## 3 Results and Discussion
### Analysis of the Aerodynamic Load on the Impeller  
The aerodynamic load refers to the differential pressure with the time between the adjacent monitors between the pressure and suction sides of the impeller. The pressure fluctuation for each monitor point was obtained by the unsteady simulation, i.e., the time domains of the aerodynamic load. Then, the frequency domains of aerodynamic load were obtained through the FFT. In this hydrogen compressor, the machine rotating and the impeller passing frequencies should be the dominant frequencies of the aerodynamic load at the impeller's leading edge. The wake of 18 guide vanes excited the impeller passing frequency due to the RSI. Table 6 shows the value of the dominant frequencies in this compressor. The parameters \(f_{\mathrm{i}}\) and \(f_{\mathrm{m}}\) represent the impeller passing and the machine rotating frequencies, respectively. Figure 12a,b illustrate the comparison of the time history oscillations of different radial inlet models near the hub and the shroud regions of the aerodynamic load, respectively. Figure 12a refers to the differential pressure value between the P3 and S3 points, and Figure 12b refers to the differential pressure value between the P10 and S10 points. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type of Frequency** & **Formula** & **Value (Hz)** \\ \hline Impeller passing frequency & \(f_{\mathrm{i}}\) = \(f_{\mathrm{m}}\times 18\) & 2394.6 \\ \hline Machine rotating frequency & \(f_{\mathrm{m}}\) = \(n/60\) & 133.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Summary of compressor dominant frequencies. Figure 11: The total pressure comparison of (**a**) UGV, (**b**) SIS, and (**c**) TEB at cross-section 1-1. The time history oscillations of the aerodynamic load at different spans showed periodicity and stability in all models. Due to RSI caused by the guide vane's wake, 18 small fluctuations in each revolution were raised, which agrees with the count of guide vanes. Meanwhile, the fluctuation intensity reflects the wake intensity, and the fluctuation intensity near the shroud region was more vigorous compared with the hub region. Considering the radial inlet structure, the streamwise distance was different between the guide vane and the impeller from the hub to the shroud. Compared with the hub region, the streamwise distance between the impeller leading edge and the guide vane trailing edge in the shroud region was shorter. This means the shroud region was influenced by the wake of the guide vane more evidently. The TEB model showed weak fluctuation intensity in both the hub and shroud regions due to the blowing flow in comparison with the UGV model. Meanwhile, the SIS model showed more vigorous fluctuation intensity in the hub region and weak fluctuation intensity in the shroud region than that of the UGV model, which was due to the flow phenomenon in the self-induced slot. After that, through the FFT, the frequency harmonic comparison of the aerodynamic load in different radial inlet models was performed and is depicted in Figure 13.  
Figure 12: The aerodynamic load comparison of the time history oscillations (**a**) P3 and S3, and (**b**) P10 and S10 in different radial inlet models. Figure 13: The aerodynamic load comparison of the frequency harmonic (**a**) P3 and S3, (**b**) P10 and S10 in different radial inlet models. As shown in Figure 13, the machine rotating frequency \(f_{\rm m}\) was the dominant frequency at the leading edge of the impeller. Meanwhile, there were many harmonic excitations with the values of \(f/f_{\rm m}\) varying from 2 to 22. The TEB and SIS models slightly impacted the amplitude at \(f_{\rm m}\) in contrast to the UGV model. Moreover, compared with the hub region, the amplitude at \(f_{\rm i}\) was higher in the shroud region, and it reflects that the guide vane's wake had a more noticeable effect in the shroud region because of the different streamwise distances.