## 3 Results  
### Simulation Results  
The results of the simulations at different operating conditions were analyzed to determine a trend in the pressure drop and the flow field inside the system as the clogging increased. Figure 6: Schematic representation of the procedure adopted for the RUL estimation. Figure 7: Schematic representation of the developed digital twin framework. First, the flow pattern inside the device was monitored by plotting the velocity streamlines inside the domain. A clear swirling flow configuration emerged, as shown in Figure 8, representing the velocity streamlines observed from four positions rotated by 90\({}^{\circ}\) one to another. The first simulation with completely clean sleeves confirmed the assumption of non-uniformity in the flow rate distribution across the filtering sleeves, as can be seen in Figure 9. Four groups of sleeves were therefore defined, based on the flow rate elaborated, reflecting their tendency to obstruct. Even though the sleeves in groups 1 and 4 processed comparable flow rates, they were divided into two separate groups based on their position with reference to the air flow inlet: the sleeves in group 1, indeed, are exposed to a much more contaminated air flow. Figure 10 represents the four groups identified and the sleeves, numbered from 1 to 31, assigned to each of them. To detect the variation in the flow field as the clogging increased, the velocity values were monitored for the eight cases simulated. Tangential velocity near the filter walls appeared to be the most appropriate value to monitor for the pilot plant simulated. Indeed, even though variations could be observed in the ascending and descending velocities at different operating conditions, tangential velocity appeared to be the best choice, both due to its magnitude and the ease of measurement (Figure 11). Figure 8: Air streamlines inside the filter. Figure 9: Velocity vectors in the filter inlet solute. Tangential velocity was monitored for the different conditions simulated on the four longitudinal lines presented in Figure 4, at a distance of 5 cm from the filter wall. In the plots presented in Figure 12, the origin of the \(x\)-axis corresponds to the top of the sleeves. A clear trend in the calculated velocities, with the plotted lines sorted according to the clogging level, can be observed on several locations of lines 2 and 3. Due to the layout and the geometrical features of the pilot plant, the new sensor was installed on line 3, at a distance of 2400 mm from the top of the sleeves. The results of the simulations, therefore, allowed the highlighting of trends in both the system pressure drop and the tangential velocity values at different clogging levels. These trends were validated with experimental tests on the pilot plant. The results for the air flow rates passing through sector 1 of each sleeve are shown in Table 9. The sleeves are sorted in descending order according to the air flow rate passing through them. Based on the results obtained, a possible cleaning sequence with the respective frequencies, expressed in terms of time between injections, is also shown in Table 9.  
Figure 11: Velocity vectors on three transversal planes. Figure 10: Classification of sleeves into four groups. Figure 12: Tangential velocity trends on the four lines represented in Figure 4 for the eight different clogging conditions. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Time between** \\ **Compressed Air** \\ **Injection** \\ \end{tabular}  } & \multicolumn{2}{c}{ \begin{tabular}{c} **Case 1** \\ **Flow** \\ **Rate** \\ **Injection** \\ \end{tabular}  } & \multicolumn{2}{c}{ \begin{tabular}{c} **Case 2** \\ **Flow** \\ **Rate** \\ **Injection** \\ \end{tabular}  } & \multicolumn{2}{c}{ \begin{tabular}{c} **Case 3** \\ **Flow** \\ **Rate** \\ **Injection** \\ \end{tabular}  } & \multicolumn{2}{c}{ \begin{tabular}{c} **Case 4** \\ **Flow** \\ **Rate** \\ **Injection** \\ \end{tabular}  } & \multicolumn{2}{c}{