Acoustic Analogy Formulations Accelerated by Fast Multipole Method for Two-Dimensional Aeroacoustic Problems

Wolf, William; Lele, Sanjiva K.

doi:10.2514/1.j050338

Cited by 27 publications

(10 citation statements)

References 25 publications

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“…However, recent studies have shown that at moderate Mach numbers, quadrupole sources can have a non-negligible effect on far-field acoustic predictions [3,4]. Additionally, it has been demonstrated that quadrupole sources have a significant impact on far-field predictions involving airframe configurations, particularly those with wake interactions [5,6].…”

Section: Doi: 102514/1j053713mentioning

confidence: 99%

“…The investigation of the noise sources for airfoil and cylinder vortex shedding frequencies is presented using a hybrid methodology which employs DNS for near field source computations and the FW-H equation as the acoustic analogy formulation. The integrations of surface dipole and volume quadrupole source terms appearing in the FW-H formulation are accelerated by a fast multipole method [5] that incorporates convective effects. Furthermore, with the present numerical formulation, it is possible to investigate the individual contributions of the quadrupole sources and separate the surface dipole sources from the airfoil and from the cylinder.…”

Section: Doi: 102514/1j053713mentioning

confidence: 99%

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Sound and Sources of Sound in a Model Problem with Wake Interaction

et al. 2015

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Aeroacoustic predictions of a model airframe noise problem are conducted to assess the effects of wake interaction on flow and acoustic fields. Simulations of unsteady low Reynolds number flows, including both noise generation and its subsequent propagation to the far field, are performed for a configuration composed of a cylinder placed above a NACA 0012 airfoil. An assessment of cylinder position and freestream Mach number effects on sound radiation is presented. It is observed that intense interference among cylinder and airfoil dipoles occurs for all configurations analyzed. In this case, each body scatters the sound emitted by the other. For moderate Mach number flows with wake interaction, quadrupole sources become important to the total acoustic prediction, specially for the downward noise radiation. In order to investigate how wake interaction affects noise radiation, a comparison between the current model problem with a single cylinder case is presented. Results show that wake interaction becomes a major feature of the airfoil-cylinder flow, causing a faster downstream decay of convecting disturbances when compared to the isolated cylinder case. This issue is further studied using a linear stability calculation for the wake interaction problem, which shows that for higher Mach numbers, compressibility effects lead to the formation of a wave-packet structure in the wake with higher maximum amplitude, higher convection Mach number and a sudden spatial decay. Therefore, wake interaction and compressibility effects play a key role in the present model problem and are proposed as responsible for the increase of quadrupole noise radiation. Nomenclature a = speed of sound c = airfoil chord d = cylinder diameter F i = dipole source f = FW-H surface G = Green's function H = Heaviside function H 2 0 = Hankel function of the second kind and order zero i = imaginary unit M = Mach number p = pressure Q = monopole source Re c = Reynolds number based on airfoil chord c Re d = Reynolds number based on cylinder diameter d T ij = quadrupole source (Lighthill stress tensor) t = time u i = fluid velocity U i = FW-H surface velocity x i = observer position y i = source position δ ij = Kronecker delta ρ = density τ ij = viscous stress ω = angular frequency Subscripts 0 = mean value ∞ = freestream quantity Superscripts 0 = perturbation valuê · = Fourier transformed quantity

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Section: Doi: 102514/1j053713mentioning

confidence: 99%

Section: Doi: 102514/1j053713mentioning

confidence: 99%

Sound and Sources of Sound in a Model Problem with Wake Interaction

et al. 2015

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“…The integrations of these volumetric sources are computed along a subset region of the flowfield including the wake plus turbulent boundary layer regions, where the magnitude of non-linear sources is non-negligible. The surface and volume integrations of dipole and quadrupole source terms are performed using a 3D convective wideband multi-level adaptive FMM [10,11,12] to reduce the computational cost of the calculation of aeroacoustic integrals in the FWH formulation. The developed numerical capability allows the analysis of each noise source individually as well as the effects of convection on the computation of noise radiated by these sources.…”

Section: Flow Simulations and Acoustic Predictionsmentioning

confidence: 99%

“…The acoustic predictions are performed by the FWH acoustic analogy formulation [9] and incorporate convective effects. The surface and volume integrations of dipole and quadrupole source terms appearing in the FWH equation are performed using the 3D convective wideband multi-level adaptive fast multipole method (FMM) developed in [10,11,12] to reduce the computational cost of the calculation of aeroacoustic integrals in the FWH formulation. With the method applied in this work the computational cost of evaluating the aeroacoustic integrals is considerably reduced.…”

Section: Introductionmentioning

confidence: 99%

Compressibility Effects on Airfoil Trailing Edge Noise Generation and Propagation

Wolf¹,

Azevedo²,

Lele³

2014

Proceedings of 10th World Congress on Computational Mechanics

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Abstract. The present investigation of airfoil trailing edge noise concerns the broadband noise that arises from the interaction of turbulent boundary layers with the airfoil trailing edge and the tonal noise that arises from vortex shedding generated by laminar boundary layers. We address aspects of noise generation and propagation such as the effects of mean flow convection on the calculation of sound directivity, of compressibility and quadrupole sources on sound radiation. Large eddy simulations (LES) are conducted for a NACA0012 airfoil with rounded trailing edge for two flow configurations with different freestream Mach numbers (M ∞ = 0.115 and 0.4) for an angle of incidence AoA = 5 deg. The Reynolds number based on the airfoil chord is fixed at Re c = 408000. The acoustic predictions are performed by the Ffowcs Williams & Hawkings (FWH) acoustic analogy formulation and incorporate convective effects. Aeroacoustic results are compared to experimental data for a case which presents a broad vortex shedding tone and good agreement is observed.

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“…The numerical tool has been previously validated for several simulations of compressible flows involving sound generation and propagation. 3,4,7 …”

Section: Flow Simulationsmentioning

confidence: 99%

Investigation of Noise Sources in a Two-Dimensional Model Airframe Noise Problem with Wake Interaction

Wolf

Backes

Azevedo

2013

19th AIAA/CEAS Aeroacoustics Conference

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Aeroacoustic predictions of a model airframe noise problem are conducted in order to assess the effects of wake and boundary layer interaction on both the flow and acoustic fields. Simulations of unsteady laminar flows, including both noise generation and its subsequent propagation to the far field, are performed for a two-dimensional configuration composed of a cylinder placed above a NACA 0012 airfoil at 5 deg. angle of incidence. The Reynolds number based on the airfoil chord is set at Rec = 5000 and the Reynolds number based on the diameter of the cylinder is Re d = 200. An assessment of cylinder position and freestream Mach number effects on sound radiation is presented for M∞ = 0.1, 0.3 and 0.5. The investigation of the noise sources for airfoil and cylinder vortex shedding frequencies is also presented using a hybrid methodology which employs direct calculation for near field source computations and the Ffowcs Williams-Hawkings (FW-H) equation as the acoustic analogy formulation. In order to verify the numerical solutions, acoustic prediction results obtained by direct noise calculation (DNC) are compared to those computed by the FW-H equation and good agreement is observed. The separate contributions of the terms composing the quadrupole sources are analyzed. Even for the low Reynolds number flows investigated, Reynolds stresses are the dominant quadrupole noise sources and viscous effects as well as entropy fluctuations can be neglected. It is also found that while quadrupole sources can be neglected in noise predictions by the FW-H equation for the M∞ = 0.1 flow calculations, they should be included for the M∞ = 0.3 and 0.5 acoustic predictions at low and high frequencies. For moderate Mach number flows, at the cylinder vortex shedding frequency, dipole sources are related to both acoustic scattering and diffraction phenomena that occur along the airfoil surface and trailing edge, respectively. However, quadrupole sources are more specifically related to diffraction effects along the airfoil trailing edge. When the cylinder vortex shedding is the driving noise source mechanism, intense dipolar interference occurs for all configurations analyzed.

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Acoustic Analogy Formulations Accelerated by Fast Multipole Method for Two-Dimensional Aeroacoustic Problems

Cited by 27 publications

References 25 publications

Sound and Sources of Sound in a Model Problem with Wake Interaction

Sound and Sources of Sound in a Model Problem with Wake Interaction

Compressibility Effects on Airfoil Trailing Edge Noise Generation and Propagation

Investigation of Noise Sources in a Two-Dimensional Model Airframe Noise Problem with Wake Interaction

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