[American Institute of Aeronautics and Astronautics 12th AIAA/CEAS Aeroacoustics Conference (27th AIAA Aeroacoustics Conference) - Cambridge, Massachusetts ()] 12th AIAA/CEAS Aeroacoustics

American Institute of Aeronautics and Astronautics

1

Incident Turbulence Interaction Noise from an Axial Fan

D. Fedala*, S. Kouidri†, and R. Rey ‡ Laboratoire d’Energétique et de Mécanique des Fluides Interne, Ecole Nationale Supérieure d’Arts et Métiers,

151, bd. de l’Hôpital, Paris, France, 75013

T. Carolus§, and M. Schneider** Institut für Fluid- und Thermodynamik, Universität Siegen, 57068 Siegen, Germany

The development of analytical methods allowing the prediction of the noise radiated by an airfoil in a turbulent flow is an active research topic. Its extension to the blades row is still in progress. However, their validation by well measurements is missing. In this paper, a prediction method of broadband noise, due to the incident turbulence and radiated in free field by a subsonic low-pressure axial fan, is reviewed then validated. This approach is an extension of the model initially established for an isolated airfoil placed in a turbulent flow to rotating blades. The formulation providing the noise produced by an airfoil in rectilinear motion is used for the calculation of the instantaneous acoustic spectrum generated by a blade segment considering the rotation effects. The acoustic calculation is based on the Amiet formulation allowing the determination of the far field acoustic power spectral density using a statistical description of the upstream turbulence. A low-pressure axial fan without guide vanes is exposed to a range of turbulent flow fields generated by five different inflow arrangements. Turbulence inflow properties and far field sound were both measured allowing comparison with the predicted results. The mean flow velocity distribution in the plane of the rotor and the turbulent intensities are measured using hot wire anemometry. The local spatial correlation lengths in circumferential direction are derived via a cross-correlation method employing two hot wire probes at various angular distances. The results thus obtained were used to calculate the power spectral density of the inflow velocity fluctuations, which are the input data for the aeroacoustic model. As expected, the inflow arrangements have a significant influence on both the statistical parameters of the flow field in the plane of the fan rotor and the broadband noise radiated by the fan. The directivity feature of the broadband turbulence interaction noise shows that the main radiation lobe is located along the fan axis. The predicted acoustic power spectra show a good agreement with the experimental results and especially for inflow arrangements generating low turbulence intensity.

Nomenclature b = airfoil semichord C0 = sound speed Ca = local axial velocity Cr = relative velocity d = airfoil semispan k = 0/ Cω , acoustic wavenumber ke = wavenumber range of the energy containing eddies

* PHD student, LEMFI-ENSAM, [email protected] † Associate Professor, LEMFI-ENSAM, [email protected] ‡ Professor, LEMFI-ENSAM, [email protected] § Professor, IFT-uni-Siegen, [email protected] ** Doctor, IFT-uni-Siegen, [email protected]

12th AIAA/CEAS Aeroacoustics Conference (27th AIAA Aeroacoustics Conference)8 - 10 May 2006, Cambridge, Massachusetts

AIAA 2006-2477

Copyright © 2006 by author(s). Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


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Kx = 0/ Cω , nominal streamwise wavenumber kx, ky = chordwise and spanwise component turbulence wavenumber L = integrated airfoil response function ly(ω) = spanwise correlation length scale M = free stream Mach number Mn = projection of the rotational Mach number in the observer direction Mt = tangential Mach number R = radius location of a blade segment Rww (kx, y) = spanwise cross-spectrum of velocity component w Spp = acoustic far-field power spectral density Sww = power spectral density of w Suu = power spectral density of u u, w = axial, and transverse turbulent component velocity U = mean velocity in axial direction V& = volume flow rate xr

= observer position x, y, z = axial, spanwise and vertical Cartesian coordinate (X, Y, Z) = reference frame fixed to the fan α = airfoil angle of attack β 2 = 1- M2

Φww (kx ,ky ) = two wavenumber spectrum of w

Γ = gamma function Λa, Λt = longitudinal and circumferential length scale of turbulence ϕ = directivity angle in (Y, Z) plane ρ0 = freestream density

σ = )( 2222 zyx ++ β ω = circular frequency ω0 = Doppler shifted frequency heard by observer Ω = blade rotational frequency Primes = denote transformed coordinate system

I. Introduction n practice, propellers and fans operate in a non-uniform flow. In static tests, it has been deduced that the dominant noise component arises from the interaction between ingested turbulence and the engine fan, Hanson1. The inflow

turbulence can be atmospheric, from inlet or casing boundary layer or upstream wakes. Several authors worked on the understanding of the physical mechanisms that are responsible for the noise due to unsteady distortion. The time and space variation of the flow incident angle leads to loading fluctuations on the blade. According to the aeroacoustic analogy, the random fluctuations of the elementary surface pressure field around an airfoil correspond to dipolar sources. These sources result from the impact of the vortices on rigid surfaces and are concentrated on the leading edge.

The noise generation by rotating blade is similar to that of an isolated airfoil in a turbulent flow if the noise frequency remains quite high compared to the rotational frequency. The present approach is based on the linearized aerodynamic theory of an isolated airfoil. The far field noise radiated by an airfoil is related to the turbulent velocity field by transfer functions independent of the aerodynamic flow characteristics. They are determined for an isolated airfoil and can be applied to rotating blades. In this case, the aerodynamic interaction of the blades is neglected. The total intensity of the radiated noise is the sum of the contributions of each blade. Extension of the theory developed to predict the broadband noise radiated by an isolated airfoil was carried out. Amiet2 used this approach to calculate the sound field from a helicopter rotating blade source, by performing the rectilinear motion analysis.

The blade segment is considered as flat plate. The spectrum average along the azimuth is carried out. It is a weighted average to take into account the different time laps spent by the rotor in the various azimuth positions.

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II. Incident turbulence interaction noise from an airfoil An airfoil with low thickness, chord 2b and span 2d is placed in a turbulent incident flow. The surface pressure

fluctuating field is expressed according to the incident turbulent velocity field. The Kirchhoff theory is then used to calculate the far field noise radiated from the surface pressure fluctuations. Thus, the far field acoustic power spectral density ppS , expressed according to the position of the observer x

r and the frequency ω, is related to the turbulent velocity field by spectral turbulent models. Figure 1. presents the geometrical characteristics of the blade as well as the calculation reference frame and the observer position.

The formulation suggested by Amiet3 is retained in this paper. The basic formulation is:

∫∞

∞−⎥⎦

⎤⎢⎣

⎡+

⎥⎦

⎤⎢⎣

⎡+

Φ⎟⎟⎠

⎞⎜⎜⎝

⎛= yyx

y

y

yxwwpp dkkKxLyk

kd

ykkd

kKdUzbk

xS2

2

22

20 ),,(

)(sin),(),(

σπ

σπ

σρ

ωv (1)

Assuming that the acoustic wavelength is sufficiently small in comparison with the semispan d, i.e., dMKx >>1, a simplified expression of Eq. (1) is obtained:

)()()0,,(),( 22

20 ωω

σρω wwyxpp SlKxLdUbzkxS ⎟

⎠⎞

⎜⎝⎛=

r (2)

The transfer function L (x, ω /U, ky), according to Paterson et al.3, is a significant term as for the spectral response to the disturbances. This theory holds for small camber, slight incidence angle, and low velocity fluctuations.

III. Noise radiated by rotating blades Considering a rotating blade segment located at radius R

and rotation angle ϕ, Fig. 2, the observer is supposed to be in the (X, Y) plan in the position O (θ, r).

A local reference frame (x’, y’, z’) is defined where y’ is in the spanwise direction and x’ is in the chordwise direction. We note re the distance from observer to the source. The blade makes an angle α with (Y, Z) plane, the relative flow is assumed parallel to the plate.

In a rotating machine, the streamline flow around a blade is not the same one as if the blade is insulated. There is interaction between the rotating blades, if the convection time of a turbulent eddy is larger than the time of blade passage, it will be cut by more than one blade. In this work, it is supposed that the streamline flow around the segment of blade is not influenced by the presence of the close blades. Therefore, the interaction between the rotating blades is not taken into account. The far field acoustic pressure power spectral density given in the case of an isolated airfoil in the previous section will be applied directly to determine the spectrum produced by a blade moving rectilinearly according to relative velocity component rC at a particular value of the azimuth angleϕ , so:

22

20 )0,,()()(),,(

rwwyrpp C

xLSldCzbkxS ωωωσ

ρωϕ ′⎟⎠⎞

⎜⎝⎛

′′

=′ ′′rv (3)

Figure 1. Schematic for the prediction of the

broadband noise


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The frequency in the reference frame fixed at the rotor blade, frequency of the source emission, is noted ω whereas ω0 is the observed frequency. The Doppler factor relates the two frequencies:

nt MM −

=+

=1

1sinsin1

10

θϕωω (4)

The results for the noise generated by an airfoil in rectilinear motion are expressed according to the absolute coordinates. Similar coordinates are used for the rotating blade, Fig. 2. As the blade segment is in circular motion, the instantaneous spectrum is then averaged on the azimuth; it is a weighted average to take into account the different time laps spent by the rotor in the various azimuth positions:

∫ ′=′π

ϕωωωϕ

πω

2

0 00 ),,(

21),( dxSxS pppp

rr (5)

The final expression for the noise produced in far field by B blade segments, of semichord b and semispan d, rotating at radius R is:

ϕωωωωω

σωρ

πω

π

dC

xLC

SlCz

CbdB

xSrr

wwyrpp ∫ ′⎟⎠

⎞⎜⎝

⎛′

′⎟⎟⎠

⎞⎜⎜⎝

⎛=′ ′′

2

0

2

0

2

2

2

0

00 )0,,()()(

2),(

rv (6)

The resulting azimuthal integral is approximated by a summation. An integral is carried out by a summation from hub to tip of 9 blade segments. The measured incident turbulence field is fed into the above equation. The model is established for an open rotor however, measurements of the acoustic pressure spectrum are affected by the presence of the duct. Thus, comparing the acoustic sound power is more significant. The sound power is calculated by performing an integral of the acoustic power spectral density over a sphere.

Figure 2. Velocity triangle and rotor blade segment of the investigated axial fan


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IV. Experimental setup The investigated fan, Fig.3, is a typical low-pressure

axial fan4. The impeller of the fan has a diameter of 299 mm, a hub/tip ratio of 0.45 and six cambered blades (NACA 4509 profile) but no guide vanes (Fig. 4, duct housing is not shown). The rotor speed for all tests was 3000 rpm (tip speed Mach number = 0.14). The Reynolds number, defined with the local values of chord length and mean flow velocity in the rotating system varies from 118,000 at the hub to 178,000 at the blade’s tip. The operating point of maximum efficiency (at a volume flow rate of V& = 0.590 m³/s, corresponding to a flow rate coefficient 179.0)/(4 32 =nDV π& , which is the design operating point) was selected for all measurements reported in this study.

The fan rotor is tested in an anechoically terminated duct test stand, according to ISO 51365, with a duct diameter D = 300 mm, Fig. 4. The suction side is located in an anechoic chamber, not shown here. The volume flow rate is controlled by an adjustable throttle at the downstream side of the duct. The fan rotor is mounted downstream of different devices by which the inflow turbulence is controlled, table 1. The double layer turbulence control screen, according to Scoles et al.6, is intended to generate very low turbulence; the porous duct section allows the removal of the duct boundary layer by applying a suction flow and thus the reduction of wall-generated turbulence. Finally, the coarse square profile grid is designed for the generation of a highly turbulent inflow.

The downstream sound power radiated into the duct is determined from the sound pressure in the duct, and the sound power radiated into the free field on the fan’s suction side from the sound pressures at several positions on a control surface around the inflow7. The overall sound power is the sum of both. Spectra are measured with a resolution of ∆f = 3.125 Hz. The amplitudes of the sound power are presented in terms of their power spectral density level (PSDL). The reference pressure is p0 = 2.10-5 Pa and the reference acoustic power W0 = Watts1210− .

Table 1. Investigated inflow arrangements

Figure 3. Impeller investigated; radial gap blade tip/housing: 0.5 mm

Designation Inflow arrangement

OE None

GA None, but suction flow rate = 4 % of overall flow rate (For boundary layer removal)

HC Honeycomb,

RPG1 Fine squared mesh grid, no suction flow

a x a = 10 mm x10 mm, b x b = 65 mm x65 mm

RPG2 Coarse squared mesh grid, no suction flow, a x a = 15 mm x15 mm, b x b = 60 mm x60 mm

a

ab

b


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Figure 4. Test stand; hemispherical inflow control screen or standard inflow bellmouth alternatively; the facility’s anechoic termination and adjustable throttle at the downstream end are not shown

The characterization of incident turbulence in a theoretical or experimental way constitutes the most significant step. The local turbulent intensity in the blade leading edge plane,

aa CcTu /2′= (7)

is measured with a single hot wire probe, aligned perpendicularly to the mean flow direction ( 2ac′ being the rms-

value of the velocity fluctuations and aC the local axial velocity). The longitudinal turbulence integral length scale is calculated as:

aa CI=Λ , where ∫∞

=0

)( ττρ dI XX (8)

The circumferential integral length scale is determined from the correlation of two hot wire signals: For any radius R, one probe is kept fixed at the three o’clock position (corresponding to ϕ = 0°), whereas the second is moved gradually counterclockwise. Thus, the circumferential distance rϕ is increasing from 0 mm to a maximum value (at 54°). For each pair of data the maximum of the correlation coefficient function ρXY (τ), employing the Matlab® Vers. 6.1 routine xcorr, is determined and finally the circumferential length scale is calculated as:

∫∞

=Λ0

)max( ϕρ rdXYt (9)

where the upper bound of the integral is replaced by the maximum circumferential distance, selected for practical reasons as recommended in Smol’yakov et al.8. All hot wire measurements in the rotor leading edge plane have been carried out with the blades being removed but the rotor’s hub present and non-rotating. The volume flow is achieved by an auxiliary fan downstream of the measurement section.

Most of the models characterize the turbulence at the fan as isotropic, i.e. the length scales are considered equal in the streamwise and transverse directions. The power spectral density of the transversal velocity fluctuation w can

be expressed in terms of the mean square velocity fluctuation 2u of the oncoming flow, the turbulent longitudinal length scale Λu and the turbulent intensity of the oncoming flow Tu. A first assumption is to suppose isotropic turbulence, described by analytical models as von Kármán9 model. The two-dimensional spectrum of the w component is written as:

3/722

22

2

2

)ˆˆ1(

ˆˆ

94),(

yx

yx

eyxww

kk

kk

kukk

++

+=Φ

π (10)


7

where eii kkk /ˆ = , and uu

ek Λ≈ΓΓ

Λ= /747.0

)3/1()6/5(π . One wavenumber spectrum is found by integration of Eq. (10)

over wave number yk . In addition, the power spectral density of the u component is given:

6/112

22

)ˆ1()ˆ3/81(

2)(

x

xuxww

kkukS

+

+Λ=

π,

( )65

2

2

ˆ1

1)(

x

uxuu

kukS

+

Λ=

π (11)

The correlation length scale, )(ωyl , is defined as

∫∞

Φ==0

)0,(/)0,(),()0,(

1)( xwwxwwxwwxww

y KRKdyyKRKR

l πω (12)

),( ykR xww represents spanwise cross-correlation of w, thus

22

22

ˆ1)ˆ83(

ˆ

)6/5()3/1(

38)(

xx

xuy

kk

kl++

⎥⎦

⎤⎢⎣

⎡ΓΓΛ

=ω (13)

In the Eq. (3), wwS ′′ must be expressed in the local reference frame. For an isotropic turbulence, the orientation of the reference frame is not important. The length scale of a turbulent eddy in chordwise direction x′ of a blade is approximated by the longitudinal length scale Λa then by the circumferential integral length scale Λt of the turbulence in the stationary system.

V. Results

A. Inflow turbulent properties The four plots of Fig. 5 show the measured local mean velocity aC , Fig. 5.a, the local turbulent intensity Tu, Fig.

5.b, the local maximum correlation function coefficient ρXY, Fig. 5.c, and the longitudinal turbulence length scale Λa Fig 5.d, in the blade LE plane for the investigated inflow arrangements.

The different inflow control devices have an important impact on all quantities: aC is rather constant and extremely „peaky“ in case of RPG2 due to the wake/vortex structure behind the grid.

70 80 90 100 110 120 130 140 1500

2

4

6

8

10

12

14

Radius, mm

Axi

al v

eloc

ity, m

/s

OEGAHC gridRPG2 GridRPG1 Grid

70 80 90 100 110 120 130 140 1500

0.05

0.1

0.15

0.2

0.25

Radius, mm

Turb

ulen

ce in

tens

ity,


a) b)


8

The turbulent intensity is very low in case of OE, GA, and HC devices. This is not the case for the RPG1, and RPG2 grids creating values of Tu which in average are one order of magnitude larger and - again - very non-uniform. The length scales Λt derived from the correlation coefficients acc. to Eq. (9) tend to increase as the turbulent intensity decreases. The largest length scale with 16 mm is found with OE. These latter parameters are used for each of the nine segments in the acoustic model.

Figure 6.a and Fig 6.b show a comparison of measured turbulence energy spectrum level of the axial velocity with von Kármán modeling for all inflow devices at an angular position fixed at the three o’clock and two radius locations; R = 143 mm near the blade tip, respectively R = 73 mm near the hub. There is a good agreement for all the arrangements. However, the model is overpredicting the energy spectrum at high frequencies.

70 80 90 100 110 120 130 140 1500

2

4

6

8

10

12

14

16

Radius, m

Λt, m

m


70 80 90 100 110 120 130 140 1500

5

10

15

20

25

30

Radius, mm

Λa, m

m


c) . d) Figure 5. Measured turbulent inflow properties: a) local axial mean velocity. b) turbulence intensity. c) circumferential turbulence length scale. d) longitudinal turbulence length scale.

101 102 103 104-70

-60

-50

-40

-30

-20

-10

Frequency, Hz

Ene

rgy

spec

trum

Suu

, dB


101 102 103 104

-70

-60

-50

-40

-30

-20

-10

Frequency, Hz

Ene

rgy

spec

trum

Suu

, dB


a) b) Figure 6. Comparison of measured turbulence energy spectrum, continue line, and von Kármán model, Eq. (11), dotted line, at radius: a) R = 143 mm. b) R = 73mm.


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B. Acoustic pressure directivity and sound power spectrum Figure 7. presents acoustic pressure level directivities for the axial fan at 2m away from the fan. An interesting

feature of the broadband turbulence interaction noise directivity is the location of main radiation lobe along the fan axis. A number of minor radiation lobes are also present in high frequencies. It tends to propagate more downstream.

The comparison between the modeling and the experimental power spectrum density level of the acoustic power is presented in Fig. 8. As expected, the inflow arrangements have a significant influence on the broadband noise radiated by the fan. The predicting results based on approximation of the turbulence length scale in chordwise direction x′ by the longitudinal length scale Λa show a better agreement, especially for the low frequencies. Indeed the length scale of the turbulence has a great effect on the acoustic power distribution according to the frequency range.

10

20

30

40

50 dB

30

210

60

240

90

270

120

300

150

330

180 0

400 Hz1 kHz2 kHz4 kHz

20

40

60 dB

30

210

60

240

90

270

120

300

150

330

180 0

a) b) Figure 7. Directivity of the acoustic pressure level 2m away from the rotor: a) GA configuration. b) RPG2 grid configurations

102 103 1040

10

20

30

40

50

60

70

80

Frequency, Hz

PS

DL W

, dB

OE Modeling, Λa

OE Modeling, ΛtOE Experimental

102 103 1040

10

20

30

40

50

60

70

80

Frequency, Hz

PS

DL W

, dB

GA Modeling, Λa

GA Modeling, ΛtGA Experimental

a) b)


10

Generally, the model gives satisfaction for the frequency band 200 Hz - 2 kHz for all configurations. The theoretical results are closer to the experimental for configurations GA, OE, and HC, which are characterized by low turbulence intensity. The numerical results for the RPG2 and RPG1, highly turbulent inflow devices, show poorer agreement. Indeed, the linearized aerodynamic theory is unreliable for significant velocity fluctuations. In addition, the difference could be explained by the upstream turbulence modeling which assumes an isotropic turbulence whenever the ingested turbulence is highly non-isotropic. The upstream turbulence in the RPG1 and RPG2 favors the emergence of narrow band noise and the decreasing of the broadband component. The distribution of measured overall sound powers radiated according to chosen frequency bands is presented in Fig. 9.a. Most relevant observation is that at high frequencies, 7 kHz - 10 kHz, the sound power radiated is independent from the inflow devices. It suggests that turbulence interaction noise is not dominating in high frequencies. In addition, the comparison of the theoretical results, Fig 9.b with measurements confirms that the prediction is satisfying on the overall one and the band of 200 Hz - 2 kHz.

102 103 1040

10

20

30

40

50

60

70

80

Frequency, Hz

PS

DL W

, dB

HC Modeling, Λa

HC Modeling, ΛtHC Experimental

102 103 1040

10

20

30

40

50

60

70

80

Frequency, HzP

SD

L W, d

B

RPG2 Modeling, Λa

RPG2 Modeling, ΛtRPG2 Experimental

c) d)

102 103 1040

10

20

30

40

50

60

70

80

Frequency, Hz

PS

DL W

, dB

RPG1 Modeling, Λa

RPG1 Modeling, ΛtRPG1 Experimental

e) Figure 8: Measured, peaks at multiples of rotor shaft frequency removed, and predicted power spectral density level of the sound power for the inflow arrangements: a) OE. b). GA. c) HC. d) RPG2. e) RPG1


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VI. Conclusion The broadband fan noise due to the inflow turbulence was measured and predicted based on measured turbulence

parameters for various inflow arrangements. The modeling is an extension of the Amiet analytical formulation for turbulence ingestion noise of an isolated airfoil to rotating blades. The fan rotor is mounted downstream of five different devices by which the inflow turbulence is controlled. The model is established for an open rotor. The directivities of incident turbulence interaction noise are obtained. The predicted feature shows that the main radiation lobe is located along the fan axis. However, measurements of the acoustic pressure spectrum are affected by the presence of the duct. Thus, the comparison of the acoustic sound power is carried out for its best significance.

The statistical noise prediction model employed yields a reasonable or even satisfying agreement with the measurements for all devices over large of the audible frequency range. The predicting results based on the approximation of the turbulence length scale in chordwise direction by the longitudinal length scale are more fitting than the results based on the approximation by the circumferential turbulence length scale. The acoustic power distribution in terms of frequencies is very sensitive to the turbulence length scale. The theoretical results are closer to measurements for configurations generating low turbulence intensity and show poorer agreement for highly turbulent inflow devices. Indeed, the linearized aerodynamic theory is unreliable for significant velocity fluctuations. From overall sound power distribution, it was observed that upstream turbulence does not have much influence on the noise spectrum in high frequencies range. This could be explained by the fact that in high frequencies range the leading edge noise is not dominating. Discrepancies between prediction and measurement may result from the model with its crude simplifications and restrictions. In addition crucial input data rely on curve fits of empirical data. Although they are based on careful measurements and subsequent data processing, they have an uncertainty, which may influence the noise prediction.

References 1Hanson, D. B., “The Spectrum of Rotor Noise Caused by Atmospheric Turbulence,” J. Acoust. Soc. Am, 56, 1974, pp. 110,

126 . 2Amiet, R.K., “Noise Produced by Turbulent Flow into a Propeller or Helicopter Rotor,” AIAA Journal, 1976, pp. 76-560 3Paterson, R. W., and Amiet, R. K., “Noise and Surface Pressure Response of an Airfoil to Incident Turbulence,” Journal

Aircraft, 1977, Vol. 14, NO 8. 4Schneider, M., and Carolus, T., “Calculation of Broadband Fan Noise due to Inflow Turbulence Employing Noise Prediction

Models,” Fan Noise International Symposium, 2003, Senlis. 5ISO 5136, “Determination of sound power radiated into a duct by fans”, 1990 6Scoles, J., and Ollerhead, J.B., “An Experimental Study of the Effects of an Inlet Flow Conditioner on the Noise of a Low

Speed Axial Flow Fan,” National Gas Turbine Establishment, Report No. AT/2170/049/XR, University of Technology, Loughborough, 1981

7ISO 3745, Determination of sound power levels of noise sources using sound pressure – Precision methods for anechoic and hemi-anechoic rooms, 2000

8Smol’yakov A.V., and Tkachenko V.M., “The Measurement of Turbulent Fluctuations, Springer-Verlag, Berlin, Heidelberg, New York, 1983

9Hinze, J. O., Turbulence, McGraw-Hill Book Company, Inc , 1975.

100Hz-10kHz 100Hz-200Hz 200Hz-2kHz 2kHz-7kHz 7kHz-10kHz50

55

60

65

70

75

80

85

90

95

100

Frequency

OP

SD

L W, d

B

OEGAHCRPG2RPG1

100Hz-10kHz 100Hz-200Hz 200Hz-2kHz 2kHz-7kHz 7kHz-10kHz

50

55

60

65

70

75

80

85

90

95

100

Frequency

PS

DL W

, dB


a) b) Figure 9. Acoutic power distribution over frequency: a) measured. b) modeling.

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[American Institute of Aeronautics and Astronautics 12th AIAA/CEAS Aeroacoustics Conference (27th AIAA Aeroacoustics Conference) - Cambridge, Massachusetts ()] 12th AIAA/CEAS Aeroacoustics