# Effect of Rotor-Stator Spacing on Compressor Performance at Variable Operating Conditions
## 4 Results and Discussions  
### Performance Analysis  
Figure 7 illustrates the transient efficiency in a 20-blade passing period (BPP), reflecting the periodic law of compressor flow. The transient efficiency of all cases except close_C periodically fluctuates with the period of one BPP, while the transient efficiency fluctuation period of close_C is 4 BPP. Thus, some flow structure is dominant in the performance change caused by rotor-stator interaction, with its fluctuation frequency equal to 0.25 blade passing frequency (BPF). Considering the axial spacing from close to far, the transient efficiency decreases at A and B but increases at C. Thus, the flow structure mentioned above is harmful to performance. Figure 8 compares the time-averaged performance between two-axial spacing. The total pressure ratio changes little at A and B, and 0.6 points from close to far almost decline the time-averaged efficiency. At high load conditions, the total pressure ratio decreases by 0.01, but time-averaged efficiency increases by 0.32 points from close to far due to the change of the unsteady interaction characteristics. [PERSON] [34] et al. used irreversible entropy generation to analyze loss in turbomachinery. Accordingly, [PERSON] et al. [32] developed a nondimensional loss coefficient, namely efficiency deficit, as defined in Equation (3), which effectively locates the axial range where performance changes most:  
\[\xi=1-\eta=\frac{\dot{W}_{lost}}{\Delta\dot{H}_{stage}}=\frac{\overline{T_{0} \varepsilon}\dot{S}_{generation}}{\Delta\dot{H}_{stage}} \tag{3}\]  
Figure 9 illustrates the development of \(\xi\) from rotor TE to the outlet, presenting the measurement station setting, which is appropriate due to the non-vertical edge. The loss generation trend for A and B operating conditions is the same. For the same operating condition with different axial spacing, the loss generated by the upstream rotor is almost  
Figure 7: Transient efficiency of the research compressor. the same, and at the front of the axial spacing, the loss generation rate of the \"far\" case is higher, before declining gradually before the stator. Overall, the loss generation rate in each stage is independent of operating conditions, regardless of the axial spacing. For operating condition C, the loss generated by the upstream rotor of \"close\" is lower than that of \"far\", but the loss has a sharp rise in stator while the loss in the spacing is smaller than that of the other two conditions. Compared with the other two operating conditions, the loss decay rate of far_C is lower in spacing but higher in the stator. The overall loss is further decomposed into four parts, as depicted in Figure 10. In the compressor stage, the rotor loss is the bulk of the total loss, and the loss generation after the rotor is up to one-third of the total loss as in close_C. The loss difference at the rotor and after the stator is almost negligible at both points A and B; the stator loss is higher, and the spacing loss is lower. The decrease in efficiency from close to far is due to the decreased spacing loss. When the axial spacing increases, the growth rate of loss in the spacing is greater than the decay rate of loss in the stator. Therefore, it can be established that the closer the axial spacing, the higher the efficiency. According to the spacing from far to close at C, the potential effect of the downstream stator is favorable to the rotor, generating lower loss of about 0.01. Simultaneously, the loss in and after the stator increases sharply by 0.017 and 0.005, respectively, leading to a more significant total loss. In addition, it is worth noting that at A and B, the stator loss decreases as the axial spacing becomes larger, failing to present a total performance benefit from wake recovery. Figure 8: Time-averaged performance of the research compressor. (**a**) Isentropic Efficiency. (**b**) Total Pressure Ratio. Figure 9: Loss generation from rotor TE to the outlet.