Measurement and Scaling of Trailing-Edge Noise * *rather an extensive look at the scaling of the related source quantities Michaela Herr

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Measurement and Scaling of Trailing-Edge Noise * *rather an extensive look at the scaling of the related source quantities Michaela Herr Institute of Aerodynamics and Flow Technology DLR Braunschweig 13 th CEAS-ASC Workshop and 4 th Workshop of X 3 -Noise, Resolving Uncertainties in Airframe Noise Testing and CAA Validation, Bucharest, Romania, 1- October 9 M. Herr > 1.1..9

Background Primary goals Set-up of an experimental database which is suitable for parametric trailing-edge (TE) noise source studies and for CAA validation Improve DLR s TE noise measurement and prediction methods With reference to the upcoming Workshop on Benchmark Problems for Airframe Noise Computations-I to be held on June 1-11, 1 Approach Definition of a simple generic test setup in the Acoustic Wind-Tunnel Braunschweig (AWB) with a reduced set of parameters, including realistic (HLD) Reynolds numbers Comparison with theoretical approaches and with other available test data to provide Validation of the chosen measurement data corrections Estimates of systematic uncertainty contributions CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9

Generic Test Setup - Acoustic Wind-Tunnel Braunschweig (AWB) Nozzle exit:.8 m x 1. m 5 deg =.8. m u = 4 6 m/s Re =.1 Mio 7.9 Mio = deg = deg LE tripping u Exchangeable TE sections Plate model 1mm.15 mm CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 3

Trailing-Edge Noise Data Assessment Measurement of related scaling parameters in the source region Measurement of the farfield TE noise; estimation of absolute levels MVb x3 Brooks & Hodgson (1981): S( ) S( ) ² r²(1 M ) V TBL mean velocity profiles and integral scales Unsteady surface pressure point and cross spectra Farfield TE noise spectra (re. unit distance and span) CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 4

CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 5 Trailing-Edge Noise Data Assessment TBL thickness wall friction velocity u w /, TBL edge velocity u e Chase (1987): Estimation of the surface pressure spectrum from TBL data 3 k 1 k k ² 1 1 k b u Vk k / ² ² ² ) ( ² ) ( ²... 1... / ² ² ² ² / ² ² ) ( ), ( 1 3 5 4 5 4 5/ 3 c k k k b b k b k k b b b c k k b k c k b b k u P k Goody (4), based on Howe (): 7.57 3.7.75 / 1.1.5 / / 3 ) / )( ( e t e e w e u R u u u S ) / ) /( / ( u u R e t

Part I Measured TBL Mean Velocity Profiles Hot-wire (CTA) measurement results u e /u =.98 ±. (4:1) 1 u/u e u = 4, 5, 6 m/s =.8m =1.m =1.6m =.m 1 3 4 x,mm CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 6

Part I Measured TBL Mean Velocity Profiles Scaling based on inner scale, /u u x u f ( x ); u x u 1 u + 4 3 u = 4, 5, 6 m/s =.8m =1.m =1.6m =.m u/u e u + = 1/.41 ln x + +5 u = 4, 5, 6 m/s =.8m =1.m =1.6m =.m 1 3 4 x,mm 1 u + + = x 1 1 1 1 1 3 1 4 x + CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 7

Part I Measured TBL Mean Velocity Profiles Scaling based on outer scale, u e u F( x); * * x x u 1 1 u = 4, 5, 6 m/s =.8m =1.m =1.6m =.m u/u e u/u e u = 4, 5, 6 m/s =.8m =1.m =1.6m =.m 1 3 4 x,mm u/u e =.84 ln(x / 99 )+.8 1-3 1-1 -1 1 x / 99 CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 8

Part I Derived Parameters Reconstruction of the velocity profiles, Coles (1956) Law of the Wake 1 x u 1 ln( ).5 1 sin e u x B 1 ln( ) ; B u u / 1 99 1,,, H 1 u w u/u e u = 4 m/s 5 m/s 6 m/s 1 3 4 x,mm These are used in the following for the scaling of unsteady surface pressure and TE noise data. CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 9

Part II Unsteady Surface Pressure Data Point PSD close to the TE Streamwise and spanwise coherence decay Streamwise and spanwise coherence lengths Convection velocities TBL mean velocity profiles and integral scales Unsteady surface pressure point and cross spectra Farfield TE noise spectra (re. unit distance and span) CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 1

Part II Point PSDs close to the TE 1 log (S (f)/p ref )=L p(f=1hz),db 9 85 8 75 7 65 6 u = 4 m/s 5 m/s 6 m/s 1 1 1 f, khz =.8 m =1. m =1.6 m =. m u TE CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 11

Part II Point PSDs close to the TE Scaling based on outer scales: Pressure scale: q e = ½ u e Time scale: 1 /u e or 99 /u e 1 log (S (f)/p ref )=L p(f=1hz),db 9 85 8 75 7 65 6 u = 4 m/s 5 m/s 6 m/s 1 1 1 f, khz =.8 m =1. m =1.6 m =. m 1 log [ S ()u e /q e 1 ], db -35-4 -45-5 -55-6 -65 u = 4 m/s 5 m/s 6 m/s 1-1 1 1 1 1 /u e =.8 m =1. m =1.6 m =. m 1 CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9

Part II Point PSDs close to the TE Scaling based on mixed scales Pressure scale: w = u Time scale: 1 /u, 99 /u, 1 /u e, 99 /u e Scaling based on inner scales Pressure scale: w Time scale: /u 1 log [ S ()u / w 99 ], db -5-1 -15 - -5-3 u = 4 m/s 5 m/s 6 m/s -.8-1 -35 1 1 1 1 3 99 /u.3 =.8 m =1. m =1.6 m =. m 1 log [ S ()u /w ], db 3 5 15 1 5 u = 4 m/s 5 m/s 6 m/s 1-1 -1 1 /u =.8 m =1. m =1.6 m =. m /u =.3 13 CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9

Part II Current Prediction Models for point PSDs Chase (1987) model: 1 log [ S ()u e / w 99 ], db 1 5-5 -1-15 - =.8 m =1. m =1.6 m l Chase (1987) c =. m u = 4 m/s 5 m/s 6 m/s 1 1 1 1 99 /u e CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 14

Part II Current Prediction Models for point PSDs Chase (1987) model: 1 log [ S ()u e / w 99 ], db 1 5-5 -1-15 - Chase (1987) coefficients changed acc. to Schewe (1993) u = 4 m/s 5 m/s 6 m/s 1 1 1 1 99 /u e =.8 m =1. m =1.6 m =. m Empirical factors need a more detailed experimental assessment CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 15

Part II Current Prediction Models for point PSDs Goody (4) model 1 log [ S ()u e / w 99 ], db 1 5-5 -1-15 - Goody (4) u = 4 m/s 5 m/s 6 m/s 99 /u e R T =51 =.8 m =1. m =1.6 m =. m R T =13 1 1 1 1 CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 16

Part II Current Prediction Models for point PSDs Goody (4) model 1 log [ S ()u e / w 99 ], db 1 5-5 -1-15 - =.8 m =1. m Goody (4) =1.6 m =. m R T =13 u = 4 m/s 5 m/s 6 m/s R T =51 1 1 1 1 99 /u e High frequency data corrections have to be taken with care! Existing deviations are due to application of high-frequency data corrections which seem to overvalue actual levels CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 17

Part II Current Prediction Models for point PSDs Goody (4) model 1 log [ S ()u e / w 99 ], db 1 5-5 -1-15 - =.8 m =1. m Goody (4) =1.6 m =. m R T =13 combined approach R T = 13 u = 4 m/s 5 m/s 6 m/s R T R=51 T =51 1 1 1 1 99 /u e High frequency data corrections have to be taken with care! Existing deviations are due to application of high-frequency data corrections which seem to overvalue actual levels A combination of both models might apply. CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 18

ij 1.8.6.4. Part II Coherence Decay and Coherence Lengths Corcos (1963) similarity approach: Streamwise ij (, ) exp Spanwise,3 /V(, ) Currently restricted to -m-plate only! ( x3, ) exp u = 6 m/s,3 =,3 / 99 =,3 mm.65,.75 17,16 mm.56,.5 7mm.3 4mm.13 3mm.1 =.16 x3 =.714 5 1 15 ij x3 S u ( 3, ) ij, ij Si ( ) S j ( ) ij (, ) / V (, ) kv k / V ( 1, ) v x3 / V (, ) / V (, ) x TE x3 CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 19

ij 1.8.6.4 Part II Coherence Decay and Coherence Lengths Corcos (1963) similarity approach: Streamwise ij (, ) exp Spanwise,3 /V(, ) Currently restricted to -m-plate only! ( ij u = 5 m/s x3, ) exp,3 =,3 / 99 =,3 mm.64,.73 17,16 mm.54,.51 7mm. 4mm.13 3mm.1. =.17 x3 =.714 5 1 15 x3 S u ( 3, ) ij, ij Si ( ) S j ( ) ij (, ) / V (, ) kv k / V ( 1, ) v x3 / V (, ) / V (, ) x TE x3 CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9

ij 1.8.6.4 Part II Coherence Decay and Coherence Lengths Corcos (1963) similarity approach: Streamwise ij (, ) exp Spanwise,3 /V(, ) Currently restricted to -m-plate only! ( ij u = 4 m/s x3, ) exp,3 =,3 / 99 =,3 mm.6,.71 17,16 mm.53,.5 7mm. 4mm.1 3mm.9. x3 =.714 =.19 5 1 15 x3 S u ( 3, ) ij, ij Si ( ) S j ( ) ij (, ) / V (, ) kv k / V ( 1, ) v x3 / V (, ) / V (, ) x TE x3 CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 1

Part II Coherence Decay and Coherence Lengths Assuming a constant V.65 u Streamwise 1/ k V / Spanwise Currently restricted to -m-plate only! x3 1/ x3 k v v V / x3.5 1.5 1 f (peak) u = 4 m/s 5 m/s 6 m/s,3 / 99.5 x3 f, khz 5 1 15 CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9

Part III Farfield TE Noise Data Absolute 1/3-octave band SPL re 1m span and 1m observer distance ¼``- Microphone MVb x3 Brooks & Hodgson (1981): S( ) S( ) ² r²(1 M ) V TBL mean velocity profiles and integral scales Unsteady surface pressure point and cross spectra Farfield TE noise spectra (re. unit distance and span) CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 3

Currently restricted to -m-plate only! Part III Farfield TE Noise Data Prediction from the surface pressure data, assuming constant V.65 u MVb x 3 Brooks & Hodgson (1981): S( ) S( ) ² r²(1 M ) V L p(1/3),db 1 9 8 7 6 Surface Pressure Kulite Data FF TE Noise Prediction FF TE Noise Mirror Data Estimation of absolute levels (re 1m span and 1m observer distance) requires extensive data corrections, as shown in the following 5 4 3 u = 4 m/s 5 m/s 6 m/s f m,khz 4 6 8 1 CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 4

Part III Elliptic Mirror Setup Elliptic mirror specifics: Focal distance: 1.15 m Reflector diameter D = 1.4 m Resolution width Aperture: 63 deg ¼``- Microphone Data correction for: Background noise (S/N 3 db) Sound wave convection Frequency response function (gain, resolution) Shear layer refraction/scattering y x CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 5

Part III Elliptic Mirror Setup Correction for frequency response (Schlinker, 1977) L p (1/3) correction, db 1-1 - -3-4 f m,khz gain correction resolution correction totaorrection 5 1 15 p H M b/ G b/ J1 ( ) ( ) p D f x 3 c R D b H ( ) dx 3 CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 6

Part III Effect of Data Corrections 1.6-m plate model with blunt TE (h = 1 mm) Focusing measurement techniques must be used because TE noise is buried by the tunnel self-noise! 8 7 empty test section u =6m/s 8 7 u =6m/s b=1.m r=1.15m (origin at TE, midspan) L p(1/3),db 6 5 L p(1/3),db 6 5 mirror focus at TE 4 3 uncorrected uncorrected L L p (1/3) M p (1/3) M L p (1/3) M, shear-layer corrected p (1/3) TE (b = 1 m) f m,khz 5 1 15 4 3 farfield mic. plate airfoil farfield mic. BGN mirror mic. plate airfoil TE f m,khz 5 1 15 7 CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9

8 7 Part III Effect of Data Corrections 1.6-m plate model with blunt TE (h = 1 mm) Focusing measurement techniques must be used because TE noise is buried by the tunnel self-noise! Validation of the procedure by alternative measurement techniques: COP empty test section u =6m/s 8 7 7 6 u =6m/s b=1.m b=1.m r=1.15mu (origin at TE, =6m/s midspan) L p(1/3),db 6 5 L p(1/3),db 6 5 5 4 u =4m/s mirror focus at TE 4 3 uncorrected uncorrected L L p (1/3) M p (1/3) M L p (1/3) M, shear-layer corrected p (1/3) TE (b = 1 m) f m,khz 5 1 15 4 3 3 directional farfield mic. plate airfoil farfield mic. microphone COP BGN mirror mic. plate airfoil TE f m,khz 5 1 15 8 CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9

Part III Comparisons with Published TE Noise Data NACA1 data by Brooks et al. (1986): COP semi-empirical prediction method (BPM, NAFNoise) 18 deg L p(1/3)norm,db 13 1 11 L p(1/3)norm =L p(1/3) -1log(M 5 b/ r ) u = 4 m/s 5 m/s 6 m/s BPM, sharp TE.4-m D- NACA1 with varying TE thickness AWB (h =.15 mm) 1 f m /u.1 1 CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 9

Part III Comparisons with Published TE Noise Data NACA1 data by Herrig et al.(8): CPV 18 deg L p(1/3)norm,db 13 1 11 L p(1/3)norm =L p(1/3) -1log(M 5 b/ r ) u = 4 m/s 5 m/s Herrig et al. 6 m/s (h BPM, = 1 mm) sharp TE.4-m D- NACA1 with varying TE thickness 1 f m /u AWB (h =.15 mm) AWB (h = 1 mm).1 1 CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 3

Conclusions Presentation of a parametric plate model TE noise data set which (with the limitation to nonzero angles-of-attack and = = /) could help to validate current CAA approaches, maximum Re of 7.9 Mio Excellent agreement of the plate model data set with theoretical models Fair agreement with published data sets as derived at comparable but not identical test conditions (e.g. zero-pressure gradient surface pressure data covered by the Goody model), estimation of absolute TE noise levels was cross-checked by comparisons of additional NACA1 measurement results with available NACA1 data Literature review: Considerable uncertainty with regard to the measurement of farfield TE noise and its related source quantities prevails even for very simple generic test configurations Need of benchmarks for TE noise measurement (with major focus on the necessary frequency response corrections and facility-related effects) to provide the necessary data quality for CAA validation CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 31

Outlook Conduct RANS/CAA based predictions (PIANO-RPM) for the presented plate model experiment respective RANS/CAA based predictions for a NACA1, (published in Ewert et al., AIAA 9-369) were promising CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 3

Outlook Conduct RANS/CAA based predictions (PIANO-RPM) for the presented plate model experiment respective RANS/CAA based predictions for a NACA1, (published in Ewert et al., AIAA 9-369) were promising Detailed comparison of directional microphone data with corresponding microphone array data NACA1 data available, but not yet analysed Numerical simulation of the mirror system transfer function (including shear-layer effects) Still open questions: determination of the various empiricaoefficients in existing surface pressure models, estimation of V ( x 1, ) based on mean TBL velocity profiles See you in June 1-11, 1 at the Workshop on Benchmark Problems for Airframe Noise Computations-I? CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 33

Thank you for your attention! michaela.herr@dlr.de CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 34

Appendix CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 35

Part II Convection velocity Currently restricted to -m-plate only! k / V ( 1, ) ij (, ) / V (, ) kv v x 1. u = 4 m/s ( 99 /u ) peak 5 m/s 1 6 m/s x3 V(, )/u.8.6 = / 99 = mm.6-.7 7mm. 3mm.1 u.4 99 /u Eq. 5. 4 6 8 TE CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 36

Part III Elliptic Mirror Setup SPL 1/3 Correction, db Shear-layer correction from comparative measurements at different x- positions, re Position 1 5 4 3 1 Shear-layer effect at: Position Position 3 Position 4 f m,khz 5 1 15 z y x x 1 3 4 CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9 37

Part III Elliptic Mirror Setup Measured point source frequency response function (Dobrzynski et al.,1998) G, db 45 4 35 3 u = m/s 4 m/s 5 m/s 6 m/s w, H(η), 1-3 db m 1 8 6 4-5 3dB w f m =.5kHz u = f m =5kHz m/s f m =1kHz 4 m/s source) moving (rel. 5 m/s 6 m/s x 1 5 theoretical prediction f m,khz 1 3 4-1 L () p(1=3) R d J1 ( ) Eq. H ( ).17 theoretical prediction - 1 4 36 4 f m η,khz relative 38 CEAS-ASC/ X 3 -Noise Workshop 9, Bucharest, (Romania) > M. Herr > 1.1.9

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