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An experimental study investigates parametrically the effects of porosity on the acoustic and aerodynamic fields about lifting- and non-lifting surfaces at two separate aeroacoustic facilities using microphone arrays and hot-wire anemometry. A single dimensionless porosity parameter characterizes the flow noise generated by a turbulent boundary layer and informs the design of the porous edge test specimens, including perforated flat plates and flat-plate extensions with a blunt or sharp trailing edge. The strong tonal peak due to vortex shedding from blunt trailing-edges diminishes in magnitude as the porosity parameter increases, and high-porosity plates eliminate this tone from the acoustic spectra. Single-microphone measurements indicate further that the porous plates examined can reduce low-frequency noise and increase high-frequency excess noise levels by up to 10 dB. DAMAS beamforming of the porous plates with sharpened edges reveal similar results on the acoustic spectra and identify that the principal effect of edge porosity on the acoustic source regions is a reduction in low-frequency noise and an increase in high-frequency noise across the entire plate. Noise generated by porous edges in the low-frequency range by the trailing- and leading-edge regions can be reduced by up to 20 dB, and porous edges increase high-frequency noise by up to 20 dB. Plates with the same dimensionless porosity perform similarly, where plates with circular holes perform slightly better (2 dB) than their counterparts with square holes at reducing low-frequency noise the most and increasing high-frequency noise the least in wind tunnel testing. Hot-wire anemometry of the flow field about blunt porous trailing edges reveals a downward shift of the bluntness-induced vortex-shedding peak in the spectra of turbulent velocity fluctuations, which are not seen in the acoustic spectra. In addition, flow field measurements for both the blunt-edged and sharp-edge plates indicate significant increases in turbulence intensity at the plate surface which are believed to be caused by the presence of holes and related to the increase in noise seen at high frequencies. The wing of a remote-controlled glider is modified with porous plates near the trailing edge to demonstrate reductions in surface pressure level fluctuations on a flying vehicle at the owl scale. Measurements of these fluctuations on the wing and fuselage indicate the capacity of porous plates to modestly reduce surface pressure levels in select frequency ranges and settings of aerial vehicles. 

The acoustic and aerodynamic fields of blunt porous plates are examined experimentally in an effort to mitigate trailing-edge bluntness noise. The plates are characterized by a single dimensionless porosity parameter identified in previous works that controls the influence of porosity on the sound field. Hot-wire anemometry interrogates the velocity field to connect turbulence details of specific regions to flow noise directivity and beamforming source maps. Porous plates are demonstrated to reduce the bluntness-induced noise by up to 17 dB and progressively suppress broadband low-frequency noise as the value of the porosity parameter increases. However, an increase in this parameter also increases the high-frequency noise created by the pores themselves. The same highly perforated plate characterized by a large value of the porosity parameter reduces the bluntness-induced vortex shedding that is present in the wake of the impermeable plate. Lastly, pore shape and positional alignment are shown to have a complex effect on the acoustic field. Among the porosity designs considered, plates with circular pores are most effective for low-frequency noise reductions but generate high-frequency noise. No meaningful difference is found between the acoustic spectra from plates of the same open-area fraction with pores aligned along or staggered about the flow direction. 

The sound generated by an acoustic source near a semi-infinite edge with uniform parameters is studied theoretically. The acoustic emission of a vortex ring passing near a semi-infinite porous or elastic edge with uniform properties is formulated as a vortex sound problem and is solved using a Green’s function approach. The time-dependent pressure signal and its directivity in the acoustic far field are determined analytically for rigid porous edges as a function of a single dimensionless porosity parameter. At large values of this dimensionless parameter, the radiated acoustic power scales on the vortex ring speed U and the nearest distance between the edge and the vortex ring L as U^6L^−5, in contrast to the U^5L^−4 scaling recovered in the impermeable edge limit for small porosity values. These analytical findings agree well with the results of a companion experimental campaign conducted at the Applied Research Laboratories (ARL) at Penn State University. A related theoretical analysis of the sound scattered by uniform, impermeable elastic edges admits analytical results in a specific asymptotic limit, in which the acoustic power scales on U^7L^−6. In complement to the analysis of vortex ring sound from edges, the acoustic scattering of a turbulent eddy near a finite edge with a graded porosity distribution is determined numerically and is validated against analytical acoustic directivity predictions from the vortex-edge model problem for a semi-infinite edge in the appropriate high frequency limit. The cardioid and dipolar acoustic directivity obtained in the vortex ring configuration for low and high dimensionless porosity parameter values, respectively, are recovered by the numerical approach. An imposed linear porosity distribution demonstrates no substantial difference in the acoustic directivity relative to the uniformly porous cases at high porosity parameter values, where the local porosity parameter value at the edge determines the scattered acoustic field. However, more modulated behavior of the acoustic directivity is found at a relatively low frequency for the case of a finite edge with small graded porosity distribution. 

We study analytically the dynamic response of membrane aerofoils subject to arbitrary, small-amplitude chord motions and transverse gusts in a two-dimensional inviscid incompressible flow. The theoretical model assumes linear deformations of an extensible membrane under constant tension, which are coupled aeroelastically to external aerodynamic loads using unsteady thin aerofoil theory. The structural and aerodynamic membrane responses are investigated for harmonic heave oscillations, an instantaneous change in angle of attack, sinusoidal transverse gusts and a sharp-edged gust. The unsteady lift responses for these scenarios produce aeroelastic extensions to the Theodorsen, Wagner, Sears and Küssner functions, respectively, for a membrane aerofoil. These extensions incorporate for the first time membrane fluid–structure interaction into the expressions for the unsteady lift response of a flexible aerofoil. The indicial responses to step changes in the angle of attack or gust profile are characterised by a slower lift response in short times relative to the classical rigid-plate response, while achieving a significantly higher asymptotic lift at long times due to aeroelastic camber. The unsteady lift for harmonic gusts or heaving motions follows closely the rigid plate lift responses at low reduced frequencies but with a reduced lift amplitude and greater phase lag. However, as the reduced frequency approaches the resonance of the fluid-loaded membrane, the lift response amplitude increases abruptly and is followed by a sharp decrease. This behaviour reveals a frequency region, controlled by the membrane tension coefficient, for which membrane aerofoils could possess substantial aerodynamic benefits over rigid aerofoils in unsteady flow conditions. 

We extend unsteady thin aerofoil theory to aerofoils with generalised chordwise porosity distributions by embedding the material characteristics of the porous medium into the linearised boundary condition. Application of the Plemelj formulae to the resulting boundary value problem yields a singular Fredholm–Volterra integral equation which does not admit an analytical solution. We develop a numerical solution scheme by expanding the bound vorticity distribution in terms of appropriate basis functions. Asymptotic analysis at the leading and trailing edges reveals that the appropriate basis functions are weighted Jacobi polynomials whose parameters are related to the porosity distribution. The Jacobi polynomial basis enables the construction of a numerical scheme that is accurate and rapid, in contrast to the standard choice of Chebyshev basis functions that are shown to be unsuitable for porous aerofoils. Applications of the numerical solution scheme to discontinuous porosity profiles, quasi-static problems and the separation of circulatory and non-circulatory contributions are presented. Further asymptotic analysis of the singular Fredholm–Volterra integral equation corroborates the numerical scheme and elucidates the behaviour of the unsteady solution for small or large reduced frequency in the form of scaling laws. At low frequencies, the porous resistance dominates, whereas at high frequencies, an asymptotic inner region develops near the trailing edge and the effective mass of the porous medium dominates. Analogues to the classical Theodorsen and Sears functions are computed numerically, and Fourier transform inversion of these frequency-domain functions produces porous extensions to the Wagner and Küssner functions for transient aerofoil motions or gust encounters, respectively. Results from the present analysis and its underpinning numerical framework aim to enable the unsteady aerodynamic assessment of design strategies using porosity, with implications for unsteady gust rejection, noise-reducing aerofoil design and biologically inspired flight.