Estelle Piot

Investigation of the PSE approach for subsonic and supersonic hot jets. Detailed comparisons with LES and Linearized Euler Equations results

A Parabolized Stability Equation (PSE) method is applied to hot inviscid Mach 0.7 and Mach 2 axisymmetric jets. The Parabolized Stability Equations are derived from the linearized Euler equations. Spatial development of pressure perturbations is computed in the vicinity of the jet, and the associated radiated noise is obtained by solving the wave equation. A Large Eddy Simulation is performed on the subsonic jet and compared with the results obtained by the PSE analysis of the LES-computed mean flow. Good agreement is found for the spatial growth of pressure instability waves, the spatial damping being slightly under-estimated in the PSE analysis. Only LES predicts acoustic radiation, which may thus be created by the turbulence cascade rather than by the Kelvin-Helmholtz instability waves. PSE method is then applied to the supersonic jet and compared to solutions of Linearized Euler Equations. The common mean flow is analytical. A very good agreement is found for pressure perturbation evolution and for directivity and levels of acoustic radiation.

Liner impedance eduction technique based on velocity fields

This paper describes a new liner impedance eduction technique. The two-dimensional Linearized Euler Equations are solved in the frequency domain with a Discontinuous Galerkin formulation. The objective function which is minimized for impedance eduction is based on two-dimensional acoustic velocity elds measured by Laser Doppler Anemometry. The optimization scheme is based on direct and adjoint equations, which allows easily the

Experimental and Numerical Investigation of the Near Field Pressure of a High Subsonic Hot Jet

The near field of a hot subsonic jet is explored through a modal decomposition of the pressure. This modal analysis is performed from pressure fields obtained both experimentally and numerically. Experimentally, an azimuthal array of twenty microphones is used to measure the near field pressure of the jet. The numerical part of the study consists of the azimuthal decomposition of the near field pressure of a Large Eddy Simulation. A linear stability analysis based on the so called PSE (Parabolized Stability Equations) is also performed to compute the pressure modes in the near field of the jet. The shape of the spectra obtained by the LES in the near field for axial positions nondimensionalized by the potential core length is in good agreement with the experimental ones (with a constant overestimation of about 8 dB/Hz). In the same manner, the axial evolution of the pressure modes from the LES is similar to the one obtained experimentally. The study based on the PSE also shows a good agreement with the modal analysis of the LES except in the region where the perturbation is spatially damped. This is believed to be due to important non linear interactions between modes.

Numerical and Experimental Study of Resonant Liners Aeroacoustic Absorption under Grazing Flow

Resonant liners such as perforated honeycomb panels are used to reduce fan noise in the inlet nacelles. In a previous paper (Roche et al ., AIAA paper 2009-3146), the results of Direct Numerical Simulations (DNS), performed with the Onera CEDRE CFD code, enabled us to identify the viscous wall friction and the vortex s hedding as their main dissipation mechanisms. The impact of a rise of Sound Pressure Level (SPL) on their acoustic properties was pointed out. In this paper, 3D Navier-Stokes and Euler computations are performed, so that the relative efficiencies of these dissipation mechanisms can be evaluated. The distinction between “linear” and “nonlinear” absorption is found to be less obvious than commonly admitted. In order to estimate the effect of the sound waves incidence, an admittance is locally defined from the acoustic fie lds over the resonator opening inlet section. The coupling of acoustics with a stationar y 0.1 Mach number grazing air flow is ultimately discussed. The additional nonlinearities introduced by the flow are highlighted with DNS computations and Laser Doppler Velocimetry (LDV) experiments. The evolution of the local admittance is studied as well.

Direct Numerical Simulation of the crosso w instabilities induced by a periodic roughness array on a swept cylinder : receptivity and stability investigations

A direct numerical simulation of the o w around a swept cylinder in the presence of a micro-roughness array has been performed. The roughness elements are placed periodically in the spanwise direction and their heigth is equal to one tenth of the boundary layer thickness. The aim of the simulation is to compute the amplitude of the crosso w instability waves generated within the laminar boundary layer by the presence of the roughness array. Results show that both a steady and an unsteady instability waves are generated, even if the roughness forcing is purely steady. A linear stability analysis based on the OrrSommerfeld equations is used to characterize these waves. The unsteady one is the traveling crosso w wave which is the most amplied according to this theory. The steady one must be distinguished from the roughness-induced response. This can be done with help of the biorthogonal decomposition method developed by Tumin and extended in this work to a swept boundary layer. This method is also a way to evaluate precisely the receptivity coecien ts. This has been done for both the unsteady and the steady crosso w waves. The results obtained for the steady crosso w wave should be considered with caution, since the non-parallel and curvature eects, not taken into account yet in the decomposition method, may be signican t for this specic zero frequency.

ONERA-NASA Cooperative Effort on Liner Impedance Eduction

As part of a cooperation between ONERA and NASA, the liner impedance eduction methods developed by the two research centers are compared. The NASA technique relies on an objective function built on acoustic pressure measurements located on the wall opposite the test liner, and the propagation code solves the convected Helmholtz equation in uniform ow using a finite element method that implements a continuous Galerkin discretization. The ONERA method uses an objective function based either on wall acoustic pressure or on acoustic velocity acquired above the liner by Laser Doppler Anemometry, and the propagation code solves the linearized Euler equations by a discontinuous Galerkin discretization. Two acoustic liners are tested in both ONERA and NASA ow ducts and the measured data are treated with the corresponding impedance eduction method. The first liner is a wire mesh facesheet mounted onto a honeycomb core, designed to be linear with respect to incident sound pressure level and to grazing ow velocity. The second one is a conventional, nonlinear, perforate-over-honeycomb single layer liner. Configurations without and with ow are considered. For the nonlinear liner, the comparison of liner impedance educed by NASA and ONERA shows a sensitivity to the experimental conditions, namely to the nature of the source and to the sample width.

Discontinuous Galerkin Method for acoustic modes computation in lined ducts

Acoustic eigenmodes analysis requires calculations with low numerical dissipation and dispersion and the ability to handle complex geometries. These di culties are overcome by use of Discontinuous Galerkin method. Moreover, the latter method is able to handle discontinuities such as boundary conditions discontinuities. The case of the eigenproblem arising from the compressible linearized Euler equations in a cross section of an in nite lined duct is considered. The validation step of the code is presented through two examples where semi-analytical results are available and a convergency study is performed on a simple case. Acoustic modes calculations results are then presented for two cases with impedance discontinuities and comparisons are made with results found in the literature.

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

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.

Non-intrusive planar velocity-based nearfield acoustic holography in moving fluid mediuma)

Nearfield Acoustic Holography (NAH) is a powerful acoustic imaging method, but its application in aeronautics can be limited by intrusive measurements of acoustic field. In this paper, a moving fluid medium NAH procedure using non-intrusive velocity measurements is proposed. This method is based on convective Kirchhoff-Helmholtz integral formula. Convective equations and convective Greens function are used to derive convective real-space propagators including airflow effects. Discrete Fourier transforms of these propagators allow the assessment of acoustic fields from acoustic pressure or normal acoustic velocity measurements. As the aim is to derive an in-flow velocity-based NAH method, this study is especially focused on real convective velocity-to-pressure propagator. In order to validate this procedure, simulations in the case of monopole sources radiating in various uniform subsonic flows have been performed. NAH provides very favorable results when compared to the simulated fields. A comparison of results obtained by the real propagator and those obtained by the wave number-frequency-domain one developed by Kwon et al. [J. Acoust. Soc. Am. 128(4), 1823-1832 (2010)] shows the interest of using the real-form in the case of pressure backward propagation from velocity measurements. The efficiency of the developed procedure is confirmed by a wind tunnel campaign with a flush-mounted loudspeaker and non-intrusive Laser Doppler Velocimetry velocity measurements.

Validation of a direct propagation model for liner impedance eduction

A Discontinuous Galerkin method used to solve the bidimensional harmonic Linearized Euler Equations is presented and tested, with the intention of building a new impedance eduction procedure in the presence of grazing ow based on Laser Doppler Anemometry measurements. Two di erent con gurations are considered for the numerical solver validation. The rst one is extracted from literature and involves Sound Pressure Level comparisons on the rigid wall opposite to the liner. The second benchmark concerns Laser Doppler Anemometry test results. Bidimensional velocity elds and projected velocity levels are studied. Despite small discrepancies, both cases generally reveal good agreement between numerical simulation and experiments. However important deviations arise at resonance frequencies, and no satisfactory explanation can be suggested at the moment. Finally, a quick re ection is initiated concerning the de nition of an adequate objective function for the inverse eduction problem.