As a first step, a comparison is made between our predicted results and the experimental data given by Wu and Patterson [22]. We note that the same geometry as that used by Wu and Patterson has been considered. Fig. 3 presents the variation of tangential velocity along the vessel height for a radial location R* = 0.185. The evolution of the tangential component of velocity along the vessel height is also followed for other radial positions: R* = 0.222 and R* = 0.285 (Fig. 4 and Fig. 5, respectively). As observed on these figures, the comparison shows a satisfactory agreement.

Tangential velocity for Re = 40000, R* = 0.185

Tangential velocity for Re = 40000, R* = 0.222

Tangential velocity for Re = 40000, R* = 0.285

The predicted results of Deglon et al. [20] are also depicted on Fig. 3. As remarked, our results are more close to the experimental data given by Wu and Patterson [22].

In the present paper, a hydrodynamic investigation inside a vessel stirred by a Rushton turbine is presented in detail with the help of the CFD method.

As a first step, we have studied the effects of presence of baffles inside the vessel. It consists of four flat vertical plates, directed radially, spaced at 90° intervals around the vessel periphery, starting from the bottom tangent line of the lower vessel head and running the length of the vessel side to the top tangent line of the upper head.

As remarked on Fig. 6, the discharge flow from the Rushton turbine is characterized by two vortices, at the top and bottom of the blade and a high velocity radial discharge flow in the middle. In a comparison between the baffled and unbaffled configurations, the radial discharge for the unbaffled vessel is directed horizontally; however, the radial discharge is inclined toward the bottom for the baffled vessel. Another remark is that the upper vortex generated in the unbaffled vessel seems very higher and it reaches the free surface of liquid.

Flow fields for Re = 40000

From these remarks, the baffled vessel is the best configuration for this kind of fluids and this range of Reynolds number. However, does the inclination of baffles have any effect on the mixing performance and energy consumption? This is the object of the following section.

The fluid flows and power consumption depend strongly of the impeller design, impeller rotational speed and the baffling provided. The stirring effect is based on the interaction between the impeller and baffles. A certain volume flow is exchanged between the baffles leading to a transfer of angular momentum.

Here, we test the effect of baffle inclination on the flow structure and the power consumption. The vessel is equipped with four baffles which is often referred as a fully baffled condition. The insertion of extra baffles to obtain more heat transfer area is very used in large scale tanks. However, the excessive baffling may cause a reduction of mass flow and localizing flow within the system.

Five geometrical configurations are realized to test the effect of baffle inclination and which are: α = 25°, 32.5°, 45°, 70° and 90°, respectively.

A particularly important feature of the flow field is the vortices generated by the blade impeller. Fig. 7 presents in vertical planes passing through the impeller blade the flow structure generated for different baffle inclinations and different rotational directions. In all cases, the discharge flow dissipates in the bulk and turns axially near the tank wall. Baffles increase the axial circulation and reduce the tangential velocities. Due to a split in the discharge flow, compartments are formed above and below the impeller. Galleti and Brunazzi [23] evaluated the energetic content of the two main vortices and showed that especially the upper vortex is rather strong with an energetic content up to 52% of the turbulent kinetic energy. This means that such vertical structures may have considerable effect on macro-mixing.

Effect of the baffle inclination on the flow behavior, for Re = 40000

In a comparison between the five cases studied, the standard baffles (α = 90°) seems to be the best configuration in terms of reducing the fluid vortexing near the free surface, thus greatly improving mixing.

In an attempt to describe more clearly this phenomenon, we present on Fig. 8 the evolution of the axial velocity along the radial coordinate of the vessel. On the other hand, when the impeller is rotating in the negative direction (−ω), the upper vortex yields to be longer (as illustrated on Fig. 9).

Axial velocity for Re = 40000, Z* = 0.8

Axial velocity for Re = 40000, R* = 0.185, α = 25°

Figs. 10 and 11 show the effect of the impeller rotational direction on the free surface of liquid for different values of α. As it is observed on these figures, the free surface of liquid is more disturbed in the case of α = 25° and (−ω).

Axial velocity for Re = 40000, R* = 0.185, + ω

Axial velocity for Re = 40000, R* = 0.185, −ω

Since trailing vortices can have a potential benefit for mixing practice, it is necessary to study their characteristics (width, length and location). Fig. 12 presents the size of upper vortex (Fig. 12(a): vortex length, Fig. 12(b): vortex width) with respect to the baffle inclination.

Effect of the baffle inclination on the vortex size for Re = 40000

From a practical point of view, the power consumption is perhaps the most important parameter in the design of stirred vessels. In this section, we present the effects of baffles on the power consumption. But first, we checked the validity of our predicted results. Table 2 resumes the values of power number Np found by other researchers for baffled and unbaffled vessels. As remarked on this table, the comparison between our results and the other available data shows a satisfactory agreement.

In the present study, we interest to the effect of baffle inclination on the power consumption. However, in our knowledge, no papers have been published yet and a limited space has been reserved to this subject. Power consumption for a stirred tank equipped with the short baffles was tested by Strek and Karcz [14] only, Karcz and Major [24] and Ammar, et al [25] studied the effect of baffle length. Strek and Karcz [26] examined the influence of the geometrical baffle parameters (number, width, length and distance between the lower edge of the baffle and the bottom of the vessel) upon both power consumption and heat transfer for an agitated vessel.

Our predicted results concerning the effects of baffle inclination on the power number are summarized on Table 3. The data presented in this table show that the greatest power numbers Np are obtained for the agitated vessels equipped with standard baffles (α = 90°), whereas, the least values Np correspond to the systems without baffles. Moreover, the reduction in power number following the baffle inclination (α = 70°, 45°, 32.5° and 25°) is 20%, 25%, 45% and 48%, respectively (compared with standard baffles α = 90°). On the other hand, the impeller rotation in the positive direction (+ω) yields a considerable increase in power number, and this is due to the resistant force caused by the baffle which is also responsible of the formation of small eddies at the tank wall (Fig. 13).

Velocity vectors for Re = 40000

The optimization criterion should take into account the type of process which occurs in the stirred tank. The consequence of employing optimal geometrical parameters is the minimum power consumption for the required operating conditions of the agitated vessel. According to the predicted results presented in this paper, the best geometrical configuration seems to be 70°.

The following figures present the effects of Reynolds number on the flow structure. Three values of Reynolds number are chosen and which are: Re = 40000, 60000 and 80000.

For all cases (Fig. 14), the fluid flows off radially from the impeller with a circumferential component, and flows towards the tank wall where it divides into two streams: one toward the vessel base and the other toward the free surface of liquid. There they are deflected toward the axis and once more drawn in axially by the impeller. Thus, a double vortex is formed in the vessel volume. The mixing occurs mainly in the flow passing through the vortex system and where the discharge flow meets the bulk flow[10].

Streamlines for different Reynolds numbers, α = 70°

Fig. 14 presents the effect of Reynolds number on the shape of the upper vortex. The higher value of Re yields the higher vortex with respect to the vertical plane. The presence of the lower vortex is also discernable.

The direction of impeller rotation has also an important effect on the vortex size with respect to the Reynolds number (Fig. 14). At the same Re, the positive angular velocity (+ω) yields the wider vortex when compared with the negative angular velocity (−ω).