Effects of Foil Camber and Non-Zero Angle of Attack on The Unsteady Forces Produced by a Turbomachine Ingesting Turbulence

Turbomachinery rotor blades experience unsteady lift forces due to turbulence and circumferential variation in the inflow velocity. These forces can be a source of unwanted vibration and radiated sound. The unsteady force spectrum is often modelled to first order using a flat plate approach. However, it is known that mean loading effects can have a significant influence on airfoil unsteady lift for sinusoidal gusts with certain wavevector orientations [1]. To this end, the Atassi [1] gust response model for airfoils with camber and non-zero angle of attack has been incorporated into a rotor turbulence ingestion model [2] to determine the effect on the unsteady force spectrum. The Atassi gust model describes the interaction between a two-dimensional sinusoidal gust with a cambered foil placed at a small angle of attack to the mean flow. To apply this single harmonic gust response to the turbulence ingestion model, the gust responses for sinusoidal components with a distribution of wavevector angles are integrated based on an isotropic turbulence energy spectrum. The updated turbulence ingestion model is then applied to a parametric study investigating the effects of foil geometry (specifically camber and non-zero angle of attack) on the unsteady forces produced from turbulence ingestion. The baseline geometry used for this study is the Sevik [3] rotor. To assess the sensitivity of the unsteady force spectrum to camber, predictions for a 0, 6, and 12% cambered foil with zero thickness at 0° angle of attack are generated. For these cases, foil camber effects are found to be largely negligible, except at low frequencies where the additional forces generated by streamwise gust components become dominant. The influence of non-zero angle of attack on the turbulence ingestion rotor force is also relatively minor for small angles of attack, but an increase of a few dB is predicted at higher frequencies as the angle of attack is increased to 15°. These results are generally consistent with measurements reported in the literature, where camber and angle of attack effects are shown to be weak, and the overall effects are much smaller than the changes in the sinusoidal gust responses due to the streamwise symmetry and averaging effect that occurs with isotropic turbulence. While the turbulence ingestion model was successfully extended to account for foil geometry effects using the Atassi gust response model, there is continued interest to explore the effects on the unsteady force spectrum when the simplifying assumption of isotropic turbulence is removed.