Detached Eddy Simulation And PIV Study Of The Macroinstability In Eccentrically Stirred Tanks

Stirring has been recognized as a common unit operation in process industry and has numerous applications in chemical engineering, food processes, biological fermentations, pharmaceutical engineering, etc. Stirring involved in the mixing, heat and mass transfer, chemical reactions and other processes. Investigation on the internal flow field of the stirred tank is of great importance to study these processes. The fluid flow in stirred tank is highly complicated and transient. Besides, there is macroinstability (MI), which is essentially a kind of large-scale, low-frequency (large-scale is referred to the replacements of flow pattern and low-frequency means the period of each flow pattern is longer than the time of one rotation of impeller) temporal mean flow variation phenomenon. MI significantly affects the mixing performance of stirred tanks and accordingly has attracted more and more attention. In this paper, the MI in the eccentrically stirred tank was studied by the combination of the computational fluid dynamics (CFD) and experimental methods. The influence of MI on the mixing process in the eccentrically stirred tank was also investigated.The numerical simulation method of the stirred tank was firstly established based on the detached eddy simulation (DES) model and the three-dimensional flow fields as well as the mixing processes in stirred tanks were numerically investigated. The velocity and turbulent kinetic energy distributions as well as the power consumption of the stirred tank were mainly investigated and the numerical results were compared with the laser doppler velocimetry (LDV), large eddy simulation (LES) and Reynolds stress model (RSM) results. It was found that there were good agreements between the DES and LDV results, indicating that the DES model can capture the mean and instantaneous flow characteristics in the stirred tank accurately. The simulation results of the turbulent kinetic energy and turbulent kinetic energy dissipation were also satisfactory. The comparisons with the LES model showed that DES model can simulate the flow at less computational cost (about 80% of the LES model) as well as with nearly the same accuracy. Besides, numerical results of the mixing time obtained by the DES model were in good agreements with the experimental data, while the results from the Reynolds-averaged Navier-Stokes (RANS) method were not so good. The results showed that the DES model has higher accuracy than the RANS model, and can be used to simulate the mixing process in stirred tanks.The MI in the centrically stirred tank was numerically studied by the numerical simulation method established based on the DES model. The MI frequencies in the laminar, transitional and turbulent regimes were studied. The results were compared with the LES and LDV results and good agreements were observed. It was found that the MI frequencies in the centrically stirred tank under different flow regimes are not the same. There is a single MI frequency under the laminar and turbulent flow regimes, respectively. However, there are two MI frequencies under the transitional flow regime, which are nearly the same as the values observed under the laminar and turbulent flow regimes. By comparison, the value under the laminar flow regime is larger than that under the turbulent flow regime, which shows that the MI phenomenon under laminar flow regime is more obvious. The good agreements between the DES and literature results show that the macroinstability in stirred tanks can be investigated by the DES model accurately.The numerical simulation method of the eccentric stirred tank was then established based on the DES model. The macroinstability in the eccentrically stirred tank was studied by the numerical and PIV experimental method. The visualization analyses of the MI vortex under different operation conditions were presented and the frequency analyses were applied to the velocity recordings obtained by PIV measurements. The PIV experimental results were compared with the DES results and good agreements were observed. The MI frequency in eccentrically stirred tank was found in the range of 0.1～0.2 Hz, which is about 10 times larger than that of the centrically stirred tank. Accordingly, it can be concluded that the MI phenomenon in eccentrically stirred tank is more obvious. The influence of eccentricity, Reynolds number and impeller-tank diameter ratio were mainly discussed. It was found that the MI frequency increases with reducing the eccentricity or increasing the impeller rotational speed. Besides, there was great influence of the impeller-tank diameter ratio on the MI frequency. A positive linear correlation can be observed, which means higher ratio corresponding to a higher MI frequency.The influence of MI on the mixing process in eccentrically stirred tanks was also investigated by the RANS and DES model. The differences between the mixing times obtained when the tracer was added either inside or outside the processing MI vortex were studied. The DES results were compared with the experimental data and good agreements were observed. The accuracy of DES model is nearly the same with that of the LES model, while the discrepancy between the RANS and experimental results is as high as 60%. The comparison between the mixing times obtained inside and outside the MI vortex indicates that, in the cases studied in this paper, the in-vortex insertion can result in a mixing time reduction of 12%～16%. Results show that the presence of MI in the stirred tank has beneficial implications for mixing operations. The MI phenomenon should be made full use to speed up the mixing process and accordingly improve the mixing efficiency.