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Coupling of Integral Acoustics Methods with

LES for Jet Noise Prediction ∗

A. Uzun†, A. S. Lyrintzis‡, and G. A. Blaisdell§

School of Aeronautics and Astronautics

Purdue University

West Lafayette, IN 47907

This study is focused on developing a Computational Aeroacoustics (CAA) method-ology that couples the near field unsteady flow field data computed by a 3-D LargeEddy Simulation (LES) code with various integral acoustic formulations for the far fieldnoise prediction of turbulent jets. Noise computations performed for a Reynolds number400,000 jet using various integral acoustic results are presented and the results are com-pared against each other as well with an experimental jet at similar flow conditions. Ourresults show that the surface integral acoustics methods (Kirchhoff and Ffowcs Williams- Hawkings) give similar results to the volume integral method (Lighthill’s acoustic anal-ogy) at a much lower cost. To our best knowledge, Lighthill’s acoustic analogy was appliedto a reasonably high Reynolds number jet for the first time in this study. A databasegreater than 1 Terabytes (TB) in size was post-processed using 1160 processors in parallelon a modern supercomputing platform for this purpose.

Introduction

JET noise remains as one of the most complicatedand difficult problems in aeroacoustics because the

details of noise generation mechanisms by the complexturbulence phenomena in a jet are still not well under-stood. Thus, there is a need for more research that willlead to improved jet noise prediction methodologiesand further understanding of the jet noise generationmechanisms, which will eventually aid in the designprocess of aircraft engines with low jet noise emissions.

With the recent improvements in the processingspeed of computers, the application of Direct Numer-ical Simulation (DNS) and Large Eddy Simulation(LES) to jet noise prediction methodologies is becom-ing more feasible. Although there have been numerousexperimental studies of jet noise to date, the experi-ments provide only a limited amount of informationand the ultimate understanding of jet noise genera-tion mechanisms will most likely be possible throughnumerical simulations since the computations can lit-erally provide any type of information needed for theanalysis of jet noise generation mechanisms. In a DNS,all the relevant scales of turbulence are directly re-solved and no turbulence modelling is used. The firstDNS of a turbulent jet was done for a Reynolds num-ber 2,000, supersonic jet at Mach 1.92 by Freund et

al.1 The computed overall sound pressure levels werecompared with experimental data and found to be in

∗AIAA 2004-0517, Presented at the 42nd AIAA AerospaceSciences Meeting and Exhibit, January 2004, Reno, NV.

†Post-Doctoral Research Associate, Florida State University,Tallahassee, FL, Member AIAA.

‡Professor, Associate Fellow AIAA.§Associate Professor, Senior Member AIAA.Copyright c© 2004 by the authors. Published by the American

Institute of Aeronautics and Astronautics, Inc. with permission.

good agreement with jets at similar convective Machnumbers. Freund2 also simulated a Reynolds number3,600, Mach 0.9 turbulent jet using 25.6 million gridpoints, matching the parameters of the experimentaljet studied by Stromberg et al.3 Excellent agreementwith the experimental data was obtained for both themean flow field and the radiated sound. Such resultsclearly show the attractiveness of DNS to the jet noiseproblem. However, due to the wide range of lengthand time scales present in turbulent flows, DNS is stillrestricted to low-Reynolds-number flows and relativelysimple geometries. DNS of high-Reynolds-number jetflows of practical interest would necessitate tremen-dous resolution requirements that are far beyond thecapability of even the fastest supercomputers availabletoday.

Therefore, turbulence still has to be modelled insome way to do simulations for problems of practicalinterest. LES, with lower computational cost, is an at-tractive alternative to DNS. In an LES, the large scalesare directly resolved and the effect of the small scalesor the subgrid scales on the large scales are modelled.The large scales are generally much more energeticthan the small ones and are directly affected by theboundary conditions. The small scales, however, areusually much weaker and they tend to have more orless a universal character. Hence, it makes sense todirectly simulate the more energetic large scales andmodel the effect of the small scales. LES methods arecapable of simulating flows at higher Reynolds num-bers and many successful LES computations for differ-ent types of flows have been performed to date. Sincenoise generation is an inherently unsteady process,LES will probably be the most powerful computationaltool to be used in jet noise research in the foreseeable

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American Institute of Aeronautics and Astronautics Paper 2004-0517

future since it is the only way, other than DNS, toobtain time-accurate unsteady data. Although the ap-plication of Reynolds Averaged Navier Stokes (RANS)methods to jet noise prediction is also a subject ofongoing research,4–8 RANS methods heavily rely onturbulence models to model all relevant scales of tur-bulence. Moreover, such methods try to predict thenoise using the mean flow properties provided by aRANS solver. Since noise generation is a multi-scaleproblem that involves a wide range of length and timescales, it appears the success of RANS-based predic-tion methods will remain limited, unless very goodturbulence models capable of accurately modelling awide range of turbulence scales are developed and im-plemented into existing RANS solvers.

It is now widely accepted among the jet noise re-search community that the low frequency noise gener-ated by the jet flow is associated with the large scaleturbulent motions with length scales on the order ofthe jet diameter, whereas the high frequency noise isrelated to the finer scales of turbulence. Moreover,the large scales are known to be strongly affected bythe jet nozzle geometry. So although LES seems tobe very suitable for directly computing the low fre-quency jet noise and a portion of the higher frequen-cies, some ingenuity is still needed so as to estimatethe noise from the unresolved higher frequencies gen-erated by the very fine turbulent scales not resolved bythe LES grid. Such an estimation necessitates subgrid-scale noise models that will somehow extrapolate theinformation contained in the scales well-resolved bythe LES to predict the high frequency noise. Al-though there has been some preliminary efforts in thisarea,9–13 a satisfactory SGS noise model is yet to bedeveloped.

At this point, it seems appropriate to give anoverview of the application of LES to jet noise predic-tion. Although the overview given here is not a com-prehensive list of all the jet noise LES computationsdone to date, it certainly includes a review of the state-of-the-art computations that are believed to be themost successful application of LES to jet noise predic-tion. One of the first attempts in using LES as a toolfor jet noise prediction was carried out by Mankbadiet al.14 They employed a high-order numerical schemeto perform LES of a supersonic jet flow to capture thetime-dependent flow structure and applied Lighthill’stheory15 to calculate the far field noise. Lyrintzisand Mankbadi16 used LES in combination with Kirch-hoff’s method for jet noise prediction. LES has beenused together with Kirchhoff’s method17 for the noiseprediction of a Mach 2.0 jet also by Gamet and Esti-valezes18 as well as for a Mach 1.2 jet with Mach 0.2coflow by Choi et al.19 with encouraging results ob-tained in both studies. Zhao et al.20 did LES for aMach 0.9, Reynolds number 3,600 jet obtaining meanflow results that compared well with Freund’s DNS

and experimental data. Their overall sound pressurelevels for this test case were in good agreement with ex-periments as well. They also studied the far field noisefrom a Mach 0.4, Reynolds number 5,000 jet. Theycompared Kirchhoff’s method results with the directlycomputed sound and observed good agreement. Mor-ris et al.21–25 simulated high speed round jet flowsusing the Nonlinear Disturbance Equations (NLDE).In their NLDE method, the instantaneous quantitiesare decomposed into a time-independent mean compo-nent, a large-scale perturbation and a small-scale per-turbation. The mean quantities are obtained using atraditional Reynolds Averaged Navier-Stokes (RANS)method. As in LES, they resolved the large-scale fluc-tuations directly and used a subgrid-scale model forthe small-scale fluctuations in their unsteady calcula-tions. They also analyzed the noise from a supersonicelliptic jet in another study.26 Chyczewski and Long27

conducted a supersonic rectangular jet flow simulationand also did far field noise predictions with a Kirch-hoff method. Boersma and Lele28 did LES for a Mach0.9 jet at Reynolds numbers of 3,600 and 36,000 with-out any noise predictions. Bogey et al.29 simulateda Reynolds number 65,000, Mach 0.9 jet using LESand obtained very good mean flow results, turbulentintensities as well as sound levels and directivity. Con-stantinescu and Lele30 did simulations for a Mach 0.9jet at Reynolds numbers of 3,600 and 72,000. They di-rectly calculated the near field noise using LES. Theirmean flow parameters and turbulence statistics werein good agreement with experimental data and resultsfrom other simulations. The peak of the near fieldnoise spectra was also captured accurately in their cal-culations. DeBonis and Scott31 simulated a Reynoldsnumber 1.2 million, Mach 1.4 jet using 1.5 milliongrid points, but they did not do any noise predictions.Bodony and Lele32 studied a Mach 0.9, Reynolds num-ber 72,000 jet using 5.9 million grid points in an LESand experimented with the inlet conditions. Theyshowed the important role of the inlet conditions inthe far field noise of the jet. More recently, Bogey andBailly’s LES33 for a Mach 0.9 round jet at Reynoldsnumber, ReD = 400, 000 using 12.5 and 16.6 milliongrid points produced mean flow and sound field re-sults that are in good agreement with the experimentalmeasurements available in the literature. They alsostudied the effect of the various inflow conditions onthe jet flow field as well as on the jet noise in anotherrecent study.34 Their study once again revealed theimportance of inflow conditions in jet noise LES. More-over, they brought up the issue of the effects of theeddy viscosity based Smagorinsky SGS model on thejet noise in yet another recent study.35 They showedthat the high-frequency portion of the noise spectrawas significantly suppressed by the eddy viscosity. Therecent jet noise computations of Bogey and Bailly33–35

are perhaps the most successful LES calculations done

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for reasonably high Reynolds number jets at the timeof this writing. In this study, we will repeat a testcase studied by Bogey and Bailly34,35 and make com-parisons with their results as part of the validation ofour CAA methodology.

In general, the LES results in the literature to dateare encouraging and show the potential promise ofLES application to jet noise prediction. Except for thestudies of Choi et al.19 and DeBonis and Scott31 whichare not well-resolved LES calculations, and the recentstudies of Bogey and Bailly,33–35 the highest Reynoldsnumbers reached in the LES simulations so far are stillbelow those of practical interest. The cutoff frequencyof the noise spectra in the LES computations is dic-tated by the grid resolution, hence only a portion ofthe noise spectra was computed in the LES computa-tions to date. Well-resolved LES calculations of jetsat higher Reynolds numbers close enough to practicalvalues of interest would be very helpful for evaluatingthe suitability of LES to such problems as well as foranalyzing the broad-band noise spectrum and possiblylooking into the mechanisms of jet noise generation atsuch Reynolds numbers.

Objectives of the Present Study

With this motivation behind the current studygiven, we now present the two main objectives of thisresearch:

1. Development and validation of a versatile 3-D

LES code for turbulent jet simulations. A high-order accurate 3-D compressible LES code utiliz-ing a robust dynamic subgrid-scale (SGS) modelhas been developed to simulate high speed jetflows with high subsonic Mach numbers. Gen-eralized curvilinear coordinates are used, so thecode can be easily adapted for calculations inseveral applications with complicated geometries.Since the sound field is several orders of mag-nitude smaller than the aerodynamic field, wemake use of high-order accurate non-dissipativecompact schemes which satisfy the strict require-ments of CAA. Implicit spatial filtering is em-ployed to remove the high-frequency oscillationsresulting from unresolved scales and mesh non-uniformities. Non-reflecting boundary conditionsare imposed on the boundaries of the domain tolet outgoing disturbances exit the domain withoutspurious reflection. A sponge zone that is at-tached downstream of the physical domain dampsout the disturbances before they reach the out-flow boundary. Initial simulations were performedwith the constant-coefficient Smagorinsky SGSmodel. However, the results were found to besensitive to the choice of the Smagorinsky con-stant.36,37 The latest version of the LES code hasthe localized dynamic SGS model implemented.

The code also has the capability to turn off theSGS model and treat the spatial filter as an im-plicit SGS model.

2. Accurate prediction of the far field noise. Eventhough sound is generated by a nonlinear process,the sound field itself is known to be linear and irro-tational. This implies that instead of solving thefull nonlinear flow equations out in the far field forsound propagation, one can use Lighthill’s acous-tic analogy15 or surface integral acoustic meth-ods such as Kirchhoff’s method17 and the FfowcsWilliams - Hawkings (FWH) method.38,39 Inthis study, we couple the near field data directlyprovided by LES with Kirchhoff’s and FfowcsWilliams - Hawkings (FWH) methods as well aswith Lighthill’s acoustic analogy for computingthe noise propagation to the far field.

The compressible LES code and the integral acous-tics codes developed in this study form the core of aCAA methodology for jet noise prediction. Using thesetools, we will attempt state-of-the-art well-resolvedLES computations for jet flows with Reynolds num-bers as high as 400,000. As will be shown in theresults section, the cutoff non-dimensional frequency(Strouhal number) in the subsequent noise computa-tions will be as high as 4.0. Such a cutoff frequency, toour best knowledge, is greater than the cutoff frequen-cies captured in all other jet noise LES computationsfor similar Reynolds numbers available in the litera-ture to date. It is expected that the coupling of thepresent CAA methodology with a future SGS modelfor high-frequency noise from unresolved scales will bea powerful jet noise prediction tool.

Governing Equations

The governing equations for LES are obtained byapplying a spatial filter to the Navier-Stokes equa-tions in order to remove the small scales. The ef-fect of the subgrid-scales is computed using the dy-namic Smagorinsky subgrid-scale model proposed byMoin et al.40 for compressible flows. Since we aredealing with compressible jet flows, the Favre-filteredunsteady, compressible, non-dimensionalized Navier-Stokes equations formulated in curvilinear coordinatesare solved in this study using the numerical methodsdescribed in the next section. More details about thecode, including the governing equations can be foundin Uzun.41

Numerical Methods

We first transform a given non-uniformly spacedcurvilinear computational grid in physical space toa uniform grid in computational space and solve thediscretized governing equations on the uniform grid.To compute the spatial derivatives at interior grid

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Tam & Dong’s radiation boundary conditions

Tam & Dong’s radiation boundary conditions

Tam & Dong’soutflow boundaryconditions

Sponge zone

Tam &Dong’sradiationbcs

Vortex ring forcing

Fig. 1 Schematic of the boundary conditions.

points away from the boundaries, we employ the non-dissipative sixth-order compact scheme developed byLele.42 For the left boundary and the right bound-ary, we apply a third-order one-sided compact schemeand for the points next to the boundaries, we use afourth-order central compact scheme formulation, re-spectively.

Spatial filtering can be used as a means of sup-pressing unwanted numerical instabilities that canarise from the boundary conditions, unresolved scalesand mesh non-uniformities. In our study, we employa sixth-order tri-diagonal filter used by Visbal andGaitonde.43

The standard fourth-order explicit Runge-Kuttascheme is used for time advancement. We apply Tamand Dong’s 3-D radiation and outflow boundary condi-tions44 on the boundaries of the computational domainas illustrated in figure 1. We additionally use thesponge zone method45 in which grid stretching andartificial damping are applied to dissipate the vorticespresent in the flowfield before they hit the outflowboundary. This way, unwanted reflections from theoutflow boundary are suppressed. Since the actualnozzle geometry is not included in the present cal-culations, randomized perturbations in the form of avortex ring are added to the velocity profile at a shortdistance downstream of the inflow boundary in orderto excite the 3-D instabilities in the jet and cause thepotential core of the jet to break up at a reasonable dis-tance downstream of the inflow boundary. This forcingprocedure has been adapted from Bogey et al.46

For subgrid-scale modelling, both the standardconstant-coefficient Smagorinsky47 as well as the dy-namic Smagorinsky40 models have been implementedinto the LES code. The main idea in the dynamicmodel is to compute the model coefficients as functionsof space and time by making use of the informationcontained within the smallest resolved scales of mo-

tion. For the dynamic model, a fifteen-point explicitfilter developed by Bogey and Bailly48 is used as thetest-filter. The ratio of the test-filter width to the gridspacing is taken as 2. The usual practice in LES cal-culations is to average certain dynamically computedquantities over statistically homogeneous directionsand then use these averaged quantities to computethe model coefficients. This is an ad hoc procedurethat is used to remove the very sharp fluctuations inthe dynamic model coefficients and to stabilize themodel. Obviously, such an approach is not useful forturbulent flows for which there is no homogeneous di-rection. In our implementation, the dynamically com-puted model coefficients are locally averaged in spaceusing a second-order three-point filter in order to avoidthe sharp fluctuations in the model coefficient. No neg-ative model coefficients are allowed. The upper limitfor the model coefficients is set to 0.5. This procedureworks reasonably well for the jet flows we are study-ing. The code also has the capability to turn off thelocalized dynamic Smagorinsky SGS model and treatthe spatial filter as an implicit SGS model. The LEScode which dynamically computes the Smagorinskyconstant requires approximately 50% more comput-ing time relative to the LES code which employs theconstant-coefficient SGS model. Dynamic evaluationof the compressibility correction coefficient and theturbulent Prandtl number require test filtering of someadditional quantities. To keep the additional cost ofthe dynamic model at an acceptable level, the com-pressibility correction coefficient, CI and the turbulentPrandtl number, Prt are not computed dynamically inthis study and are set to constant values instead.

LES for a Mach 0.9 Round Jet at a

Reynolds Number of 400,000

The initial simulations performed for relatively lowReynolds number jets using the constant-coefficientSmagorinsky model can be found in Uzun et al.,36

whereas the results of a Reynolds number 100,000jet LES performed using the localized dynamic SGSmodel are given in Uzun et al.49

In this section, we will present results from an LESthat was performed without any explicit SGS modelfor a turbulent isothermal round jet at a Mach numberof 0.9 and Reynolds number of 400, 000. The tri-diagonal spatial filter was treated as an implicit SGSmodel. The filtering parameter was set to αf = 0.47.The jet centerline temperature was chosen to be thesame as the ambient temperature and set to 286K.A fully curvilinear grid consisting of approximately 16million grid points was used in the simulation. Thegrid had 390 points along the streamwise x directionand 200 points along both the y and z directions. Thistest case corresponds to one of the test cases studiedby Bogey and Bailly.34 The physical portion of the do-main in this simulation extended to 35 jet radii in the

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Fig. 2 Schematic showing the 3 open control sur-faces surrounding the jet flow. (Divergence of ve-locity contours are shown.)

streamwise direction and 30 jet radii in the transversedirections. The coarsest resolution in this simulation isestimated to be about 400 times the local Kolmogorovlength scale. The following mean streamwise velocityprofile was imposed on the inflow boundary

u(r) =Uo

2

[

1 + tanh

[

10

(

1 −r

ro

)]]

. (1)

There are about 14 grid points in the initial jet shearlayer. The following Crocco-Buseman relation for anisothermal jet is specified for the density profile on theinflow boundary33

ρ(r) = ρo

(

1 +γ − 1

2M2

r

u(r)

Uo

(

1 −u(r)

Uo

))−1

, (2)

where Mr = 0.9.In a recent study, Bogey and Bailly34 took a close

look at the effects of the inflow conditions on the jetflow and noise. They found out that reducing the am-plitude of the initial disturbances results in an increasein radiated noise. On the other hand, a thinner ini-tial jet shear layer thickness was observed to causeincreased noise levels in the sideline direction and re-duced noise levels in the downstream direction. Themost important changes were obtained when the first4 azimuthal modes of forcing were removed. In thiscase, the noise levels were noticeably reduced. Theyconcluded that further improvements are still neededto reduce the sideline noise levels which are overesti-mated with respect to experimental data. The readeris referred to Bogey and Bailly34 for more detailedinformation. Based on their findings, we decided touse the inflow forcing which was found by Bogey andBailly34 to match the available experimental data best.There are 16 azimuthal modes total and the first 4modes are not included in the forcing. The forcing pa-rameter α is set to 0.007. A more detailed study ofthe inflow forcing can be found in Lew et al.50

Computations were done on an IBM-SP3 machineusing 200 processors in parallel. A total of about

5.5 days (132 hours) of computing time was needed.The initial transients exited the domain over the first10,000 time steps. Time history of the unsteady flowdata inside the jet was saved at every 10 time stepsover period of 40,000 time steps. These data are usedin the volume integrals in the next section of this paperwhere the far field noise of the jet is computed usingLighthill’s acoustic analogy. The sampling period cor-responds to a time scale in which an ambient soundwave travels about 23 times the domain length in thestreamwise direction.

The first task performed in this test case was to in-vestigate the sensitivity of far field noise predictionsto the position of the control surface on which aeroa-coustic data are collected. For this purpose, we put 3control surfaces around our jet as illustrated in figure2. This figure plots the divergence of velocity contourson a plane that cuts the jet in half. By analyzingthese contours, one can clearly identify the non-linearsound generation region inside the jet flow as well asthe linear acoustic wave propagation outside the jet.The control surfaces start 1 jet radius downstream ofthe inflow boundary and extend to 35 jet radii alongthe streamwise direction. Hence the total streamwiselength of the control surfaces is 34ro. Control surfaces1, 2 and 3 are initially at a distance of 3.9, 5.9 and8.1 jet radii from the jet centerline, respectively. Theyopen up to a distance of 9.1, 10.8 and 12.2 jet radiifrom the jet centerline, respectively, at the far down-stream location of 35ro. We gathered flow field dataon the control surfaces at every 5 time steps over aperiod of 25, 000 time steps during our LES run. Thetotal acoustic sampling period corresponds to a timescale in which an ambient sound wave travels about14 times the domain length in the streamwise direc-tion. Both the FWH and Kirchhoff’s methods wereemployed in the far field noise predictions. Detailsof the FWH and Kirchhoff’s methods can be foundin Lyrintzis.51 It should be noted that the controlsurfaces employed here are open surfaces. The mainassumption in the surface integral acoustics methodsis that the control surface must be placed outside thenon-linear flow region. It is known from the study con-ducted by Brentner and Farassat52 that Kirchhoff’smethod will yield inaccurate predictions if one putsa control surface in the non-linear region and doesnot include any further corrections to account for thenon-linearities. On the other hand, the FWH methodcan produce some reasonable predictions depending onhow strong the non-linearities are in the region wherethe control surface is placed. In fact, one can takethe non-linearities into account accurately by includ-ing the quadrupole sources outside the control surfacein the original FWH formulation. The disadvantageof including this term is that computationally expen-sive volume integrals are needed for its computationor sometimes (as it is the case here) this information

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is beyond the end of the computational domain, andthus not available.

For simplicity, we decided to use open control sur-faces in the first part of this study. Flow data neededby Kirchhoff’s and the FWH methods were gatheredon the lateral surfaces surrounding the jet only. Nodata were gathered on the inflow and outflow surfaces.Towards the end of this section, we will also show farfield noise predictions obtained by including the con-tribution of the data gathered on an outflow surface.No refraction corrections53 will be used when the out-flow surface is included and only the FWH method willbe employed in that case.

The far field acoustic pressure signals were calcu-lated at 36 equally spaced azimuthal points on a fullcircle at a given θ location on a far field arc. The ra-dius of the arc is equal to 60 jet radii and its center ischosen as the jet nozzle exit. θ values on the arc rangefrom 25◦ to 90◦ with an increment of 5◦. The run timeof the Kirchhoff code is almost the same as that of theFWH code. For control surface 1, the computation ofthe 4096-point time history of acoustic pressure at agiven far field location with both methods took about6 minutes of computing time using 136 processors inparallel on an IBM-SP3. Hence, for control surface 1,both methods needed a total of 50 hours to computethe acoustic pressure history at a total of 504 far fieldpoints. Calculations on control surface 2 and 3 us-ing 136 processors in parallel required 59 and 65 hourstotal, respectively.

Figures 3 and 4 plot the acoustic pressure spectraat the 60◦ observation location on the far field arc.The time signals were broken into 4 1024-point signalswhich were then used in the Fast Fourier Transformsto get the acoustic pressure spectra. We then aver-aged the acoustic pressure spectra over the equallyspaced 36 azimuthal points to obtain the final averagedspectrum at the given observer location. It should bementioned here that since the computed spectra arenoisy, the spectra that are shown are polynomial fitsto the actual computed spectra. As can be seen fromfigures 3 and 4, for a given control surface, the FWHand Kirchhoff’s methods give almost identical results.Although not shown here, comparisons at other lo-cations along the arc yielded the same observations.This means that all of the control surfaces chosen inthis study were indeed sufficiently far away from thejet (i.e. in the linear acoustic field) such that theydid not encounter any non-linear sound generating re-gions. Also, the grid allows wave propagation withoutdiffusion. Hence, the Kirchhoff’s method predictionwas just as good as the FWH method prediction forall control surfaces.

Assuming at least 6 points per wavelength areneeded to accurately resolve an acoustic wave usingcompact difference schemes, we see that the maximumfrequency resolved with our grid spacing around the

Strouhal number, St = f Dj / Uo

SP

L(d

B/S

t)

0 0.5 1 1.5 2 2.5 390

95

100

105

110

115

Control Surface 1Control Surface 2Control Surface 3

Cutoff frequency Cutoff frequencyfor Control Surface 2 for Control Surface 1

Cutoff frequencyfor Control Surface 3

Fig. 3 The Ffowcs Williams - Hawkings methodprediction for the acoustic pressure spectra at R =

60ro, θ = 60◦ location on the far field arc.


SP

L(d

B/S

t)

0 0.5 1 1.5 2 2.5 390

95

100

105

110

115

Control Surface 1Control Surface 2Control Surface 3

Cutoff frequency Cutoff frequencyfor Control Surface 2 for Control Surface 1

Cutoff frequencyfor Control Surface 3

Fig. 4 Kirchhoff’s method prediction for theacoustic pressure spectra at R = 60ro, θ = 60

◦ lo-cation on the far field arc.

control surfaces corresponds to a Strouhal number ofapproximately 3.0, 2.0 and 1.5 for control surface 1,2 and 3, respectively. The Nyquist frequency, whichis the maximum frequency that can be resolved withthe time increment of our data sampling rate, corre-sponds to a Strouhal number of about 11.11. However,we choose the maximum frequency that is based onspatial resolution as our cutoff frequency. The timeincrement used in the LES corresponds to a Strouhalnumber of about 55.56. As will be evident shortly, 6points per wavelength are indeed sufficient to resolvean acoustic wave using compact difference schemes.When compared to the spectra predicted by controlsurface 1, the spectra predicted by control surface 2

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will show a drop-off starting at around Strouhal num-ber 2.0. Similarly, the spectra predicted by controlsurface 3 will show a drop-off at around Strouhal num-ber 1.5. Based on the data sampling rate, the numberof temporal points per period in these highest resolvedfrequencies are 8, 12, and 16, respectively. Hence, thetemporal resolution is adequate. Since grid stretchingwas employed in the computational grid used in thissimulation, the grid spacing gets coarser towards theouter domain boundaries. This means that grid spac-ing around control surface 1 is finer than that aroundcontrol surface 2 and similarly the grid spacing aroundcontrol surface 2 is finer than that around control sur-face 3. Hence, the maximum frequency that can becaptured by a control surface decreases as one putsthe control surface further away from the jet becauseof the grid stretching. The spectra comparison figuresshow solid vertical lines corresponding to the cutofffrequency for every control surface. Until Strouhalnumber 1.5, the spectra predicted by the three con-trol surfaces are seen to be very similar. Then, thespectra predicted by control surface 3 start to dropsharply due to the fact that the grid spacing aroundcontrol surface 3 is too coarse to sufficiently resolvehigher frequencies. Similarly, the spectra predicted bycontrol surface 2 are very similar to those predicted bycontrol surface 1 until Strouhal number 2.0 and thenwe observe a sharp drop in the spectra predicted bycontrol surface 2 for the higher frequencies. From thefindings in this study, we see that control surface 1 isthe optimal surface to choose among the 3 control sur-faces. Control surface 1 does not go through any flownon-linearities even though it has been placed quiteclose to the jet flow and at the same time it has ahigher frequency resolution than the other two controlsurfaces since the grid spacing around it is finer thanthat around the other two surfaces.

It should be also mentioned at this point that al-though Bogey and Bailly33,34 used a computationalgrid that is comparable in size to our grid, their cutoffStrouhal number was 2.0 which is lower than our cutoffStrouhal number of 3.0 obtained with control surface1. In their LES calculations, Bogey and Bailly33,34

use direct LES data in the immediate surroundings ofthe jet to evaluate the near field jet noise only. Theydo not employ integral acoustics methods to estimatethe far field noise. Since they directly compute thenoise in the near field only, their computational gridis more mildly stretched compared to ours. However,since we are employing integral acoustics methods inour methodology to compute the far field noise, wechoose to pack most of the grid points inside the jetflow and do rapid grid stretching outside. Then, plac-ing a control surface such as control surface 1 quiteclose to the jet flow allows us to obtain higher cutofffrequencies in the subsequent noise calculations.

The acoustic pressure spectra predicted by the 3

θ (deg)

OA

SP

L(d

B)

20 30 40 50 60 70 80 90104

106

108

110

112

114

116

LES + FWH Control Surface 1LES + FWH Control Surface 2LES + FWH Control Surface 3

Fig. 5 Overall sound pressure levels along the farfield arc obtained with the data gathered on the 3control surfaces and the Ffowcs Williams - Hawk-ings method.

θ (deg)

OA

SP

L(d

B)

20 30 40 50 60 70 80 90104

106

108

110

112

114

116

LES + Kirchhoff Control Surface 1LES + Kirchhoff Control Surface 2LES + Kirchhoff Control Surface 3

Fig. 6 Overall sound pressure levels along the farfield arc obtained with the data gathered on the 3control surfaces and Kirchhoff’s method.

control surfaces were integrated over their correspond-ing resolved frequency range to determine the over-all sound pressure levels (OASPL). The overall soundpressure level predictions of the FWH and Kirchhoff’smethods using the data gathered on the 3 controlsurfaces are given in figures 5 and 6, respectively.Since control surface 3 has the lowest cutoff frequency,the OASPL values predicted by control surface 3 areslightly lower than those predicted by control surface2. Similarly, the OASPL values predicted by controlsurface 2 are lower than those predicted by control sur-face 1 that has the highest cutoff frequency. It shouldalso be noted here that since a relatively short domain

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θ (deg)

OA

SP

L(d

B)

10 20 30 40 50 60 70 80 90 100 110 120100

102

104

106

108

110

112

114

116

118

120

LES + FWH Control Surface 1SAE ARP 876C predictionPrevious ReD = 105 jet LES + FWHMollo-Christensen et al. data (cold jet)Lush data (cold jet)Stromberg et al. data (cold jet)

Fig. 7 The Ffowcs Williams - Hawkings methodprediction for the overall sound pressure levelsalong the far field arc and comparison with otherdata.

θ (deg)

OA

SP

L(d

B)

10 20 30 40 50 60 70 80 90 100 110 120100

102

104

106

108

110

112

114

116

118

120

LES + Kirchhoff Control Surface 1SAE ARP 876C predictionPrevious ReD = 105 jet LES + FWHMollo-Christensen et al. data (cold jet)Lush data (cold jet)Stromberg et al. data (cold jet)

Fig. 8 Kirchhoff’s method prediction for the over-all sound pressure levels along the far field arc andcomparison with other data.

length of 34ro was used in this study, the streamwiselength of the control surfaces is not sufficient to cap-ture the acoustic waves travelling at the shallow angles,i.e. θ < 40◦. Hence, the predicted OASPL values showa sharp drop-off at the shallow angles. Figures 7 and8 compare the OASPL predictions of the FWH andKirchhoff’s methods with the experimental data aswell as with the SAE ARP 876C54 database predictionand the previous Reynolds number 100,000 jet LES re-sult.49 Although the numerical predictions are a fewdB louder than the experiments, the overall agreementis encouraging. One reason for the overprediction ofthe numerical results relative to experimental measure-


SP

L(d

B/S

t)

0 0.5 1 1.5 2 2.5 390

100

110

120

130 Our spectrum at x = 29ro and r = 12roBogey and Bailly’s spectrum at x = 29ro and r = 12ro

Our cutoff frequencyBogey and Bailly’scutoff frequency

Fig. 9 The Ffowcs Williams - Hawkings methodprediction for the acoustic pressure spectrum atx = 29r0, r = 12ro and comparison with the spec-trum of Bogey and Bailly.34


SP

L(d

B/S

t)

0 0.5 1 1.5 2 2.5 390

100

110

120

130 Our spectrum at x = 11ro and r = 15roBogey and Bailly’s spectrum at x = 11ro and r = 15ro

Our cutoff frequency

Bogey and Bailly’scutoff frequency

Fig. 10 The Ffowcs Williams - Hawkings methodprediction for the acoustic pressure spectrum atx = 11r0, r = 15ro and comparison with the spec-trum of Bogey and Bailly.34

ments is believed to be the inflow forcing employed inthe simulations.

Next, we will do comparisons of our acoustic pres-sure spectra at 2 observation points with those ofBogey and Bailly.34 Figures 9 and 10 do the com-parisons at the observation points x = 29r0, r = 12ro

and x = 11r0, r = 15ro, respectively. Our spectra atthese points were computed by coupling the data oncontrol surface 1 with the FWH method, while thoseof Bogey and Bailly34 are based on data directly pro-vided by their LES. As can be seen from figure 9, thetwo spectra are quite similar at the observation point

8 of 20


x / ro

(vx’)

rms/U

o

0 5 10 15 20 250

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Current LESBogey and Bailly’s LES

Fig. 11 Axial profile of the root mean square ofaxial fluctuating velocity along r = ro and compar-ison with the profile of Bogey and Bailly.34

x = 29r0, r = 12ro. At this observation point, thecutoff frequency of Bogey and Bailly34 corresponds toStrouhal number of 2.0, while our cutoff frequency isat Strouhal number 3.0 since that is the maximumfrequency we can accurately resolve using the datagathered on control surface 1. These cutoff frequen-cies are also shown in the figure. It is seen that thespectrum of Bogey and Bailly is a few dB louder thanours. Figure 10 shows the spectra comparison at theobservation point at x = 11r0, r = 15ro. This time,Bogey and Bailly’s34 cutoff frequency correspond toStrouhal number of about 1.1 due to their coarsenedgrid spacing at the given observation point. Our cut-off frequency at this location is still 3.0. The figureshows that Bogey and Bailly’s34 spectrum is similarto ours until Strouhal number 1.1, then their spec-trum exhibits a sharp drop-off while ours continuesuntil Strouhal number 3.0. Again, it is observed thattheir spectrum is a few dB louder than ours. At thisstage, one might wonder as to why the far field noisepredictions of Bogey and Bailly34 are not identical toours since exactly the same inflow forcing was usedand all other flow parameters were kept the same inboth simulations. The answer is to be found in the dif-ferent numerical methods used in the two simulations.Bogey and Bailly34 employed high-order accurate ex-plicit finite differencing and explicit spatial filteringschemes in their calculations, whereas we have usedimplicit compact differencing and implicit spatial fil-tering schemes in our simulation. Since different nu-merical techniques have different characteristics, thedifferences observed are not surprising.

The differences between the two simulations canbe further examined by comparing some turbulencestatistics. The streamwise profiles of the root mean

x / ro

(vr’)

rms/U

o

0 5 10 15 20 250

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18


Fig. 12 Axial profile of the root mean square ofradial fluctuating velocity along r = ro and compar-ison with the profile of Bogey and Bailly.34

square of the fluctuating axial and radial velocitiesalong r = ro are plotted in figures 11 and 12, re-spectively and comparisons are done with the corre-sponding profiles of Bogey and Bailly.34 Although ourprofiles and theirs are qualitatively similar, their pro-files have higher peak levels than ours. Furthermore,their peaks are located slightly downstream of ours.Bogey and Bailly34 have observed that the sidelinenoise levels are directly linked to the radial velocityfluctuations in the shear layer. They showed that thelower the peak of the radial velocity fluctuations inthe jet shear layer, the lower the sideline noise lev-els. This observation and the fact that the peak ofour fluctuating radial velocity profile given in figure12 is lower than that of Bogey and Bailly34 explainwhy our acoustic pressure spectrum at the x = 11r0,r = 15ro observation location is lower than theirs overthe frequency range 0 < St < 1.1 in figure 10. Thereader is once again reminded of the fact that the Bo-gey and Bailly’s34 spectrum has a cutoff frequencyat St = 1.1 at this observation location. Figures 13and 14 show the centerline variation of the root meansquare of the fluctuating axial and radial velocitiesand compare them with those of Bogey and Bailly.34

Our centerline profiles peak at a location downstreamof their peaks. Our peaks are also seen to be lowerthan those of Bogey and Bailly.34 Our peak valuesfor (v′

x)rms/Uo and (v′r)rms/Uo on the jet centerline

are 0.117 and 0.100, respectively, while those of Bogeyand Bailly34 are 0.120 and 0.106, respectively. Arak-eri et al.55 obtained an experimental value of 0.12 forthe peak (v′

x)rms/Uo on the centerline of a jet withinitially transient shear layers. The experimental jetstudied by Arakeri et al.55 was a Mach 0.9 jet withReynolds number 500,000. Lau et al.56 measured a

9 of 20


x / ro

(vx’)

rms/U

o

0 5 10 15 20 250

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13


Fig. 13 Centerline profile of the root mean squareof axial fluctuating velocity and comparison withthe profile of Bogey and Bailly.34

peak value of 0.14 for (v′x)rms/Uo on the centerline of

a Mach 0.9, Reynolds number 1 million jet with ini-tially turbulent shear layers. Lau et al.56 also reporteda value of 0.11 for the peak (v′

r)rms/Uo on the jetcenterline from the same experiment. The numericalpredictions for the peak (v′

x)rms/Uo and (v′r)rms/Uo on

the jet centerline are seen to be in reasonable agree-ment with the experimental measurements. In theirstudy, Bogey and Bailly34 have also noted that thedownstream noise levels are related to the centerlineturbulence intensities. They showed that the lower thepeak of the centerline turbulence intensities, the lowerthe downstream noise levels. Since our jet’s centerlineturbulence intensities are lower than those of Bogeyand Bailly,34 we can now see why our spectrum at thex = 29r0, r = 12ro location is lower than theirs.

The aeroacoustics results presented so far were ob-tained using an open control surface. Due to therelatively short streamwise control surface length, theacoustic pressure signals at observation angles lessthan 40◦ on the far field arc were not accurately cap-tured. To see the effects of closing the control surfaceat the outflow, a new study was conducted. A new con-trol surface that starts one jet radius downstream ofthe inflow boundary and extends to 31ro in the down-stream direction was generated. This control surfaceis the same as the open control surface 1 used in theaeroacoustics studies presented earlier in this section.The current control surface is truncated at x = 31ro

whereas the previous open control surface extended upto x = 35ro. The outflow surface of the new controlsurface was placed at x = 31ro. Since the physical por-tion of the domain ends at around x = 35ro, placingthe outflow surface a few radii away from the end of thephysical domain ensures that the flow data gathered on

x / ro

(vr’)

rms/U

o

0 5 10 15 20 250

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12


Fig. 14 Centerline profile of the root mean squareof radial fluctuating velocity and comparison withthe profile of Bogey and Bailly.34

θ (deg)

OA

SP

L(d

B)

10 20 30 40 50 60 70 80 90 100 110 120100

102

104

106

108

110

112

114

116

118

120

Open control surfaceClosed control surfaceSAE ARP 876C predictionMollo-Christensen et al. data (cold jet)Lush data (cold jet)Stromberg et al. data (cold jet)

Fig. 15 Overall sound pressure levels along the farfield arc obtained using the open and closed controlsurfaces of streamwise length 30ro.

the outflow surface are not affected by the presence ofthe sponge zone. The data gathered on the new con-trol surface were coupled with the FWH method tocompute the far field noise. No refraction correctionswere included when the control surface was closed onthe outflow surface. The FWH method required about59 hours of computing time on 136 POWER3 proces-sors of an IBM-SP3 to compute the 4096-point timehistory at a total of 504 far field points. Figure 15 plotsthe OASPL predictions on the far field arc which wereobtained using the data gathered on the closed controlsurface and makes comparisons with other data. TheOASPL values at all observation angles are shifted upby some amount when the control surface is closed at

10 of 20


the outflow. The effect of the closed control surfaceappears to be minimal for the range of observationangles where 50◦ < θ < 65◦, though. The increaseof the OASPL at the shallow observation angles is ex-pected, however, we clearly see a spurious effect for therange where θ > 80◦. The OASPL profile in this rangeis very slowly decreasing with the observation angle.A similar observation was recently made by Rahier et

al.57 who conducted a study of surface integral acous-tic methods and looked at the sensitivity of far fieldnoise results to the placement of closed control sur-faces in the non-linear flow field. The spurious effectobserved here is attributed to the fact that we haveplaced a control surface inside the non-linear flow re-gion ignoring the noise due to the quadrupole sourcesoutside the control surface. Rahier et al.57 also gavethe same reason for the similar spurious effects theyhave observed. We also believe that an effective lineof dipole sources is created as the quadrupoles exit thedownstream surface. These dipole sources can also bepartially responsible for the spurious effects observedhere. It is believed that moving the outflow surface fur-ther downstream will reduce the strength of the lineof dipoles appearing on the outflow surface. This issupported by the observation of Rahier et al.57 whichsays that the spurious effects weaken as the outflowFWH control surface is moved further downstream.Finally, we look at the acoustic pressure spectra pre-dictions at the θ = 30◦ and θ = 60◦ locations on thefar field arc. Figure 16 shows the two spectra at theθ = 30◦ observation point which were computed usingthe open and closed control surfaces. It is clear that atthe θ = 30◦ location, the spectral energy is shifted upat all frequencies when the control surface is closed onthe outflow surface. The spectra at θ = 60◦ computedusing the open and closed control surfaces are shownin figure 17. The differences in the two spectra are mi-nor at this observation point, hence the outflow surfacedoes not have much influence on the noise spectrumat the θ = 60◦ observation location.

Computation of the Far Field Noise

Using Lighthill’s Acoustic Analogy

We also computed the far field noise of the Reynoldsnumber 400,000 jet using Lighthill’s acoustic anal-ogy. As mentioned in the previous section, data fromthe simulation which was performed without any ex-plicit SGS model were used for this purpose. Thespatial filter was treated as the effective SGS modelin the LES. Far field noise computations done usingLighthill’s acoustic analogy will be compared with theFWH method results as well as with some experimen-tal noise spectra in this section. Due to space limita-tions, only a short summary of the noise computationsusing Lighthill’s acoustic analogy will be presented inthis section. More details can be found in Uzun.41


SP

L(d

B/S

t)

0 0.5 1 1.5 2 2.5 388

92

96

100

104

108

112

116

120

Open control surfaceClosed control surface

Fig. 16 Acoustic pressure spectra at R = 60ro, θ =

30◦ location on the far field arc. (Obtained using

the open and closed control surfaces of streamwiselength 30ro.)


SP

L(d

B/S

t)

0 0.5 1 1.5 2 2.5 392

96

100

104

108

112

Open control surfaceClosed control surface

Fig. 17 Acoustic pressure spectra at R = 60ro, θ =

60◦ location on the far field arc. (Obtained using

the open and closed control surfaces of streamwiselength 30ro.)

Lighthill’s equation15 can be written as

∂2ρ′

∂t2− c2

∞

∂2ρ′

∂xi∂xi

=∂2Tij

∂xi∂xj

, (3)

where the Lighthill stress tensor, Tij is given as

Tij = ρuiuj + (p − c2∞ρ)δij , (4)

with the viscous stress term neglected. In Lighthill’sequation, all effects other than propagation, such asrefraction, are lumped into the right hand side. Itshould be stated here that the right hand side of the

11 of 20


above equation is by no means a true or unique repre-sentation of the acoustic sources in the turbulent flow.The double divergence of Tij only serves as a nominalacoustic source and what it provides is an exact con-nection between the near field turbulence and the farfield noise.

In Lighthill’s acoustic analogy, the sound gener-ated by a turbulent flow is equivalent to what thequadrupole distribution Tij per unit volume wouldemit if placed in a uniform acoustic medium at rest. Inother words, in this analogy the quadrupole source dis-tribution replaces the actual fluid flow and moreover,the sources may move, but the fluid in which they areembedded may not. The sources are embedded in amedium at rest that has the constant properties ρ∞,p∞ and c∞, the same as those in the ambient fluidexternal to the flow.

Lighthill15 shows that an approximation to the pres-sure fluctuations at points far enough from the flowregion is given by a volume integral whose integrandcontains the second time derivative of Tij that is eval-uated at retarded times. This volume integral isperformed over the entire turbulent flow region thatcontains the acoustic sources. The time derivative for-mulation of Lighthill’s volume integral will be used inthis section for computing the far field noise.

Following Freund,58 we can split the Lighthill stresstensor, Tij into a mean component, Tm

ij , a component

that is linear in velocity fluctuations, T lij , a component

that is quadratic in velocity fluctuations, Tnij and the

so-called entropy component, T sij , as follows

Tij = Tmij + T l

ij + Tnij + T s

ij , (5)

where

Tmij = ρuiuj + (p − c2

∞ρ)δij , (6)

T lij = ρuiu

′j + ρuju

′i, (7)

Tnij = ρu′

iu′j , (8)

T sij = (p′ − c2

∞ρ′)δij . (9)

By definition, the mean component Tmij does not make

noise. In the above equations, density in the ρuiuj

terms has not been decomposed into a mean and fluc-tuating part. Freund58 shows that the noise from Tij

is nearly the same as that from

T ρij = ρuiuj + (p′ − c2

∞ρ′)δij . (10)

Hence, the effect of the density fluctuations in theρuiuj terms is not considered in this study. The noisefrom T l

ij is called the shear noise since this componentconsists of turbulent fluctuations interacting with thesheared mean flow. On the other hand, the noise fromTn

ij is called the self noise since this component consistsof turbulent fluctuations interacting with themselves,whereas the noise from T s

ij is called the entropy noise

since it is composed of the density and pressure fluc-tuations in the turbulent flow that differ from theisentropic relation.

The 5 primitive flow variables were saved in nearly7.5 million cell volumes inside the jet flow at every 10time steps over a period of 40,000 time steps during theLES run. The sampling period corresponds to a timescale in which an ambient sound wave travels about 23times the domain length in the streamwise direction.The flow data were saved in double precision formatand the entire flow field database consisted of almost1.2 Terabytes (TB) of data. Figures 18 through 20 de-pict the distribution of the second time derivative ofTnn (where n is the direction of the observer) that ra-diates noise in the direction of the observers located at30◦, 60◦, and 90◦ on an arc of radius 60ro from the jetnozzle. The solid dark lines in these figures correspondto the boundaries of the volume in which time accurateLES data were saved. The volume starts at the inflowboundary and extends to 32 jet radii in the streamwisedirection. The initial width and height of the volumeare 10ro at the inflow boundary. At x = 32ro, thewidth and height of the volume are 20ro. As can beseen from the figures, the lateral boundaries are suf-ficiently far away from the sources that radiate noise.After a careful analysis of the spatial extent of thesources that radiate noise and based on the grid reso-lution in the region where the sources are located, thecutoff frequency in the subsequent noise calculationswas found to be located at around Strouhal number4. Based on the data sampling rate, there are about4 temporal points per period in this highest resolvedfrequency. An 8th-order accurate explicit scheme willbe employed for computing the time derivatives whilecomputing the noise and 4 points per period is suffi-cient for this numerical scheme.48 It should also benoted here that this cutoff frequency is higher thanthe Strouhal number 3 cutoff frequency of the previ-ous aeroacoustics computations that employed surfaceintegral acoustics methods. This is because the gridspacing is finest inside the jet and gets coarser outsidethe jet flow. Hence, the maximum frequency that canbe accurately captured by the control surfaces placedaround the jet flow is lower than that can be capturedin the volume integrals. Lighthill’s volume integralwas computed using 1160 processors in parallel onthe Lemieux cluster at the Pittsburgh SupercomputingCenter.

As we had done previously, we computed the over-all sound pressure levels and acoustic pressure spectraalong a far field arc of radius 60ro from the jet nozzlein this study. There are 14 observer points on the farfield arc. Even though acoustic pressure spectra wereaveraged over 36 equally spaced azimuthal points on afull circle at a given observer location in the previoussection, we determined through numerical experimen-tation that averaging the spectra over 8 equally spaced

12 of 20


x / ro

y/r

o

0 4 8 12 16 20 24 28 32-10

-5

0

5

10Boundary of the integration volume

Fig. 18 Instantaneous distribution of the secondtime derivative of Tnn that radiates noise in thedirection of the observer at R = 60ro, θ = 30

◦ on thefar field arc.

x / ro

y/r

o

0 4 8 12 16 20 24 28 32-10

-5

0

5




azimuthal points gives almost the same averaged spec-trum as that obtained by averaging the spectra over36 equally spaced azimuthal points. Hence, in orderto save computing time, the acoustic pressure signalswere computed at only 8 equally spaced azimuthalpoints on a full circle at a given θ location on the arc.The 3072-point time signal at a given observer loca-tion was then broken up into 3 1024-point signals andthe 1024-point signals were used in the spectral analy-sis. Hence, there were a total of 24 1024-point signalsavailable for a given observer point on the arc. The 24acoustic pressure spectra were used to obtain the aver-aged spectrum which was integrated later to computethe overall sound pressure level at the given θ locationon the arc. For 112 far field points, the total run timeneeded was about 15 hours on 1160 processors.

The distribution of the Lighthill sources that radiatenoise in the direction of the observers located at 30◦,60◦, and 90◦ on the far field arc was previously shown

x / ro

y/r

o

0 4 8 12 16 20 24 28 32-10

-5

0

5




in figures 18 through 20. As can be seen from these fig-ures, although the sources near the outflow boundaryat x = 32ro seem to be relatively weak for the ob-servers located at 30◦ and 60◦ on the arc, the sourcesthat radiate noise in the direction of the observer at90◦ are somewhat stronger near the outflow boundary.Thus it seems that a longer streamwise domain lengthwill help the convecting acoustics sources to decay suf-ficiently. The implications of truncating the domain atx = 32ro will be discussed in more detail shortly.

We first looked at the effect of the integration do-main size on the far field noise estimations. For thispurpose, Lighthill’s volume integral was carried outfor 3 different streamwise domain lengths. The do-main lengths considered were 24ro, 28ro and 32ro,respectively. Figure 21 shows the Lighthill’s volumeintegral predictions for the 3 different streamwise do-main lengths and makes comparisons with experimen-tal data as well as with the open and closed controlsurface predictions of the FWH method from the pre-vious section. From this figure, it is clear that as theintegration domain size is increased from 24ro to 32ro,the overall sound pressure levels at all observation an-gles other than those in the range 60◦ < θ < 80◦,decrease as much as 2 dB. The changes in OASPLfor observation angles greater than 90◦, on the otherhand, are on the order of 2 to 3 dB. This observa-tion implies that there are significant noise cancella-tions taking place as one includes a longer streamwiselength in the volume integration and such cancella-tions cause a reduction in the overall sound pressurelevels for certain observation angles in the far field.The difference in the OASPL predictions when the in-tegration domain size is increased from 28ro to 32ro

is within 1 dB for the observation angles θ < 80◦.The OASPL curve that is obtained when the integra-tion domain length is 32ro has an almost flat portionin the range where 80◦ < θ < 120◦. On the other

13 of 20


θ (deg)

OA

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0 10 20 30 40 50 60 70 80 90 100 110 120100

102

104

106

108

110

112

114

116

118

120

122

Lighthill’s integral until x = 24roLighthill’s integral until x = 28roLighthill’s integral until x = 32roLES + FWH open control surfaceLES + FWH closed control surfaceMollo-Christensen et al. data (cold jet)Lush data (cold jet)Stromberg et al. data (cold jet)

Fig. 21 Overall sound pressure levels of the noisefrom Tij along the far field arc.

hand, the experimental data show a continuous dropat those observation angles. The spurious effects ob-served here are quite similar to those observed in theprevious section when the FWH method was appliedon a closed control surface. It is also interesting tonote that the MGB method59 shows that the sourcesbeyond 32ro in a jet are not significant. It can also beargued at this point that the sudden truncation of thedomain in the current computations creates spuriousdipole sources on the outflow surface as the quadrupolesources pass through downstream surface. Such spuri-ous dipole sources could be partially responsible for thebehavior seen in the OASPL plot for the range whereθ > 80◦. Since all acoustic sources decay as we movedownstream, a longer streamwise domain will improvethe predictions for θ > 80◦. In his study, Freund58

also observed substantial noise cancellations happen-ing among the noise generated in different streamwisesections of the jet, however he did not get the spuriouseffects we observe here. His streamwise domain sizewas 31ro. So it appears that although the acousticsources decay by x = 31ro for a low Reynolds numberjet, they have a larger streamwise extent in the presenthigh Reynolds number jet.

Figure 22 shows the OASPL values of the noise fromTij and its individual components T l

ij , Tnij and T s

ij

when the streamwise integration domain extends upto 32ro. Even though the current jet is an isothermaljet (To/T∞ = 1), the entropy noise from T s

ij is signif-icant near the jet axis where the observation angle issmall, but becomes insignificant at large angles. It isalso observed from the figure that the shear noise fromT l

ij and the self noise from Tnij are louder than the total

noise from Tij for observation angles θ < 40◦ while theentropy noise from T s

ij is louder than the total noisefor θ < 15◦. The shear noise reaches its minimum

θ (deg)

OA

SP

L(d

B)

0 20 40 60 80 100 120 140 1609092949698

100102104106108110112114116118120122124126

total noise from Tijshear noise from Tlijself noise from Tnijentropy noise from Tsij

Fig. 22 Overall sound pressure levels of the noisefrom Tij and its components along the far field arc.(Volume integrals are performed until x = 32ro.)

θ (deg)

Co

rrel

atio

nco

effic

ien

t

0 20 40 60 80 100 120 140 160-1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

Cln

Cls

Cns

Fig. 23 Variation of the correlation coefficientsalong the far field arc.

OASPL value at around θ = 80◦ and starts to increasefor larger angles, whereas the self noise exhibits a con-tinuous drop. The fact that the shear noise, self noiseand entropy noise components are more intense thatthe total noise for some observation angles near thejet axis implies that the noise from the different com-ponents must be correlated as suggested by Freund58

so that significant cancellations are happening amongthe noise generated by the individual components. Tosee the correlation between the noise components, wecan define the following correlation coefficients,58

Cln =〈plpn〉

plrmsp

nrms

, Cls =〈plps〉

plrmsp

srms

, Cns =〈pnps〉

pnrmsp

srms

,

(11)

14 of 20



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94

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106

108

110

112

114

116

118

120

Lighthill’s integral until x = 24roLighthill’s integral until x = 28roLighthill’s integral until x = 32ro

Fig. 24 Spectra of the noise from Tij at the R =


where the superscripts l, n, and s indicate the shearnoise from T l

ij , the self noise from Tnij and the entropy

noise from T sij , respectively. The correlation coeffi-

cients Cln, Cls and Cns are plotted in figure 23. Forobservation angles in the range θ < 40◦, the shearnoise from T l

ij cancels the self noise from Tnij with a

correlation coefficient on the order of -0.6. There isalso some correlation between the self noise from Tn

ij

and the entropy noise from T sij at the small observa-

tion angles where the correlation coefficient has a valuearound -0.3. The shear noise from T l

ij and the entropynoise from T s

ij also cancel each other at very small an-gles near the jet axis with a correlation coefficient ofalmost -0.3. The correlation coefficient between thesetwo noise components starts to rapidly move towardszero as the observation angle increases and reaches apositive value in between 0.1 and 0.2 at the θ = 40◦

observation point. It then starts to approach towardsthe zero line for larger observation angles. All correla-tions reach a value close to zero at around the θ = 80◦

and θ = 90◦ locations.

Figures 24 through 26 depict the acoustic pressurespectra at the observation angles of 30◦, 60◦, and 90◦

on the far field arc. Comparisons are shown for 3streamwise domain lengths over which Lighthill’s vol-ume integral is carried out. As mentioned earlier, thecutoff noise frequency in the current computations islocated around Strouhal number 4, hence the portionof the spectra for frequencies greater than Strouhalnumber 4 is cut off. The spectra at the θ = 60◦

location show minor changes as the integration do-main is increased from 24ro to 32ro, whereas thereare more significant changes at the other observationangles. At the 30◦ and 90◦ observation angles, thehigh frequency part of the spectra shifts down as theintegration domain increases along the streamwise di-


SP

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t)

0 0.5 1 1.5 2 2.5 3 3.5 486

88

90

92

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112





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0 0.5 1 1.5 2 2.5 3 3.5 474767880828486889092949698

100102104106108110




rection. Spurious dipole line strength is reduced as theoutflow surface is moved further downstream.

Next, we look at the noise spectra of the individualcomponents of Tij at the observation locations of 30◦

and 60◦ on the far field arc. Figures 27 and 28 plotthe total noise from Tij , shear noise from T l

ij , self noisefrom Tn

ij and entropy noise from T sij for these two ob-

servation angles, respectively. As can be seen in figure27, at 30◦, the peak of the shear noise spectrum coin-cides with that of the total noise at around Strouhalnumber 0.3. We see the high frequency part of boththe shear noise and the self noise spectra is more ener-getic than that of the total noise. The entropy noise isrelatively weak over most of the frequency range whencompared with the shear noise and the self noise. Fig-ure 23 shows that at the observation angle of 30◦, the

15 of 20



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96

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Fig. 27 Spectra of the noise from Tij and its com-ponents at the R = 60ro, θ = 30

◦ location on the farfield arc.


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0 0.5 1 1.5 2 2.5 3 3.5 472

76

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Fig. 28 Spectra of the noise from Tij and its com-ponents at the R = 60ro, θ = 60

◦ location on the farfield arc.

shear noise and the self noise cancel each other witha correlation coefficient of about -0.6, whereas the selfnoise and the entropy noise cancel each other with acorrelation coefficient of about -0.3. Hence, the inter-action of the shear noise, self noise and entropy noiseat the 30◦ location results in a total noise spectrumthat that has reduced spectral energy levels in the highfrequency range.

From figure 28, it is seen that the total noise spec-trum is very similar to the self noise spectrum at the60◦ location. The portion of the shear noise spectrumfor Strouhal number greater than 2 has the same spec-tral energy levels as the self noise spectrum. Exceptfor the low frequency region, the entropy noise is very

weak over the entire frequency range. From figure 23,we now see that at the observation angle of 60◦, theshear noise and the self noise cancel each other with acorrelation coefficient of about -0.4, whereas the selfnoise and the entropy noise cancel each other witha correlation coefficient of about -0.15. Such an in-teraction among the noise components at the givenobservation point causes the total noise spectrum tobe essentially the same as the self noise spectrum.

It seems appropriate at this point to compare thecurrent far field noise spectra predictions with the re-sults previously obtained by using the FWH methodand also with some experimental noise spectra recentlyobtained from the NASA Glenn Research Center.60

Experimental noise data from a Mach 0.85 cold jetwill be shown in the comparisons. The Mach numberof this jet is close enough to that of our simulated jet.The estimated Reynolds numbers of the experimentaljet is approximately 1.2 million, while the ratio of thejet temperature to the ambient temperature is 0.88.The far field noise spectra of the experimental jet wereobtained at 40 jet diameters away from the nozzle. Inorder to facilitate the comparison with numerical re-sults, the experimental noise spectra were shifted to 30jet diameters away from the nozzle using the 1/r decayassumption of the acoustic waves. In this adjustment,the experimental SPL values were shifted upwards byapproximately 2.5 dB/St. Moreover, since the Machnumber of the experimental jet was not exactly 0.9, theexperimental noise spectra were also adjusted for Mach0.9 following the SAE ARP 876C guidelines.54 Thespectra obtained from the previous Reynolds number100,000 jet simulation49 will also be included in thecomparisons. Figures 29 through 31 make compar-isons at the observation locations of 30◦, 60◦ and 90◦,respectively. All spectra shown in these figures arecurve fits to the actual data. The FWH method resultsfor the Reynolds number 400,000 jet are shown bothfor the open and closed control surfaces. The readeris reminded here that the open control surface extendsuntil x = 31ro and the outflow surface which closesthe control surface is placed at the x = 31ro location,whereas the Lighthill volume integral was performeduntil the x = 32ro downstream location. The slightdifference in the streamwise extent of the surface andvolume integrals is not expected to cause a signifi-cant difference in the comparisons. The FWH methodresults for the Reynolds number 100,000 jet were ob-tained using an open surface that extended 59ro inthe streamwise direction. At the 30◦ location, we seethat the closed surface FWH method prediction for theReynolds number 400,000 jet is in fairly good agree-ment with Lighthill’s acoustic analogy until Strouhalnumber 2 or so. Then, we observe higher spectral en-ergy levels in Lighthill’s acoustic analogy predictionfor higher frequencies. The open surface FWH methodprediction for the Reynolds number 400,000 jet, on the

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other hand, shows lower spectral energy levels at allfrequencies. This is due to the fact that the relativelyshort open control surface cannot effectively capturethe acoustic waves travelling at the shallow angles. Itis interesting to note that the agreement of the shapeof the Reynolds number 100,000 jet noise spectrumwith the experimental spectrum until Strouhal num-ber 1 is better than that between the Reynolds number400,000 jet noise spectra and the experiment. The rea-son for this is believed to be the fact that the largerdomain in the Reynolds number 100,000 LES allowsa better evaluation of the lower frequencies. For theReynolds number 400,000 jet, the Lighthill predictionseems to be showing the best qualitative agreementwith the experimental noise spectrum at this observa-tion location. The peaks of all noise spectra in thefigure are seen to be in the Strouhal number 0.25 -0.3 range. However, the experimental spectrum ex-hibits a much stronger decay right after the peak. Thedecay rate of the spectrum obtained from Lighthill’sacoustic analogy seems to be similar to the experimen-tal spectrum decay rate in the frequency range where1.5 < St < 3.0. Then, the Lighthill spectrum decayswith a faster rate for the higher frequencies. At the60◦ location, for the Reynolds number 400,000 jet, theFWH method yields almost identical results for theopen and the closed control surfaces. The Lighthillprediction is also in acceptable agreement with theFWH prediction, considering the fact that the twomethods are based on completely different formula-tions. The comparison with the experimental noisespectrum at this observation location reveals that theexperimental peak is located at a lower frequency thanthat of the numerical predictions. Furthermore, thenumerical results for the Reynolds number 400,000 jetshow a faster spectrum decay rate at the higher fre-quencies. The decay of the Reynolds number 100,000jet spectrum after the peak takes place at a faster ratethan that observed in the Reynolds number 400,000jet spectra as well as in the experiment. Finally, thecomparison at the 90◦ location shows that the closedsurface FWH prediction gives increased spectral en-ergy levels relative to those given by the open surfaceFWH prediction. The Lighthill prediction is seen tobe in between the two predictions given by the FWHmethod. It should be repeated here once again thatfrom our previous analysis, the spectra of the Reynoldsnumber 400,000 jet for observation angles in the rangeθ > 80◦ are expected to be affected by a spuriousline of dipoles appearing on the outflow surface as thequadrupole sources move out of the control volume.The numerical predictions at this observation locationonce again reveal a spectrum decay rate that is largerthan that of the experimental noise spectra. The de-cay of the the Reynolds number 100,000 jet spectrumtakes place at a faster rate than that of the Reynoldsnumber 400,000 jet spectra. The experimental peak is


SP

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0 0.5 1 1.5 2 2.5 3 3.5 485

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125

Open control surface + FWHClosed control surface + FWHLighthill’s volume integral until x = 32roPrevious ReD = 105 jet LES + FWHNASA M=0.85 cold jet adjusted to M=0.9

Fig. 29 Acoustic pressure spectra comparisons atthe R = 60ro, θ = 30

◦ location on the far field arc.


SP

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0 0.5 1 1.5 2 2.5 3 3.5 485

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again located at a lower frequency than that of the nu-merical predictions. The comparison of the numericalOASPL predictions against the OASPL values of theNASA Mach 0.85 cold jet and the SAE ARP 876C54

database prediction along the far field arc is plotted infigure 32. We see OASPL differences as high as 6 dBbetween the numerical predictions and the NASA ex-perimental jet. The agreement between the numericalOASPL values and the SAE ARP 876C54 predictionseems to be better.

The differences observed between the shape of thenumerical and experimental noise spectra might bedue to various reasons. One reason could be themismatch of the inflow conditions in the numericalsimulations with those in the actual experiment. Theexperiment was performed at a high enough Reynolds

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number so that the jet shear layers at the nozzle exitwere fully turbulent. In the numerical simulations,since it was deemed computationally too expensive toinclude the nozzle geometry, laminar shear layers werefed into the domain and randomized velocity fluctua-tions in the form of a vortex ring were imposed intothe jet shear layers. Moreover, it has been observedexperimentally61,62 that high-frequency sources are lo-cated a small distance downstream of the jet nozzleand a significant portion of the noise spectrum orig-inates from this near field of the jet. Hence, thehigh-frequency noise generated in the near-nozzle jetshear layer within a few diameters downstream of thenozzle exit is missing in the current simulations. Theabsence of the noise generated just downstream of thenozzle could be responsible for the faster decay ratesin the high frequency range of the spectra in the cur-rent computations. The present findings once againemphasize the importance of correctly modelling theinflow conditions in jet noise simulations. It is also be-lieved that the limited domain size in the simulationsmight influence the low frequencies.

Concluding Remarks

Using state-of-the-art numerical techniques, we havedeveloped and tested a Computational Aeroacoustics(CAA) methodology for jet noise prediction. TheCAA methodology has two main components. Thefirst one is a 3-D Large Eddy Simulation (LES) code.The latest version of the LES code employs high-order accurate compact finite differencing as well asimplicit spatial filtering schemes together with Tamand Dong’s boundary conditions on the LES domainboundaries. Explicit time integration is accomplishedby means of the standard 4th-order, 4-stage Runge-Kutta method. The localized dynamic Smagorinskysubgrid-scale model is utilized to model the effect of

θ (deg)

OA

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0 10 20 30 40 50 60 70 80 90102

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Open control surface + FWHClosed control surface + FWHLighthill’s integral until x = 32roPrevious ReD = 105 jet LES + FWHSAE ARP 876C predictionNASA M=0.85 cold jet adjusted to M=0.9

Fig. 32 Overall sound pressure levels along the farfield arc.

the unresolved scales on the resolved scales. The codealso has the capability to turn off the dynamic SGSmodel and perform simulations by treating the spatialfilter as an implicit SGS model. The second com-ponent of the CAA methodology consists of integralacoustics methods. We have developed acoustics codesthat employ Kirchhoff’s and Ffowcs Williams - Hawk-ings (FWH) methods as well as Lighthill’s acousticanalogy.

In this paper, we presented results from an LESdone for a Reynolds number 400,000 jet. A muchmore detailed report of this research can be foundin Uzun.41 The time accurate LES data were cou-pled with integral acoustics methods for far field noisecalculations. Far field aeroacoustics results also com-pared favorably with existing experimental measure-ments. The possible reasons for the discrepanciesbetween numerical predictions and experiments werediscussed. In our Reynolds number 400,000 jet sim-ulations, the highest noise frequency resolved in thesurface integral acoustics calculations corresponded toStrouhal number 3, while the highest frequency re-solved when Lighthill’s acoustic analogy was employedcorresponded to Strouhal number 4. Both of thesefrequencies are larger than Bogey and Bailly’s cut-off frequency of Strouhal number 2 in their recentReynolds number 400,000 jet LES.33–35 Hence, to ourbest knowledge, the LES and the noise computationsdone for the Reynolds number 400,000 jet in this studyare certainly some of the biggest calculations ever donein jet noise research. Moreover, our noise computa-tions for the Reynolds number 400,000 jet have cutofffrequencies which are greater than the cutoff frequen-cies of all other jet noise LES results in the literatureto date. Use of integral acoustics methods allows clus-tering of the majority of the grid points inside the jet

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flow where non-linear noise generation takes place andrapid grid stretching outside the jet. Consequently, themaximum frequency resolved in noise computationsusing integral acoustics methods is higher compared tothat captured in the simulations (with similar numberof grid points) in which only the near field jet noise iscomputed using direct LES data. Finally, to the bestof our knowledge, computation of the Lighthill volumeintegral over the turbulent near field of a turbulent jetat a reasonably high Reynolds number has been car-ried out for the first time in this study. The Lighthillstress tensor was decomposed into several componentsand the noise generated by the individual componentswas analyzed in detail. We found that significantcancellations occur among the noise generated by theindividual components of the Lighthill stress tensor.Far field noise predictions using the FWH method onthe closed control surface were found be comparable tothose given by Lighthill’s volume integral. Moreover,Lighthill’s acoustic analogy was found to be about 40times more computationally expensive than the FWHmethod. Hence, it is preferable to use the cheaperFWH method over the very expensive Lighthill vol-ume integral if one’s sole purpose is to predict the farfield noise. However, if a connection between the nearfield jet turbulence and the far field noise is sought,then an analysis of the Lighthill source term insidethe jet would be very useful. Both FWH (applied ona closed control surface) and Lighthill’s methods showincreased OASPL levels for observation angles greaterthan 80◦ on the far field arc. Such spurious effects arebelieved to be due to the spurious line of dipoles ap-pearing on the outflow surface and the relatively shortdomain size in the streamwise direction. A longer do-main will decrease the strength of the line of dipolesappearing on the outflow surface.

Acknowledgments

This work was sponsored by the Indiana 21st Cen-tury Research & Technology Fund. A portion of thecomputing time was provided by the National Compu-tational Science Alliance under the grant CTS010032Non the SGI Origin 2000 computer systems located atthe University of Illinois at Urbana-Champaign. Thisresearch was also supported in part by National Sci-ence Foundation cooperative agreement ACI-9619020through computing resources provided by the NationalPartnership for Advanced Computational Infrastruc-ture at the San Diego Supercomputer Center. Compu-tations of the very expensive Lighthill volume integralswere performed on the National Science FoundationTerascale Computing System at the Pittsburgh Su-percomputing Center. The access provided to us byIndiana University to its IBM-SP3 Research Computerfor this research is also gratefully acknowledged. Someof the preliminary computations in this research weredone on the IBM-SP3 computer of Purdue University.

We are grateful to Dr. Christophe Bogey for his helpwith the vortex ring forcing method and the dynamicsubgrid-scale model as well as for sharing some of hisjet simulation results. Sincere thanks also go to Dr.James Bridges for supplying some experimental jetnoise data to us.

References1Freund, J. B., Lele, S. K., and Moin, P., “Direct Numerical

Simulation of a Mach 1.92 Turbulent Jet and Its Sound Field,”AIAA Journal , Vol. 38, No. 11, November 2000, pp. 2023–2031.

2Freund, J. B., “Noise Sources in a Low-Reynolds-numberTurbulent Jet at Mach 0.9,” Journal of Fluid Mechanics,Vol. 438, 2001, pp. 277–305.

3Stromberg, J. L., McLaughlin, D. K., and Troutt, T. R.,“Flow Field and Acoustic Properties of a Mach Number 0.9 Jetat a Low Reynolds Number,” Journal of Sound and Vibration,Vol. 72, No. 2, 1980, pp. 159–176.

4Khavaran, A., Krejsa, E. A., and Kim, C. M., “Com-putation of supersonic jet mixing noise for an axisymmet-ric convergent-divergent nozzle,” Journal of Aircraft , Vol. 31,No. 3, May-June 1994, pp. 603–609.

5Khavaran, A., “Role of anisotropy in turbulent mixingnoise,” AIAA Journal , Vol. 37, No. 7, July 1999, pp. 832–841.

6Koch, L. D., Bridges, J., and Khavaran, A., “Flow fieldcomparisons from three Navier-Stokes solvers for an axisymmet-ric separate flow jet,” AIAA Paper 2002-0672, January 2002.

7Self, R. H. and Bassetti, A., “A RANS based jet noiseprediction scheme,” AIAA Paper 2003-3325, May 2003.

8Hunter, C. A. and Thomas, R. H., “Development of a jetnoise prediction method for installed jet configurations,” AIAAPaper 2003-3169, May 2003.

9Piomelli, U., Streett, C. L., and Sarkar, S., “On the Com-putation of Sound by Large-eddy Simulations,” Journal of En-

gineering Mathematics, Vol. 32, 1997, pp. 217–236.10Rubinstein, R. and Zhou, Y., “Characterization of Sound

Radiation by Unresolved Scales of Motion in ComputationalAeroacoustics,” Tech. Rep. NASA/CR-1999-209688, ICASE Re-port No. 99-39, ICASE, NASA Langley Research Center, Octo-ber 1999.

11Seror, C., Sagaut, P., Bailly, C., and Juve, D., “On theRadiated Noise Computed by Large-eddy Simulation,” Physics

of Fluids, Vol. 13, No. 2, February 2001, pp. 476–487.12Zhao, W., Frankel, S. H., and Mongeau, L., “Effects of

Spatial Filtering on Sound Radiation from a Subsonic Axisym-metric Jet,” AIAA Journal , Vol. 38, No. 11, November 2000,pp. 2032–2039.

13Bodony, D. J. and Lele, S. K., “A Statistical Subgrid ScaleNoise Model: Formulation,” AIAA Paper 2003-3252, May 2003.

14Mankbadi, R. R., Hayder, M. E., and Povinelli, L. A.,“Structure of Supersonic Jet Flow and Its Radiated Sound,”AIAA Journal , Vol. 32, No. 5, May 1994, pp. 897–906.

15Lighthill, M. J., “On Sound Generated Aerodynamically: I.General Theory,” Proceedings of the Royal Society of London,

Series A: Mathematical and Physical Sciences, Vol. 211, No.1107, 1952, pp. 564–587.

16Lyrintzis, A. S. and Mankbadi, R. R., “Prediction of theFar-field Jet Noise Using Kirchhoff’s Formulation,” AIAA Jour-

nal , Vol. 1, No. 2, 1996, pp. 1–4.17Kirchhoff, G. R., “Zur Theorie der Lichtstrahlen,” Annalen

der Physik und Chemie, Vol. 18, 1883, pp. 663–695.18Gamet, L. and Estivalezes, J. L., “Application of Large-

eddy Simulations and Kirchhoff Method to Jet Noise Predic-tion,” AIAA Journal , Vol. 36, No. 12, December 1998, pp. 2170–2178.

19Choi, D., Barber, T. J., Chiappetta, L. M., and Nishimura,M., “Large Eddy Simulation of High-Reynolds Number JetFlows,” AIAA Paper 99-0230, January 1999.

19 of 20


20Zhao, W., Frankel, S. H., and Mongeau, L., “Large EddySimulations of Sound Radiation from Subsonic Turbulent Jets,”AIAA Journal , Vol. 39, No. 8, August 2001, pp. 1469–1477.

21Morris, P. J., Wang, Q., Long, L. N., and Lockhard, D. P.,“Numerical Predictions of High Speed Jet Noise,” AIAA Paper97-1598, May 1997.

22Morris, P. J., Long, L. N., Bangalore, A., and Wang,Q., “A Parallel Three-Dimensional Computational Aeroacous-tics Method Using Nonlinear Disturbance Equations,” Journal

of Computational Physics, Vol. 133, 1997, pp. 56–74.23Morris, P. J., Long, L. N., Scheidegger, T. E., Wang, Q.,

and Pilon, A. R., “High Speed Jet Noise Simulations,” AIAAPaper 98-2290, 1998.

24Morris, P. J., Long, L. N., and Scheidegger, T., “Parallelcomputations of High Speed Jet Noise,” AIAA Paper 99-1873,1999.

25Morris, P. J., Scheidegger, T. E., and Long, L. N., “JetNoise Simulations for Circular Nozzles,” AIAA Paper 2000-2080,June 2000.

26Boluriaan, S., Morris, P. J., Long, L. N., and Scheidegger,T., “High Speed Jet Noise Simulations for Noncircular Nozzles,”AIAA Paper 2001-2272, May 2001.

27Chyczewski, T. S. and Long, L. N., “Numerical Predictionof the Noise Produced by a Perfectly Expanded RectangularJet,” AIAA Paper 96-1730, May 1996.

28Boersma, B. J. and Lele, S. K., “Large Eddy Simulation ofa Mach 0.9 Turbulent Jet,” AIAA Paper 99-1874, May 1999.

29Bogey, C., Bailly, C., and Juve, D., “Computation of theSound Radiated by a 3-D Jet Using Large Eddy Simulation,”AIAA Paper 2000-2009, June 2000.

30Constantinescu, G. S. and Lele, S. K., “Large Eddy Simu-lation of a Near Sonic Turbulent Jet and Its Radiated Noise,”AIAA Paper 2001-0376, January 2001.

31DeBonis, J. R. and Scott, J. N., “Large-Eddy Simulation ofa Turbulent Compressible Round Jet,” AIAA Journal , Vol. 40,No. 7, 2002, pp. 1346–1354.

32Bodony, D. J. and Lele, S. K., “Influence of Inlet Condi-tions on the Radiated Noise of High Speed Turbulent Jets,” In-ternational workshop on “LES for Acoustics”, DLR Gottingen,Germany, October 2002.

33Bogey, C. and Bailly, C., “Direct Computation of theSound Radiated by a High-Reynolds-number, Subsonic RoundJet,” CEAS Workshop From CFD to CAA, Athens, Greece,November 2002.

34Bogey, C. and Bailly, C., “LES of a High Reynolds, HighSubsonic Jet : Effects of the Inflow Conditions on Flow andNoise,” AIAA Paper 2003-3170, May 2003.

35Bogey, C. and Bailly, C., “LES of a High Reynolds, HighSubsonic Jet : Effects of the Subgrid modellings on Flow andNoise,” AIAA Paper 2003-3557, June 2003.

36Uzun, A., Blaisdell, G. A., and Lyrintzis, A. S., “RecentProgress Towards a Large Eddy Simulation Code for Jet Aeroa-coustics,” AIAA Paper 2002-2598, June 2002.

37Uzun, A., Blaisdell, G. A., and Lyrintzis, A. S., “Sensitivityto the Smagorinsky Constant in Turbulent Jet Simulations,”AIAA Journal , Vol. 41, No. 10, October 2003, pp. 2077–2079.

38Ffowcs Williams, J. E. and Hawkings, D. L., “Sound Gen-eration by Turbulence and Surfaces in Arbitrary Motion,” Pro-

ceedings of the Royal Society of London, Series A: Mathematical

and Physical Sciences, Vol. 264, No. 1151, 1969, pp. 321–342.39Crighton, D. G., Dowling, A. P., Williams, J. E. F., Heckl,

M., and Leppington, F. G., Modern Methods in Analytical

Acoustics: Lecture Notes, Springer–Verlag, London, 1992.40Moin, P., Squires, K., Cabot, W., and Lee, S., “A Dynamic

Subgrid-Scale Model for Compressible Turbulence and ScalarTransport,” Physics of Fluids A, Vol. 3, No. 11, November 1991,pp. 2746–2757.

41Uzun, A., 3-D Large Eddy Simulation for Jet Aeroacous-

tics, Ph.D. thesis, School of Aeronautics and Astronautics, Pur-due University, West Lafayette, IN, December 2003.

42Lele, S. K., “Compact Finite Difference Schemes withSpectral-like Resolution,” Journal of Computational Physics,Vol. 103, No. 1, November 1992, pp. 16–42.

43Visbal, M. R. and Gaitonde, D. V., “Very High-order Spa-tially Implicit Schemes for Computational Acoustics on Curvi-linear Meshes,” Journal of Computational Acoustics, Vol. 9,No. 4, 2001, pp. 1259–1286.

44Bogey, C. and Bailly, C., “Three-dimensional Non-reflective Boundary Conditions for Acoustic Simulations: FarField Formulation and Validation Test Cases,” Acta Acustica,Vol. 88, No. 4, 2002, pp. 463–471.

45Colonius, T., Lele, S. K., and Moin, P., “Boundary Con-ditions for Direct Computation of Aerodynamic Sound Genera-tion,” AIAA Journal , Vol. 31, No. 9, September 1993, pp. 1574–1582.

46Bogey, C., Bailly, C., and Juve, D., “Noise Investigationof a High Subsonic, Moderate Reynolds Number Jet Using aCompressible LES,” Theoretical and Computational Fluid Dy-

namics, Vol. 16, No. 4, 2003, pp. 273–297.47Smagorinsky, J. S., “General Circulation Experiments with

the Primitive Equations,” Monthly Weather Review , Vol. 91,No. 3, March 1963, pp. 99–165.

48Bogey, C. and Bailly, C., “A Family of Low Dispersive andLow Dissipative Explicit Schemes for Computing AerodynamicNoise,” AIAA Paper 2002-2509, June 2002.

49Uzun, A., Blaisdell, G. A., and Lyrintzis, A. S., “3-D LargeEddy Simulation for Jet Aeroacoustics,” AIAA Paper 2003-3322, May 2003.

50Lew, P., Uzun, A., Blaisdell, G. A., and Lyrintzis, A. S.,“Effects of Inflow Forcing on Jet Noise Using Large Eddy Sim-ulation,” AIAA Paper 2004-0516, January 2004.

51Lyrintzis, A. S., “Surface Integral Methods in Compu-tational Aeroacoustics - From the (CFD) Near-Field to the(Acoustic) Far-Field,” International Journal of Aeroacoustics,Vol. 2, No. 2, 2003, pp. 95–128.

52Brentner, K. S. and Farassat, F., “Analytical Comparisonof the Acoustic Analogy and Kirchhoff Formulation for Mov-ing Surfaces,” AIAA Journal , Vol. 36, No. 8, August 1998,pp. 1379–1386.

53Pilon, A. R. and Lyrintzis, A. S., “Mean Flow RefractionCorrections for the Modified Kirchhoff Method,” Journal of Air-

craft , Vol. 35, No. 4, July-August 1998, pp. 661–664.54Society of Automotive Engineers, SAE ARP 876C : Gas

Turbine Jet Exhaust Noise Prediction, November 1985.55Arakeri, V. H., Krothapalli, A., Siddavaram, V., Alkislar,

M. B., and Lourenco, L., “Turbulence suppression in the noiseproducing region of a Mach 0.9 jet,” AIAA Paper 2002-2523,June 2002.

56Lau, J. C., Morris, P. J., and Fisher, M. J., “Measurementsin subsonic and supersonic free jets using a laser velocimeter,”Journal of Fluid Mechanics, Vol. 93, No. 1, 1979, pp. 1–27.

57Rahier, G., Prieur, J., Vuillot, F., Lupoglazoff, N., andBiancherin, A., “Investigation of Integral Surface Formulationsfor Acoustic Predictions of Hot Jets Starting from UnsteadyAerodynamic Simulations,” AIAA Paper 2003-3164, May 2003.

58Freund, J. B., “Noise-source turbulence statistics and thenoise from a Mach 0.9 Jet,” Physics of Fluids, Vol. 15, No. 6,June 2003, pp. 1788–1799.

59Mani, R., Gliebe, P. R., and Balsa, T. F., “High VelocityJet Noise Source Location and Reduction,” Federal AviationAdministration, Task 2, FAA-RD-76-79-II, May 1978.

60Bridges, J., NASA Glenn Research Center, Private Com-munication, November 2003.

61Simonich, J., Narayanan, S., Barber, T. J., and Nishimura,M., “High Subsonic Jet Experiments Part 1: Aeroacoustic Char-acterization, Noise Reduction and Dimensional Scaling Effects,”AIAA Paper 2000-2022, 2000.

62Narayanan, S., Barber, T. J., and Polak, D. R., “HighSubsonic Jet Experiments: Turbulence and Noise GenerationStudies,” AIAA Journal , Vol. 40, No. 3, 2002, pp. 430–437.

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