Case Impeller speed

Single phase 4 000

HOW

1000

Reynolds number

73926

75071.85

81946.97

Power number

4.972403

4.950144

4.63385

dency of drag on volume  fiaction and density into  consideration

448 D. Wndnerknr ct aJ. Advanced Powder Technology 23 (20 12) 445—453

value of power number that did not change with further refine- ment of the grid. The details of cases simulated and discussed in the paper are given in Table 1.

5. Results and discussion

S.J. Preliminary  numerical simulations

Initial simulations were conducted to assess the effect of turbu— lence dispersion force. The flow field was analysed and it was found that there was negligible effect of this force in this particular case of 0.01 volume fraction. The turbulence dispersion force has higher influence at higher concentration of solids where its magni— tude will be high enough to be comparable with the other forces being exerted on the secondary phase [4 5].

In order to verify that the simulations have converged, the residuals as well as additional parameters namely turbulence dis- sipation over the volume and torque on the shaft were monitored. Once the residuals and additional parameters were constant, a simulation was deemed to be convei’ged.

S.B. flow field

Fig. 2 shows the velocity vectors on a centre plane. For the Rushton turbine, an outward jet stream is formed due to the out- ward thrust of the impeller. This high velocity jet approaches to— wards the wall of the stirred tanl‹ and stril‹es  it. The jet splits into two streams. One stream moves in axially upward and another in axially downward dii ection. It creates an anticloc1‹wise velocity field in the region above the impeller and a clocl‹wise velocity field in the region below the impeller. The velocity near walls for the re- gion above impeller is upwards and below the impeller is down— wards. It is opposite when the velocity field is observed near the centre. The intensity of the recirculation in the region below the impeller is stronger than that above the impeller. Converged solu— tion showed similai- flow field (velocity field vectors) as compared to that available in the literature [8]. All the flow characteristics discussed above were captured by the CFD simulation and of the flow are clearly visible in Fig. 2. The simulations were  also able to capture the upward inclination of the jet and its asymmetry (Fig. 2). This inclination is the result of the imbalance in the forces

Fig. 1. Computational domain and grid distribution in stirred   tank.

1.268

0.845

6.423

0.0tXl

Fig 2. Solid velocity vectors on plane between the baffles foi‘ solid volume fraction of 0.01 and 1000 rpm.

exerted on the flow due to the presence of bottom wall and ab- sence of top wall. In the simulations, different boundary conditions imposed on the vessel on the top wall (free slip) and bottom wall (no slip) result in this angular inclination. This effect was also shown in the simulation of Sbrizzai et al. [I9]. The velocity vectors near the top surface of the stirred tan1‹ show a very weak flow field in this region.

5.3. Analysis of drag mode!s

5.3. 1. Slip velocity

The slip velocity in the stirred tanl‹s was analysed using Gidas— pow, Brucato and modified Brucato drag models. A significant dif— ference in the magnitude of slip velocity was observed between Gidaspow and Brucato drag model in the impeller zone (Fig. 3). The reason behind the disparity in the predictions of drag models is the basis. Brucato drag correlation is entirely dependent on the turbulence and is calculated from the ratio of diameter to Itol— mogorov  length  scale.  Gidaspow  drag  model  is valid  when the