CFD simulations of mixing in single-phase multi-Rushton stirred tanks based on the RANS methodology frequently show an over-prediction of the mixing time. This hints at an underprediction of the mass exchange between the compartments formed around the individual impellers. Some studies recommend tuning the turbulent Schmidt number to address this issue, but this appears to be an ad-hoc correction rather than physical adjustment, thereby compromising the predictive value of the method. In this work, we study the flow profile in between two Rushton impellers in stirred tank. The data hints at the presence of macroinstabilities, and a peak in turbulent kinetic energy in the region of convergent flow, which both may promote inter-compartment mass exchange. CFD studies using the steady-state multiple reference frame model (unsteady simulations are treated in part II) inherently fail to include the macro-instability, and underestimate the turbulent kinetic energy, thereby strongly overestimating mixing time. Furthermore, the results are highly mesh-sensitive, with increasing mesh density leading to a poorer prediction of the mixing time. Despite proper results for 1-impeller studies, we do not deem MRF-RANS models suitable for mixing studies in multi-impeller geometries.

Steady state multiple reference frame-RANS (MRF-RANS) simulations frequently show strong over-predictions of the mixing time in single-phase, multi-impeller mixing tanks, which is sometimes patched by ad hoc tuning of the turbulent Schmidt-number. In Part I of this work, we experimentally revealed the presence of macro-instabilities in the region between the impellers, as well as a peak in the turbulent kinetic energy in the region where the flow from the individual impellers converges. The MRF-RANS method was found unable to capture both. In this second paper, we show that the sliding-mesh RANS (SM-RANS) approach does capture the effect of macro-instabilities, while still underestimating the turbulent kinetic energy. Consequently, the SM-RANS method mildly overestimates the mixing time, while being less sensitive to the exact mesh geometry. Large eddy simulations with the dynamic Smagorinsky model reasonably capture the kinetic energy contained in macroinstabilities, and properly assess the turbulent kinetic energy in the region between the impellers, even for crude meshes. Consequently, the mixing time is reasonably assessed, and even under-predicted at the crudest meshes. However, the turbulent kinetic energy and energy dissipation in the impeller discharge stream are poorly assessed by the dynamic Smagorinsky model.