Sesquipoles in aeroacoustics

Chapman, C. J.

doi:10.1016/j.jsv.2006.09.002

Cited by 3 publications

(5 citation statements)

References 17 publications

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“…Chapman has proposed a transfer function between incoming gusts (i.e. the source) and flowinduced noise [26,27] (which can be measured) by using the Wiener-Hopf technique. Munt [11] and Gabarb & Astley [6] have proposed the forward model for duct acoustic problems by using the Wiener-Hopf technique, which is adopted in this work to (1) theoretically clarify the inherent principle of the forward model and to (2) rapidly provide a big volume of high-fidelity data for machine learning.…”

Section: Preliminary Knowledge (A) Statement Of the Problemsmentioning

confidence: 99%

“…More specifically, the Wiener-Hopf method will be tried in this work to guide (supervise) neural networks to learn transfer functions between inputs (wave sources) and outputs (scattered wave fields). Chapman has studied the transfer function between incoming gusts and flowinduced noise sources [26,27] by using the Wiener-Hopf technique. In essentially the same way, the Wiener-Hopf technique can be used to produce the transfer function between fan noise sources and sensor measurements of the scattered sound waves.…”

Section: Introductionmentioning

confidence: 99%

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Deep neural networks for waves assisted by the Wiener–Hopf method

Huang

2020

Proc. R. Soc. A.

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In this work, the classical Wiener–Hopf method is incorporated into the emerging deep neural networks for the study of certain wave problems. The essential idea is to use the first-principle-based analytical method to efficiently produce a large volume of datasets that would supervise the learning of data-hungry deep neural networks, and to further explain the working mechanisms on underneath. To demonstrate such a combinational research strategy, a deep feed-forward network is first used to approximate the forward propagation model of a duct acoustic problem, which can find important aerospace applications in aeroengine noise tests. Next, a convolutional type U-net is developed to learn spatial derivatives in wave equations, which could help to promote computational paradigm in mathematical physics and engineering applications. A couple of extensions of the U-net architecture are proposed to further impose possible physical constraints. Finally, after giving the implementation details, the performance of the neural networks are studied by comparing with analytical solutions from the Wiener–Hopf method. Overall, the Wiener–Hopf method is used here from a totally new perspective and such a combinational research strategy shall represent the key achievement of this work.

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Section: Preliminary Knowledge (A) Statement Of the Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Deep neural networks for waves assisted by the Wiener–Hopf method

Huang

2020

Proc. R. Soc. A.

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“…The pressure field may be called the three-dimensional supersonic edgelet, since it is the sound produced by an individual point on the leading edge. This field is much simpler than the subsonic three-dimensional edgelet, given as a contour integral in [8], where it is referred to as the edgelet function E 1 ; and it is slightly simpler than the two-dimensional supersonic edgelet given in [10]. Expression (7) applies in the Mach cone |ȳ 2 +z 2 | 1/2 <x emanating downstream from the origin; elsewhere the field is zero.…”

Section: The Delta-function Gustmentioning

confidence: 99%

“…In its general form, this is a problem of some complexity, especially when account is taken of such important matters as the blade angle of attack, thickness, and camber. Substantial progress has been made over many years in related subsonic problems, of which representative work in two dimensions is [1][2] and in three dimensions is [3][4][5][6][7][8]. For the supersonic problem, the amount of published work is smaller, but important two-dimensional fields have been determined in [9][10][11], and three-dimensional fields in [12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Canonical sound fields in the frequency-domain theory of supersonic leading-edge noise

Powles

Chapman

2019

Wave Motion

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This paper determines the three-dimensional structure of certain single-frequency canonical sound fields occurring in the theory of blade-vortex interaction when the flow velocity relative to the blade is supersonic. A relative velocity of this magnitude occurs at the outer part of the fan blades in an aeroengine, at which the incoming vorticity has either been ingested from the atmosphere or created in the aeroengine itself. The sound fields analysed are those produced by the leading edge of a flat-plate blade at zero angle of attack on being struck by a gust which is either (i) localised along the span, or (ii) non-localised but discontinuous. The canonical gusts of type (i) have either a deltafunction or Gaussian shape, and those of type (ii) are either anti-symmetric or described by a Heaviside function; these gusts give rise to the four basic canonical sound fields. The paper also analyses a fifth sound field, produced by a single-frequency top-hat gust. This sound field has a complex structure involving aspects of both (i) and (ii), but can nevertheless be analysed in terms of the canonical sound fields. The main results of the paper are exact and approximate analytical formulae giving the dependence of the acoustic field on gust-shape and flow parameters, and also a simple formula which is ideal for numerical work. The last of these is used to assess in detail the numerical accuracy of all the approximate formulae, which are of either Fresnel or Keller type. A key result is that Keller-type formulae, representing sound rays produced in accord with the geometrical theory of diffraction, have a very wide range of validity. A companion paper (Chapman & Powles 2019) in this special issue of Wave Motion determines the canonical sound fields in the corresponding time-domain theory.

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“…The maximum pressure is especially great when the interaction between gust and edge takes place at high speed, as in modern aeroengines. For a subsonic edge, a large body of theory has been worked out, with many three-dimensional impulsive sound fields calculated exactly [1][2][3][4][5][6][7][8][9]. For a supersonic edge, some three-dimensional impulsive fields have been calculated in [10][11][12][13], and a general theory of the generation of such fields is given in [14].…”

Section: Introductionmentioning

confidence: 99%

Basic singular fields in the theory of impulsive supersonic leading-edge noise

Chapman

Powles

2019

Wave Motion

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This paper determines the impulsive sound fields produced by sharp-edged gusts striking the leading edge of a supersonic blade or aerofoil. A full three-dimensional theory is provided, so that the gust edges can be at any orientation relative to the blade, and the paper gives complete details of the sound fields produced by gust edges in the spanwise and streamwise directions, and by many combinations of such edges, including corners. The mathematical theory depends on singular sound fields produced by gusts with a delta-function upwash; these are used to derive exact analytical formulae for impusive sound fields of different three-dimensional shapes, and also a Green's function representation of the field which is especially adapted to numerical evaluation. Gusts with top-hat profiles are given particular attention, and also the effect of Gaussian-function smoothing of both delta-function and top-hat profiles. The investigation is complementary to that in a companion paper (Powles & Chapman 2019) in this special issue of Wave Motion, which determines the smooth sound fields produced by single-frequency gusts. Fourier integration provides the relation between the two types of field.

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Sesquipoles in aeroacoustics

Cited by 3 publications

References 17 publications

Deep neural networks for waves assisted by the Wiener–Hopf method

Deep neural networks for waves assisted by the Wiener–Hopf method

Canonical sound fields in the frequency-domain theory of supersonic leading-edge noise

Basic singular fields in the theory of impulsive supersonic leading-edge noise

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