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Fig. S. Radial velocity at axial plane r/P — 0.5 for 0.01 solid volume fraction and Fig 7. Axial velocity at axial plane rJR — 0.5 for 0.01 solid volume fraction and JOOO rpm. t Guha et aI. (2007), - - Wen and Yu model, - - - Gidaspow Model, - - 1000 rpm. t Gtiha et aI. (2007), - - Wen and Yu model, Gidaspow Model, - - Brucato drag model, — Modified Brucato drag model. Brucato drag model, — Modified Brucato drag model.
where the effect of turbulence is not as prominent as the upper re— gion, the predictions from all the drag models compared well with experimental data. In the upper region, discrepancy was observed. Around the impeller zone, when-e, the turbulence and velocity fluc- tuations are higher, the Wen and Yu and Gidaspow drag models show large overprediction compared to the experimental data. On the other hand, the Brucato and modified Brucato drag show reason- able agreement. Fig. 6 shows the comparison between the simula— tions results and experimental data for tangential velocity at axial plane r/fi = —0.5. Similar trend to that observed in radial velocity is observed.
The axial velocity profile is shown in Fig. 7. The reversal of flow can be clearly seen. Above the impeller, the axial velocities are neg— ative that means the flow is in downward direction. It reverses in the region below impeller. At the impeller, the axial velocity is zero and is distributed as the other two components of velocities viz. ra— dial and tangential. All the drag models were able to capture the flow reversal qualitatively. Moreover, the predictions of all the drag models were comparable. The experiments show higher axial velocity in the lower region compared to the upper region. Whereas, the simulations predicted similar velocities in the lower and upper region of the impeller. Although this phenomenon is vis—
Ub*ip
ible in Fig. 2, the axial velocities shown in Fig. 6 fail to predict it. It is because of the bigger circular loop in the lower region of the impeller clearly seen in Fig. 2, which also affects the ensemble averaging of values in this particular zone. At the impeller plane, the axial velocity is zei-o as it is disti-ibuted as the other two com- ponents of velocities.
Modified Brucato drag model was found to be the most appro- priate drag model and, therefore, the remaining analysis showed in the paper is based on the simulations conducted using this drag model.
S.3.3. Turbulent kinetic energy (TUE)
The flow in a stirred tanl‹ is turbulent flow that results in the fluctuating components of velocity due to formation of eddies. The l‹-s model used in the RANS simulation assumes isotropic tur— bulence and uses the Boussinesq hypothesis to relate the Reynolds stresses to the mean velocity gradients. The TIME represents the magnitude of turbulence present in the system. The presence of particles dampens turbulence. In order to access the impact of par- ticles, the TIME for single phase flow is compared with the TKE at solid loadings of 1 and 7é.
For a single phase system, the liquid is agitated by the impeller. The high velocity and trailing vortices result in large velocity fluc- tuations in the impeller plane. For this reason TIME was found to be the maximum at the blade tip (Fig. 8(a)). As the velocity decrease radially in this plane, the TIME also decreases. The magnitude of TIME in the other par-ts of the tanl‹ is appi-oximately 10’ times lower than those in the impeller plane. Michelleti et at. [28] used LDA technique to measure dissipation rates at various points in the stir— red tanl‹ and found the variation by more than 2 orders of magni- tude between impeller region and the bulls. Dissipation rate follows the same trend as TUE not only in the impeller region but in the other regions of the stirred tan1‹s as well. The TUE, sim- ilar to the trend observed by Michelleti et al. [28] for turbulence dissipation rate, is comparatively high near the walls and near the axially centre line where the axial velocity field is dominant. Similar behaviour is observed in presence of particles (Fig. 8(b)). However, the magnitude of TUE is much lower.