Time-Domain Impedance Formulation Based on Recursive Convolution

Reymen, Yves; Baelmans, Martine; Desmet, Wim

doi:10.2514/6.2006-2685

Cited by 13 publications

(15 citation statements)

References 10 publications

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“…For this reason, the time-domain impedance boundary conditions are provided by means of a general parameter fitting method. 59,60 Assume a uniform relation for (19), (20), and (21),…”

Section: B Flow-acoustic Coupling Methods and Time-domain Impedance Mmentioning

confidence: 99%

Flow-excited acoustic resonance of a Helmholtz resonator: Discrete vortex model compared to experiments

Dai

Sun

2015

Physics of Fluids

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The acoustic resonance in a Helmholtz resonator excited by a low Mach number grazing flow is studied theoretically. The nonlinear numerical model is established by coupling the vortical motion at the cavity opening with the cavity acoustic mode through an explicit force balancing relation between the two sides of the opening. The vortical motion is modeled in the potential flow framework, in which the oscillating motion of the thin shear layer is described by an array of convected point vortices, and the unsteady vortex shedding is determined by the Kutta condition. The cavity acoustic mode is obtained from the one-dimensional acoustic propagation model, the time-domain equivalent of which is given by means of a broadband time-domain impedance model. The acoustic resistances due to radiation and viscous loss at the opening are also taken into account. The physical processes of the self-excited oscillations, at both resonance and off-resonance states, are simulated directly in the time domain. Results show that the shear layer exhibits a weak flapping motion at the off-resonance state, whereas it rolls up into large-scale vortex cores when resonances occur. Single and dual-vortex patterns are observed corresponding to the first and second hydrodynamic modes. The simulation also reveals different trajectories of the two vortices across the opening when the first and second hydrodynamic modes co-exist. The strong modulation of the shed vorticity by the acoustic feedback at the resonance state is demonstrated. The model overestimates the pressure pulsation amplitude by a factor 2, which is expected to be due to the turbulence of the flow which is not taken into account. The model neglects vortex shedding at the downstream and side edges of the cavity. This will also result in an overestimation of the pulsation amplitude.

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“…For this reason, the time-domain impedance boundary conditions are provided by means of a general parameter fitting method. 59,60 Assume a uniform relation for (19), (20), and (21),…”

Section: B Flow-acoustic Coupling Methods and Time-domain Impedance Mmentioning

confidence: 99%

Flow-excited acoustic resonance of a Helmholtz resonator: Discrete vortex model compared to experiments

Dai

Sun

2015

Physics of Fluids

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“…To account for impedance ground surfaces, we use in this study a time-domain boundary-condition (TDBC) derived by Reymen et al (2006) on the basis of work done in electromagnetism (Luebbers and Hunsberger, 1992). This TDBC has been introduced in outdoor sound propagation community by Cott e et al (2009) and is general in that it is not based on any impedance model.…”

Section: Impedance Groundmentioning

confidence: 99%

“…The causality condition is verified for this type of impedance model if and only if the real parts of k k are positive (Reymen et al, 2006). The condition Re½ZðxÞ > 0 for x > 0 must be checked for each set of coefficients (A k ,k k ).…”

Section: Impedance Groundmentioning

confidence: 99%

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Time-domain solver in curvilinear coordinates for outdoor sound propagation over complex terrain

Dragna

Blanc‐Benon

Poisson

2013

The Journal of the Acoustical Society of America

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The current work aims at developing a linearized Euler equations solver in curvilinear coordinates to account for the effects of topography on sound propagation. In applications for transportation noise, the propagation environment as well as the description of acoustic sources is complex, and time-domain methods have proved their capability to deal with both atmospheric and ground effects. First, equations in curvilinear coordinates are examined. Then time-domain boundary conditions initially proposed for a Cartesian coordinate system are implemented in the curvilinear solver. Two test cases dealing with acoustic scattering by an impedance cylinder in a two-dimensional geometry and by an impedance sphere in a three-dimensional geometry are considered to validate the boundary conditions. Accurate solutions are obtained for both rigid and impedance surfaces. Finally, the solver is used to examine a typical outdoor sound propagation problem. It is shown that it is well-suited to study coupled effects of topography, mixed impedance ground and meteorological conditions.

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“…Borrowed from the computational electromagnetic community, 13 so-called "recursive" (recurrent) convolution techniques have been employed by many authors. 14,15,16,8,17 Bin et al 18 used an alternative implementation, relying instead on N additional differential equations. A comprehensive study by Dragna et al 19 showed the benefit of this technique, known as the auxiliary differential 1 Electronic mail: florian.monteghetti@onera.fr 1 equations method, over recursive convolution.…”

Section: Introductionmentioning

confidence: 99%

Design of broadband time-domain impedance boundary conditions using the oscillatory-diffusive representation of acoustical models

Monteghetti

Matignon

Piot

et al. 2016

The Journal of the Acoustical Society of America

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A methodology to design broadband time-domain impedance boundary conditions (TDIBCs) from the analysis of acoustical models is presented. The derived TDIBCs are recast exclusively as first-order differential equations, well-suited for high-order numerical simulations. Broadband approximations are yielded from an elementary linear least squares optimization that is, for most models, independent of the absorbing material geometry. This methodology relies on a mathematical technique referred to as the oscillatory-diffusive (or poles and cuts) representation, and is applied to a wide range of acoustical models, drawn from duct acoustics and outdoor sound propagation, which covers perforates, semi-infinite ground layers, as well as cavities filled with a porous medium. It is shown that each of these impedance models leads to a different TDIBC. Comparison with existing numerical models, such as multi-pole or extended Helmholtz resonator, provides insights into their suitability. Additionally, the broadly-applicable fractional polynomial impedance models are analyzed using fractional calculus.

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Time-Domain Impedance Formulation Based on Recursive Convolution

Cited by 13 publications

References 10 publications

Flow-excited acoustic resonance of a Helmholtz resonator: Discrete vortex model compared to experiments

Flow-excited acoustic resonance of a Helmholtz resonator: Discrete vortex model compared to experiments

Time-domain solver in curvilinear coordinates for outdoor sound propagation over complex terrain

Design of broadband time-domain impedance boundary conditions using the oscillatory-diffusive representation of acoustical models

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