# CFD Assessment of the Hydrodynamic Performance of Two Impellers for a Baffled Stirred Reactor
## 1 Introduction  
Stirred reactors have applications in many chemical processes where mixing is important for the overall performance of the system. In such systems, detailed information on the fluid characteristics resulting from the effect of the reactor and impeller geometries is required [1; 2; 3]. Computational fluid dynamics (CFD) techniques have been used in the recent years to provide such information of the hydrodynamic and design parameters. Hydrodynamics and mixing efficiency in stirred reactors are important for the design of many industrial processes. Due to its practical importance, the turbulent fluid flow inside stirred tanks, with various geometries and applications, has been simulated with various expert CFD codes (Fluent, CFX) [4; 5; 6; 7; 8; 9]. The results obtained have shown the robustness of these codes to characterize the flow hydrodynamics in stirred tanks. The accuracy of different simulation methods (k-\(\epsilon\), RSM and LES) used to describe the turbulent flow has been studied [5; 6]. Taking into consideration the results of the previous studies, we decided to use the RNG k-\(\epsilon\) turbulence model, which allows sufficient accuracy of the turbulent quantities within a reasonable calculation time. For the modelling of the solid suspension there are two models mentioned in the literature: the Eulerian multiphase model and the Eulerian mixture model. In the Eulerian multiphase model, continuity and momentum balance equations are solved for each phase. The Eulerian mixture model is a simplified version of the previous model and it is suitable for dilute suspensions and small particle Stokes number. For this model continuityand momentum balance equations are solved for one mixture phase, the hydrodynamics parameters of which are computed from mass-averaged properties of each phase. Only one equation for the transport of volume fraction is added and solved for the dispersed phase from the continuous phase. This term consists of four different interphase forces: lift force, Basset force, virtual mass force and drag force. Due to the small influence of lift, Basset and virtual mass forces on the simulated solid hold-up profile, only the drag force may be considered in the interphase momentum exchange term (Schiller-Naumann). In the literature [10; 11; 12; 13; 14], there are available results obtained from using these two models and these results show that the Eulerian multiphase model is more accurate than the Eulerian mixture model when working with a particle size higher than 100 \(\upmu\)m and solid fraction ranging between 0.2 and 16%. The Eulerian mixture model is better adapted for low particle size and concentration. [PERSON] et al. [15] presents the analysis of the operation for different types of optimized impellers using the professional code CFX. The standard k-\(\epsilon\) model was employed to model the turbulence together with the sliding mesh method and a residual error for all the equations set at \(10^{-4}\). The numerical results were validated with experimental results. [PERSON] et al. [16] analyzed the turbulent flow of the non-Newtonian fluid with the help of the software Fluent. The k-\(\epsilon\) model was considered for modeling the turbulence and a convergence criterion of \(10^{-6}\). The distribution of the velocity and pressure was investigated inside spiral tubes and the conclusion was that the friction coefficient is higher than for the straight tube and the friction coefficient decreases while the Reynolds number increases. [PERSON] et al. [17] presents the results of CFD investigation of the hydrodynamic field of a baffled stirred tank equipped with two impellers. The professional software Ansys Fluent was employed with the realizable k-\(\epsilon\) model for the turbulence and the volume-of-fluid method formulation for the multiphase flow. Two approaches were studied for modelling the movement of the impellers: moving reference frame and sliding mesh.