Equivalent Acoustic Source Research Articles

Characterization of multi-rotor aircraft using truss support structure

Characterization of multi-rotor drone aircraft noise is vital to expanded use within the United States. To provide compatibility with current propagation and perception models, acoustic noise characterization focuses on the creation of equivalent lower hemispheres, and application of methods developed for manned aircraft for description of the noise directivity patterns. But a previous measurement determined that a refinement of these methods was required for the application to drone noise. One of these refinements was the use of a larger truss support rig, which was selected to provide sufficient clearance for the aircraft. The rig also provided regular holes where the microphones’ support arms could be mounted; the rigid structure possessed no flat faces and minimal cylindrical truss structures to minimize scattering of reflected signals. In addition to the lighting rig array, a number of additional microphones were placed along the flight path, and in-plane but outside of the measurement array for validation of the acoustic sources. With this improved array, another measurement of a multi-rotor aircraft was conducted, equivalent acoustic sources constructed, and validation performed. This measurement validates the use of the square array to characterize these types of aircraft.

Construction of interpolated source from dynamic flights (UAV/AAM Special Issue)

A previous comparison of far-field predictions from equivalent acoustic sources generated from dynamic flight measurements of small unmanned aircraft systems demonstrated that a single pass over an acoustic array was insufficient to accurately predict far-field acoustic levels. In effort to reduce the uncertainty in the current study, measurements of multiple passes of dynamic flight within finite engine speed/airspeed bins were combined. From these measurements, equivalent acoustic sources were decomposed using spherical harmonics fitted to levels depropagated on a spherical surface. Two source descriptions, one at a low speed and one at high speed, represent end points on the noise-power-distance curve, which was similar to a technique demonstrated in a previous study of static measurements. Interpolation of spherical harmonic coefficients between the two sources permitted the determination of intermediate speed conditions. The resulting equivalent acoustic sources removed more than 10 dB of uncertainty from the dynamic flight definitions.

Holographic reconstructions of large-eddy simulations of a highly heated laboratory-scale jet

Near-field acoustical holography allows for the reconstruction of a sound field from a limited measurement. For aeroacoustic noise generated by military aircraft, reconstructions of the pressure field within the jet plume have provided insight into equivalent acoustic noise source distributions, though the relationship between these equivalent sources and actual flow pressures and velocities within the plume remain unknown. This study reconstructs the sound field of a highly heated laboratory-scale jet simulated by the Naval Research Lab's Jet Noise Reduction (JENRE) large eddy simulation solver. The simulated data allow for comparisons of the holographic reconstructions of the pressure and particle velocity fields to points along the nozzle lipline, to the Ffowcs Williams and Hawkings integration surface (FWHS), and to the far field. Pressure field reconstructions outside and inside of the FWHS match well, while particle velocity reconstructions follow similar trends as the velocities generated by the LES but severly underestimate the time harmonic complex amplitdues.

Characterizing distinct components of tactical aircraft noise sources

Noise from a tactical aircraft can impact operations due to concerns regarding military personnel noise exposure and community annoyance and disturbance. The efficacy of mission planning can increase when the distinct, complex acoustic source mechanisms creating the noise are better understood. For each type of noise, equivalent acoustic source distributions are obtained from a tied-down F-35B operating at various engine conditions using the hybrid method for acoustic source imaging of Padois, Gauthier, and Berry [J. Sound Vib. 333, 6858-6868 (2014)]. The source distributions for the distinct noise types are obtained using different sections of a 71 element, ground-based linear array. Using a subarray close to the nozzle exit plane, source distributions are obtained for fine-scale turbulent mixing noise and broadband shock-associated noise, although grating lobes complicate interpretations at higher frequencies. Results for a subarray spanning the maximum sound region show that the multiple frequency peaks in tactical aircraft noise appear to originate from overlapping source regions. The observation of overlapping spatial extent of competing noise sources is supported by the coherence properties of the source distributions for the different subarrays.

Data-educed broadband equivalent acoustic source model for supersonic jet noise.

A broadband equivalent acoustic source distribution can be used to model the sound field near a high-speed jet. Such models must account for the spatiospectral variation of the sound levels. This work presents a technique for obtaining such a model using a spectral decomposition method associated with large and fine-scale turbulent mixing noise to create broadband equivalent source distributions for each noise type. The large-scale turbulent mixing noise is represented by frequency-dependent wavepackets, while the fine-scale turbulent mixing noise is modeled as a frequency-dependent incoherent, extended source distribution. This technique is applied to acoustical measurements from an ideally expanded, unheated Mach 1.8 jet. The wavepackets model the sound field levels in the maximum radiation region, but the second incoherent source distribution is required to obtain the levels at the other locations. The combination of the incoherent source distribution and the wavepacket provides a broadband, equivalent acoustic source representation that adequately models the sound field for Strouhal numbers between 0.04 and 0.25. At higher Strouhal numbers, better agreement is obtained when accounting for a frequency-dependent shift in the apparent acoustic source region. This frequency-dependent source region is more important closer to the jet than in the far field.

Characterization of equivalent acoustic sources to reproduce the acoustic field generated by engines on an aircraft fuselage

This work presents a general procedure to characterize equivalent acoustic sources to reproduce the sound pressure field generated by the engines on an aircraft fuselage. The procedure would allow to set up ground experimental tests on aircraft components, by means of distributed loudspeakers, to obtain their vibro-acoustic performances as if they were tested in flight conditions.A FEM model of an aircraft fuselage mock-up was built up, comprising the structure, the internal acoustic cavities and the external air. The sound pressure field generated by the engines was considered as the reference solution, whereas an equivalent sound field, produced by distributed monopole sources surrounding the structure, was obtained by leveraging on the proposed Multi-Disciplinary Optimization (MDO) procedure.The MDO procedure was based on the mutual interaction between the commercial codes Siemens NX, for the CAE/FEM simulations, and Noesis Optimus, for the optimization framework.

Localization of directional noise sources from high-performance military aircraft through subarray beamforming analysis

High-performance military aircraft noise is created by multiple sound generation mechanisms that need to be understood to guide noise reduction efforts and for adequate sound field predictions. Phased-array methods can be used to produce frequency-dependent equivalent acoustic source models. The Hybrid (beamforming) method [Padois et al., J. Sound Vib. 333 (2014)] is applied to an acoustical measurement along a 71-microphone ground-based array, spanning 32 m, placed in the vicinity of a high-performance military aircraft as the engine was operated at different powers. Application of the Hybrid method to the full-array creates an overall equivalent source model that is sufficient for predicting overall field radiation but fails to separate the different noise sources. Applying the Hybrid method to subarrays separates broadband shock-associated noise from the main radiation lobes of turbulent mixing noise. Results show that the subarray-based equivalent source distributions for the different types of noise originate from overlapping source locations. Further analysis of the subarray-based equivalent noise sources using coherence and directionality from the unwrapped phase of the cross-spectral source reconstructions identifies overlapping, frequency-dependent source regions with characteristics unique to broadband shock-associated noise and turbulent mixing noise. [Work supported by an Air Force Research Laboratory SBIR.]

Self-similarity of level-based wavepacket modeling of high-performance military aircraft noise

Construction of the equivalent acoustic source model for high-performance military aircraft noise presented in this paper begins with a decomposition of sound levels, from ground-based microphones 11.7 m from a high-performance military aircraft, into portions matching the similarity spectra associated with large-scale and fine-scale turbulent mixing noise (LSS and FSS). [Tam et al. AIAA Paper 96-1716 (1996)]. A Fourier transform of the spatial distribution of the decomposed levels yields frequency-dependent wavenumber spectra [Morris, Int. J. Aeroacoust. 8, 301-316 (2009)]. Each LSS-educed wavenumber spectrum corresponds to a wavepacket, consisting of a spatially varying amplitude distribution with a constant axial phase relationship. This wavepacket model produces a directional, coherent sound field. However, the asymmetry in the LSS-educed wavenumber spectra may indicate that a nonuniform phase relationship is a more physical choice that could be correlated to the axial variation in convective speed. The FSS component is modeled with a line of incoherent monopoles whose amplitude distribution is related to the FSS-educed wavenumber spectrum. While this level-based model is limited, the addition of the FSS-related source yields a better match to the noise environment of a high-performance military aircraft than is found using a single coherent wavepacket. [Work supported by ONR.]

Analysis of Hydrodynamic Noise around Acoustic Modem on the AUV Using Hybrid LES-Lighthill Method

Acoustic modem is one of the most important sensors on the deep sea AUV. A good performance of the acoustic modem has great effect on the safety and operation of deep sea AUV. According to the construction of deep sea AUV, acoustic modem is installed in the cavity behind the GPS antenna, it would cause flow noise around the acoustic modem and thus interference will occur when the communication is established between deep sea AUV and surface. Flow-induced noise around the acoustic modem is studied in this paper. Firstly the unsteady flow around the acoustic modem is studied by large eddy simulation (LES) method. Secondly based on the resolved information of flow field, acoustic noise distribution is studied using equivalent acoustic sources method. Compared with different positions of GPS antenna, flow noise distribution around the acoustic modem and the effect on communication is investigated. Then acoustic modem layout on the AUV is optimized.

Source Height Determination for Several Sources at the Same Height

Equivalent acoustic source height is an important parameter for accurate predictions of the acoustic impact of transportation infrastructures. Research has shown that this parameter can be obtained from a two-microphone technique in the case of one broadband omnidirectional point source above an homogeneous ground, modeled as a Delany-Bazley absorber. It is shown in this paper that this method can be generalized to n broadband sources with same height, above an homogeneous ground or a ground with an impedance discontinuity. All sources are considered to have the same emission spectrum. The method is based on the comparison of the level difference spectrum between two microphones - hereinafter called attenuation spectrum - measured and computed. Numerical and experimental validations confirm the reliability of the method for controlled noise sources. Furthermore, it is demonstrated that qualitative assessment of ground parameters is sufficient to obtain an accurate source height determination.

Determination of the Far Field Sound Radiation from Flames Using the Dual Reciprocity Boundary Element Method

The present work addresses the calculation of the radiated sound power spectrum in the far field of open or enclosed flames based on the application of the dual reciprocity boundary element method (DRBEM). The focus of this work is the development of a technique that allows a good representation of the sound field, assuming that the sound sources originated by the combustion are known. Following the acoustic analogy approach, the sound radiation of open flames can be evaluated by a volume integral over the equivalent acoustic source terms in the combustion zone. The DRBEM allows replacing the volume integral by a series of surface integrals. The technique is applied to the theoretical model of a spherical flame. The accuracy of the DRBEM model can be studied by comparing it with available analytical solutions for the sound radiation of this flame type. For enclosed flames, the DRBEM is used to calculate the sound propagation in the region of temperature gradients that appears at the exhaust of the combustion chamber. The sensitivity of the radiated sound field to this adjacent inhomogeneous temperature field is investigated. The non-uniqueness problem of the boundary integral equation method is tackled by the Burton and Miller approach. The DRBEM allows an effective determination of the radiated acoustic field because it can take into account inhomogeneities and satisfies automatically the radiation condition at infinity.

Measuring derived acoustic power of an ultrasound surgical device in the linear and nonlinear operating modes

Objective and motivation The method for measuring derived acoustic power of an ultrasound point source in the form of a sonotrode tip has been considered in the free acoustic field, according to the IEC 61847 standard. The main objective of this work is measuring averaged pressure magnitude spatial distribution of an sonotrode tip in the free acoustic field conditions at different electrical excitation levels and calculation of the derived acoustic power at excitation frequency ( f 0 ≈ 25 kHz). Finding the derived acoustic power of an ultrasonic surgical device in the strong cavitation regime of working, even in the considered laboratory conditions (anechoic pool), will enable better understanding of the biological effects on the tissue produced during operation with the considered device. Experimental method The pressure magnitude spatial distribution is measured using B&K 8103 hydrophone connected with a B&K 2626 conditioning amplifier, digital storage oscilloscope LeCroy Waverunner 474, where pressure waveforms in the field points are recorded. Using MATLAB with DSP processing toolbox, averaged power spectrum density of recorded pressure signals in different field positions is calculated. The measured pressure magnitude spatial distributions are fitted with the appropriate theoretical models. Theoretical approaches In the linear operating mode, using the acoustic reciprocity principle, the sonotrode tip is theoretically described as radially oscillating sphere (ROS) and transversely oscillating sphere (TOS) in the vicinity of pressure release boundary. The measured pressure magnitude spatial distribution is fitted with theoretical curves, describing the pressure field of the considered theoretical models. The velocity and displacement magnitudes with derived acoustic power of equivalent theoretical sources are found, and the electroacoustic efficiency factor is calculated. When the transmitter is excited at higher electrical power levels, the displacement magnitude of sonotrode tip is increased, and nonlinear behaviour in loading medium appears, with strong cavitation activity produced hydrodynamically. The presence of harmonics, subharmonics and ultraharmonics as a consequence of stable cavitation is evident in the averaged power spectral density. The cavitation noise with continuous frequency components is present as a consequence of transient cavitation. The averaged pressure magnitude at the frequency components of interest (discrete and continous) in the field points is found by calculating average power spectral density of the recorded pressure waveform signal using the welch method. The frequency band of interest where average power spectral density is calculated is in the range from 15 Hz up to 120 kHz due to measurement system restrictions. The novelty in the approach is the application of the acoustic reciprocity principle on the nonlinear system (sonotrode tip and bubble cloud) to find neccessary acoustic power of the equivalent acoustic source to produce the measured pressure magnitude in the field points at the frequency components of interest. Results In the nonlinear operating mode, the ROS model for the considered sonotrode tip is chosen due to the better agreement between measurement results and theoretical considerations. At higher excitation levels, it is shown that the averaged pressure magnitude spatial distribution of discrete frequency components, produced due to stable cavitation, can be fitted in the far field with the inverse distance law. The reduced electroacoustic efficiency factor, calculated at excitation frequency component as ratio of derived acoustic power with applied electrical power, is reduced from 40% in the linear to 3% in the strong nonlinear operating mode. The derived acoustic power at other frequency components (subharmonic, harmonic and ultraharmonic) is negligible in comparison with the derived acoustic power at excitation frequency. Discussion and conclusions The sonotrode tip and loading medium are shown in the strong cavitation regime as the coupled nonlinear dynamical system radiating acoustic power at frequency components appearing in the spectrum. The bubble cloud in the strong nonlinear operating mode decreases the derived acoustic power significantly at the excitation frequency.

The role of structural acoustics in the space shuttle flowliner crack investigation

During normal inspection of the Space Shuttle main propulsion fuel line system small cracks were identified in a slotted flowliner just upstream of the main propulsion engines. The cause is believed to be resonance excited by pressure fluctuations originating from the downstream fuel pump. This presentation highlights the analyses that were performed to characterize the structural acoustic environment surrounding the flowliner during waterflow and liquid hydrogen laboratory experiments, as well as in-flight conditions. Analyses employed a combination of analytical and finite-element methods to model fluid structure interaction and inverse methods to reconstruct equivalent acoustic sources representative of the fuel pump. Numerical results will be presented that compare experimental strain and pressure data with theoretical counterparts. Implications will be drawn regarding the applicability of the theory to the actual shuttle fuel line system. [Work was sponsored by NASA Marshall Flight Center.]

The Acoustic Spectrum in the Sound Field of Isotropic Turbulence

Lighthill's theory of Aerodynamic Noise uses an acoustic analogy by which the equivalent acoustic sources in a turbulent flow have first to be calculated, measured or modeled from a time-accurate evaluation of the unsteady flow. Proudman considered the application to the noise radiated from weakly compressible isotropic turbulence, by evaluating the fourth-order space-time covariance of Lighthill's stress tensor. The resulting acoustic power per unit volume of turbulence was found to follow the eighth power law of velocity and showed the efficiency of conversion of turbulent kinetic energy into sound was extremely small, being proportional to the fifth power of the turbulent Mach number. These results are of particular interest today, since, all turbulent shear flows were shown by Kolmogorov to become locally isotropic near the dissipation range. Hence the high frequency asymptotic far-field radiated noise spectrum generated from eddies in the inertial subrange of all turbulent shear flows should obey a universal frequency law as obtained from isotropic turbulence, namely f−7/ 2, a result first found by Meecham and Ford. From studies of the fluctuations in this nonlinear energy transfer cascade from large to small eddies it is possible to gain a better insight as to the physical process, and the reason for its weak efficiency, whereby sound is generated and radiated as a broadband spectrum. A key factor is shown to be the weak fluctuations in the rate of dilatation in the compressible turbulent flow, which explains the reason for the efficiency of sound conversion obtained by Lighthill.

Prediction of source characteristics of engine exhaust manifolds

Engine exhaust noise source is often described in frequency domain by the impedance and strength of an equivalent acoustic one-port source at a reference plane downstream of the exhaust manifold. These parameters can be measured by experimental methods, however, it is also desirable to develop methods for their prediction. A pre-requisite for the prediction of the equivalent one-port acoustic source parameters of an engine manifold is a linear mathematical model of the breathing noise generation mechanism at the valves. The present paper proposes new mathematical models for this source mechanism and the prediction of the one-port source characteristics of engine exhaust noise. The analysis is based on basic fluid dynamic equations for inviscid one-dimensional flow and encompasses both linear time-invariant, linear time-variant and non-linear one-port source models. A systematic procedure is presented for the calculation of one-port source characteristics of engine manifolds, with an application to a 4 cylinder engine exhaust manifold. The theory of the paper is applicable, with almost no modification, also to the prediction of one-port source characteristics of engine intake noise and the pressure fluctuations associated with discharge and suction processes in compressors.

Aeroacoustics, moving boundaries, and bursting balloons: Acoustic sources revisited

The use of equivalent acoustic sources to describe scattering in a nonuniform medium dates back to Rayleigh’s theory of sound. The idea of equivalent sources in a uniform medium at rest was later developed by Lighthill into his ‘‘acoustic analogy,’’ capable of describing the generation of sound by turbulence and other vortical flows. In the present paper Lighthill’s acoustic analogy formulation is generalized to encompass initial-value problems; the initial conditions are represented by impulsive sources and dipoles distributed over the domain, and boundary conditions are represented in the usual manner by surface sources and dipoles. David Blackstock’s bursting balloon example, discussed in Chapter 3 of Fundamentals of Physical Acoustics, can be solved by this method. However, in situations where the medium is of nonuniform density (for example, a gas with a specified temperature distribution at the initial time), the impulsive source distribution obtained by a direct application of time windowing to the acoustic analogy is nonphysical. The apparent paradox is resolved by introducing the energy conservation equation, and reformulating the acoustic analogy with pressure, rather than density, as the wave variable.

The Source of Aerodynamic Noise

This paper is a tribute to Alan Powell's achievements and his extensive publications in hydro and aeroacoustics.1 The theory of Aerodynamic Noise was established by Sir James Lighthill in 1952. The beauty of Lighthill's treatment was that he based this theory on the exact Navier-Stokes equations and showed, by their rearrangement, how the source of aerodynamic noise could be obtained from exact time-accurate calculations or experiment. Lighthill used the emission or propagation theory whereby an observer in a uniform medium at rest receives acoustic radiation from a distribution of moving sources of sound. Their properties are found using an acoustic analogy. The relevant fluctuations in a turbulent fluid flow can be expressed in terms of Lighthill's stress tensor Tij, which is used to define a distribution of equivalent acoustic sources, which move through an otherwise uniform stationary fluid. An alternative procedure is to concentrate on the acoustic generation and to regard the sources of sound at rest or in motion in a uniform medium moving at a constant speed. (The approach can be extended to consider any arbitrary mean fluid motion.) The advantage of the present approach, involving the convective wave equation is that flow-acoustic interaction becomes part of the solution. In Lighthill's theory, flow-acoustic interaction is either ignored or at best is included as an equivalent source. The purpose of the present paper is to show there is no unique source of aerodynamic noise for it depends on the flow quantity used to describe the radiated sound. The convective wave equation is introduced and shown to involve similar sources to those found by Lighthill for the wave equation in a medium at rest. The source function found for the convective wave equation for a turbulent flow is shown to involve a modified Lighthill's stress tensor, which is non-linear in velocity and temperature fluctuations. It is further shown when the rate of dilatation covariance is examined, which can be derived from Lighthill's solution, that this small quantity, which Lighthill so carefully treated in retaining the exact properties of the compressible flow, is itself directly responsible for the rate of change of volume in the fluid and the creation of the noise which is radiated from the turbulent flow.

On one-port characterization of noise sources in ducts by using external loads

Equivalent acoustic source characterization of duct-borne fluid machinery noise is often undertaken by interpolating the results of two-microphone pressure measurements with different external acoustic loads over a linear one-port source model. If the source is time-invariant, the one-port source characteristics can be determined by using only two external loads. This is well known as the two-load method. An extension of the two-load method for time-variant sources is also available and known as the multiple-load method. In these methods the source is treated as a ‘black-box’. This paper addresses the problem of one-port source characterization when the linear operations inherent in the ‘black-box’ are known explicitly. The equations governing the explicit one-port source models are derived and the source characteristics are shown to be measurable using only few acoustic loads. It is not the purpose of this paper to discuss the application of these models to any specific fluid machinery; however, of particular interest are the explicit source models that require only two loads. Numerical results are presented to show some features of such time-invariant and time-variant explicit one-port source models.

On the effects of structural joints on sound scattering.

By examining scattering from a joint connecting two perpendicularly attached plates, this paper addresses the acoustic effects of different structural joints, ranging from clamped connection, which transmits both forces (normal and tangential) and bending moment, to various pinned connections that allow free motions in one or two dimensions at the attachment point. It is shown that the normal force and the bending moment dominate the scattering process, respectively, in the low- and high-frequency domains. For low frequencies well below the plate coincidence frequency, the scattered field is dominantly given by the contribution from the normal force so that joints which support normal forces of equal value, but are otherwise different, lead to identical scattered fields. In the high-frequency region well above the coincidence frequency, the bending moment yields the dominant contribution. Thus, joints such as rotation-free hinges scatter much less sound at high frequencies than those that transmit bending moment. It is shown that the amplitude ratio of the bending moment contribution to that due to the normal force closely follows a power law of frequency (normalized by the coincidence frequency) with the power index being 1.25, which results both from the respective dipole and quadrupole characteristics of the equivalent acoustic sources due to the force and the bending moment, and from the frequency-dependent strengths of these sources that are determined by the dynamic balance of the overall coupled problem. The predominance of the normal force and the bending moment in different frequency domains is shown to also govern the energy flow into the structure. At low frequencies, this energy is in the form of longitudinal motions associated with the normal force, while at high frequencies, transverse vibrations in the structure are most energetic because most of the energy is then transmitted to the structure through the bending moment. [Work supported by ONR.]

Determination of noise source height, part I: The measurement of equivalent acoustic source height above a reflecting surface

This is the first of two companion papers which describe the measurement of the equivalent noise source height on highway vehicles. The first paper considers the measurement method, and the second its application to highway vehicles. This paper shows how measurements may be made of the equivalent source height of a distribution of sources above a reflecting plane. First the equivalent point source position is defined for an arbitrary distribution of acoustic sources. The effects of source directionality and the impedance of the reflecting surface are also discussed. A measurement method is proposed which minimizes the effect of horizontal source mislocation and ground impedance. This method is then used to measure the equivalent height of a number of source distributions, and is shown to be accurate over the frequency range 200–2500 Hz for sources which are less than 2.5 m above the ground.