Marc C. Jacob

Large eddy simulation of a forward–backward facing step for acoustic source identification

The feasibility of using a commercial CFD code for large eddy simulation (LES) is investigated. A first test on homogeneous turbulence decay allows a fine-tuning of the eddy viscosity with respect to the numerical features of the code. Then, a flow over forward–backward facing step at Reynolds number Reh ¼ 1:7 � 10 5 is computed. The results found show good agreement with the new LDA data of Leclercq et al. [Forward backward facing step pair: aerodynamic flow, wall pressure and acoustic characterization. AIAA-2001-2249]. The acoustic source term, recorded from the LES and to be fed into a following acoustic propagation simulation, is found to be largest in the separation from the forward step. The source terms structures are similar to the vortical structures generated at the front edge of the obstacle and advected downstream. Structures generated from the backward step rapidly break down into smaller scale structures due to the background turbulence. 2003 Published by Elsevier Science Inc.

Prediction of Rod-Airfoil Interaction Noise Using the Ffowcs-Williams-Hawkings Analogy

SoundgeneratedatlowMachnumberbyanairfoilin thewakeofarodisinvestigatednumerically.TheGaussian spanwise loss of coherence of the vortex shedding is shown to have a signie cant ine uence on the broadband noise. Spanwise effects are successfully introduced into a time-domain formulation of the Ffowcs-Williams ‐Hawkings analogy, which is applied to aerodynamicdata computed on various contoursaround the sourceregion. Itisshown that a careful choice of these contours is required. The e owe eld is obtained from a two-dimensional Reynolds averaged Navier ‐Stokes calculation. Computed far-e eld spectra compare very well to measurements obtained in an accompanying experiment. Nomenclature Cp = pressure coefe cient c = airfoil chord d = rod diameter f = frequency g = integration surface, 0 k = turbulent kinetic energy Lg = Gaussian correlation length l = span length Mi = Mach number of g D0 Moi = observer Mach number vector Mref = reference Mach number M1 = ine ow Mach number

Prediction of aerodynamic sound from circular rods via spanwise statistical modelling

The Ffowcs Williams and Hawkings’ acoustic analogy is combined in the time domain with a statistical model in order to take into account the three-dimensional character of the vortex shedding process from a rod in a uniform stream. By applying the model to a two-dimensional unsteady Reynolds averaged Navier–Stokes flow computation, it is shown that the three-dimensional effects, like spectral broadening around the shedding frequency, are partially recovered. The ad hoc statistical model relates a spanwise random distribution of the vortex shedding phase and wall pressure modulations to an arbitrary spanwise correlations. The phase distribution is applied to the tonal pressure signals of the computation and the resulting ad hoc signals are fed into the acoustic analogy. The study is carried out for a rod based Reynolds number of 2.2×104 for which the rod wake is turbulent. Numerical results compare favourably to those of an accompanying experiment.

Broadband Noise Reduction With Trailing Edge Brushes

Airfoil broadband trailing edge noise is reduced by modification of the trailing edge geometry. A brush made of a single row of flexible polypropylene fibers is integrated in the trailing edge of a cambered airfoil. Far field acoustic measurements show a noise reduction potential reaching 3 dB on a wide frequency range. Due to high curvature of the incident flow, a secondary acoustic source partly masks the trailing edge noise reduction. Hot wire correlation measurements in the very near wake of the airfoil show that longitudinal as well as transversal length scales are affected by the brush. Span wise coherence length of boundary layer eddies falls off by 25 % in the presence of a brush in the adequate frequency range, possibly explaining a 1.3 dB contribution to the noise reduction mechanism. Boundary layer turbulence exhibits a preferred coherence length l y v on a wide frequency range. l y v /d ≈ 2, is considered a proper brush design law, d being the diameter of the brush.

Wake-airfoil interaction as broadband noise source: a large-eddy simulation study

A large-eddy simulation is carried out on a rod-airfoil configuration and compared to an accompanying experiment as well as to a RANS computation. A NACA0012 airfoil (chord c = 0.1 m) is located one chord downstream of a circular rod (diameter d = c/10, Red = 48 000). The computed interaction of the resulting sub-critical vortex street with the airfoil is assessed using averaged quantities, aerodynamic spectra and proper orthogonal decomposition (POD) of the instantaneous flow fields. Snapshots of the flow field are compared to particle image velocimetry (PIV) data. The acoustic far field is predicted using the Ffowcs Williams & Hawkings acoustic analogy, and compared to the experimental far field spectra. The large-eddy simulation is shown to accurately represent the deterministic pattern of the vortex shedding that is described by POD modes 1 & 2 and the resulting tonal noise also compares favourably to measurements. Furthermore higher order POD modes that are found in the PIV data are well predicted by the computation. The broadband content of the aerodynamic and the acoustic fields is consequently well predicted over a large range of frequencies ([0 kHz; 10 kHz]).

Prediction of Sound Propagation in Ducted Potential Flows Using Green's Function Discretization

The sound propagation in ducted mean potential flows is computed by using a Greens function discretization (GFD) technique. Linear combinations of the free-space Greens functions of the locally uniform convected Helmholtz problem are analytically differentiated to build shape functions for the derivatives of the acoustic potential. These are used to discretize both the field governing equation and the boundary conditions. The GFD approach is validated by computing the sound propagation in annular ducts with hard/soft walls and uniform flow. Acoustic modes of increasing wave number are computed without changing the computational mesh. A good level of accuracy is ensured up to three points per wavelength. As a first step toward relevant applications, the propagation in nonconstant annular ducts, with/without wall treatment and with/without flow, is computed. The numerical solutions compare favorably with the well-known analytical multiscale solutions.

Experimental study of a tip leakage flow: wavelet analysis of pressure fluctuations

A wavelet-based conditional analysis of unsteady flow and sound signals highlights the role of intermittent perturbations both in the sound generation and the unsteady field of an aerofoil tip leakage flow experiment. It is shown how the most probable flow perturbations generated at the pressure side tip edge are convected through the gap and swept downstream along the suction side past the trailing edge tip corner, where they radiate sound. The nascent sound sources are identified and localized in the clearance between 40 % and 60 % of the chord. It is also found that the time dependence of the averaged intermittent structures scales with the inverse of the square root of the mean velocity and a physical interpretation based on a simple potential vortex model is proposed. The data are retrieved from an experiment that has been carried out at low Mach number (Ma < 0.3) in an anechoic test facility. A single motionless instrumented NACA 5510 aerofoil was mounted into the potential core of an open rectangular jet between two plates with an adjustable clearance. The tip leakage flow was ensured by the 5 % camber and a 15° angle of attack. A large database obtained by a variety of measurement techniques is thus available for the present analysis. More specifically, the conditional approach is applied to joint far field, wall pressure and particle image velocimetry (PIV) measurements. The wall pressure probes are located along the suction side tip edge and on the tip inside the gap, whereas the PIV plane is parallel to the mid-gap plane. Additional joint wall pressure and single hot-wire anemometry (HWA) measurements are also analysed with a hot-wire probe located near the trailing edge tip corner. The conditional averaging is triggered by high-energy wavelet events selected in a reference signal by setting a threshold to the so-called local intermittency measure.

Aeroacoustic Investigation of a Single Airfoil Tip Leakage Flow

Combined near and far field aeroacoustic measurements have been carried out during an original laboratory scale low Mach number (0–0.3) experiment about the tip leakage flow past a single non-rotating airfoil. Such measurements were made possible by the use of a single airfoil located in the potential core of an open jet flow in the anechoic wind tunnel of the Ecole Centrale de Lyon. The airfoil was mounted between two flat plates. A strong tip clearance flow was achieved without rotation by paying a special attention to the choice of the airfoil which was a 5% camber, 10% thickness NACA5510 airfoil that provided a high lift at a 15° angle of attack. The experiment gave rise to an extensive data set obtained with several flow velocity measurement techniques (HWA, LDA, PIV), steady and unsteady pressure measurements on the airfoil and the casing plate as well as far field pressure measurements. Further, cross-analyses of various velocity and pressure signals allowed to locating sources and identifying their mechanisms. Results showed evidence of two components of tip leakage broadband self noise.

Experimental Study of Sound Generated by Backward-Facing Steps Under Wall Jet

Sound radiation by a backward facing step under a plane wall jet is examined. The investigation is based on an experiment where the mean velocity, the step heights, and the cross-stream extent of the jet are varied. The comparison between the backward-facing-step e ow and the corresponding wall jet shows an acoustic source near the step. Both near- and far-e eld measurements indicate how the step changes the radiation pattern of this source. The sound level is signie cantly increased into the upstream directions and accompanied by strong low-frequency peaks in the spectra. Aerodynamic results show that the reattachment length is much shorter for a step placed under a wall jet than for a step placed in a channel and that the most turbulent e ow regions, namely, the jet mixing layer and the step reattachment region, coincide with the acoustic source locations.

Cross-wavelet analysis of wall pressure fluctuations beneath incompressible turbulent boundary layers

Pressure fluctuations measured at the wall of a turbulent boundary layer are analysed using a bi-variate continuous wavelet transform. Cross-wavelet analyses of pressure signals obtained from microphone pairs are performed and a novel post-processing technique aimed at selecting events with strong local-in-time coherence is applied. Probability density functions and conditionally averaged equivalents of Fourier spectral quantities, usually introduced for modelling purposes, are computed. The analysis is conducted for signals obtained at low Mach numbers from two different non-equilibrium turbulent boundary layer experiments. It is found that that the selected events, though statistically independent, exhibit bi-modal statistics while the conditional coherence function coincides with its non-conditional Fourier equivalent. The physical nature of the selected events has been further explored by the computation of ensemble-averaged pressure time signatures and the results have been physically interpreted with the aid of numerical and experimental results from the literature. In both experiments, it has been found that the major physical mechanisms responsible for the observed conditional statistics are represented by sweep-type events which can be ascribed to the effect of streamwise vortices in the near-wall region. More precisely, the wavelet analysis highlights the convection of the selected structures in both cases. Conversely, compressibilty effects could be related to these events only in one case.