# Effect of Rotor-Stator Spacing on Compressor Performance at Variable Operating Conditions
## 1 Introduction  
With the continuous development of aero-engines having a high thrust-to-weight ratio, the design of a multistage axial flow compressor tends to reduce the number of stages by increasing load and reducing the axial spacing between blade rows. This strategy increases the compressor's compactness and enhances the interaction between the blade rows. For the heavy-duty gas turbine, the blade design with a large aspect ratio reduces the interplay between the flow created at most of the blade height and the secondary flow, affording an appropriate wake shape on the SI surface. Therefore, the unsteady effect can be used to tap performance and provide refined compressor improvement. Generally, the performance change caused by variable and sufficiently large axial spacing is almost all attributed to wake mixing [1], and other flow interaction phenomena do not occur, as only a minor potential disturbance influences the fore blade row, while the vast majority of the wake deficit is mixing up before the flow arrives to the rear blade. In addition to wake mixing, other secondary flows, non-uniform bulk flow, and end-wall boundary layer development are also essential sources of axial spacing loss; however, in a real compressor, the blade rows are always coupled [2; 3] with strong wake interference and potential interference. Thus, studying the interaction between adjacent blade rows is reasonable and practical only when the axial spacing is small enough. In the study by [PERSON] et al. [4], the researchers experimentally and numerically proved that a higher time-averaged stator load increases the rotor wake decay rate and reduces the stator's response level. [PERSON] [5] observed that a closer axial spacing improved efficiency by more than one point and produced a higher total pressure ratio in an experiment of subsonic multistage compressors. Moreover, [PERSON] [6; 7] proposed a new concept named wake recovery with a simple analytical model, where wake mixing loss decreased by reducing the wake velocity deficit due to the inviscid stretch effect of the downstreamblade row on the upstream wake reversibly as it transported. [PERSON] [8] developed a model that employed an unsteady kinetic energy variation to express the degree of wake recovery and also found that the recovery process reduces more than 70% of the mixing loss. [PERSON]'s model has been extended by [PERSON] [9], [PERSON] [10], and [PERSON] [11]. Moreover, [PERSON] [12] suggested a kinematic model to analyze the wake recovery process and concluded that higher load, lower flow coefficient, and closer axial spacing were advantageous to wake recovery. The research of [PERSON] and [PERSON] [13; 14] highlighted that the tip leakage vortex experiences the same recovery as the wake and claimed that wake and vortices' energy recovery, and the corresponding non-transitional boundary layer response, contribute to the maximum performance. Nevertheless, any disturbance passing through a blade passage generates a performance benefit as soon as possible instead of mixing up completely [10]. Additionally, [PERSON] [15] confirmed the wake recovery process through a Large Eddy Simulation (LES) in a low-speed compressor. Although all the investigations mentioned above highlighted that a close axial spacing is appealing for rotor-stator configuration, [PERSON] and [PERSON] [16] observed that the harm of turbulence production outweighed the benefit of wake recovery. [PERSON] and [PERSON] [17] performed 2-D simulations at subsonic and transonic operating points for a stator-rotor configuration and demonstrated two different flow mechanisms. At a transonic operating point, the stator wake reduces the pre-shock Mach, decreasing the shock loss and reducing efficiency. At a subsonic operating point, the loss of the wake-boundary layer interaction occupies a dominant position in influencing the overall performance. [PERSON] et al.