## Materials and Methods
### Numerical Simulation
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Type of analysis** & \multicolumn{2}{c}{steady-state} \\ \hline
**Solver** & \multicolumn{2}{c}{pressure-based} \\ \hline
**Turbulence** & \multicolumn{2}{c}{k-w model [53]} \\ \hline  & velocity inlet & 15; 17.5; 20 and 22.5 m/s \\
**Boundary conditions** & \multicolumn{2}{c}{pressure outlet} & 0 gauge pressure \\  & \multicolumn{2}{c}{sleeve walls} & porous jump model with known permeability \\  & \multicolumn{2}{c}{and thickness of the medium} \\ \hline
**Pressure–velocity coupling** & \multicolumn{2}{c}{Coupled} \\ \hline  & Gradient & Least squares cell based \\  & Pressure & PRESTO; [51; 52] \\
**Spatial discretization** & \multicolumn{2}{c}{Momentum} & Second order upwind \\  & Turbulent Kinetic Energy & Second order upwind \\  & \multicolumn{2}{c}{Specific Dissipation rate} & Second order upwind \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Main settings used for CFD simulations. Figure 3: Three-dimensional reproduction of the filter for fluid dynamic simulation. On the right is the detail of the division of the sleeves into three vertical sectors. Apart from the division into sectors along the sleeve length, a non-uniformity in clogging among sleeves of the same sector was also hypothesized. To confirm these assumptions, a first simulation with completely clean sleeves was carried out. The flow rates of the air processed by each sleeve, as well as the velocity streamlines inside the domain, were evaluated, confirming both hypotheses. A division of the sleeves into four groups was then performed, clustering the sleeves that processed comparable flow rates into the same group. This division allowed the definition of a \"clogging sequence\" based on the position of the sleeves with reference to the inlet of the particulate-laden airflow and the magnitude of the flow rate passing through the filtering medium. A simulation campaign was carried out by gradually increasing the levels of clogging, reproduced in the simulation by decreasing the permeability value of the sleeves. In particular, the obstruction conditions of each case were based on the distribution of the flow rates calculated in the previous one, e.g., the conditions of the second simulation were defined according to the results of the first one, and so on. To model the different clogging conditions, the permeability of the filtering medium was gradually decreased, proportionally to the obstruction percentage, according to Equation (1). \[\alpha_{c}=\alpha\cdot(1-c_{\%}) \tag{1}\]  
where \(\alpha_{c}\) is the sleeve permeability for the case under study, \(\alpha\) is the permeability of the clean sleeve and \(c_{\%}\) is the obstruction percentage of the sleeve. The conditions simulated are presented in Table 3, with the indication of the percentage of clogging of each group of sleeves divided into three longitudinal sectors. The results of the simulations and the flow field inside the device were finally analyzed to assess the impact of the filter obstruction, with the aim of identifying some locations for additional sensors that would allow monitoring and evaluating the clogging conditions during the real-time functioning of the filter. To this end, the evaluation of the tangential velocity values in the near wall region was performed on four longitudinal lines, displaced at 90\({}^{\circ}\) from the other (Figure 4). The results of the simulations were also used to quantify the air flow rate passing through each sleeve under different clogging conditions. We referred specifically to the flow rate filtered by the top sector of each sleeve, which is the sector most impacted by the compressed air jet. The results were then used to modify both the sequence and the frequency of cleaning operations with compressed air according to the magnitude of the air flow rate. Since CFD simulations are time-expensive they were launched in advance, building a database containing all their results. This database can then be used for real-time control of the system.