The problem of the transmission of sound in a duct with very thin shear layers at the walls is treated by an inner expansion method. The results show that the formulation of the problem of the transmission of sound in a duct with a shear layer at the wall converges, in the case of a vanishingly thin shear layer, to the formulation of the same problem when uniform flow is assumed and the wall boundary condition is that of continuity of particle displacement.
The impedance properties of acoustic duct liners are affected by airflow in the duct. Measurements have shown that interactions between the duct flow and the acoustically induced flow at and within the acoustic liners can cause significant changes in the effective liner impedance. Acoustic measurements in a flow environment are used to develop acoustic impedance mathematical models for use in lining design. These impedance measurements are made in a 2 × 2-in. cross-section flow duct using waveguide principles. The design of the duct and the data analysis technique are based on solution of the convected wave equation in an infinite waveguide. The sheared boundary layer velocity profiles in the duct are measured and used to calculate the acoustic impedance of the liner. Examples of measured attenuation and phase rate data are presented which show effects of duct flow velocity and wall impedance. A comparison with standing-wave impedance tube measurements in the limiting case at zero flow is also presented.
Representatives of the family Strephocladidae have been considered as fossil relatives (i.e., stem-group) of Mantodea (mantises) based on characters of the forewing morphology. Here we describe new specimens from the Wellington Formation that we assign to the strephocladid species Homocladus grandis Carpenter, 1966. The range of morphological variation exhibited by the new material, in addition to wing morphology variability documented in extant mantises and roaches, suggest that H. ornatus Carpenter, 1966 and Paracladus retardatus Carpenter, 1966, reported from the same formation, are new junior subjective synonyms of H. grandis. We describe the first hind wing for this species based on a well-preserved specimen. It exhibits a combination of character states unique to dictyopteran insects.
The inviscid compressible flow stability problem is mathematically similar to that of sound propagation in a sheared flow field. This similarity has been exploited by applying an inner expansion technique to study the effect of finite shear gradients on free parallel flow instabilities. This technique had previously been used to investigate the effect of thin boundary layers on sound propagation in ducts. The expansion, which is applicable to flow profiles involving thin, but finite, shear layers separating regions of uniform flow, offers a significant computational advantage over the numerical methods commonly employed to determine the stability of continuous mean flow profiles. Although equally applicable to three-dimensional and to spatially growing hydrodynamic instabilities, the procedure is demonstrated by application to the eigenvalue problem for temporal instabilities of shear layers and jets in plane inviscid compressible flow.For the case of vanishingly thin shear layers, the eigenvalue equations derived here reduce to those obtained by Miles (1958) for parallel flows bounded by vortex sheets. The series solution of Graham & Graham (1969), valid for linear shear-layer profiles of arbitrary thickness, provides a basis of comparison for the expansion-method results. Unstable-mode eigenvalues obtained using the two methods are found to be in good agreement for a significant range of values of the ratio of shear-layer thickness to axial wavelength.
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