2.5.

Radius [in]

Fig 3. Slip velocity on impeller plane for solid volume fraction  of 0.01  and 1000 rpm. - - - - Gidaspow model, - - Brucato drag model, — Modified Brucato drag model.

D.     'ndiierknr ct aI./ Advanced  Powder Technology 23  (20 12) 445—453 449

internal forces are negligible which means that the viscous foi’ces dominate the flow behaviour. The flow in the stirred tanl‹ is mainly turbulent. Although k-u turbulence model is not able to simulate turbulence effects at the Itolmogorov length scale, this effect has been taken into account in the modified Brucato drag model. I4hopl‹ar et at. [3], while simulating the array of cylinders, have incorporated a source term in order to keep the lambda of the or- der as is observed in a stirred tank. As a result, the underprediction of slip velocities in the impeller zone is addressed by using the Bru- cato and modified Brucato drag model. The magnitude of the drag increases with turbulence and hence, influences the slip velocity between primary and secondary phase. As seen from Fig. 3, the Brucato drag modifies the Wen—Yu drag to a greater extent than the modified Brucato drag, but still the value of slip velocity it is predicting is below that predicted by modified Brucato drag model. This is because of the impact of these models on the turbulence. Brucato drag, due to its magnitude, has a higher influence on the turbulence. The simulations show a high value of turbulent kinetic energy with the modified Brucato drag rather than the Brucato drag model. And the dissipation noticed in the former case was smaller than the latter case. It has a negative impact on the drag calculated and hence the drag is underpredicted due to the low turbulence calculated in the stirred tanl‹. In the cases simulated, the maximum observed difference in dampening of turbulence was 4 0$. The impact of turbulence  on drag is maximum  visible in the impellei- plane where turbulence is dominant. In this region, the rati dp is greater than 10 add US dari > 1O, the ifttefaction between energy dissipating eddies and particles become important for the solids concentration distribution [20]. Derl‹sen et al. [9] have compared the slip velocities in terms of linear and rotational Reynolds number and pointed out the dominance of high slip velocity in this impeller zone. All the compared drag models were able to capture the high slip velocities in this region. But, only modified Brucato drag model predicted reasonable values of slip velocities. When compared with the linear slip velocity values for vertical plane midway between two baffles, predictions by the Gidaspow and Brucato drag model were below the respective values from Derl‹sen et al. [9]. The maximum slip velocity values obtained were 0.58, 0.63 and 0.72 for Gidaspow, Brucato and mod- ified Brucato drag models, respectively in the plane as compared to

0.75 in case of Derksen et al. [9].

Another zone of highei slip velocities is the region in which the direction of axial velocities is upwards. In this zone, the velocity of the particles is against the force of gravity and increases the differ- ence in the velocity of continuous phase and the dispersed phase. The observed phenomenon is exactly opposite in the regions with axial velocity vectors pointing downwards [15,20—24]. The slip velocities  for  I  volume  fraction  and  7é  volume   fraction at 1000 rpm wei-e compared. All the parameters of the study were l‹ept the same for the two cases except the solid volume fraction. Since, the velocity in the case of I volume fraction case  was greater than the just suspension speed and that in the case of 7é volume fraction was below the speed of just suspension, a greater non-uniformity was observed in the solid concentration in the stirred tan1‹. It resulted in an increased local value of slip velocity in regions with low solid concentration in the cases of higher average concentration of solids. Although the increase in concen- tration should result in the decrease in slip velocity, but for cases with impeller speed below and above the just suspension speed, local regions with higher slip velocities can be noticed. This behaviour was also observed by Sardeshpande et at. [25].