# Effect of Rotor-Stator Spacing on Compressor Performance at Variable Operating Conditions
## 1 Introduction
[18; 19] studied the wake-shock interaction in detail and found that the closer the axial spacing, the bigger the vortices generated by the interaction between the shock and the upstream wake. Both stator load and shock strength increased the vortex strength linearly, while the vortex shed only when the bow shock passed, which is called the \"phase-locked\" phenomenon [20]. Their research group also studied the bow shock's reflection and propagation behavior in the fore stator and its corresponding influence. Additionally, they found that the axial spacing at which the upstream wake is mainly transported through the rotor's center line optimized performance [21; 22]. [PERSON] and [PERSON] [23] studied the interaction between the rotor wake and the three-dimensional separation region in an annular compressor cascade experimentally. The results show that the stator separation presents periodicity due to the delay of wake propagation and wake amplification near the hub at high incidence. The wakes in the bulk flow and the separated flow are out of phase. [PERSON] and [PERSON] [24] studied the interaction between upstream stator wake and rotor tip leakage flow and its influence on rotor performance using an unsteady numerical method. When secondary leakage occurs, the pressure pulse induced by the wake interacts with tip leakage flow to reduce secondary leakage and improve performance. [PERSON] et al. [25] found that the change of wake phase near the casing may affect the tip leakage vortex core when studying the influence of the upstream wake phase on rotor work. The effect can not only increase the peak pressure of the compressor but also expand the flow margin. [PERSON] et al. [26; 27] found that the upstream wake will cause the tip leakage vortex to be periodically cut into several segments, and the development direction and blockage degree of the leakage vortex will periodically vary accordingly. [PERSON] et al. [28] systematically investigated the influence of the upstream wake on the leakage flow in a compressor cascade and found that the upstream wake can reduce secondary loss by improving pressure distribution when the pitch ratio is appropriate. [PERSON] and [PERSON] [29] experimentally studied the influence of axial spacing variation on the clocking effect, and the change of position where the IGV wake impacts the stator is equivalent to changing the indexing of the two-blade rows. In the tip region, the high loss of fluid caused by the interaction between the IGV wake and rotor clearance becomes the most crucial loss influencing factor, and when it arrives on the suction side of the stator, the stator loss is maximized. In the hub region, the IGV wake increases the loss of the hub leakage vortex, and the axial spacing determines the total loss. The flow mechanism plays a leading role in the unsteady interaction for compressors with different blade-row matching and radial aerodynamic load distribution. Therefore, the most direct and effective method to explore unsteady interaction is considering variable axial spacing. However, the related research aiming at a rotor-stator configuration where the axial spacing and operating condition change simultaneously is not detailed. Thus, this paper performs extensive unsteady simulations evaluating the rotor-stator spacing and operating condition effects on the performance of a transonic compressor stage. The principle of improving performance by the wake recovery effect and the critical role of the wake negative jet effect in improving tip pressure distribution and reducing leakage flow loss were studied. Furthermore, a detailed analysis reveals the dominant flow mechanism causing the change in the time-averaged performance.