Direct numerical simulations of creeping to early turbulent flow in unbaffled and baffled stirred tanks

It has been known for a long time that the fluid flow and several global quantities, such as the power and pumping numbers, are about the same in baffled and unbaffled mechanically stirred vessels at low Reynolds numbers, but bifurcate at some intermediate Re and take drastically different values in fully turbulent flow. However, several details are not yet completely understood, notably concerning the relation of this bifurcation with the flow features and the transition to turbulence. In order to shed light on these issues, computational fluid dynamics was employed to predict the flow field in two vessels stirred by a six-bladed Rushton turbine at Reynolds numbers from 0.2 to 600 (covering the range from creeping flow to early turbulent flow). The two vessels differed only for the presence or absence of peripheral baffles. All simulations were conducted by a finite volume method in time-dependent mode, and a sliding-mesh technique was used in the baffled case to deal with the relative motion of baffles and impeller blades. A sensitivity analysis proved that a grid of about 5 million finite volumes was adequate to yield grid-independent results. The study proved that the bifurcation between quantities related to baffled and unbaffled tanks occurs when the inner (near-impeller) and outer (near-wall/baffles) flow fields interact significantly. It also elucidated the mechanisms of transition to turbulence in baffled and unbaffled tanks, notably showing in this latter case the existence (in the rotating reference frame of the impeller) of a periodic flow regime which involves a travelling wave instability.