Lennart S. Hultgren

Glenn Research Center, Cleveland, Ohio

A First Look at the DGEN380 Engine Acoustic Data

From a Core-Noise Perspective

NASA/TM—2015-218924

December 2015
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Lennart S. Hultgren

Glenn Research Center, Cleveland, Ohio

A First Look at the DGEN380 Engine Acoustic Data

From a Core-Noise Perspective

NASA/TM—2015-218924

December 2015

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

This work was supported by the Quiet Performance Subproject of the NASA Fundamental Aeronautics Program Fixed Wing 

Project. Thanks to Joseph W. Connolly of the NASA GRC Intelligent Control and Autonomy Branch for supplying relevant engine 

operational parameters obtained from the DGEN Simmot simulation system.

Available from

Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 

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This report is available in electronic form at http://www.sti.nasa.gov/ and http://ntrs.nasa.gov/
Abstract

This work is a first look at acoustic data acquired in the NASA Glenn Research Center Aero-Acoustic

Propulsion Laboratory using the Price Induction DGEN380 small turbofan engine, with particular emphasis on broadband combustor (core) noise. Combustor noise is detected by using a two-signal source

separation technique employing one engine-internal sensor and one semi-far-field microphone. Combustor noise is an important core-noise component and is likely to become a more prominent contributor to

overall airport community noise due to turbofan design trends, expected aircraft configuration changes,

and advances in fan-noise-mitigation techniques. This work was carried out under the NASA Fundamental Aeronautics Program, Fixed Wing Project, Quiet Performance Subproject.

1 Introduction

Commercial air traffic is expected to significantly increase in the future and, consequently, subsonic transportaircraft community noise needs to be further reduced in order to minimize the associated negative environmental and

economic impacts. For current-generation engines, noise generated in the core by components such as the compressor,

combustor, and turbine can be significant contributors to the overall noise signature at low-power conditions, typical

of approach flight, but it is typically overwhelmed by jet and fan noise at high engine-power settings during takeoff.

However, current design trends and expected technological advances in engine-cycle design as well as noise-reduction

methods are likely to increase the relative importance of core noise at all engine-power levels.1 Consequently, core

noise needs to be addressed in order to meet future aircraft noise-reduction goals. In fact, core noise may well set a

propulsion-noise floor limiting the effects of future fan and jet noise reduction techniques if not further controlled.

The present work represents a first look at the core-noise aspects of acoustic data acquired in the NASA Glenn

Research Center (GRC) Aero-Acoustic Propulsion Laboratory (APPL) using the Price Induction DGEN380 small

turbofan engine during July 2014. In particular, this report is concerned with the detection of combustor noise using

a source-separation technique. Combustor noise is a low-frequency broadband contributor to the noise generated in

the turbofan engine core. It can be a significant aspect of the aft-quadrant overall noise signature at typical approach

conditions for today’s turbofan engines and it is predicted1to make a significant contribution to all certification noise

levels for near-future engine designs. Direct measurement of turbofan-engine combustor noise is difficult because of

the presence of jet noise in the frequency range of interest. Since flight effects reduce jet noise more than combustor

noise, 2combustor noise can be a significant contributor to aircraft in-flight noise but may be masked by jet noise under

the corresponding static-engine test conditions. Summaries of the current status of combustor-noise source modeling,

as well as historical perspectives, are given in the review chapters by Mahan and Karchmer2and Hultgren et al. 3as

well as in Hultgren. 4

2 The DGEN380 Testing Program

The DGEN380 testing program was a one day test in the NASA GRC APPL facility. A Price Induction DGEN380

turbofan engine was brought into the anechoic facility mounted on the back on a small flatback truck. The engine

controller, engine-internal steady state sensors, and fuel supply were all integrated in the truck-engine assembly. NASA

supplied an inflow control device, some acoustic treatment on relevant truck surfaces, two arrays of microphones for

NASA/TM—2015-218924 1

A First Look at the DGEN380 Engine Acoustic Data 

From a Core-Noise Perspective 

Lennart S. Hultgren 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 
far field and semi-far-field acoustic measurements, as well as a sting-mounted Kulite pressure sensor to meassure the

unsteady pressure fluctuations in the core exit nozzle. A system-level in-flight noise prediction, based on the obtained

static data, is presented by Berton5for a notional twin-engine very light jet (VLJ) aircraft. Berton’s 5report also

contains a brief description of the DGEN engine and its target market. The testing program will also be fully described

in other forthcoming reports.

3 Experimental Results

The instrumentation layout consisted of 30 microphones arranged on a 12-foor arc and an engine-internal Kulite

sensor located in the core exit duct. The microphone distance from the engine is not large enough for the measurements

to be truly in the far field, but they are not in the near field either. Consequently, they will be referred to herein as

semi-far-field measurements. The signals were bandpass-filtered with the analog filter settings of 50 Hz and 50 kHz.

The signals were digitally sampled at 100 kHz for a total observation time of 60 seconds leading to time series with 6

million data points. The pressure time histories at the internal Kulite sensor and the aft-quadrant far-field microphone

located in the 130o polar direction (measured from the inlet) are used herein. Each time series is here analyzed using

an FFT length of 8192 points (corresponding approximately to an 12.2 Hz frequency resolution or bin width), Hanning

windowing, and a 50 percent data-segment overlap. The resulting narrow-band spectra are then the average of M =

1463 realizations, or instantaneous spectra.

3.1 Engine-Internal Kulite and Far-Field Microphone Spectra

Narrowband (12.2 Hz bin width) sound pressure levels, SPL, for the engine-internal kulite and the 130osemi-farfield microphone are shown in Fig. 1. The results in panels (a) and (h) are without the engine running at the beginning

and end of the test and, consequently show the background noise levels for the test. Panels (b) through (g) correspond

to the engine-power settings of 47 %, 60 %, 70 %, 80 %, 90 %, and 95.6 %, respectively. For the microphone data, it is

clear that the signal to noise ratio, S/N, is very good, except possibly at the very lowest frequencies—but even there,

the margin is about 20 dB.

The ambient, or background, noise level for the Kulite measurements is quite high, however. The reason for

this is not totally obvious at this point. Some understanding can be obtained by considering the smallest pressure

perturbation that can be detected by the pressure transducer and the instrumentation chain. Assuming that proper

signal conditioning has been carried out, then this pressure fluctuation is given by

(∆p)min = PFS ×maxsI,2

−L



, (1)

where PFS is the full-scale pressure of the transducer, sIis the transducer relative inaccuracy (the combined effect

of nonlinearity, repeatability, and hysteresis), and L is the number of bits used in the analog-to-digital conversion

circuitry. The manufacturer’s specification sheet lists the combined uncertainty as typically ±0.1% of the full scale,

i.e. sI = 1×10−3. For 24 bit analog-to-digital conversion (ADC), as used here, 2−L ≈ 6×10−8. Consequently, ADC

quantization can be eliminated as the reason for the noise floor. Furthermore, if it is assumed that this error is evenly

distributed over all frequencies under consideration, then it follows that the noise floor, or noise pressure level (NPL),

is given by

NPL = 10log"

2

NFFT 

(∆p)min

Pre f 2

#

= 10log"

2

NFFT 

sIPFS

Pre f 2

#

≈ 102.6dB, (2)

where NFFT is the number of points used in the spectral analysis (twice the number of frequency bins), and Pre f =

2 × 10−5 Pa is the reference pressure in SI units. The estimate in Eq. (2) is in line with what can be observed in

Fig. 1, thus indicating that transducer quantization is at the source of the high noise level. Furthermore, eventhough

the S/N ratio for the Kulite signal is not stellar, it is at least 10 dB for frequencies less than about 1000 Hz, which is

the expected range for combustor broadband noise.

3.2 Combustor-Noise Narrowband Results

The two-signal coherent-power method6is used here to detect the core-noise component of the total noise signature captured by the far-field microphone. Following the notational convention used in Hultgren and Miles,7

the

total measured signals by the engine-internal sensor and the free-stream microphone are denoted by x and y, and the

NASA/TM—2015-218924 2
frequency, Hz

narrow-band SPL, dB

0 2000 4000 6000 8000 10000

20

40

60

80

100

120

140

Kulite

FF Microphone

frequency, Hz

narrow-band SPL, dB

0 2000 4000 6000 8000 10000

20

40

60

80

100

120

140

Kulite

FF Microphone

(a) (b)

frequency, Hz

narrow-band SPL, dB

0 2000 4000 6000 8000 10000

20

40

60

80

100

120

140

Kulite

FF Microphone

frequency, Hz

narrow-band SPL, dB

0 2000 4000 6000 8000 10000

20

40

60

80

100

120

140

Kulite

FF Microphone

(c) (d)

Figure 1. Kulite and 130o direction far-field microphone narrowband (12.2 Hz) SPL versus frequency; (a): 0 % engine power; (b): 47 %

engine power; (c): 60 % engine power; (d): 70 % engine power.

coherent core-noise signals at the same locations are denoted by u and v. It then follows that the coherent output signal

is estimated by

Gvv = γ

2

xyGyy , (3)

where Gαα, Gαβ, γαβ = |Gαβ|/

p

GααGββ denote the one-sided auto spectrum, cross spectrum, and coherence of the

two signals α and β, where α and β are dummy indexes.

Figure 2 shows the 130ofar-field narrowband results obtained using this two-signal source-separation method

for various engine power settings. The black, red, and grey curves show the total noise signature Gyy, the core-noise

component Gvv, and the threshold value for the coherent output power ε

2Gyy, where

ε =

q

1−(1−P)

1/(M−1)

(4)

is a statistical coherence threshold. If the coherence computed from measurements, using M independent averages, is

less than ε, then P is the probablity that the two signals are independent, i.e. that the actual coherence is zero. P = 0.95

is used herein to establish the threshold value (ε ≈ 0.0452).

Figure 2 clearly shows the presence of broadband combustor noise below about 500 Hz. The detected frequency

range appears to be shrinking with increasing engine power, but that is only an artifact of the source-separation

NASA/TM—2015-218924 3
frequency, Hz

narrow-band SPL, dB

0 2000 4000 6000 8000 10000

20

40

60

80

100

120

140

Kulite

FF Microphone

frequency, Hz

narrow-band SPL, dB

0 2000 4000 6000 8000 10000

20

40

60

80

100

120

140

Kulite

FF Microphone

(e) (f)

frequency, Hz

narrow-band SPL, dB

0 2000 4000 6000 8000 10000

20

40

60

80

100

120

140

Kulite

FF Microphone

frequency, Hz

narrow-band SPL, dB

0 2000 4000 6000 8000 10000

20

40

60

80

100

120

140

Kulite

FF Microphone

(g) (h)

Figure 1, continued. Kulite and 130o direction far-field microphone narrowband (12.2 Hz) SPL versus frequency; (e): 80 % engine

power; (f): 90 % engine power; (g): 95.6 % engine power; (h): 0 % engine power.

method—once the core-noise level falls to about 27 dB below the total signal level (10logε

2

), it can no longer be

detected. In addition, the inherent positive bias error 6,7 in the approximation of the coherent input signal strength used

in the two-signal method tends to also lead to an underestimation of the output power, which has been observed to

increase in severity with increasing frequency. 7

Several discreete tones can also be discerened in the spectra. The tones can be more effectively identified, or

verified, by employing the deliberate dealignment technique of Miles.8 This is implemented here by delaying the microphone signal by 16384 data points, which is twice the data segment length. Figure 3 shows the resulting coherence

for the six engine power settings under consideration. The red and blue curves represent the computed coherence

for aligned signals and deliberately dealigned signals. The gray line indicates the statistical coherence threshold in

Eq. (4). The figure shows, as earlier noted by Miles 8, that this threshold is a good estimate even though the data

segments stricly speaking are not fully independent when the 50 % overlap technique is employed. The discreete tones

are clearly idenfieable in the dealigned cases and are listed in Table 1.

For each power setting, this table lists the shaft speeds for the Low-Pressure Turbine (NLPT ) and the High-Pressure

Turbine (NHPT ) as well as any discrete tones A–E that are observable in the coherence data. The shaft speeds were

obtained by averaging engine data (10 Hz sample rate) over the last minute spent at each set point. The instantaneous

NLPT tracks the requested set point quite well, with a root-mean-square deviation less than about 7 rpm.

NASA/TM—2015-218924 4
frequency, Hz

narrow-band SPL, dB

0 500 1000 1500 40

50

60

70

80

90

100

Total

NOP

Combustor-2s

frequency, Hz

narrow-band SPL, dB

0 500 1000 1500 40

50

60

70

80

90

100

Total

NOP

Combustor-2s

(a) (b)

frequency, Hz

narrow-band SPL, dB

0 500 1000 1500 40

50

60

70

80

90

100

Total

NOP

Combustor-2s

frequency, Hz

narrow-band SPL, dB

0 500 1000 1500 40

50

60

70

80

90

100

Total

NOP

Combustor-2s

(c) (d)

frequency, Hz

narrow-band SPL, dB

0 500 1000 1500 40

50

60

70

80

90

100

Total

NOP

Combustor-2s

frequency, Hz

narrow-band SPL, dB

0 500 1000 1500 40

50

60

70

80

90

100

Total

NOP

Combustor-2s

(e) (f)

Figure 2. Far-field narrowband (12.2 Hz) SPL in the 130o direction versus frequency; (a)–(f): black curve—total noise signature; red

curve—two-signal-method educed core noise; gray curve—noise floor; engine power: (a) 47 %, (b) 60 %, (c) 70 %, (d) 80 %, (e) 90 %,

(f) 95.6 %.

NASA/TM—2015-218924 5
frequency, Hz

coherence

0 500 1000 1500 0

0.2

0.4

0.6

0.8

noise floor

dealigned

aligned

A

B

frequency, Hz

coherence

0 500 1000 1500 0

0.2

0.4

0.6

0.8

noise floor

dealigned

aligned

A

B

C

(a) (b)

frequency, Hz

coherence

0 500 1000 1500 0

0.2

0.4

0.6

0.8

noise floor

dealigned

aligned

A

B

D

frequency, Hz

coherence

0 500 1000 1500 0

0.2

0.4

0.6

0.8

noise floor

dealigned

aligned

A

B

D

E

F

(c) (d)

frequency, Hz

coherence

0 500 1000 1500 0

0.2

0.4

0.6

0.8

noise floor

dealigned

aligned

A

B

D

E

frequency, Hz

coherence

0 500 1000 1500 0

0.2

0.4

0.6

0.8

noise floor

dealigned

aligned

A

B

D E

(e) (f)

Figure 3. Narrowband (12.2 Hz) coherence between engine-internal sensor and 130o-direction microphone versus frequency; (a)–

(f): red curve—aligned signals; blue curve—deliberately dealigned signals; gray line—noise floor; engine power: (a) 47 %, (b) 60 %,

(c) 70 %, (d) 80 %, (e) 90 %, (f) 95.6 %; the tones labeled A–F are listed in Table 1 and explained in the text.

NASA/TM—2015-218924 6
Table 1. Major core-noise tones, Hz

power NLPT NHPT A B C D E F

47 % 20506 34806 341.8 585.9

60 % 26182 40316 439.5 671.4 73.2

70 % 30545 43691 512.7 732.4 219.7

80 % 34909 46554 585.9 781.3 231.9 1172 1563

90 % 39271 49076 659.2 817.9 231.9 1318

95.6 % 41370 50477 695.8 842.3 231.9 1404

The tones A and B are observable at all the power settings and they are simply the shaft frequencies of the

low-pressure and high-pressure turbines, respectively. The tones E and F are the first harmonic of the tones A and

B. The tone C is only seen at one condition and could be a combustor rumble tone. The tone D is essentially at a

fixed frequency, i.e. independent power setting for the four conditions for which it is seen. It is possible that it is a

bleed-valve tone.

Figure 4 shows the phase-angle variation of the cross-spectrum between the engine-internal-sensor signal and

the 130o-far-field-microphone signal over the frequency range relevant to combustor noise. The phase angle is only

computed for frequences where the coherence is larger than the threshold given in Eq. (4), i.e. only when γxy > ε.

The phase angle is unwrapped (removing the effects of the branch cuts in the arctan function) and then normalized

by 2π radians. The red symbols denote the computed normalized, unwrapped phase angle and the black curve is the

least-square linear fit to the data,



arg(Gxy)

2π

(LSF)

= τ f +b, (5)

where τ is the time delay. The good fit in each of the panels indicates, as expected, that there is a constant time delay

between the two measuring stations for signals in this frequency range. The so-determined time delays, together with

their 95 % confidence intervals, are shown in Table 2. Note that the time resolution from the sampling is 0.01 ms,

which is smaller than the one-sided confidence bands. The typical (average) time delay is about 6.9 ms, which for the

speed of sound of 345 m/s (1130 ft/s), corresponding to the average ambient conditions during the testing, leads to a

virtual travel distance of about 2.4 m (7.8 ft). This virtual distance is, as it should be, smaller than the microphonearray radius since the acoustic waves travel through hotter flow regions where the speed of sound is higher before

entering the ambient region.

Table 2. Time delays determined through least-square-fit procedure

power 47 % 60 % 70 % 80 % 90 % 95.6 %

τ, ms 6.91 ±0.05 6.79 ±0.09 6.77 ±0.06 6.89 ±0.06 6.97 ±0.05 6.97 ±0.09

3.3 Combustor-Noise 1/3-Octave Results

The narrow-band results of the preceeding subsection are summed up to yield the corresponding 1/3-octave SPL

spectra. Figure 5 shows the results for the 1/3-octave frequency range of 100ato 1000 Hz for the six power settings.

The black, red, and grey symbols denote the total signature, the combustor-noise component, and the threshold value

for the source-separation method. Any combustor-noise results below the latter would not be meaningful using the

present source separation and data processing techniques. The presence of broadband combustor noise up to about

500 Hz is evident in all of the panels, (a)–(f). The distinct shaft-frequency tones, A and B, clearly affect the 1/3-octave

spectra above about 500 Hz for the three highest power settings, (d)–(f).

aLower frequency bands are affected by roll-off effects of the high-pass filter at 50 Hz and, consequently, are not shown in the figure.

NASA/TM—2015-218924 7
frequency, Hz

normalized unwrapped phase

0 500 1000 1500

0

2

4

6

8

frequency, Hz

normalized unwrapped phase

0 500 1000 1500

0

2

4

6

8

(a) (b)

frequency, Hz

normalized unwrapped phase

0 500 1000 1500

0

2

4

6

8

frequency, Hz

normalized unwrapped phase

0 500 1000 1500

0

2

4

6

8

(c) (d)

frequency, Hz

normalized unwrapped phase

0 500 1000 1500

0

2

4

6

8

frequency, Hz

normalized unwrapped phase

0 500 1000 1500

0

2

4

6

8

(e) (f)

Figure 4. Unwrapped and normalized, engine-internal sensor and 130o-direction microphone cross-spectrum phase versus frequency; (a)–(f): red symbols—cross-spectrum phase; black line—least-square linear fit; engine power: (a) 47 %, (b) 60 %, (c) 70 %,

(d) 80 %, (e) 90 %, (f) 95.6 %.

NASA/TM—2015-218924 8
frequency, Hz

1/3-octave SPL, dB

100 400 700 1000 0

20

40

60

80

100

Total

NOP

Combustor-2s

GECOR-PW

GECOR-PW-COR

frequency, Hz

1/3-octave SPL, dB

100 400 700 1000 0

20

40

60

80

100

Total

NOP

Combustor-2s

GECOR-PW

GECOR-PW-COR

(a) (b)

frequency, Hz

1/3-octave SPL, dB

100 400 700 1000 0

20

40

60

80

100

Total

NOP

Combustor-2s

GECOR-PW

GECOR-PW-COR

frequency, Hz

1/3-octave SPL, dB

100 400 700 1000 0

20

40

60

80

100

Total

NOP

Combustor-2s

GECOR-PW

GECOR-PW-COR

(c) (d)

frequency, Hz

1/3-octave SPL, dB

100 400 700 1000 0

20

40

60

80

100

Total

NOP

Combustor-2s

GECOR-PW

GECOR-PW-COR

frequency, Hz

1/3-octave SPL, dB

100 400 700 1000 0

20

40

60

80

100

Total

NOP

Combustor-2s

GECOR-PW

GECOR-PW-COR

(e) (f)

Figure 5. Total and combustor-noise far-field 1/3-octave SPL in the 130o-direction versus 1/3-octave-band center frequency; (a)–

(f): black symbols—total noise signature; red symbols—combustor-noise component; and gray symbols—noise floor; engine power:

(a) 47 %, (b) 60 %, (c) 70 %, (d) 80 %, (e) 90 %, (f) 95.6 %.

NASA/TM—2015-218924 9
The solid lines in Fig. 5 represent ANOPP 1/3-octave SPL predictions for the combustor noise using the smallengine (SmE) method with the PW turbine attenuation formula, SmE-PW. See the Appendix for more information

about the combustor-noise models in ANOPP. Clearly these curves overpredict the educed combustor noise. The

dashed curves represent the ANOPP 1/3-octave SPL predictions for the combustor noise after applying a thrust-class

correction. The proposed thrust-class correction is based on the thrust ratio of the two engine classes, very small

engines (VSE) and small engines (SmE), and leads to a change in the total acoustic power level of -11.5 dB. By

applying this thrust-class correction to the ANOPP SmE-PW predictions, the results (dashed curves) compares well

with data for all the conditions of the full-engine test. Using a thrust-class correction is not without precedent since

this is really the difference between the original SAE method (1970s) and the newer small-engine method (1990s) in

the GECOR module of ANOPP.

4 Summary and Conclusions

A first analysis of the broadband combustor (core) noise component of the acoustic data acquired in the NASA

GRC APPL facility using the Price Induction DGEN380 small turbofan engine has been performed. Combustor noise

was detected by using a two-signal source separation technique employing one engine-internal sensor and one semifar-field microphone. Broadband combustor noise is clearly present in the microphone data below about 500 Hz and

is likely to be present also up to about 1000 Hz even though it was not detected by the source separation technique in

this higher frequency range due to the inherent limitations of the technique. Several low-frequency discrete tones were

also discerned in the core-noise signature. ANOPP GECOR predictions (i.e. combustor noise only) for the staticengine test were carried out using relevant engine-operational parameters. By applying a thrust-class correction to the

predictions they compare well with data for all the conditions of the full-engine test. Using a thrust-class correction

is not without precedent since this is really the difference between the original SAE method (1970s) and the newer

small-engine method (1990s) in the GECOR module of ANOPP. The interim scaling is based on the thrust ratio of

the different engine classes and appears to give satisfactory results. This preliminary finding is subject to further

evaluation and might change if and when more engine data becomes available.

Appendix ANOPP GECOR 1/3-Octave Combustor-Noise Models

Combustor-noise prediction in the semi-empirical NASA Aircraft Noise Prediction Program (ANOPP)9,10 is provided by the GECOR subroutine. The current module (ANOPP L30v3) essentially contains two basic models with

variations. The first model is fully 1/3-octave based and in its original implementation11,12 is customarily referred to

as the SAE method. This method also contains a small-engine revision13 (referred to as SmE herein) as well as an

option for an alternate turbine-transmission-loss formula. 2,4,14–16 The second class of models, that will not be further

discussed or utilized here, has an intermediate-narrow-band formulation17 in order to account for tail-pipe resonances.

For a static-engine test, the (dimensional) combustor-noise mean-square pressure in each 1/3-octave band (b) is

given by

< p

2 >(b)=

ρ∞c∞ΠD(θ)S(fb)

4πr

2

s

(A 1a)

for both the SAE and SmE methods in ANOPP, where rsis the distance between the source and the observer and ρ∞

and c∞ are the ambient density and speed of sound. D(θ) is a directivity function that depends only on the polar angle

θ and satisfies the normalization condition

Z π

0

D(θ)sinθdθ = 2. (A 1b)

S(fb) is a spectrum function satisfying

∑

b

S(fb) = 1 (A 1c)

NASA/TM—2015-218924 10
and fb is the 1/3-octave-band center frequency. Π is the total acoustic power

Π =

Z

A

∑b < p

2 >(b)

ρ∞c∞

dA, (A 1d)

where dA = r

2

s

sinθdθdφ, with φ denoting the azimuthal angle. The sound pressure level SPL(b)in an 1/3-octave

frequency band, the overall sound pressure level OASPL, and the power level PWL are given by

SPL(b) = 10log(< p

2 >(b)

/p

2

re f), (A 2a)

OASPL = 10log(∑b < p

2 >(b)

/p

2

re f) = 10log[ρ∞c∞ΠD(θ)/4πr

2

s p

2

re f ], (A 2b)

PWL = 10log(Π/Πre f), (A 2c)

where pre f = 2 × 10−5 Pa and Πre f = 1 × 10−12 W if SI units are used. The ANOPP GECOR formula for the total

acoustic power is

Π = 10K/10c

2

∞m ̇ core 

Tt,ce −Tt,ci

Tt,ci 2 

Pt,ci

P∞

2

×FTA , (A 3a)

where the constant K = −60.53... in the SAE method and K = −64.53... in the SmE method.  ̇mcore is the mass

flow rate into the combustor, Tt,ci and Tt,ce are the total temperature at the combustor inlet and exit, Pt,ci is the total

combustor-inlet pressure, and P∞ is the reference (static) pressure. The reference state is ambient conditions, actual or

standard sea-level values. Note that the only difference between the SAE and SmE methods is the value of the constant

K leading to a 4 dB difference in the acoustic power level!

FTA is a turbine attenuation, or loss, factor and, in the original formulation, is given by18

FTA =



∆Tdes

T∞

−4

, (A 3b)

where ∆Tdes is the design-point temperature drop across the turbineband T∞ is the reference temperature. Note that the

acoustic transmission loss is independent of the engine operating condition with this formulation. The GECOR module

recently has been updated to also have an option to use an alternative turbine-transmission-loss formula, namely the

simplified2 Pratt & Whitney14,15 acoustic-turbine-loss formula,

FTA =

0.8ζ

(1+ζ )

2

, (A 3c)

where ζ is the ratio of the characteristic impedances across the turbine, i.e. ζ = ρtecte/ρticti with ρ and c denoting

density and speed of sound, respectively, and the subscripts ’te’ and ’ti’ indicating turbine exit and inlet. With this

formulation, the turbine acoustic transmission loss depends on the engine operation conditions since the impedance

ratio does. Hultgren16,cfound that predictions using this formula compared well with data for flight idle, approach,

cutback, and takeoff power settings from a full-scale static-engine test. 19 Eqs. (A 3b) and (A 3c) will be referred to

as the GE and PW turbine-transmission-loss formulas, respectively. Note that both these loss formulas are frequency

independent.

REFERENCES

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Florida, 2009.

b

If this value is not available, the corresponding takeoff value can be used.

cDue to a typographical error, Eq. 13 in Hultgren 16 corresponding to Eq. (A 3c) here is inverted, but the computations therein are correct.

NASA/TM—2015-218924 11
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