Rotary sloshing induced by impeller action in unbaffled stirred vessels

Unbaffled stirred tanks are characterized by a highly swirling fluid motion and, unless they are completely filled and closed with a lid, a central whirlpool takes place, whose depth depends on the impeller rotational speed. In some cases, periodic rotating waves appear, regardless of the axial symmetry of the system. These waves may result into undesirable periodic stresses for the structure, the vessel and the process connections. In this paper, a comprehensive experimental study on the onset and the characterization of periodic free-surface oscillations in unbaffled stirred vessels is carried out. Different wave shapes (or oscillation modes) may be observed, depending on the operating conditions. The oscillation mode of the free liquid surface is experimentally evaluated by both visual observation and measurements of the local dynamic pressure time traces. The oscillation frequency is identified from the time traces by means of simple Fast Fourier Transform. The natural frequency of each oscillation mode is in excellent agreement with predictions obtained by the theory of sloshing in case of still liquids in cylinders, but the effect of impeller is here analyzed in detail. Several experiments using different tank geometries, filling ratios and liquid viscosities were carried out. In all cases, the observed frequency was found to increase linearly with the impeller speed, with a slope that depends on the impeller geometry and on the oscillation mode under analysis. A simple predictive model is developed and validated by comparison with experimental data.