The effects of section shape on the lift spectrum for a foil in turbulent flow

The effects of section shape, specifically thickness and camber, on the lift spectrum for a foil immersed in a turbulent flow are analytically and experimentally investigated. The lift response functions to incident cross-stream vortices drifting along streamlines offset from the foil within two chord lengths are computed using an analytical solution to the Blasius force equation, achieved by way of using an expanded Joukowsky mapping function that can map a circle in the complex plane to any selected foil shape. The vortex lift responses are convolved with the vorticity wavenumber–frequency spectrum for a homogenous turbulent flow to compute the overall foil lift due to incident turbulence. Calculations of the lift spectra for a series of foils with increasing maximum thickness, NACA 651A-0008, -0012 and -0016 foils, immersed in grid-generated turbulent flow agree very well with measurements up to the maximum measured frequency, $\omega C/2U \approx 40$ , where $C$ is the chord and $U$ is the free-stream speed, which showed an increasing level of lift attenuation at high frequencies with increasing foil thickness. The analytical model showed that the high-frequency lift was controlled by the inertia of the incident vortices, and that the thickness of the foil near the leading-edge controls these high-frequency lift levels by decreasing the drift velocities of the approaching vortices. A simplified analytical model of the vortex inertia force, which avoided the need to implement the unsteady Kutta condition, was developed to estimate the high-frequency lift for thick foils with less computational demand. A wind tunnel experiment involving unsteady lift measurements for a foil in a turbulent flow was performed to physically confirm the model-based prediction that increasing the foil leading-edge thickness can significantly attenuate high-frequency lift, while maintaining the overall maximum thickness. Undesired components of the unsteady force measurements associated with foil vibration were removed using a novel technique of analysing measured force spectra over a series of wind tunnel speeds. The unsteady lift spectra measured for a NACA 0007-61 foil, modified to have constant thickness from 10 % to 50 % chord, showed an approximate attenuation of 8–10 decibels at reduced frequency, $\omega C/2U = 30$ , relative to a NACA 0007-65 foil, which agreed well with the model-based predictions and confirmed that increasing the foil thickness in the vicinity of the leading edge yields significant high-frequency lift attenuation.