Michael Carley

Numerical Quadratures for Singular and Hypersingular Integrals in Boundary Element Methods

A method is developed for the computation of the weights and nodes of a numerical quadrature which integrates functions containing singularities up to order

Acoustic Velocity Formulation for Sources in Arbitrary Motion

1/x^{2}

Series expansion for the sound field of rotating sources

, without the requirement to know the coefficients of the singularities exactly. The work is motivated by the need to evaluate such integrals on boundary elements in potential problems and is a simplification of a previously published method, but with the advantage of handling singularities at the endpoints of the integral. The numerical performance of the method is demonstrated by application to an integral containing logarithmic, first, and second order singularities, characteristic of the problems encountered in integrating a Greens function in boundary element problems. It is found that the quadrature is accurate to 11-12 decimal places when computed in double precision.

Inversion of spinning sound fields.

This paper deals with the acoustic velocity field simulation generated by interaction of flow with moving bodies. Starting from the Ffowcs Williams and Hawkings equation, an analytical formulation of the acoustic velocity is derived for sources in arbitrary motion. This makes the imposition of the boundary condition on a (rigid) scattering surface much more straightforward, as, if the traditional pressure formulation is used, then the pressure gradient must be calculated. Computational results for a pulsating sphere, dipole source, and a propeller case with subsonic tips verify this formulation.

Series expansion for the sound field of a ring source

A method is derived for the fast, exact prediction of acoustic fields around rotating sources by using a series expansion which generalizes a previously published method for a circular piston. The technique gives exact predictions for the field outside the sphere containing the rotor in a computational time two orders of magnitude less than that required for direct numerical evaluation of the acoustic integrals. Its use is demonstrated by application to two sample problems characteristic of real aircraft propellers.

Analytical formulae for potential integrals on triangles

A method is presented for the reconstruction of rotating monopole source distributions using acoustic pressures measured on a sideline parallel to the source axis. The method requires no a priori assumptions about the source other than that its strength at the frequency of interest varies sinusoidally in azimuth on the source disk so that the radiated acoustic field is composed of a single circumferential mode. When multiple azimuthal modes are present, the acoustic field can be decomposed into azimuthal modes and the method applied to each mode in sequence. The method proceeds in two stages, first finding an intermediate line source derived from the source distribution and then inverting this line source to find the radial variation in source strength. A far-field form of the radiation integrals is derived, showing that the far-field pressure is a band-limited Fourier transform of the line source, establishing a limit on the quality of source reconstruction, which can be achieved using far-field measurements. The method is applied to simulated data representing wind-tunnel testing of a ducted rotor system (tip Mach number of 0.74) and to control of noise from an automotive cooling fan (tip Mach number of 0.14), studies which have appeared in the literature of source identification.

Aeroacoustic sources of motorcycle helmet noise

An exact series expansion for the field radiated by a monopole ring source with angular variation in source strength is derived from a previously developed expression for the field from a finite disk. The derived series can be used throughout the field, via the use of a reciprocity relation, and can be readily integrated to find the field radiated by arbitrary circular sources of finite extent, and differentiated to find the field due to higher order sources such as dipoles and quadrupoles.

Scattering by quasi-symmetric pipes

The problem of evaluating potential integrals on planar triangular elements has been addressed using a polar coordinate decomposition, giving explicit formulae for the regular and for the principal value and finite part integrals used in hypersingular formulations. The resulting formulae are general, exact, easily implemented, and have only one special case, that of a field point lying in the plane of the element. Results are presented for the evaluation of the potential and its gradients, where the integrals must be treated as principal values or finite parts, for elements with constant and linearly varying source terms. These results are tested by application to a single triangular element to the evaluation of the potential gradient outside the unit cube. In both cases, the method is shown to be accurate and convergent.

Aeroacoustics research in Europe: The CEAS-ASC report on 2013 highlights

The prevalence of noise in the riding of motorcycles has been a source of concern to both riders and researchers in recent times. Detailed flow field information will allow insight into the flow mechanisms responsible for the production of sound within motorcycle helmets. Flow field surveys of this nature are not found in the available literature which has tended to focus on sound pressure levels at ear as these are of interest for noise exposure legislation. A detailed flow survey of a commercial motorcycle helmet has been carried out in combination with surface pressure measurements and at ear acoustics. Three potential noise source regions are investigated, namely, the helmet wake, the surface boundary layer and the cavity under the helmet at the chin bar. Extensive information is provided on the structure of the helmet wake including its frequency content. While the wake and boundary layer flows showed negligible contributions to at-ear sound the cavity region around the chin bar was identified as a key noise source. The contribution of the cavity region was investigated as a function of flow speed and helmet angle both of which are shown to be key factors governing the sound produced by this region.

Noise mechanisms in motorcycle helmet noise

A hypersingular boundary integral method for the prediction of radiation from a straight circular pipe with arbitrary end profile has been developed. The technique represents an extension of established procedures for axisymmetric pipes with the addition of recent advances in special function and quadrature theory to simplify the implementation. The resulting code is applied to two sample problems: first, the prediction of radiation of a plane wave mode from a pipe with its ends cut by an inclined plane, representing the “scarfed intake” proposed for reduction of aircraft engine noise. Second, the method is used to examine scattering of an incident azimuthal mode by a multi-lobed profile, characteristic of the “chevron” nozzles proposed for jet engine exhausts.