**3.2 Velocity profiles and shear stress**

In this part, we present the simulation results for four rotational speeds: 20, 40, 60 and 100 rpm. **Figure 5** shows the cross section of the velocity field within the digester at the agitator height and **Figure 6** extends the longitudinal section of the velocity flied.

The results obtained are consistent. In fact, by increasing the rotation velocity of the stirrer, the maximum velocity increases, the volume of dead zones decreases and the volume of continuously agitated zones increases. The maximum velocity value obtained for each case is the agitator velocity. The maximum velocity is obtained at the blade extremities. The velocity decreases gradually with the distance from the agitator.

For each case, we find that the velocity at the edges of the digester is zero. Likewise, the velocity at the axis of the agitator increases with the increase of the rotational speed. The interest of the study of the velocity field at this level relates in particular to the influence of the agitation on the biofilm which tends to develop on

**Figure 5.**

*Axial cross-section of the velocity flied (m.s<sup>1</sup> ) within the digester at the agitator level (z = 0.06 m) for four rotational speeds: 20, 40, 60 and 100 rpm (the maximum velocity in m.s<sup>1</sup> at the impeller extremity is mentioned below the figures).*

**Figure 6.**

*Longitudinal cross-section of the velocity field (m.s<sup>1</sup> ) within the digester for four rotational speeds: 20, 40, 60 and 100 rpm (the maximum velocity in m.s<sup>1</sup> at the impeller extremity is mentioned below the figures).*

the axis of the agitator. The interest is even greater in the case of intermittent mixing. This mode of agitation is particularly interesting because it leads to the reduction of energy consumption. Overall, the optimization of the mechanical agitation must allow to properly stir the medium, so as to improve the biogas yields, while reducing the rotational speed and frequency of agitation.

From both the axial and longitudinal sections of the flow field, we observe that the maximum velocity field is mainly concentrated in the area close to the agitator and quickly becomes zero away from the influence zone of the impeller blades.

We assume that the dead zones are defined by a velocity magnitude less than 0.001 m.s<sup>1</sup> as [5]. Considering this hypothesis, we find that, in our case study, almost the whole area is dead zones except in the zone of influence of the agitator, which is more important with the increase of the rotation speed. Regarding the contours of the longitudinal cross-section, it can be seen that low-speed velocities are observed near the impeller axis. Furthermore, the area at the upper edges of the digester as well as the lower area of the conical section remains dead zones despite a rotational speed of 100 rpm. CFD simulations are useful for defining the volume of

#### *CFD Simulations in Mechanically Stirred Tank and Flow Field Analysis: Application… DOI: http://dx.doi.org/10.5772/intechopen.93926*

dead zones. Indeed, the dead zones within a digester lead to the heterogeneity of the medium. There will be areas where the substrate will not be digested or acidic areas. This can eventually lead to intoxication of the digester generating significant costs on an industrial scale.

Experimentally it would result in an accumulation of solid and undigested matters, and thus the formation of sludge. It is therefore necessary to adapt the agitation according to the digester technology (with or without sludge bed). In addition, in the case of anaerobic digestion of a recalcitrant waste, such as vinasse, it is important to apply sufficient agitation to re-suspend the undigested matter in order to improve yields.

Similarly, since the upper part of the digester is not agitated, the digestion medium would not be homogenized. Overall, this mode of agitation (mechanical, a three-bladed agitator) would result in a significant stratification of the reaction medium with the presence of dead zones.

In view of the obtained results, it would be recommended to use a stirring system with several rows of blades to agitate the lower and upper areas of the digester to avoid stratification of the digestion medium. In addition, it would be desirable that the diameter of the stirrer be close to that of the digester in order to limit the development of biofilm on the walls. In addition, theses simulations provide information on the velocity field within the digester as a function of agitator rotational speed; however, we have no information on their impact on the biochemical reactions and the biogas production and quality.

A study has been carried out on the impact of shear stress and impeller design on the production of biogas in anaerobic digesters [29]. An impact of the shear stress on the biogas production was highlighted [29] and the abrasion of the anaerobic sludge granule due to the shear rate increase above 5 s<sup>1</sup> [29, 30]. Therefore, it was suggested to estimate the shear stress value for the impeller type and mixing rotation [29]. In the present study, the shear stress is negligible in the digester expected at the wall and impeller levels. We obtained 0.31 Pa at 20 rpm and 1.24 Pa at 100 rpm at the tank wall. At the impeller wall, we reported 453 Pa at 20 rpm and 1883 Pa at 100 rpm. Therefore, the shear stress was multiplied by 4.15 at the impeller wall and by 3.9 at the digester wall, with the increase of the stirring speed from 20 to 100 rpm.

CFD simulations accompanied by experimental studies allow to relate the stirring velocity, the volume of dead zones, the homogenization of the medium (physicochemical properties) and the biogas yields. Thus, a better understanding of the physical phenomena involved in the digesters is necessary for the optimization of anaerobic digestion on an industrial scale. An experimental study on the anaerobic digestion of vinasse on this same geometry (digester and agitation system) would provide knowledge on the yields obtained with the velocity fields obtained in modeling. This would make it possible to relate the yields obtained experimentally to the flows.

#### **3.3 Pressure**

During the anaerobic digestion process, the pressure applied on the medium has an impact. Indeed, there are processes involving free microorganisms that are in the form of flocs or biofilm [31]. There are two types of biofilms, those formed on a mineral or organic support (fixed or mobile) and granules (natural agglomeration of microorganisms from a few tens of microns to several millimeters in diameter). In fact, the flow study through the digester provide information on the pressure imposed on the digestion medium. The interest is to evaluate the impact of pressure on the flocs and biofilms.

**Figures 7** and **8** show the kinematic pressure in continuous flow regime at 40 and 100 rpm respectively. The pressure is due to the impeller rotation. At 20 rpm, it varies from 0 to 5.86.10<sup>5</sup> m<sup>2</sup> .s<sup>2</sup> (0 to 5.86.10<sup>2</sup> Pa). The pressure range at 40 rpm is 0.50 to 0.40 m<sup>2</sup> .s<sup>2</sup> which corresponds to 500 to 400 Pa. At 60 rpm, the pressure varies from 0.73 to 0.61 m<sup>2</sup> .s<sup>2</sup> (730 to 610 Pa). At 100 rpm, it varies from 1.16 to 1.05 m<sup>2</sup> .s<sup>2</sup> (1160 to 1050 Pa).
