An input-output analysis on flow stability of transonic compressors with impedance boundary condition

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.