Non-negative aeroacoustic source contributions to radiated sound power.

A new approach that determines the contribution of aeroacoustic sources to sound power is presented. The method combines the Lighthill source distribution with an acoustic impedance matrix constructed from radiation kernels of the free-field Green's function. To demonstrate the technique, the flow noise produced by a pair of co-rotating vortices is examined. Results are initially compared with those obtained using Möhring's analogy of two-dimensional vortex sound radiation. The contribution to sound power for each component of the Lighthill tensor is presented for a range of wave numbers and vortex separation distances. For acoustically compact cases, the aeroacoustic source contributions for the diagonal components of the Lighthill tensor show a similar trend observed in sound maps for longitudinal quadruples. In contrast to the acoustically compact cases where the central focal area is mostly unchanged with variation in Mach number, significant variation in the focal areas occurs for non-acoustically compact cases. Using the aeroacoustic source contribution technique, the nature and location of dominant flow noise sources to sound power can be identified.

A computational flow-induced noise and time-reversal technique for analysing aeroacoustic sources.

A simulation technique to analyse flow-induced noise problems that combines computational fluid dynamics (CFD), the boundary element method (BEM) and an aeroacoustic time-reversal (TR) source localisation method is presented. Hydrodynamic data are obtained from a high-fidelity CFD simulation of flow past a body and aeroacoustic sources are extracted based on Lighthill's acoustic analogy. The incident pressure field on the body due to the aeroacoustic sources is combined with a BEM representation of the body to obtain the spectrum of the direct, scattered and total acoustic pressure fields at far-field microphone locations. The microphone data are then used as input for the time-reversal simulations which are implemented by numerically solving two-dimensional linearized Euler equations. Decomposing the far-field pressure enables the TR simulation of the direct, scattered and total acoustic fields to be performed separately which yields the location and nature of the corresponding aeroacoustic sources. To demonstrate the hybrid CFD-BEM-TR technique, the sound generated by a cylinder in low Mach number cross-flow is considered. The nature of the aeroacoustic sources at the vortex shedding frequency and its second harmonic for the direct, scattered and total fields are identified.

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.

Non-negative intensity for coupled fluid-structure interaction problems using the fast multipole method.

The non-negative intensity (NNI) method is applied to large-scale coupled fluid-structure interaction (FSI) problems using the fast multipole boundary element method (FMBEM). The NNI provides a field on the radiating structure surface that consists of positive-only contributions to the radiated sound power, thus avoiding the near-field cancellation effects that otherwise occur with the sound intensity field. Thus far the NNI has been implemented with the boundary element method (BEM) for relatively small problem sizes to allow for the full BEM coefficient and inverse matrices to be explicitly constructed and stored. In this work, the FMBEM is adapted to the NNI by calculating the eigenvalue solution of the symmetric acoustic impedance matrix using the FMBEM via a two-stage solution method. The FMBEM implementation of the NNI is demonstrated for a large-scale model of a submerged cylindrical shell. The coupled FSI problem is first solved using a finite element-FMBEM model and the resulting surface fields are then used in the FMBEM calculation of the NNI. An equivalent reactive NNI field representing the evanescent near-field radiation is demonstrated and the effect of the chosen number eigenvectors on the NNI field is investigated.