Daniel Juvé

Computation of Flow Noise Using Source Terms in Linearized Euler's Equations

An acoustic analogy using linearized Euler’ s equations (LEE) forced with aerodynamic source terms is investigated to computetheacousticfare eld. Thishybridmethod isappliedto threemodelproblemssimulatedby solving Navier‐Stokes equations. In this way, its validity is estimated by comparing the predicted acoustic e eld with the reference solution given directly by the Navier ‐Stokes equations. The noise radiated by two corotating vortices is studied: e rst, in a medium at rest and, second, in a mean sheared e ow with no convection velocity. Then the sound e eld generated by vortex pairings in a subsonic mixing layer is investigated. In this case, a simplie ed formulation of LEE is proposed to prevent the exponential growth of instability waves. The acoustic e elds obtained by solving LEE are in good agreement with the reference solution. This study shows that the source terms introduced into the LEE are appropriate for free sheared e ows and that acoustic ‐mean e ow interactions are properly taken into account in the wave operator. Nomenclature b = half-width of the monopolar source c = sound velocity E;F;H = vectors in linearized Euler’ s equations (LEE) f = frequency f0 = fundamental frequency of the mixing layer k = complex wave number, kr Ciki M = Mach number p = pressure Re = Reynolds number rc = vortex core radius r0 = initial half distance between the two vortices S = sound source vector in LEE Si = source terms in the momentum equations T = period Tij = Lighthill’ s tensor t = time U = unknown vector in LEE U1 = slow stream velocity of the mixing layer U2 = rapid stream velocity of the mixing layer u = velocity vector, .u1;u2/ Vµ = initial tangential velocity of vortices

Numerical Solution of Acoustic Propagation Problems Using linearized Euler's Equations*

Some numerical solutions of acoustic propagation problems using linearized Euler equations are studied. The two-dimensional Euler equations are linearized around a known stationary mean flow. The computed solution is obtained by using a dispersion-relation-preserving scheme in space, combined with a fourth-order Runge-Kutta algorithm in time. This numerical integration leads to very good results in terms of accuracy, stability, and low storage. The implementation of source terms in these equations is studied very carefully in various configurations, inasmuch as the final goal is to improve and to validate the stochastic noise generation and radiation model. In this approach, the turbulent velocity field is modeled by a sum of random Fourier modes through a source term in the linearized Euler equations to predict the noise from subsonic flows. The radiation of a point source in a subsonic and a supersonic uniform mean flow is investigated. The numerical estimates are shown to be in excellent agreement with the analytical solutions. Then, the emphasis is on the ability of the method to describe correctly the multipolar structure of aeroacoustic sources. The radiation of dipolar and quadrupolar extended sources is, thus, studied. Next, a typical problem in jet noise is considered with the propagation of acoustic waves in a sheared mean flow. The numerical solution compares favorably with ray tracing. Finally, a nonlinear formulation of Eulers equations is solved to limit the growth of instability waves excited by the acoustic source terms.

Direct computation of the noise radiated by a subsonic cavity flow and application of integral methods

Abstract The goal of this paper is to investigate the acoustic field generated by the flow over a cavity using two different and complementary numerical methods. First, a Direct Numerical Simulation of the 2-D compressible Navier–Stokes equations is performed to obtain directly the radiated noise. The results of the acoustic and aerodynamic fields are compared to the experimental data in the literature. Second, this reference solution is compared to solutions provided by hybrid methods using the flowfield computed inside the cavity combined with an integral formulation to evaluate the far-field noise. Numerical issues of three integral methods are studied: the Ffowcs Williams and Hawkings analogy that extends Lighthills theory to account for solid boundaries and two Wave Extrapolation Methods from a control surface, the Kirchhoff and porous Ffowcs Williams and Hawkings methods. All methods show a good agreement with the Direct Numerical Simulation, but the first one is more expensive owing to an additional volume integral. However, the analogy can help in the analysis of wave patterns, by separating the direct waves from the reflected ones. The wave extrapolation methods from a surface are more efficient and provide a complementary tool to extend Computational Aeroacoustics near field to the very far field.

Numerical Simulation of Sound Generated by Vortex Pairing in a Mixing Layer

A numerical code solving the filtered Navier-Stokes equations is developed using special techniques of computational aeroacoustics. This approach allows a direct determination of the compressible field on a computational domain including the acoustic far field. A two-dimensional mixing layer between two flows at M 1 = 0.12 and M 2 = 0.48 is simulated. The Reynolds number built up from the initial vorticity thickness and the velocity difference across the mixing layer is Re ω = 1.28 x 10 4 . An appropriate forcing of the mixing layer is defined to have only one pairing in the computational domain at a fixed location. The sound generation pattern for a single pairing displays a double spiral structure, corresponding to the rotating quadrupole associated to two corotative vortices. Successive pairings produce an acoustic radiation at the frequency of this mechanism. The directly computed far-field sound is then compared to the prediction of Lighthills acoustic analogy (Lighthill, M. J., On Sound Generated Aerodynamically-I. General Theory, Proceedings of the Royal Society of London, Vol. 211, Series A 1107, 1952, pp. 564-587) based on the aerodynamic fluctuations provided by the large-eddy simulation code. Two integral formulations of the analogy, based on spatial derivatives and time derivatives, respectively, are tested. Results are in good qualitative agreement with the results of direct simulation. The accuracy is, however, greater with the formulation using time derivatives instead of spatial derivatives.

Jet-Noise Reduction by Impinging Microjets: An Acoustic Investigation Testing Microjet Parameters

The effects of microjets on the aerodynamic characteristics of a Mach 0.9 high-Reynolds axisymmetric jet are investigated and are interpreted in the light of previous acoustic results. These measurements are obtained by means of Stereoscopic Particle Image Velocimetry in planes normal to the jet axis. Three parameters of the microjets system are varied: the outgoing mass flux per microjet, the number of microjets and their layout in the azimuth of the main jet. The aerodynamic results indicate a strong correlation between the maximum level of turbulence just behind the nozzle exit and the high-frequency noise, previously shown to potentially balance the acoustic benefits obtained for lower frequencies. The maximum level of turbulence measured at the longitudinal position corresponding to half the potential core length is also highly correlated to the jet noise reduction, which is highlighted by the similar evolution of these two quantities regarding the mass flux per microjet and the number of microjets. For low values of the number of microjets, the microjets are shown to act independently, and their contributions to the turbulence reduction are retrieved far downstream the impinging point without any noticeable azimuthal diffusion.

Space-Time Correlations in Two Subsonic Jets Using Dual Particle Image Velocimetry Measurements

Dual particle image velocimetry (dual PIV) measurements have been performed to investigate the space-time correlations in two subsonic isothermal round jets at Mach numbers of 0.6 and 0.9. The correlation scales are analyzed along the centerline and in the shear-layer center over the first 11 jet diameters from the nozzle exit To provide robust results over a wide range of flow conditions, these correlation scales are given in terms of their appropriate quantities, namely, the mean or rms velocity in reference to velocity and the momentum thickness or the half-velocity diameter in reference to length in the shear layer and on the jet axis, respectively. From these results, a discussion on the modeling of turbulence in jets is addressed. The self-similarity of some space correlation functions in the shear layer and on the jet axis is shown. Furthermore, far enough downstream in the shear layer, some of the ratios between the space and time scales are relatively close to the values expected in homogeneous and isotropic turbulence. It is also found that the ratio between the integral length and the time scales in the fixed frame is of the order of the local mean flow velocity. In the convected frame, the appropriate scaling factor is the rms velocity.

On the radiated noise computed by large-eddy simulation

This paper addresses the problem of the estimation of the noise radiated by forced isotropic turbulence using an hybrid large-eddy simulation/Lighthill analogy approach. The scale separation associated with the LES approach leads to splitting the acoustic source term as the sum of several contributions. The subgrid scale and high frequency contributions to radiated acoustic spectrum are first evaluated on the ground of filtered direct numerical simulations. The parametrization of subgrid scale effects based on a scale similarity model is addressed. Both a priori and a posteriori tests demonstrate the efficiency of the proposed model.

Simulation of a hot coaxial jet : Direct noise prediction and flow-acoustics correlations

A coaxial jet originating from parallel coplanar pipe nozzles is computed by a compressible large eddy simulation (LES) using low-dissipation and low-dispersion schemes in order to determine its acoustic field and to study noise generation mechanisms. The jet streams are at high velocities, the primary stream is heated, and the Reynolds number based on the primary velocity and the secondary diameter is around 106. High levels of turbulence intensity are also specified at the nozzle exit. The jet aerodynamic field and the near-pressure field are both obtained directly from the LES. The far-field noise is calculated by solving the linear acoustic equations, from the unsteady LES data on a cylindrical surface surrounding the jet. A good agreement is observed in terms of directivity, levels, and narrow-band spectra with noise measurements carried out during the EU project CoJeN for a coaxial jet displaying same stream velocities and temperatures, coplanar nozzle outlets with identical area ratio, and a high R...

Experimental Study of the Spectral Properties of Near-Field and Far-Field Jet Noise:

The near and far pressure fields generated by round, isothermal and cold jets of diameter D = 38 mm with Mach numbers varying over the range 0.6 ≤ Mj ≤ 1.6 are investigated experimentally, and characterized in terms of sound spectra and levels. Properties of near-field jet noise, obtained in particular at 7.5 diameters from the jet centerline, are documented. They differ appreciably from properties of far-field noise, and form a database that can be used for the validation of the acoustic fields determined by compressible Navier-Stokes computations. The near pressure fields originating from simulations can thus be directly compared, without resorting to extrapolation methods which might lead to uncertainties in the far pressure fields. In the present paper, sound source localizations are also carried out from the near-field pressure signals. The experiments provide in addition far-field results evaluated at 52 diameters from the nozzle exit, in good agreement with the data of the literature. The classical dependence of jet noise features with the emission angle is observed. The level and frequency scalings of the pressure spectra obtained for subsonic jets in the sideline and downstream directions are also studied. For small radiation angles, the narrow-banded sound spectra measured are found to scale as the Strouhal number, whereas, as previously noted by Zaman & Yu [1], the one-third octave spectra seem to scale as the Helmholtz number.

Aerodynamic noise induced by laminar and turbulent boundary layers over rectangular cavities

The structure of an unsteady o w past a rectangular, open cavity is investigated using numerical simulations. Particular attention is drawn to the three-dimensional geometry eects, and to the turbulent state of the incoming boundary layer. The consequences on noise generation are studied. Two-dimensional DNS allows a reconstruction of the feedback loop giving rise to the selfsustained oscillations, but DNS is restricted to thick laminar upstream boundary layers. Cavity o ws with higher Reynolds numbers are computed by 3-D Large Eddy Simulations, based on high order algorithms, by considering that the interactions of coherent structures with the downstream edge are predominant in such o ws. The three-dimensional structure of the recirculating zone is illustrated and its inuence on the shear layer dynamics is shown . In the same way as the incoming turbulence level, these modulations induce jittering of vortex-corner interactions, a decrease in feedback coherence, and thus a reduction of the radiated noise.