# A numerical and experimental study of the solidification rate in a twin-belt caster

- Received:

DOI: 10.1007/BF02649667

- Cite this article as:
- Farouk, B., Apelian, D. & Kim, Y.G. MTB (1992) 23: 477. doi:10.1007/BF02649667

- 13 Citations
- 112 Downloads

## Abstract

A numerical and experimental study was carried out to investigate the solidification process in a twin-belt (Hazelett) caster. The numerical model considers a generalized energy equation that is valid for the solid, liquid, and mushy zones in the cast. A*k-ε* turbulence model is used to calculate the turbulent viscosity in the melt pool. The process variables considered are the belt speed, strip thickness, nozzle width, and heat removal rates at the belt-cast interface. From the computed flow and temperature fields, the local cooling rates in the cast and trajectories of inclusions were computed. The cooling rate calculations were used to predict the dendrite arm spacing in the cast. The inclusion trajectories agree with earlier findings on the distribution of inclusion particles for near horizontally cast surfaces. This article also reports the results of an experimental study of the measurement of heat flux values at the belt-cast interface during the solidification of steel and aluminum on a water-cooled surface. High heat fluxes encountered during the solidification process warranted the use of a custom-made heat flux gage. The heat flux data for the belt surface were used as a boundary condition for the numerical model. Objectives of the measurements also included obtaining an estimate of the heat-transfer coefficient distribution at the water-cooled side of the caster belt.

### List of Symbols

*A*solidified shell thickness, mm

*B*solidification retardation constant, mm

*c*_{v},*c*_{1}*c*_{2}turbulence model constants

- C
_{D} drag coefficient

*C*_{p}specific heat, kJ/kg K

*d*half thickness of the nozzle, m

*D*_{0}half thickness of the cast slab, m

- DAS
secondary dendrite arm spacing, mm

*E*sensible heat, J/kg

*E*_{w}sensible heat for water cooling temperature, J/kg

*F*force, N

*f*_{s}solid fraction

*f*_{L}liquid fraction

*g*gravitational acceleration, m/s

^{2}*H*enthalpy, J/kg

*h*global heat-transfer coefficient, W/m

^{2}K*h*_{c}interface heat-transfer coefficient between belt and cast metal, W/m

^{2}K- ΔL
latent heat content, J/kg

*k*turbulent kinetic energy, m

^{2}/s^{2}*L*axial belt caster length, m

*L*_{f}latent heat of fusion, J/kg

*m*mass, kg

*n*normal direction

- Pe
Peclet number

*q*heat flux at the belt of cooling water side, MW/m

^{2}- Re
_{t} turbulence Reynolds numbez

*(k*^{2}/*v·*ε)- r
_{p} radius of inclusion particle, mm

*S*_{ϕ}generalized source term

*t*_{f}local solidification time, s

*T*temperature, K

- ΔT
_{m} temperature interval of mushy zone, K

*U*_{b}belt speed, cm/s

*U*_{i}mean velocity of melt at the nozzle exit, m/s

*Ū*_{p}instantaneous velocity of a particle

*u*velocity in

*x*direction, m/s*v*velocity in

*y*direction, m/s*x*coordinate parallel to the belts

*y*coordinate normal to the belts