Partial Field Decomposition Research Articles

Acoustical Holography and Coherence-Based Noise Source Characterization of an Installed F404 Engine

Understanding the acoustic source characteristics of supersonic jets is vital to accurate noise field modeling and jet noise reduction strategies. This paper uses advanced, coherence-based partial field decomposition methods to characterize the acoustic sources in an installed, supersonic GE F404 engine. Partial field decomposition is accomplished using an equivalent source reconstruction via acoustical holography. Bandwidth is extended through the application of an array phase-unwrapping and interpolation scheme. The optimized-location virtual reference method is used. Apparent source distributions and source-related partial fields are shown as a function of frequency. Local maxima are observed in holography reconstructions at the nozzle lipline, distinct in frequency and space. The lowest-frequency local maximum may relate to noise generated by large-scale turbulence structures in the convectively subsonic region of the flow. Other local maxima are correlated primarily with Mach wave radiation originating from throughout the shear layer and into the fully mixed region downstream of the potential core tip. Source-elucidating decompositions show that the order and behavior of the decomposition lend to the local maxima being related to distinct subsources. Between the local maxima, however, there may be a combination of sources active, which is likely the cause of the spatiospectral lobes observed in other full-scale, supersonic jets.

Source decomposition and reduced-order modeling of an installed F404-GE-103 engine using the optimized-location virtual reference method

Principal component analysis-related methods (i.e., proper orthogonal decomposition or partial field decomposition) are used widely in aeroacoustic applications for source characterization and reduced-order modeling. A previous paper [A. T. Wall et al., J. Acoust. Soc. Am. 144, 1356 (2018)] developed a coherence-based, virtual-reference method for performing physically meaningful PFD known as the optimized-location virtual references (OLVR) method. This paper performs a source decomposition using the OLVR method on acoustical holography data from an installed GE F404 engine. The OLVR-derived partial fields are compared with far-field radiation characteristics and partial equivalent sources are fitted to analytical wavepackets. Characteristics of this reduced-order model are discussed as a function of frequency and engine condition. [Work supported ONR Grant No. N00014-21-1-2069.]

Drag Decomposition Using Partial-Pressure Fields: ONERA M6 Wing

Drag decomposition has classically been undertaken using a far-field approach both from a wind-tunnel testing and computational fluid dynamics standpoint. It has been suggested by Schmitz (“Drag Decomposition Using Partial-Pressure Fields in the Compressible Navier-Stokes Equations,” AIAA Journal, Vol. 57, No. 5, 2019, pp. 2030–2038) that a decomposition of static pressure into partial pressure fields can allow one to decompose a computational fluids dynamics solution in the near field. This paper covers the implementation process of partial pressure fields on the ONERA M6 wing at conditions relevant to commercial transport aircraft. Relations between partial pressure field decomposition, the classical far-field theory, and physical drag sources are discussed. It is demonstrated that the near-field partial pressure field decomposition is equivalent to classical far-field analysis. In transonic flow, a new method to compute wave drag using a combination of both partial pressure fields and the far-field method is demonstrated.

Partial field decomposition using particle velocity references

In existing partial field decomposition methods, the pressures are generally used as references. This paper is going to use the particle velocities as the references to decompose the sound field radiated by incoherent or partially coherent sources into mutually incoherent partial fields, and evaluate its performance by comparing with the method using pressure references. Both numerical simulations and experiment confirm the effectiveness of the method using particle velocity references for partial field decomposition and demonstrate its superiority over the method using pressure references, and it is also shown through numerical simulations that the particle velocity references almost always perform better than the pressure references as long as the references are located close to the sources and the directions of particle velocity references are perpendicular to the source plane as far as possible.

Partial field decomposition of the simulated noise from a highly heated laboratory-scale jet

The decomposition of jet noise fields into self-coherent and mutually incoherent parts is an important step preliminary to the application of acoustical holography techniques. Cross-spectral matrices of point arrays sampled from large eddy simulations of a laboratory-scale jet operating at a high temperature ratio are decomposed using a singular value decomposition to obtain partial fields. The shape and relative strengths of the individual partial fields highlight the difference between the coherent radiation in the aft direction and the incoherent portion of the radiation towards the sideline. Azimuthally, levels are mostly constant but require multiple partial fields to accurately represent the low coherence at high frequency.

Partial-field decomposition analysis of full-scale supersonic jet noise using optimized-location virtual references.

Supersonic jet noise reduction efforts benefit from targeted source feature extraction and high-resolution acoustic imaging. Another useful tool for feature extraction is partial field decomposition of sources into independent contributors. Since such decomposition processes are nonunique, care must be taken in the physical interpretation of decomposed partially coherent aeroacoustic fields. The optimized-location virtual reference method (OLVR) is a partial field decomposition designed to extract physically meaningful source and field information through the strategic placement of virtual references within a reconstructed field. The OLVR method is applied here to obtain spatially distinct and ordered partial sources at multiple frequencies of a full-scale, high-performance supersonic jet engine operating at 100% engine power. Partial sources are shown to mimic behaviors of the total source distributions including monotonic growth and decay. Because of finite spatial coherence, multiple partial sources are used to reproduce far-field radiation away from the main lobe, and the number of required sources increases with increasing frequency. An analytical multiwavepacket model is fitted to the partial sources to demonstrate how OLVR partial fields can be leveraged to produce reduced-order models.

Military jet noise source imaging using multisource statistically optimized near-field acoustical holography

The identification of acoustic sources is critical to targeted noise reduction efforts for jets on high-performance tactical aircraft. This paper describes the imaging of acoustic sources from a tactical jet using near-field acoustical holography techniques. The measurement consists of a series of scans over the hologram with a dense microphone array. Partial field decomposition methods are performed to generate coherent holograms. Numerical extrapolation of data beyond the measurement aperture mitigates artifacts near the aperture edges. A multisource equivalent wave model is used that includes the effects of the ground reflection on the measurement. Multisource statistically optimized near-field acoustical holography (M-SONAH) is used to reconstruct apparent source distributions between 20 and 1250 Hz at four engine powers. It is shown that M-SONAH produces accurate field reconstructions for both inward and outward propagation in the region spanned by the physical hologram measurement. Reconstructions across the set of engine powers and frequencies suggests that directivity depends mainly on estimated source location; sources farther downstream radiate at a higher angle relative to the inlet axis. At some frequencies and engine powers, reconstructed fields exhibit multiple radiation lobes originating from overlapped source regions, which is a phenomenon relatively recently reported for full-scale jets.

Near-field acoustical array measurements of an impinging supersonic jet

Impingement significantly alters the rocket plume in the near-launch pad environment, which in turn affects the acoustic radiation. Prior laboratory measurements of an unheated, Mach 1.8 ideally expanded jet impinging on 45-degree inclined flat plate were carried out using a microphone that was moved within a relatively dense grid [Akamine et al., AIAA J. 53, 2061–2067 (2015)]. A multi-institution collaboration by the authors was begun in order to conduct array measurements of the acoustic radiation from both impinging and free jets. Measurements comprised a total of 42 measurement channels located within 40 nozzle diameters. An array of two-dimensional microphone probes was placed so as to examine the transition from the hydrodynamic near field to the acoustic radiation. A scanning linear array of microphones and a stationary polar array were also designed to enable beamforming, cross correlation, and partial field decomposition. This paper describes the jet facility, experiment design, and initial analyses conducted on the data collected. [Measurements supported by the Japanese Society for the Promotion of Science.]

Cylindrical acoustical holography applied to full-scale jet noise.

Near-field acoustical holography methods are used to predict sound radiation from an engine installed on a high-performance military fighter aircraft. Cylindrical holography techniques are an efficient approach to measure the large and complex sound fields produced by full-scale jets. It is shown that a ground-based, one-dimensional array of microphones can be used in conjunction with a cylindrical wave function field representation to provide a holographic reconstruction of the radiated sound field at low frequencies. In the current work, partial field decomposition methods and numerical extrapolation of data beyond the boundaries of the hologram aperture are required prior to holographic projection. Predicted jet noise source distributions and directionality are shown for four frequencies between 63 and 250 Hz. It is shown that the source distribution narrows and moves upstream, and that radiation directionality shifts toward the forward direction, with increasing frequency. A double-lobe feature of full-scale jet radiation is also demonstrated.

References per coherence length: A figure of merit for multireference acoustical holography

Multireference partial field decomposition (PFD) can be used to generate coherent holograms for scan-based near-field acoustical holography measurements. PFD is successful when the reference array completely senses all independent subsources, but meeting this requirement is not straightforward when the number of subsources and their locations are ambiguous (such as in aeroacoustic sources). A figure of merit based on spatial coherence lengths, called references per coherence length (RPLc), is a useful metric to guide inter-reference spacing in the array design so that the source is spanned. Coherence length is defined as the axial distance over which the ordinary coherence drops from unity to some desired value. Numerical experiments involving an extended, partially correlated source show that sufficiency of the reference array for different source conditions may be simply expressed in terms of RPLc. For sources of varying spatial coherence and over a large range of frequencies, one reference per coherence length is equivalent to sensing all independent subsources.

Partial field decomposition of jet noise using optimally located virtual reference microphones

The application of partial field decomposition (PFD) techniques based on a singular value decomposition to jet noise fields is useful for estimating the number of incoherent (equivalent) noise sources within a jet and for implementing near-field acoustical holography, but it does not generally provide physically meaningful partial fields (i.e. partial fields related to individual sources). Among several PFD methods that were designed to generate physically meaningful partial fields, the method developed by Kim et al. [JASA 115(4), 2004] finds the optimal locations of references in a sound field and places virtual references at those locations. In past investigations this method has been successfully applied to locate discrete numerical and physical sources and to generate partial fields related to each source. In this study, Kim’s method is applied to a full-scale jet installed on a military aircraft in an attempt to obtain physically meaningful partial fields. The partial fields obtained using these optimally located virtual references are compared to the partial fields obtained from other PFD methods.

Coherence length as a figure of merit in multireference near-field acoustical holography

Multireference partial field decomposition (PFD) can be used to generate coherent holograms for near-field acoustical holography measurements. PFD is most successful when the reference array completely senses all independent subsources, but meeting this requirement is not straightforward when the number of subsources and their locations are ambiguous (such as in aeroacoustic sources). A figure of merit based on spatial coherence lengths, called references per coherence length (RPL(C)), is a useful metric to guide inter-reference spacing in the array design. For numerical, extended, arbitrarily coherent sources one reference per coherence length results in a sufficient reference array.

An investigation of partial field decomposition using pressure gradient reference

The incoherent sound field obtained by scanning measurement cannot be used directly for nearfield acoustic holography to reconstruct the sound field. And therefore, the incoherent sound field needs to be decomposed into fully coherent partial fields. In previous methods, the pressure is used as reference to obtain the partial fields. In this paper, the pressure gradient is used as the reference for the partial field decomposition. Because the pressure gradient decays faster than the pressure, the interaction of the pressure gradient between the incoherent sources is weaker than that of the pressure, which may improve the effect of the partial field decomposition. A numerical simulation and an experiment are conducted to test the feasibility of the method. And it is shown that the partial field decomposition method based on pressure gradient reference is robust and the decomposed results are better than those based on pressure references.

Partial field decomposition of multi-source cyclostationary sound field

The cyclostationary sound field is a kind of special non-stationary field which has obvious modulation phenomena. Conventional planar near-field acoustic holography (PNAH) technique cannot exactly reflect its modulation characteristics. If the cyclic spectral density (CSD) instead of the complex sound pressure is adopted as the reconstruction variable, the modulating wave and carrier wave components of the cyclostationary sound field can be extracted effectively. A new technique called cyclostationary PNAH utilizing the CSD is proposed in this paper. Based on this technique, the problem of partial field decomposition by singular value decomposition (SVD) of multiple incoherent cyclostationary sound sources is researched. The results of numerical simulation and experiments show that the CPNAH technique and SVD decomposition method are effective.

Multi‐reference methods for nearfield acoustical holography.

Holographic projection requires that sound fields be spatially coherent. That condition can be satisfied if data at all locations on the hologram surface are measured simultaneously. However, more commonly, a scanning procedure is used in which measurements are made on parts of the hologram surface in sequence. In the latter case, it is necessary to record signals from fixed‐location reference transducers so that the phase of the pressure in each scan segment can be determined. Further, if the sound field is radiated by statistically incoherent sub‐sources, the sound field must be decomposed into coherent partial fields before holographic projection is performed on the individual partial fields. For the partial field decomposition to be successful, the number of reference transducers must be greater than or equal to the number of incoherent sources generating the field. In this presentation, the state‐of‐the‐art of multi‐reference procedures applied to nearfield acoustical holography will be described. Requirements for the number and positioning of reference transducers will be given along with procedures to verify that the number of references chosen is sufficient. Further, post‐processing of measured data to position virtual reference transducers close to physically meaningful sources and to compensate for source non‐stationarity will be discussed.

Vector intensity reconstructions in a volume surrounding a rigid spherical microphone array

A technique is described to image the vector intensity in the near field of a spherical array of microphones flush mounted in a rigid sphere. The spatially measured pressure is decomposed into Fourier harmonics in order to reconstruct the volumetric vector intensity outside the sphere. The theory for this reconstruction is developed in this paper. The resulting intensity images are very successful at locating and quantifying unknown exterior acoustic sources, ideal for application in noise control problems in interior spaces such as automobiles and airplanes. Arrays of varying numbers of microphones and radii are considered and compared and errors are computed for both theory and experiment. It is demonstrated that this is an ill-posed problem below a cutoff frequency depending on array design, requiring Tikhonov regularization below cutoff. There is no low frequency limit on operation, although the signal-to-noise ratio is the determining factor for high-spatial resolution at low frequencies. It is shown that the upper frequency limit is set by the number of microphones in the array and is independent of noise. The accuracy of the approach is assessed by considering the exact solution for the scattering of a point source by a rigid sphere. Several field experiments are presented to demonstrate the utility of the technique. In these experiments, the partial field decomposition technique is used and holograms of multiple exterior sources are separated and their individual volumetric intensity fields imaged. In this manner, the intensity fields of two uncorrelated tube sources in an anechoic chamber are isolated from one another and separated intensity maps are obtained from over a broad frequency range. In a practical application, the vector intensity field in the interior of an automobile cabin is mapped at the fundamental of the engine vibration using the rigid sphere positioned at the driver's head. The source regions contributing to the interior cabin noise are identified.

이동 프레임 음향 홀로그래피를 이용한 주행 중인 차량의 베어링 결함 위치 추정

This paper deals with a bearing faults localization technique based on holographic approach by visualizing sound radiated from the faults. The main idea stems from the phenomenon that bearing faults in a moving vehicle generate impulsive sound. To visualize fault signal from the moving vehicle, we can use the moving frame acoustic holography [Kwon, H.-S. and Kim, Y.-H., 1998, "Moving Frame Technique for Planar Acoustic Holography," J. Acoust. Soc. Am. Vol. 103, No. 4, pp. 1734<TEX>${\sim}$</TEX>1741]. However, it is not easy to localize faults only by applying the method. This is because the microphone array measures noise(for example, noise from other parts of the vehicle and the wind noise) as well as the fault signal while the vehicle passes by the array. To reduce the effect of noise, we propose two ideas which utilize the characteristics of fault signal. The first one is to average holograms for several frequencies to reduce the random noise. The second one is to apply the partial field decomposition algorithm [Nam, K.-U., Kim, Y.-H., 2004, "A Partial Field Decomposition Algorithm and Its Examples for Near-field Acoustic Holography," J. of Acoust. Soc. Am. Vol. 116, No. 1, pp. 172<TEX>${\sim}$</TEX>185] to the moving source, which can separate the fault signal and noise. Basic theory of those methods is introduced and how they can be applied to localize bearing faults is demonstrated. Experimental results via a miniature vehicle showed how well the proposed method finds out the location of source in practice.

Beamforming-based partial field decomposition in NAH

In this paper, a methodology for partial field decomposition is presented that is based on the beamforming algorithm for the application of acoustical holography to the composite sound fields generated by multiple incoherent sound sources. The unique aspect of the method is the use of estimated source signals identified via beamforming as reference source signals in the decomposition procedure. Numerical simulations are performed with particular emphasis on the robustness of the proposed technique under various situations. The experimental results show that the method identifies source signals very effectively regardless of the distance from source to reference and also has potential for use in distributed sources.

Scan-based near-field acoustical holography and partial field decomposition in the presence of noise and source level variation

Practical holography measurements of composite sources are usually performed using a multireference cross-spectral approach, and the measured sound field must be decomposed into spatially coherent partial fields before holographic projection. The formulations by which the latter approach have been implemented have not taken explicit account of the effect of additive noise on the reference signals and so have strictly been limited to the case in which noise superimposed on the reference signals is negligible. Further, when the sound field is measured by scanning a subarray over a number of patches in sequence, the decomposed partial fields can suffer from corruption in the form of a spatially distributed error resulting from source level variation from scan-to-scan. In the present work, the effects of both noise included in the reference signals, and source level variation during a scan-based measurement, on partial field decomposition are described, and an integrated procedure for simultaneously suppressing the two effects is provided. Also, the relative performance of two partial field decomposition formulations is compared, and a strategy for obtaining the best results is described. The proposed procedure has been verified by using numerical simulations and has been applied to holographic measurements of a subsonic jet.

Beamforming-based partial field decomposition in nearfield acoustical holography

In this paper, a methodology for partial field decomposition is presented that is based on the beamforming algorithm for the application of acoustical holography to the composite sound field generated by multiple incoherent sound sources. The unique aspect of the method is the use of the estimated sources identified via beamforming as the reference sources in the decomposition procedure. Numerical simulations are performed with particular emphasis on the robustness of the proposed technique under various situations. The experimental results show that the method identifies the sources very effectively regardless of the distance from source to reference and also has potential to be used for application to distributed sources.