Use of angle resolved PIV to estimate local specific energy dissipation rates for up- and down-pumping pitched blade agitators in a stirred tank

Up-pumping pitched blade turbines (and similar impellers) have recently been shown to be particularly effective for achieving a variety of mixing duties. Here, their turbulent flow characteristics are analysed by angle-resolved particle image velocimetry (PIV) for the first time and compared with their down-pumping equivalent, the usual time-averaged parameters also being determined for each. The work was conducted in 0.15 m diameter vessel (T) with a 45° impeller of diameter D (=0.45T  ) in water. The angle-resolved PIV enables a number of novel features to be identified. Firstly, the two pumping directions are shown to give very different vortex structures, even though the flow numbers, Fl, are the same (=0.79). In addition, the ‘spottiness’ of the normalized kinetic energy along a radius as the trailing vortex moved away from each impeller can be identified, which is not shown from time-averaged data. Often, the most important parameter for processing is the local normalized specific energy dissipation rate, εT* and this is estimated using three methodologies: by measurement of the components of the stress tensor directly, (εT*)DE; by dimensional analysis, (εT*)DA, with measured integral length scales (ILS); and by the Smagorinsky closure method, (εT*)SGS, to model unresolved scales (with a Smagorinsky constant used in the literature on stirred vessels). Again, only the angle-resolved results show the spottiness of εTmax* and also higher values than the time-averaged. Differences in the values obtained by the three methods are discussed and compared with the existing literature. Most importantly, for the first time, the power input in the PIV-interrogated region is calculated from the three methods and compared to the input based on the impeller torque. Both DA and SGS methods are shown to overestimate the true power by a factor of 5 and 2, respectively, whilst the DE method provided a significant underestimate (1/5th) due to the limitation of the resolved length scales. The SGS method shows the greatest promise and by changing the value of the Smagorinsky constant in accordance with recent recommendations, good agreement is obtained. Nevertheless, it is concluded that there is still a need for improved methods for determining the important mixing parameter, εTmax*.