Aeroacoustic study of a wavy stator leading edge in a ...isromac-isimet.univ-lille1.fr/upload_dir/finalpaper17/66.86_Casalino_et_Al_2017.pdfand radiated noise of the 22-in source diagnostic

Aeroacoustic study of a wavy stator leading edge in arealistic fan/OGV stageDamiano Casalino1*, Francesco Avallone1, Ignacio Gonzalez-Martino2, Daniele Ragni1

SYM

POSI

A

ON ROTATING MACH

INERY

ISROMAC 2017

InternationalSymposium on

Transport Phenomenaand

Dynamics of RotatingMachinery

Maui, Hawaii

December 16-21, 2017

Abstracte eect of sinusoidal serrations applied to the leading-edge of the vanes of a realistic fan stage isinvestigated using high-delity numerical simulations. e CFD solver PowerFLOW based on ahybrid laice-Boltzmann/very-large-eddy-simulation model is used to compute the unsteady owand radiated noise of the 22-in source diagnostic test fan rig of the NASA Glenn Research Center. Acomputational model validated for three dierent geometries of the outlet guide vanes with straightleading edge is used. A subset of validation results is reported to prove the capability of the solverto accurately predict the inuence of the stator geometry on the far-eld noise. Dierent sinusoidalleading edge serrations are investigated for a radial and a swept stator and the same rotor andoperating conditions. e inuence of the serrations on the acoustic far-eld and noise power levelis reported in relation to the statistical properties of the velocity uctuations in the wake of therotor. Some noise reductions are obtained when the undulation amplitude and wavelength arelarge enough compared to the integral scales of the impinging turbulence uctuations.KeywordsFan noise — wavy leading edge — SDT1Aerodynamics, Wind Energy, Flight Performance and Propulsion Department, Del University of Technology, Del, TheNetherlands2Aerospace Application Management, Exa Corporation, Paris, France*Corresponding author: [email protected]

INTRODUCTIONCurrent turbofan design trends towards large bypass ratioengines (up to 12-13), dictated by the necessity of reducingthe fuel consumption without increasing the engine weight,result in axially compact engines[1], with a smaller distancebetween the rotor and the Outlet Guide Vane (OGV). Ro-tor/stator interaction noise is the dominant source of tonaland broadband noise, which is expected to be enhanced bysmaller interstage distances.

One of the passive noise reduction concepts for rotor/statorinteraction noise that has received the aention of the aeroa-coustic community is the wavy leading edge. e eect of aserration is to reduce the correlation in the radial directionby decorrelating the source in adjacent undulation roots, tocreate a destructive interference along the serration edgethrough the generation of vanishing subcritical gust com-ponents, or simply to decorrelate the uctuations inducedat the root and the peak of the undulations. As discussedhereaer, these eects have been experimentally observedand conrmed by Computational Aero-Acoustics (CAA) sim-ulations for wing sections. is serves as motivation for thepresent numerical investigation carried out on a realistic fanstage conguration.

Inspired by whale ippers, the eects of leading edge ser-rations on the aerodynamic performances of wing sectionshave been studied since the Seventies. Soderman[2] per-formed li and drag measurements in a closed wind tunnelof an aerofoil with small sharp serrations on the leading-edge.He observed an increase of the incidence of maximum li

and a small drag penalty at low angle of aack. e delayedstall was related to the generation of streamwise vortices atthe leading edge that energize the boundary layer throughmomentum transfer and delay the leading edge ow separa-tion. Further experiments conrmed the eects of serrationson the stall behaviour of wings[3, 4] and whale ipper withtubercles[5, 6].

Aeroacousticians have been also inspired by nature. Inthe pioneering work by Graham[7], the silent ight of owlwas related with the special adaptations of the feathers inseveral species. By comparing the wing and the feathersof silently ying owls with the ones of an owl that belongsto a species that does not y silently, he identied threepeculiarities that are responsible for the quiet ight: theleading edge comb, the trailing edge fringe and the downyupper surface of the feathers. He also proposed to use similarfeatures for the reduction of aircra noise, together withlower wing loading and ight speed, as also inspired by owls.Using simple modelling assumptions, Lilley[8] concludedthat the feather adaptations of the owl lead to a major noisereduction above 2 kHz.

Recent works on the use of leading-edge serrations forthe reduction of the aerofoil/turbulence interaction noisehave focused on the eects of the ratio between the undu-lation amplitude hs and the turbulence length scale Lt ofthe impinging ow, the eect of the serration angle θs , andthus the undulation wavelength λs . Recent experiments[9]conducted on a at plate and a NACA-65(12)10 aerofoil of0.15m chord and 0.45m span interacting with grid-induced

Aeroacoustic study of a wavy stator leading edge in a realistic fan/OGV stage — 2/12

turbulence in a free stream with velocity U in the range 20to 60m/s, determined the existence of an optimal undula-tion wavelength λopts ' 4Lt , corresponding to a conditionat which adjacent sources in the undulation roots are inco-herently excited. ey nally argued that the noise powerlevel ratio between serrated and straight edge aerofoil at thefrequency f is inversely proportional to the Strouhal numberSth = f hs/U , i.e. the ratio between hs and the streamwisewavelength U/ f , for Sth & 0.2 up to the value where serra-tion self-noise starts to dominate.

Several numerical studies have been conducted by us-ing Euler equations with ingested turbulence modelled as aconvected harmonic upwash gust[10], a Kraichnan-Fouriersuperposition of upwash gust components matching the spec-tral energy content of homogeneous isotropic turbulence[11],and a stochastic three-dimensional divergence-free velocityeld also matching the spectral energy content of homoge-neous isotropic turbulence[12]. ese studies showed thatthe noise reduction increases when the ratio of the lead-ing edge undulation amplitude to the gust wavelength isincreased. Moreover, Clair et al[11], in the framework of theEuropean project FLOCON, separated the eects of subcrit-ical and supercritical gust components along the serrationedge, as analytically investigated by Roger et al[13], thusrecognising the role of the serration angle and wavelengthon the radiated noise. More recently, Gea-Aguilera et al[14]solved linearized Euler equations past a NACA 0012 aerofoilwith stochastic anisotropic turbulence of prescribed levelsand integral scales in the streamwise (Lx ) and spanwise (Lz )directions. ey observed that the maximum decorrelationbetween noise sources along the leading edge and consequentmaximum noise reduction are achieved when Lx < 2hs(root-to-peak decorrelation) and Lz . λs/2 (root-to-rootdecorrelation).

e goal of the present paper is to investigate the bene-ts associated with a wavy OGV leading edge for a realisticengine geometry and turbulence anisotropy, by performingnon-linear compressible ow simulations of a fan stage con-guration. An extensively validated numerical model of the22-in Source Diagnostic Test (SDT) fan rig of the NASA GlennResearch Center[15, 16] is used as a reference for a series ofsimulations performed by using dierent sinusoidally ser-rated OGVs. Two reference congurations are considered, aradial stator (baseline) and a swept stator (low-noise). All sim-ulations are performed at approach conditions correspondingto 61.7% of the nominal rotational speed.

e organization of the paper is as follows. Section 1provides information about the geometry of the problem anddetails about the wavy leading edge. e ow solver andthe computational model are identical to the ones used byCasalino et al[17] and reported, for the sake of completeness,in Section 2, together with a subset of reference results forthe straight OGVs in Section 3. e integral scales of theturbulent uctuations in the interstage are estimated usingthe approach presented in Section 4. Results for the wavyOGVs are reported and discussed in Section 5 in relation to

Figure 1. SDT engine congurations: baseline (top-le),low-noise (top-right), low-count (boom-le), nacelle(boom-right).

the radiated far-eld noise and to the integral length scalesin the wake of the rotor. Due to the limited number of serra-tion considered, only provisional conclusions for one singleoperating conditions are given in the conclusive section.

1. FAN STAGE CONFIGURATIONS AND SI-NUSOIDAL LEADING EDGEe reference engine is the SDT fan rig of the NASA GlennResearch Center[15, 16], made available by NASA in theframework of the AIAA Fan Broadband Noise (FBN) predic-tion workshop. e engine model and the wavy OGV aredescribed in this section.

1.1 Reference geometriesFig. 1 shows three variants of the OGV congurations: a54-vane baseline radial OGV, a 26-vane low-noise swept OGVand a 26-vane low-count radial OGV. All the other parts, withthe exception of very small variations of the inner and outercasing proles downstream the OGV, are the same for thethree congurations. e nacelle is perfectly axisymmetricwithout struts. In order to reproduce the stinger used in theexperiment, a cylindrical prolongation of the centerbody hasbeen added to the model released by NASA. e rotor radiusis 0.2786m, the bypass exhaust radius is 0.2710m and thelip intake radius is 0.2962m. e rotor is constituted of 22blades, and the casing/blade-tip gap is about 0.5mm.

1.2 Wavy OGVe wave leading edge is originated using the following pro-cedure:


• A structured mesh is initially created starting from animported unstructured surface mesh of a stator bladeby individuation of the leading- and trailing-edge lines,dened as a sequence of Ns equally-spaced constantpoints along the span from a minimal to maximal radialdistance, and by construction of the chord line forevery radial section.

• For every radial strip j delimited by the grid cuts jand j+1, a xed point x jF is individuated on the chordof length c j , such that ��x

jF−x

jLE�� = σc

j , where x jLE isthe local leading-edge point, and σ is a prescribedrelative portion of the chord aected by the morphingprocedure.

• For every radial strip, the coordinates of the bladepoints such that d = ��x

j − x jLE�� /c

j ≤ σ are modiedusing the following formula:

x jw =xjF+

(x j − x jF

)[1+cos(2πr/λs )] (1−d/σ) h̃s,

(1)

where r is the radial coordinate of the point, h̃s =hs/(σ c j ) is the prescribed undulation amplitude fac-tor, and hs is the amplitude.

Six dierent wavy stator designs are considered in thepresent study, all obtained using the chord ratio σ=0.15 andthe parameters reported in Table 1. Corresponding images ofthe stator blades are shown in Fig. 2. e choice of these pa-rameters for designs #1 and #2, was quite arbitrary, whereasfor the other ones was based on a prior estimation of theintegral scales of the turbulent uctuations in the interstagevolume, as discussed hereaer.

Table 1. Wavy OGV design parameters

Design # OGV Conf. λs ( mm) h̃s hs ( mm)

1 Low-Noise 7 0.15 1.882 Low-Noise 3.5 0.075 0.943 Low-Noise 14 0.3 3.764 Baseline 14 0.3 1.805 Baseline 14 0.6 3.606 Baseline 16 0.8 4.80

2. NUMERICAL MODELe Laice-Boltzmann (LB) CFD/CAA solver PowerFLOW5.4a is used to compute the transient ow inside and aroundthe engine. A Ffowcs-Williams and Hawkings (FW-H) ap-proach is then used to extrapolate the near eld solutionsampled on a permeable surface to the far-eld. Exa fan-noise best practice setup is used for all simulations.

Figure 2. Wavy OGVs: design #1, to #2 and #3 (top), anddesign #4, #5 and #6 (boom)

2.1 CFD/CAA computational approachPowerFLOW solves the Boltzmann equation for the distribu-tion function f (x, t, v) on a hexahedral mesh automaticallygenerated around bodies, which consist of one or more con-nected solid parts. e function f represents the probabilityto nd, in the elementary volume dx around x and in the in-nitesimal time interval (t, t+ dt), a number of uid particleswith velocity in the interval (v, v+ dv). e Boltzmann equa-tion is solved by discretizing the particle velocity space intoa prescribed number of values, in magnitude and direction.ese discrete velocity vectors are such that, in a prescribedtime step, one particle is advected from one point of the meshto 19 neighbouring points, including the point itself, whichconstitute the computational stencil of the so-called D3Q19scheme (three-dimensional 19 states model). It can be demon-strated that using 19 particle velocity states ensures sucientlaice symmetry to recover the Navier-Stokes equations foran isentropic ow[18]. For high subsonic Mach number sim-ulations, e.g, ows with local Mach number greater than0.5, as in the present case, the LB solver is coupled with thesolution of the entropy equation through a Lax-Wendronite dierence scheme on the Cartesian LB mesh[19]. Oncethe distribution function is computed, the macroscopic owquantities, density and linear momentum, are simply deter-mined through discrete integration: ρ(x, t) = ∑ j f j (x, t) andρu(x, t) =

∑j f j (x, t) v j . All the other quantities are de-

termined through thermodynamic relationships for an idealgas.

Solving the laice Boltzmann equation is equivalent toperforming a Direct Numerical Simulation (DNS) of the Navier-Stokes equations in the limits of the dynamic range (Machnumber) that can be accurately covered by the number of dis-crete particle velocity vectors, and in the limits of the laiceresolution required to capture the smallest scales of turbu-lence. For high Reynolds number ows, turbulence modelingis incorporated into the LB scheme by changing the relax-ation time in the collision operator that is computed accord-


ing to a Bhatnagar-Gross-Krook (BGK) approximation[20].e turbulent kinetic energy and the turbulent dissipationare obtained by solving a variant of the Re-NormalisationGroup (RNG) k-� model for the unresolved scales[21]. isapproach is referred to as LB Very Large Eddy Simulation(LB-VLES). Since it is prohibitive to resolve the wall boundarylayer using a Cartesian mesh approach down to the viscoussub-layer in high Reynolds number applications, a wall func-tion approach is used to model boundary layers on solidsurfaces.

e LB equation is solved on a grid composed of cubiccells. A variable resolution by a factor two is allowed be-tween adjacent regions. Consistently, the time step is variedby a factor two between two adjacent resolution regions.Solid surfaces are automatically facetized within each cellintersecting the wall geometry using planar surface elements.No-slip and slip wall boundary conditions on these elementsare imposed using a particle bounce-back process and a spec-ular reection process, respectively[22]. Extremely complexgeometries can be treated automatically.

e far-eld noise is computed through an integral extrap-olation based on a solid FW-H acoustic analogy formulation.A forward-time solution[23] of the FW-H equation based onFarassat’s formulation 1A[24] is used. e free-stream con-vective eects are taken into account directly in the integralformulation[25].

2.2 Computational setupImages of the computational setup are shown in Fig. 3. erotor and the spinner are encompassed by a volume (pur-ple) that denes the rotating mesh region. e centerbodyis extended with a solid cylinder since, similarly to the ex-periments, no primary jet is included in the simulation. egreen and yellow surfaces in the interstage volume in thetop-le image denote regions explored by Hot-Wire (H-W)measurements and are referred to as station # 1 and station #2, respectively. e second one is at the same axial locationas the baseline OGV leading edge, and measurements aretherefore available only for the low-noise conguration. eFW-H integration surface consists of three parts: a sphericalsector around the intake, a cylindrical connector and a coni-cal surface in the exhaust region. e cone is opened at itsdownstream extremity in order to avoid contamination of theacoustic signals due to integration of jet shear-layer hydrody-namic uctuations. e downstream extension of the cone ishowever sucient to recover the bypass duct radiation overthe angular range of interest. e present setup is identicalto the one used by Casalino et al[17], with the exceptions ofthe shape of the trip added on the suction side of the rotorblades to trigger the turbulent transition in the wake of therotor. Instead of a trip with a rectangular section, a zig-zagtrip of height linearly varying from 0.3mm at 5% of the span(root) to 0.1mm at 95% ot the span, 5mm wavelength and1mm amplitude, located at 10% of the chord, has been used,and all the simulations have been repeated, revealing a slightimprovement of the prediction of noise levels at high fre-quencies. For the sake of consistency, the reference results

Figure 3. Computational setup (low-noise OGV) and detailview of the zig-zag trip and FW-H surface.

reported in Section 3 are the new ones obtained using thezig-zag trip.

All simulations reported in this paper have been per-formed by using, as initial condition, the solution obtainedby using a coarser mesh and achieving an acceptable statis-tical convergence. en, the simulations are performed bysampling the solution along 10 rotor revolutions aer a veryshort initial transient of three blade passages. e CPU costis of the order of six thousand CPU hours per rotor revolutionusing 720 cores Intel Sandybridge 2.7 GHz.

All the narrow band far-eld noise and sound powerlevel spectra have been computed using the Welch’s peri-odogram method, using a signal length of 2.738 · 10−1 s, abandwidth of 28.63Hz, and 13 spectral averages with 43%overlap. e noise signal at each microphone has been ob-tained by appending four FW-H signals computed at fourazimuthal locations (every 90◦), and truncated at an integernumber of blade passage periods.

3. REFERENCE RESULTSIn this section a subset of the available results for the threeOGV congurations with straight leading edge are reportedand shortly discussed. ese results have been presentedby Exa during the 4th FBN Prediction Workshop held onJune 8th 2017 in Denver, as a special session of the 23rdAIAA/CEAS Aeroacoustics Conference. Only results for theapproach operating condition are reported in this work.

Fig. 4 shows a comparison between H-W measurementsand simulation results at station #1 for the baseline congu-ration. e three components of the phase-locked averagevelocity, and the corresponding standard-deviation (SDV)values are ploed on an angular sector covering one rotorblade passage. e average eld is fairly well predicted, themain discrepancy being an underestimation of about 10% ofthe axial velocity component. It is worth mentioning that,


Figure 4. Phase-locked average (le block) and SDVvelocity (right block) at station #1 for the baseline OGV[m/ s]. Axial, radial and azimuthal velocity in the top,middle and boom rows, respectively. Measurements on thele column, simulations on the right.

for all congurations, the mass ow rate is predicted withinan error of 1%, whereas the total pressure ratio across the fullstage is predicted within an error of 0.4%. e predicted SDVlevels are also in fair agreement with the measurements, withtwo main negative marks: an overestimation of about 20%of the axial and azimuthal velocity uctuation levels closeto the outer wall, and an overestimation of about 10% of theradial velocity uctuation levels in the half-span region. Itis worth mentioning that the predicted SDV elds are alsoaected by a statistical convergence error, since averageshave been performed over 10 rotor revolutions only.

Figs. 5 and 6 show comparisons between H-W measure-ments and simulation results at stations #1 and #2, respec-tively, for the low-noise conguration. At station #1 thesame trends observed for the baseline conguration can bereported. Indeed, at this distance from the OGV, the velocityeld is not aected by the OGV geometry in a signicant way.At station #2 we can also observe a fairly good agreementbetween measurements and predictions. In particular, thelevels are quite well captured by the simulations, as well asthe turbulent mixing and spreading of the rotor wake. Simi-larly to what observed at station #1, an underestimation ofabout 10% of the average axial velocity component and anoverestimation up to about 20% of the azimuthal velocityuctuation levels.

e velocity maps at station #2 provide a certain con-dence of the capability of the method to predict the correct

Figure 5. Phase-locked average (le block) and SDVvelocity (right block) at station #1 for the low-noise OGV[m/ s]. Axial, radial and azimuthal velocity in the top,middle and boom rows, respectively. Measurements on thele column, simulations on the right.

velocity eld upstream of the OGV. is is proven for thelow-noise conguration, and reasonably expected for thebaseline one, for which no measurements are available atstation #2. erefore, the main discrepancy between H-Wmeasurements and simulations remains an underestimationof about 10% of the axial velocity and an overestimation ofabout 20% of the azimuthal velocity SDV. e impact of theseerrors on the predicted far-eld noise can be evaluated byconsidering the formula obtained by Amiet[26] for an iso-lated airfoil of chord c and span L at zero incidence in aturbulent stream. e Power Spectral Density (PSD) of thefar-eld noise in the airfoil midspan plane, at a distance rfrom the airfoil midpoint and an angle θ from the streamwiseow direction, reads:

S(r, θ, ω) =(ρ∞U∞ sin θ

2r

)2(kc)2

L2 |L|

2 l (ω) Sv (ω) , (2)

where ρ∞ and U∞ are the free-stream density and velocity,k =ω/c∞ is the acoustic wavenumber, ω is the radian fre-quency, c∞ is the speed of sound, L is the airfoil responsefunction, l is the spanwise correlation length, and Sv is thePSD of the upwash velocity component. e Helmholtz num-ber kc can be wrien as U∞kxc/c∞, where kx =ω/U∞ is thestreamwise wavenumber of an impinging turbulent pertur-bation of frequency ω. Hence, the far-eld noise PSD reads:


Figure 6. Phase-locked average (le block) and SDVvelocity (right block) at station #2 for the low-noise OGV[m/ s]. Axial, radial and azimuthal velocity in the top,middle and boom rows, respectively. Measurements on thele column, simulations on the right.

S(r, θ, ω) =(ρ∞U2∞ kxc sin θ

2rc∞

)2 L2 |L|

2 l (ω) Sv (ω) . (3)

is expression reveals a U4∞ power-law of the far-eld noiselevels, and a quadratic proportionality to the magnitude of theFourier component v of the upwash velocity uctuation. erelative error of S in logarithmic scale can be thus evaluatedas:

δSdB = 10 log(1 + 4 δU∞

U∞+ 2 δv

v

). (4)

From this expression, an error of 10% of the free-stream ve-locity results in an error of 1.46 dB of the far-eld noise levels.e same error is provided by an error of 20% of the upwashvelocity component. It could be therefore argued that, in thepresent fan noise simulations, a certain fortunate compensa-tion may occur between the underestimation of the averageaxial velocity and the overestimation of the azimuthal SDVvelocity.

A more quantitative comparison between measurementsand simulation results can be performed by considering thevelocity spectra at the same interstage locations. Fig. 7 shows,for the baseline conguration, spectra of the three velocitycomponents ploed as a function of the harmonic countat about 80% and 60% of the casing-relative radial location.

1e-05

0.0001

0.001

0.01

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u [

m/s

]

Harmonic count [-]

r = 80.07 %

H-W measurementsLBM simulation

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r = 60.11 %


Figure 7. Velocity spectra at station #1 for the baselineOGV. Axial, radial and azimuthal velocity on the top, centerand boom, respectively (in m/s). Comparison betweenH-W measurements (symbols) and PowerFLOW results atr=0.223292m (r/R=80.07%) on the le and r=0.167640m(r/R=60.11%) on the right.

e comparison is quite satisfactory, both in terms of tonaland broadband levels. Beer comparisons, in particular forthe tonal components, are expected by covering a longertransient time.

Figs. 8 and 9 show comparisons between H-W measure-ments and simulation results at stations #1 and #2, respec-tively, for the low-noise conguration. As for the baselineconguration, the agreement is quite satisfactory, at bothstations, both in terms of broadband and tonal levels.

e analysis of the unsteady velocity eld in the inter-stage volume have demonstrated that the accuracy of thenumerical results is quite well preserved along the whole pathof the rotor wake. is is a necessary but not sucient con-dition to predict accurate absolute and relative rotor/statorinteraction noise levels, and therefore capture the eects ofOGV modications on the radiated noise. As relevant tothe present study, Fig. 10 shows the comparisons betweenmeasurements and predictions in terms of deltas betweenthe baseline conguration and the other two congurations.Two quantities are considered: the overall sound pressurelevel (OASPL) at microphone located on a linear sideline ar-ray, 2.25044m away from the engine axis, with a constantangular spacing of 5◦ from 30◦ to 140◦, and the sound powerlevel (PWL) computed by integration of the far-eld acousticintensity over a spherical surface portion corresponding to acircular array of 10m radius, with a constant angular spacingof 5◦, extending from 30◦ (front) to 150◦. e agreement for


1e-05

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Figure 8. Velocity spectra at station #1 for the low-noiseOGV. Axial, radial and azimuthal velocity on the top, centerand boom, respectively (in m/s). Comparison betweenH-W measurements (symbols) and PowerFLOW results atr=0.223292m (r/R=80.07%) on the le and r=0.167640m(r/R=60.11%) on the right.

both quantities is very good, being within the experimentaluncertainty of ±1 dB.

From the analysis of the reference SDT results, we couldargue that the employed computational methodology canprovide reliable indications about possible noise reductiontrends associated with the usage of wavy OGVs.

4. INTEGRAL SCALES OF TURBULENCE IM-PINGING ON THE OGVSimilarly to a wing section in a turbulent ow, the acousticeectiveness of an OGV leading edge serration is expected todepend on ratios between the integral scales of the turbulentuctuations in the impinging rotor wake and the amplitudeand wavelength of the undulation. As shown by Gea-Aguileraet al[14] for cases of impinging anisotropy turbulence, themaximum noise reduction can be achieved when the inte-gral scale of the chordwise velocity component along thechordwise direction is smaller than the root-to-peak serra-tion distance (Lx


a time-shi, based on the convection velocity Uc computedby cross-correlating the phase-locked average signals. eintegral length scales of the resulting turbulence velocity uc-tuations are then computed following the statistical approachproposed by Gea-Aguilera et al[14] and further veried by us-ing the magnitude-square-coherence approach used, amongseveral others, by Avallone et al[27]. e former estimatesLki j in the direction k as:

Lki j (x) =∫ ∞0

〈u′i

(x + sek

)u′j (x)

〉〈u′i (x) u

′j (x)

〉 ds, (5)where ek is the unitary vector in the kth direction, 〈·〉 is theensemble average, and s is the separation distance. In orderto estimate the integral length scale of turbulent uctuationsin dierent frequency bands, the two-point coherence be-tween dierent velocity components is computed and usedto calculate the following integral scales:

Lki j (x, f ) =∫ ∞0

γi j(

f , x, x + sek)

ds, (6)

where

γ2i j(

f , x, x + sek)=

��φuiu j(

f , x, x + sek) ��2

φuiui ( f , x) φu ju j(

f , x + sek) , (7)

is the coherence square and φuiu j is the cross-spectral densityof the two velocity components u′i and u

′j . Due to the non-

homogeneity of the turbulent ow in the wake of the rotor,usage of this expression can lead to wrong estimates of theintegral scales. is risk can be reduced by comparing thelength scales computed at dierent points, and by using thephase-locked average removed velocity to compute the cross-spectrum in Eq.7. is procedure should provide length scalesthat can be interpreted in relation with the canonical problemof an airfoil in a homogeneous turbulent eld.

e correlations are computed between signals extractedalong ve lines from a volume transient solution le sam-pled at the frequency of 458 kHz and covering one bladepassage, from the rotor to the stator. ese lines are ex-tracted along the radial and azimuthal directions about tworeference points at the same radial location, about 80% of thepassage, and two axial locations, the rst one at at x=0.18m(5mm upstream of the baseline OGV), and the second oneat x = 0.15m, the origin of the reference system being lo-cated in the midpoint of the rotor. e two pairs of radialand azimuthal extraction directions are denoted as (er1, eθ1 )and (er2, eθ2 ), respectively. e solution is also extractedalong the axial direction ex connecting the two points. enon-dimensional cross-correlation of the dierent velocitycomponents is ploed in Fig. 11, and the corresponding inte-gral scales are reported in Table 2. Interestingly, the integralscales along the radial and azimuthal directions are slightlysmaller at the location closer to the OGV, and this is probablydue to a local distortion induced by the OGV. is observationis not necessarily in contrast with the measurements made by

Figure 11. Non-dimensional cross-correlation of thevelocity uctuations as in Eq.5.

Table 2. Integral scales of turbulent velocity uctuations inthe SDT engine interstage

Integral length Value ( mm)

Lxuu 8.3Lr1vr vr 3.8Lθ1vθ vθ 5.0Lr2vr vr 5.7Lθ2vθ vθ 5.7

Podboy et al[29] who evaluated the integral scales at the twoaxial locations, say the H-W stations #1 and #2 introduced insection 3, and reported integral scales that increase fartherdownstream of the rotor. Indeed these measurements werecarried out for the swept stator for which both H-W stationsare suciently far from the OGV leading edge to exclude anyinuence on the velocity cross correlation.

As expected from previous literature works[28], the inte-gral scale along the axial direction is larger than along theother directions. On the base of these results, only the base-line OGV designs #5 and #6 are expected to satisfy both theaxial and radial criteria for noise reduction, although onlymarginally for designs #5. It is indeed worth mentioning that,as shown by Maunus et al[28], all the integral scales increasemonotonically along the radial direction. erefore, sincethe correlations have been computed at about 80% of the in-terstage radial passage, it is reasonable to expect that, for theradial OGV design #5, the axial integral satises the conditionLx . 2hs over a certain passage percentage. Whereas, thecondition should be satised along the whole radial passage


Figure 12. Frequency-dependent integral scales as in Eq.6.

for design #6. Conversely, this is likely not the case for theswept OGV design #3, because of its larger distance from therotor and the expected increasing scales farther downstreamof the rotor, as observed experimentally for the SDT fan stageby Podboy et al[29].

Finally, Fig. 12 shows the frequency-dependent integralscales. Consistently with the previous estimations, the ax-ial integral scale is higher than in the other directions andbelow the threshold values of about 7mm in both the ax-ial and radial directions for the baseline OGV designs # 5.An interesting property of these results is that, aer a rapiddrop below about 2-3 kHz, the integral scales decay veryslowly with frequency. It is therefore expected that, in agree-ment with the experimental observation made by Chaitanyaet al[9], if the serration amplitude and wavelength are largeenough compared to the overall integral scales, the noisereduction should have a broadband character, with a slowlyincreasing trend above a certain frequency threshold.

5. EFFECTS OF SERRATIONSree serration designs are initially considered for the Low-Noise OGV (Table 1). According to the estimated integralscales of the interstage turbulence at a location close to theleading edge of the baseline OGV, non of them has the poten-tial to reduce the noise. Successively, three serration designsare considered for the baseline OGV, and two of them (designs#5 and #6) are expected to satisfy the criteria for the integralscales and thus result in some signicant noise reduction.e results are reported in this section in their chronologicalorder.

Fig. 13 shows deltas of the far-eld OASPL and noisePWL for the three serrated low-noise OGVs. Far-eld noisereductions up to 0.5 dB can be observed, with slightly beer

performances for designs #1 and #3. is conrms that theundulation amplitude for design #2 is too small comparedto the integral scales of the impinging uctuations, both inthe axial and radial directions. However, all the achievednoise reductions are too small and likely in the order of thestatistical convergence error of the simulations. e PWLdeltas exhibit a large spectral variance around 1 dB and it ishard to identify a clear noise reduction trend, as well as aclear dierence between the three designs. Both the axial andradial integral scales are indeed too large compared to theroot-to-peak distance and semi-wavelength of the serrations,thus resulting in no signicant noise reduction.

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Figure 13. Eect of dierent leading-edge serrations for thelow-noise conguration (designs #1-#3). Relative far-eldOASPL along the sideline array (top) and PWL (boom).

Fig. 14 shows absolute far-eld OASPL and noise PWL forthe reference Low-Noise OGV and the serrated edge design#3. e only visible eect in the PWL spectrum is a 1 dBreduction of the BPF2 peak.

Fig. 15 shows deltas of the far-eld OASPL and noisePWL for the serrated baseline OGV. Far-eld noise reductionsbetween 0.2 dB and 0.75 dB have been predicted for design #4,between 0.5 dB and 1.25 dB for design #5, and between 0.75and 1.5 for design #6. e PWL spectra exhibit a clear noisereduction trend for the three designs starting from about 2-3 kHz. In agreement with the integral scale geometric criteria,


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Figure 14. Eect of leading-edge serration for thelow-noise conguration (designs #3). Far-eld OASPL alongthe sideline array (top) and PWL (boom).

design #6 is more ecient than designs #3 and #4. Veryinterestingly, the far-eld OASPL exhibits the same noisereduction directivity paerns.

Finally, Fig. 16 shows absolute far-eld OASPL and noisePWL for the reference Baseline OGV and the serrated edgedesign #6. In this case, the PWL shows some broadband noisereduction starting from a frequency of about 3 kHz, and a netreduction trend above 6 kHz. e laer value corresponds toa Strouhal number f hs/U of about 0.2, the average axial ve-locity U being about 110m/s at a distance of 5mm from theleading edge. Interestingly, Chaitanya et al[9], determined athreshold Strouhal number of 0.2 also for the case of an aero-foil in isotropic turbulence. Further simulations are requiredin order to conrm the generality of this result.

CONCLUSIONSDierent designs of serrated OGV leading edges have beensimulated using a validated CFD/CAA solver based on theLB-VLES method. e NASA SDT engine geometry has beenconsidered as a reference. Serrations have been applied bothto a radial and a swept stator. In the explored design space,which is indeed limited to six dierent serration designs,no signicant noise reduction has been observed, with the

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Figure 15. Eect of dierent leading edge serrations for thebaseline conguration (designs #4-#6). Relative far-eldOASPL along the sideline array (top) and PWL (boom).

exception of two designs for the radial OGV, for which theserration root-to-peak distance and spanwise wavelengthwere suciently large compared to the integral scales of theimpinging turbulent uctuations. More precisely, averagenoise reductions along the sideline microphone array of about1 dB and 0.2 dB for the radial and swept OGVs, respectively,have been obtained. e second value is below the numericaland experimental accuracy, thus revealing the usefulness ofthe leading-edge serration to reduce the noise of the low-noise OGV. Although the explored design space is rathersmall, the present results seem to conrm previous literatureobservations, both in terms of scale thresholds, say root-to-peak distance larger than the axial integral scale and thehalf-wavelength smaller equal to or slightly larger than theradial integral scale, and the 0.2 Strouhal number threshold.Additional designs will be explored in the future in orderto achieve more denitive conclusions about the interestof a wavy leading edge for rotor/stator interaction noisereduction. e analysis will be also extended to dierentengine congurations, like a modern ultra-high-bypass-ratioengine, and higher power operating conditions.


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Figure 16. Eect of leading edge serration for the baselineconguration (design #5). Far-eld OASPL along the sidelinearray (top) and PWL (boom).

ACKNOWLEDGMENTSe authors wish to acknowledge Dr. Edmane Envia fromNASA Glenn Research Center for providing the geometry andexperimental data of the NASA 22-in fan source diagnostictest.

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IntroductionFan stage configurations and sinusoidal leading edgeReference geometriesWavy OGV

Numerical modelCFD/CAA computational approachComputational setup

Reference resultsIntegral scales of turbulence impinging on the OGVEffects of serrationsAcknowledgmentsReferences

Documents

Aeroacoustic study of a wavy stator leading edge in a ...isromac-isimet.univ-lille1.fr/upload_dir/finalpaper17/66.86_Casalino_et_Al_2017.pdfand radiated noise of the 22-in source diagnostic