# CFD Assessment of the Hydrodynamic Performance of Two Impellers for a Baffled Stirred Reactor
## 2 Materials and Methods  
In this paper the Eulerian multiphase model was chosen to describe the flow behavior of each of the liquid and solid phase. This model is the most complex model and it solves a set of momentum equations for each phase. Figure 1: Schematic representation of the industrial reactor with original stirring mechanism fitted with the new designed impeller. Figure 2: Schematic representation of the two impellers: (**a**) original; (**b**) new design. For simulating the turbulence effects, the RNG k-\(\epsilon\) model with the dispersed option was chosen. The dispersed turbulence model is the appropriate model when using the granular model. Geometry reconstruction of the industrial stirred reactor fitted with the new designed impeller and its meshing were performed with the software Gambit 2.4. The mesh consists of approximately 0.6 million tetrahedral elements. As regards the mesh quality, we use tetrahedral mesh cells as recommended for such complex geometries, [2; 3]. In this study a good quality of mesh (skewness < 0.96) was ensured throughout the computational domain. As in previous research paper we used the sliding mesh approach, and four fluid zones were defined: an inner rotating cylindrical volume centered on the impeller and three other volumes containing the rest of the reactor and the baffles. The interface was located at an equal distance from the blades of the impeller and the inside edge of the baffles. An illustration of the domain and the mesh of the domain is given in Figure 3, which shows that finer meshes were used around the impeller where the velocity spatial gradients were expected to be large. Good care was taken in keeping the same mesh dimension between the rotating and the stationary interface to ensure a good exchange of the hydrodynamic quantities between the two zones during calculation. A \"no-slip\" condition was applied on all walls of the geometry. Simulations of the turbulent multiphase flow were then performed with the help of the commercial CFD code Fluent 16 [19] using the RNG k-\(\epsilon\) model. There were three working materials corresponding to the three phases: liquid with the density \(\rho_{l}=690\) kg\(\cdot\)m\({}^{-3}\), powder with the density \(\rho_{p}=1520\) kg\(\cdot\)m\({}^{-3}\) and the particle size \(d=171\) um and air with the density \(\rho_{a}=1.225\) kg\(\cdot\)m\({}^{-3}\). At the liquid surface, a gas zone consisting of air was added at the free surface of water, a method that was reported to dampen the instabilities, which means top surface being exposed to atmospheric pressure. The limitations of the k-\(\epsilon\) turbulence models in predicting the dissipation rate and the power number are well known [5; 17] and also the numerical results depend on the limitation of the model employed for modeling the impeller rotation. Our analysis was centered on the prediction of the flow field inside the reactor in order to assess the performances of the original impeller. For this purpose, the accuracy of the turbulence model that was employed is satisfactory, as stated by previous research [5; 6; 8; 17; 20]. Using the sliding mesh approach, the flow resolution is unsteady. At each time step, the position of the rotating zone relative to the stationary one was recomputed and the grid interface of the rotating zone slides along the interface of the stationary zone. For all simulations, the time step was set as a function of the impeller speed, 65 rot/min, and the number of the cells from the interface surface, approximately 140 elements, so that the time step was set to a value of 0.01 s.  
At the end of each time step, after a maximum of 5 iterations, the convergence criterion reaches \(10^{-3}\) for the continuity, for momentum and turbulence quantities. Simulations were performed in double precision with the segregated implicit solver. Transient formulation is of the second order and spatial discretization scheme for pressure is PRESTOI and for momentum and turbulence is QUICK.