Evaluation and further analysis of unsteady pressure response measurements on an airfoil at angle of attack (2002)

An investigation into sources of error in the lift spectra presented in Mish and Devenport (2001) is undertaken. Mish, et al. (2001) calculated the unsteady lift from pressure measurements made on a NACA 0015 immersed in grid generated turbulence. The following sources of error are investigated: calculating unsteady lift discretely, rotating the unsteady force spectrum from airfoil to flow aligned coordinates, acoustic reflection, and data symmetry. Error resulting from these items is shown to be negligible. Having validated lift spectra the effects of angle of attack on the space-time correlation of surface pressure fluctuations, root-mean-square (RMS) pressure, and mean square lift are explored. The spacetime correlation shows the domination of the inviscid response up to α = 20o. Convected pressure fluctuations become significant on the suction side of the airfoil at α = 12o. As the angle of attack is increased the mean square lift decreases nearly as α up to α = 12o. Additionally, it is shown that the data of Mish, et al. (2001) may be useful as the source term in a time domain solution for far-field loading noise. NOMENCLATURE α = Angle of attack (deg) b = Half-chord (m) c = Wing chord (m) ∆P = Pressure difference, defined as PL-PU (Pa) E = Expected value f = Frequency (Hz) G∆P1∆P1 = Pressure difference auto-spectrum (N/m) G∆P1∆Px = Pressure difference cross-spectrum (N/m) Gds = Spatial spectrum derivative Gdt = Temporal spectrum derivative GLL = Lift spectrum (N/m) GNN = Normal-to-chord force spectrum (N/m) GPP = Pressure cross-spectral density (N/m) GTN = Tangential to normal force cross-spectrum (N/m) GTT = Tangential-to-chord force spectrum (N/m) λ = Turbulence lengthscale (m) L = Lift (N) N = Normal force (N) p = Pressure (Pa) q = Dynamic pressure (Pa) Re = Real part RPP = Space-time correlation T = Tangential force (N) τ = Time (sec) U∞ = Free-stream velocity (m/s) ω = Angular frequency (rad/s) ωr = 2πfb/U∞, Reduced frequency x = Axis pointing from the leading edge towards the trailing edge, with origin at 1/3 span. y = Axis pointing in the lateral direction. z = Axis pointing along the leading edge INTRODUCTION When a lifting airfoil moves through a turbulent stream an unsteady pressure field develops around the airfoil which produces acoustic waves that manifest into broadband noise. Such phenomena can readily be identified in nearly all types of vehicles (e.g. planes, helicopters, ships, submarines, etc.) the results of which can be quite troublesome. For example, sophisticated submarine propulsors (which may be similar in form to an axial compressor) in a turbofan engine can produce considerable noise as the propulsor blades slice through boundary layer produced turbulence. In combat scenarios such noise levels obviously hamper the stealth capability of these vehicles. In addition, with the passage of Bills such as the “Silent Skies Act of 1999” industry is increasingly coming under pressure to reduce the levels of noise pollution associated with turbo-machinery propulsors (i.e. turbofans, turbojets, etc) on their aircraft. For these † Graduate student, student member AIAA *Professor, senior member AIAA Copyright © 2002 by P. Mish, W. Devenport and A. Borgoltz. Published by American Institute of Aeronautics and Astronautics, Inc. with permission.