A direct-adjoint mean flow global stability investigation of self-excited instabilities in an idealized, two-dimensional compressor blade row at off-design conditions is carried out, with a focus on acoustic feedback mechanisms underlying the observed instabilities. This paper is the first part of this work, where nonlinear flows, impulse responses and the global modes are computed for a single-passage system, with good agreement between the linear and nonlinear structures. Structural sensitivities and feedback loops are identified with the aid of wavemakers and show that dominant structures arise due to feedback mechanisms linking the pressure and suction sides of the aerofoil via acoustic waves emanating from the trailing edge. A separate, second part extends this analysis to multiple-blade passages per period window by exploiting the theory of block-circulant matrices and Bloch-wave theory.
Glazkov, A., Fosas de Pando, M., Schmid, P. J., & He, L. (2023). Global stability analysis of an idealized compressor blade row. I. Single-blade passage analysis. Physical Review Fluids, 8(10). https://doi.org/10.1103/physrevfluids.8.103903
The authors gratefully acknowledge financial support from Ministerio de Economía y Competitividad AEI/FEDER UE through Grant No. DPI2016-75777-R, as well as computer resources at FinisTerrae II and the technical support provided by CESGA (IM-2019-3-0013 and IM-2020-1-0024). This work also used the ARCHER and ARCHER2 UK National Supercomputing Service.