Acoustic Scattering for Rotational and Translational Symmetric Structures in Nonuniform Potential Flow

Karimi, Mahmoud; Croaker, Paul; Peake, N.; Kessissoglou, Nicole

doi:10.2514/1.j055844

Cited by 10 publications

(10 citation statements)

References 32 publications

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“…25,26 The effect of non-uniform potential flow and flow-induced noise can be taken into account by well-known Taylor transformation. 27,28 Taylor's transformation is a simple time transformation that decouples the mean-flow and acoustic-field calculations and is valid under assumptions of low Mach number. 29 Astley and Bain 64 proposed an approximate formulation for wave propagation in non-uniform mean flow based on Taylor transformation.…”

Section: Bem3d For Aero-acoustic Problemsmentioning

confidence: 99%

Development of 3D boundary element method for the simulation of acoustic metamaterials/metasurfaces in mean flow for aerospace applications

Bashir

Carley

2020

International Journal of Aeroacoustics

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Low-cost airlines have significantly increased air transport, thus an increase in aviation noise. Therefore, predicting aircraft noise is an important component for designing an aircraft to reduce its impact on environmental noise along with the cost of testing and certification. The aim of this work is to develop a three-dimensional Boundary Element Method (BEM), which can predict the sound propagation and scattering over metamaterials and metasurfaces in mean flow. A methodology for the implementation of metamaterials and metasurfaces in BEM as an impedance patch is presented here. A three-dimensional BEM named as BEM3D has been developed to solve the aero-acoustics problems, which incorporates the Fast Multipole Method to solve large scale acoustics problems, Taylor’s transformation to account for uniform and non-uniform mean flow, impedance and non-local boundary conditions for the implementation of metamaterials. To validate BEM3D, the predictions have been benchmarked against the Finite Element Method (FEM) simulations and experimental data. It has been concluded that for no flow case BEM3D gives identical acoustics potential values against benchmarked FEM (COMSOL) predictions. For Mach number of 0.1, the BEM3D and FEM (COMSOL) predictions show small differences. The difference between BEM3D and FEM (COMSOL) predictions increases further for higher Mach number of 0.2 and 0.3. The increase in difference with Mach number is because Taylor’s Transformation gives an approximate solution for the boundary integral equation. Nevertheless, it has been concluded that Taylor’s transformation gives reasonable predictions for low Mach number of up to 0.3. BEM3D predictions have been validated against experimental data on a flat plate and a duct. Very good agreement has been found between the measured data and BEM3D predictions for sound propagation without and with the mean flow at low Mach number.

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Section: Bem3d For Aero-acoustic Problemsmentioning

confidence: 99%

Development of 3D boundary element method for the simulation of acoustic metamaterials/metasurfaces in mean flow for aerospace applications

Bashir

Carley

2020

International Journal of Aeroacoustics

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“…Karimi et al [12] found that applying the BEM to periodic structures leads to the formation of a block Toeplitz matrix due to the translational invariance of the free-space Green's function. The method is termed the periodic boundary element method and has been applied to problems with multi-directional periodicity [13], problems involving rotational symmetry [14] and aeroacoustic predictions of airfoils [15,16]. In the latter case, sequences of linear block Toeplitz systems are considered which are block Toeplitz systems with many right-hand sides.…”

Section: Introductionmentioning

confidence: 99%

Efficient solution of block Toeplitz systems with multiple right-hand sides arising from a periodic boundary element formulation

Jelich¹,

Karimi²,

Kessissoglou³

et al. 2021

Engineering Analysis with Boundary Elements

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Block Toeplitz matrices are a special class of matrices that exhibit reduced memory requirements and a reduced complexity of matrix-vector multiplications. We herein present an efficient computational approach to solve a sequence of block Toeplitz systems arising from a block Toeplitz system with multiple right-hand sides. Two different numerical schemes are implemented for the solution of the sequence of block Toeplitz systems based on global and block variants of the generalized minimal residual (GMRES) method. The performance of the schemes is assessed in terms of the wall clock time of the iterative solution process, the number of multiplications with the block Toeplitz system matrix and the peak memory usage. To demonstrate the method, two numerical examples are presented. In the first case study, aeroacoustic prediction of an airfoil in turbulent flow is examined, which requires multiple solutions of the wall pressure field beneath the turbulent boundary layer. The fluctuating pressure on the surface of the airfoil is synthesized in terms of uncorrelated wall plane waves, whereby each realization of the wall pressure field is an input to the acoustic solver based on the boundary element method (BEM). The total acoustic response from the airfoil in turbulent flow is then obtained from an ensemble average for the number of realizations considered. The number of realizations to yield a converged solution for the wall pressure field leads to a sequence of block Toeplitz systems. The second case study examines the nonlinear eigenvalue analysis of a sonic crystal barrier composed of locally resonant C-shaped sound-hard scatterers. The periodicity of the sound barrier leads to a block Toeplitz system matrix whereas the nonlinear eigenvalue problem requires the solution of sequences of linear systems. The combined technique to solve the sequences of block Toeplitz systems using the proposed variants of the GMRES is shown to yield a computationally efficient approach for flow noise prediction and nonlinear eigenvalue analysis.

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“…[2][3][4][5][6][7] The LES simulations are able to capture the fluctuating flow noise sources with great detail over a wide range of frequencies. [2][3][4][5][6][7] The LES simulations are able to capture the fluctuating flow noise sources with great detail over a wide range of frequencies.…”

Section: Introductionmentioning

confidence: 99%

“…Hybrid large eddy simulation (LES)-acoustic analogy techniques have been developed that provide a high-fidelity approach to predict the flow induced noise from a body submerged in the flow. [2][3][4][5][6][7] The LES simulations are able to capture the fluctuating flow noise sources with great detail over a wide range of frequencies. An incompressible large eddy simulation was performed by Wang and Moin 2 to simulate turbulent flow over a flat strut, with the predicted hydrodynamics comparing well with experimental results reported by Blake.…”

Section: Introductionmentioning

confidence: 99%

Numerical prediction of turbulent boundary layer noise from a sharp‐edged flat plate

Karimi

Croaker

Skvortsov

et al. 2019

Numerical Methods in Fluids

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Summary An efficient hybrid uncorrelated wall plane waves–boundary element method (UWPW‐BEM) technique is proposed to predict the flow‐induced noise from a structure in low Mach number turbulent flow. Reynolds‐averaged Navier‐Stokes equations are used to estimate the turbulent boundary layer parameters such as convective velocity, boundary layer thickness, and wall shear stress over the surface of the structure. The spectrum of the wall pressure fluctuations is evaluated from the turbulent boundary layer parameters and by using semi‐empirical models from literature. The wall pressure field underneath the turbulent boundary layer is synthesized by realizations of uncorrelated wall plane waves (UWPW). An acoustic BEM solver is then employed to compute the acoustic pressure scattered by the structure from the synthesized wall pressure field. Finally, the acoustic response of the structure in turbulent flow is obtained as an ensemble average of the acoustic pressures due to all realizations of uncorrelated plane waves. To demonstrate the hybrid UWPW‐BEM approach, the self‐noise generated by a flat plate in turbulent flow with Reynolds number based on chord Rec = 4.9 × 105 is predicted. The results are compared with those obtained from a large eddy simulation (LES)‐BEM technique as well as with experimental data from literature.

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Acoustic Scattering for Rotational and Translational Symmetric Structures in Nonuniform Potential Flow

Cited by 10 publications

References 32 publications

Development of 3D boundary element method for the simulation of acoustic metamaterials/metasurfaces in mean flow for aerospace applications

Development of 3D boundary element method for the simulation of acoustic metamaterials/metasurfaces in mean flow for aerospace applications

Efficient solution of block Toeplitz systems with multiple right-hand sides arising from a periodic boundary element formulation

Numerical prediction of turbulent boundary layer noise from a sharp‐edged flat plate

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