A transformation of the acoustic equation with implications for low-speed flight and wind-tunnel tests

Taylor, Keith

doi:10.2514/6.1977-1307

Cited by 24 publications

(52 citation statements)

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“…In the presence (Figure 1) of a non-uniform, steady, low Mach number potential mean flow, of potential φ (x i ), the retarded time in (100) is changed [43] to (5a): In the case of sound generation in an inhomogeneous low Mach number mean flow the sound sources are associated with turbulence (90a, b) and entropy (97a, b) noise:…”

Section: §4 Sound Generation By Moving Surfaces and Convected Noise mentioning

confidence: 99%

“…The moving surfaces or bodies causing the non-uniform flow in an incident free stream of velocity U -i at infinity, also scatter sound; both the convection of sound and the scattered wave are represented [42][43][44] by replacing x i , y i by X i , Y i given by (98b) in (102):…”

Section: §4 Sound Generation By Moving Surfaces and Convected Noise mentioning

confidence: 99%

“…This suggests an extension of the FWH equation allowing (Figure 1) for sound generation by surfaces in arbitrary motion in a flowing medium. The effect of a steady, potential, low Mach number mean flow on sound has been shown [42][43][44] to be equivalent to a change in retarded time; this can be explained as the effect of convection of sound by the mean flow. Thus it may be expected that sound generation by surfaces in arbitrary motion in a steady, low Mach number potential flow, be represented by the Kirchhoff integral extended in three ways: (i) with the spherical spatial decay modified by a Doppler factor due to source motion, as in the FWH equation; (ii) the effect of a mean flow, either uniform with no restriction on Mach number [45][46][47][48][49] or steady, potential of low Mach number [42][43][44] is to modify the retarded time; (iii) both in the Doppler factor and in the retarded time the position vectors of observer and source are replaced by modified position vectors incorporating the unit perturbation potential of the mean flow.…”

Section: §1 Introductionmentioning

confidence: 97%

“…In the latter may be ommited [43] the term φ (y i ) on the grounds that the flow potential is defined to…”

Section: §1 Introductionmentioning

confidence: 99%

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On Sound Generation by Moving Surfaces and Convected Sources in a Flow

Campos¹,

Lau²

2012

International Journal of Aeroacoustics

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The theory of sound generation by surfaces in arbitrary motion is presented, with two generalizations relative to the Ffowcs-William Hawkins (FWH) equation: (i) it allows for the presence of a steady, non-uniform potential flow of low Mach number; (ii) it includes the effects on the radiation field of reflections from solid surfaces, e.g. these which cause non-uniformity of the flow. The final result is a generalization of the Kirchhoff integral with: (i) a retarded time modified by sound convection by the mean flow; (ii) position coordinates of observer and source modified to account for the presence of the obstacles which reflect sound waves and cause the mean flow to be non-uniform. An alternative generalization of the Kirchhoff integral is presented for sources in arbitrary motion in an uniform mean flow with unrestricted Mach number. The two generalized forms of the Kirchhoff integral also apply to convected sources of sound, such as the turbulence noise associated with vorticity and the entropy noise due to convected fluid inhomegeneities. The two noise sources are shown to be dominant at low Mach number, relative to other noise sources present in an inhomogeneous potential flow with unrestricted Mach number. In the latter case applies the (i) inhomogeneous high-speed wave equation, that includes as particular cases the (ii) convected and (iii) classical wave equations. The latter two (ii-iii) are obtained from (α) the Laplace equation using the retarded time. All three (i-iii) are obtained by two more distinct methods: (β) elimination among the equations of fluid mechanics for the stagnation enthalpy as acoustic variable; (γ) an acoustic variational principle for the acoustic potential in a steady homentropic nonhomogeneous potential mean flow with unrestricted Mach number. §1. INTRODUCTION In most of the aeroacoustics literature [1], the modeling of sound generation by surfaces in arbitrary motion is based on the FWH-equation [2], which has effectively superseded an earlier attempt at the same result [3]. Two of the most important applications of the FWH equation are propeller and rotor noise. A variety of methods have been used in connection with the noise aircraft propellers and the noise of helicopter rotors *luis.campos@ist.utl.pt

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Section: §4 Sound Generation By Moving Surfaces and Convected Noise mentioning

confidence: 99%

Section: §4 Sound Generation By Moving Surfaces and Convected Noise mentioning

confidence: 99%

Section: §1 Introductionmentioning

confidence: 97%

“…In the latter may be ommited [43] the term φ (y i ) on the grounds that the flow potential is defined to…”

Section: §1 Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On Sound Generation by Moving Surfaces and Convected Sources in a Flow

Campos¹,

Lau²

2012

International Journal of Aeroacoustics

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“…Boundary element methods are more suited to problems in the absence of flow, due to boundary integral formulations relying on the use of Green's functions. However, boundary element formulations that approximate uniform flow 4 and non-uniform flow 5,6 effects do exist in the literature. Another aim of the present investigation was to determine which of these approximations is more suitable for simulation of installation effects of landing gears under lifting wings, and boundary element simulations using these two flow approximations were conducted to this end.…”

mentioning

confidence: 99%

The Effect of Flow Circulation on the Scattering of Landing Gear Noise

Heffernon

Angland

Zhang

et al. 2015

21st AIAA/CEAS Aeroacoustics Conference

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An investigation into the scattering of landing gear noise sources by a lifting wing is presented. A two-dimensional test case is used in the investigation. The noise sources are represented by a monopole, which is located at the approximate position of a landing gear underneath a wing geometry. A linearized Euler equation solver is used to simulate the scattering of the monopole by the wing. The effect of a non-uniform flowfield due to circulation induced by a lifting wing is quantified as the difference in acoustic scattering over uniform and non-uniform base flows. The results show that increasing the angle of attack, or increasing the Mach number, leads to a small increase in the sound pressure level towards the ground. However, the observed increase is relatively small. A boundary element method solver is then used to investigate the same problem, and existing uniform and non-uniform flow boundary element formulations are evaluated to see which more accurately predicts the effect of flow. The results show that the uniform flow boundary element formulation is more accurate in predicting the effect of flow than the non-uniform flow approximation for this particular problem, and that the extra computational effort required for the non-uniform flow approximation does not yield a more accurate result.

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Installation: numerical investigation

Lummer

2019

CEAS Aeronaut J

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Acoustic installation effects are considered as scattering problem. Two methods to investigate them are presented. First, a Fast Multipole Method Boundary Element Method (FMM-BEM) which can solve the Helmholtz wave equation for full scale aircraft configurations at frequencies of some kHz. There, low Mach number potential mean flow fields can be taken into account by a so-called Taylor transformation. Second, a Discontinuous Galerkin Method (DGM) which solves Acoustic Perturbation Equations (APE) for realistic mean flow fields is presented. DGM calculations are very expensive and can be performed for full scale aircrafts only at low frequencies. Its main purpose so far is to assess the accuracy of the FMM for selected cases. The Taylor transformed Helmholtz equation is derived and the fundamentals of the FMM are introduced. Some details of the DLR FMM code FMCAS are given. The basic DGM equations are derived for the APE and some implementation details of the DLR DGM code DISCO++ are discussed. For generic geometries results of the FMM and DGM are compared and the limits of the Taylor transfor

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A transformation of the acoustic equation with implications for low-speed flight and wind-tunnel tests

Cited by 24 publications

References 1 publication

On Sound Generation by Moving Surfaces and Convected Sources in a Flow

On Sound Generation by Moving Surfaces and Convected Sources in a Flow

The Effect of Flow Circulation on the Scattering of Landing Gear Noise

Installation: numerical investigation

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