Validation of time–space collocation method for simulating asymmetric unsteady flows in eccentric compressors

Circumferentially non-uniform tip clearances induced by rotor eccentricity significantly affect the overall performance of axial compressors, particularly the stability margin. Currently, Computational Fluid Dynamics (CFD) plays a crucial role in the aerodynamic analysis of eccentric compressors. However, conventional full-annulus Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations are prohibitively expensive for routine design and analysis purposes. To address this issue, the paper presents a novel Fourier-based method, called the Time-Space Collocation (TSC) method, for efficient simulations of eccentric compressors. This method coherently treats temporal and spatial harmonics, making it well-suited to tackle the rotor eccentricity problem, as the perturbation waves induced by eccentricity are time-periodic with respect to the rotor and space-periodic with respect to the stator. Three numerical cases, including NASA Rotor 67, original Stage 67, and Stage 67 with a reduced rotor-stator axial gap, were conducted to verify the effectiveness of the TSC method. The results indicate that, for the rotor eccentricity levels studied in this paper, the influence of weak rotor-stator interactions can be disregarded in the original Stage 67. In this situation, applying three harmonics can accurately capture both the performance variations and the non-uniformly distributed flowfields of eccentric compressors, while achieving a reduction in run time by two orders of magnitude compared to full-annulus URANS simulations. However, in Stage 67 with a reduced rotor-stator axial gap, the results that include rotor-stator interactions align much more closely with the URANS results. Nevertheless, the TSC simulations can still achieve speed-ups of several dozen times. Overall, the TSC method shows promising potential for application within the engineering community.