Numerical Simulation of a Gas-Stirred Ladle - Selected Topics of Computational and Experimental Fluid Mechanics - page 265

Fig. 1 Pathline velocity curves describing the flow within the ladle for a volumetric airflow rate of
9 . 01 × 10 − 6 m 3 s − 1 .The colour-scale bar and numbers on the left border indicate the magnitude
of the velocity in units of m s − 1
reach the flat water surface almost perpendicularly. Strong recirculation in the water
phase is observed away from the vessel wall on one side of the plume, which occupies
most of the ladle volume as shown by the green and blue pathlines. In the upper parts
of the recirculation region, the water flows towards the walls with velocities that
are nearly half the maximum velocities at the plume centre. In the proximity of the
wall, the pathlines bend and the water flows down along the wall with progressively
decreasing velocities. A further bending of the pathlines is produced when the flow
reaches the bottom of the ladle, converging to the lower parts of the plume region.
A small dead volume is formed below the recirculation region at the bottom of the
ladle as indicated by the arrow in Fig. 1 .
A striking aspect of the present calculations is the formation of an open eye in
close contact with the wall, as is shown in Fig. 1 just behind the plume where a
blue pathline is observed to follow a spiral-like trajectory in a clockwise sense. This
interesting feature has been observed in air-water experiments with two eccentric
porous plugs (Méndez et al. 2002 ). The open eye forms at a height where the plume
is closest to the wall (its upper part) because part of the kinetic energy that would be
transferred to the water is lost by viscous friction and so the flow velocities involved
there are close to zero.
The predicted air volume fraction is depicted in Fig. 2 , where a systematic
attraction of the plume by the wall is seen towards its upper part. This behaviour
was observed in model experiments of eccentric air injection in a square-section
water channel for small and moderate flow rates and predicted by two-phase flow,