High-Frequency Gust Response of Realistic Airfoils

The existing high-frequency gust response model of a Joukowski or von Karman–Trefftz airfoil is extended to a 2D airfoil section with an arbitrary chordwise thickness profile by means of the generalized Joukowski transformation. The problem is cast into a constrained optimization problem, which is solved using the Lagrange multiplier method. To investigate the effect of the airfoil leading-edge thickness on the high-frequency airfoil response, the frequency response function (FRF) of NACA sections with the same thickness-to-chord ratio but with different leading-edge thicknesses are calculated for thickness-to-chord ratios of 0.16 and 0.1. The effect of the angle of attack and of the camber on the FRF is also investigated with the generalized Joukowski transformation for von Karman–Trefftz airfoils. In addition, combining the FRF with the uncorrelated wall plane wave technique, the lift spectra are computed and compared with experimental and numerical results of the homogeneous and isotropic turbulence ingestion of scaled NACA65-series hydrofoils in the literature. NACA sections with different leading-edge thicknesses and constant chord ratio are also tested for the same experimental conditions to highlight the effect of the leading-edge thickness on the lift spectra. Finally, Amiet’s theory of leading-edge noise is employed with the FRF to compute the acoustic pressure spectra and compare them with corresponding wind tunnel measurements for a NACA0012 and a cambered S831 airfoil at various angles of attack in a homogeneous and isotropic turbulent stream.