Acoustic Resonance in Aeroengine Intake Ducts

[+] Author and Article Information
A. J. Cooper

School of Engineering, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK

A. B. Parry

Rolls-Royce plc, P.O. Box 31, Derby DE24 8BJ, UK

N. Peake

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK

J. Turbomach 126(3), 432-441 (Sep 03, 2004) (10 pages) doi:10.1115/1.1776586 History: Received April 01, 2003; Revised February 01, 2004; Online September 03, 2004
Copyright © 2004 by ASME
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Grahic Jump Location
(a) Contours of ln(RCond) when m=−2,L=0.7 and MΩ=0.5W/Wmax. The dashed lines denote fan speeds at which RCond displays a sharp minimum corresponding to numerical singularity. The variation in RCond at these fan speeds is shown in the subplots (b) W/Wmax=0.575, (c) W/Wmax=0.775, (d) W/Wmax=0.885.
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Effect of wall impedance on the parameter |T| defined in Eq. (10), when m=2,W/Wmax=0.5, ω=2.5. Solid line: Z2=λ−i; dashed line: Z2=4−λi.
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Solid lines show when the resonance condition is satisfied for m=2 with the intake shape given by Eq. (6) and Eq. (7). Dashed lines show the frequencies ω12 and ω3. Region A corresponds to the behavior shown in Fig. 1(a) and here |K|=1. Region B denotes the situation in Fig. 1(b). Region C corresponds to the case in Fig. 1(c) and here |K|=1/|R|.
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Intake shape used in examples. The duct dimensions at the fan, inlet and throat (denoted here by Rc) are important aspects of the duct shape which define the frequency ranges for the cut on/cut off characteristics shown in Fig. 1.
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Effect of rotor-stator gap length, L, on the narrow-band resonance for m=3. Lines correspond to fan speeds where |K|=1 along the line ω=ω1.
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Effect of degree of mean swirl on the resonance bands for m=2, where MΩ=kW/Wmax. Lines correspond to fan speeds where |K|=1 along the line ω=ω1.
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Frequencies and fan speeds corresponding to potential acoustic resonance in an arbitrary intake. Dashed lines denote the frequency range for which there is, at most, one mode cut on along the duct. The lower line is ω1, and the upper line is ω4. The shaded (gray) regions correspond to |K|>1, the edges of the bands are where |K|=1, and elsewhere |K|<1. (a) m=2, (b) m=3, (c) m=4, (d) m=5.
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Variation in the real part of the reduced axial wave number, σ, of the first radial mode along a slowly varying duct. Solid lines represent right-propagating modes and dashed lines left-propagating modes; modes are cut off when Re(σ)=0. (a) Single turning point upstream of the fan, ω1<ω<ω2, (b) two turning points in the intake, ω2<ω<ω3, (c) mode cut on along the entire length of the duct, ω3<ω<ω4. All higher-order radial modes are cut off when ω<ω4. Duct inlet is located at x=0 and fan located at x=xf.



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