Compressible Resolvent Analysis for Receptivity and Separation Control in Turbomachinery

Receptivity mechanisms in the separated boundary-layer flow over a high-work-and-lift, low-Reynolds-number airfoil are studied using resolvent analysis. Three-dimensional harmonic forcing is applied to the two-dimensional model airfoil to mimic acoustic excitation, and the corresponding optimal response field is examined. The analysis identifies regions of maximal receptivity and amplification, revealing a convective mechanism in which upstream forcing of wall modes predominantly drives the downstream oscillating shear layer response. Temporal and spatial filters are applied to the resolvent analysis to better simulate physically-realistic excitation fields, and the resulting optimal gain variation with frequency is obtained. Previous, matched experimental measurements validate both the receptivity mechanism identification and the gain analysis obtained using the resolvent approach. This study demonstrates that resolvent analysis can predict frequency-dependent disturbance amplification and its impact on experimentally measured lift. Thus, the resolvent technique should be applicable for the future design of high-work-and-lift airfoil geometries.