Numerical solution of acoustic scattering by finite perforated elastic plates

A computational study of trailing edge noise suppression with embedded structural compliance

A unique concept for suppression of trailing edge noise scattering from a splitter plate in a low Reynolds number flow is proposed. The key idea of the concept is the adoption of a structural compliance system embedded with a finite number of elastic panels. Specific compliance system designs are devised for promotion of panel structural resonance that effectively absorbs broadband flow/acoustic fluctuation energy responsible for noise scattering. The concept is examined using high-fidelity direct aeroacoustic simulation together with spatiotemporal aeroacoustic-structural interaction analysis. The concept is confirmed feasible and outperforms many similar trailing edge noise reduction approaches reported in the literature.

Introduction to the Symposium: Bio-Inspiration of Quiet Flight of Owls and Other Flying Animals: Recent Advances and Unanswered Questions

Animal wings produce an acoustic signature in flight. Many owls are able to suppress this noise to fly quietly relative to other birds. Instead of silent flight, certain birds have conversely evolved to produce extra sound with their wings for communication. The papers in this symposium synthesize ongoing research in "animal aeroacoustics": the study of how animal flight produces an acoustic signature, its biological context, and possible bio-inspired engineering applications. Three papers present research on flycatchers and doves, highlighting work that continues to uncover new physical mechanisms by which bird wings can make communication sounds. Quiet flight evolves in the context of a predator-prey interaction, either to help predators such as owls hear its prey better, or to prevent the prey from hearing the approaching predator. Two papers present work on hearing in owls and insect prey. Additional papers focus on the sounds produced by wings during flight, and on the fluid mechanics of force production by flapping wings. For instance, there is evidence that birds such as nightbirds, hawks, or falcons may also have quiet flight. Bat flight appears to be quieter than bird flight, for reasons that are not fully explored. Several research avenues remain open, including the role of flapping versus gliding flight or the physical acoustic mechanisms by which flight sounds are reduced. The convergent interest of the biology and engineering communities on quiet owl flight comes at a time of nascent developments in the energy and transportation sectors, where noise and its perception are formidable obstacles.

A Mathieu function boundary spectral method for scattering by multiple variable poro-elastic plates, with applications to metamaterials and acoustics

Many problems in fluid mechanics and acoustics can be modelled by Helmholtz scattering off poro-elastic plates. We develop a boundary spectral method, based on collocation of local Mathieu function expansions, for Helmholtz scattering off multiple variable poro-elastic plates in two dimensions. Such boundary conditions, namely the varying physical parameters and coupled thin-plate equation, present a considerable challenge to current methods. The new method is fast, accurate and flexible, with the ability to compute expansions in thousands (and even tens of thousands) of Mathieu functions, thus making it a favourable method for the considered geometries. Comparisons are made with elastic boundary element methods, where the new method is found to be faster and more accurate. Our solution representation directly provides a sine series approximation of the far-field directivity and can be evaluated near or on the scatterers, meaning that the near field can be computed stably and efficiently. The new method also allows us to examine the effects of varying stiffness along a plate, which is poorly studied due to limitations of other available techniques. We show that a power-law decrease to zero in stiffness parameters gives rise to unexpected scattering and aeroacoustic effects similar to an acoustic black hole metamaterial.

Bioinspired aerofoil adaptations: the next steps for theoretical models

The extended introduction in this paper reviews the theoretical modelling of leading- and trailing-edge noise, various bioinspired aerofoil adaptations to both the leading and trailing edges of blades, and how these adaptations aid in the reduction of aerofoil-turbulence interaction noise. Attention is given to the agreement between current theoretical predictions and experimental measurements, in particular, for turbulent interactions at the trailing edge of an aerofoil. Where there is a poor agreement between theoretical models and experimental data the features neglected from the theoretical models are discussed. Notably, it is known that theoretical predictions for porous trailing-edge adaptations do not agree well with experimental measurements. Previous works propose the reason for this: theoretical models do not account for surface roughness due to the porous material and thus omit a key noise source. The remainder of this paper, therefore, presents an analytical model, based upon the acoustic analogy, to predict the far-field noise due to a rough surface at the trailing edge of an aerofoil. Unlike previous roughness noise models which focus on roughness over an infinite wall, the model presented here includes diffraction by a sharp edge. The new results are seen to be in better agreement with experimental data than previous models which neglect diffraction by an edge. This new model could then be used to improve theoretical predictions for far-field noise generated by turbulent interactions with a (rough) porous trailing edge. This article is part of the theme issue 'Frontiers of aeroacoustics research: theory, computation and experiment'.

Sound from aeroelastic vortex-fibre interactions

The motion of a line vortex moving past a one-dimensional flexible fibre is examined theoretically. A Schwarz-Christoffel conformal mapping enables the analytical solution of the potential flow field and its hydrodynamic moment on the flexible fibre, which is composed of a rigid segment constrained to angular motions on a wedge. The hydroelastic coupling of the vortex path and fibre motion affects the noise signature, which is evaluated for the special case of acoustically compact fibres embedded in a half plane. Results from this analysis attempt to address how the coupled interactions between vortical sources and flexible barbules on the upper surface of owl wings may contribute to their acoustic stealth. The analytical formulation is also amenable to application to vortex sound prediction from flexible trailing edges provided that an appropriate acoustic Green's function can be determined. This article is part of the theme issue 'Frontiers of aeroacoustics research: theory, computation and experiment'.

Effects of structural damping on acoustic scattering by flexible plates

We investigate the effects of structural damping on the interaction of a turbulent eddy with flexible plates with respect to the efficiency of aerodynamic noise generation. Potential benefits are studied using a model based on a point-reacting compliant semi-infinite plate on a spring-damper foundation. This scattering problem is solved using the Wiener–Hopf technique. We compare results for semi-infinite compliant plates with finite ones. In both cases, plate vibration lead to reductions of sound radiation, especially at resonance; damping tends to reduce such acoustic benefits. We also present a formulation that considers the effect of structural damping on the acoustic properties of finite elastic plates. Numerical results are obtained by applying a boundary element method to solve the Helmholtz equation subject to the boundary conditions imposed by the plate vibration. Under specific conditions, such as high fluid loading factor and low bending-wave Mach number, the acoustic power scattered by an edge tends to be smaller than that which propagates over the plate as bending waves. Results show that structural damping attenuates these waves and may modify the far-field acoustic pressure, mostly by reducing the scattered sound at structural resonances. All models show that large damping coefficients lead to locally over-damped responses. There is thus an ideal range of structural damping to reduce both plate vibration and acoustic scattering.

Acoustic scattering by finite composite plates

Trailing edge scattering is a significant source of sound, and elasticity is known to decrease the radiated sound by a process involving coupled acoustic and bending waves. Most of the analysis available in the literature to deal with this problem is limited to structures of isotropic material. A numerical method is extended, based on the solution of a boundary element method with boundary conditions given by the structural problem, to account for anisotropic composite plates, restricted to symmetric laminates. These conditions are recast in terms of the vibration modes of a rectangular plate. To obtain these modes, the hierarchical finite element method is used to model an elastic flat plate. Expressions for bending waves propagating in such plates are derived, and how the solution of the problem is modified to account for these effects is shown. Results show modifications in the scattered sound as a function of ply orientation and stacking sequence. Composite materials are shown to be advantageous, since laminates lead to lower acoustic scattering when compared to structurally equivalent metallic plates. This is due to a lower specific mass, leading to higher coupling between fluid and solid, and thus to more significant elasticity effects, decreasing substantially the radiated sound.

The steady aerodynamics of aerofoils with porosity gradients

This theoretical study determines the aerodynamic loads on an aerofoil with a prescribed porosity distribution in a steady incompressible flow. A Darcy porosity condition on the aerofoil surface furnishes a Fredholm integral equation for the pressure distribution, which is solved exactly and generally as a Riemann-Hilbert problem provided that the porosity distribution is Hölder-continuous. The Hölder condition includes as a subset any continuously differentiable porosity distributions that may be of practical interest. This formal restriction on the analysis is examined by a class of differentiable porosity distributions that approach a piecewise, discontinuous function in a certain parametric limit. The Hölder-continuous solution is verified in this limit against analytical results for partially porous aerofoils in the literature. Finally, a comparison made between the new theoretical predictions and experimental measurements of SD7003 aerofoils presented in the literature. Results from this analysis may be integrated into a theoretical framework to optimize turbulence noise suppression with minimal impact to aerodynamic performance.