Chapter 5 Conclusions
Chapter 5
Conclusions
A complete fluid dynamic study of an axially stirred vessel, with two different flow configurations, has been carried out by mean of the PIV technique. The main differences in the flow structures created in the up pumping and down pumping settings, have been discussed, with particular attention to their effect on the local energy dissipation levels.
Next to the time average study, more focus was set in the study flow in the vessel, using an angle resolved technique. The distance between two subsequent blades was divided in 20 parts, thus having a degree of separation of 3°.
No significant difference in the power input passing from Up to Down pumping configuration was observed, therefore the same rotational velocity was used for both cases. The flow number was also investigated.
The first observable difference when studying the flow for the two configurations, obtained by a 6-PBT, is the structure of the flow field. In the up pumping mode two main recirculation loops are present. The main loop has an out of plane clockwise rotational direction pumping the fluid towards the vessel wall, while the upper loop, of lower rotational intensity, rotates counterclockwise. In the down pumping configuration, the flow off the blade tip is pumped down, towards the bottom of the vessel, and flows back to the top of the tank, creating one main counterclockwise loop, and a small clockwise loop beneath the impeller.
The turbulent kinetic energy (kt*) was measured in the vessel for every operating
condition. During the analysis of the results, sensibly higher values of kt* were observed in the
discharge jet of the up pumping configuration, the opposite trend was observed when comparing the values in the zones not directly influenced by the discharge stream. Every angle studied reported the same characteristic behavior first observed in the time average experiments.
Chapter 5 Conclusions
The dissipation of the turbulent energy, as explained during this work, occurs at lower length scales. This has been the main motivation to investigate energy dissipation rates with three methods.
The first method adopted was the dimensional analysis, which more than the others over estimated the dissipation rates. The main reason lies in the integral length scale chosen to be D/10, which limits its application to the comparison between impellers with very different diameters. The strong assumption behind this method, that the dimension of the turbulent scales is constant through the vessel is another limiting factor.
For this reason a direct evaluation from the definition was introduced, recurring to the isotropy assumption to overcome the problems due to the absence of the term of tangential velocity component. The low spatial resolution of the system did not allow to measure directly the energy dissipation rates. Thus a third, and as seen previously, more effectively, has been adopted. The sub grid scale method with Smagorinsky closure model which, with the same approximation adopted in LES, gave the closest result compared to literature. A comparison criterion was introduced to compare with the total power input the energy dissipated for every angle, operating volume integration over the whole vessel, the result confirmed the considerations done and the good evaluation of the SGS method.
Complete qualitative and quantitative understanding of the flow was possible and gave a clear view of where the area of maximum energy dissipation occurred, at varying angles. The same periodicity was found either for the turbulent kinetic energy and the energy dissipation rates.
For every case studied levels of the turbulent kinetic energy dissipation rates were generally higher near the impeller discharge in the up pumping configuration compared to the down pumping. The opposite trend was observed in regions not directly influenced by the discharge jet.
Vorticity was adopted in the time average experiments to understand the rotational intensity of the recirculation loops present in the two configurations. In the angle resolved analysis, the analysis of the rotational direction and intensity helped to understand the movement of the fluid masses at the blade passage. What evinced from this measurement is that the two zones above the impeller in the up pumping case, where are present higher energy dissipation rates, are dependent from each other; the main intensity area, the one just of the blade tip, moving away from the blade, pushes inward a liquid with a certain energy, that dissipates when encounters the upcoming flow from upper recirculation loop. This is true also
Chapter 5 Conclusions
from the less neat separation in the energy contour in the discharge jet of the down pumping configuration.
The flow number was also evaluated as a function of the blade angle and compared between the two configurations. To change the flow configuration, two identical impellers but with opposite inclination angle of the blades were used, therefore, the rotational direction of both the impellers was the same and for the two flow configurations, the flow number versus the blade angle, followed the same profile.
The maximum in the flow number for both cases was obtained for the same angle and the mean value of the two flow numbers were the same and comparable to those reported in literature.
The flow number so studied highlights the periodicity of the events described before and underlines that the power number studied at the beginning to obtain the same energy input, has effectively created a situation of equal energy consumption.
In the Appendix I is described and explained a possible solution to the problems correlated to the estimation of the energy dissipation rate through the dimensional analysis, which is the evaluation on the Integral length scale. The use of a constant length scale, not only gives erroneous values of the energy dissipation rates, as seen by integrating over the volume the local dissipation rates, but also does not allow the comparison between different impellers, because the different geometry of various impellers reflect in a wide range of diameters (D) and Widths (W); thus making impossible to adopt a constant length scale (often estimated as D/10 or W/2). The use of the autocorrelation function solved the problem, giving results very similar to the ones obtained with the Sub-Grid-Scale method.
