A Physical Model to Study the Effects of Nozzle Design on Dispersed Two-Phase Flows in a Slab Mold Casting Ultra-Low-Carbon Steels

Abstract

The effects of nozzle design on dispersed, two-phase flows of the steel-argon system in a slab mold are studied using a water-air model with particle image velocimetry and ultrasound probe velocimetry techniques. Three nozzle designs were tested with the same bore size and different port geometries, including square (S), special bottom design with square ports (U), and circular (C). The meniscus velocities of the liquid increase two- or threefold in two-phase flows regarding one-phase flows using low flow rates of the gas phase. This effect is due to the dragging effects on bubbles by the liquid jets forming two-way coupled flows. Liquid velocities (primary phase) along the narrow face of the mold also are higher for two-phase flows. Flows using nozzle U are less dependent on the effects of the secondary phase (air). The smallest bubble sizes are obtained using nozzle U, which confirms that bubble breakup is dependent on the strain rates of the fluid and dissipation of kinetic energy in the nozzle bottom and port edges. Through dimensionless analysis, it was found that the bubble sizes are inversely proportional to the dissipation rate of the turbulent kinetic energy, ε^0.4. A simple expression involving ε, surface tension, and density of metal is derived to scale up bubble sizes in water to bubble sizes in steel with different degrees of deoxidation. The validity of water-air models to study steel-argon flows is discussed. Prior works related with experiments to model argon bubbling in steel slab molds under nonwetting conditions are critically reviewed.

Appendix A

Equation [1A] in text is rewritten here:

$$ {\text{C}} = - {\text{D}}\left( {{\text{A}}^{ - 1} {\text{B}}} \right)^{\text{T}} + \left( {{\text{A}}^{ - 1} q} \right)^{\text{T}} . $$

(1A)

As an example, the square, 3 × 3 matrix A is located in the right corner of the subsequent general matrix. The 3 × 1 matrix in the left corner is B. The C matrix is built by 1 × 3 elements and is located just below matrix A. Finally, the D matrix with 1 × 1 elements (called the identity matrix) is that located just below matrix B. Matrices A and B constitute the complete dimensional matrix, whereas matrixes C and D constitute the matrix of dimensionless numbers, as shown in Figure A1.

Fig. A1

Dimensional matrix

The variables used to build the dimensional matrix were the following: D_b is the bubble diameter (m), σ_m-s is the surface tension metal (kg/s²), ρ_m is the metal density (kg/m³), ε is the dissipation of kinetic energy (m²/s³), $\pi_{1}$ is a constant number equal to 1.26.[26]