Cyclic turbulent instabilities in a thin slab mold. Part II: Mathematical model

Mathematical simulations are employed to describe short-and large-scale flow distortions observed in a water model of a thin slab mold using a submerged entry nozzle (SEN) located at deep and shallow positions, operating at two casting speeds of 5 and 7 m/min. Two types of meniscus oscillations are identified; the first (high frequencies) has a relatively long life and short length scales, whereas the second (low frequencies) has a short life and its length scales are similar to those length scales in the mold. It was found, by turbulent flow principles, that the high-oscillation frequencies of the discharging jets are the same as those of the oscillating meniscus. Therefore, the discharging jets transfer vibrating momentum, with frequencies of 1.1 to 5 Hz, to the two upper roll flows during long periods of time, inducing those meniscus oscillations. The large-scale and short-life oscillations originate a dynamic distortion of the flow, forming deep meniscus depressions, especially for a casting speed of 7 m/min with the SEN in a shallow position. These dynamic distortions give origin to rotational flows in the lower boundaries of both jets, below the SEN tip, and even in the recirculatory eyes of the upper roll flows. The time scale of low-frequency oscillations agrees with the time scale of the production rate of kinetic energy along the jet's length. Their origin is linked to a kinetic energy unbalance by the generation of a negative production rate. Because the flow must keep its energy budget, the fluid will transport, through mean convection and pressure-viscous mechanisms, further increases of momentum transfer during a short time, giving place to those dynamic distortions. Because of their large length scale, these dynamic and energetic distortions are the most dangerous to slab quality.