Green's Functions for the Acoustic Field in Lined Ducts with Uniform Flow

Alonso, Jose S.; Burdisso, Ricardo A.

doi:10.2514/1.29872

Cited by 16 publications

(15 citation statements)

References 13 publications

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“…Tester & de Mercato (2006) extended this work to a finite-length duct including the propagation to the far field, and demonstrate for a realistic intake geometry the complex far-field directivity patterns that can be caused by liner splices. A variant of this method was given by Alonso & Burdisso (2007), who considered pistons placed along the splice (with two pistons per wavelength) driven so as to approximately satisfy the rigid wall boundary condition on the splice. An approximation for resolving thin splices in time-domain simulations without overly refining the computational mesh, effectively a sub-grid-scale model, was proposed by Tam & Ju (2009).…”

Section: Introductionmentioning

confidence: 99%

Eigenmodes of lined flow ducts with rigid splices

Davis¹,

Peake²

2011

J. Fluid Mech.

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This paper presents an analytic expression for the acoustic eigenmodes of a cylindrical lined duct with rigid axially running splices in the presence of flow. The cylindrical duct is considered to be uniformly lined except for two symmetrically positioned axially running rigid liner splices. An exact analytic expression for the acoustic pressure eigenmodes is given in terms of an azimuthal Fourier sum, with the Fourier coefficients given by a recurrence relation. Since this expression is derived using a Green’s function method, the completeness of the expansion is guaranteed. A numerical procedure is described for solving this recurrence relation, which is found to converge exponentially with respect to number of Fourier terms used and is in practice quick to compute; this is then used to give several numerical examples for both uniform and sheared mean flow. An asymptotic expression is derived to directly calculate the pressure eigenmodes for thin splices. This asymptotic expression is shown to be quantitatively accurate for ducts with very thin splices of less than 1 % unlined area and qualitatively helpful for thicker splices of the order of 6 % unlined area. A thin splice is in some cases shown to increase the damping of certain acoustic modes. The influences of thin splices and thin boundary layers are compared and found to be of comparable magnitude for the parameters considered. Trapped modes at the splices are also identified and investigated.

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Section: Introductionmentioning

confidence: 99%

Eigenmodes of lined flow ducts with rigid splices

Davis¹,

Peake²

2011

J. Fluid Mech.

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“…The functions ϕ j (x)ϕ q (y) satisfy all four boundary conditions for a clamped plate and form a complete set of normal eigenvectors. 28 The duct pressure modes satisfying Equation (5) for a wave moving in the x-direction in a hard-walled infinite duct with a uniform mean flow are given by 29,30 p mn (x, y, z) = e −ik ±…”

Section: Iiia Solution Methodologymentioning

confidence: 99%

“…The continuity of pressure gives A + mn c + mn = −A − mn c − mn = A mn c mn . The reciprocity principle for a circular duct with uniform mean flow has been shown by Alonso et al 29 Their procedure can be extended to show the reciprocity principle in a rectangular duct with uniform mean flow. The governing equation is integrated along the axis to find the coefficients…”

Section: Appendix a Duct Modesmentioning

confidence: 98%

Coupled structural-acoustic response of a duct-mounted elastic plate with grazing flow

Sucheendran

Bodony

Geubelle

2012

18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference)

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We present an analytical solution for the fully coupled structural-acoustic response of a thin elastic plate mounted in a rectangular duct assuming linear dynamics and acoustics. The plate is subjected to harmonic planar acoustic waves at grazing incidence in the presence of a subsonic uniform mean flow in the duct. Both clamped and simply-supported plates are considered. We identify regimes in which the structural-acoustic coupling plays a significant role on the response of the plate. Four metrics characterizing the coupled response are considered: the deviation of the peak response frequency from the in vacuo natural frequency of plate, the amplitude of the peak response, the effective acoustic damping of the plate, and the plate modal coupling through the duct acoustic field. The method is also used to estimate the onset of instability in the structural response of a duct-mounted clamped-plate with flow for estimating the range of applicability of the theory. For a typical aerospace structure, the panel-fluid coupling does little to change the fundamental vibration frequencies from their in vacuo values but significantly alters the amplitudes of the plate vibration. This is a result of the acoustic radiation being a strong function of the in-duct flow Mach number M∞. Further, the inter-modal coupling through the acoustic field is also a strong function of M∞. Therefore, reduced order models relying on the panel's in vacuo modes require Mach number-dependent coupling coefficients for accurate predictions.

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“…with q 0 being the air mass density and G the Green's function for a point source in a hard-walled duct with uniform mean flow, which has been extensively studied. 11,12 So, the radiated sound pressure from the vibrating membrane in duct is given by…”

Section: Duct Acoustics With Mean Flowmentioning

confidence: 99%

“…The approach has been used to solve the radiation of a vibration source inside a duct with uniform mean flow. 11,12 The coupled response of a ductplate-cavity system in the presence of a subsonic uniform mean flow was obtained by Bodony 13 using Green's functions combined with the Galerkin method. Using the same method, Zhang et al 14 carried out theoretical investigations on a so-called drum-like silencer with mean flow, with focus put on the thermo-acoustic instability.…”

Section: Introductionmentioning

confidence: 99%

Analytical coupled vibro-acoustic modeling of a cavity-backed duct-membrane system with uniform mean flow

Liu

2018

The Journal of the Acoustical Society of America

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Sound propagation in a flow duct is a complex and technically challenging problem. The presence of flexible vibrating walls inside the duct creates additional difficulties to the problem due to the complex vibro-acoustic and aero-acoustic couplings involved in the system. An accurate prediction of the coupled system response is of great importance for a good understanding of the underlying physics as well as the optimal design of relevant noise suppression devices. In the present work, a unified energy formulation is proposed for the fully coupled structural-acoustic modelling of a duct-mounted membrane backed by an acoustic cavity with a grazing flow. Sufficiently smoothed admissible functions, taking the form of a combination of Fourier series and supplementary polynomials, are constructed to overcome the differential discontinuities for various boundary and/or coupling conditions. The formulation allows the obtention of all relevant vibro-acoustic field information in conjunction with the generalized Lighthill equation and Rayleigh-Ritz procedure. The validation and convergence studies show the accuracy and the efficiency of the proposed model. Results show the strong structural-acoustic interaction in such a duct-membrane-cavity system, and the flow affects resonant amplitude of membrane-dominant modes significantly. Some cross-zones can be observed for the membrane kinetic energy frequency response with low Mach number cases, especially when a higher tension is applied to the membrane. Analyses on the structural-acoustic coupling strength indicate that the coupling between the odd-even structural modes becomes more significant at a higher Mach number compared with odd-odd and even-even mode pairs. It is also shown that adjusting the boundary constraint of the membrane or imposing a higher tensile force allows impairing the adverse influence of the flow in the duct on sound attenuation. V

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Green's Functions for the Acoustic Field in Lined Ducts with Uniform Flow

Cited by 16 publications

References 13 publications

Eigenmodes of lined flow ducts with rigid splices

Eigenmodes of lined flow ducts with rigid splices

Coupled structural-acoustic response of a duct-mounted elastic plate with grazing flow

Analytical coupled vibro-acoustic modeling of a cavity-backed duct-membrane system with uniform mean flow

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