On Sound Generation in Cylindrical Flow Ducts with Non-Uniform Wall Impedance

Abstract

The use of acoustic liners is a common means of noise reduction in jet engine exhausts. The quest for more effective sound absorption mechanisms in cylindrical ducts has led to the consideration of non-uniform liners, with impedance varying circumferentially, axially, or in both directions. The present paper is based on the theory of mode coupling in a non-uniformly lined cylindrical duct and considers the complementary problem of generation of sound or excitation of coupled modes by a source distribution. The sound field due to an arbitrary source distribution is obtained as a superposition of eigenfunctions corresponding to complex eigenvalues for the radial wavenumbers and natural frequencies taking into account that the radial, axial and azimuthal modes are coupled by the non-uniform wall impedance, and including resonant and non-resonant cases. The waveforms are illustrated for point monopole, dipole and quadrupole sources and a continuous monopole distribution. It is shown that a non-uniform liner provides a greater attenuation than a uniform liner with the same average impedance if it is 'well-matched' to the sound field, that is, if it has higher impedance at the peaks and lower at the nodes of the standing modes.

Sound propagation in a lined nozzle with shear and bias flows

“…The implications are that these non-sinusoidal acoustic-shear waves unlike sound rays can exchange energy with the mean flow. Thus, the sound attenuation by the wall liners [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] is coupled to acoustic-shear waves in the boundary layer that are of second-order as for sound in the absence of cross-flow, that is not considered in most of the aeroacoustic literature. The inclusion of a cross-flow raises the order of the acoustic wave equation from two to three, implying the existence of a third "vortical" mode in the boundary layer in addition to the two acoustic waves.…”

“…[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] In order to reduce noise, the nozzle walls often use liners that, if locally reacting, can be represented by an impedance distribution. [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] The bias flow out perforated liners can have a significant effect on sound in a boundary layer 42 even for small velocities. The boundary layer may be modeled as a "double deck," with a shear flow matched to a uniform stream.…”

On Physical Aeroacoustics with Some Implications for Low-Noise Aircraft Design and Airport Operations

“…The account on sound transmission from the aircraft noise sources to the interior of the near airport resident (Section 3) has included: (i) the spectral and directional broadening of noise [255][256][257][258][259][260][261]; (ii) the psychoacoustic distinctions between noise components. The noise mitigation measures (Section 4) mentioned include: (i) optimization of non-uniform acoustic liners [406][407][408][409][410][411][412][413][414][415][416] and use of partial chevron nozzle [417]; (ii) low noise operating procedures [432,433] consistent with flight safety and air traffic management rules [444][445][446][447][448][449][450][451][452][453][454]. Both can reduce noise exposure near airports [346][347][348][349][350][351][352][353][354][355][356][357]…”

“…The noise reduction provided by acoustic liners involves several penalties: (i) increased drag, hence loss of thrust, increased fuel consumption and emissions; (ii) the weight, volume, cost, installation and eventual maintenance or refurbishment of the liner. For a given weight or area of acoustic liner it is desirable to maximize the noise reduction by using [400][401][402][403][404][405][406][407][408][409][410][411][412][413][414][415][416] non-uniform liners tailored (Figure 12) to have higher impedance in regions of peak noise levels and lower impedance in regions of low noise. This tailoring of the non-uniform impedance of the liner to the sound field, may lead to adaptive liners, since the noise field of an engine changes with flight condition.…”

“…Thus an acoustic liner is a palliative or compromise solution, and should be optimized to give the best possible noise reduction with the least penalty by: (i) using the lining at the most effective locations; (ii) optimizing the impedance distribution (a) to absorb more sound at the peaks and less at the thoughts of the sound wave. For the same amount of liner material the optimized non-uniform liner [416] leads to a greater noise reduction by absorbing preferentially the noise peaks. The noise spectrum of an engine changes with thrust and flight condition and optimal noise attenuation would be achieved by an adaptive liner, with impedance distribution adjustable to the noise field to be absorbed.…”