Rigid-walled Duct Research Articles

The effects of flow and geometry on the acoustic characteristics of bends

A two‐dimensional finite element technique was used to investigate the acoustic characteristics of 90° bends for plane wave and for cross‐mode propagation. An experimental procedure was also developed which permitted measurement of these characteristics in terms of rigid walled duct modes when several higher order modes were admitted simultaneously. Numerical and experimental results displayed excellent agreement over a range of frequencies extending to the cut‐on value of the third cross mode. Characteristics were studied in terms of modal amplitudes of the reflected and transmitted waves and in terms of the corresponding energy coefficients. The energy transfer was also examined for the case when an evanescent mode was incident on a mitred bend. The influence of changes in geometry was established over a range of inner and outer radii and the effects of locating a turning vane in the bend were also examined. The energy reflected was related, where possible, to published aerodynamic characteristics. The effects of a mean compressible flow on the acoustic characteristics was examined for one geometry.

Ducts with axial temperature gradients: An approximate solution for sound transmission and generation

This paper is concerned with rigid-walled ducts in which axial temperature gradients exist. An acoustic wave equation is derived (an independently specified source distribution is assumed to be present) and its solution is discussed. It is shown that an approximate analytical solution, valid at sufficiently high frequencies, may be obtained for the fundamental mode of propagation, and that this has certain advantages over a purely numerical solution. Experimental results on sound transmission and generation are compared to numerical, and approximate analytical, theoretical results and the agreement is shown to be good.

Acoustical Characteristics of an Open-Ended Duct with Flow

The acoustical characteristics of an open-ended, rigid-walled duct carrying flows with mean velocities up to half the speed of sound have been studied. The pressure reflection coefficients from the upstream and downstream ends of the duct have been measured, and the results have been used in the evaluation of the Green's function for the duct. The bandwidths of the duct resonances have been determined as a function of the Mach number, and it is demonstrated that the resonances practically disappear at sufficiently high Mach numbers. The steady-state pressure distribution in a duct from a source inside the duct is measured, as well as the response of the duct to an external sound source. The results are discussed in the light of calculated results. [This work was supported by the U.S. Navy (Office of Naval Research) by Contract N00014-67-A-0204-0019.]

Infinitesimal and Finite-Amplitude Effects in a Real Duct

Further measurements of the nonlinear behavior of standing waves in an air-filled rigid-walled duct were carried out in an effort to test the agreement between theoretical development of Coppens-Sanders and experimental results for standing-wave amplitudes near shock formation. The pressure waveforms observed at the rigid end of a 6-ft tube driven near its gravest mode were recorded on analog tape, digitized, and Fourier analyzed for all harmonic components with amplitudes greater than 1% of the fundamental. It was found that, while the shapes of the experimental curves were in essential agreement with the theoretical predictions, the frequency at which each harmonic peaked was greater than that predicted, the difference becoming greater as harmonic number increased. These results inspired a careful restudy of the infinitesimal-amplitude behavior of the duct. It was found that while the experimental attenuation coefficients agreed with those predicted by the Rayleigh-Kirchhoff treatment of wall losses (at least up to frequencies for which cross modes are possible), the experimentally determined phase speeds differed. The direction and amounts of these differences seem sufficient to explain the discrepancy between experiment and the finite-amplitude predictions. The finite-amplitude theory was generalized by replacing the Rayleigh-Kirchhoff predictions with the observed infinitesimal amplitude behavior of the system.

On the Propagation of Sound Waves in an Axisymmetric Viscous Flow Bounded by an Elastic Cylindrical Duct

In this paper, the problem of propagation of sound waves in a viscous fluid moving through a cylindrical duct bounded by elastic walls is pursued. The field equations are the linearized variational equations of the conservation equations of gas dynamics in which the viscous shear terms and thermal losses are retained. Solutions of the field equations in this form yield the effects of the coupling of shear flow, heat transfer, fluid motion, and wall response on the propagation and attenuation of sound waves through the cylindrical duct. Specifically the problem of the axisymmetric velocity field is being investigated for rigid walls and for elastic walls. Solutions to these problems are obtained numerically and the first few modes of flow, viscosity, and impedance on the wave parameters and the propagation and attenuation of the sound waves through the duct. These results are compared with the stationary fluid, the nonviscous fluid and the case of rigid wall duct.