Christophe Bogey

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

Direct Noise Computation of the Turbulent Flow Around a Zero-Incidence Airfoil

A large eddy simulation of the flow around a NACA 0012 airfoil at zero incidence is performed at a chord-based Reynoldsnumber of500,000 anda Machnumberof 0.22.Theaim istoshow thathigh-order numericalschemes can successfully be used to perform direct acoustic computations of compressible transitional flow on curvilinear grids. AtaReynoldsnumberof500,000,theboundarylayersaroundtheairfoiltransition fromaninitially laminarstateto a turbulent state before reaching the trailing edge. Results obtained in the large eddy simulation show a well-placed transition zone and turbulence levels in the boundary layers that are in agreement with experimental data. Furthermore, the radiated acoustic field is determined directly by the large eddy simulation, without the use of an acoustic analogy. Third-octave acoustic spectra are compared favorably with experimental data.

Decrease of the Effective Reynolds Number with Eddy-Viscosity Subgrid-Scale Modeling

TECHNICAL NOTES are short manuscripts describing new developments or important results of a preliminary nature. These Notes cannot exceed six manuscript pages and three figures; a page of text may be substituted for a figure and vice versa. After informal review by the editors, they may be published within a few months of the date of receipt. Style requirements are the same as for regular contributions (see inside back cover).

Investigation of a High-Mach-Number Overexpanded Jet Using Large-Eddy Simulation

a n = relative contribution of azimuthal modes n c = local sound speed c1 = ambient field sound speed f = frequency fc = cutoff frequency fshock = central frequency of the broadband shockassociated noise fup = frequency of the upstream-propagating shockassociated noise LVS = first shock length from vortex sheet, 2 M j 1 rj= 1, 1 2:40483 L1 = first shock length measured on the jet axis Ma = acoustic Mach number Mc = convection Mach number Me = exit Mach number Mj = equivalent fully expanded exit Mach number, uj=c1 n = azimuthal mode pe = exit static pressure pj = equivalent fully expanded exit static pressure p0 = fluctuating static pressure hpi = mean static pressure Re = Reynolds number based on exit conditions re = nozzle radius rj = equivalent fully expanded nozzle radius Stc = cutoff Strouhal number Ste = Strouhal number based on exit conditions Stup = Strouhal number of the upstream-propagating shock-associated noise Te = exit temperature uaxis = centerline mean axial velocity uc = convection velocity ue = exit velocity uj = equivalent fully expanded exit velocity huzi = mean axial velocity hu02 z i = mean-square axial velocity fluctuations hu02 z in = mean-square axial velocity fluctuations due to mode n juz j Ste; n = two-dimensional power spectral densities z1 = first shock location on the jet axis = specific heat ratio r = mesh size in the radial direction z = mesh size in the axial direction = boundary-layer thickness in the pipe nozzle

A Family of Low Dispersive and Low Dissipative Explicit Schemes for Computing Aerodynamic Noise

Explicit numerical methods for spatial derivation, ltering and time integration are proposed. They are developed with the aim of computing directly the aerodynamic noise, but they are not limited to this application. All the methods are constructed in the same way by minimizing the dispersion and the dissipation errors in the wave number space up to k x= =2. They are shown to be more accurate, and also more eÆcient numerically, than most of the standard explicit high-order methods. Two problems involving long-range sound propagation are resolved to illustrate their respective precisions.

Time-Domain Impedance Boundary Conditions for Simulations of Outdoor Sound Propagation

B = Gaussian half-width, m c0 = speed of sound, m=s dL = porous layer thickness, m f = frequency, Hz Im = imaginary part j = imaginary unit k = complex wave number, m 1 p = pressure, Pa q = tortuosity Re = real part S = number of first-order systems in the impedance approximation sf = coefficient of the selective filter T = number of second-order systems in the impedance approximation t = time, s v = velocity component normal to impedance surface, m=s Z = complex impedance, kg=m=s = ratio of specific heats L = sound pressure level relative to the free field, dB t = time step, s x = spatial mesh size, m 0 = air density, kg=m 0, e = flow resistivity, Pa s=m = porosity ! = angular frequency, rad=s

Simulation of Subsonic Turbulent Nozzle Jet Flow and Its Near-Field Sound

A direct numerical simulation framework is developed and validated for investigating a jet-flow configuration in which a short cylindrical nozzle and the acoustic near field are included in the simulation domain. The nozzle flow is modeled by a potential flow core and a developing turbulent wall boundary layer, which is numerically resolved. The setup allows to create well-controlled physical nozzle-exit flow conditions and to examine their impact on near-nozzle flow dynamics, jet-flow development, and the near-field sound. Turbulence at the nozzle inflow is generated by the synthetic-eddy method using flat-plate boundary-layer direct numerical simulation data and imposed softly in a sponge layer. The jet Mach number in the present investigation is Ma=0.9, the diameter-based jet Reynolds number is ReD=18,100, and the maximum axial rms fluctuations attain 13% at the nozzle exit. The accuracy of the numerical results is checked by varying grid resolution and computational domain size. The rapid flow develop...

Simulations of Initially Highly Disturbed Jets with Experiment-Like Exit Boundary Layers

Two isothermal round jets at a Mach number of 0.9 and a diameter-based Reynolds number of 2×105 have been computed by compressible large-eddy simulation using high-order finite differences on a grid of 3.1 billion points. At the exit of a straight pipe nozzle in which a trip forcing is applied, the jet flow velocity parameters, including the momentum thickness and the shape factor of the boundary layer, the momentum-thickness-based Reynolds number, and the peak turbulence intensity, roughly match those found in experiments using two nozzles referred to as the ASME and the conical nozzles. The boundary layer is in a highly disturbed laminar state in the first case and in a turbulent state in the second. The exit flow conditions, the shear-layer and jet flowfields, and the far-field noise provided by the large-eddy simulation are described. The jet with the ASME-like initial conditions develops a little more rapidly, with slightly higher turbulence levels than the other. Overall, however, the results obtain...

A computational study of the effects of nozzle-exit turbulence level on the flow and acoustic fields of a subsonic jet

Five isothermal round jets at Mach number M = 0.9 and diameter-based Reynolds number ReD = 10 5 originating from a pipe nozzle are computed by Large-Eddy Simulations to investigate the effects of initial turbulence on flow development and noise generation. In the pipe, the boundary layers are tripped in order to impose, at the nozzle exit, laminar mean velocity profiles of momentum thickness equal to 1.8% of the jet radius, yielding Reynolds number Re� = 900, and peak turbulence intensities of 0, 3, 6, 9 and 12% of the jet velocity. As the nozzle-exit turbulence level increases, the shear-layer development is strongly modified. Vortex roll-ups and pairings and, more generally, coherent structures gradually disappear, leading to lower shear-layer spreading rate and rms fluctuating velocities. The jets also develop farther downstream, resulting in longer potential cores. With rising exit turbulence intensity, the noise levels generated by the present jets at ReD = 10 5 are moreover found to decrease, and to tend asymptotically towards the levels measured for jets at Reynolds numbers higher than 5 × 10 5 , which are likely to be initially turbulent and to emit negligible vortex-pairing noise. These results correspond well to experimental observations available in the literature, usually obtained separately for either mixing layers, jet flow or sound fields.

Experimental study of the 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 sources 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 specially found to scale as the Strouhal number, whereas the one-third octave spectra seem to scale as the Helmholtz number, as previously shown by Zaman & Yu. 1