## 3 Results and Discussion  
For the analysed industrial reactor is important that the stirring mechanism to generate a homogenous suspension of the solid particles in the entire volume of the liquid phase. The stirring mechanism must generate an appropriate hydrodynamic field of the multiphase flow so that no sedimentation of the solid particles to appear in the lower part of the reactor. It is important for obtaining a good quality chemical product that all the solid particles remain suspended in the volume of liquid for a sufficient period of time for the chemical reaction to take place. The results presented in the next figures correspond to the operation of the single new designed impeller and the operation of the two new designed impellers in tandem. For both cases, the initial state of the flow corresponds to the homogeneous distribution of the volume fraction of the solid phase in the entire volume of liquid. As in our previous research work, this is the most favourable situation for the best operation of the reactor. To analyse the suspension of the solid phase inside the volume of liquid, the distribution of the volume fraction of the solid phase is plotted on a vertical plane through the middle part of the reactor. The most relevant quantitative representation for the analysis of the performance of the stirring mechanism is represented by the histogram of the distribution of the volume fraction of the solid phase. Similar results of the distribution of the solid phase were presented by [PERSON] et al. [3], in order to analyse the performance of the stirring mechanism. Analysing the distribution of the solid phase inside the industrial reactor in Figure 3, it is shown that by using two new designed impellers in tandem, a better homogenization of the liquid-solid mixture is obtained. Moreover, the level of the liquid that contains a low loading of solid particles is reduced to an acceptable value and the sedimentation of the solid particles in the lower part of the reactor is avoided. Comparing the two histograms presented in Figure 3a,b clearly shows that the volume of liquid containing no solid particles has decreased from 20% to a value of approximately 13%. This value might be even lower because the numerical simulation of the flow did not take in consideration the lift effect of the gas bubbles developed during the chemical reaction upon the solid particles. Figure 2: Computational domain: (**a**) components of the reactor; (**b**) mesh of the computational domain. The stirring mechanism fitted with the two impellers in tandem manage to prevent the sedimentation of the solid particles on the lower cover of the reactor, as supported by all the distributions presented in Figure 3.  
To underline the reasons for different performances of the stirring mechanism for both cases, once equipped with one impeller and once with two impellers in tandem, the distribution of the velocity components, axial, \(v\)-\(a\), [m/s], radial, \(v\)-\(r\), [m/s], and tangential \(v\)-\(u\), [m/s], are plotted on a vertical plane through the middle of the reactor and on three axial planes situated above (y+), at the impellers level (y0) and below the impellers (y\(-\)). A similar representations of the velocity field, employed for analysing the hydrodynamic performance of the impeller and also for the validation of the numerical results, are presented in other research papers [3; 5; 6; 7]. Figure 3: Final state of the volume fraction distribution of the solid phase, instantaneous results: (**a**) single new impeller; (**b**) new impellers in tandem. Analysing the distribution of the axial velocity on the vertical plane in Figure 4, and on three horizontal sections, in Figure 5, shows that the two new impellers in tandem generates a larger value for the axial component of the velocity, oriented towards the lower cover of the reactor. The two new impellers generate, in the central zone, a downward jet below the two impellers that keeps the entire volume fraction of the solid phase in suspension.