M. Karimi

Acoustic scattering for 3D multi-directional periodic structures using the boundary element method

An efficient boundary element formulation is proposed to solve three-dimensional exterior acoustic scattering problems with multi-directional periodicity. The multi-directional periodic acoustic problem is represented as a multilevel block Toeplitz matrix. By exploiting the Toeplitz structure, the computational time and storage requirements to construct and to solve the linear system of equations arising from the boundary element formulation are significantly reduced. The generalized minimal residual method is implemented to solve the linear system of equations. To efficiently calculate the matrix-vector product in the iterative algorithm, the original matrix is embedded into a multilevel block circulant matrix. A multi-dimensional discrete Fourier transform is then employed to accelerate the matrix-vector product. The proposed approach is applicable to a periodic acoustic problem for any arbitrary shape of the structure in both full space and half space. Two case studies involving sonic crystal barriers are presented. In the first case study, a sonic crystal barrier comprising rigid cylindrical scatterers is modeled. To demonstrate the effectiveness of the proposed technique, periodicity in one, two, or three directions is examined. In the second case study, the acoustic performance of a sonic crystal barrier with locally resonant C-shaped scatterers is studied.

Effect of a serrated trailing edge on sound radiation from nearby quadrupoles

A periodic boundary element technique is implemented to study the noise reduction capability of a plate with a serrated trailing edge under quadrupole excitation. It is assumed for this purpose that the quadrupole source tensor is independent of the trailing edge configuration and that the effect of the trailing edge shape is to modify sound radiation from prescribed boundary layer sources. The flat plate is modelled as a continuous structure with a finite repetition of small spanwise segments. The matrix equation formulated by the periodic boundary element method for this 3D acoustic scattering problem is represented as a block Toeplitz matrix. The discrete Fourier transform is employed in an iterative algorithm to solve the block Toeplitz system. The noise reduction mechanism for a serrated trailing edge in the near field is investigated by comparing contour plots obtained from each component of the quadrupole for unserrated and serrated trailing edge plate models. The noise reduction due to the serrated trailing edge is also examined as a function of the source location.

Acoustic scattering for rotational and translational symmetric structures in nonuniform potential flow

© Copyright 2017 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. An efficient approach is proposed to predict acoustic scattering with nonuniform potential flow effects for structures with rotational and translational symmetries. The convected wave equation is transformed to Helmholtz and Laplace equations using a time transformation. The boundary-element method is used to formulate scattering by rotationally symmetric structures as two separate block circulant matrix equations and, similarly, as two separate block Toeplitz matrix equations for structures with translational symmetry. Discrete Fourier transform is employed to solve the block circulant systems. The block Toeplitz systems are solved using the generalized minimal residual method along with the discrete Fourier transform. Solving the convected wave equation using structured matrices significantly reduces computational time and storage requirements. To demonstrate the application of the formulation, two exterior acoustic case studies are considered. The first case study examines acoustic scattering from a sphere submerged in potential flow under monopole source excitation. Directivity plots obtained using the proposed technique are compared with analytical results. The second case study examines flow-induced noise generated by a rigid cylinder immersed in low-Mach-number flow, with the effect of mean flow on the scattered acoustic field taken into account using nonuniform potential flow. The fluctuating flowfield is obtained using an incompressible computational fluid dynamics solver. Acoustic sources based on Lighthills analogy are extracted from the flowfield data using a high-order reconstruction scheme. Results from the hybrid computational fluid dynamics-boundaryelement method technique are presented for turbulent flow past the cylinder, with Reynolds number based on cylinder diameter of ReD = 46;000 and Mach numberM = 0.21. The aeroacoustic results are compared with data from literature.

Aeroacoustic analysis of a cylinder in low mach number flow using a periodic CFD-BEM technique

© 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.The flow-induced noise generated by a rigid cylinder immersed in low Mach number flow is predicted using a hybrid computational fluid dynamics (CFD)-boundary element method (BEM) technique. The fluctuating flow field is obtained using an incompressible CFD solver. A high-order reconstruction scheme is used to extract acoustic sources based on Lighthills acoustic analogy from the flow field data. The convected wave equation is transformed to Helmholtz and Laplace equations, with the effect of the mean flow on the scattered acoustic field taken into account using non-uniform potential flow. A periodic BEM technique is used to formulate the acoustic problem as two separate block Toeplitz systems. Solving the aeroacoustic problem using block Toeplitz systems significantly reduces computational time and storage requirements. The generalized minimal residual method is then employed along with the discrete Fourier transform to solve the block Toeplitz systems. The results from the hybrid CFD-BEM technique are presented for turbulent flow past a circular cylinder, with Reynolds number based on the cylinder diameter of ReD= 46000 and Mach number M=0.21. The aeroacoustic results are compared with experimental data from literature.

Numerical and Experimental Investigation of the Flow-Induced Noise of a Wall-Mounted Airfoil

A numerical and experimental investigation into the flow field around a finite wall-mounted airfoil is presented. Measurements were performed in an open-jet anechoic wind tunnel for a finite wall-mounted NACA 0012 airfoil with an aspect ratio of one. The airfoil was tested at zero degree angle of attack, with a Mach number of 0.06 and Reynolds number based on chord of 274,000. The measurements include single hotwire anemometry in the near-wake of the airfoil at a number of locations in the mid-span and tip regions. A large eddy simulation (LES) of flow past the airfoil was performed, and good agreement with measurements was obtained. Based on Lighthill’s acoustic analogy, flow-induced noise sources were then extracted from the LES data. Sound radiation to the far-field and the incident acoustic pressure on the airfoil were both predicted using a near-field formulation for the aeroacoustic pressure. The boundary element method (BEM) was then used to predict the scattering of the incident pressure field by the airfoil as well as the total far-field acoustic pressure.

Trailing-Edge Noise Prediction Using a Periodic BEM Technique

The noise generated by a sharp-edged strut under quadrupole excitation is predicted using a periodic boundary element method technique. The strut is considered as a continuous periodic structure so that the matrix equation formulated by periodic boundary element method for this acoustic scattering problem is a block Toeplitz matrix. By exploiting the Toeplitz structure, the computational time and storage requirements for constructing the coefficient matrix are significantly reduced. The original matrix is embedded into a larger and more structured matrix called the block circulant matrix. Discrete Fourier Transform is then employed in an iterative algorithm to solve the block Toeplitz system. Directivity plots obtained using the proposed method are compared with numerical results obtained using a conventional boundary element model.