Flow field and mixing in stirred vessels with regular and fractal impellers

Abstract

The goal of this thesis is to explore the potential benefits of fractal objects in dynamic mixing applications. To this end, the performance of an impeller with fractal blades was evaluated and compared to the one with regular, rectangular-shaped blades. Direct Numerical Simulations (DNS) were performed to compute the flow and passive scalar fields inside an unbaffled stirred vessel in the transitional flow regime. It was observed that at Re=1600 the mean power consumption decreases by ca. 8% when the regular blades are replaced by fractal ones. The physical explanation for this reduction was provided by comparing several characteristics of the flows generated by the two types of impellers, such as the pressure distribution on blade surfaces, the time-average recirculation pattern and the trailing vortex system in wake of the blades, the radial transport of angular momentum and the distribution of energy dissipation inside the tank. Furthermore, fluctuations were observed in the power consumption with a peak frequency at ca. three times the impeller rotational speed, for both impeller types. It was discovered that these fluctuations are associated with a periodic event in the wake of the blades, which involves alternating growth and decay of the upper and lower cores of the trailing vortex pair as well as up-and-down swinging motion of the radial jet. Moreover, the mixing time required to homogenize an injected passive scalar was evaluated for both impeller types, at Sc=1. It was observed that the fractal impeller can lead to a shorter mixing time by 10-12%. This result was explained by the differences in characteristics of flow and scalar fields generated by regular and fractal blades. A simple mathematical model was suggested which is able to approximate the decay rate of the passive scalar fluctuations integrated over the tank volume.