Simulation of Reflection and Transmission Properties of Multiperforated Acoustic Liners

Semin, Adrien; Thöns‐Zueva, Anastasia; Schmidt, Kersten

doi:10.1007/978-3-319-63082-3_9

Cited by 2 publications

(3 citation statements)

References 7 publications

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“…We model the array by the impedance boundary conditions in (2.12) and compare it to the boundary conditions according to Guess We use the formulation for the acoustic pressure, see (2.12), with a source term corresponding to an incoming field p inc (r, θ, z) = exp(iωz/c) from the left. The scattered field is computed numerically using the mode matching procedure as described in a previous work [52] with N = 5 radial modes. We computed the eigenmodes numerically using the C++ Finite Elements Library CONCEPTS [17,13].…”

Section: Dissipation By An Array Of Helmholtz Resonators In a Ductmentioning

confidence: 99%

Surface homogenization of an array of Helmholtz resonators for a viscoacoustic model using two-scale convergence

Schmidt,

Semin

2020

Preprint

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We derive the weak limit of a linear viscoacoustic model in an acoustic liner that is a chamber connected to a periodic repetition of elongated chambers -the Helmholtz resonators. As model we consider the time-harmonic and linearized compressible Navier-Stokes equations for the acoustic velocity and pressure. Following the approach in Schmidt et al., J. Math. Ind 8:15, 2018 for the viscoacoustic transmission problem of multiperforated plates the viscosity is scaled as δ 4 with the period δ of the array of chambers and the size of the necks as well as the wall thickness like δ 2 such that the viscous boundary layers are of the order of the size of the necks. Applying the method of two-scale convergence we obtain with a stability assumption in the limit δ → 0 that the acoustic pressure fulfills the Helmholz equation with impedance boundary conditions. These boundary conditions depend on the frequency, the length of the resonators and through the effective Rayleigh conductivity -that can be computed numerically -on the shape of their necks. We compare the limit model to semi-analytical models in the literature.

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Section: Dissipation By An Array Of Helmholtz Resonators In a Ductmentioning

confidence: 99%

Surface homogenization of an array of Helmholtz resonators for a viscoacoustic model using two-scale convergence

Schmidt,

Semin

2020

Preprint

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“…It appears that the outward flux of the imaginary part of ṽ over Γ + (S) is negative (resp. positive over Γ − (S)) corresponding to a positive real part of the approximate Rayleigh conductivity k R (S) (see (24)) and so of the Rayleigh conductivity k R . This is in line with the inviscid case, where k R is real and positive.…”

Section: Numerical Computation Of K Rmentioning

confidence: 99%

“…This setup is also simulated numerically using the equivalent problem (22a)-(22b) for the pressure with a source term corresponding to an incoming field p inc (r, θ, z) = exp(ıωz/c) from the left. The scattered field is computed numerically using the mode matching procedure with N = 5 modes [24]: we seek for the scattered field p 0 under the form (see Fig. 9(b))…”

Section: Numerical Simulation Of Dissipation Lossesmentioning

confidence: 99%

On impedance conditions for circular multiperforated acoustic liners

et al. 2018

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Background The acoustic damping in gas turbines and aero-engines relies to a great extent on acoustic liners that consists of a cavity and a perforated face sheet. The prediction of the impedance of the liners by direct numerical simulation is nowadays not feasible due to the hundreds to thousands repetitions of tiny holes. We introduce a procedure to numerically obtain the Rayleigh conductivity for acoustic liners for viscous gases at rest, and with it define the acoustic impedance of the perforated sheet. ResultsThe proposed method decouples the effects that are dominant on different scales: (a) viscous and incompressible flow at the scale of one hole, (b) inviscid and incompressible flow at the scale of the hole pattern, and (c) inviscid and compressible flow at the scale of the wave-length. With the method of matched asymptotic expansions we couple the different scales and eventually obtain effective impedance conditions on the macroscopic scale. For this the effective Rayleigh conductivity results by numerical solution of an instationary Stokes problem in frequency domain around one hole with prescribed pressure at infinite distance to the aperture. It depends on hole shape, frequency, mean density and viscosity divided by the area of the periodicity cell. This enables us to estimate dissipation losses and transmission properties, that we compare with acoustic measurements in a duct acoustic test rig with a circular cross-section by DLR Berlin.Conclusions A precise and reasonable definition of an effective Rayleigh conductivity at the scale of one hole is proposed and impedance conditions for the macroscopic pressure or velocity are derived in a systematic procedure. The comparison with experiments show that the derived impedance conditions give a good prediction of the dissipation losses.

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Simulation of Reflection and Transmission Properties of Multiperforated Acoustic Liners

Cited by 2 publications

References 7 publications

Surface homogenization of an array of Helmholtz resonators for a viscoacoustic model using two-scale convergence

Surface homogenization of an array of Helmholtz resonators for a viscoacoustic model using two-scale convergence

On impedance conditions for circular multiperforated acoustic liners

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