5.2. Effect of impeller rotational speed

The second factor that may affect the structure of flows in such agitation system is discussed in this section. Various tests were performed in a range of Reynolds number from 0.1 to 200.

Figures 11 and 12 illustrate the various flow structures ob- tained at various stirring velocities. Generally, we observe a zone of flow repression; the liquid is pumped from the impeller to the vessel walls. For a small Reynolds number,

Figure 9. Radial velocity for double helical ribbon impeller, at Reg =

,  ∗ = 0.74, θ = 00 .

the flow is limited in the neighborhood of the stirrer, and the velocity vectors measured close to the walls are almost negligible. For more significant Reynolds number, the outgoing flow from the blades becomes larger and a better recirculation throughout the vessel is obtained. Figure 13 is presented to highlight the size of vortices generated when changing the Reynolds number.

The power consumption is a macroscopic result obtained by integration on the impeller surface of the local power transmitted by the impeller to the fluid. It is quite equiva-

Figure 10. Flow field for double helical ribbon impeller, at Reg = 60.

Figure 11. Flow fields for double helical ribbon impeller, at n = 0.6, c/D = 0.26, h/D = 0.5.

Figure 12. Streamlines for double helical ribbon impeller, n = 0.6, c/D = 0.26, h/D = 0.5.

τrr = −2η∂vr/∂r (7)

. .

τrθ  = −η r∂(vθ/r)/∂r + (1/r)∂vr/∂θ

(8)

. .

τrz = −η ∂vr/∂z + ∂vz /∂r

(9)

The power number is calculated according to this equation:

Np  =

     P   ρN3 D5

(10)

In Figure 14 is presented the variation of power number

in a logarithmic scale. If the impeller rotational speed in- creases, the viscous dissipation is more pronounced, which generated lower power consumption. On the other hand, the increasing of flow behavior index requires higher power consumption due to the viscous forces.

Figure 13. Axial velocity for double helical ribbon impeller, at n = 0.4,

θ = 00 , Z∗ = 0.4, c/D = 0.26, h/D = 0.5

Figure 14. Power number for double helical ribbon impeller, c/D = 0.26, h/D = 0.5.

lent to say that the power consumption P is entirely given by the impeller to the fluid. In these conditions:

Z

5.3. Effect of the impeller size

Agitation of shear thinning fluids results in the formation of a zone of intense motion around the impeller (the so called cavern) with essentially stagnant and/or slow moving fluids elsewhere. When the stagnant zones exist in a stirred vessel, heat and mass transfer are weak with high temperature gradients, and if aerated, the possibility of oxygen starvation during fermentation will occur, thus it is necessary to eliminate the undesirable poor mixing regions in the tank [26].

The effect of impeller size on the flow patterns and power consumption has also been studied. To perform this test, four geometrical configurations have been realized, which are: h/D = 0.5, 0.62, 0.56 and 0.9, respectively.

The flow fields generated for different impeller sizes are plotted on Figure 15. We can remark that the area swept by the impeller becomes greater with the increase in blade size, the cavern size is then larger (Fig. 15), but the re- quired power consumption becomes more significant when the Reynolds number and the structural index remain the same (Figure 16).