An Experimental and Computational Study of Vortex Formation in Stirred Tanks

In stirred tanks operating under unbaffled conditions, a surface depression, referred to as a ‘vortex’, may develop in the stirred medium. It is often of interest to estimate, a priori, the vortex depth as too deep a vortex can lead to issues such as air bubble entrainment into the process fluid, mechanical vibrations of the equipment, and noisy operation. While it is common to characterize vortex depth in terms of an impeller based Froude number alone (Nagata, Mixing: Principles and Applications, 1975), some attempts with limited success have also been made to correlate vortex depth with fluid viscosity. In the present work, we first investigate the Nagata’s inviscid theory and outline the key requirements for a simple Froude number dependence to hold. Specifically, it is shown that the key feature needed for a simple Froude number dependence is presence of a tangential flow and absence of radial and axial flow. Using multiphase flow simulations based on a volume of fluid method in OpenFOAM, we show that precisely this requirement is violated at relatively low Reynolds numbers (Re<10⁴). Experiments are then used to build a new correlation for vortex depth in terms of Froude number, Reynolds number and impeller submergence. Scalability of the correlation is then successfully tested using additional experiments and computer simulations.