Far-field Directivity Pattern Research Articles

Relevance of quadrupolar sound diffraction on flow-induced noise from porous-coated cylinders

This paper elucidates the link between the near-wake development of a circular cylinder coated with a porous material in a low Mach-number flow and the related aerodynamic sound attenuation. It accomplishes this by formulating the cylinder flow-induced noise as a diffraction problem. The necessity for such an approach is driven by experimental evidence obtained through acoustic beamforming and particle-image-velocimetry measurements, which reveal that the dominant noise sources for a coated cylinder are not localised on the body surface but rather in the wake, specifically at the outbreak position of the shedding instability. The acoustic field at the vortex-shedding frequency can be hence modelled by considering a compact lateral quadrupole at this location and employing an exact Green’s function tailored to a cylindrical geometry. Because of the diffraction of the sound waves radiated by the quadrupolar source on the cylinder surface, the resulting far-field directivity pattern resembles that of a dipole. The study demonstrates that the porous coating has the two-fold effect of decreasing the strength of the point quadrupole in the wake and moving its origin further downstream, reducing, in turn, the efficiency of the sound scattering. Consequently, the diffracted part of the acoustic field, which dominates the far-field noise for a bare cylinder in accordance with classical theory, provides a contribution that is comparable to the direct part. The results eventually indicate that quadrupolar sources must be considered to accurately predict the noise radiated from a porous-coated cylinder, even at low Mach numbers.

Directivity of horns mounted in finite enclosures: A multimodal formulation.

The beamwidth is a primary directivity metric for the design of a constant directivity horn. To date, investigations on this property have predominantly been restricted to the half-space radiation or idealized geometries. This paper examines the beamwidth behavior of an axisymmetric horn mounted in a finite cylindrical enclosure by proposing an elegant multimodal solution to the far-field directivity pattern. The variation of beamwidth is examined for the frequency, dimensions of the enclosure, and shape of the horn. At low frequencies, a fitted model is proposed to precisely depict the intrinsic beam narrowing governed by the enclosure diffraction. The asymptotic behavior of the beamwidth is explored as the flange width increases. In the high-frequency range, the horn profile is a determinant of the directivity characteristics. We report the possibility of extending the bandwidth of a constant directivity horn by leveraging the enclosure diffraction effects. The proposed analytical method is highly accurate and much faster than the finite element method for wideband analysis. It allows for an arbitrary velocity distribution at the mouth of the horn and incorporates idealized flange configurations such as an infinite baffle, a zero-thickness closed baffle, and an infinitely long enclosure as limit cases.

Directional characteristics of two gamelan gongs.

The distinctive geometry and structural characteristics of Balinese gamelan gongs lead to the instrument's unique sound and musical style. This work presents high-resolution directivity measurements of two types of gamelan gongs to quantify and better understand their acoustic behavior. The measured instruments' structural modes clearly impact their far-field directivity patterns, with the number of directional lobes corresponding to the associated structural mode shapes. Many of the lowest modes produce dipole-like radiation, with the dipole moment determined by the positions of the nodal and antinodal regions. Higher modes exhibit more complex patterns with multiple lobes often correlated with the location and number of antinodal regions on the gong's edge. Directivity indices correspond to dipole radiation at low frequencies and quadrupole radiation at intermediate and higher frequencies. Symmetry analysis confirms that the gong's rim significantly impacts the resultant directivity.

Frequency-Dependent F-Number Suppresses Grating Lobes and Improves the Lateral Resolution in Coherent Plane-Wave Compounding.

Ultrafast imaging modes, such as coherent plane-wave compounding (CPWC), increase image uniformity and reduce grating lobe artifacts by dynamic receive apertures. The focal length and the desired aperture width maintain a given ratio, which is called the F-number. Fixed F-numbers, however, exclude useful low-frequency components from the focusing and reduce the lateral resolution. Herein, this reduction is avoided by a frequency-dependent F-number. This F-number derives from the far-field directivity pattern of a focused aperture and can be expressed in closed form. The F-number, at low frequencies, widens the aperture to improve the lateral resolution. The F-number, at high frequencies, narrows the aperture to avoid lobe overlaps and suppress grating lobes. Phantom and in-vivo experiments with a Fourier-domain beamforming algorithm validated the proposed F-number in CPWC. The lateral resolution, which was measured by the median lateral full widths at half maximum of wires, improved by up to 46.8% and 14.9% in a wire and a tissue phantom, respectively, in comparison to fixed F-numbers. Grating lobe artifacts, which were measured by the median peak signal-to-noise ratios of wires, reduced by up to 9.9 dB in comparison to the full aperture. The proposed F-number thus outperformed F-numbers that were recently derived from the directivity of the array elements.

Low-frequency directional characteristics of a gamelan gong

The structural modes of gamelan gongs often have clear impacts on their far-field directivity patterns with the number of directional lobes corresponding to the associated structural mode shapes. Many of the lowest modes produce dipole-like radiation with the dipole moment determined by the positions of the nodal and antinodal regions. Spherical harmonic and multipole expansions facilitate further understanding of the gongs' low-frequency directional characteristics. The expansions also yield practical simplifications to model their radiation.

Acoustic source centering of musical instrument directivities using acoustical holography

The acoustic center of a source is commonly defined as the point from which spherical wavefronts appear to diverge. Measuring directivities of sound sources with a surrounding spherical array whose geometric origin is not aligned with the acoustic center of the source can lead to distortions in directivity patterns. Thus, a method is desired to obtain both the far-field directivity pattern and to determine the acoustic center of a source. This work illustrates how acoustical holography can identify the reference frame from which spherical waves diverge by studying various musical instruments' acoustic centers.

Prediction of sound radiation from an unbaffled long enclosure with the ground

A theoretical model is presented for the prediction of sound radiated from a semi-infinite unbaffled long enclosure with the ground. This geometrical arrangement forms an idealized representation of traffic tunnels and railway stations where noise propagates inside the long enclosures and radiates to the outside through the openings. Despite the fact that the model described here applies only to idealized situations, it contains essential elements of realistic configurations which are conducive to understanding the physics of the sound radiation phenomenon and significant for the proposal of appropriate noise control strategies. First of all, by expressing the sound field in terms of the superposition of propagating modes inside the long enclosure and adopting the Fourier transform in other regions, the intractable boundary value problem in the natural domain is reduced to a scalar modified Wiener-Hopf (W-H) equation of the second kind in the spectral domain. Then, its solution is obtained using the standard factorization and decomposition procedures, and the radiated sound field is attained through the inverse Fourier transform which involves a contour integral that can be evaluated approximately via the saddle point method. After that, the finite element method (FEM) is adopted to validate the model. Far-field directivity patterns of the radiated sound fields are presented. Finally, the properties of the sound fields both inside and outside three enclosures with different boundary conditions are analyzed, based on which, potential noise reduction methods by using acoustic liners are discussed.

Applying an iterative method numerically to solve n × n matrix Wiener-Hopf equations with exponential factors.

This paper presents a generalization of a recent iterative approach to solving a class of 2 × 2 matrix Wiener-Hopf equations involving exponential factors. We extend the method to square matrices of arbitrary dimension n, as arise in mixed boundary value problems with n junctions. To demonstrate the method, we consider the classical problem of scattering a plane wave by a set of collinear plates. The results are compared to other known methods. We describe an effective implementation using a spectral method to compute the required Cauchy transforms. The approach is ideally suited to obtaining far-field directivity patterns of utility to applications. Convergence in iteration is fastest for large wavenumbers, but remains practical at modest wavenumbers to achieve a high degree of accuracy. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 2)'.

Direct and integral noise computation of two square cylinders in tandem arrangement

The present paper presents a comparison between two different approaches for calculating far-field noise of two square cylinders in tandem arrangement. Experimental data show that a flow past such an arrangement results in aeolian tones as well as broadband noise. The turbulent flow past the cylinders is computed using a compressible solver for low-Mach number flows. In order to validate the direct computation of acoustic waves, the complete span including endplates is calculated. Wind tunnel measurements show two different but stable flow states past the cylinders: a quiet state, where no vortex shedding is present in the wake of the upstream cylinder, and a loud state, where separated shear layers flow into the gap between the cylinders intermittently. Different initialisations of the velocity field are used in order to capture both flow states. Mean flow quantities as well as surface pressure spectra are compared to wind tunnel measurements. Far-field noise is calculated directly using the compressible solver, as well as indirectly using a hybrid method based on a Ffowcs Williams Hawkings formulation for stationary rigid surfaces. Far-field spectra and directivity patterns are compared to wind tunnel measurements. Results of both methods show good agreement with experimental data.

Scattering of an arbitrary order acoustical Bessel beam by a rigid off-axis spheroid.

In this study, the authors use the partial-wave series expansion method in the spherical coordinate system and provide a theoretical formula for the off-axis acoustical scattering by rigid prolate and oblate spheroids illuminated by an arbitrary-order Bessel beam to explore the physical characteristics of the off-axis far-field scattering (the axis of the Bessel beam is parallel to the axis of the spheroids). The proposed method is verified and several three-dimensional far-field directivity patterns of rigid spheroids illuminated by zeroth- and first-order Bessel beams are depicted to explore the off-axis scattering. A special emphasis is placed on the geometry size of the prolate and oblate spheroids, the half-cone angle of the Bessel beam, the order of the Bessel beam, and the offset position. Compared with the on-axis scattering, the derivation and calculation of the off-axis scattering takes into account the spherical harmonic function using a numerical integral procedure. In addition, no symmetry was observed in the patterns of the far-field acoustic scattering form function for the zeroth- and higher-order Bessel beams with the off-axis illumination. This investigation provides a tool for the exploration of the complex scattering problems of underwater non-spherical particles under the illumination of the Bessel beam.

Far-Field Performances Prediction of High Frequency Projectors Using Secondary Source Array Method

This paper investigates the prediction of the far-field performances of high frequency projectors using the second source array method (SSAM). The far-field parameters can be calculated accurately using the complex acoustic pressure data of two very close parallel planes which lie in the near-field region of the projector. The paper simulates the feasibility of predicting the far-field parameters such as transmitting voltage response and the far-field directivity pattern. The predicting results are compared with that calculated using boundary element method (BEM). It shows very good agreement between the two methods. A planar high frequency projector is measured using the near-field method. In order to verify the predicting results, the far-field measurement is performed for the same projector. The comparison of the results shows that the near-field method is capable to precisely predict the far-field parameters of the projector.

Numerical investigation on radiation characteristics of aero-intake noise with ground effects

A hybrid method for the prediction of far-field Aero-intake noise from gas turbine engine with ground effects has been developed. The near-field predictions were obtained by solving the linearized Euler equations with computational aeroacoustic techniques composed of high-order finite difference scheme, non-reflecting boundary condition, overset grids, and parallel computational methods. Kirchhoff integral method was used for the prediction of far-field directivity patterns. In order to predict the noise propagation, ray theory is applied with Geographical Information System (GIS) terrain profile data. Then, the noise level on the ground has been predicted and analyzed, including the effects of air absorption, ground reflection, and diffraction.

Integrated Structural Electromagnetic Analysis of Mesh Reflectors with Structural Random Dimensional Errors

A new procedure for the integrated structural electromagnetic analysis of cable mesh reflectors with structural random dimensional errors is presented. The procedure combines the integrated structural electromagnetic analysis with reliability analysis and aims to investigate the effects of structural random dimensional errors on the antenna far-field directivity pattern. Both the antenna far-field directivity pattern and structural member dimensions are taken as random variables in this procedure. The computational expressions of the mean value and variance of the far-field directivity are developed by means of the random factor method and the random variable’s functional moment method. The influences of structural random dimensional errors on the randomness of radiation directivity pattern are inspected via an offset cable mesh reflector.

A Study of Far Field Directivity Pattern of Bio-Inspired EMFit Emitters

Bats use echolocation to navigate their environment and to localize and identify prey. A biomimetic sensor uses propagation of acoustic energy at higher frequencies to extract information from the environment. EMFit is a new material with very good properties for air. In our attempt to optimize the actual sonar head used by self-governed robots we used this material to construct ultrasound transducers capable of working in a similar way as bats' emitter. We performed measurements, calculated and analyzed the far field directivity pattern for two types of transducers: linear array and hemi-cylindrical array. Experimental studies of the directivity pattern in far field for these two types of EMFit transducers highlighted the capabilities of these two emitters.

On the sound fields of infinitely long strips

Exact solutions are derived for sound radiation from four kinds of infinitely-long strips: namely a rigid strip in a baffle of finite width, a resilient strip in free space, and a resilient or rigid strip in an infinite baffle. In one limit, the strip in a finite baffle becomes a rigid strip in free space and in the other, a line source in a finite baffle. Here "rigid" means that the surface velocity is uniform, whereas "resilient" means that the surface pressure is uniform, and the strip is assumed to have zero mass or stiffness, as if a force were driving the acoustic medium directly. According to the Babinet-Bouwkamp principle, radiation from a resilient strip in an infinite baffle is equivalent to diffraction of a plane wave through a slit in the same. Plots are shown for the radiation impedances, far-field directivity patterns, and on-axis pressure responses of the four kinds of strip. A simple relationship between the radiation admittance of the rigid strip in an infinite baffle and the resilient strip in free space is presented. The two-dimensional rectangular wave functions developed in this paper can be applied to related problems.

Estimation of the far-field directivity of broadband aeroengine fan noise using an in-duct axial microphone array

Abstract This paper presents a measurement technique for estimating the far-field directivity of the sound radiated from a duct using measurements of acoustic pressure made inside the duct. The technique is restricted to broadband, multi-mode sound fields whose directivity patterns are axi-symmetric, and whose modes are mutually uncorrelated. The technique uses a transfer function to relate the output from an in-duct axial beamformer to measurements of the far-field polar directivity. A transfer function for a hollow cylindrical duct with no flow is derived, and investigated in detail. Transfer functions for practical cases concerning aeroengine exhausts are also presented. The transfer function is shown to be insensitive to the mode-amplitude distribution inside the duct, and hence can be used to predict the directivity in practice where the noise source distribution is unknown. The technique is then validated using a no-flow facility, and is shown to be able to predict variations in the far-field directivity pattern and also estimate the far-field sound pressure levels to within 2 dB. It is suggested that the proposed technique will be especially useful for fan rig experiments, where direct measurement of directivity, for example by use of an anechoic chamber, is impossible.

원통면 음향 홀로그래피를 이용한 수중음향 곡면배열센서의 빔 해석

As an experimental technique to analyze the far-field characteristics of underwater cylindrical array sensors, cylindrical acoustic holography is studied. Inside an laboratory water tank, far-field directivity patterns as well as near-field source images are reconstructed from the measured hologram by hydrophone array. Approximate equation for far-field directivity estimation is derived based on stationary phase method. The simulation and experiment show well usefulness of the proposed method in application of underwater array sensors.

Numerical investigation on radiation characteristics of discrete-frequency noise from scarf and scoop aero-intakes

Numerical studies have been carried out to investigate the detailed geometrical effects of full three-dimensional aero-intakes on the radiation of the discrete-frequency rotor–stator interaction noise. The near-field acoustic radiation characteristics and the far-field directivity patterns from the scarf and scoop aero-intakes with three different scarf/scoop angles are quantitatively analyzed and compared. The near-field predictions were obtained by solving the linearized Euler equations with computational aeroacoustic techniques consisting of high-order finite difference scheme, non-reflecting boundary conditions, overset grids and parallel computational methods. For the prediction of far-field directivity pattern, the Kirchhoff integral method was applied. By comparing the directivities of discrete-frequency noise radiating from the scarf and the scoop aero-intakes with that from an axisymmetric aero-intake, it is shown that the 7 dB noise reduction at downward peak radiation angle can be achieved by using the scoop aero-intake with scoop angle of 15°, and the 5 dB noise reduction by the scarf aero-intake with the scarf angle of 15°. The scattering of the radiating acoustic wave by the background mean flow around the aero-intakes shifts the peak lobe radiation angle toward ground and increases the amplitude of the acoustic pressure compared with the cases without mean flow effect. Overall, the scoop aero-intake was found to be more effective than the scarf and the axisymmetric aero-intakes in view of the lower noise radiation toward ground.

COMPUTATION OF ACOUSTIC FIELD RADIATED BY A SPHERICAL SOURCE NEAR A THERMOVISCOUS FLUID SPHERE

Acoustic radiation from a spherical source, vibrating with an arbitrary, axisymmetric, time-harmonic surface velocity distribution, while immersed near a thermoviscous fluid sphere suspended in an unbounded viscous thermally conducting fluid medium is computed. The formulation utilizes the appropriate wave field expansions and boundary conditions along with the translational addition theorem for spherical wave functions to develop a closed-form solution in form of infinite series. The prime objective is to investigate the thermoviscous loss effects on acoustic radiation and its associated field quantities. The analytical results are illustrated with a numerical example in which the spherical source, that may vibrate either in a monopole-like or a dipole-like mode, is suspended in a thermoviscous fluid medium near an equal-sized viscous thermally conducting fluid sphere. To avoid numerical difficulties normally arising in process of solving thermoviscous radiation/scattering problems in the frequency range of interest, a basic multiple precision FORTRAN computation package was utilized in developing specialized codes for computing special mathematical functions including spherical Bessel functions of complex argument and performing large complex matrix manipulations on floating point numbers of arbitrarily high precision. The essential acoustic field quantities such as the modal acoustic radiation impedance load on the source, the radiated far-field pressure directivity pattern and the radiated on-axis pressure are evaluated and discussed for representative values of the parameters characterizing the system. Limiting cases are examined and excellent agreements with well known solutions are attained.

Optimal windowing for wideband linear arrays

The problem of constructing a wideband beam pattern that is concentrated in both angle and frequency is discussed. This paper is a direct extension of the work of Slepian and co-workers on time- and frequency-limited functions. It is shown that the singular vectors and singular functions of the mapping relating the set of weights of a linear wideband array to its far-field directivity pattern have both concentration properties and double orthogonality properties and so they can be thought of as the wideband equivalents of the discrete prolate spheroidal sequences and wave functions. These singular functions are used to obtain approximations to a frequency-invariant beam pattern