A 3D mathematical model of 180 mm × 220 mm billet continuous casting process has been established, which includes electromagnetic field, flow field, solidification and solute transport, and the effect of stirrer position on multiple physical fields distribution is investigated. The results show that, when the stirrer centre positions are located at Y = 515 mm, Y = 615 mm and Y = 715 mm, the growth of the solid shell near the stirrer centre slows down. And the solid shell is remelted and thinned at the mould exit for the stirrer centre position placed at Y = 815 mm. As the stirrer centre position is lowered, the carbon concentration at the mould top reduces gradually. Furthermore, when the stirrer centre position is moved from Y = 515 mm to Y = 815 mm, the carbon concentration on the surface of billet reduces from 0.00211 to 0.00197.

KEYWORDS:

• Billet continuous casting
• mould
• electromagnetic stirring
• different stirrer positions
• flow streamlines
• solidification
• liquid fraction
• carbon concentration

Disclosure statement

No potential conflict of interest was reported by the author(s).

Nomenclature

Symbols
$A_{\mathrm{m}\mathrm{u}\mathrm{s}\mathrm{h}}$:	=	mushy zone constant (–),
$C$:	=	carbon concentration (–),
$C_{\mathrm{p}}$:	=	specific heat (J kg−1 K−1),
$D_{\mathrm{l}}$:	=	carbon diffusive coefficient in the liquid (cm2 s−1),
$D_{\mathrm{l}\mathrm{a}}$:	=	laminar diffusive coefficient (cm2 s−1),
$D_{\mathrm{s}}$:	=	carbon diffusive coefficient in the solid (cm2 s−1),
$f_{\mathrm{l}}$:	=	liquid fraction (–),
${\overrightarrow{F}}_{\mathrm{m}\mathrm{a}\mathrm{g}}$:	=	electromagnetic force (kg·m−2·s−2),
$f_{\mathrm{s}}$:	=	solid fraction (–),
$F_{\mathrm{T}}$:	=	thermal buoyancy (kg·m−2·s−2),
$\overrightarrow{g}$:	=	gravitational acceleration (m·s−2),
$G_{\mathrm{k}}$:	=	generation of $k$ (kg m−1 s−3),
$G_{\omega }$:	=	generation of $\omega$ (kg m−3 s−2),
$h$:	=	total enthalpy (J kg−1),
$h_{\mathrm{r}\mathrm{e}\mathrm{f}}$:	=	reference enthalpy (J kg−1),
$k$:	=	turbulence kinetic energy (m2 s−2),
$k_{\mathrm{e}\mathrm{f}\mathrm{f}}$:	=	thermal conductivity (W m−1 K−1),
$k_i$:	=	equilibrium partition coefficient of element i (–),
$L$:	=	latent heat (J kg−1),
$m_i$:	=	liquidus slope of solute element i (–),
$p$:	=	pressure (Pa),
$S{c}_{\mathrm{t}}$:	=	turbulent Schmidt number (–),
$S_{\mathrm{k}}$:	=	source term for $k$ (kg m−1 s−3),
$S_{\mathrm{p}}$:	=	momentum sink (kg·m−2·s−2),
$S_{\mathrm{s},\mathrm{d}\mathrm{i}\mathrm{f}}$:	=	molecular diffusion (kg m−3 s−1),
:	=	convection diffusion (kg m−3 s−1),
$S_{\omega }$:	=	source term for $\omega$ (kg m−3 s−2),
$t$:	=	time (s),
$T$:	=	temperature of molten steel (K),
$T_{\mathrm{l}}$:	=	liquidus temperature (K),
$T_{\mathrm{s}}$:	=	solidus temperature (K),
$\overrightarrow{u}$:	=	velocity (m·s−1),
$\overrightarrow{\underset{\mathrm{c}}{u}}$:	=	casting speed (m s−1),
$Y_{\mathrm{k}}$:	=	dissipation of $k$ (kg m−1 s−3),
$Y_{\omega }$:	=	dissipation of $\omega$ (kg m−3 s−2),

Greek letters
$\rho$:	=	molten steel density (kg·m−3),
${\mu }_{\mathrm{e}\mathrm{f}\mathrm{f}}$:	=	effective viscosity (kg·m−1·s−1),
${\mu }_{\mathrm{t}}$:	=	turbulent viscosity (kg m−1 s−1),
${\text{β}}_{\mathrm{T}}$:	=	thermal expansion coefficient (K−1),
$\omega$:	=	specific dissipation rate (s−1),
${\mathrm{\Gamma }}_{\mathrm{k}}$:	=	effective diffusivity of $k$ (kg m−1 s−1),
${\mathrm{\Gamma }}_{\omega }$:	=	effective diffusivity of $\omega$ (kg m−1 s−1),

Additional information

Funding

The present study was supported by the National Key R&D Program of China [grant number 2017YFC0805100] and the National Natural Science Foundation of China [grant numbers 51774077, 51974079]. The authors greatly appreciate their support.