Harmonic Forcing from Distortion in a Boundary Layer Ingesting Fan

Integrating a fan with a boundary layer ingestion (BLI) configuration into an aircraft fuselage can improve propulsion efficiency by utilizing the lower momentum airflow in the boundary layer developed due to the surface drag of the fuselage. As a consequence, velocity and total pressure variations distort the flow field entering the fan in both the circumferential and radial directions. Such variations can negatively affect fan aerodynamics and give rise to vibration issues. A fan configuration to benefit from BLI needs to allow for distortion without large penalties. Full annulus unsteady computational fluid dynamics (CFD) with all blades and vanes is used to evaluate the effects on aerodynamic loading and forcing on a fan designed to be mounted on an adapted rear fuselage of a Fokker 100 aircraft, i.e., a tail cone thruster. The distortion pattern used as a boundary condition on the fan is taken from a CFD analysis of the whole aircraft with a simplified model of the installed fan. Detailed simulations of the fan are conducted to better understand the relation between ingested distortion and the harmonic forcing. The results suggest that the normalized harmonic forcing spectrum is primarily correlated to the circumferential variation of inlet total pressure. In this study, the evaluated harmonic forces correlate with the total pressure variation at the inlet for the first 12 engine orders, with some exceptions where the response is very low. At higher harmonics, the distortion content as well as the response become very low, with amplitudes in the order of magnitude lower than the principal disturbances. The change in harmonic forcing resulting from raising the working line, thus, increasing the incidence on the fan rotor, increases the forcing moderately. The distortion transfers through the fan resulting in a non-axisymmetric aerodynamic loading of the outlet guide vane (OGV) that has a clear effect on the aerodynamics. The time average aerodynamic load and also the harmonic forcing of the OGV vary strongly around the circumference. In particular, this is the case for some of the vanes at higher back pressure, most likely due to an interaction with separations starting to occur on vanes operating in unfavorable conditions.

Saturation of a turbulent mixing layer over a cavity: response to harmonic forcing around mean flows

Turbulent mixing layers over cavities can couple with acoustic waves and lead to undesired oscillations. To understand the nonlinear aspects of this phenomenon, a turbulent mixing layer over a deep cavity is considered and its response to harmonic forcing is analysed with large-eddy simulations (LES) and linearised Navier–Stokes equations (LNSE). The Reynolds number is $Re=150\,000$. As a model of incoming acoustic perturbations, spatially uniform time-harmonic velocity forcing is applied at the cavity end, with amplitudes spanning the wide range 0.045–8.9 % of the main channel bulk velocity. Compressible LES provide reference nonlinear responses of the shear layer, and the associated mean flows. Linear responses are calculated with the incompressible LNSE around the LES mean flows; they predict well the amplification (both measured with kinetic energy and with a proxy for vortex sound production in the mixing layer) and capture the nonlinear saturation observed as the forcing amplitude increases and the mixing layer thickens. Perhaps surprisingly, LNSE calculations based on a monochromatic (single-frequency) assumption yield a good agreement even though higher harmonics and their nonlinear interaction (Reynolds stresses) are not negligible. However, it is found that the leading Reynolds stresses do not force the mixing layer efficiently, as shown by a comparison with the optimal volume forcing obtained from a resolvent analysis. Therefore they cannot fully benefit from the potential for amplification available in the flow. Finally, the sensitivity of the optimal harmonic forcing at the cavity end is computed with an adjoint method. The sensitivities to mean flow modification and to a localised feedback (structural sensitivity) both identify the upstream cavity corner as the region where a small-amplitude modification has the strongest effect. This can guide in a systematic way the design of strategies aiming at controlling the amplification and saturation mechanisms.