Conditional averaging methodology for periodic data with time jitter and spatial scatter

Kazan, Russia - September 11-13, 2007

Conditional Averaging Methodology for Periodi

Data with Time Jitter and Spatial S atter

Berend G. van der Wall,OliverS hneider

DLR, Inst.of FlightSystems, Brauns hweig, Germany

The onditional averaging methodology is shown to be mandatory to proper average

essentiallyperiodi datathatarebiasedbyspatials atterandtimejitteree tswhi hare

always presentin both ightand windtunneltest.This isdemonstratedatvarious data

of ompletely dierent physi al origin as obtained from the Higher Harmoni Control

Aeroa ousti RotorTest(HARTII)performedintheLargeLow-SpeedFa ility(LLF)of

the German/Dut hWind Tunnel (DNW):blade positionand tip vortex ow eld data

(bothobtainedinstantaneouslyand withopti almeasurementte hniques),bladesurfa e

pressureanda ousti data(measured ontinuouslybyabsolutepressuretransdu ersand

mi rophones,respe tively).

1 Introdu tion

Inheli opterrotorexperimentaldata-eitheroriginatingfromthe yingheli opterorfromthewindtunnel

model-periodi andnon-periodi motionsofthetestvehi learepresentduetogustsandtransientmotion

oftheheli opterordueto exibilityofmodelsupportandunsteadinessinthewindtunnelenvironment.

Thesemotionsusuallyareoflow-frequen ynature omparedtotherotorrotationalfrequen y,but they

slightly hangetheaerodynami environmentrevolutionbyrevolution.Consequentlythedatalikerotor

bladeposition,bladepressure,vortexposition,mi rophonepressureexhibitdisturban esinspa eand/or

timethatmustproperlybeaddressedindataanalysis,espe iallywhenthetime(orspa e)averageddata

aretobe omputed.Theseaverageddata(velo ityelds,positionorpressuretimehistories)arethebasis

for odevalidation eortsandthusspe ialalgorithmsmustbeapplied toeliminatethesespatials atter

and/ortimejitteree tsappropriately.

Themostfrequentlyusedmethod ofaveragingis theso- alledsimple(= arithmeti )averaging.

Pro-videdthatanumberofperiodsN

p

(oneperiod=onerotorrevolution)havebeenre ordedforea hsensor

-favorablywitha onstantnumberofsamplesN

s

perperiodandadditionallyea hsampley

i

atthesame

phaselo ation

i

withinea hperiod(whi hisusuallythe aseinrotarywingdatathataretriggeredto

themain rotorazimuth with1/revasthedominatingfrequen y)-, su h analgorithmto omputean

averagesampley

i

(j); i=1;2;:::;N

s

ofatimehistoryreadsinageneralizedform

 y i = m v u u t 1 N p Np X j=1 y m i (j) i=1;2;:::;N s (1) with m= 1 harmoni average m!0 geometri average

m=1 simple(arithmeti )average

m=2 quadrati average(oree tivevalue)

and y i;min y i (m= 1)y i (m!0)y i (m=1)y i (m=2)y i;max

Thesimpleaverage(m=1)iswidelyusedinstatisti alanalysisofvariationsintheindividualsamples

andeliminatesnoiseinapropermannerinordertoobtainasmoothtime-averagedhistory.Theharmoni

ofthesamplesis tobeinterpreted,thegeometri averagem!0isoftenused, thatis  y i = N p v u u t Np Y j=1 y i (j) i=1;2;:::;N s (2)

Anotherimportantparametertojudgetheindividualsamples onden eintherelationtotheaverage

valueistomakeuseofthestandarddeviation,whi hisdenedas

 i = v u u t 1 N p 1 N p X j=1 ( y i (j) y i ) 2 i=1;2;:::;N s (3)

In a Gaussian normal distribution, whi h is expe ted in most ases, about 68% of all samples are

withintherangeofy

i  i ,about95%within y i 2 i

, andabout99.8%within y

i 3

i .

In ase the data are ontaminated by spurious elements being either by far too large and/or too

small omparedto themajorityofsamplesanotherpro edure shouldbeappliedrstbyeliminating the

samefra tion ofN

p

at both endsof thes alebefore applying oneof theaveragingmethods mentioned

before. This is alled the trun ated average,but the trun ation threshold(usually 5to 15%) must be

adapted manuallyto theindividualdistribution of dataand thusrequires somedegreeofexperien ein

order to distinguishbetweeen those data beingobviouslyerroneousand those that should beretained.

Oftenavaluebetween2 and3 is usedas athreshold toidentify those samplesas outliers.However,

the mathemati al formulation requires trun ation at both ends of the s ale with the same number of

samples,whi hin some asesdoesnotmat hthe physi softhedata.Some otherhigherorder variants

ofthetrun atedaverageexistthatuseweighingfun tions.

As anexamplefor instantaneous datathat are notavailable in timerather thanin spa ethe result

of ow eld measurementslikePIV an be seen.Herein neighboring data (velo ity ve tors) are

spa e- orrelated.Theprepro essingofparti leimagestovelo ityve torsusuallyleadstosomespuriousve tors

thatmustbeeliminatedbeforeanalysingthevelo ityve toreld.Theiridenti ationisbasedon

statis-ti alanalysisofa ertainsubsetofve torsaroundthatoneinquestion.On eidentiedasspurious,these

ve torsnormallyareofsigni antlylargermagnitudeanddierentorientation(althoughtheorientation

alone annot be used as indi ator, forexample theorientationnaturally hangesto the oppositewhen

passingthe enterofavortex)thanthoseve tors omputed orre tly,butrarely ofsigni antlysmaller

length.Thus, lipping thesamenumberofve torsatbothendsofthelengths alewouldeliminatealot

of orre tsamplesatthelowerendandappearsnotappropriatetotheproblem.

Another example is given with ontinuous data as obtained from strain gauges, pressure sensors

or mi rophones. Within ea h sensor time history the individual samples are time- orrelated to form a

ontinuous urve. Any spikes - like those aused by slip-ring problems or broken ables - an easily

be dete ted either by orrelation to the neighboring samples within an individual time history, or by

orrelationwiththesamplesatthesamephaseoftherestoftheperiodsmeasured.However,in asethis

is arepetetive problem o uring in ea h period relyingon the lattermethod alonewould notwork.A

spa e- orrelationmustalsoexistto ontinuousdataobtainedfrom anothersensorlo ated loseenough,

su hthatthisinformation ouldalsobeusedtoidentifyspuriousdata,but aremustbetakensin ethis

oftenin ludesnon-linearphaseshiftsbetweenthetimehistories.

So far, the averaging methods mentioned are mainly useful when statisti ally distributed, mainly

one-dimensional, data are to be averaged and no other information about the physi s behind has to

be obeyed. Yet, a fundamental problem annot be addressed by those averaging methods, and this is

the spatial s atter of individual events of interest. Applying any of the averagingmethods mentioned

wouldresultin arti iallysmoothingtheindividualeventswhi hmakesananalysisoftheseobsolete.To

illustratetheproblemseeFig.1.

As an be seen in this example, in ea h individual time history an identi al event is seen and the

nal goalis to providean averagedtimehistoryas indi atedby CA = onditionally average.The line

denotedSArepresentstheresultofsimpleaveragingusingEq.1withm=1anditis learlyvisiblethat

the individual hara teristi sare widely lost.In asethis was ameasurement of theindu ed velo ities

ofavortexwhenpassingtheprobeea hindividual analysiswouldleadto orre t oreradiusandswirl

velo ity,buttheaveragedtimehistorywouldgive ompletelywrongresultsforbothparametersdespite

a orre taveragepositionof theevent.Thereasonisthetime jitteroftheeventthat leadstoarti ial

-1,5

-1,0

-0,5

0,0

0,5

1,0

1,5

0

10

20

30

40

50

time, index

y

i

(j)

SA

CA

Figure1:Ee toftimejitteronaveragedtimehistory(SA-simpleaverage;CA- onditional average).

of the individual time history. To ir umvent the time jitter ee t, two possible solutions have been

elaboratedand usedinthepast:

1. in thespa e-timedomain: toidentify theparametersoftheeventin ea h individualmeasurement

andthenapplyoneoftheaveragingmethodstotheparametersidenties.However,theindividual

analysis oftenisbiasedorhinderedbynoiseandtheresultisasetofparameters,but noaveraged

timehistoryorspatialdistribution ofdataisavailable.

2. in the frequen y domain: for ea h individual period of the time history the Fourier spe trum is

omputed, thenall spe traare averaged.This isappropriatefor themagnitudesof thespe trum,

but thetimeinformation(=phase)getslostand againnoaveragedtimehistoryisavailable.

Theee t oftimejitterontheresultsofthespe trumand orre tionstoitin thefrequen ydomain

were elaborated, for example by [5℄. In this arti le an alternative method is presented known as the

onditionally averagingthat takes into a ount spatial s atter and time jitter and as a resultprovides

averagedspatial distributions or timehistories that eliminatenoisebutstill in lude alltheinformation

oftheindividualevent.Intimehistorydata,thegoalistogenerateaveragedtimehistories thathavea

Fourierspe trumsimilartotheaveragedspe trum.

2 The HART II data base

AlltheanalysismethodologiesareappliedtotheHARTIItestdataobtained2001intheDNWbyDLR,

ONERA, NASA Langley, US Army AFDD and DNW. These data en ompass measurements of wind

tunnel data,rotorbalan e,blademotion,bladepressure,a ousti radiationanddetailed tipvortex ow

eld data. The HARTII test is des ribedin [1℄ and details of thetest set-up and of themeasurement

te hniques applied are given in [2℄. Representativeresultsapplying partof the te hniques des ribed in

thispaperareshownin[3℄.Thesereportsandpartofthedataareavailablefortherotor raft ommunity

withintheframeworkoftheinternationalHARTIIworkshopheldsemi-annuallyatboththeAHSForum

andtheEuropean Rotor raftForum[4℄,sponsoredbytheHARTIIteam.

Within HARTII aMa h-s aledanddynami allys aledBo105modelrotorwithN

b

=4re tangular

blades at a pre- oneof 

p

=2:5deg, having alinear twist of 

tw

= 8deg=R , aradius of R =2m, a

hordof =0:121mandaNACA23012airfoilwithtrailingedgetabwas operatedin6degdes ent ight

ondition that is known to generate strong blade-vortexintera tion (BVI) noise.The blade rotational

speedwas =109rad=s andthe wind speedV

1

=33m=s, resultingin anadvan eratio of=0:151.

Thethrust oeÆ ientwassettoC

T

=0:0044representingalightlyloadedBo105andzerohubmoments.

ThesetupisshowninFig.2.

Oneofthemaingoalswastoidentify thephysi alme hanismsofhigherharmoni ontrol(HHC)on

noiseandvibrationredu tionbymeansofextensive oweldmeasurements.Threedistin tive onditions

weremainlyinvestigated,thesearethebaseline ase(referredtoasBL)withashaftangleof

S

=5:3deg

and zero roll and pit h moments. The appli ation of HHC features twovariants trimmed to the same

onditionastheBL ase:theminimumnoise ase(MN)with3/revpit h ontrolof 

3

=0:8degat the

bladerootat aphaseof

3

=300deg,andtheminimumvibration ondition(MV)with thesamepit h

amplitude,butadierentphaseof

3

=180deg.These onditionswereidentiedintherstHARTtest

mentedBo105modelrotorwas usedwheretwobladeswereequippedwithin total51absolutepressure

transdu erspriortothetest.Theleadingedgedierentialpressureat3% hord ouldthusbemeasured

from 40-97%radius at 11 radial se tions,and the hordwise pressuredistribution at 87% radius ould

bere ordedbymeans of 17sensors assket hedin Fig. 2.By hordwiseintegration ofthese sensor

sig-nalsthe lo al lift timehistoryin termsof thenormal for e oeÆ ientC

n M

2

or lo al blade ir ulation

b =C

n

V =2 with V( ) as the time-varying airspeed at the se tion an be evaluated. 80 su essive

rotorrevolutionswerere orded,triggeredtotherotorazimuthatadatarateof2048samples/revwithin

ea h ondition.

(a) ModelrotorintheLLFoftheDNW

0

-2

-1.5

-1

-0.5

0.5

1

1.5

2

x

V

0.45m

0.5m

0

1

-1.5

-1

-0.5

0.5

1.5

y

hub

hub

/R

/R

hub

z

/R = 0.4575

z

mic

+

/R = -0.65

(b)Mi rophonemeasurementpositions

*

*

*

*

*

*

#

#

#

#

*

*

*

*

*

*

*

#

#

#

*

#

*

*

*

*

_*

**

_*

#

*

r/R

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0

Absolute pressure transducers (51)

Strain gages: flap (3), lead−lag (2), torsion (1)

*

17

reference blade (25 Kulites)

preceeding blade (26)

( ) Distributionofpressuresensorsontheblades

.228

.318

.408

.498

.588

.678 .768

.858 .948

.993

.903

.813

.723

.633

.543

.453

.363

.273

r/R

5 6

7

21

22

23

40

Marker no.

(d)DistributionofSPRmarkersontheblades

Figure2:HARTII equipmentusedformeasurementofa ousti s,bladepressuresandbladede e tion.

A ousti pressuredata were re orded1:1075R belowthe rotorusing anarraywith 13 mi rophones

spa ed equallyat adistan eof 0:225Rthat was traversedforeandaftof therotor entreby arangeof

2Rat 17 downstream lo ationsseparatedby 0:25R , seeFig. 2.Atea htraverselo ation mi rophone

datawerere ordedfor100su essiverotorrevolutionsatadatarateof2048samples/rev,againtriggered

totherotorazimuth.Thepost-pro essingprovidesnoiselevelsateverylo ationbasedonspe tralanalysis

Thebladepositionwasmeasuredopti allyusingStereoPatternRe ognition(SPR)[9℄.Four ameras

weremountedonthe oortakingimagesoftherotorat24spe iedazimuthallo ationsequallydistributed

aroundtherevolution.Allfour bladeswereequippedwith 18markersallalongtheleadingedgeas well

as alongthetrailingedge asgivenin Fig.2.The omputationofthemarker enters bymeansofimage

pro essingandaproper alibrationresultedintheabsolutepositioninspa eofthesemarker enterswith

an a ura y of 0:4mm, whi h is 0.33% hord (or 0.02% radius). Sin e the ameras ould not measure

ontinuouslyratherthanwerelimitedbyamaximumfrequen yofabout10Hz,oneimagewas re orded

every7threvolutionandaminimumof50repeatswastakenateverybladeazimuthpositiontoallowa

statisti alanalysis.

The post-pro essing is des ribed in detail in [6℄ and allows the identi ation of ap and lead-lag

positionofthequarter hordlinealongthespanatea hazimuth.Puttingtogetherallazimuthalpositions

insequen ethetimehistoryofblademotion anbe omputedbymeansofFourieranalysisandsynthesis

for intermediate azimuth lo ations. The elasti deformation is obtained subtra ting the pre- one rigid

bladeposition.Dierentiating theleadingedgeandtrailingedge markerpositions providesinformation

abouttheradialdistribution ofthelo al pit h anglewith ana ura yof0:4deg.Whensubtra ting the

build-inpre-twistandthe ommandedbladerootpit h ontroltheelasti torsionis obtained.

Floweld measurementwereperformedusingStereoParti leImageVelo imetry(SPIVod3C-PIV)

[10℄. A large observation area of 0:45m0:37m was taken by DNW ameras for the global velo ity

distribution and globalwakestru ture analysis and simultaneouslyasmall observationareaof0:15m

0:13mwas gatheredbyDLR amerasforanalysis ofthebladetipvortexstru tures. Thepre-pro essing

of the amera images results in velo ity ve tor elds, while the post-pro essing is devoted to analyse

theseve tormapsrstforthevortexspatialposition,thenforthevortexpropertiesinorder toidentify

parameters like the ore radius r

, the maximum swirl velo ity at the ore radius V

and the swirl

velo ityproleV

s

(r).Otherparameterslikevortex ir ulationmaybe omputedbasedonthese results.

Themethodsofpost-pro essingaredex ribedin[7℄.

(a)PIVlo ations,MV (b)Rawdata PIVimage,BL,Pos.21,lower

amera

Figure3:PIVmeasurementpositionsandexemplaryrawdataimages.

As in SPR measurements, the ameras were triggered to the rotor azimuth and re orded an

im-age every7th revolution, with 100 repeats. A traversingsystem allowed to overthe entire rotor disk

outside jyj=R = 0:4 su h that on either side of the rotor disk the tip vorti es were tra ed from their

reation at the trailing edge downstream until the rear end of the disk in lateral planes lo ated at

y=R=0:4;+0:55;0:7;0:85;0:97.Thepositionsmeasuredareindi atedinFig.3attheexampleof

theMV ase,where dualvortexsystemsexistoverpartof therevolutiondueto downloadattheblade

tip itself.The rightgureexemplarilyshowsarawdata imageof theBL aseat position 21where the

fullsize representsthelargeobservation areaand theinnerimagerepresentsthesmallobservationarea

withaboutthreetimesthespatialresolution.

A se ondary post-pro essing puts together the downstream measurements of the tip vortex whi h

resultsin the vortextraje tory (andlo ations where thevortex passedthepath ofthe blades),as well

as theagingof thevortexby meansofthe developmentofits identiedparametersliker

or V

.Some

By means of stereo pattern re ognition te hnique (SPR) the spatial position of markers atta hed to

ea h of thefour blades and to the bottom of the fuselage (Fig. 4) was determined opti ally. The SPR

te hniqueis basedona3-dimensionalre onstru tion ofvisible markerlo ationsbyusingstereo amera

images.Thea ura yofmarkerpositionre ognitiondependsontheresolutionandangularset-upofthe

ameras and on the marker shape and size.For the onditions of the HART II test measurement the

theoreti alresolutionis0:4mminx ,y andz dire tion.Amoredetaileddes riptionofthemethodis

presentedin[6℄and[9℄.The amerasweretriggeredtotherotorazimuthand50,sometimes100repeats

perposition were re orded.Thedata ontainthelowfrequen ymotionof themodelas spatial s atter.

Thismotionis in reasingwithblade radialpositionsin etheairloads generatingtheblademotionare

alsosubje ttovarya ordingtothemodelmotion.

Figure4:SPRimageofthedownsreamright ameraat90deg

Togetsmoothdatawithredu ederrorsandeliminatedvibrationsitisne essarytodetermineaverages

ofthe oordinates.Toaveragethemarker oordinatesasimplemeanvalueforea h orre tlyre ognized

marker of all repeats was omputed. In Fig. 5(a)and Fig.5(b) an exampleis shown for twodierent

markersatthe90degazimuth position ofblade1ofthebaseline ase.

−0.1

0

0.1

−0.2

−0.1

0

0.1

0.2

100y/R

100z/R

σ

2

σ

σ

_y

= 0.0463

σ

_z

= 0.0202

(a)Bodymarker

−0.1

0

0.1

−0.2

−0.1

0

0.1

0.2

100y/R

100z/R

σ

2

σ

σ

_y

= 0.0446

σ

_z

= 0.1020

(b)Bladetipmarker(trailing

edge)at99%R

0.2

0.4

0.6

0.8

1

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

r/R

100

σ

x

/R, 100

σ

z

/R

σ

_x

LE

σ

_y

LE

σ

_z

LE

σ

_x

TE

σ

_y

TE

σ

_z

TE

( ) Standarddeviationinx andz dire tionfor

leadingandtrailingedgemarkers

Figure5:S atterofbodyandblademarkersat90degBL

Atthelo ationofthebodymarker(leftgure)thes atteringisbyabout4mminy dire tion(lateral)

horizontaldire tionno hange ins atteringisvisible(the bladeisstiradially).

In Fig.5( ) the standarddeviations  in alldire tions are shown for both theleading and trailing

edge markersdepending onthe bladeradius. It learly an beseenthat there isno dependen e of the

y s atterontheradiusduetolargeradialstinessoftheblade,itisnearly onstantandonlyin uen ed

by the low elasti ity of the wind tunnel sting. The x and z s atter in rease with the blade radial

lo ationbe auseofthe hangingairloads,thebladeelasti ityin ap,andmodelmotion.

TheanalysisofSPRresultsrequiressomepost-pro essingsin ethedata ontainonlypositionsofthe

markers alongleading and trailingedge in spa e, i.e. in thewind tunnel oordinate system.The goals

are ap,lead-lagandtorsiondispla ementsofthequarter hordlinein theshaft oordinatesystemwith

origin in the enter of the rotor hub. To obtain these results, the position of the hub enter must be

knownandseveralpro edureshavetobeapplied(Fig. 6).

Rawdatainthewindtunnelsystem

+

Averagingofrawdata

+

Motionanddrift omp ensation

+

Rotationbytheshaftangle

+

Rotationbytherollangle

+

Rotorhub enterx ; y p ositionidentifi ation

+

Rotorhub enterz p ositionidentifi ation

+

Shiftof o ordinatesintotherotorhub enter

+

Analysisofelasti blademotion

+

Fourieranalysisoftheblademotion

(a)SPRanalysis owdiagram

0

90

180

270

360

−2

−1.5

−1

−0.5

0

0.5

1

ψ

/ deg

100z

el

/ R

precone alone

BL

MN

MV

(b)Flapmotion

0

90

180

270

360

1

1.5

2

2.5

ψ

/ deg

100y

el

/ R

BL

MN

MV

( )Lagmotion

0

90

180

270

360

−4

−3

−2

−1

0

1

2

3

ψ

/ deg

θ

el

/ deg

BL

MN

MV

(d)Torsionmotion

Figure6:Post-pro essingpro edure andresultsofSPR:Elasti tip motiondepending onrotorazimuth

forHHC-sweep,blade1(measurementa ura y:100
z=R=0:02in apandlag;
=0:5deg;

airfoilthi kness:100
z=R=0:726)

During the measurements dynami markerposition displa ements due to low frequen y motionsof

thewind tunnel sting,vibrationsoftherotormodel andof thestingsupportwerepresent.Alsoadrift

in stingyawled to alateraldrift ofthe entire model. To orre t this drift(up to 10mm within the23

azimuth lo ations)thedriftofthebody markersisused. Thedieren e betweenthe meanvalueat one

azimuth tothemeanvaluefromallazimuths denethebody drift.Basedonthisdriftallblademarker

oordinatesweremodied.Theresultshaveshownthatthebodymarkerpositionsdierinmeasurements

ofthe advan ing and retreatingside.That is why thedrift ompensationwas madeseparatelyfor ea h

side.

After drift ompensationthedatain DNW oordinatesystemhavetobetransformedintotherotor

hub oordinatesystemtoobtaintheparametersofblademotion.Thisisdonebyrotatingthe oordinates

bytherotorshaftangleandtherotorrollangleinto a oordinatesystemparallel totherotorshaftand

transformation(shifting)ofallmarker oordinatesintotherotorhub enter oordinatesystem.Thenthe

elasti blademotion an beextra tedandasmotheddistributionofthethree omponents ap, leadlag

shaftanglethatwerenon-zero.Therollanglewasmeasuredto0.145deginsteadofzero.Duetosupport

elasti ity therotor shaftangle hashad an osetof about0.15deg that was alsotaken into a ountin

thefurtheranalysis.

Unfortunatelytherotorhub enter ouldnotdire tlybemeasured,sin etheSPR ameraswerelo ated

belowthemodel.Asuitablemethod forhub enter identi ationwas foundin the ir ularregressionof

singleblademarkers( omputebestt ir lesofthepositionsfromonerevolutiontogetthex y enter

point). There is one ir le enter point obtainedfor ea h blade marker whi h resulted in a s attering

of about 1:0mmin x dire tion and 1:1mmin y dire tion in all ongurations.When thehub enter

positions al ulatedbyusingdierentbladesare ompared,the maximumdeviationisabout0:8mmin

x-dire tionandonly0:2mmin y dire tion whi hisin theorderoftheSPRmeasurementa ura y.

Afterthehub enter oordinatesinx andy dire tionarefound,thepositionin z dire tionofthe

rotorhub enter isindemand.Atrstthe oordinatesystemmustbeshiftedintothehub enterfound

so far. This means atransformation of all blade and body markersinto a oordinate systemwith the

originin therotor hubx , y enter point, while theoriginin z is yet anywhere ontheshaft axis.To

identifytherotorhubz oordinate,apolynomialoffourthorderwithanadditionally onstraintisused.

It is assumed that the gradientdz=dr at theposition where theblade is xed is equalto the pre one

angleof2:5deg asaboundary ondition.Finallythe oordinats anbeshiftedintotherotorhub enter

oordinatesystemandtheblademotionparameters anbe omputed.

The elasti blade ap de e tion z

el

(positiveup) is omputedby the distan e between the quarter

hordlineandastraightlinedened bythepre- oneangle.Thereforeapproximatelythedistan eofthe

quarter hordline z position to thepre- one line atdened radialpositions is used. Theelasti blade

lead-lagde e tiony

el

isgivenbythedistan ebetweentheradialpositionofthequarter hordlineand

astraightlinedenedbythe urrentazimuthpositionoftheblade(lagpositive).Thepureelasti pit h

deformation

el

(positivenoseup) anbe al ulatedbythedistan eofthez oordinateofthefrontand

rearblademarkeraftersubtra tingtheasso iatedpit h ontrolangle, thepre-twistangle andthepit h

osetinz dire tionduetothedierentdistan eofthefrontandrearblademarkerstothequarter hord

line.

Fig.6(b),Fig.6( )andFig.6(d)showthe omparisonoftheelasti ap,lead-lagandtorsionmotion

of the rotorblade tip for the referen e bladedepending on azimuth forthe ongurations with higher

harmoni ontrol andthebase line aseat thebladeposition r=R=99%.When3=rev HHC isapplied

( asesMNandMV),a3=rev appingdominatesthegure(Fig.6(b))asexpe ted.Wendlo al

ampli-tudesofupto0:6%RotheBLposition atthebladetipintheminimumnoise ase.Theresultsofthe

bladelagmotionshownearlyidenti alvalueswith1=revamplitudesofabout0:5%Rindependentofthe

higherharmoni ontrol (Fig.6( )).With 3=rev HHC astrong3=rev torsionis theresponsewhi h was

expe tedduetothenaturalfrequen yintorsionat3:6=revofthisrotor.Thelo alamplitudesintorsion

areupto1:5degotheBLvaluesintheminimumnoise aseandupto2:5degintheminimumvibration

ase.

4 Tip vortex position and ow eld analysis

ThePIVmeasurementsweretriggeredtotherotorreferen ebladeazimuthsu htoobtainimagesofthe

tipvortexfromthesamereferen ebladeandthesameobservationareainspa eandintimeforaveraging

purposesandstatisti alanalysis.

As an example,the tip vortex of theMV ase reatedat y = 0:7Ronthe advan ing side at about

=135degis reatedbyalo al downloadwithaprettysharpgradientoftheblade ir ulationtowards

thetip. This vortex isni ely shaped rightfrom the beginning and basedon theanalysis of 100repeat

measurements these have a verti al s atter of 0:068%R and a horizontal s atter of 0:058%R in the

observation areawhen thevortexisjust reated,Fig.7(a).Theverti als atterrepresentsthevariation

in thebladetipposition asgivenby meansofSPRresultsshownin Fig.5,while thehorizontals atter

representstheradialposition onthebladewhere thevortexis generated, whi h isbiased alsobybody

motioninthisdire tion.Morethanonerotorrevolutionlaterthes atterhassigni antlygrowninboth

dire tionsduetotheso alledvortexwanderee t[3,7℄anddueto loseen ounterswithpassingblades

(BVI),Fig.7(b).It analsobeseenthatthedistributionofvortexpositionsisratherhomogenouswithin

therangeof  insteadofbeing lustered withhigherdensityaroundthe meanvalueandthus doesnot

represent aGaussian normaldistribution. The growthtrend is progressiveas an be seen in both the

V V

a,b:s atterof vortex entrepositionatdierentvortexage,MV,y=R=0:7

0,0

0,5

1,0

1,5

2,0

0

90

180

270

360

450

540

Ψ

V

/deg

1

0

0

σ

x

/R

+0.7, BL

-0.7, BL

+0.7, MN

-0.7, MN

+0.7, MV

-0.7, MV

y/R =

_{BVI at}

( )Standarddeviationofvortexhorizontalposition

0,0

0,5

1,0

1,5

2,0

0

90

180

270

360

450

540

Ψ

V

/deg

100

σ

z

/R

+0.7, BL

-0.7, BL

+0.7, MN

-0.7, MN

+0.7, MV

-0.7, MV

y/R =

_{BVI at}

(d)Standarddeviationofvortexverti alposition

Figure7:Tipvortexpositions atter(observationarea oordinates).

wellasthegrowthofs atterisfoundtobesimilarforallthree asesandindependentofapplyinga tive

ontrolor not.

Twomethods of averaginghavenow been applied: the simple averaging (SA), and the onditional

averaging(CA)method.TheSAissuspe tedtoleadtoin reasinglyerroneousresultsintermsofvortex

properties like ore radius, swirl velo ityand vorti itywhen the vortex position s atter is growing.To

ir umventthese problems, a onditional averagingmust be applied as des ribedin [7℄. TheSA needs

nofurtherexplanationssin eitappliesthearithmeti averagingtothe100datasetsoneveryindividual

ve torof the eld. TheCA method rst identies all individual vortex entre oordinates, then shifts

allindividual vorti eswiththeir entreto theaverage entre position(= alignmentofthe entres)and

nallyaveragesallindividual measurementsforea hve tor.Duetotheshifts,theve torsat theborder

of the observation area are not overed by ea h data set su h that the resulting eld is based on a

non-homogenous number of samples. However, this does not ae t the vortex analysis as long as the

vortexis lose to the image entre, whi h is the ase in virtuallyall measurements.The ow hartof

post-pro essingtheindividualve tormapsisillustratedinFig.8.Mostoptions anbeswit hedonoro

using ontrolparameters,andanautomati pro essingis possibleinmostofthedataavailable.Manual

ontrol however, is ne essaryin tri ky ases, for example, when a blade has passed very lose to the

vortexandade isionmustbemadewhi hofthevorti estosele tforaveraging.

Theee tofaveragingmethodologyontheresultingvelo ityeldisshownnextattheexamplefora

vortexof theMN aseontheadvan ing side.Dueto a tive ontrol thisvortexis generatedbyahigher

blade loadingat thepoint of vortex reation, ompared to theBL ase.In Fig.9(a)and Fig.9(b) the

rstindividual measurementsat avortex ageof

V

=5:5deg and335:5deg,respe tively,are shownfor

omparision with the averagingmethods. In-plane velo ity omponents are shown as ve tors and the

ross- owvelo ityis olor- oded. Theyare noisydue to owturbulen e andmeasurementun ertainty.

ω

y

λ

2

ω

_y

λ

₂

ω

_y

λ

₂

ω

y

λ

2

Read control parameter

Select Dpt, image, averaging method

Average (simple, conditional)

Compute Gauss’ bell function

Identification of vortex center

Remove mean flow components

Compute rotation angles

Rotate into vortex axis

Iteration

Compute Gauss’ bell function in sheared grid

Dialog / automatic

Statistical analysis, plot of scalars and profiles

Stop

Plot of scalars f(x), f(z), f(x,z), f(r)

Store scalars and profiles

Subtract identified vortex from field

New image: yes / no

Data smoothing (Fourier synthesis)

Spurious vector elimination

Image clipping

Identification of sense of rotation

Read Image

Compute flow derivatives

Compute flow derivatives in sheared grid

Convolution with u, v, w, , Q,

Convolution with u, v, w, , Q,

Compute operators , Q,

Compute operators , Q,

Non−dimensionalization of

Ω

coordinates (R) and velocities ( R)

Figure8:Post-pro essing owdiagramfor3C-PIVdata.

in-plane velo ity omponents and the ross- ow velo ity, see Fig. 9( ) and Fig. 9(e). This means the

positions atterissmallenough omparedtothedimensionsofthetipvortexandtheshearlayerbehind

therotorblade.The oreradius,indi atedbythe ir le,isessentiallythesameinbothaveragingmethods,

andthemeasurementnoiseisalsosu essfullysuppressedbybothmethods.Fortheoldvortex,however,

the dieren es be ome visible in all parameters.The axial velo ity in the vortex enter is mu h more

pronoun edandthe oreradiusissigni antlysmallerintheresultoftheCAmethod,Fig.9(f), ompared

totheSAmethod inFig.9(d). Inthis asethepositions atter issigni antlyex eedingthedimensions

ofthe owstru turetobeobservedandthusCAmustbeapplied.

Thisresultisfurtherdemonstratedatthevelo ityprolesinahorizontal utthroughthevortex entre

for the samedata sets. For theyoungvortex in Fig. 10(a) and the old vortex in Fig. 10(b) the result

ofthe SA andtheCA method are ompared withea hother andwith therst 5ofthe100individual

measurements.Duetothesmallspatials attertheyoungvortexallowstheappli ationoftheSAmethod,

but thisis obsoletefortheold vortexwithlarges atter wherethe SAmethod leadstoarti ially large

ore radiiand smaller swirl velo ities than any of the individuals. In ontrast, the CA method retains

boththe oreradiiandtheswirlvelo ity.Thesespatialdistributionsoftheswirlvelo ityareananalogon

to the prin iple shown in Fig.1, and sin e the vortex entre is s attered in bothdire tions this ee t

isvisible in bothvelo ityprolesu(z)andw(x). Thus, atwo-dimensional orre tionhasto beapplied,

whi hisrepresentedbytheCAmethod.

Itmustbere ognizedthatthisspatials atterintwodimensionswillbere e tedtwo-foldintheblade

aerodynami loadingand onsequentlyin thea ousti time histories. First,theverti al vortexposition

s atter will be visible in as atter of BVI-related pressurepeaks (and theasso iated C

n M

2

) and thus

as atter ofBVI intensity, whi h an behandled using standardaveragingpro edures.In ontrast, the

horizontalvortexposition s atterwilltranslateinto azimuthalvariationsofwherethisBVI happens. In

this ase,astandardaveragingpro edurearti iallysmoothes theBVI signatureandagainaderivative

oftheCAmethodmustbeapplied.

5 Blade pressure and se tion loading time histories

DuringtheHARTIItest,bladepressuredatawerere ordedbymeansofabsolutepressuresensorswith

adatarateof2048=rev,triggeredto therotorazimuth.80 ontinuous revolutionsweretakensu hthat

low frequen yos illationsof themodel aredire tly visible in these data. Thevortexwanderaddressed

in the last se tion leadsto atwofold ee t:First,the verti alposition s atter translatesinto as atter

( ) simpleaverage(SA) (d)simpleaverage(SA)

(e) onditionalaverage(CA) (f) onditionalaverage(CA)

a, ,e:Pos.17a,

V

=5:5deg b,d, f:Pos.22,

V

=425:5deg

Ve tors:in-planevelo itiesuandw; olor- oded: ross- owvelo ityv.Meanvaluesaresubtra ted,

observationarea oordinates.The oreradiusisindi atedbythe ir le, every5thve torshown.

Figure 9:Ee tofaveragingmethodonthevelo ityeld, MN,y=R=0:7.

revolutionbyrevolution.Se ond,thehorizontalpositions atterofthevortextranslatesintoanazimuth

(or time)jitterfor bladepressuretimehistories, withoutmagnitudeee t. Allthese ee ts ombine to

produ e both a magnitude s atter and a time jitter of these BVI-events in ea h revolution. A simple

averagingwould leadto arti ialsmoothingof su h BVI-events(as isthe aseforPIV analysis),while

the onditional averagingmethod applied to thetimehistories isableto ompletely eliminatethetime

jitterbefore averagingonlythemagnitudes atter.

The omputationsweremade usingthe for e oeÆ ientnormal tothe hord enterline, C

n M

2

Bla ksolid:CA,dashed:SA;red:5individual;meanvaluesaresubtra ted,observationarea

oordinates.

Figure10:Ee tofaveragingmethodontheswirlvelo ity,MN,y=R=0:7.

thethree operational onditionsBL, MNand MV. Toget aphysi ally orre t averagedblade pressure

time historyofall 80 onse utivelymeasuredrotorrevolutionswith respe t to BVIphenomena (whi h

arein thefrequen yrangeofabout20 200=rev),itis notenoughto simpleaveragetheC

n M

2

values

at ea h sample(forrotorloadingpurposes,whi h are overingthefrequen yrangeof about0 6=rev,

simpleaveragingisbyfarsuÆ ient).Further,amoredetailed viewontherawdataisneededto getthe

orre ttime historyby onditional averaging.For al ulationof thenormalfor e oeÆ ientC

n M

2

the

pressuretime histories at aradius of r=R = 0:87of 11 Kulite sensors on theupperside and 6 on the

lowersideofthereferen ebladewereavailable.The hord-wisedistributionisshowninFig.11.

Corre tionofdefe tsensorsignals

+ C n M 2 omputation +

Bandpassfilterfrom20to250/rev

+

Simpleaverage(SA)of80revolutionsasreferen e

+

DefinitionofBVIeventsasreferen ep ositions

+

ConvolutionofindividualwithSAtimehistory)QC

+

ShiftvaluedefinedatmaximumQC

+

Corre tionofindividualtimehistories

+

Conditionalaverage(CA)of80 orre tedtimehistories

(a)Pressureanalysis ow hart

.32

.86

.66

.44

.24

.18

.06

.12

.03 .09 .15

.55

.80

(b)Airfoilse tion

Figure11:Chordwisebladepressuresensordistribution asusedin HARTII,r=R=0:87

In[3℄aliasingproblemsaredes ribedfordistin tfrequen iesofspe i multiplesofthesamplingrate.

Isolatedspikeswerefoundat128=rev,256=rev,512=rev,and768=revwithabout20dBmagnitudemore

than thesignalshould exhibit. An explanation of this problem ould beveryhighfrequen y signalsin

somedataa quisition ablesthatleadtodisturbedpressuresignals.Toremovethedisturbedfrequen ies

aharmoni analysisofthea ordingpressuresignalismadeforea hfrequen ywhi hhastobe orre ted

to get the sine and osine oeÆ ients. Thereafter, by using a harmoni synthesis, all parts of these

frequen iesare addedtogetherandnally subtra tedfromtheoriginaltimehistory.

Totallindividualtimehistories togetherfor orre tedamplitudeandphasewidthoftheaveraged

timehistorya oupleofpro eduresareneeded(Fig.11(a)).Themainproblemsarethedierentlo ations

ofthe entreofaBVI-event(=itstimes atter)andthusthes atterinlo ationoftheasso iatedminimum

andmaximumpeaks(beginningandendingofaBVI-event)whi his ausedby u tuationsinrotational

speed and varying vortex lo ations due to vortex wander when passing the blade. The typi al BVI

entretheswirlvelo ityisdire tedupwardswhi hprodu esanin reasingC

n M

2

.Attheretreatingside,

theBVIsignatureis theotherwayround sin ethebladeapproa hesthevortexfrom theoppositeside.

A steep de reasing ank is presentwhile passing the vortex entre. The azimuth lo ations where BVI

takespla e are strongly dependent on the operating onditionand an best be visualizedby the high

frequen y ontentofthebladeleadingedgepressurealongradiusandazimuth.Forthe asesinvestigated

here,theyaremainlybetween =10degand =90degattheadvan ingsideandbetween =270deg

and =350degattheretreatingside.

TondtheBVI-eventswhere a orre tionof thetimephaseisneededaband passlteringbetween

20=rev and 250=rev is donefor allindividual C

n M

2

timehistories in order to eliminate thelarge

low-frequen y ontent and thus to leave overonly the interesting frequen y range of BVI-events.Therein,

the signature of one BVI-event time historyis hara terizedby a de reasing ank followed by asteep

in reasing ank and again a de reasing ank at the advan ing side and the other way round at the

retreating side due to the physi sof vortexintera tions as des ribed above.The simpleaveragedtime

historyalready provides the orre t lo ation of BVI-events,but neither the orre tmagnitude nor the

orre tazimuthalextensiontotherightandleftoftheeventitself.Itisusedasreferen efora onvolution

withtheindividualtimehistories.Thevortex entreofaBVIlo ationisdenedusingthesimpleaveraged

data whereC

n M

2

=0. For ea h BVI-eventthere isone onvolutionfun tion (=CF),whi his dened

bytheband-passlteredvaluesof thesimpleaveragedtime historybetweenthea ordingstartingand

ending point ofa BVI-event.For the onvolutionitself, theregion ofinterest of ea h individual C

n M

2

timehistoryismultipliedwiththeCF togetaquality riteria(=QC).Thestartingpointisshiftedfrom

15samplesto+15samples(2:6degofazimuth),whi h oversthemaximumshiftofeventsobserved.

TheresultingQC (Eq.4) is ameasurefor the oin iden e betweenboth theindividual andthe simple

averagedtimehistories.

QC(j)= +15 X j= 15 BVIend X i=BVIstart CF(i)
C n M 2 (i+j) ! (4)

This pro edure,applied to all BVI-events,leads to individual valuesof shift for theadvan ing and

retreating side a ording to the number of BVI-events. In general, the shift values obtained dier by

about 5.5samples, whi h orrespondsto about =1degof rotorazimuth. It was found, that there is

nodependen ybetween thevaluesof shiftofthe advan ing andtheretreating side. For one individual

rotor revolutionthe shiftsof advan ing and retreating side are ompletely dierent and no systemati

behaviouris visiblein all three ight ases.On theother hand theshiftis nearly onstant within ea h

side, thus, the phaseshift orre tion hasto be applied independently on theadvan ing and retreating

side. When all shifts of ea h BVI-event are known, the phase orre tion an be done. The orre tion

is made by the assumption that the referen e lo ation is at an integer sample numberat theposition

where thesteepin reasing ank(advan ing side)or steep de reasing ank (retreatingside)hasavalue

nearC n M 2 =0.Todispla etheC n M 2

valuesin timealinearstret hingor ompression(depending on

positiveornegativeshift) betweentworeferen epointsisused. Sin etherequiredshiftsfoundhavereal

inde esan interpolationis ne essarytoget nally thenew C

n M

2

valuesdependingon anintegertime

index(whi hisneededforaveraging).

All individualtimehistoriesare orre ted(shiftedandinterpolated)that wayandanewmeanvalue

anbe omputed.InFig.12all80C

n M

2

timehistoriesareplottedfortheretreatingsideoftheBL ase

before(Fig.12(a))andafter(Fig.12(b))thetimephase orre tion.After orre tion,thelo ationofthe

steepde reasing ankisnearlyidenti alforalltimehistoriesandthemaximumandminimumpeaksare

atthesamelo ationsaswell.Finally,theaveragetimehistory anbe omputed,whi hisnow alledthe

onditionallyaveragedtimehistory.

For omparisonbetweenthesimpleaveragedand onditionalaveragedtimehistories,thepeak-to-peak

amplitudes and peak-to-peak time dieren es for the sele ted BVI-events were investigated. Changes

ould be found with respe t to the peak-to-peak amplitudes between the onditional average and the

simpleaverage,whi h ledalwaysto in reasesofupto C

n M

2

=+3:610 3

or +8:4%aroundthe

BVI-events.However,thesevaluesarenotsomu hexpressive,sin ethemagnitudeoftheamplitudesarevery

dierent. The peak-to-peak azimuthal distan es between the C

n M

2

extreme valuesof the onditional

averagedC

n M

2

values omparedtothepeak-to-peakazimuthwidthofthesimpleaveragedvaluesshow

de reasesofupto 1:8samples( 0:32deg).Theper entagedieren esarebetween+0:3%upto 7:8%

(seealsoFig.13(a)).

Inany ight ase,the onditional averagehaslargerC

n M

2

amplitudesat theBVI-events,while the

290

295

300

305

0.07

0.08

0.09

0.1

0.11

ψ

/deg

C

n

M

2

(a)before orre tion

290

295

300

305

0.07

0.08

0.09

0.1

0.11

ψ

/deg

C

n

M

2

(b)after orre tion Figure12:80 individual C n M 2

time histories before (a) and after (b) time jitter orre tion (BL, data

band passlteredfrom20-250/rev)

tothesimpleaveragedtimehistories.Althoughthedieren esbetweensimpleand onditionallyaveraged

datamayappearasnotimportant,thephysi sofrotorBVInoisearebasedontimederivativeofC

n M

2

,

whi hsigni antlyexaggeratesthedieren es(Fig.13(b)).

290

295

300

305

0.075

0.08

0.085

0.09

0.095

0.1

0.105

0.11

Ψ

/deg

C

n

M

2

C

n

M

2

(SA)

C

n

M

2

(CA)

(a)Normalfor e oeÆ ientCnM 2

290

295

300

305

−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

Ψ

/deg

dC

n

M

2

/d

Ψ

/ rad

dC

n

M

2

/d

Ψ

(SA)

dC

n

M

2

/d

Ψ

(CA)

(b)TimederivativeofCnM 2

Figure13:Comparisonofnormalfor e oeÆ ientC

n M

2

anditstimederivativeforsimpleand onditional

average(BL,databandpasslteredfrom 20-250/rev),r=R=0:87

6 Mi rophone time histories

Sin e blade pressuretime histories (Se t. 5) are the sour e ofnoise generation allee ts of timejitter

andmagnitudes atterarealsofoundin mi rophonepressuretimehistorydatainthesamemanner.For

investigationsoftheee t of onditionalaveragingonmi rophonesignalstheunltered rawdata ofthe

baseline ase(BL)of mi rophone11attheadvan ing sideandmi rophone4at theretreatingsideare

used. For ea h mi rophonelo ationdata were storedfor100 onse utiverevolutionswith anin rement

11.Theselo ationswere hosenbe ausetheyare very losetothemaximumpeaksofthenoise ontour

(Fig.14),one attheadvan ing andoneattheretreatingside.

(a)Simpleaverage (b)Spe traaverage

Figure14:Noisedire tivity ontourbaseline ase(BVI-SPL)

Thespe trumofthesimpleaveragedmi rophonetimehistoriesthenleadstosigni antlylowernoise

levelsthantheindividualspe tra,sin ethepeaksofpressurearesmoothedunrealisti allylarge.To over

theproblems asso iatedwith thistime jitter,in thepasttheaverageof allindividual spe trawasused

asbeingrepresentativefortheaveragednoisespe trum.Ea hofthemi rophonepressuretimehistories

show fourtypi aleventswithinone rotorrevolution.These eventsare ausedby theBVI-eventsof the

rotorbladesandsin ethemodelrotorisfour-bladedtherearefourmain eventsatea hmi rophoneper

revolution.AsmentionedinSe t.5thesimpleaveragedtimehistoryalreadyprovidesthe orre tlo ation

ofBVI-events,butnotthe orre tmagnitudenorthe orre tazimuthalwidthoftheeventitself.Again,a

onvolutionismadeandthebest onvolutionfun tiontobe omparedtoasingletimehistoryisassumed

tobethesimpleaveragedtimehistoryofallthe100revolutions.Itisalsousedtosetthereferen epoints

respe tivelythereferen eazimuthlo ations.Forthemi rophonedatanolteringisne essary,sin ethere

areonlypressureos illationsaroundthestati pressure.Herethereferen epointswere hosentobeon

thesteepin reasing ankatthezero rossingbetweentheminimumandthefollowingpositivemaximum

valueofaBVI-event.

Shiftto overmainBVIevents

+

Simpleaverage(SA)of100revolutionsasreferen e

+

DefinitionofBVIeventsasreferen eazimuthlo ations

+

ConvolutionofindividualwithSAtimehistories)quality riterionQC

+

ShiftvaluedefinedatminimumQC

+

Corre tionofindividualtimehistories

+

Conditionalaverage(CA)of100 orre tedtimehistories

+

Cal ulationofp owersp e tra

+

Cal ulationofBVISPLandBWISPL

history at the main BVI-events again a onvolution is made in a range of 32 samples around the

a ording referen e point (RP) to havebest oin iden e. By means of the least error squares method

aquality riteriaQC(j)is omputed where CF is the onvolutionfun tion extra ted from the simple

averagedtime history. The onvolutionismade in arangeof16samples, whi h oversthe maximum

shiftof eventsobserved(Eq. 5). Atthe shiftvaluewhere the individual timehistorybest ts with the

CFthe QC at this sample is minimal. To ndthe minimumQC, abest t polynomialof 2 nd

order is

omputedbymeansofregressionanalysisusingvevaluesaroundtheminimum.

QC(j)= +16 X j= 16 RP+32 X i=RP 32 (CF(i) p(i+j)) 2 ! (5)

Sin e four main eventsare presentwithin one rotor revolution,this pro edure has to be applied to

allofthem.Finallywegetfour individualshiftvaluesforea hmi rophonetimehistory.All BVI-events

havenearlythesameshiftvalueswithinone revolution.As inbladepressuredata theshiftvaluesdier

byabout5:5samplesinmaximum,whi h orrespondstoabout =1degofrotorazimuth.Comparing

this magnitudeto theshift resultsfoundin the C

n M

2

analysis in Se t. 5asimilar behaviour isfound.

The u tuationsinrotationalspeedandvaryingvortexlo ations,whi hleadtothese shifts,arepresent

at thebladesas lo ationofnoisesour eas wellas atthemi rophonepositions. Finallytheadjustment

of the individual time histories is done a ording to the pro edure (by linearstret hing/ ompression)

mentionedinSe t.5andanewaverage anbe omputed-now alledthe onditionalaverage.InFig.15

thepost-pro essing ow hartformi rophonedataisshownandFig.16showsthe omparisonoftheraw

dataandthe orre tedmi rophonepressuretimehistories.

294

296

298

300

302

304

−40

−30

−20

−10

0

10

20

30

40

50

ψ

/ deg

p / Pa

(a)before orre tion

294

296

298

300

302

304

−40

−30

−20

−10

0

10

20

30

40

50

ψ

/ deg

p / Pa

(b)after orre tion

Figure16:100 individualpressure time histories before (a) and after (b)time jitter orre tion

(Mi ro-phone4)

The omparison of simple and onditional averages leads to in reases in peak-to-peak amplitudes

between +4:4% and +6:5% for both mi rophones while the peak-to-peak azimuth dieren es always

de reasebyabout 1%to 10%.Thisleadstoremarkable hanges ofthegradientsdp=d atthemain

BVI-events.Thedieren eofthegradientsofmi rophone4(+15:4%to+34:2%)isabouttwi easlarge

asthedieren esfoundinthemi rophone11results(+8%to +13:4%).

In heli optera ousti s thesoundpressurelevelor powerspe trumof mi rophonedatais important

for noise estimations. There are twomain frequen y bands of interest. With respe t to the BVI-noise

therelevantfrequen yrangeisbetweenthe6 th

and40 th

bladepassagefrequen y(bpf)whi h is24=rev

to 160=rev forafour-bladedrotor,fortheBWI-noise(Blade WakeIntera tion)therangebetween40 th

and100 th

bpf(160=revto400=rev forafour-bladedrotor).Inthesetwofrequen yrangesthea ording

sound pressurelevels(SPL in de ibel) an be omputed as logarithm of the square root of the sumof

pressureamplitudes,dividedbyareferen epressurep

ref

BVISPL=20
log 0  u u t 160 X i=24
p(i)
1 p ref 1 A (p ref =2
10 5 Pa) (6)

Atrstthepowerspe tra(SPL)are al ulatedbymeansofaFFTforboththesimpleand

ondition-allyaveragedtimehistories(Fig.17(a)).Additionallythespe traaverageisplotted,whi histheaverage

oftheindividualspe trafromea hofthe100timehistories.The onditionalaveragespe trum, ompared

tothesimpleaveragespe trum,showshigheramplitudes inthelowerfrequen yrangesasexpe tedand

thusis losertotheaveragespe trum.Tohaveabetterrelationbetweenthethreespe traonlythepeaks

atmultiplesofthebladepassagefrequen iesaresele tedandplotted intheBVI-SPLfrequen yrangeas

theupperenvelopeinFig.17(a). It learly an beseenthat the onditionalaverageisvery loseto the

spe traaverageandthus more apabletogeta urateBVI-SPL al ulations.

Finally theBVI-SPL results an be ompared(Fig. 17(b)). Thevaluess atter byabout2to 2:5dB

forbothmi rophonedata. Whilefor mi rophone4theBVI-SPLof thesimpleaverageddatais 0:38dB

lowerthan thespe traaverageBVI-SPL (111:66dB),the BVI-SPLof the newly omputed onditional

average is only 0:1dB lower.The same tenden y ould be found in the mi rophone 11 results , where

thedieren eto thespe traaverageBVI-SPL (113:56dB)nowisredu edfrom 0:64dB (SA)to 0:18dB

(CA). Even the blade wake intera tion (BWI) noise spe trum is mu h better omputed basedon the

onditionalaveragedpressuretimehistories, omparedtosimpleaveraging.

40

60

80

100

120

140

160

65

70

75

80

85

90

95

100

105

n/rev

SPL [dB]

Spectra average

Spectrum SA t.h.

Spectrum CA t.h.

(a)Upperenvelopeofthepowerspe traofmi rophone4,

onlybladeharmoni sinBVI-SPLrange

0

20

40

60

80

100

110.5

111

111.5

112

112.5

Revolution

BVISPL [dB]

Individual t.h.

Simple average t.h.

Cond. average t.h.

Spectra average

(b)BVI-SPLofmi rophone4

Figure17:Resultsof onditionalaveragingwrtsoundpressurelevel(Mi rophone4)

7 Con lusions

The physi s of time jitter and its ee ts on simple averaged time history data are demonstrated and

lariedin thispaper.Themethod of onditionalaveragingprovidesagoodmeansto eliminatespatial

s atter ee ts requiredfor the analysis of ow eld ve tor maps, and also to eliminate thetime jitter

of BVI events in the individual time histories. This is espe ially valid for highly sensitive data like

mi rophonepressuretime histories. Consequently, onditionally averagingis intended tobemandatory

forthegenerationofreliableaveragedtimehistoriesofblade(andmi rophone)pressureor owelds(in

ordertoretainthehighfrequen yee tslikeBVIor smallstru turesliketipvorti esin theirindividual

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