# Effect of Rotor-Stator Spacing on Compressor Performance at Variable Operating Conditions
## 4 Results and Discussions
### Hub Leakage Flow  
From Figures 11 and 12, we observe that the hub leakage flow's unloading effect makes the rotor's loading capacity near the hub not change significantly with overall load increases. Additionally, the loss coefficient of \"close\" is always lower at every condition than \"far\". According to the analysis, the mechanism of this phenomenon under the three operating conditions is consistent. Therefore, this paper considers condition C as an example to explain this. By comparison, we find that the intensity of the leakage vortex is greater at close_C (Figure 13). Indeed, the driving force of hub leakage vortex (HLV) is the pressure difference between the pressure surface (PS) and suction surface (SS) near the hub clearance, and the pressure distribution comparison at the 0.05 span between close_C and far_C is illustrated in Figure 14. The pressure distribution is the same in the fore 10% axial chord. The SS pressure of \"close\" is higher than that of \"far\" from 15% to 55% of the axial chord, but the pressure at PS of \"close\" is lower from 10% to 80% of the axial chord. The corresponding increase is also greater than the previous, indicating that the \"close\" driving force is lower and the formed HLV is weaker. Figure 14: Time-averaged pressure distribution of the 0.05 span at C condition. Figure 13: Time-averaged entropy contour near the hub. Next, we analyze five specific transient moments, t1, t2, t3, t4, and t5 (Figure 15), as well as, at each moment, the wake impacts of PS at positions 0.2, 0.3, 0.4, 0.5, and 0.6 times the axial chord. Figure 15a distinguishes the wake using the Q-criterion and reveals the wake mixing in the axial spacing reduces the vortex structure in the wake section, and the corresponding velocity deficit is also lower in the far_C. Additionally, the deflection angle of the wake passing through the stator passage is very small, which leads to the close chord-wise position of the wake sections on both sides of the blade. In Figure 15b, the dotted line represents the position of the wake. The flow transport caused by the wake negative jet [35] makes the fluid at the SS flow towards the pressure side, and the transverse transport makes the pressure field along the wake direction consistent. In Figures 15b and 16, when at t1, the slip velocity of the wake is relatively large, and the high-pressure fluid transported to the PS significantly increases the pressure enhancing the pressure rise gradient. However, the high-pressure area near the trailing edge is smaller owing to its lower outlet pressure at close_C. Then at t2, the pressure distribution on the PS  
Figure 15: Flow field comparison at five time-steps. (**a**) Q; (**b**) Pressure. is almost the same. At t3, the pressure from 0.2 to 0.55 axial chord at close_C drops, and the pressure drop decreases in the next two moments. These findings indicate that the pressure at a particular position of the PS depends on the influence of the downstream pressure field and the combined action of wake transport. The wake transport has three factors affecting pressure: (1) wake slip velocity and wake decay that characterizes the fluid transport mass flow along the flow direction, (2) chord-wise load distribution and deflection angle of the wake that decides the pressure of the initial transported fluid, and (3) transverse pressure gradient that influences the pressure variation during the wake transport to the PS. Considering these factors comprehensively, the transport fluid's pressure is higher than that of the downstream pressure field at t1, and the two functions are balanced at t2. When at t3, the low-pressure fluid transported by the wake has the most apparent effect on the pressure surface. The high pressure of the downstream pressure field has a greater influence on the interaction position of the wake and the PS. Meanwhile, Figure 15 illustrates a reduced slip velocity, increased pressure of the initial transported fluid, and higher pressure in the wake transport path.