An experimental and computational investigation of vortex formation in an unbaffled stirred tank

The present article focuses on the quantification of the depth of a depression (i.e. a vortex) formed when stirring liquids in an unbaffled stirred vessel. Based on several experiments, we show that while the vortex depth may be described very well by Nagata's (1975) inviscid model for large Reynolds number (ReD=ND2ν≳104) this model does not apply for smaller Reynolds numbers. A number of researchers (e.g. Zlokarnik (1971), Rieger et al. (1979)) have addressed this difficulty by including Reynolds number in their correlations. However, those correlations produce unphysical estimates for ReD≲103 - a situation still of considerable industrial relevance. To this end, we have developed a new correlation based on 100 experiments where viscosity, impeller size, agitation speed, and impeller submergence were independently varied. The new correlation significantly extends the range of Reynolds numbers over which it can be applied (ReD∈(102,105)), and has the appropriate inviscid behavior, unlike the prior models. Using validated computer simulations in OpenFOAM, and additional experiments the correlation has been validated at various scales (0.046 m to 0.92 m tank diameters). The computational results also provide insights into the effect of fluid viscosity on the overall flow structure within the tank. In particular, the flow velocity magnitude rapidly decays away from the impeller for ReD≲103, and the flow is no longer dominated by tangential motion of the fluid. Consequently, under viscous conditions, the surface motion and vortexing diminish rapidly as impeller submergence is increased.