## 2 Problem Description and Mathematical Modeling  
The stirred tank used in this work is a standard cylindrical configuration with dimensions given by Figure 1 and Table 1. Figure 1a shows the upper view of the tank, and Figure 1b is a cut view of section A-A. The height of the tank is equal to its diameter, \(H=2R\). The working fluid is water at atmospheric pressure with thermophysical properties at a temperature of \(T=293\) K. The impeller is a six-bladed Rushton turbine with standard dimensions (often found in the literature) mounted at a certain height from the tank bottom (C). If geometric similarity is kept, the flow system can be fully described by the Reynolds flow number \(Re_{D}=\rho ND^{2}/\mu\). For this work, the impeller speed is \(N=300\) rpm (5 rps), which is imposed in an anticlockwise direction, \(\rho\) is the water density, \(\mu\) is the dynamic viscosity and \(D\) is the impeller diameter. The simulations were performed here with a Reynolds number of \(Re_{D}=47\),790. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**2R** & **\(H\)** & **\(D\)** & **\(C\)** & **\(W\)** & **\(B\)** & **\(H\)** \\ \hline
0.296 & 0.296 & \(2R/3\) & \(2R/3\) & \(D/4\) & \(2R/10\) & \(D/5\) \\ \end{tabular}
\end{table} 
Table 1: Dimensions (m) of the tank shown in the Figure 1.  
Figure 1: Dimensions of the stirred tank with four baffles: (**a**) upper view (**b**) view of Section A–A. The side, top and bottom walls of the tank, as well as the surfaces of the baffles, have no-slip and impermeability boundary conditions. For all cases, the flow is at rest for the initial condition. The turbulent, incompressible, isothermal flows in the three-dimensional domain of the tank are modeled by the time-averaged conservation equations of mass and momentum, as defined by [26]:  
\[\frac{\partial\overline{u}}{\partial x}+\frac{\partial\overline{v}}{\partial y }+\frac{\partial\overline{w}}{\partial z}=0 \tag{1}\]  
\[\frac{\partial\overline{u}}{\partial t}+u\frac{\partial\overline{u}}{\partial x }+v\frac{\partial\overline{u}}{\partial y}+w\frac{\partial\overline{u}}{ \partial z}=-\frac{1}{\rho}\frac{\partial\overline{p}}{\partial x}+(\hat{\theta }+\hat{\sigma}_{T})\bigg{(}\frac{\partial^{2}\overline{u}}{\partial x^{2}}+ \frac{\partial^{2}\overline{u}}{\partial y^{2}}+\frac{\partial^{2}\overline{u }}{\partial z^{2}}\bigg{)}+f \tag{2}\]  
\[\frac{\partial\overline{v}}{\partial t}+u\frac{\partial\overline{v}}{\partial x }+v\frac{\partial\overline{v}}{\partial y}+w\frac{\partial\overline{v}}{ \partial z}=-\frac{1}{\rho}\frac{\partial\overline{p}}{\partial x}+(\hat{ \theta}+\hat{\sigma}_{T})\bigg{(}\frac{\partial^{2}\overline{v}}{\partial x^{ 2}}+\frac{\partial^{2}\overline{v}}{\partial y^{2}}+\frac{\partial^{2} \overline{v}}{\partial z^{2}}\bigg{)}+f \tag{3}\]  
\[\frac{\partial\overline{w}}{\partial t}+u\frac{\partial\overline{w}}{\partial x }+v\frac{\partial\overline{w}}{\partial y}+w\frac{\partial\overline{w}}{ \partial z}=-\frac{1}{\rho}\frac{\partial\overline{p}}{\partial x}+(\hat{ \theta}+\hat{\sigma}_{T})\bigg{(}\frac{\partial^{2}\overline{u}}{\partial x^ {2}}+\frac{\partial^{2}\overline{w}}{\partial y^{2}}+\frac{\partial^{2} \overline{w}}{\partial z^{2}}\bigg{)}+f \tag{4}\]  
where \(\overline{u}\), \(\overline{v}\) and \(\overline{z}\) are the time-averaged velocities in \(x\), \(y\) and \(z\) directions, \(p\) is the pressure, \(\hat{\sigma}\) is the kinematic viscosity, \(f\) is a source term of momentum and \(\hat{\sigma}_{T}\) is the turbulent viscosity of the fluid flow, which is given by:  
\[\hat{\sigma}_{T}=C_{\mu}\frac{k^{2}}{\varepsilon} \tag{5}\]  
where \(C_{\mu}\) is an ad hoc constant, \(k\) is the turbulent kinetic energy and \(\varepsilon\) is the turbulent kinetic energy dissipation rate.