5. Results and discussion

With CFD calculations, a very detailed hydrodynamic study is performed and knowledge of fluid flow in the entire volume of the tank is given. The  determination of local parameters allowed us to clarify some general characteristics such as the stirring power, which is of particular interest.

We present then the most interesting elements. First, we have seen necessary to validate some results. To this end, we realized a geometrical configuration similar to that undertaken by Anne-Archard et al. [11], it’s about a flat-bottomed unbaffled cylindrical vessel equipped with a double ribbon agitator. For an angular position correspond- ing to θ = 900 , two velocity components were identified: the axial and tangential ones. As illustrated on Figures 3 and 4, the comparison shows a satisfactory agreement.

Figure 3. Axial velocity for n = 1.

Figure 4. Tangential velocity for n = 1.

We referred also to the work of Wang et al. [25] to confirm the validity of our CFD code and numerical method. With the same geometry and same fluid as those undertaken by Wang et al. [25] we calculated the power number for the structural index n = 0.4 (Figure 5). As shown in this figure, our predicted results agree well with the experimental data given by Wang et al.

5.1. Effect of fluid rheology

The flow structure depends on the nature of the fluid con- sidered, on the impeller rotational speed and geometric

Figure 5. Power number for n = 0.4.

Figure 6.  Tangential velocity for double helical ribbon impeller,   at

Reg = 60, Z∗ = 0.48, θ = 00 .

conditions. Figures 6 and 7 are presented to highlight the effect of the first factor. Along the lines corresponding to the angular positions θ = 00 and 900 respectively, the evolution of the tangential velocity is followed for different structural indices.

The first important conclusion of this work is that the in- tensity of the flow is marked at the tips of the blade, where there are strong shear stresses (Figure 6). This intensity will be loosed when approaching to the side walls of the tank, until it becomes negligible at the immediate contact with the wall. Note that the decay is faster for the lowest

Figure 7.  Tangential velocity for double helical ribbon impeller,   at

Reg = 60, Z∗ = 0.48, θ = 900 .

Figure 8. Radial velocity for double helical ribbon impeller, at Reg =

, R∗ = 0.74, θ = 00 .

behavior index (n), and this is due to the viscous forces. In moving to the stirrer mediator (θ = 900 ), the curves tend towards parabolic profiles, with a more pronounced intensity when increasing n (Figure 7).

Within the area swept by the blades of the stirrer, the velocity gradients are stronger when compared to the rest of the vessel volume; this phenomenon is illustrated in Figure 8.  It is also noticed that the evolving  rheology of the fluid plays an important role on the variation of this gradient, the movement of fluid particles become more intense with increasing structural index.

For a radius located at θ = 900 , the axial velocity profiles are shown in Figure 9. At the immediate contact with the

side wall and at the stirrer axis, the velocity is negligible whatever the value chosen for n, on the other hand, the maximum absolute value is reached for n = 1. The minus sign indicates the existence of an opposite flow caused by the streamlined shape of the blade, which is expanding if the structural index continues to increase. Consequently, the well stirred region will be larger (Figure 10).