1999
DOI: 10.1017/s0022112098003607
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Sound transmission in slowly varying circular and annular lined ducts with flow

Abstract: Sound transmission through straight circular ducts with a uniform inviscid mean flow and a constant acoustic lining (impedance wall) is classically described by a modal expansion. A natural extension for ducts with axially slowly varying properties (diameter and mean flow, wall impedance) is a multiple-scales solution. It is shown in the present paper that a consistent approximation of boundary condition and isentropic mean flow allows the multiple-scales problem to have an exact solution. Since th… Show more

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Cited by 156 publications
(120 citation statements)
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“…We denote BC1 as the nonlocal boundary conditions at the inflow and outflow boundaries consisting of Eqs. (11), (22), (24), (27) and (28) at the inlet and Eqs. (11) and (23) at the exit.…”
Section: Boundary Condition Implementation For Incident Vortical and mentioning
confidence: 99%
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“…We denote BC1 as the nonlocal boundary conditions at the inflow and outflow boundaries consisting of Eqs. (11), (22), (24), (27) and (28) at the inlet and Eqs. (11) and (23) at the exit.…”
Section: Boundary Condition Implementation For Incident Vortical and mentioning
confidence: 99%
“…The propagation of disturbances in a nonuniform fully developed flow has been examined in [19][20][21] and the disturbances are governed by a nonconstant coefficient wave equation for the potential. Moreover, recent work [22][23][24] on the propagation of potential disturbances has shown that this model can also be easily extended to incorporate the effect of slow changes in the area of the duct in the high frequency limit. In what follows, we start with a potential mean flow and determine the conditions where the exact nonreflecting boundary conditions derived for a uniform mean flow can be extended to swirling flows.…”
Section: Inflow/outflow Boundary Conditions For Nonuniform Potential mentioning
confidence: 99%
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“…In many cases these ducts are axially non-uniform, but their properties vary relatively slowly with distance along the duct, and this allows asymptotic analysis to be used to derive simplified solutions. In this direction a key advance was made by Rienstra [1], who considered a circular lined duct with a mean flow with the duct radius varying slowly along the axis. Since then a number of extensions have been made, including to ducts of arbitrary cross section with mean flow [2], ducts with a mean swirling flow [3], curved ducts [4] and ducts carrying axially sheared vortical mean flow [5].…”
Section: Introductionmentioning
confidence: 99%
“…Early work concerning Webster's equation can be found in [7,27,28,32], and a selection of contemporary approaches is provided by [13,14,[21][22][23][24] and, in particular, by [25]. The derivation of Webster's equation in [23] (see also [20]) is based on asymptotic expansion that, however, does not give estimates for the approximation error.…”
Section: Introductionmentioning
confidence: 99%