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AIAA JOURNALVol. 41, No. 10, October 2003

Analysis of Flow Conditions in Freejet Experimentsfor Studying Airfoil Self-Noise

Stephane Moreau and Manuel Henner

Valeo Motors and Actuators, 78321 La Verriere, FranceGianluca Iaccarino and Meng Wang

Stanford University, Stanford, California 94305

and

Michel Roger

Ecole Centrale de Lyon, 69134 Ecully, France

A new set of mean wall pressure data has been collected on a controlled diffusion airfoil at a chord Reynolds

number of 1.2 105 in a freejet anechoic wind tunnel. Comparisons of the experimental data with Reynolds-

averaged NavierStokes (RANS) simulationsi n free air show signicant oweld and pressure loading differences,

indicatingsubstantialjet interference effects. To analyzetheseeffects, a systematicRANS-based computationaluid

dynamicsstudy of theexperimentalow conditionshas been carried out,which quanties thestrong inuence of the

nite jet (nozzle) width on the aerodynamic loading and ow characteristics. When the jet width is not sufcientlylarge compared to the frontal wetted area of the airfoil, the airfoil pressure distribution is found to be closer to

the distribution on a cascade than that of an isolated prole. The airfoil lift is signicantly reduced. Accounting

for the actual wind-tunnel setup recovers the wall pressure distribution on the airfoil without further empirical

angle-of-attack corrections. These jet interference effects could be responsible for the discrepancies among some

earlier experimental and computational studies of airfoil self-noise. They should be accounted for in future noise

computations to ensure that the experimental ow conditions are simulated accurately.

I. Introduction

W HEN considering the sound emitted by a rotating machinesuch as an enginecooling fan, an airplane turbofan,or an air-conditioningunit, one signicant contributorto the overall noise is

the trailing-edge noise from the blades. It comes from the conver-sion of local ow perturbationsi n the boundary layer into acousticwaves through interaction with the acoustically thin trailing edge.Depending on the ow Reynolds number (based on the local chordlength) and the geometry of the blade trailing edge, the acousticscatteringis associatedwith most of the broadband component andsome narrower-band structures of the far-eld acoustic spectrum.1

The noiseradiationis generallymore severefor loadedblades,whenow separationoccurs at the trailingedge.This mechanismalso pro-vides the minimum noise conguration of such machines when allinteractions with their environment (turbulence ingestion and owdistortionat the inlet, rotor stator interactionwith downstreamsta-tionary components, etc.) are removed.2;3 As another example, thesame edge scatteringmechanism constitutesan important sourceof

wind-turbine noise.4;5

The study of trailing-edge noise or airfoil self-noise receivedmuch attention mainly in the late 1970s and early 1980s. It in-volved measurements of wall pressure uctuation spectra and far-eld acoustic spectra on two-dimensional mock-ups of various

Received 17 July 2002; revision received 5 February 2003; accepted forpublication 5 April 2003. Copyright c 2003 by the American Institute ofAeronautics and Astronautics, Inc. All rights reserved. Copies of this papermay be made for personal or internal use, on condition that the copier paythe $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rose-wood Drive, Danvers, MA 01923; include the code 0001-1452/03 $10.00 incorrespondence with the CCC.Senior Research Engineerand Research and Development Manager, En-

gine Cooling Fan Systems Core Competencies Group. Research Engineer, Engine Cooling Fan Systems Core Competencies

Group. Research Associate, Center for Turbulence Research. Member AIAA. Senior Research Scientist, Center for Turbulence Research. Member

AIAA. Professor, Laboratoire de Mecanique des Fluides et Acoustique.

aerodynamic proles in freejet anechoic wind tunnels.68 The ex-perimental data were then been used in the late 1990s to validatenumerical prediction methods for trailing-edge aeroacoustics.913

For typical engine cooling fan applications involving transitionalandturbulentowsat Reynoldsnumbersof order 105 , thenumericalpredictionrequires information of the noise-generatingeddiesovera wide range of length scales. The traditional Reynolds-averagedNavier Stokes (RANS) approachis insufcient. It needs to be sub-stituted by the more expensive large-eddy simulations (LES) orcombined with a suitable statistical model to yield the necessaryunsteady surface pressure uctuations and the near-eld uctuat-ing Reynolds stresses, which provide the acousticsource functions.The radiated noise can then be computed using an aeroacousticthe-ory such as Ffowcs Williams and Halls application14 of Lighthillsanalogy.

As with the application of any computational uid dynamics(CFD) methods, the validity and accuracy of the solutions mustbe established rst against known solutions or experimental mea-surements.This is particularly importantin the case of aeroacousticcomputation given the relatively small magnitude of noise signals.In the validation process, to have a valid comparison with exper-iments, the computation should reproduce as exactly as possiblethe experimentalenvironment.In practice,however, simplied owcongurations are often employed in simulations. For instance, inall previous LES studies,10;13 the airfoil has been assumed to be ina uniformly moving medium (free-air conguration). In contrast,most trailing-edge aeroacoustics experiments have been conductedin open-jet wind-tunnel facilities, where the airfoil is immersed ina jet downstream of the nozzle exit. The proximity of the airfoilto the jet nozzle exit and the limited jet width relative to the airfoilthicknessand chordlengthcan causethe airfoilpressureloadingandow characteristics to deviate signicantly from those measured infree air and, hence, alter the radiated noise eld.

The present work is aimed at quantifyingthese experimentalin-stallation effects as well as proposing more suitable experimentaland numericalprocedures.The characteristicsof thepreviousexper-iments are rst reviewed. They are then compared to new measure-mentscollectedin recentexperimentsat Ecole CentraleLyon (ECL)

on a cambered controlleddiffusion (CD) airfoil developed at Valeo

1895


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Motors and Actuators. A systematic CFD study, based on RANSmodels,of ow conditionsin the ECL experiment is carriedout andcompared with ows over an isolated airfoil in a uniform stream.The results shed some light on the delity of the ow conditions inthe previousnumerical simulationsof trailing-edgeexperimentsandprovide guidance for the appropriate boundary conditions neededin future LES of such experiments.

II. Review of Experimental Setup and Data

To measure the pure airfoil self-noise, the aerodynamic prolemust be placedin a largequiet environmentand isolated as much aspossible from the inlet duct providing the necessary airow. More-over, the inlet duct should have a low background noise and lowresidual turbulence (


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Table 1 Characteristic dimensions in some airfoil self-noise experiments (in centimeters)

Airfoil Nozzle LE Jet width,Airfoil Chord c Span s (c) thickness (w) distance (c) w (c)

Flat strut 107.3 119.4 (1.11 c) 5.1 (0.02 w) 240 (2.24 c)

Blake6 130

Blake and Gershfeld1 10 (0.1 c)

NACA 0012

Brooks and Hodgson7 61 46 (0.75 c) 7.2 (0.24 w) 15 (0.25 c) 30 (0.49 c)

Roger 10 30 (3.00 c) 1.2 (0.09 w) 10 (1.00 c) 13 (1.30 c)Valeo CDRoger (small wind tunnel) 13.6 30 (2.21 c) 0.5 (0.04 w) 10 (0.73 c) 13 (0.96 c)Roger (large wind tunnel) 13.6 30 (2.21 c) 0.5 (0.01 w) 20 (1.47 c) 50 (3.68 c)

Fig. 2 Experimental pressure coefcient on the Valeo cambered CD prole.

microphone is placed in the far eld to collect the acoustic spec-tra simultaneously.Finally, tuft visualizations are used to estimatequalitativelyt he ow separation zones, and a hot-wire rake is usedto measure the wake velocity prole close to the trailing edge. Thecorresponding mean wall pressure measurements on the Valeo CDairfoil for ve different geometric angles of attack are shown inFig. 2. Good repeatabilitywas achieved on this data set, and a max-imum change of angle of attack of 0.5 deg causes a variation of 0.1

on the pressure coefcient. Note that, for w D 12 deg, the ow isattached along the entire chord. At w D 14 deg, the ow starts toseparate near the trailing edge. This regime corresponds to turbu-lent vortex shedding with no mean backow. Increasing the angleof attack to w D 16 deg leads to a laminar recirculation zone nearthe leading edge. At w D 18 deg, the separated zones, particularlythe one near the leading edge, are increasedin size. At much largerincidence (w D 27 deg), the airfoil seems to be stalled with a re-circulationbubble at the trailing edge, which is conrmed by a tuftsurvey along the chord.

C. Comparison of Experimental Dimensions

The variousgeometricalparametersinvolved in the describedex-perimentsare compared in Table 1. By examiningthe span-to-chordratio s=c we can estimate the possible three-dimensionalityeffectsinduced by the side plates. Brooks and Hodgsons experiment7 ex-hibitssome three-dimensionalinuence as indicatedby the nonuni-form surface pressure spectra in Fig. 8 of Ref. 7. In contrast, theRoger et al. experimentsare expectedto be less affected at midspanwhere the RMPs are mounted.A comparison of the airfoil thickness

and the jet width (or nozzle exit width) allows an estimate of theblockageinducedby theairfoilin thejet.The latteris largein Brooksand Hodgsons experiment.7 Moreover, data on jet boundary cor-rections for airfoil tests in open wind-tunnel jets18 suggest that allexperiments listed in Table 1 will yield signicant differences be-tween the actual angleof attackand the effective one, dened as theexpectedone in free airthat would leadto the same lift distribution.The jet width also determines the extent of its potential core and,

therefore, gives an estimate of the interaction of the shear layersgenerated at the nozzle lips with the airfoil surface. If a typical corelength of four to ve jet widths is assumed, by comparison withthe airfoil chord length and thickness, it becomes clear that suchan interaction may be present in Brooks and Hodgsons setup. Fi-nally, the distance from the nozzle exit to the airfoil leading edgegives a hint at the potential interaction between the nozzle and air-foil and the consequ ent local modication of the effective angle ofattack. These effects are irrelevant in Blakes experiment6 becausethe airfoil is fully inside the jet nozzle (hence, the negative distancein Table 1) and the nozzle width is 48 times the airfoil thickness.However, they cannot be neglected in the experiment of Blake andGershfeld.1

III. Numerical and Physical ModelsA. Overall Formulation

As shown in Refs. 19 and20, the aerodynamicsof enginecoolingfan systems in the bladereferenceframeinvolvesessentially incom-pressible, transitional, or turbulentows depending on the sectionsconsideredfrom hub (lower speed) to tip (higherspeed). To account


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a) b) c)

Fig. 3 Free-air and wind-tunnel topologies and boundary conditions.

Fig. 4 Isolated airfoil unstructured ne grid.

for this usual environment, the oweld has been modeled by theRANS equations with several two-equation turbulence models. Atthe solid boundaries, both wall functions and a two-layer approachhavebeen used.The resultingset of conservativeequationshas beensolved with either CFX-TASCow 2.10 on multiblock structuredgrids or FLUENT 5 .5 on unstructured grids. Details of the numer-ical schemes used for these computations and the correspondingvalidation test cases may be found in Ref. 20 for CFX-TASCowand in Ref. 21 for FLUENT. The least diffusivesecond-order accu-rate schemes have always been used with both commercial codes.In the CFX-TASCow simulations, four different turbulence mod-els have been employed: the k" model with wall functions, thetwo-layer low-Reynolds-number k" model, the k! model, andMenters shear stress transport (SST) model.22 Only the v2 f (vari-ables as k, ", or !) (V2F) model23 has been used with FLUENT.Previous comparisonswith both codes using the same k" formula-tionled to very similar resultsfor a cascadecongurationof this CDairfoil, under the same ow conditions as in the current ECL tests.

To investigatethe wind-tunnelinstallationeffects, threeow con-gurations are considered in the numerical simulations. They in-clude an isolatedairfoil in free air (Fig. 3a), a simplied wind tunnelwith nite jet width but no explicit account of the nozzle (Fig. 3b),and the so-called full wind tunnel, which includes the jet nozzle in

the computational domain (Fig. 3c). All of the computations havebeen two dimensional as justied by the aspect ratio in Table 1.

B. Grid Analysis

The isolated airfoil simulations have been performed in a rect-angulardomain with about four chord lengths above and below theairfoil and six chordlengthsupstreamand downstreamof the airfoil.To test the grid sensitivity of the solutions, a multiblock structuredgrid (66,000 cells) and two unstructured grids (30,000 and 55,000cells) are employed. All of the grids have very similar clusteringofpoints near the wall to capturethe boundary layer properly (Fig. 4).Even though the unstructuredne grid has more points and is moreregular chordwise at the leadingedge, it has a smaller overall meshsize than the structured one because of the unstructured topologyand grid adaptation based on the shear stresses. The solutions onall grids are very similar, and the wall pressure and friction dis-tributions are seen to be grid and topology independent for eachturbulencemodel studied.The correspondingresults using the V2Fmodel at a chord-referencedangleof attacki D 8 deg areplottedinFigs. 5 and 6. The subscript i hereafter refers to the isolated airfoilow conditions. On all grids, the dimensionless wall-normal gridspacing in wall units,1yC , is smaller than 1 over most of the chordlength on both pressure and suction sides.


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Fig. 5 Comparison of pressure coefcients on the CD prole computed on different grids.

Fig. 6 Comparison of skin-friction coefcients on the CD prole computed on different grids.

In the simplied wind-tunnel simulations, the same grid densitynear the airfoil is used as shown in Fig. 3. The airfoil is placedcloser to the left boundaryaccording to the distance in Table 1. Thecomputational box, shown in Fig. 3b is also extended farther awayfromtheairfoil (1 1 m) tocaptureawakedeectionindependentofthe distantboundaries.Thefull wind-tunnelsimulationalso includesthe complete nozzle geometry to assess the effect of the nozzle

airfoil interaction.The resulting grid is presented in Fig. 7.

C. Boundary Conditions

For theisolatedairfoil,theincomingowis assumed uniformandcorrespondsto thenozzle exit meanvelocity.It is imposed at the leftand bottom boundaries of the CFD domain. On the upper and rightboundaries, an outlet pressure is applied. In the simplied wind-tunnel geometry, the inow velocity is uniform within the nozzlewidth and is inclined with respect to the airfoil chord by the anglew . This simplied model allows a quick evaluationof the effect of

theairfoilincidenceon thesamegrid independentlyof the actualex-perimental setup,whichis notalways known precisely (particularlythe center of rotation of the airfoil with respect to the nozzle). Yet,by rotating the jet instead of the mock-up, a small variation in theposition of the airfoil within the jet core is introduced, which willmainly affect the pressure-sidepressure distribution.The rest of theleft boundary is a solid wall. On the upper and lower boundaries,anoutlet pressure is imposed again. If the boundaries are sufcientlyfar from the jet, they should yield the same solutions. In the com-plete wind-tunnel simulations, the inlet boundary condition is setinside the nozzle and adjusted to provide a mean velocity of 16 m/s

at the nozzle exit. The nozzle geometry and the relative position ofthe airfoil with respect to the nozzle are also exact.

D. Turbulence Modeling

The effect of different turbulence models has rst been exam-ined for the case of an isolated airfoil. Flow simulations have been


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Fig. 7 Unstructured ne grid for the ECL wind tunnel.

Fig. 8 Comparison of pressure coefcients on the CD prole in free air at i = 8 deg, predicted using different turbulence models.

run for i between 0 and 10 deg with increments of 1 deg. Allmodels agree at low angles of attack. At higher angles of attack(beyond 5 deg), two groups of results emerge. The two k" simu-lations predict no laminar ow separation at the leading edge andhardlyany turbulentrecirculationnear the trailing edge.In contrast,the k!, SST, and V2F models predict increasing ow separationswith i in both thetrailing-edgeand leading-edgeregions, in agree-ment with experimentalevidence (Fig. 2). The overall ow patterns

are very similar to those reported by Winklemann and Barlow24 orBastedo and Mueller25 on lifting surfaces in low-Reynolds-numberows. Figures 8 and9 show thepressureand friction coefcientsfori D 8 deg. Figure 9 indicates that the largest turbulentrecirculationzone is predicted by the SST model.

Thedifferentbehaviorat theleadingedge of thek"modelpredic-tionscan be traced to the overproductionof turbulentkineticenergyat the stagnation point, which prevents a local relaminarization of


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Fig. 9 Comparison of skin-friction coefcients on the CD prole in free air at i = 8 deg, predicted using different turbulence models.

Fig. 1 0 Comparison of pressure coefcients on the NACA 0012 airfoil between isolated airfoil simulations and ECL test data.

the ow and, thus, the ow separation. This was also demonstratedin the cascade simulations reported in Ref. 26.

IV. Results

A. Isolated Airfoil Simulations

In Ref. 27, Brooks et al. found that the NACA 0012 airfoil in anopen-jet tunnel could have the same loading as in free unboundedow provided that a correction to the angle of attack was appliedto account for the jet deection. In the recent experiment at theECL test facility with the same airfoil section, Roger (unpublishedprole) found again a possible correction to the angle of attack asshown in Fig. 10. The correction is based on a comparisonbetweenthe measured pressure coefcient distributionand a set of computedresults in free air. In this case, the equivalent free-air angle of at-tack is found to be about i D 6 deg for a wind-tunnel angle ofattackw D 14:5 deg, resulting in a correction of 8.5 deg. When thedata in Table 1 are used, Eq. (2) of Ref. 27 yields a similar value,

i D 5:3 deg. Note that, although the integrated lift can be adjustedin this way, the precise distribution of pressure coefcient is notperfectly recovered, especially in the leading-edge area, indicatingsome installation effects in this experiment.

The same methodology has then been applied to the Valeo CDairfoil. However, as Fig. 11 shows, no correction on angle of at-tack could recover the experimental lift, which is much lower thanthe one computed in free air. Figure 11 shows the best qualitativecomparison that can be achieved using angle-of-attackco rrectionsof 8 9 deg. The CD airfoil seems to be far more sensitiveto the in-stallation effects than the NACA 0012 with a similar chord, whichis most likely due to the difference in airfoil thicknesses and thecamber of the CD airfoil.

Furthermore,Fig. 12 shows thatthe pressurelevelsobtainedfromthe experiment relate quite well to the cascade loading obtained inprevious simulations at Valeo. This suggests that the shear layersoriginatingfrom thenozzlelipsconne the owin a mannersimilar


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Fig. 1 1 Comparison of pressure coefcients on the CD airfoil between isolated airfoil simulationsa nd ECL test data.

Fig. 12 Comparison of pressure coefcients on the CD airfoil between cascade and isolated airfoil simulations and ECL test data.

to a blade passage in a cascade (as will be seen clearly later). Thelarge discrepancy between the ECL test data and free-air simula-tion results has motivated the following wind-tunnel simulations.Note that the large discrepancies between the boundary-layer mo-mentum thickness found in Ref. 13 relative to that in Brooks andHodgsons experiment7 can most likely be attributedto this type ofinstallation effects and the incorrect pressure gradients computedin free air compared to the actual ones in the open-jet experiments.Similar unsatisfactory pressure results have been reported in Fig. 5of Ref. 12, although in Blakes experiment,6 they are most likelyattributed to other installation effects because the airfoil is inside

the nozzle.

B. Simplied Wind-Tunnel Simulations

All wind-tunnel ow simulations presented here have been per-formed with the V2F model and a jet width of 13 cm. The initialfocus is the simplied conguration whose geometry and boundary

conditions were described earlier. Several angles of attackw havebeen considered in the current ECL setup corresponding to the ex-perimentaldata in Fig. 2. Figure 13, compared with Fig. 11, clearlyshows that the suction side pressure coefcient is now much betterpredicted, without further semi-empirical corrections. The laminarow separation at high angle of attack (w D 18 deg) is captured.Similar results are achieved with the k! and SST models as inFig. 8 for the free-air case, which emphasizesthe superiority of thisset of turbulence models in predicting separated ow as comparedto the k" model. The pressure levels on the pressure side are stillquite different, especiallyclose to the leading edge.

C. Full Wind-Tunnel Simulations

To address the latter problem and assess the effect of the sim-plied wind-tunnel model, a two-dimensional simulation of thefull wind tunnel including the nozzle (compare Figs. 3 and 7)

has been carried out, with the correct experimental position of the


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Fig. 13 Comparison of pressure coefcients on the CD airfoil between simplied wind-tunnel simulations and ECL test data.

Fig. 14 Comparison of pressure coefcients on the CD airfoil atw = 12 deg between wind-tunnel simulations and ECL test data.

airfoil in the jet potential core. As shown in Fig. 14, for an an-gle of attackw D 12 deg the pressure levels on the pressure sideare nicely recovered. However no major change is found on thesuction side: No ow separation is numerically predicted at thetrailing edge. These remaining discrepanciesseen at 10% of chordand, consequently, near the trailing edge are most likely causedby a transition to turbulence that occurs too early in the RANSsimulations.

D. Jet Width Effect

With the large differences between the isolated airfoil case andthe same airfoil in an open-jet acoustic tunnel established and ex-plained, the inuence of the jet width on the pressure and velocitydistributionsis now investigated.The motivation for this study is toprovideguidancefor the design of futureexperimentswith minimalinterference effects and for setting up the appropriate LES bound-ary conditions if such an interference is present. The simplied

wind-tunnelmodel is used for this parametricstudy in which the jetwidth varies from 13 to 50 cm and the angle of attackw D 8 deg.

Our calculations indicate that with a jet width at least twice aslarge as the current experimentalvalue, most of the turbulent zoneon the suction side is now very close to the free-air case. Howeverat theleading edge, the wind-tunnelcalculation does not show largelaminar ow separation observed in the free-air case. To conrmthesetrends, an additionalexperimenthas been dedicatedin a largerwind tunnel available at ECL on the same CD airfoil mock-up atthe same incidence with a jet width of 50 cm. The correspondinggeometrical characteristics of this new setup is summarized in thelast row of Table 1. As shown in Fig. 15, the measured pressurecoefcient agrees with the simplied wind-tunnel simulation, as inthe13-cm case.The trailing-edgeowis evenbetterpredictedfor thewider jet case. However, large discrepancies with the free-air casepersist, which underlines the importance of accounting for the jetinterferenceeffectin aeroacousticcalculations.Thegood agreement


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Fig. 15 Comparison of pressure coefcients on the CD airfoil atw = 8 deg for different nozzle widths.

a)

b)

c)

d)

Fig. 16 Normalized mean velocity magnitudefor free-jet ow over the CD airfoil atw = 8 deg, with different jet widths: a) w= 13 cm, b) w= 50 cm,c) free air, and d) closeup view of case b (w= 50 cm) in the nose region.


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between experimentalresultsand wind-tunnelcalculationssuggeststhat reliable information for dening the boundary conditions offuture LES computations of trailing-edgenoise can be provided byRANS in the case of a wide nozzle.

The velocity contours of Figs. 16 also conrm the earlier cascadendings. With the current ECL setup, the nite jet width induces aloadingon the bladethat spreadsover the whole chord as in the cas-cade case. The wider the jet becomes, the more forward the loadingshiftsand the closer it approachesthe free-air value. However, even

with a 50-cm jetwidth, there is no evidenceof ow separationat theleading edge, as clearly shown in the closeup view of the velocitycontours in Fig. 16d and the wall pressure distribution in Fig. 15.

V. Conclusions

Detailed RANS simulations of typical freejet wind-tunnel ex-periments on airfoils have shown strong effects of the jet on theaerodynamicloadingand ow characteristics.When the jet width isnot sufciently large compared to the streamwise projectedarea ofthe airfoil (width-to-chordratio of about 1), the airfoil behaves in amanner closer to a blade cascade than to an isolated airfoil. The sig-nicant modication of the lift distributionand oweld can in turnaffect the nature of the sound radiation. These effects have impli-cations for the appropriate boundary conditions needed to conduct

LES of open-jet aeroacoustic experiments and could be respon-sible for the discrepancies among some earlier experimental andcomputational studies, for example, the different boundary-layerthicknesses observed by Manoha et al.13 To reproduce the experi-mental ow conditions accurately, freestream boundary conditionsare not adequate (unless the jet is very wide). More realistic condi-tions based on experimentalvelocity proles or RANS calculationsshould be imposed.

RANS simulations with the V2F and SST models compare morefavorablywith the measured pressure distribution on the Valeo CDairfoil than those with the k" model. Remaining differences aremost likely due to the incoming ow conditions at the wind-tunnelnozzle outlet and particularly the local turbulence level that canmodify the transition point on the suction side of the airfoil and

consequentlythe ow separation at the trailing edge.In addition to the full wind-tunnel simulation, a simpler compu-

tational model of the open-jet acoustic tunnel with an inlet velocityprole of variable width has also been devised. This congurationcaptures most of the experimental setup effects in open-jet facili-ties, particularly in the aft section of the airfoil, which is critical totrailing-edge noise. The simplied conguration allows for quickparametric studiesof the dependence of ow conditionson the air-foil proles and the angle of attack, which is particularly useful forthedesign of experimentsas well as forRANS andLES simulations.

The knowledgeand techniquesdevelopedthroughthis studyhavebeen utilized in an ongoing LES of an open-jet airfoil self-noiseexperiment with jet width of 50 cm. As shown in the earlier RANScalculations,the oweld in the wind-tunnelconguration deviates

signicantlyfromthatofanisolatedairfoilinuniformfreestream.Toaccountfor thiseffectin theaeroacousticanalysis,themean velocityproles from the RANS calculationare used to dene the boundaryconditions for the LES, which is performed in a smaller domainwithin the core of the jet to save computationalc ost. This approachallows an accurate simulation of the experimental ow conditionsand, hence, promotes the accuracy of noise computation.

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ing Edges, Frontiers in Experimental Fluid Mechanics, edited byM. Gad-el-Hak, Springer-Verlag, Berlin, 19 88, Chap. 10, pp. 457532.

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4 Glegg, S. A. L., Baxter, S. M., and Glendinning, A. G.,The Predictionof Broadband Noise from Wind Turbines, Journalof Sound and Vibration,Vol. 118, No. 2, 1987, pp. 217239.

5 Hubbard, H. H., and Shepherd, K. P., Aeroacoustics of Large WindTurbines, Journal of the Acoustical Society of America, Vol. 89, No. 6,1991, pp. 2495 2507.

6 Blake, W. K., A Statistical Description of Pressure and Velocity Fieldsat the Trailing Edge of a Flat Strut, David Taylor Naval Ship Research andDevelopment Center, DTNSRD Rept. 4241, Bethesda, MD, Dec. 1975.

7 Brooks, T. F., andHodgson,T. H., Trailing EdgeNoise Prediction from

Measured Surface Pressures,Journal of Soundand Vibration, Vol.78,No.1,1981, pp. 69 117.

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13 Manoha, E., Delahay, C., Sagaut, P., Mary, I., Ben Khelil, S., andGuillen, P., Numerical Prediction of the Unsteady Flow and Radiated Noisefrom a 3D Lifting Airfoil, AIAA Paper 2001-2133, May 2001.

14 Ffowcs Williams, J. E., and Hall, L. H., Aerodynamic Sound Genera-tion by Turbulent Flow in the Vicinity of a Scattering Half-Plane, Journalof Fluid Mechanics, Vol. 40, 19 70, pp. 657 670.

15 Roger, M., and Moreau, S., Trailing Edge Noise Measurements andPredictionsfor SubsonicLoaded Fan Blades,AIAAPaper20022460,June2002.

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17 Perennes, S., and Roger, M., Aerodynamic Noise of a Two-Dimensional Wing with High-Lift Devices, AIAA Paper 98-2338,July 1998.

18 Knight, M., and Harris, T. A., Experimental Determination of JetBoundary Corrections for Airfoil Tests in Four Open Wind Tunnel Jets ofDifferent Shapes, NACA Rept. 361, 1930.

19 Moreau, S., and Bennett, E., Improvement of FanDesign usingCFD,Society of Automotive Engineers, Paper SAE-970934, Feb. 1997.

20 Coggiola, E., Dessale, B., Moreau, S., and Broberg, R., On the Use ofCFD in the Automotive Engine Cooling Fan System Design, AIAA Paper98-0772, Jan. 1998.

21 Iaccarino, G., Predictions of a Turbulent Separated Flow UsingCommercial CFD Codes, Journal of Fluid Engineering, Vol. 123, 2001,pp. 110.

22 Menter, F. R., Two-Equation Eddy-Viscosity Turbulence Modelsfor Engineering Applications, AIAA Journal, Vol. 32, No. 8, 1994,pp. 1598 1605.

23 Durbin, P. A., Separated Flow Computations with the kv2 Model,AIAA Journal, Vol. 33, 1995, pp. 659 664.

24 Winklemann, A. E., and Barlow, J. B., A Floweld Model for a Rect-angular Platform Wing, AIAA Journal, Vol. 18, 1980, pp. 10061008.

25 Bastedo, W. G., andMueller,T. J.,SpanwiseVariation of LaminarSep-aration Bubbles on Wings at Low Reynolds Numbers, Journal of Aircraft,Vol. 23, 1986, pp. 687694.

26 Henner, M., Stanciu, M., Moreau S., Aubert, S., and Ferrand, P.,Unsteady RotorStator Interactions in Automotive Engine Cooling FanSystems, Proceedings of the ISUAAAT 2000 Conference, edited byP. Ferrand and S. Aubert, PUG, 2000, pp. 570 579.

27 Brooks, T.F.,Marcollini, M. A.,and Pope, D. S.,AirfoilTrailing-EdgeFlow Measurements, AIAA Journal, Vol. 24, No. 8, 1986, pp. 12451251.

R. M. C. SoAssociate Editor

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