Spiral Flow Instability in Interstage Flow of High-speed Fan Rigs

We investigate hydrodynamic instabilities in the interstage of a turbofan engine, which potentially amplify the fan noise associated with the rotor-stator interaction. By applying linear stability analysis of the incompressible Navier-Stokes equations to the velocity pro files of two NASA's high-speed fan rigs, Source Diagnostic Test (SDT) and Advanced Ducted Propulsor (ADP), we reveal multiple distinct unstable regimes: The first unstable mode amplifies disturbances right outside the outer-wall boundary layer over a wide mid-frequency range including the rotor speed. The second mode rotates much slower and develops inside the outer-wall boundary layer with a smaller axial wavenumber. In addition, the analysis of ADP indicates an unstable mode near the inner wall. We extract these modes using an approach analogous to dynamic mode decomposition (DMD) from databases of our improved-delayed-detached eddy simulation (IDDES) solving the SDT geometry at approach and cut-back conditions. The extracted modes generally capture the characteristics, e.g. the dispersion relations and the eigenfunctions, predicted by the linear stability analysis. At the approach condition, the two unstable modes seem to interact inside the outer-wall boundary layer, while at the cut-back condition, disturbances associated with the first modemigrate away fromthe outer wall. These trends seem to be consistent with the azimuthal contents of the fan broadband noise simulated using the IDDES and measured using a mode ring.