# Effect of Rotor-Stator Spacing on Compressor Performance at Variable Operating Conditions
## 4 Results and Discussions
### Performance Fluctuation Analysis  
Figure 7 reveals that the efficiency of close_C fluctuates at 0.25 BPF. The simple flow analysis highlights that three-dimensional corner separation occurs in close_C, but a minor separation occurs in far_C near the shroud. The wake is transported in the form of a negative jet, weakening the attached ability of the boundary layer of the suction surface. A high enough load and deep wake with great slip velocity work together to determine the occurrence of separation, and therefore, corner separation occurs in close_C. This paper focuses on analyzing the reasons for performance fluctuation frequency. Since the major loss generated is above the 0.80 span, we use the monitoring scheme described in Section 3.4 to collect the total pressure data of close_C. Moreover, we propose a dominant frequency screening method based on Fast Fourier Transform (FFT). FFT is used to analyze the data of every monitor point, and then we obtained the frequency corresponding to the maximum amplitude called dominant frequency. Figure 20 highlights that only three frequencies as dominant frequencies exist in the flow field, and they are 0.25, 1, and 4 times the BPF. The dominant frequency of four BPF is  
Figure 19: Turbulence eddy dissipation in freestream and boundary layer. Figure 18: Comparison of the DKE decay. scattered in several isolated locations, and the effect on the entire flow is not apparent. The dominant frequency of one BPF occupies most positions inside the stator passage, but its dominant positions gradually decrease after the TE. The positions dominated by 0.25 BPF are very few in the stator passage, and one of them coincides with the tip separation boundary. However, this area discontinues before it develops to the TE. After the TE, the region dominated by 0.25 BPF gradually develops, becomes larger, and the frequency dominates the entire flow. We performed a Dimensionless Power Spectral Density (PSD) analysis on all data (Figure 21). At the same time, the ratio of the dominant frequency power to the total power of all frequencies is analyzed (Figure 22). Although the analysis ignores the phase relationship between every frequency component, it is dominant as long as the power ratio of the dominant frequency exceeds 0.5, even when all other frequencies are in the reverse phase. The zones whose PSD of the dominant frequency is relatively large are the zones before the TE at the tip and the wake region at the tip (Figure 21(1)), while the dominant frequency of the second one is 0.25 BPF. Figure 21(2) shows that the PSD of 0.25 BPF frequency is very low in the stator passage and very high in the wake region. These two reasons, combined with the discontinuity of the dominant frequency of 0.25 BPF at the separation boundary, indicate that the excitation of the separation boundary does not generate the dominant  
Figure 21: PSD analysis of close_C. Figure 20: Dominant frequency analysis of close_C. frequency of 0.25 BPF in the wake region. The wake's self-excited oscillation is why the wake oscillates at 0.25 BPF, and the region dominated by 0.25 BPF gradually expands to the entire spanwise range. At the LE, the one BPF frequency occupies a dominant position, and either its PSD is relatively large, or the power ratio is close to one. Thus, the 0.25 BPF frequency is not generated by the excitation of the flow that contains the frequency component from the upstream rotor. The one BPF flow covers the initial position of the separation boundary with a much higher PSD and power ratio. Therefore, the oscillation of the separation boundary with the dominant frequency of 0.25 BPF is caused by wake interaction. In Figure 21(2), the wake and mid-pitch regions have a 0.25 BPF frequency with high power at the outlet. The flow formed by the backward development of the separation boundary after interacting with the wake (Figures 21 and 22) can be verified by the evolution process in four BPP at the 0.95 span (Figure 23).