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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. 

Abstract A transient two-dimensional acoustic boundary element solver is coupled to a potential flow boundary element solver via Powell's acoustic analogy to determine the acoustic emission of isolated hydrofoils performing biologically-inspired motions. The flow-acoustic boundary element framework is validated against experimental and asymptotic solutions for the noise produced by canonical vortex-body interactions. The numerical framework then characterizes the noise production of an oscillating foil, which is a simple representation of a fish caudal fin. A rigid NACA 0012 hydrofoil is subjected to combined heaving and pitching motions for Strouhal numbers ($0.03 < St < 1$) based on peak-to-peak amplitudes and chord-based reduced frequencies ($0.125 < f^* < 1$) that span the parameter space of many swimming fish species. A dipolar acoustic directivity is found for all motions, frequencies, and amplitudes considered, and the peak noise level increases with both the reduced frequency and the Strouhal number. A combined heaving and pitching motion produces less noise than either a purely pitching or purely heaving foil at a fixed reduced frequency and amplitude of motion. Correlations of the lift and power coefficients with the peak root-mean-square acoustic pressure levels are determined, which could be utilized to develop long-range, quiet swimmers. 

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. 

The sound of a vortex ring passing near a semi-infinite porous edge is investigated analytically. A Green's function approach solves the associated vortex sound problem and determines the time-dependent pressure signal and its directivity in the acoustic far field as a function of a single dimensionless porosity parameter. At large values of this 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 $$U^6 L^{-5}$$ , in contrast to the $$U^5 L^{-4}$$ scaling recovered in the impermeable edge limit. Results for the vortex ring configuration in a quiescent fluid furnish an analogue to scaling results from standard turbulence noise generation analyses, and permit a direct comparison to experiments described in Part 2 that circumvent contamination of the weak sound from porous edges by background noise sources that exist as a result of a mean flow. 

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.