Far-field Acoustic Pressure Research Articles

Experimental characterization of stall noise on a pitching airfoil in an anechoic wind tunnel

Dynamic stall noise is one of the potential source of amplitude modulations associated with wind turbine noise. This phenomenon is related to the periodic separation and reattachment of the boundary layer on the wind turbine blade suction side during its rotation. Within the framework of the PIBE project (Predicting the Impact of Wind Turbine Noise), experiments were conducted in an anechoic wind tunnel in order to characterize stall noise on a pitching airfoil in both static and dynamic conditions. A first set of measurements was performed using an airfoil equiped with pressure taps to measure both steady and unsteady wall pressure as well as far-field acoustic pressure. These measurements were used to identify the noise regimes associated with different angles of attack, and to relate them with the boundary layer evolution. In a second experiment, synchronized flow and acoustic measurements have been obtained to identify the coherent aerodynamic structures responsible for the noise radiation. The velocity fluctuations evaluated from the time-resolved particle image velocimetry (TR-PIV) data are correlated with acoustic pressure to localize aeroacoustic sources, and various tools such as vortex detection methods and spectral proper orthogonal decomposition are applied to identify the nature of these sources.

Sound transmission through an unbaffled plate

Commonly occurring complex structures can often be modelled as simple finite plates mounted without baffles. Thus, the objective here is to study the sound transmission loss of a simply-supported rectangular finite unbaffled plate impinged upon by an acoustic plane wave. The total pressure jump across the plate surface is expressed as the sum of the pressure jump due to pure diffraction, where the plate normal displacement is zero and the pressure jump due to plate radiation. These pressure jumps are computed using the definition of the free-space Green's function in the wavenumber domain and the Euler equation. Then, the coupled equation of motion is solved for the plate displacement. The method of stationary phase is used to derive the closed-form expression for the improper double integral that appears in the far-field acoustic pressure. Finally, the far-field transmitted power is numerically computed and the sound transmission loss of the unbaffled plate is compared with that of the baffled one.

Experimental investigation on aerodynamic noise and flow structures of a vibrissa-shaped cylinder

The noise mitigation effect of bio-inspired geometries has attracted growing attention from both research and industry, such as the vibrissa-shaped cylinder derived from the harbor seal. Experiments were conducted to investigate the far-field noise and the near-field wake of the flow past a vibrissa cylinder, a circular cylinder, and an elliptical cylinder at Re=3.6×104, in the subcritical flow regime. The frequency characteristic of the far-field acoustic pressure and the near-field velocities are analyzed. The mean and fluctuating velocities, dominant flow modes from proper orthogonal decomposition in both vertical and horizontal planes as well as the time-frequency behavior of the dominant flow structures from wavelet transform are also presented to better understand the wake dynamics and the direct relation of these flow structures with the far-field noise. The vibrissa cylinder reduces the overall sound pressure level by 13.2 dB and 8.3 dB compared with the circular and the elliptical cylinders, respectively, with a remarkable attenuation of the tonal peak associated with vortex shedding. From the detailed velocity measurements in multiple wake planes, it is clearly observed that vortex shedding of the vibrissa cylinder is weaker in strength and significantly less coherent in the spanwise direction than the other two cylinder cases, accompanied by more transient changes. The results also reveal the distinct flow behaviors behind the nodal and saddle planes of the vibrissa cylinder, further contributing to this three-dimensional vortex shedding. Consequently, the power spectral density of the tonal peaks associated with the vortex shedding in both near-field velocities and far-field acoustic pressure are attenuated, leading to a lower noise level. Understanding the detailed flow dynamics of the vibrissa cylinder will provide useful insights into more efficient bio-inspired cylinder designs in noise mitigation and wake control.

Near- and far-field radiated acoustic pressures from a vibrating three-dimensional cylindrical shell in an underwater acoustic waveguide

The vibroacoustic behavior of a vibrating infinitely-long thin three-dimensional cylindrical shell immersed in a perfect underwater acoustic waveguide is predicted using an analytical method. Vibration is induced by a point force excitation on the surface of the shell that is ingested into the equations of motion modeled using Flügge’s shell theory. Radiated acoustic pressures are then investigated in relation to an influence from the acoustic boundaries of an underwater acoustic waveguide. The waveguide, which simulates a simplified shallow water environment, is composed of an upper free surface and a lower rigid floor. Its influence is modeled with the image-source method. Graf’s addition theorem is employed to reconcile the coordinate systems of the infinite image sources in the fluid–structure coupling analytical expressions. Predictions of the near-field acoustic pressure are obtained by a direct numerical evaluation of the inverse Fourier integral, while the far-field acoustic pressure uses the stationary phase method. Axial directivities are of interest as the longitudinal length of the 3D shell imposes an additional dimension to the most commonly used 2D models in the literature to which radiated acoustic waves can dissipate energy. The far-field sound propagation from the shell in different fluid domain configurations is also shown.

Experimental studies on simultaneously reducing flow drag and noise of a circular cylinder with a downstream porous material plate

Pressure drag and noise level are two key parameters related to flow past a bluff body, thus various active and passive methods have been developed to reduce the drag and noise. The paper presents a passive method of simultaneously reducing the pressure drag and aerodynamic noise associated with flow past a smooth circular cylinder by placing a porous material plate (PMP) downstream the cylinder. Multi-points instantaneous wall pressure and far-field acoustic pressure have been measured in an anechoic wind-tunnel facility. The experimental results confirm that the PMP is effective to reduce both the pressure drag and the noise level, showing an attractive advantage compared with the impermeable splitter plate and porous coating. Parametric studies reveal effects of the pores per inch (PPI) of PMP, PMP-cylinder spacing and incoming flow velocity on the pressure drag and noise level.

Full Acoustic Analogy of the fluid-dynamics noise of an immersed cube

The estimation of fluid dynamic noise generated by anthropogenic sources in realistic marine basins and on land is paramount for human safety and environmental protection. Classical acoustic analogies have limited capabilities when considering the natural variability and peculiarities of the acoustic propagation domain. The Full Acoustic Analogy (FAA), based on the combination of an acoustic analogy for source characterization and a propagation model for far-field transmission, allows the estimation of detailed soundmaps, practical when assessing the risk associated with exposure to fluid-dynamic noise, both impulsive and continuous. The verification of the methodology, consisting of comparing of the far-field acoustic pressure signal obtained with the FAA and with the Ffowcs-Williams and Hawkings equation (classical acoustic analogy for moving immersed bodies), is proven for the first time for the quadrupole non-linear terms. The latter may contribute significantly to the total noise field at small-to-medium distances from the source. In conjunction, the ability of the FAA method to predict the acoustic pressure distribution within the three-dimensional propagation domain is highlighted.

Trailing-edge fringes enable robust aerodynamic force production and noise suppression in an owl wing model

As one of the unique owl-wing morphologies, trailing-edge (TE) fringes are believed to play a critical role in the silent flight of owls and have been widely investigated using idealized single/tandem airfoils. However, the effect of TE fringes and associated mechanisms on the aeroacoustics of owl wings, which feature curved leading edges, wavy TEs, and several feather slots at the wingtips, have not yet been addressed. In this study, we constructed two 3D owl wing models, one with and one without TE fringes, based on the geometric characteristics of a real owl wing. Large-eddy simulations and the Ffowcs Williams‒Hawkings analogy were combined to resolve the aeroacoustic characteristics of the wing models. Comparisons of the computed aerodynamic forces and far-field acoustic pressure levels demonstrate that the fringes on owl wings can robustly suppress aerodynamic noise while sustaining aerodynamic performance comparable to that of a clean wing. By visualizing the near-field flow dynamics in terms of flow and vortex structures as well as flow fluctuations, the mechanisms of TE fringes in owl wing models are revealed. First, the TE fringes on owl wings are reconfirmed to robustly suppress flow fluctuations near the TE by breaking up large TE vortices. Second, the fringes are observed to effectively suppress the shedding of wingtip vortices by mitigating the flow interaction between feathers (feather-slot interaction). These complementary mechanisms synergize to enhance the robustness and effectiveness of the TE fringe effects in owl wing models, in terms of aerodynamic force production and noise suppression. This study thus deepens our understanding of the role of TE fringes in real owl flight gliding and points to the validity and feasibility of employing owl-inspired TE fringes in practical applications of low-noise fluid machinery.

Contribution of Lighthill tensor components to far-field acoustic pressure

We numerically investigate the contribution of different components of the Lighthill tensor to the far-field acoustic pressure arising from laminar flow noise around a rigid cylinder. Computational fluid dynamics simulations were used to obtain the flow field, from which the time histories of the velocity components were stored to calculate the Lighthill tensor. The acoustic pressure was then calculated based on the Lighthill source distribution and free-field Green's function. The contribution and characteristics of the different components of the Lighthill tensor to the far-field pressure are described.

Acoustic characteristics of supersonic planar impinging jets

The present work aims to study the tonal and broadband noise associated with a supersonic planar jet, of Mach number 1.28 and Reynolds number 50000, impinging on a flat plate. Five different cases are considered corresponding to different plate distances and angles of impingement. The near-field noise is analyzed using Large Eddy Simulation (LES). For this, we employ a low dispersive and dissipative Finite Volume solver using AUSM for inviscid fluxes and third-order Runge–Kutta method for temporal discretization. The far-field noise is calculated using a hybrid approach in which the acoustic sources and mean flow are provided by the fluid solver while the far-field acoustic pressure is calculated by an acoustic solver. It solves Acoustic Perturbation Equations using a spectral/hp element method with a Discontinuous Galerkin projection. The present work highlights many important acoustics studies of impinging jets. Firstly, the far-field sound with the effect of non-uniform base fields is obtained which is important as the far-field acoustic pressure in most of the literature is reported either without any base fields or by the application of uniform base fields. Secondly, a correlation between the different modes of oscillations of the impinging jet and the production of impinging tones is studied using Modal Decomposition techniques. This analysis also sheds some light on the number of concurrent cycles for the different nozzle-to-plate distances. Lastly, the relation between the phase lag term and the distance between the plate and the nozzle exit is highlighted using a vortex tracking method. These observations can serve to provide a better understanding of the sound generation process.

Experimental studies on pressure drag and aerodynamic noise of cylinder with porous coatings

Previous numerical studies hold inconsistent viewpoints of the porous coating on a circular cylinder reducing or increasing drag, and the present experimental study aims to clarify this argument. Additionally, a common viewpoint is that the porous coatings can suppress both the near-field wall pressure fluctuations and far-field acoustic pressure, but optimal parameters of the porous materials are still unclear. In this paper, the experimental studies reveal effects of three parameters, i.e., incoming flow velocity, pores per inch, and thickness of metal foams, on the pressure drag, wall pressure fluctuations, and associated noise level.

Experimental Analysis of Rotor Blade Noise in Edgewise Turbulence

This paper presents an experimental investigation into the effects of turbulence ingestion on the aerodynamic noise characteristics of rotor blades in edgewise flight. A small-scaled, two-bladed rotor was used in the study. The test utilised two turbulence-generating grids, to generate turbulence inflows with different characteristics, and to compare them to the baseline configuration of the laminar inflow. The experiments were set at forwarding edgewise flight configuration, with freestream inflow velocity ranging from 10 m/s to 22 m/s. Simultaneous measurements of far-field acoustic pressure and load were conducted, along with a separate flow measurement using particle image velocimetry. The acoustic spectra demonstrated a larger contribution to the tonal noise radiation at blade passing frequency, and to the broadband noise radiation at the mid-frequency domain, due to turbulence ingestion. However, the broadband responses in the high-frequency domain were comparable between the tested laminar and turbulence inflow cases, with similar broadband humps featuring in the acoustic spectra. The directivity patterns of the overall sound pressure level showed that the noise radiation was lowest near the plane of rotation, and highest downstream. Turbulence ingestion effects could also be seen in the elevated noise levels throughout the observation positions for the grid inflow cases, particularly at larger advance ratios.

Acoustic Radiation From Stiffened Double Concentric Large Cylindrical Shells: Part II Creeping Waves

Abstract Acoustic radiation from stiffened double concentric large cylindrical shells with periodic cavities is analytically examined in the medium and high frequency range using the Sommerfeld–Watson transform. Creeping wave acoustic model of the stiffened double cylindrical shells in the shadow, penumbra, and illuminated regions is established by the residue theorem. An asymptotic expression of far-field acoustic pressure is derived in the geometrical acoustic zone according to the stationary phase method. Sound field of the bare or stiffened double cylindrical shells with annular fluid is determined by the creeping wave poles in the broad circumferential region. Mechanisms of creeping wave propagation through the stiffened double cylindrical shells are shown. There are a great many elastic and acoustic waves that cannot transmit through the annular fluid, annular bulkheads, and periodic cavities with a moderate gap between the double circular cylindrical shells. Acoustic boundary layer theories are proposed to describe sound propagation through the annular fluid and bulkheads for the creeping waves.

Effect of porosity on Curle’s dipolar sources on an aerofoil in turbulent flow

Integrating a porous material into the structure of an aerofoil constitutes a promising passive strategy for mitigating the noise from turbulence–body interactions that has been extensively explored in the past few decades. When a compact permeable body is considered in the aeroacoustic analogy derived by Curle to predict this noise source, a dipole associated with the non-zero unsteady Reynolds stresses appears on the surface in addition to the dipole linked to the pressure fluctuations. Nevertheless, the relative contribution of this source to the far-field noise radiated by a porous wing profile has not been clarified yet. The purpose of the current research work is twofold. On the one hand, it investigates the impact of porosity on the surface-pressure fluctuations of a thick aerofoil immersed in the wake of an upstream circular rod at a Mach number of 0.09. On the other hand, it quantifies the relevance of the Reynolds-stresses term on the surface as a sound-generation mechanism. The results from large-eddy simulations show that the porous treatment of the wing profile yields an attenuation of the unsteady-pressure peak, which is localised in the low-frequency range of the spectrum and is induced by the milder distortion of the incoming vortices. However, porosity is ineffective in breaking the spanwise coherence or in-phase behaviour of the surface-pressure fluctuations at the vortex-shedding frequency. The Reynolds-stresses term is found to be considerable in the stagnation region of the aerofoil, where the transpiration velocity is larger, and partly correlated with the unsteady surface pressure, suggesting constructive interference between the two terms. This results in a non-negligible contribution of this term to the far-field acoustic pressure emitted by the porous wing profile for observation angles near the stagnation streamline. The conclusions drawn in the present study eventually provide valuable insight into the design of innovative and efficient passive strategies to mitigate surface–turbulence interaction noise in industrial applications.

Experimental investigation of aerofoil tonal noise at low Mach number

This paper presents an experimental investigation of aerofoil tones emitted by a controlled-diffusion aerofoil at low Mach number ( $0.05$ ), moderate Reynolds number based on the chord length ( $1.4 \times 10^{5}$ ) and moderate incidence ( $5^{\circ }$ angle of attack). Wall-pressure measurements have been performed along the suction side of the aerofoil to reveal the acoustic source mechanisms. In particular, a feedback loop is found to extend from the aerofoil trailing edge to the regions near the leading edge where the flow encounters a mean favourable pressure gradient, and consists of acoustic disturbances travelling upstream. Simultaneous wall-pressure, velocity and far-field acoustic measurements have been performed to identify the boundary-layer instability responsible for tonal noise generation. Causality correlation between far-field acoustic pressure and wall-normal velocity fluctuations has been performed, which reveals the presence of a Kelvin–Helmholtz-type modal shape within the velocity disturbance field. Tomographic particle image velocimetry measurements have been performed to understand the three-dimensional aspects of this flow instability. These measurements confirm the presence of large two-dimensional rollers that undergo three-dimensional breakdown just upstream of the trailing edge. Finally, modal decomposition of the flow has been carried out using proper orthogonal decomposition, which demonstrates that the normal modes are responsible for aerofoil tonal noise. The higher normal modes are found to undergo regular modulations in the spanwise direction. Based on the observed modal shape, an explanation of aerofoil tonal noise amplitude reduction is given, which has been previously reported in modular or serrated trailing-edge aerofoils.

On the use of numerical Green’s functions in acoustic analogies for edge noise prediction at low Mach number

The interaction between a turbulent flow and a rigid obstacle leads to a far-field broadband acoustic radiation which can have a significant impact in many industrial applications. Depending mainly on the Mach number, different prediction methods have been developed. At low Mach number, direct noise computation methods are too expensive. Other approaches must be chosen, based on acoustic analogies which consist in separating noise generation and noise propagation mechanisms. In this study, we focus on the Lighthill’s wave equation solved using both analytical and numerical tailored Green’s functions. The latter is computed using an accelerated Boundary Element Method. Also, a statistical model for the velocity fluctuations in the turbulent flow is used to estimate the far-field radiated noise spectrum. It can be built from either a simulation of the mean flow or an estimation of the boundary layer parameters. To validate numerical predictions for the far-field acoustic pressure spectrum, a NACA 0012 airfoil is considered. Both leading edge and trailing edge predictions are validated against experimental data. Moreover, the impact of both the inflow velocity and the angle of attack on spectra and directivity diagrams is investigated.

A sharp interface immersed boundary method for flow-induced noise prediction using acoustic perturbation equations

In this paper, a hybrid computational aero/hydro-acoustic approach is proposed to deal with acoustic scattering and flow-induced noise problems based on the sharp interface immersed boundary method (IBM). For the flow field, the incompressible Navier–Stokes equations are solved by an in-house direct numerical simulation solver. The acoustic field is predicted by solving acoustic perturbation equations (APEs). Both flow and acoustic solid boundaries with complexity and mobility are dealt with by the sharp interface IBM. Benchmark acoustic problems with varied scatterers in two and three dimensions are presented to validate the accuracy of the acoustic codes and boundary treatments. Then, the feasibility and accuracy of the present hybrid approach are validated by considering the problem of flow past a circular cylinder at a Reynolds number of 200. Subsequently, the present method is used to predict the noise generated by flow around a four-cylinder array in two-dimensions with two arrangements (i.e., square array and diamond array), and the flow and acoustic physics are investigated in detail. The results show that the square array retains a monopole-like sound-radiation shape, while the directivity pattern of the diamond array produces a dipole-like shape. In both the square and diamond arrays, the propagation of acoustic waves is affected by the Doppler effect, and the latter array results in a larger alternation of the propagation angle compared with the single cylinder due to the influence of the geometric configuration. The intensity of the radiated acoustic pressure is much greater for the diamond array compared to the square one in most circumferential directions, and the acoustic intensity of both arrays is greater than that of the single cylinder. The spectrums of the far-field acoustic pressure indicate that the two arrays and the single cylinder have similar peak frequencies and profiles, with vortex shedding playing the predominant role in noise generation in all three configurations.

Annular acoustic black holes to reduce sound radiation from cylindrical shells

Annular acoustic black holes (ABHs) have been recently proposed as a potential means for reducing vibrations of cylindrical shells. The latter are very common structures in the naval, aeronautic and industrial sectors so widening ABH applications from flat plates to curved structures seems worth exploring. This work focuses on the benefits of embedding annular ABH indentations on cylindrical shells to reduce outward sound radiation. The goal of the paper is to propose a semi-analytical method to determine the acoustic power, radiation efficiency, source location and far-field acoustic pressure of ABH shells and compare them with those of uniform thickness shells. The vibration field of the ABH and uniform cylindrical shells is computed by means of the Gaussian expansion method (GEM) within the Rayleigh–Ritz approach. Then, the radiated pressure is obtained by solving the Helmholtz equation in cylindrical coordinates using the Green’s function method. The surface of the cylinder is discretized into small finite size radiators and an impedance matrix is used to obtain the acoustic surface pressure in terms of the shell radial velocity. To determine those regions of the cylinder responsible for the far field radiated sound, use is made of supersonic sound intensity (SSI). A method is proposed to calculate the SSI in the spatial domain for cylindrical shell structures which allows one to make direct use of the previously computed surface pressure and velocity distributions. The whole methodology is validated against finite element method (FEM) simulations and after that, results are presented for an acoustically thick shell. The roles played by the critical and ring frequencies are reported and the spectra of the acoustic power, radiation efficiency and far field acoustic pressure get analysed. It is shown that the annular ABH can become very effective when the cylinder flexural motion dominates over the circumferential one. The slow down of bending waves inside the ABH makes structural supersonic waves (in relation to sound speed) become subsonic at some point, which clearly diminishes the shell radiation efficiency. Overall, it is described why embedding an annular ABH on a cylindrical shell can strongly help reducing the radiated sound to the far-field.

A wave and finite element method for calculating sound transmission through rectangular panels

A wave based methodology is proposed to investigate sound transmission through rectangular, rigidly-baffled panels, including the modal behaviour of the structure. The panel is homogeneous in-plane, but the through-thickness construction can be of arbitrary complexity. The fluids are modelled analytically, the structure by the wave and finite element method: a small segment of the structure is meshed to predict the behaviour of an infinite panel with the same properties. The transverse displacement of the panel is modelled as a sum of sine terms, each associated with a specific mode. Neglecting fluid loading, the blocked pressure of the incident wave is decomposed into space harmonics with given trace wavenumbers. An equivalent, infinite plate, excited by a periodic continuation of the loading on the finite panel, is considered. The natural frequencies of the finite panel follow from free wave propagation, its response estimated from that of the infinite panel. The far-field acoustic pressure and sound transmission loss are presented. Numerical results agree well with analytical solutions, other numerical solutions and measurements. The proposed method takes the modal effects fully into account, and is efficient and straightforward to implement.

Trailing-edge broadband noise prediction of an airfoil with boundary-layer tripping

Hybrid methods for trailing edge noise prediction are applied to a NACA 6512-63 airfoil at zero angle of attack embedded in the actual narrow stream of the Siegen open-jet anechoic wind-tunnel. Incompressible large-eddy simulations (LES) of the airfoil trailing-edge flow yield the noise sources, and different analytical acoustic analogies then predict the acoustic far-field pressure. The chord-based Reynolds number of 1.9 × 105 triggers long laminar flow regions along the airfoil, leading to instability waves with an associated broadband noise radiation. To avoid this laminar-instability noise, the airfoil boundary layer is experimentally tripped on both sides. The actual serration tripping is included in the numerical grid as well as a simplified stair-step trip. Aerodynamic and acoustic results of the performed LES are compared with measurements and compressible direct numerical simulation (DNS) results. No noticeable influence of the trip geometry is found whereas the numerical schemes play a more important role. LES predictions with boundary layer trip compare well with experimental measurements and DNS cases. If the boundary-layer trip is not sufficiently thick in the numerical model, or not present at all, the far-field acoustic pressure is overpredicted and resembles more closely the sound radiation from the untripped airfoil with laminar instability noise.

Vibroacoustic responses of a heavy fluid loaded cylindrical shell excited by a turbulent boundary layer

A fully coupled structural–acoustic model of a cylindrical shell under external turbulent boundary layer excitation is herein developed. The numerical process requires computation of the wall pressure cross spectral density function as well as sensitivity functions for the fluid-loaded cylindrical shell. A semi-empirical model from literature is used to describe the wall pressure field induced by the turbulent boundary layer in the wavenumber–frequency domain. An analytical expression of the wall pressure field for a flat surface is adapted to describe the wall pressure field for a cylindrical surface. Circumferential sensitivity functions are derived using a wavenumber-point reciprocity principle. Results for the near-field and far-field acoustic pressure spectra are presented. Contributions of individual circumferential modes to the acoustic pressure spectra are examined, showing distinct trends below and above the ring frequency. The proposed method is computationally efficient and provides an effective approach to investigate vibroacoustic responses for maritime platforms.