This paper presents a sensitivity analysis method for analyzing the key factors affecting the stability problem of the transonic compressors. The adjoint method is integrated into the meridional stability model, a linear stability prediction model utilized to analyze the flow stability problem of the compressor, and the sensitivity analysis method is further developed for the flow stability problem of the compressor. The study selects the NASA Rotor37, a transonic compressor, as the research object to verify the proposed method and explore the sensitive factors leading to the stall inception. The results of sensitivity analysis to both the flow parameters and the external source terms reveal that the stall inception is sensitive to the base flow field at the rotor tip and the stability margin of the compressor can be enhanced by improving the flow field at this region. Physical explanations are presented and discussed to correlate the three-dimensional flow field to the results obtained via the employed analysis method, which shows that flow structures and characteristics near the end-wall region, especially the tip leakage flow or the tip leakage vortex and its interaction with the shock wave, contribute to the stall inception.

The influence of Impedance Boundary Condition (IBC) on transonic compressors is investigated. A systematic input–output analytical framework is developed, which treats the nonlinearities as unknown forcing terms. The framework is validated through the experiments of rotating inlet distortion within a low-speed compressor. The input–output method is subsequently applied to transonic compressors, including NASA Rotor37 and Stage35, wherein impedance optimization is studied along with the exploration of its fundamental mechanisms. The IBC is employed to model the effect of Casing Treatment (CT). The optimal complex impedance values are determined through predicted results and tested across a range of circumferential modes and forcing frequencies. The IBC significantly reduces the energy and Reynolds stress gain, notably at the first-order circumferential mode and within the Rotor Rotating Frequency (RRF) range. Output modes reveal that transonic compressors with fine-tuned impedance values exhibit a more confined perturbation distribution and redistribute the perturbations compared to the uncontrolled case. Additionally, the roles of resistance and reactance are elucidated through input–output analysis, and resistance determines the energy transfer direction between flow and pressure waves and modulates the amplitude, whereas reactance modifies the phase relationships and attenuates the perturbations.

A modified small perturbation stability prediction model for axial compressors with circumferential inlet distortions is established and applied to investigate the effect of fore/aft-loaded rotor on compressor stability under circumferentially distorted inlet conditions. The inlet total pressure distribution downstream of the distortion screen is measured in experiments and employed for simulations which are implemented via time–space spectral method. The stall inception prediction results via the stability model indicate that the compressor with aft-loaded rotor not only performs better in terms of stability under uniform inlet, but also maintains a larger stability margin under circumferentially distorted inlet. The experiments for compressors with fore-loaded and aft-loaded rotor are respectively carried out. The results validate the reliability of numerical simulations and the predicted conclusion that the aft-loaded rotor is beneficial for compressor stability. Besides, the ability of the developed theoretical model for compressor stability prediction under circumferential distortions is confirmed. In addition, dynamic pressure signals at rotor tip measured in experiments illustrate that the circumferential distortion has little effect on the compressor stall pattern.