Showing papers by "Gwenael Gabard published in 2022"

Compact resonant systems for perfect and broadband sound absorption in wide waveguides in transmission problems

Abstract: This work deals with wave absorption in reciprocal asymmetric scattering problem by addressing the acoustic problem of compact absorbers for perfect unidirectional absorption, flush mounted to the walls of wide ducts. These absorbers are composed of several side-by-side resonators that are usually of different geometry and thus detuned to yield an asymmetric acoustic response. A simple lumped-element model analysis is performed to link the dependence of the optimal resonators surface impedance, resonance frequency, and losses to the duct cross-sectional area and resonator spacing. This analysis unifies those of several specific configurations into a unique problem. In addition, the impact of the potential evanescent coupling between the resonators, which is usually neglected, is carefully studied. This coupling can have a strong impact especially on the behavior of compact absorbers lining wide ducts. To reduce the evanescent coupling, the resonators should be relatively small and therefore their resonances should be damped, and not arranged by order of increasing or decreasing resonant frequency. Finally, such an absorber is designed and optimized for perfect unidirectional absorption to prove the relevance of the analysis. The absorber is 30 cm long and 5 cm thick and covers a single side of a 14.8 × 15 cm2 rectangular duct. A mean absorption coefficient of 99% is obtained experimentally between 700 and 800 Hz.

Fundamental constraints on broadband passive acoustic treatments in unidimensional scattering problems

Abstract: In a passive lossy acoustical system, sum rules derived from passivity explicitly relate the broadband response to the spatial dimension of the system, which provide important design criteria as well. In this work, the theory of Herglotz function is applied systematically to derive sum rules for unidimensional scattering problems relying on passive acoustic treatments which are generally made of rigid, motionless and subwavelength structures saturated by air. The rigid-boundary reflection, soft-boundary reflection and transmission problems are analysed. The derived sum rules are applied for guiding the designs of passive absorbers and mufflers: the required minimum space is directly predicted from the target (i.e. the desired absorption or transmission-loss spectra) without any specific design. Besides, it is possible to break this type of sum rules and fundamental constraints in particular cases. This property, if well used, could result in ultra-compact absorbers working at long wavelength up to infinity.

Drum-like liners to attenuate low frequencies in presence of flow: an analytical, experimental and numerical study

Abstract: Over the last twenty years, many ideas have been suggested to design sub-wavelength absorbers that couple a classical single-degree of freedom liner with a vibrating part that resonates at low frequencies. In this paper, the acoustic behaviour of a light and thin sound absorber composed of an elastic latex membrane placed on top of a closed 3D-printed cavity is studied. It is found experimentally and analytically that membrane modes imply a great shift of the cavity resonance towards the low frequencies and add several supplementary transmission drops. To investigate the effects of flow, numerical time-domain simulations are conducted and validated after comparisons with experimental data. The three approaches show that membrane absorbers are highly resistive, with a weak sensibility against flow and non linear effects. They are thus well-suited for absorption purposes in aeronautic applications.

Direct and adjoint problems for sound propagation in non-uniform flows with lined and vibrating surfaces

Abstract: Abstract This paper presents a systematic analysis of direct and adjoint problems for sound propagation with flow. Two scalar propagation operators are considered: the linearised potential equation from Goldstein, and Pierce's equation based on a high-frequency approximation. For both models, the analysis involves compressible base flows, volume sources and surfaces that can be vibrating and/or acoustically lined (using the Myers impedance condition), as well as far-field radiation boundaries. For both models, the direct problems are fully described and adjoint problems are formulated to define tailored Green's functions. These Green's functions are devised to provide an explicit link between the direct problem solutions and the source terms. These adjoint problems and tailored Green's functions are particularly useful and efficient for source localisation problems, or when stochastic distributed sources are involved. The present analysis yields a number of new results, including the adjoint Myers condition for the linearised potential equation, as well as the formulation of the direct and adjoint Myers condition for Pierce's equation. It is also shown how the adjoint problems can be recast in forms that are readily solved using existing simulation tools for the direct problems. Results presented in this paper are obtained using a high-order finite element method. Several test cases serve as validation for the approach using tailored Green's functions. They also illustrate the relative benefits of the two propagation operators.

Time-domain broadband impedance model for computational aeroacoustics: application to shock-wave propagation in lined intakes

Abstract: Rotor shock noise is one of the main noise sources of today’s aircraft engines in take-off and climb flight conditions. The control and reduction of this noise source is of paramount importance for aircraft manufacturers for complying international regulations and improve passengers comfort. High fidelity simulation tools are required for its study, with inclusion of all 3D geometric and flow effects as well as the modelling of the acoustic treatments incorporated in the walls of the engine intake. Euler and Navier-Stokes solvers offer solutions to compute the nonlinear propagation of the high amplitude pressure fluctuations of the rotor shocks in the intake. However, modelling acoustic liners in these solvers remains a challenge of current state-of-the-art numerical acoustics, due to their natural belonging to the frequency domain. The present work focuses on the validation and extension of the Time-Domain Impedance Boundary Condition (TDIBC) based on the Oscillo-Diffusive Representation (ODR) and its implementation in an industrial CFD solver. The ODR already proved to be a powerful mathematical tool to translate the impedance (or scattering) operator in the time-domain. A numerical development in a Navier-Stokes Characteristic Boundary Condition (NSCBC) formalism allowed the implementation of this time-domain model in the finite-volume Navier-Stokes solver elsA. Validations of this methodology are carried out against acoustic benchmarks from the literature and industrial experimental measurements. They all demonstrated that the novel TDIBC is correctly implemented in the CFD solver and proved its efficiency in terms of computational time and numerical stability. Finally, an application to the propagation and attenuation of rotor shock waves in an aircraft engine intake is proposed.

Propagation of acoustic waves in axially varying ducts with potential flow using the multimodal formulation

Abstract: This paper presents a multimodal method applicable to the computation of the acoustic field in an axisymmetric duct with multiple-scales potential mean flow. The original three-dimensional set of equations is rearranged into a set of coupled one-dimensional equations by using the Fourier transform of the sound disturbances in the azimuthal direction and a projection on shifted Chebyshev polynomials in the radial direction. To keep the computation resources identical to that of the standard multimodal formulation (without flow), only the leading order effects of the mean flow are encapsulated using a multiple-scales approach. The formulation is checked using a numerical finite element method and is shown to give consistent results for modes propagating inside ducts with or without acoustic liners and in the presence of potential flows. This method can be easily adapted to take into account more complex flows and geometries.

Multimodal characterisation of acoustic liners using the MAINE Flow facility

Abstract: MAINE Flow is a large-scale duct facility that allows investigating the acoustic properties of liners with flow and acoustic conditions close to the ones typically found in nacelles of aircraft engines: the incident acoustic level can go up to 150 dB and the flow velocity up to Mach 0.63. Compared to other large-scale duct experiments, this facility permits a precise control of the modal content and amplitude, as well as the measurement of the scattering matrix of the liner. In this paper, we compare three methods that allow calculating the insertion losses of a test liner by measuring the transmission losses with and without liner. Two are direct methods that use noise level measurements upstream and downstream the sample: one with an uncorrelated broadband excitation and one with a modal sine-sweep excitation. In the broadband case, robust measurements up to 10 kHz are obtained but the modal content is not controlled. The third method uses the coefficients of the liner scattering matrix to compute transmission losses. More physical insights are provided by this method which works on a more limited range of frequency.