Potential Amplification Mechanism of Rotor–Stator-Interaction Noise via Spiral-Poiseuille-Flow Instability

Abstract

This study investigates the instabilities of the interstage flow between a rotor and a stator in turbomachinery and evaluates their impact on the fan noise. By viewing the interstage flow as the so-called spiral-Poiseuille flow, linear stability analysis of the incompressible Navier–Stokes equations reveals two distinct instability regimes at the Reynolds numbers up to $\mathit{Re}\le \mathcal{O}({10}^5)$ : The first mode excites disturbances over wide frequencies, including the rotor speed, and forms wavepacket-like structures above the outer-wall boundary layer. The second mode evolves inside the outer-wall boundary layer with slower velocity and possesses much smaller axial wavenumbers. We extract these modes using an approach analogous to dynamic mode decomposition from a database of our improved–delayed–detached eddy simulation solving NASA’s turbofan-rig test at low speed. The dynamic mode decomposition technique successfully visualizes these two instability modes even at $\mathit{Re}\approx 4\times {10}^6$ , and their dispersion relations approximately agree with the characteristics predicted by the linear stability analysis. These analyses suggest that the instabilities amplify coherent disturbances in the rotor wakes and vortices near the tip until they interact with the stator; moreover, coherent structures associated with the second instability may act as stationary objects, possibly resulting in an additional fan-noise source.