Lennart S. Hultgren

Glenn Research Center, Cleveland, Ohio

A Comparison of Combustor-Noise Models

NASA/TM—2012-217671

August 2012

AIAA–2012–2087
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Lennart S. Hultgren

Glenn Research Center, Cleveland, Ohio

A Comparison of Combustor-Noise Models

NASA/TM—2012-217671

August 2012

AIAA–2012–2087

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

18th Aeroacoustics Conference

cosponsored by the American Institute of Aeronautics and Astronautics and Confederation of 

European Aerospace Societies

Colorado Springs, Colorado, June 4–6, 2012
Acknowledgments

This work was supported by the NASA Fundamental Aeronautics Program Subsonic Fixed Wing Project (SFW). The NASA 

Fundamental Aeronautics Program has the principal objective of overcoming today’s national challenges in air transportation. 

The work herein is aligned with the SFW Reduce-Perceived-Noise Technical Challenge, which aims to enable concepts and 

technologies to dramatically reduce the perceived aircraft noise outside of airport boundaries. It is part of a NASA-internal and 

NASA-sponsored external research effort for the development and improvement of aircraft noise-prediction capability and tools. 

The author thanks Russell W. Claus for providing the existing NPSS simulation mean-line data for the E3 engine.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://www.sti.nasa.gov

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. 
A Comparison of Combustor-Noise Models

The current status of combustor-noise prediction in the NASA Aircraft Noise Prediction Program (ANOPP)

for current-generation (N) turbofan engines is summarized. Best methods for near-term updates are reviewed.

Long-term needs and challenges for the N+1 through N+3 time frame are discussed. This work was carried out

under the NASA Fundamental Aeronautics Program, Subsonic Fixed Wing Project, Quiet Aircraft Subproject.

I. Introduction

The anticipated increase in future air traffic makes further reduction of subsonic transport-aircraft noise an imperative. Currently, noise generated in the jet engine 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. For

existing engines, core noise is typically dominated 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 will need 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 paper is concerned with combustor noise, which is a low-frequency 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.

Combustor noise can be of either the direct or indirect type. The noise frequency for either type is set by the

unsteady combustion process and the peak value is generally believed to fall in the range of 400–500 Hz. The unsteady

combustion process is the source of pressure, entropy, and vorticity fluctuations. A fraction of the pressure disturbances

are acoustic pressure fluctuations with the balance being hydrodynamical unsteadiness. The former is what is referred

to as direct combustor noise. Its spectrum can be modified by the combustor geometry as well as pressure feedback on

the unsteady combustion process itself. The direct combustor noise is reduced due to transmission effects during its

propagation through the turbine stages. The combustor entropy (temperature) fluctuations are convected downstream

with the local mean velocity and are converted to acoustic pressure fluctuations in the turbine and other regions where

flow properties change rapidly. This is the indirect process of turbomachinery combustor-noise generation. This is

potentially a very effective mechanism and occurs at all turbine stages. The indirect noise occurs in the same basic

frequency range as the direct noise, but their spectral-distribution shapes could be quite different and both are affected

by the propagation through the engine core. Figure 1 illustrates the dual paths of combustor noise. Note that the direct

and indirect noise contributions are correlated at the source because both are caused by the unsteady heat addition.

The relative importance of the two combustor-noise components is still an unresolved issue.2–7

Major advances in combustor-noise source modeling occurred during the 1970s and early 1980s and are discussed in the review chapter by Mahan and Karchmer8

and references therein. Semi-empirical relations that correlate

noise levels with engine operating parameters based on full-engine test data were mainly developed by aircraft engine companies, often with support from Department of Transportation/Federal Aviation Administration (DOT/FAA)

or National Aeronautics and Space Administration (NASA). Significant development of diagnostic techniques also

took place during this time period. However, research resources were generally redirected towards the more pressing

† Associate Fellow AIAA

NASA/TM—2012-217671 1

Lennart S. Hultgren 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 
Figure 1. Dual paths for turbofan combustor noise

non-core noise issues in the late 1980s. Combustor noise, consequently, received very limited attention until the early

2000s when reduction techniques for jet and fan noise had further matured to a point, coupled with turbofan design

trends, where further noise reduction would require core noise to also be addressed. It was also realized at that time

that core noise was an important contributor to airport ramp noise due to auxiliary power units (APU).

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, combustor 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. To overcome this obstacle, researchers9–23 developed coherence techniques utilizing engine-internal,

as well as far-field, measurements to identify the far-field combustor-noise component. Modal analyses24–29 were also

carried out to determine the source and propagation characteristics of combustor noise.

The current paper discusses several semi-empirical models for turbofan combustor noise. The three-spectrum

model proposed by Stone et al.30 for GE turbofan-engine combustor noise will be discussed and compared with

ANOPP predictions for several relevant cases. The connection to the work by von Glahn and Krejsa,31 Karchmer,24

and Royalty and Schuster29 will also be discussed.

II. Combustor-Noise Models

Semi-empirical models for the total acoustic power are, in general, developed based on physical considerations

with model coefficients/constants determined using isolated-component and static-engine test data. Then the far-field

directivity and universal spectral distribution are obtained empirically. In the case of full-engine tests, the measured

total far-field acoustic signature normally is adjusted by subtracting the low-frequency jet noise using an appropriate

model to reveal the core noise. This represents a weakness since combustor noise is not always a dominant noise

source at low engine-power settings.

A. Early Models

Huff et al.32 reviewed the early 1970s state-of-the-art in engine combustor-noise prediction and recommended an interim semi-empirical method to provide such a capability for the NASA Aircraft Noise Prediction Program (ANOPP).33, 34

The proposed direct-combustor-noise method combined a General Electric35 developed formula for the total acoustic

power as a function of the engine operating condition, a Boeing36 obtained result for polar directivity, and a singlepeak spectral distribution based on the in-flight SAE ARP87637 jet-noise spectrum. As recommended in the Boeing36

work, Huff et al.32 suggested using a fixed peak frequency of 400 Hz. Emmerling et al.38 improved the GeneralElectric model by correlating the combustor-noise attenuation by the turbine with the design-point work extraction

of the turbine and validated the resulting model using several sets of engine data. Ho and Doyle39 provided further validation and discussion of this model (see also Mahan and Karchmer8

). This simple direct combustor-noise

model38, 39 still forms the kernel of the ANOPP core-noise module and is referred to therein as the SAE method. The

current ANOPP module also contains a small-engine revision40 of this method (referred to as SmE herein) and an

intermediate-narrow-band method41 to account for tail-pipe resonances.

Also during the latter half of the 1970s, researchers at Pratt & Whitney5, 42 developed a semi-empirical prediction

method for direct combustor noise. They derived models for the total acoustic power level, turbine coupling/ transNASA/TM—2012-217671 2
mission losses, and peak frequency; and they empirically determined model constants, the directivity pattern, and a

universal normalized spectral distribution using a range of burner-rig and full-scale static engine tests. Mathews et

al.5also measured the dynamic temperature characteristics at the exit as well as inside of a burner in a rig experiment

to provide inputs for an existing Pratt & Whitney indirect combustor noise model.43 They found experimentally that

the unsteady temperature level (roughly 9 % at the exit) depended mainly on the total temperature increase across

the burner and that the corresponding length scales were approximately proportional to a burner flow rate parameter.

Based on these measurements and the prediction codes, they found that indirect combustor noise should be 18-22 dB

lower than direct noise in the absence of turbine attenuation.

There are similarities and differences between the General Electric and Pratt & Whitney direct combustor-noise results (see also discussion in Mahan and Karchmer8

). In both, the total acoustic power level is proportional to the second

power of the combustor pressure and the second power of the temperature rise across the combustor (the Pratt & Whitney model uses the air-fuel ratio which essentially is equivalent to the temperature rise). The combustor mass-flow rate

linearly affects the total acoustic power in the General-Electric model, whereas in the Pratt & Whitney formula it enters

through a burner-flow parameter to the fourth power. The Pratt & Whitney result also depends on burner-geometry

information such as the number of fuel nozzles and the burner cross-sectional area. Their formulas for turbine losses

are different but both are frequency independent. The latter fact implies that, in the absence of resonances, measured

spectra for burner-rig and full-engine static tests should be quite similar. Furthermore, their directivity patterns are

in good agreement and their single-peak universal spectral distributions are similar when frequencies are normalized

with the peak frequency. The peak frequency in the General-Electric model is always 400 Hz, but the corresponding Pratt & Whitney formula involves burner design and geometry parameters. In general, each of these prediction

tools has shown good agreement with data from the engine manufacturer that developed the method, but not with data

from other companies. The need for distinct models may be caused by differences in burner design philosophy.44

Zuckermann44 summarized the history and results of the DOT/FAA sponsorship of core-noise research and provided

further comments. The report also pointed out the need for continued improvements in turbine-attenuation and indirect

combustor-noise source modeling.

B. Current ANOPP Models

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

by

< p2 >

(b)=

ρ∞c∞ΠD(θ)S(fb)

4πr2

s

(1a)

for both the SAE and SmE methods in ANOPP, where rs is 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) sin θdθ = 2 . (1b)

S(fb) is a spectrum function satisfying

X

b

S(fb) = 1 (1c)

and fb is the 1/3-octave-band center frequency. Π is the total acoustic power

Π = Z

A

P

b < p2 >(b)

ρ∞c∞

dA , (1d)

where dA = r

2

s

sin θdθdφ, 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) = 10 log(< p2 >

(b)

/p2

ref ), (2a)

OASPL = 10 log(P

b < p2 >

(b)

/p2

ref ) = 10 log[ρ∞c∞ΠD(θ)/4πr2s

p

2

ref ] , (2b)

PWL = 10 log(Π/Πref ), (2c)

NASA/TM—2012-217671 3
where pref = 2 × 10−5 Pa and Πref = 1 × 10−12 W if SI units are used. The ANOPP 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 , (3a)

where the constant K = −60.53 . . . in the SAE method and K = −64.53 . . . in the SmE method.a m ̇ core 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. FTA is a turbine attenuation, or loss, factor and is given by35

FTA =



∆Tdes

T∞

−4

, (3b)

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

the acoustic transmission loss is independent of the engine operating condition. Eq. (3b) will be referred to as the

ANOPP-GE formula for turbine-transmission loss herein.

In the ANOPP intermediate-narrow-band method,41 the combustor-noise mean-square pressure, < p2 >(n), associated with each narrow-band frequency range (n) is given by

< p2 >

(n)=

ρ∞c∞ΠD(θ, fn)S(fn)

4πr2

s

, (4a)

which is analogous to Eq. (1a), but with a directivity function D(θ, fn) that now also depends on the narrow-band

center frequency, fn, in addition to the polar angle, and with a spectrum function S(fn) that also can account for a

tail-pipe resonance. The product D(θ, fn)S(fn) satisfies a normalization condition equivalent to Eqs. (1b) and (1c),

Z π

0

X

n

D(θ, fn)S(fn) sin θdθ = 2 . (4b)

The total acoustic power is also here given by Eqs. (3a) and (3b). The narrow-band results are then summed up to

yield the customary 1/3-octave results in ANOPP, i.e.

< p2 >

(b)=

X

n∈b

< p2 >

(n)

. (5)

C. Turbine-Transmission-Loss Update

Figure 2. Honeywell TECH977 turbofan engine-internal sensors

Time-series data obtained from the NASA/Honeywell

Engine Validation of Noise and Emission Reduction

Technology program45 (EVNERT) was used by Hultgren46 to assess the turbine transfer of direct combustornoise and to recommend an update to the turbineattenuation formula used in ANOPP. This static-engine

test activity was carried out in Honeywell Aerospace’s

San Tan outdoor facility from 2005 to 2007. The program used the Honeywell TECH977 research engine,

which is typical of a business-jet application in the

6,000–8,000lbs thrust class.

The engine-internal instrumentation in one of the

many EVNERT test configurations included hightemperature pressure sensors with air cooling located in

a combustor ignitor port (one sensor) and at the turbine

exit (two sensors), see Fig. 2. The true combustion-noise turbine-transfer function was educed from the EVNERT

data by using a three-signal approach. Note that the true turbine gain factor is always underpredicted by a directly

measured one, using only two sensors, because of a positive bias error caused by the presence of pressure fluctuations

in the combustor that are uncorrelated with the combustor noise.46 The resulting gain factors were compared with

aThe SAE and SmE methods differ only by 4 dB in the acoustic power level.

NASA/TM—2012-217671 4
the corresponding constant values obtained from Eq. (3b) and a simplified8 Pratt & Whitney5, 42 acoustic-turbine-loss

formula,

FTA =

0.8ζ

(1 + ζ)

2

, (6)

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. Both

empirical formulas, (3b) and (6), are frequency independent. Hultgren46,bfound that the gain factor obtained from

the simplified Pratt & Whitney formula (6) agreed better with the experimental results for frequencies of practical

importance.

frequency, Hz

1/3-octave SPL, dB

101102103

ANOPP total-modified

ANOPP total

ANOPP combustor-modified

ANOPP combustor

Experiment

10 dB

frequency, Hz

1/3-octave SPL, dB

101102103

10 dB

(a) (b)

frequency, Hz

1/3-octave SPL, dB

101102103

10 dB

frequency, Hz

1/3-octave SPL, dB

101102103

10 dB

(c) (d)

Figure 3. Total and combustor noise 1/3-octave SPL versus 1/3-octave center frequency in the 130o direction; symbols and solid lines—

data and ANOPP predictions from Ref. 23; dashed lines—ANOPP predictions modified to use the P&W turbine-attenuation from Ref. 46;

(a): 48 % corrected fan speed (flight idle); (b): 60 % corrected fan speed (approach); (c): 71 % corrected fan speed (cutback); (d): 87 %

corrected fan speed (takeoff)

Hultgren46 reexamined the far-field 1/3-octave SPL results in the 130o direction by Hultgren and Miles,23 for

the same EVNERT dataset as above, by applying a post-correction to the original ANOPP predictions for both the

total noise signature and the combustion-noise component. It was found that replacing the ANOPP-GE combustornoise turbine-attenuation function (3b) with the simplified Pratt & Whitney one (6) clearly improved the total-noise

predictions and also improved the combustion-noise predictions. The latter comparison was not as conclusive as the

former due to the inherent difficulty in extracting the combustion-noise component from the total noise signature.

However, the former would not be true if the combustion-noise component predictions had not been improved by the

attenuation-formula change.

bDue to a typographical error, the formula in Ref. 46 (Eq. 13) corresponding to Eq. (6) is inverted, but the computations therein are correct.

NASA/TM—2012-217671 5
Figure 3 shows the original23 far-field results in the 130o direction as well as the effects46 on the ANOPP predictions by replacing the ANOPP-GE turbine-attenuation factor by the simplified Pratt & Whitney formula. The

1/3-octave sound-pressure-level (SPL) results are shown at the four engine power settings of 48, 60, 71, and 87 percent corrected fan speed (flight-idle, approach, cutback, and takeoff conditions) for the 1/3-octave center frequency

range of 20 to 1000 Hz. The solid lines represent the original ANOPP 1/3-octave SPL predictions for the total (black)

and combustion (red) noise. The black squares correspond to the total noise signature from the EVNERT experiment,

which is reasonably well predicted by the original ANOPP results (see Ref. 23 for details). The dashed curves represent the post-corrected46 ANOPP 1/3-octave SPL predictions for the total (black) and combustion (red) noise using

the simplified Pratt & Whitney acoustic turbine-transmission formula (6) rather than the ANOPP-GE one (3b). It is

clear from panels (a)–(c) in Fig. 3 that the total noise signature is better predicted by the modified ANOPP results as

compared to the original ones.

D. A General Multi-Component Model

In general, there could be several independent combustor-noise sources. The (dimensional) combustor-noise meansquare pressure in each 1/3-octave band can then, in line with Eq. (1a), be written as

< p2 >

(b)=

ρ∞c∞

PNc

k=1 ΠkDk(θ, fb)

4πr2

s

(7a)

for the static-engine-test case, where Nc is the number of independent noise sources and Πk and Dk(θ, fb) denote the

total acoustic power and a combined directivity and spectrum function for the k

th source. The overall mean-square

pressure is given by

< p2 >=

X

b

< p2 >

(b)=

ρ∞c∞

PNc

k=1 ΠkDk(θ)

4πr2

s

=

ρ∞c∞ΠD(θ)

4πr2

s

, (7b)

where Dk(θ) = P

b Dk(θ, f(b)

) is a directivity function for the k

th component, Π = PNc

k=1 Πk is the total combustornoise power, and D(θ) = PNc

k=1 ΠkDk(θ)/Π is the overall combustor-noise directivity. Both Dk(θ) and D(θ) satisfy

the normalization condition (1b).

E. Stone et al. Empirical Model

Stone et al.30 have developed a combustor-noise model based on an empirical fit of static-test data for four common

General-Electric turbofan engines (CF6, CF34, CFM56, and GE90) in current use. The core noise was extracted

from the experimental total far-field acoustic signature by a clever and iterative application of a jet-noise model.47, 48

For frequencies below the (lowest) turbine blade-passing frequency, they deduced that the combustor noise could

be described by a spectrum comprised of three components corresponding to the low-, mid-, and high-frequency

(∼ 1 kHz) peaks observed in the revealed core-noise spectrum. The contribution of each component to the total was

then correlated with the engine operational parameters.

Stone et al.30 presented their results in terms of formulas for the component OASPL at the 90o polar angle

OASPLk(θ= 90o) = Ck + 10 αk log Q − βk log nf − log(4πr2

s

)



, k = 1, 2, 3 , (8a)

where

Q =  ̇mcoreT

2

∞



Tt,ce − Tt,ci

Tt,ci 2 

Pt,ci

P∞

2

(8b)

is the combustion-noise parameter recommended by Huff et al.,32 the subscript k indicates combustor noise component, nf is the number of fuel nozzles, and Ck, αk, and βk are constants (Table 1). The k = 1 through 3 cases are

referred to as the low-, mid-, and high-frequency components, respectively. In regard to the parameter nf in Eq.

(8a), the authors of Ref. 30 state that during their data reduction: “The fuel nozzle number nf emerged as a possible

correlating parameter, but further analyses might yield better alternative approaches.”

The values of constants αk and βk in Table 1 agree with the corresponding ones given in Ref. 30. However,

the constants Ck are modified here for two reasons. First, and the major reason, their formula (Ref. 30, Eq. 3)

corresponding to Eq. (8a) does not strictly represent the predicted component OASPL at the 90o polar angle. Their

quantity UOL, somewhat in contradiction to their nomenclature, represents only an intermediate result of the fitting

NASA/TM—2012-217671 6
Table 1. Modified Stone et al.30 Constants

k = 1 k = 2 k = 3

Ck 89.69 71.30 53.93

αk 0.7 1.0 0.9

βk 1.4 1.8 0.0

procedure and not the final result. To remove this artifact of their fitting procedure, and for clarity, (0.70, 0.01, 0.44)

should be added to their values. Second, for consistency with other formulas herein, the factor 4π is explicitly used in

the spherical spreading term in Eq. (8a). This means that 10 log(4π) ≈ 10.99 should also be added to the constants

to obtain the Ck values used herein. Furthermore, note that the constant Ck in Eq. (8a) depends on the units used,

i.e., the underlying formulation is not quite dimensionally correct. In addition, as the fitting parameter αk is changed,

the underlying dimension of Ck also changes.c The consequence of this is that in Eqs. (8a,b), the source-to-observer

distance must be in ft, the mass flow rate must be in lbm/s, and the ambient temperature must be in oR. No other

equation in this paper has this type of restriction.

The component sound pressure level SPL(b)in each 1/3-octave frequency band and component OASPL are given

by

SPL(b)

k = OASPLk(θ= 90o

) + Ik(θ, St(b)

k

), k = 1, 2, 3 , (9a)

OASPLk = OASPLk(θ= 90o) + ∆OASPLk(θ), k = 1, 2, 3 , (9b)

where Ik(θ, St(b)

k

) is a directivity and frequency index (Tables 2–4),

∆OASPLk(θ) = 10 log "X

b

10Ik(θ,St(b)

k

)/10#

, (9c)

and St(b)

k

is a nondimensional frequency (Strouhal number), all for the k

th component. The index function Ik(θ, St(b)

k

)

in Eq. (9a) is simply the component 1/3-octave SPL normalized by the component OASPL value in the 90o polar

direction. The Tables 2–4 correspond to the Tables I–III in Ref. 30 adjusted such that ∆OASPLk(θ = 90o) = 0. The

Strouhal number Stk for the three components are given by

St1 = fbd

(h)

cn /c∞ , (9d)

Stk = fbdc/cce k = 2, 3 , (9e)

where d

(h)

cn is the hydraulic diameter of the core nozzle, dc is the combustor diameter, and cce is the speed of sound

at the combustor exit. The authors of Ref. 30 state: “The characteristic lengths and velocities used in these Strouhal

relations may very well change if data for other engines over a wider range of correlating variables become available.

The selection of the currently used characteristic velocities and lengths was based simply on identifying a set that

approximately correlated engine-to-engine trends and the fairly small trends with engine power. No claim is made

that better relationships cannot be found with further study.”

The fit of the model to the extracted component OASPL at 90o polar angle is reasonably good (Ref. 30, Fig. 12),

with only a few data points outside of ±3 dB error bands. The SPL-predictions for the low-, mid-, and high-frequency

components (Ref. 30, Figs. 13-15) are also reasonable (again using ±3 dB as a measure), with the low-frequency

and high-frequency component predictions being the best and the least good, respectively. Stone et al.30 make the

following comment on the quality of their fit: “Since it is impossible to exactly determine the contribution of core

noise, statistical accuracy is evaluated on the basis of total noise at frequencies below blade passage. On this basis,

the prediction agrees with the data for the four GE engines exactly on average, with root-mean-square error of 1.7

dB.” The fit to the underlying data set is, in fact, remarkably good and is a testament to the well-honed modeling skills

of the investigators.

As an initial test of the applicability of the developed model to other turbofan engines, Stone et al.30 compared

predictions to available combustor-noise data, extracted using a three-signal source-separation method17 from staticengine test data, for a Pratt & Whitney JT15D engine31 (Ref. 30, Fig. 19) and an Avco Lycoming YF102 engine17

cThis is not uncommon for empirical relationships used in engineering practice and does not limit the potential value for practical application.

NASA/TM—2012-217671 7
(Ref. 30, Fig. 20). For this type of validation testing, it is often difficult to obtain both the required noise and enginecycle data as well as sufficient engine-geometry information. Stone et al.30 had to estimate some of the geometric

parameters and assume the number of fuel nozzles for both engines—see their report for a discussion of the details

and possible impacts on their comparison. For the JT15D-engine and YF102-engine comparisons, the low-frequency

combustor-noise component predictions were reduced by 8 dB and 15 dB, respectively, to produce the results shown

in their figures. Even with these significant adjustments of the predictions, their results are only in “rough agreement”

with the experimental data, with differences well exceeding 3 dB for several frequencies. They indicate: “At present,

the reason for the substantial adjustment required for the level of the lowest frequency component is unknown. It will

probably be necessary to adjust both the jet and core noise models to improve the accuracy and generality of the

model. Differences for the other components may be due to approximations in the combustor parameters, including

frequency-scaling effects. Data from more engine geometries and manufacturers would be useful to resolve these

issues.” Contrary to their30 determination, it is concluded here that, at present, their model is not capable of predicting

the combustion noise associated with the two non-GE engines examined. Thus, for now, the use of the new Stone

et al.30 combustor-noise prediction method should be limited to situations involving only General-Electric turbofan

engines.

F. Previous Multi-Component Models

The combustor-noise data for the YF102 and JT15D engines, discussed above, as well as corresponding data for a

CF6-50 engine were further examined and correlated by von Glahn and Krejsa.31 The suggested correlations utilized

one, two, and four spectral segments to capture perceived peaks in the far-field combustor-noise spectra. Generally,

the sound pressure levels at the single-segment spectrum peak, the higher frequency two-segment spectrum peak, and

the two higher frequency four-segment spectrum peaks scaled with a heat-release parameter, as in the semi-empirical

models described above, whereas the low-frequency segments scaled with the combustor exit velocity to the fourth

power. They stated that the four-segment spectra provided the best overall fit to the data, but also that the two-segment

spectrum appeared to be a reasonable representation of the combustion noise. However, their data comparisons do

not generally show the expected 3 dB increase at the intersection of the multisegment spectra, which renders their

conclusions less clear. Nevertheless, their results show that the assumption of a single-peaked far-field combustionnoise spectrum with the peak fixed at 400 Hz, as used in ANOPP, can be questioned.

Gliebe et al.49 also developed empirical combustor-noise correlations based on existing static-engine test data

for a selection of modern high-bypass-ratio engines. The data used was from General Electric CF6-80C2 and CFM

International CFM56-5B/7B engines equipped with single-annular combustors (SAC) and General Electric GE90 and

CFM56-5B/7B engines equipped with dual-annular combustors (DAC). They adopted the multi-element spectrum

ideas of von Glahn and Kresja31 and found that the best fits were obtained by using a three-segment spectrum (peaks

at 63, 160, and 630 Hz) for SAC engines and two spectral segments (peaks at 160 and 500 Hz) for DAC engines.

III. Combustor Modal Analysis

The essential ingredients in predicting combustor noise are: first, the understanding of the fluctuating pressure

and entropy fields, i.e., the source characteristics, inside the combustor and, second, their further propagation and

interaction with turbine stages through the turbofan core. Karchmer24 and Royalty and Schuster29 have documented the

modal structure of the unsteady pressure field in combustors. Karchmer’s24 rig-experiment utilized a ducted full-scale

YF102 annular-combustor, whereas Royalty and Schuster29 analyzed measurements in a real-engine environment.

Krejsa and Karchmer26 have documented the modal structure in the core nozzle of a turbofan engine. The combustor

unsteady entropy field and its propagation and interaction with the turbine are still areas of emerging understanding and

active research (eg. the propulsion-noise component of the NASA Fundamental Aeronautics Program Quiet Aircraft

Subproject).

In the rig experiment, Karchmer24 analyzed unsteady pressure data obtained from six probes arranged circumferentially in the outer annular wall of the combustor liner at a single axial location for operating conditions roughly

corresponding to 30 through 60 percent YF102-engine power. For all conditions, his modal decomposition showed

that higher-order azimuthal modes were present in the combustor for frequencies higher than about 400 Hz and that

each mode, in sequence, dominated the spectrum near its estimated cut-on frequency (Ref. 24, Fig. 7). That is, successive distinct portions of the pressure spectrum in the combustor could be uniquely identified with a single mode,

starting with the plane wave and followed in turn by modes with increasing azimuthal indexes. He concluded that

the basic source generating mechanism is relatively smooth and somewhat featureless, but that the annular geometry

NASA/TM—2012-217671 8
of the combustor is extremely effective in modifying the unsteady pressure spectrum in the combustor. Karchmer24

also carried out limited comparisons with existing far-field results11 from an YF102 turbofan engine and found rough

similarities between his isolated-component results and the full-engine measurements.

Royalty and Schuster29 analyzed the acoustic modes in the combustor for a particular EVNERT45 configuration of

the TECH977 turbofan engine in which the fan was replaced by a water brake in order to remove fan sources from the

total noise signature. The no-fan configuration could be operated up to a power setting corresponding to the approach

condition of 60 % corrected fan speed. The combustor internal instrumentation consisted of a circumferential array

of 16 equally-spaced pressure probes. They29 (see their Fig. 19) found that for low frequencies most of the acoustic

energy was associated with the plane wave (m = 0) mode, that the first circumferential mode (m = ±1) was dominant

in the frequency range of 500–1000 Hz, and that higher circumferential modes (m = ±2, m = ±3, m = ±3, . . .)

sequentially became the most significant feature at successively higher frequencies, where m is the azimuthal wave

number or mode order. One can observe in their figure that at 500 Hz, the plane wave mode is about 8 dB and 5 dB

below the total acoustic level at the 48 % and 60 % power settings, respectively. They also reported that the higher

modes (m = 0 6 ) were not present in the far-field data. It is concluded here that this indicates that the non-plane-wave

modes are cut-off in the turbine/duct downstream of the combustor for this particular engine. This is in agreement

with the results of Hultgren and Miles23 in which coherent combustor noise was only detected for frequencies less

than about 400+ Hz.

Krejsa and Karchmer26 documented the modal structure of the pressure field near the inlet and exit of the core

nozzle of an AiResearch Quiet-Clean-General-Aviation-Turbofan (QCGAT) engine for several operating conditions

using an array of five circumferentially spaced probes at each axial location. The QCGAT engine was derived from

the AiResearch TFE731-3 engine for use in the NASA QCGAT program50 to demonstrate the applicability of large

turbofan engine noise and pollution reduction technology to small general aviation turbofan engines. Their analysis

of the pressure data showed that the plane-wave mode was dominant at the very lowest frequencies and that, up to

the 1500 Hz upper limit of their analysis, the most recently cut-on azimuthal mode was dominant with increasing

frequency. The contribution of modes other than the dominant mode was usually small. At the core tailpipe exit, this

meant that the plane wave mode was dominant for frequencies below about 800–900 Hz and that the first azimuthal

mode was dominant for higher frequencies.

As pointed out by Schuster and Lieber,41 these results24, 26 strongly suggest that resonances in the the combustor

and tailpipe play an important role in determining the peaks observed in external spectra. They remark that these peaks

arise from the modulation of a base spectrum due to the location of the source inside a partially confined geometry

consisting of the combustor, turbine, and exhaust nozzle. Further, the far-field spectrum can be thought of as the

product of a single peak broadband combustion noise spectrum, that is representative of the spectrum of an open

turbulent flame, and a spectral transfer function that is representative of the resonance and propagation effects in the

engine core and exhaust. They observe that this transfer function should depend on the duct geometry, gas properties,

and impedance conditions at system boundaries, and that “it is unrealistic to expect that a single transfer relation

will be generally applicable to the wide variety of combustor, turbine and exhaust geometries.” However, through an

analysis of narrowband acoustic data from turbofans, turboshafts, and auxiliary power units (APUs) manufactured by

Honeywell, they found that the far-field combustor-noise peak frequencies correlated strongly with the exhaust duct

length and mean exhaust duct sound speed according to plane-wave radiation from an unflanged circular pipe. This led

to the development and ultimate implementation of the intermediate-narrow-band model, briefly discussed in § IIB,

into ANOPP.

NASA/TM—2012-217671 9
IV. Results

The three-spectrum model proposed by Stone et al.30 for GE turbofan-engine combustor noise is compared

with ANOPP-formula predictions for several relevant cases. The computations are carried out using MATLAB

scripts implementing Eqs. (1)–(3) and (6) for the ANOPP models and Eqs. (8) and (9) for the Stone et al. model.

The static-engine-test results are presented for a free-space virtual observer at a one-foot distance and are lossless,

i.e. atmospheric attenuation is not included in the predictions. The engine operational parameters are taken to correspond to Rolling-Takeoff (RTO) power at Sea-Level-Standard 25 oC (SLS+10K) conditions (warm day).

A. GE90-94B Predictions

Figure 4 shows the 1/3-octave SPL spectra in the 90, 120, and 150 degree directions and the OASPL versus polar

angle for the takeoff condition (RTO-SLS+10K). The engine operational point corresponds to the related far-field

results presented in Figs. 10(c)–(e) and 11 of Ref. 30. The figure shows the contributions from the low-, mid-, and

high-frequency components as well as the total from the Stone et al. model, and the prediction using the SAE method

with the GE turbine-attenuation factor (SAE-GE).

log f

1/3-octave SPL, dB

1 2 3 4

Stone-C1

Stone-C2

Stone-C3

Stone

SAE-GE

log f

1/3-octave SPL, dB

1 2 3 4

Stone-C1

Stone-C2

Stone-C3

Stone

SAE-GE

(a) (b)

log f

1/3-octave SPL, dB

1 2 3 4

Stone-C1

Stone-C2

Stone-C3

Stone

SAE-GE

polar angle, deg

OASPL, dB

0 20 40 60 80 100 120 140 160 180

Stone-C1

Stone-C2

Stone-C3

Stone

SAE-GE

(c) (d)

Figure 4. Comparison of one-foot loss-less combustor-noise predictions using the Stone et al.30 and ANOPP SAE-GE formulas for a

GE90-94B turbofan engine at Rolling Takeoff power and Sea-Level-Standard 25 oC conditions; red, green, and blue lines—Stone method

low-, mid-, and high-frequency contributions; black lines—Stone method; dashed magenta lines—SAE-GE method; major tick marks on

vertical axis represent 10 dB increments; (a)–(c): 1/3-octave SPL versus 1/3-octave center frequency in the 90o, 120o, and 150o, directions;

(d): OASPL versus polar angle

A visual overview of the difference between the predictions is shown in Fig. 5 where side-by-side carpet plots of

NASA/TM—2012-217671 10
the 1/3-octave SPL as function of frequency and polar angle are shown also for the takeoff condition. The left panel

in the figure shows the total Stone et. al. model result and the right panel shows the SAE-GE result.

log f

1

2

3

4

polar angle, deg

0

50

100

150

1/3-octave SPL, dB

log f

1

2

3

4

polar angle, deg

0

50

100

150

1/3-octave SPL, dB

(a) (b)

Figure 5. Predicted one-foot loss-less combustor-noise 1/3-octave SPL as function of 1/3-octave center frequency and polar angle for a GE90-

94B turbofan engine at Rolling Takeoff power and Sea-Level-Standard 25 oC conditions; major tick marks on vertical axis represent 20 dB

increments; (a): Stone et al.30 method; (b): ANOPP SAE-GE method

As can be seen in Figs. 4 and 5, essentially the SAE spectral distribution is replaced by the more narrow midfrequency component distribution, with basically the same spectral-peak frequency, as well as with low- and highfrequency components. The peak levels of the SAE prediction and the mid-level Stone et al. component are comparable, with a difference of less than about 3 dB, which is also reflected in their OASPL distributions shown in Fig. 4(d).

Because the high-frequency component has, clearly, a higher level than the other two components in the aft quadrant,

the total Stone et al. OASPL levels are higher compared to the SAE-GE prediction, with the peak being about 5 dB

higher. The total Stone et al. OASPL peak also occurs at a 10o more shallow angle with respect to the downstream

direction than the corresponding SAE-GE peak.

B. Energy Efficient Engine Predictions

The Energy Efficient Engine (E3) Program51–53 (late 1970s to mid 1980s) was a NASA funded effort to develop

technologies that would significantly reduce fuel consumption and operating costs of (then) future transport aircraft

engines. Both Pratt & Whitney and General Electric were major participants in this highly successful project. Both

companies initially conducted separate flight-propulsion-system design and analysis studies (see Ref. 51 for references), but because of budget constraints only General Electric was selected to build a technology-demonstration engine,54 for integrated core/low-spool testing, whereas the Pratt & Whitney effort was limited to component-technology

testing. The technologies developed during this program have been effectively adopted by the engine manufacturers.

In particular, the General Electric demonstrator engine, commonly referred to as the E3engine, formed the kernel of

what eventually became their GE90 turbofan. Because the E3engine can be thought of as part of the GE-turbofan

family, but was not part of the data fit in Ref. 30, it is a suitable candidate for the comparisons carried out here. In

addition, there are non-proprietary mean-flow properties available,d obtained through use of the Numerical Propulsion

System Simulation55 (NPSS) computer program, for the E3engine.

Figure 6 shows the 1/3-octave SPL spectra in the 90, 120, and 150 degree directions and the OASPL versus polar

angle for the takeoff condition (RTO-SLS+10K). The figure shows the contributions from the low-, mid-, and highfrequency components as well as the total from the Stone et al. model, and the prediction using the SAE method

with the GE turbine-attenuation factor (SAE-GE). As can be seen in Fig. 6, the spectral-peak frequencies for the SAE

distribution and the more narrow mid-frequency component distribution are essentially the same, but their spectral

peak levels are not as close as in Fig. 4. The OASPL levels of the SAE-GE method and the total Stone et al. prediction

are comparable in the aft quadrant. However, the latter has a slightly higher peak at a shallower polar angle due to

dClaus, R. W., Private Communication

NASA/TM—2012-217671 11
log f

1/3-octave SPL, dB

1 2 3 4

100

110

120

130

140

150

160

Stone-C1

Stone-C2

Stone-C3

Stone

SAE-GE

log f

1/3-octave SPL, dB

1 2 3 4

100

110

120

130

140

150

160

Stone-C1

Stone-C2

Stone-C3

Stone

SAE-GE

(a) (b)

log f

1/3-octave SPL, dB

1 2 3 4

100

110

120

130

140

150

160

Stone-C1

Stone-C2

Stone-C3

Stone

SAE-GE

polar angle, deg

OASPL, dB

0 20 40 60 80 100 120 140 160 180 120

130

140

150

160

Stone-C1

Stone-C2

Stone-C3

Stone

SAE-GE

(c) (d)

Figure 6. Comparison of one-foot loss-less combustor-noise predictions using the Stone et al.30 and ANOPP SAE-GE formulas for an

E

3

turbofan engine at Rolling Takeoff power and Sea-Level-Standard 25 oC conditions; red, green, and blue lines—Stone method low-,

mid-, and high-frequency contributions; black lines—Stone method; magenta lines—SAE-GE method; major tick marks on vertical axis

represent 10 dB increments; (a)–(c): 1/3-octave SPL versus 1/3-octave center frequency in the 90o, 120o, and 150o, directions; (d): OASPL

versus polar angle

contributions from the high-frequency component. The difference in the predicted OASPL levels in the 110oto 140o

polar angle range, which from a practical point of view is the important direction, is less than about 3 dB.

C. TECH977 Predictions

Figure 7 shows the 1/3-octave SPL spectra in the 90, 120, and 150 degree directions and the OASPL versus polar

angle for the takeoff condition (RTO-SLS+10K). The figure shows the contributions from the low-, mid-, and highfrequency components as well as the total from the Stone et al. model, and the prediction using the SmE method with

the PW turbine-attenuation factor (SmE-PW). Here, the SmE-PW spectral distribution is essentially mimicked by the

low-frequency component in the Stone et al. method. The peak levels are within about 6 dB of each other in the 120o

direction, but the peak of the low-frequency component occurs at one 1/3-octave frequency band lower than SmE-PW

peak does. Their OASPL distributions are also quite similar, with values within 3 dB of each other, but the SmE-PW

peak occurs at a 10oless shallow angle (120o versus 130o) with respect to the downstream direction. The total Stone

et al. OASPL peak is also about 4 dB higher than the SmE-PW one. Figure 7 also shows that the spectral peaks of

the mid- and high-frequency components in the Stone et al. method predictions fall above 1 kHz, with levels at least

comparable to that of the low-frequency component. The implication from the Stone et al. method prediction shown

in this figure, i.e., that there would be a significant amount of combustor noise present for frequencies higher than

NASA/TM—2012-217671 12
log f

1/3-octave SPL, dB

1 2 3 4

Stone-C1

Stone-C2

Stone-C3

Stone

SmE-PW

log f

1/3-octave SPL, dB

1 2 3 4

Stone-C1

Stone-C2

Stone-C3

Stone

SmE-PW

(a) (b)

log f

1/3-octave SPL, dB

1 2 3 4

Stone-C1

Stone-C2

Stone-C3

Stone

SmE-PW

polar angle, deg

OASPL, dB

0 20 40 60 80 100 120 140 160 180

Stone-C1

Stone-C2

Stone-C3

Stone

SmE-PW

(c) (d)

Figure 7. Comparison of one-foot loss-less combustor-noise predictions using the Stone et al.30 and ANOPP SmE-PW formulas for a

TECH977 turbofan engine at Rolling Takeoff power and Sea-Level-Standard 25 oC conditions; red, green, and blue lines—Stone method

low-, mid-, and high-frequency contributions; black lines—Stone method; dashed cyan lines—SmE-PW method; major tick marks on

vertical axis represent 10 dB increments; (a)–(c): 1/3-octave SPL versus 1/3-octave center frequency in the 90o, 120o, and 150o, directions;

(d): OASPL versus polar angle

1 kHz, is in direct contradiction with prior analyses22, 23, 29, 46 of EVNERT TECH977 acoustic data. Even though there

are some uncertainties in the actual values used for the geometry parameters in Eqs. (9d) and (9e), to determine the

component Strouhal numbers, these are not large enough to invalidate the conclusion that the Stone et al.30 method is

not suitable for combustor-noise predictions for the Honeywell TECH977 research turbofan.

V. Summary and Conclusions

A brief history of semi-empirical combustor noise modeling has been given. The current status of combustor-noise

prediction in NASA ANOPP has been described and near-term improvements have been discussed. The alternate

turbine-transmission factor, described in §IIC, will appear as a user selectable option in the combustor-noise module

GECOR in the next release of ANOPP and the Stone et al.30 method is scheduled to be implemented as a separate

ANOPP module later this year.e Based on the discussion and results presented herein, it is recommended that the

application of the new empirical Stone et al.30 combustor-noise prediction method be limited to situations involving

only General-Electric turbofan engines.

Further progress on an intermediate time frame is probably best achieved by following the research direction

eBurley, C. L., Private Communication

NASA/TM—2012-217671 13
of Schuster and Lieber,41 based partly on insights in Karchmer’s24 work, namely to develop better engine-transfer

functions for combustion noise rather than pursuing empirical multi-peak modeling activities that have less direct

connection to the underlying physics.

Because the impact of other propulsion-noise sources continues to be reduced due to turbofan design trends,

advances in noise-mitigation techniques, and expected aircraft configuration changes, the relative importance of core

noise is expected to greatly increase in the future. Combustor noise, an important core-noise component, needs to be

studied and mitigated in order to meet future noise goals. The noise-source structure in the combustor, including the

indirect one, and the effects of the propagation path through the engine and exhaust nozzle need to be better understood.

In particular, the acoustic consequences of the expected trends toward smaller, highly efficient gas-generator cores and

low-emission fuel-flexible combustors need to be fully investigated since future designs are quite likely to be outside

of the parameter space of existing (semi-empirical) prediction tools. This will require a concerted research effort

involving rig-testing at near-engine conditions, full-engine testing, high-fidelity simulations, as well as reduced-order

and multi-fidelity modeling activities. This will enable the required further development of propulsion-noise prediction

methods and core-noise mitigation technologies.

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36Dunn, D. G. and Peart, N. A., “Aircraft Noise Source and Contour Estimation,” Tech. Rep. NASA CR-114649, NASA, 1973.

37Society of Automotive Engineers International, “Gas Turbine Jet Exhaust Prediction,” Tech. Rep. SAE ARP876 Rev. E, 2006.

38Emmerling, J. J., Kazin, S. B., and Matta, R. K., “Core Engine Noise Control Program, Volume III, Supplement 1—Prediction Methods,”

Tech. Rep. FAA RD-74-125 III-I, FAA, 1976.

39Ho, P. Y. and Doyle, V. L., “Combustion Noise Prediction Update,” Tech. Rep. AIAA Paper 1979-0588, 5th AIAA Aerocoustics Conference,

Seattle, Washington, 1979.

40Hough, J. W. and Weir, D. S., “Small Engine Technology (SET)—Task 13 ANOPP Noise Prediction for Small Engines: Jet, Core, and

Turbine Module Revisions,” Tech. Rep. No. 21-9655, AlliedSignal Engines, Phoenix, Arizona, 1997.

41Schuster, B. and Lieber, L., “Narrowband Model for Gas Turbine Engine Combustion Noise Prediction,” Tech. Rep. AIAA Paper 2006-2677,

12th AIAA/CEAS Aerocoustics Conference, Cambridge, Massachusetts, 2006.

42Mathews, D. C. and Rekos, Jr, N. F., “Prediction and Measurement of Direct Combustion Noise in Turbopropulsion Systems,” J. Aircraft,

Vol. 14, No. 9, 1977, pp. 850–859.

43Pickett, G. F., “Core Engine Noise Due to Temperature Fluctuations Convecting Through Turbine Blade Rows,” Tech. Rep. AIAA Paper

1975-0528, 2nd AIAA Aero-Acoustics Conference, Hampton, Virginia, 1975.

44Zuckerman, R. S., “Core Engine Noise Reduction: Definition and Trends,” Tech. Rep. AIAA Paper 1977-1273, 4th AIAA Aeroacoustics

Conference, Atlanta, Georgia, 1977.

45Weir, D. S., “Engine Validation of Noise and Emission Reduction Technology Phase I,” Tech. Rep. NASA CR-2008-215225, NASA, 2008,

Honeywell Report No. 21-13843, Honeywell Aerospace, Phoenix, Arizona.

46Hultgren, L. S., “Full-Scale Turbofan-Engine Turbine-Transfer Function Determination Using Three Internal Sensors,” Tech. Rep. AIAA

Paper 2011-2912 (NASA TM-2012-217252), 17th AIAA/CEAS Aeroacoustic Conference, Portland, Oregon, 2011.

47Stone, J. R., Krejsa, E. A., and Clark, B. J., “Semi-Empirical Model for Coannular Nozzle Component Noise Extraction and Correlation

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48Stone, J. R., Krejsa, E. A., Clark, B. J., and Berton, J. J., “Jet Noise Modeling for Suppressed and Unsuppressed Aircraft in Simulated

Flight,” Tech. Rep. TM 2009-215524, NASA, 2009.

49Gliebe, P., Mani, R., Shin, H., Mitchel, B., Ashford, G., Salamah, S., and Connell, S., “Aeroacoustic Prediction Codes,” Tech. Rep. NASA

CR-2000-210244, NASA, 2000.

50Heldenbrand, R. W. and Norgren, W. M., “Airesearch QCGAT Program,” Tech. Rep. NASA CR-159758, NASA, 1979.

51Ciepluch, C. C., Davis, D. Y., and Gray, D. E., “Results of NASA’s Energy Efficient Engine Program,” J. Propulsion, Vol. 3, No. 6, 1987,

pp. 560–568.

52Ethell, J. L., “Fuel Economy in Aviation,” Tech. Rep. NASA SP-462, NASA, 1983.

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54Davis, D. Y., “Energy Efficient Engine Flight Propulsion System Final Design and Analysis,” Tech. Rep. NASA CR-168219, NASA, 1985.

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Vol. 2, No. 4, 1991, pp. 357–364.

NASA/TM—2012-217671 15
Table 2. Modified Stone et al30 Low-Frequency Combustor-Noise Component (k=1) Distribution Index

log St1 θ = 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0

-3.60 -59.70 -59.70 -59.70 -59.70 -59.70 -59.20 -58.70 -58.20 -57.20 -56.20

-3.50 -57.70 -57.70 -57.70 -57.70 -57.70 -57.20 -56.70 -56.20 -55.20 -54.20

-3.40 -55.70 -55.70 -55.70 -55.70 -55.70 -55.20 -54.70 -54.20 -53.20 -52.20

-3.30 -53.70 -53.70 -53.70 -53.70 -53.70 -53.20 -52.70 -52.20 -51.20 -50.20

-3.20 -51.70 -51.70 -51.70 -51.70 -51.70 -51.20 -50.70 -50.20 -49.20 -48.20

-3.10 -49.70 -49.70 -49.70 -49.70 -49.70 -49.20 -48.70 -48.20 -47.20 -46.20

-3.00 -47.70 -47.70 -47.70 -47.70 -47.70 -47.20 -46.70 -46.20 -45.20 -44.20

-2.90 -45.70 -45.70 -45.70 -45.70 -45.70 -45.20 -44.70 -44.20 -43.20 -42.20

-2.80 -43.70 -43.70 -43.70 -43.70 -43.70 -43.20 -42.70 -42.20 -41.20 -40.20

-2.70 -41.70 -41.70 -41.70 -41.70 -41.70 -41.20 -40.70 -40.20 -39.20 -38.20

-2.60 -39.70 -39.70 -39.70 -39.70 -39.70 -39.20 -38.70 -38.20 -37.20 -36.20

-2.50 -37.70 -37.70 -37.70 -37.70 -37.70 -37.20 -36.70 -36.20 -35.20 -34.20

-2.40 -35.70 -35.70 -35.70 -35.70 -35.70 -35.20 -34.70 -34.20 -33.20 -32.20

-2.30 -33.70 -33.70 -33.70 -33.70 -33.70 -33.20 -32.70 -32.20 -31.20 -30.20

-2.20 -31.70 -31.70 -31.70 -31.70 -31.70 -31.20 -30.70 -30.20 -29.20 -28.20

-2.10 -29.70 -29.70 -29.70 -29.70 -29.70 -29.20 -28.70 -28.20 -27.20 -26.20

-2.00 -27.70 -27.70 -27.70 -27.70 -27.70 -27.20 -26.70 -26.20 -25.20 -24.20

-1.90 -25.70 -25.70 -25.70 -25.70 -25.70 -25.20 -24.70 -24.20 -23.20 -22.20

-1.80 -23.70 -23.70 -23.70 -23.70 -23.70 -23.20 -22.70 -22.20 -21.20 -20.20

-1.70 -21.70 -21.70 -21.70 -21.70 -21.70 -21.20 -20.70 -20.20 -19.20 -18.20

-1.60 -19.70 -19.70 -19.70 -19.70 -19.70 -19.20 -18.70 -18.20 -17.20 -16.20

-1.50 -17.70 -17.70 -17.70 -17.70 -17.70 -17.20 -16.70 -16.20 -15.20 -14.20

-1.40 -15.70 -15.70 -15.70 -15.70 -15.70 -15.20 -14.70 -14.20 -13.20 -12.20

-1.30 -13.70 -13.70 -13.70 -13.70 -13.70 -13.20 -12.70 -12.20 -11.20 -10.20

-1.20 -11.70 -11.70 -11.70 -11.70 -11.70 -11.20 -10.70 -10.20 -9.20 -8.20

-1.10 -9.70 -9.70 -9.70 -9.70 -9.70 -9.20 -8.70 -8.20 -7.20 -6.20

-1.00 -10.80 -10.80 -10.80 -10.80 -10.80 -10.30 -9.80 -9.30 -8.30 -7.30

-0.90 -13.30 -13.30 -13.30 -13.30 -13.30 -12.80 -12.30 -11.80 -10.80 -9.80

-0.80 -17.30 -17.30 -17.30 -17.30 -17.30 -16.80 -16.30 -15.80 -14.80 -13.80

-0.70 -22.30 -22.30 -22.30 -22.30 -22.30 -21.80 -21.30 -20.80 -19.80 -18.80

-0.60 -28.30 -28.30 -28.30 -28.30 -28.30 -27.80 -27.30 -26.80 -25.80 -24.80

-0.50 -34.30 -34.30 -34.30 -34.30 -34.30 -33.80 -33.30 -32.80 -31.80 -30.80

-0.40 -40.30 -40.30 -40.30 -40.30 -40.30 -39.80 -39.30 -38.80 -37.80 -36.80

-0.30 -46.30 -46.30 -46.30 -46.30 -46.30 -45.80 -45.30 -44.80 -43.80 -42.80

-0.20 -52.30 -52.30 -52.30 -52.30 -52.30 -51.80 -51.30 -50.80 -49.80 -48.80

-0.10 -58.30 -58.30 -58.30 -58.30 -58.30 -57.80 -57.30 -56.80 -55.80 -54.80

0.00 -64.30 -64.30 -64.30 -64.30 -64.30 -63.80 -63.30 -62.80 -61.80 -60.80

NASA/TM—2012-217671 16
Table 2. Modified Stone et al30 Low-Frequency Combustor-Noise Component (k=1) Distribution Index, continued (1)

log St1 θ = 90.0 100.0 110.0 120.0 130.0 140.0 150.0 160.0 170.0 180.0

-3.60 -56.20 -54.70 -53.00 -50.50 -46.90 -47.90 -50.90 -55.90 -60.90 -65.90

-3.50 -54.20 -52.70 -51.00 -48.50 -44.90 -45.90 -48.90 -53.90 -58.90 -63.90

-3.40 -52.20 -50.70 -49.00 -46.50 -42.90 -43.90 -46.90 -51.90 -56.90 -61.90

-3.30 -50.20 -48.70 -47.00 -44.50 -40.90 -41.90 -44.90 -49.90 -54.90 -59.90

-3.20 -48.20 -46.70 -45.00 -42.50 -38.90 -39.90 -42.90 -47.90 -52.90 -57.90

-3.10 -46.20 -44.70 -43.00 -40.50 -36.90 -37.90 -40.90 -45.90 -50.90 -55.90

-3.00 -44.20 -42.70 -41.00 -38.50 -34.90 -35.90 -38.90 -43.90 -48.90 -53.90

-2.90 -42.20 -40.70 -39.00 -36.50 -32.90 -33.90 -36.90 -41.90 -46.90 -51.90

-2.80 -40.20 -38.70 -37.00 -34.50 -30.90 -31.90 -34.90 -39.90 -44.90 -49.90

-2.70 -38.20 -36.70 -35.00 -32.50 -28.90 -29.90 -32.90 -37.90 -42.90 -47.90

-2.60 -36.20 -34.70 -33.00 -30.50 -26.90 -27.90 -30.90 -35.90 -40.90 -45.90

-2.50 -34.20 -32.70 -31.00 -28.50 -24.90 -25.90 -28.90 -33.90 -38.90 -43.90

-2.40 -32.20 -30.70 -29.00 -26.50 -22.90 -23.90 -26.90 -31.90 -36.90 -41.90

-2.30 -30.20 -28.70 -27.00 -24.50 -20.90 -21.90 -24.90 -29.90 -34.90 -39.90

-2.20 -28.20 -26.70 -25.00 -22.50 -18.90 -19.90 -22.90 -27.90 -32.90 -37.90

-2.10 -26.20 -24.70 -23.00 -20.50 -16.90 -17.90 -20.90 -25.90 -30.90 -35.90

-2.00 -24.20 -22.70 -21.00 -18.50 -15.00 -16.00 -19.00 -24.00 -29.00 -34.00

-1.90 -22.20 -20.70 -19.00 -16.50 -13.20 -14.20 -17.20 -22.20 -27.20 -32.20

-1.80 -20.20 -18.70 -17.00 -14.50 -11.50 -12.50 -15.50 -20.50 -25.50 -30.50

-1.70 -18.20 -16.70 -15.00 -12.50 -9.90 -10.90 -13.90 -18.90 -23.90 -28.90

-1.60 -16.20 -14.70 -13.00 -10.50 -8.40 -9.40 -12.40 -17.40 -22.40 -27.40

-1.50 -14.20 -12.70 -11.00 -8.60 -6.90 -7.90 -10.90 -15.90 -20.90 -25.90

-1.40 -12.20 -10.70 -9.00 -6.80 -5.40 -6.40 -9.40 -14.40 -19.40 -24.40

-1.30 -10.20 -8.70 -7.00 -5.10 -3.90 -4.90 -7.90 -12.90 -17.90 -22.90

-1.20 -8.20 -6.70 -5.20 -3.80 -2.70 -3.70 -6.70 -11.70 -16.70 -21.70

-1.10 -6.20 -4.90 -3.70 -2.70 -1.70 -2.70 -5.70 -10.70 -15.70 -20.70

-1.00 -7.30 -6.00 -4.70 -3.60 -2.50 -3.50 -6.50 -11.50 -16.50 -21.50

-0.90 -9.80 -8.50 -7.20 -6.10 -5.00 -6.00 -9.00 -14.00 -19.00 -24.00

-0.80 -13.80 -12.50 -11.20 -10.10 -9.00 -10.00 -13.00 -18.00 -23.00 -28.00

-0.70 -18.80 -17.50 -16.20 -15.10 -14.00 -15.00 -18.00 -23.00 -28.00 -33.00

-0.60 -24.80 -23.50 -22.20 -21.10 -20.00 -21.00 -24.00 -29.00 -34.00 -39.00

-0.50 -30.80 -29.50 -28.20 -27.10 -26.00 -27.00 -30.00 -35.00 -40.00 -45.00

-0.40 -36.80 -35.50 -34.20 -33.10 -32.00 -33.00 -36.00 -41.00 -46.00 -51.00

-0.30 -42.80 -41.50 -40.20 -39.10 -38.00 -39.00 -42.00 -47.00 -52.00 -57.00

-0.20 -48.80 -47.50 -46.20 -45.10 -44.00 -45.00 -48.00 -53.00 -58.00 -63.00

-0.10 -54.80 -53.50 -52.20 -51.10 -50.00 -51.00 -54.00 -59.00 -64.00 -69.00

0.00 -60.80 -59.50 -58.20 -57.10 -56.00 -57.00 -60.00 -65.00 -70.00 -75.00

NASA/TM—2012-217671 17
Table 2. Modified Stone et al30 Low-Frequency Combustor-Noise Component (k=1) Distribution Index, continued (2)

log St1 θ = 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0

0.00 -64.30 -64.30 -64.30 -64.30 -64.30 -63.80 -63.30 -62.80 -61.80 -60.80

0.10 -70.30 -70.30 -70.30 -70.30 -70.30 -69.80 -69.30 -68.80 -67.80 -66.80

0.20 -76.30 -76.30 -76.30 -76.30 -76.30 -75.80 -75.30 -74.80 -73.80 -72.80

0.30 -82.30 -82.30 -82.30 -82.30 -82.30 -81.80 -81.30 -80.80 -79.80 -78.80

0.40 -88.30 -88.30 -88.30 -88.30 -88.30 -87.80 -87.30 -86.80 -85.80 -84.80

0.50 -94.30 -94.30 -94.30 -94.30 -94.30 -93.80 -93.30 -92.80 -91.80 -90.80

0.60 -100.30 -100.30 -100.30 -100.30 -100.30 -99.80 -99.30 -98.80 -97.80 -96.80

0.70 -106.30 -106.30 -106.30 -106.30 -106.30 -105.80 -105.30 -104.80 -103.80 -102.80

0.80 -112.30 -112.30 -112.30 -112.30 -112.30 -111.80 -111.30 -110.80 -109.80 -108.80

0.90 -118.30 -118.30 -118.30 -118.30 -118.30 -117.80 -117.30 -116.80 -115.80 -114.80

1.00 -124.30 -124.30 -124.30 -124.30 -124.30 -123.80 -123.30 -122.80 -121.80 -120.80

1.10 -130.30 -130.30 -130.30 -130.30 -130.30 -129.80 -129.30 -128.80 -127.80 -126.80

1.20 -136.30 -136.30 -136.30 -136.30 -136.30 -135.80 -135.30 -134.80 -133.80 -132.80

1.30 -142.30 -142.30 -142.30 -142.30 -142.30 -141.80 -141.30 -140.80 -139.80 -138.80

1.40 -148.30 -148.30 -148.30 -148.30 -148.30 -147.80 -147.30 -146.80 -145.80 -144.80

1.50 -154.30 -154.30 -154.30 -154.30 -154.30 -153.80 -153.30 -152.80 -151.80 -150.80

1.60 -160.30 -160.30 -160.30 -160.30 -160.30 -159.80 -159.30 -158.80 -157.80 -156.80

1.70 -166.30 -166.30 -166.30 -166.30 -166.30 -165.80 -165.30 -164.80 -163.80 -162.80

1.80 -172.30 -172.30 -172.30 -172.30 -172.30 -171.80 -171.30 -170.80 -169.80 -168.80

1.90 -178.30 -178.30 -178.30 -178.30 -178.30 -177.80 -177.30 -176.80 -175.80 -174.80

2.00 -184.30 -184.30 -184.30 -184.30 -184.30 -183.80 -183.30 -182.80 -181.80 -180.80

2.10 -190.30 -190.30 -190.30 -190.30 -190.30 -189.80 -189.30 -188.80 -187.80 -186.80

2.20 -196.30 -196.30 -196.30 -196.30 -196.30 -195.80 -195.30 -194.80 -193.80 -192.80

2.30 -202.30 -202.30 -202.30 -202.30 -202.30 -201.80 -201.30 -200.80 -199.80 -198.80

2.40 -208.30 -208.30 -208.30 -208.30 -208.30 -207.80 -207.30 -206.80 -205.80 -204.80

2.50 -214.30 -214.30 -214.30 -214.30 -214.30 -213.80 -213.30 -212.80 -211.80 -210.80

2.60 -220.30 -220.30 -220.30 -220.30 -220.30 -219.80 -219.30 -218.80 -217.80 -216.80

2.70 -226.30 -226.30 -226.30 -226.30 -226.30 -225.80 -225.30 -224.80 -223.80 222.80

2.80 -232.30 -232.30 -232.30 -232.30 -232.30 -231.80 -231.30 -230.80 -229.80 -228.80

2.90 -238.30 -238.30 -238.30 -238.30 -238.30 -237.80 -237.30 -236.80 -235.80 -234.80

3.00 -244.30 -244.30 -244.30 -244.30 -244.30 -243.80 -243.30 -242.80 -241.80 -240.80

3.10 -250.30 -250.30 -250.30 -250.30 -250.30 -249.80 -249.30 -248.80 -247.80 -246.80

3.20 -256.30 -256.30 -256.30 -256.30 -256.30 -255.80 -255.30 -254.80 -253.80 -252.80

3.30 -262.30 -262.30 -262.30 -262.30 -262.30 -261.80 -261.30 -260.80 -259.80 -258.80

3.40 -268.30 -268.30 -268.30 -268.30 -268.30 -267.80 -267.30 -266.80 -265.80 264.80

3.50 -274.30 -274.30 -274.30 -274.30 -274.30 -273.80 -273.30 -272.80 -271.80 -270.80

3.60 -280.30 -280.30 -280.30 -280.30 -280.30 -279.80 -279.30 -278.80 -277.80 -276.80

∆OASPL -3.500 -3.500 -3.500 -3.500 -3.500 -3.000 -2.500 -2.000 -1.000 0.000

NASA/TM—2012-217671 18
Table 2. Modified Stone et al30 Low-Frequency Combustor-Noise Component (k=1) Distribution Index, continued (3)

log St1 θ = 90.0 100.0 110.0 120.0 130.0 140.0 150.0 160.0 170.0 180.0

0.00 -60.80 -59.50 -58.20 -57.10 -56.00 -57.00 -60.00 -65.00 -70.00 -75.00

0.10 -66.80 -65.50 -64.20 -63.10 -62.00 -63.00 -66.00 -71.00 -76.00 -81.00

0.20 -72.80 -71.50 -70.20 -69.10 -68.00 -69.00 -72.00 -77.00 -82.00 -87.00

0.30 -78.80 -77.50 -76.20 -75.10 -74.00 -75.00 -78.00 -83.00 -88.00 -93.00

0.40 -84.80 -83.50 -82.20 -81.10 -80.00 -81.00 -84.00 -89.00 -94.00 -99.00

0.50 -90.80 -89.50 -88.20 -87.10 -86.00 -87.00 -90.00 -95.00 -100.00 -105.00

0.60 -96.80 -95.50 -94.20 -93.10 -92.00 -93.00 -96.00 -101.00 -106.00 -111.00

0.70 -102.80 -101.50 -100.20 -99.10 -98.00 -99.00 -102.00 -107.00 -112.00 -117.00

0.80 -108.80 -107.50 -106.20 -105.10 -104.00 -105.00 -108.00 -113.00 -118.00 -123.00

0.90 -114.80 -113.50 -112.20 -111.10 -110.00 -111.00 -114.00 -119.00 -124.00 -129.00

1.00 -120.80 -119.50 -118.20 -117.10 -116.00 -117.00 -120.00 -125.00 -130.00 -135.00

1.10 -126.80 -125.50 -124.20 -123.10 -122.00 -123.00 -126.00 -131.00 -136.00 -141.00

1.20 -132.80 -131.50 -130.20 -129.10 -128.00 -129.00 -132.00 -137.00 -142.00 -147.00

1.30 -138.80 -137.50 -136.20 -135.10 -134.00 -135.00 -138.00 -143.00 -148.00 -153.00

1.40 -144.80 -143.50 -142.20 -141.10 -140.00 -141.00 -144.00 -149.00 -154.00 -159.00

1.50 -150.80 -149.50 -148.20 -147.10 -146.00 -147.00 -150.00 -155.00 -160.00 -165.00

1.60 -156.80 -155.50 -154.20 -153.10 -152.00 -153.00 -156.00 -161.00 -166.00 -171.00

1.70 -162.80 -161.50 -160.20 -159.10 -158.00 -159.00 -162.00 -167.00 -172.00 -177.00

1.80 -168.80 -167.50 -166.20 -165.10 -164.00 -165.00 -168.00 -173.00 -178.00 -183.00

1.90 -174.80 -173.50 -172.20 -171.10 -170.00 -171.00 -174.00 -179.00 -184.00 -189.00

2.00 -180.80 -179.50 -178.20 -177.10 -176.00 -177.00 -180.00 -185.00 -190.00 -195.00

2.10 -186.80 -185.50 -184.20 -183.10 -182.00 -183.00 -186.00 -191.00 -196.00 -201.00

2.20 -192.80 -191.50 -190.20 -189.10 -188.00 -189.00 -192.00 -197.00 -202.00 -207.00

2.30 -198.80 -197.50 -196.20 -195.10 -194.00 -195.00 -198.00 -203.00 -208.00 -213.00

2.40 -204.80 -203.50 -202.20 -201.10 -200.00 -201.00 -204.00 -209.00 -214.00 -219.00

2.50 -210.80 -209.50 -208.20 -207.10 -206.00 -207.00 -210.00 -215.00 -220.00 -225.00

2.60 -216.80 -215.50 -214.20 -213.10 -212.00 -213.00 -216.00 -221.00 -226.00 -231.00

2.70 -222.80 -221.50 -220.20 -219.10 -218.00 -219.00 -222.00 -227.00 -232.00 -237.00

2.80 -228.80 -227.50 -226.20 -225.10 -224.00 -225.00 -228.00 -233.00 -238.00 -243.00

2.90 -234.80 -233.50 -232.20 -231.10 -230.00 -231.00 -234.00 -239.00 -244.00 -249.00

3.00 -240.80 -239.50 -238.20 -237.10 -236.00 -237.00 -240.00 -245.00 -250.00 -255.00

3.10 -246.80 -245.50 -244.20 -243.10 -242.00 -243.00 -246.00 -251.00 -256.00 -261.00

3.20 -252.80 -251.50 -250.20 -249.10 -248.00 -249.00 -252.00 -257.00 -262.00 -267.00

3.30 -258.80 -257.50 -256.20 -255.10 -254.00 -255.00 -258.00 -263.00 -268.00 -273.00

3.40 -264.80 -263.50 -262.20 -261.10 -260.00 -261.00 -264.00 -269.00 -274.00 -279.00

3.50 -270.80 -269.50 -268.20 -267.10 -266.00 -267.00 -270.00 -275.00 -280.00 -285.00

3.60 -276.80 -275.50 -274.20 -273.10 -272.00 -273.00 -276.00 -281.00 -286.00 -291.00

∆OASPL 0.000 1.383 2.801 4.268 5.590 4.590 1.590 -3.410 -8.410 -13.410

NASA/TM—2012-217671 19
Table 3. Modified Stone et al30 Mid-Frequency Combustor-Noise Component (k=2) Distribution Index

log St2 θ = 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0

-3.60 -176.31 -175.31 -174.31 -173.31 -172.31 -170.81 -169.81 -168.81 -168.31 -167.81

-3.50 -170.31 -169.31 -168.31 -167.31 -166.31 -164.81 -163.81 -162.81 -162.31 -161.81

-3.40 -164.31 -163.31 -162.31 -161.31 -160.31 -158.81 -157.81 -156.81 -156.31 -155.81

-3.30 -158.31 -157.31 -156.31 -155.31 -154.31 -152.81 -151.81 -150.81 -150.31 -149.81

-3.20 -152.31 -151.31 -150.31 -149.31 -148.31 -146.81 -145.81 -144.81 -144.31 -143.81

-3.10 -146.31 -145.31 -144.31 -143.31 -142.31 -140.81 -139.81 -138.81 -138.31 -137.81

-3.00 -140.31 -139.31 -138.31 -137.31 -136.31 -134.81 -133.81 -132.81 -132.31 -131.81

-2.90 -134.31 -133.31 -132.31 -131.31 -130.31 -128.81 -127.81 -126.81 -126.31 -125.81

-2.80 -128.31 -127.31 -126.31 -125.31 -124.31 -122.81 -121.81 -120.81 -120.31 -119.81

-2.70 -122.31 -121.31 -120.31 -119.31 -118.31 -116.81 -115.81 -114.81 -114.31 -113.81

-2.60 -116.31 -115.31 -114.31 -113.31 -112.31 -110.81 -109.81 -108.81 -108.31 -107.81

-2.50 -110.31 -109.31 -108.31 -107.31 -106.31 -104.81 -103.81 -102.81 -102.31 -101.81

-2.40 -104.31 -103.31 -102.31 -101.31 -100.31 -98.81 -97.81 -96.81 -96.31 -95.81

-2.30 -98.31 -97.31 -96.31 -95.31 -94.31 -92.81 -91.81 -90.81 -90.31 -89.81

-2.20 -92.31 -91.31 -90.31 -89.31 -88.31 -86.81 -85.81 -84.81 -84.31 -83.81

-2.10 -86.31 -85.31 -84.31 -83.31 -82.31 -80.81 -79.81 -78.81 -78.31 -77.81

-2.00 -80.31 -79.31 -78.31 -77.31 -76.31 -74.81 -73.81 -72.81 -72.31 -71.81

-1.90 -74.31 -73.31 -72.31 -71.31 -70.31 -68.81 -67.81 -66.81 -66.31 -65.81

-1.80 -68.31 -67.31 -66.31 -65.31 -64.31 -62.81 -61.81 -60.81 -60.31 -59.81

-1.70 -62.31 -61.31 -60.31 -59.31 -58.31 -56.81 -55.81 -54.81 -54.31 -53.81

-1.60 -56.31 -55.31 -54.31 -53.31 -52.31 -50.81 -49.81 -48.81 -48.31 -47.81

-1.50 -50.31 -49.31 -48.31 -47.31 -46.31 -44.81 -43.81 -42.81 -42.31 -41.81

-1.40 -44.31 -43.31 -42.31 -41.31 -40.31 -38.81 -37.81 -36.81 -36.31 -35.81

-1.30 -38.31 -37.31 -36.31 -35.31 -34.31 -32.81 -31.81 -30.81 -30.31 -29.81

-1.20 -32.31 -31.31 -30.31 -29.31 -28.31 -26.81 -25.81 -24.81 -24.31 -23.81

-1.10 -26.31 -25.31 -24.31 -23.31 -22.31 -20.81 -19.81 -18.81 -18.31 -17.81

-1.00 -20.31 -19.31 -18.31 -17.31 -16.31 -14.81 -13.81 -12.81 -12.31 -11.81

-0.90 -16.31 -15.31 -14.31 -13.31 -12.31 -10.81 -9.81 -8.81 -8.31 -7.81

-0.80 -14.31 -13.31 -12.31 -11.31 -10.31 -8.81 -7.81 -6.81 -6.31 -5.81

-0.70 -15.01 -14.01 -13.01 -12.01 -11.01 -9.51 -8.51 -7.51 -7.01 -6.51

-0.60 -16.91 -15.91 -14.91 -13.91 -12.91 -11.41 -10.41 -9.41 -8.91 -8.41

-0.50 -19.81 -18.81 -17.81 -16.81 -15.81 -14.31 -13.31 -12.31 -11.81 -11.31

-0.40 -23.81 -22.81 -21.81 -20.81 -19.81 -18.31 -17.31 -16.31 -15.81 -15.31

-0.30 -28.81 -27.81 -26.81 -25.81 -24.81 -23.31 -22.31 -21.31 -20.81 -20.31

-0.20 -34.11 -33.11 -32.11 -31.11 -30.11 -28.61 -27.61 -26.61 -26.11 -25.61

-0.10 -39.71 -38.71 -37.71 -36.71 -35.71 -34.21 -33.21 -32.21 -31.71 -31.21

0.00 -45.71 -44.71 -43.71 -42.71 -41.71 -40.21 -39.21 -38.21 -37.71 -37.21

NASA/TM—2012-217671 20
Table 3. Modified Stone et al30 Mid-Frequency Combustor-Noise Component (k=2) Distribution Index, continued (1)

log St2 θ = 90.0 100.0 110.0 120.0 130.0 140.0 150.0 160.0 170.0 180.0

-3.60 -167.81 -167.31 -166.81 -166.31 -165.81 -167.31 -169.51 -171.71 -173.91 -176.11

-3.50 -161.81 -161.31 -160.81 -160.31 -159.81 -161.31 -163.51 -165.71 -167.91 -170.11

-3.40 -155.81 -155.31 -154.81 -154.31 -153.81 -155.31 -157.51 -159.71 -161.91 -164.11

-3.30 -149.81 -149.31 -148.81 -148.31 -147.81 -149.31 -151.51 -153.71 -155.91 -158.11

-3.20 -143.81 -143.31 -142.81 -142.31 -141.81 -143.31 -145.51 -147.71 -149.91 -152.11

-3.10 -137.81 -137.31 -136.81 -136.31 -135.81 -137.31 -139.51 -141.71 -143.91 -146.11

-3.00 -131.81 -131.31 -130.81 -130.31 -129.81 -131.31 -133.51 -135.71 -137.91 -140.11

-2.90 -125.81 -125.31 -124.81 -124.31 -123.81 -125.31 -127.51 -129.71 -131.91 -134.11

-2.80 -119.81 -119.31 -118.81 -118.31 -117.81 -119.31 -121.51 -123.71 -125.91 -128.11

-2.70 -113.81 -113.31 -112.81 -112.31 -111.81 -113.31 -115.51 -117.71 -119.91 -122.11

-2.60 -107.81 -107.31 -106.81 -106.31 -105.81 -107.31 -109.51 -111.71 -113.91 -116.11

-2.50 -101.81 -101.31 -100.81 -100.31 -99.81 -101.31 -103.51 -105.71 -107.91 -110.11

-2.40 -95.81 -95.31 -94.81 -94.31 -93.81 -95.31 -97.51 -99.71 -101.91 -104.11

-2.30 -89.81 -89.31 -88.81 -88.31 -87.81 -89.31 -91.51 -93.71 -95.91 -98.11

-2.20 -83.81 -83.31 -82.81 -82.31 -81.81 -83.31 -85.51 -87.71 -89.91 -92.11

-2.10 -77.81 -77.31 -76.81 -76.31 -75.81 -77.31 -79.51 -81.71 -83.91 -86.11

-2.00 -71.81 -71.31 -70.81 -70.31 -69.81 -71.31 -73.51 -75.71 -77.91 -80.11

-1.90 -65.81 -65.31 -64.81 -64.31 -63.81 -65.31 -67.51 -69.71 -71.91 -74.11

-1.80 -59.81 -59.31 -58.81 -58.31 -57.81 -59.31 -61.51 -63.71 -65.91 -68.11

-1.70 -53.81 -53.31 -52.81 -52.31 -51.81 -53.31 -55.51 -57.71 -59.91 -62.11

-1.60 -47.81 -47.31 -46.81 -46.31 -45.81 -47.31 -49.51 -51.71 -53.91 -56.11

-1.50 -41.81 -41.31 -40.81 -40.31 -39.81 -41.31 -43.51 -45.71 -47.91 -50.11

-1.40 -35.81 -35.31 -34.81 -34.31 -33.81 -35.31 -37.51 -39.71 -41.91 -44.11

-1.30 -29.81 -29.31 -28.81 -28.31 -27.81 -29.31 -31.51 -33.71 -35.91 -38.11

-1.20 -23.81 -23.31 -22.81 -22.31 -21.81 -23.31 -25.51 -27.71 -29.91 -32.11

-1.10 -17.81 -17.31 -16.81 -16.31 -15.81 -17.31 -19.51 -21.71 -23.91 -26.11

-1.00 -11.81 -11.31 -10.81 -10.31 -9.81 -11.31 -13.51 -15.71 -17.91 -20.11

-0.90 -7.81 -7.31 -6.81 -6.31 -5.81 -7.31 -9.51 -11.71 -13.91 -16.11

-0.80 -5.81 -5.31 -4.81 -4.31 -3.81 -5.31 -7.51 -9.71 -11.91 -14.11

-0.70 -6.51 -6.01 -5.51 -5.01 -4.51 -6.01 -8.21 -10.41 -12.61 -14.81

-0.60 -8.41 -7.91 -7.41 -6.91 -6.41 -7.91 -10.11 -12.31 -14.51 -16.71

-0.50 -11.31 -10.81 -10.31 -9.81 -9.31 -10.81 -13.01 -15.21 -17.41 -19.61

-0.40 -15.31 -14.81 -14.31 -13.81 -13.31 -14.81 -17.01 -19.21 -21.41 -23.61

-0.30 -20.31 -19.81 -19.31 -18.81 -18.31 -19.81 -22.01 -24.21 -26.41 -28.61

-0.20 -25.61 -25.11 -24.61 -24.11 -23.61 -25.11 -27.31 -29.51 -31.71 -33.91

-0.10 -31.21 -30.71 -30.21 -29.71 -29.21 -30.71 -32.91 -35.11 -37.31 -39.51

0.00 -37.21 -36.71 -36.21 -35.71 -35.21 -36.71 -38.91 -41.11 -43.31 -45.51

NASA/TM—2012-217671 21
Table 3. Modified Stone et al30 Mid-Frequency Combustor-Noise Component (k=2) Distribution Index, continued (2)

log St2 θ = 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0

0.00 -45.71 -44.71 -43.71 -42.71 -41.71 -40.21 -39.21 -38.21 -37.71 -37.21

0.10 -51.71 -50.71 -49.71 -48.71 -47.71 -46.21 -45.21 -44.21 -43.71 -43.21

0.20 -57.71 -56.71 -55.71 -54.71 -53.71 -52.21 -51.21 -50.21 -49.71 -49.21

0.30 -63.71 -62.71 -61.71 -60.71 -59.71 -58.21 -57.21 -56.21 -55.71 -55.21

0.40 -69.71 -68.71 -67.71 -66.71 -65.71 -64.21 -63.21 -62.21 -61.71 -61.21

0.50 -75.71 -74.71 -73.71 -72.71 -71.71 -70.21 -69.21 -68.21 -67.71 -67.21

0.60 -81.71 -80.71 -79.71 -78.71 -77.71 -76.21 -75.21 -74.21 -73.71 -73.21

0.70 -87.71 -86.71 -85.71 -84.71 -83.71 -82.21 -81.21 -80.21 -79.71 -79.21

0.80 -93.71 -92.71 -91.71 -90.71 -89.71 -88.21 -87.21 -86.21 -85.71 -85.21

0.90 -99.71 -98.71 -97.71 -96.71 -95.71 -94.21 -93.21 -92.21 -91.71 -91.21

1.00 -105.71 -104.71 -103.71 -102.71 -101.71 -100.21 -99.21 -98.21 -97.71 -97.21

1.10 -111.71 -110.71 -109.71 -108.71 -107.71 -106.21 -105.21 -104.21 -103.71 -103.21

1.20 -117.71 -116.71 -115.71 -114.71 -113.71 -112.21 -111.21 -110.21 -109.71 -109.21

1.30 -123.71 -122.71 -121.71 -120.71 -119.71 -118.21 -117.21 -116.21 -115.71 -115.21

1.40 -129.71 -128.71 -127.71 -126.71 -125.71 -124.21 -123.21 -122.21 -121.71 -121.21

1.50 -135.71 -134.71 -133.71 -132.71 -131.71 -130.21 -129.21 -128.21 -127.71 -127.21

1.60 -141.71 -140.71 -139.71 -138.71 -137.71 -136.21 -135.21 -134.21 -133.71 -133.21

1.70 -147.71 -146.71 -145.71 -144.71 -143.71 -142.21 -141.21 -140.21 -139.71 -139.21

1.80 -153.71 -152.71 -151.71 -150.71 -149.71 -148.21 -147.21 -146.21 -145.71 -145.21

1.90 -159.71 -158.71 -157.71 -156.71 -155.71 -154.21 -153.21 -152.21 -151.71 -151.21

2.00 -165.71 -164.71 -163.71 -162.71 -161.71 -160.21 -159.21 -158.21 -157.71 -157.21

2.10 -171.71 -170.71 -169.71 -168.71 -167.71 -166.21 -165.21 -164.21 -163.71 -163.21

2.20 -177.71 -176.71 -175.71 -174.71 -173.71 -172.21 -171.21 -170.21 -169.71 -169.21

2.30 -183.71 -182.71 -181.71 -180.71 -179.71 -178.21 -177.21 -176.21 -175.71 -175.21

2.40 -189.71 -188.71 -187.71 -186.71 -185.71 -184.21 -183.21 -182.21 -181.71 -181.21

2.50 -195.71 -194.71 -193.71 -192.71 -191.71 -190.21 -189.21 -188.21 -187.71 -187.21

2.60 -201.71 -200.71 -199.71 -198.71 -197.71 -196.21 -195.21 -194.21 -193.71 -193.21

2.70 -207.71 -206.71 -205.71 -204.71 -203.71 -202.21 -201.21 -200.21 -199.71 -199.21

2.80 -213.71 -212.71 -211.71 -210.71 -209.71 -208.21 -207.21 -206.21 -205.71 -205.21

2.90 -219.71 -218.71 -217.71 -216.71 -215.71 -214.21 -213.21 -212.21 -211.71 -211.21

3.00 -225.71 -224.71 -223.71 -222.71 -221.71 -220.21 -219.21 -218.21 -217.71 -217.21

3.10 -231.71 -230.71 -229.71 -228.71 -227.71 -226.21 -225.21 -224.21 -223.71 -223.21

3.20 -237.71 -236.71 -235.71 -234.71 -233.71 -232.21 -231.21 -230.21 -229.71 -229.21

3.30 -243.71 -242.71 -241.71 -240.71 -239.71 -238.21 -237.21 -236.21 -235.71 -235.21

3.40 -249.71 -248.71 -247.71 -246.71 -245.71 -244.21 -243.21 -242.21 -241.71 -241.21

3.50 -255.71 -254.71 -253.71 -252.71 -251.71 -250.21 -249.21 -248.21 -247.71 -247.21

3.60 -261.71 -260.71 -259.71 -258.71 -257.71 -256.21 -255.21 -254.21 -253.71 -253.21

∆OASPL -8.500 -7.500 -6.500 -5.500 -4.500 -3.000 -2.000 -1.000 -0.500 0.000

NASA/TM—2012-217671 22
Table 3. Modified Stone et al30 Mid-Frequency Combustor-Noise Component (k=2) Distribution Index, continued (3)

log St2 θ = 90.0 100.0 110.0 120.0 130.0 140.0 150.0 160.0 170.0 180.0

0.00 -37.21 -36.71 -36.21 -35.71 -35.21 -36.71 -38.91 -41.11 -43.31 -45.51

0.10 -43.21 -42.71 -42.21 -41.71 -41.21 -42.71 -44.91 -47.11 -49.31 -51.51

0.20 -49.21 -48.71 -48.21 -47.71 -47.21 -48.71 -50.91 -53.11 -55.31 -57.51

0.30 -55.21 -54.71 -54.21 -53.71 -53.21 -54.71 -56.91 -59.11 -61.31 -63.51

0.40 -61.21 -60.71 -60.21 -59.71 -59.21 -60.71 -62.91 -65.11 -67.31 -69.51

0.50 -67.21 -66.71 -66.21 -65.71 -65.21 -66.71 -68.91 -71.11 -73.31 -75.51

0.60 -73.21 -72.71 -72.21 -71.71 -71.21 -72.71 -74.91 -77.11 -79.31 -81.51

0.70 -79.21 -78.71 -78.21 -77.71 -77.21 -78.71 -80.91 -83.11 -85.31 -87.51

0.80 -85.21 -84.71 -84.21 -83.71 -83.21 -84.71 -86.91 -89.11 -91.31 -93.51

0.90 -91.21 -90.71 -90.21 -89.71 -89.21 -90.71 -92.91 -95.11 -97.31 -99.51

1.00 -97.21 -96.71 -96.21 -95.71 -95.21 -96.71 -98.91 -101.11 -103.31 -105.51

1.10 -103.21 -102.71 -102.21 -101.71 -101.21 -102.71 -104.91 -107.11 -109.31 -111.51

1.20 -109.21 -108.71 -108.21 -107.71 -107.21 -108.71 -110.91 -113.11 -115.31 -117.51

1.30 -115.21 -114.71 -114.21 -113.71 -113.21 -114.71 -116.91 -119.11 -121.31 -123.51

1.40 -121.21 -120.71 -120.21 -119.71 -119.21 -120.71 -122.91 -125.11 -127.31 -129.51

1.50 -127.21 -126.71 -126.21 -125.71 -125.21 -126.71 -128.91 -131.11 -133.31 -135.51

1.60 -133.21 -132.71 -132.21 -131.71 -131.21 -132.71 -134.91 -137.11 -139.31 -141.51

1.70 -139.21 -138.71 -138.21 -137.71 -137.21 -138.71 -140.91 -143.11 -145.31 -147.51

1.80 -145.21 -144.71 -144.21 -143.71 -143.21 -144.71 -146.91 -149.11 -151.31 -153.51

1.90 -151.21 -150.71 -150.21 -149.71 -149.21 -150.71 -152.91 -155.11 -157.31 -159.51

2.00 -157.21 -156.71 -156.21 -155.71 -155.21 -156.71 -158.91 -161.11 -163.31 -165.51

2.10 -163.21 -162.71 -162.21 -161.71 -161.21 -162.71 -164.91 -167.11 -169.31 -171.51

2.20 -169.21 -168.71 -168.21 -167.71 -167.21 -168.71 -170.91 -173.11 -175.31 -177.51

2.30 -175.21 -174.71 -174.21 -173.71 -173.21 -174.71 -176.91 -179.11 -181.31 -183.51

2.40 -181.21 -180.71 -180.21 -179.71 -179.21 -180.71 -182.91 -185.11 -187.31 -189.51

2.50 -187.21 -186.71 -186.21 -185.71 -185.21 -186.71 -188.91 -191.11 -193.31 -195.51

2.60 -193.21 -192.71 -192.21 -191.71 -191.21 -192.71 -194.91 -197.11 -199.31 -201.51

2.70 -199.21 -198.71 -198.21 -197.71 -197.21 -198.71 -200.91 -203.11 -205.31 -207.51

2.80 -205.21 -204.71 -204.21 -203.71 -203.21 -204.71 -206.91 -209.11 -211.31 -213.51

2.90 -211.21 -210.71 -210.21 -209.71 -209.21 -210.71 -212.91 -215.11 -217.31 -219.51

3.00 -217.21 -216.71 -216.21 -215.71 -215.21 -216.71 -218.91 -221.11 -223.31 -225.51

3.10 -223.21 -222.71 -222.21 -221.71 -221.21 -222.71 -224.91 -227.11 -229.31 -231.51

3.20 -229.21 -228.71 -228.21 -227.71 -227.21 -228.71 -230.91 -233.11 -235.31 -237.51

3.30 -235.21 -234.71 -234.21 -233.71 -233.21 -234.71 -236.91 -239.11 -241.31 -243.51

3.40 -241.21 -240.71 -240.21 -239.71 -239.21 -240.71 -242.91 -245.11 -247.31 -249.51

3.50 -247.21 -246.71 -246.21 -245.71 -245.21 -246.71 -248.91 -251.11 -253.31 -255.51

3.60 -253.21 -252.71 -252.21 -251.71 -251.21 -252.71 -254.91 -257.11 -259.31 -261.51

∆OASPL 0.000 0.500 1.000 1.500 2.000 0.500 -1.700 -3.900 -6.100 -8.300

NASA/TM—2012-217671 23
Table 4. Modified Stone et al30 High-Frequency Combustor-Noise Component (k=3) Distribution Index

log St3 θ = 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0

-3.60 -199.24 -198.64 -198.04 -197.44 -196.84 -196.14 -195.44 -195.24 -194.84 -194.04

-3.50 -193.24 -192.64 -192.04 -191.44 -190.84 -190.14 -189.44 -189.24 -188.84 -188.04

-3.40 -187.24 -186.64 -186.04 -185.44 -184.84 -184.14 -183.44 -183.24 -182.84 -182.04

-3.30 -181.24 -180.64 -180.04 -179.44 -178.84 -178.14 -177.44 -177.24 -176.84 -176.04

-3.20 -175.24 -174.64 -174.04 -173.44 -172.84 -172.14 -171.44 -171.24 -170.84 -170.04

-3.10 -169.24 -168.64 -168.04 -167.44 -166.84 -166.14 -165.44 -165.24 -164.84 -164.04

-3.00 -163.24 -162.64 -162.04 -161.44 -160.84 -160.14 -159.44 -159.24 -158.84 -158.04

-2.90 -157.24 -156.64 -156.04 -155.44 -154.84 -154.14 -153.44 -153.24 -152.84 -152.04

-2.80 -151.24 -150.64 -150.04 -149.44 -148.84 -148.14 -147.44 -147.24 -146.84 -146.04

-2.70 -145.24 -144.64 -144.04 -143.44 -142.84 -142.14 -141.44 -141.24 -140.84 -140.04

-2.60 -139.24 -138.64 -138.04 -137.44 -136.84 -136.14 -135.44 -135.24 -134.84 -134.04

-2.50 -133.24 -132.64 -132.04 -131.44 -130.84 -130.14 -129.44 -129.24 -128.84 -128.04

-2.40 -127.24 -126.64 -126.04 -125.44 -124.84 -124.14 -123.44 -123.24 -122.84 -122.04

-2.30 -121.24 -120.64 -120.04 -119.44 -118.84 -118.14 -117.44 -117.24 -116.84 -116.04

-2.20 -115.24 -114.64 -114.04 -113.44 -112.84 -112.14 -111.44 -111.24 -110.84 -110.04

-2.10 -109.24 -108.64 -108.04 -107.44 -106.84 -106.14 -105.44 -105.24 -104.84 -104.04

-2.00 -103.24 -102.64 -102.04 -101.44 -100.84 -100.14 -99.44 -99.24 -98.84 -98.04

-1.90 -97.24 -96.64 -96.04 -95.44 -94.84 -94.14 -93.44 -93.24 -92.84 -92.04

-1.80 -91.24 -90.64 -90.04 -89.44 -88.84 -88.14 -87.44 -87.24 -86.84 -86.04

-1.70 -85.24 -84.64 -84.04 -83.44 -82.84 -82.14 -81.44 -81.24 -80.84 -80.04

-1.60 -79.24 -78.64 -78.04 -77.44 -76.84 -76.14 -75.44 -75.24 -74.84 -74.04

-1.50 -73.24 -72.64 -72.04 -71.44 -70.84 -70.14 -69.44 -69.24 -68.84 -68.04

-1.40 -67.24 -66.64 -66.04 -65.44 -64.84 -64.14 -63.44 -63.24 -62.84 -62.04

-1.30 -61.24 -60.64 -60.04 -59.44 -58.84 -58.14 -57.44 -57.24 -56.84 -56.04

-1.20 -55.24 -54.64 -54.04 -53.44 -52.84 -52.14 -51.44 -51.24 -50.84 -50.04

-1.10 -49.24 -48.64 -48.04 -47.44 -46.84 -46.14 -45.44 -45.24 -44.84 -44.04

-1.00 -43.24 -42.64 -42.04 -41.44 -40.84 -40.14 -39.44 -39.24 -38.84 -38.04

-0.90 -37.24 -36.64 -36.04 -35.44 -34.84 -34.14 -33.44 -33.24 -32.84 -32.04

-0.80 -31.24 -30.64 -30.04 -29.44 -28.84 -28.14 -27.44 -27.24 -26.84 -26.04

-0.70 -25.24 -24.64 -24.04 -23.44 -22.84 -22.14 -21.44 -21.24 -20.84 -20.04

-0.60 -20.04 -19.44 -18.84 -18.24 -17.64 -16.94 -16.24 -16.04 -15.64 -14.84

-0.50 -15.94 -15.34 -14.74 -14.14 -13.54 -12.84 -12.14 -11.94 -11.54 -10.74

-0.40 -13.04 -12.44 -11.84 -11.24 -10.64 -9.94 -9.24 -9.04 -8.64 -7.84

-0.30 -12.04 -11.44 -10.84 -10.24 -9.64 -8.94 -8.24 -8.04 -7.64 -6.84

-0.20 -12.34 -11.74 -11.14 -10.54 -9.94 -9.24 -8.54 -8.34 -7.94 -7.14

-0.10 -13.34 -12.74 -12.14 -11.54 -10.94 -10.24 -9.54 -9.34 -8.94 -8.14

0.00 -15.54 -14.94 -14.34 -13.74 -13.14 -12.44 -11.74 -11.54 -11.14 -10.34

NASA/TM—2012-217671 24
Table 4. Modified Stone et al30 High-Frequency Combustor-Noise Component (k=3) Distribution Index, continued (1)

log St3 θ = 90.0 100.0 110.0 120.0 130.0 140.0 150.0 160.0 170.0 180.0

-3.60 -194.04 -192.54 -190.84 -189.04 -187.64 -191.14 -193.64 -195.64 -197.64 -199.64

-3.50 -188.04 -186.54 -184.84 -183.04 -181.64 -185.14 -187.64 -189.64 -191.64 -193.64

-3.40 -182.04 -180.54 -178.84 -177.04 -175.64 -179.14 -181.64 -183.64 -185.64 -187.64

-3.30 -176.04 -174.54 -172.84 -171.04 -169.64 -173.14 -175.64 -177.64 -179.64 -181.64

-3.20 -170.04 -168.54 -166.84 -165.04 -163.64 -167.14 -169.64 -171.64 -173.64 -175.64

-3.10 -164.04 -162.54 -160.84 -159.04 -157.64 -161.14 -163.64 -165.64 -167.64 -169.64

-3.00 -158.04 -156.54 -154.84 -153.04 -151.64 -155.14 -157.64 -159.64 -161.64 -163.64

-2.90 -152.04 -150.54 -148.84 -147.04 -145.64 -149.14 -151.64 -153.64 -155.64 -157.64

-2.80 -146.04 -144.54 -142.84 -141.04 -139.64 -143.14 -145.64 -147.64 -149.64 -151.64

-2.70 -140.04 -138.54 -136.84 -135.04 -133.64 -137.14 -139.64 -141.64 -143.64 -145.64

-2.60 -134.04 -132.54 -130.84 -129.04 -127.64 -131.14 -133.64 -135.64 -137.64 -139.64

-2.50 -128.04 -126.54 -124.84 -123.04 -121.64 -125.14 -127.64 -129.64 -131.64 -133.64

-2.40 -122.04 -120.54 -118.84 -117.04 -115.64 -119.14 -121.64 -123.64 -125.64 -127.64

-2.30 -116.04 -114.54 -112.84 -111.04 -109.64 -113.14 -115.64 -117.64 -119.64 -121.64

-2.20 -110.04 -108.54 -106.84 -105.04 -103.64 -107.14 -109.64 -111.64 -113.64 -115.64

-2.10 -104.04 -102.54 -100.84 -99.04 -97.64 -101.14 -103.64 -105.64 -107.64 -109.64

-2.00 -98.04 -96.54 -94.84 -93.04 -91.64 -95.14 -97.64 -99.64 -101.64 -103.64

-1.90 -92.04 -90.54 -88.84 -87.04 -85.64 -89.14 -91.64 -93.64 -95.64 -97.64

-1.80 -86.04 -84.54 -82.84 -81.04 -79.64 -83.14 -85.64 -87.64 -89.64 -91.64

-1.70 -80.04 -78.54 -76.84 -75.04 -73.64 -77.14 -79.64 -81.64 -83.64 -85.64

-1.60 -74.04 -72.54 -70.84 -69.04 -67.64 -71.14 -73.64 -75.64 -77.64 -79.64

-1.50 -68.04 -66.54 -64.84 -63.04 -61.64 -65.14 -67.64 -69.64 -71.64 -73.64

-1.40 -62.04 -60.54 -58.84 -57.04 -55.64 -59.14 -61.64 -63.64 -65.64 -67.64

-1.30 -56.04 -54.54 -52.84 -51.04 -49.64 -53.14 -55.64 -57.64 -59.64 -61.64

-1.20 -50.04 -48.54 -46.84 -45.04 -43.64 -47.14 -49.64 -51.64 -53.64 -55.64

-1.10 -44.04 -42.54 -40.84 -39.04 -37.64 -41.14 -43.64 -45.64 -47.64 -49.64

-1.00 -38.04 -36.54 -34.84 -33.04 -31.64 -35.14 -37.64 -39.64 -41.64 -43.64

-0.90 -32.04 -30.54 -28.84 -27.04 -25.64 -29.14 -31.64 -33.64 -35.64 -37.64

-0.80 -26.04 -24.54 -22.84 -21.04 -19.64 -23.14 -25.64 -27.64 -29.64 -31.64

-0.70 -20.04 -18.54 -16.84 -15.04 -13.64 -17.14 -19.64 -21.64 -23.64 -25.64

-0.60 -14.84 -13.34 -11.64 -9.84 -8.44 -11.94 -14.44 -16.44 -18.44 -20.44

-0.50 -10.74 -9.24 -7.54 -5.74 -4.34 -7.84 -10.34 -12.34 -14.34 -16.34

-0.40 -7.84 -6.34 -4.64 -2.84 -1.44 -4.94 -7.44 -9.44 -11.44 -13.44

-0.30 -6.84 -5.34 -3.64 -1.84 -0.44 -3.94 -6.44 -8.44 -10.44 -12.44

-0.20 -7.14 -5.64 -3.94 -2.14 -0.74 -4.24 -6.74 -8.74 -11.14 -13.14

-0.10 -8.14 -6.64 -4.94 -3.14 -1.74 -5.24 -7.74 -9.74 -12.64 -14.64

0.00 -10.34 -8.84 -7.14 -5.34 -3.94 -7.44 -9.94 -11.94 -15.44 -17.44

NASA/TM—2012-217671 25
Table 4. Modified Stone et al30 High-Frequency Combustor-Noise Component (k=3) Distribution Index, continued (2)

log St3 θ = 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0

0.00 -15.54 -14.94 -14.34 -13.74 -13.14 -12.44 -11.74 -11.54 -11.14 -10.34

0.10 -19.14 -18.54 -17.94 -17.34 -16.74 -16.04 -15.34 -15.14 -14.74 -13.94

0.20 -23.64 -23.04 -22.44 -21.84 -21.24 -20.54 -19.84 -19.64 -19.24 -18.44

0.30 -29.64 -29.04 -28.44 -27.84 -27.24 -26.54 -25.84 -25.64 -25.24 -24.44

0.40 -35.64 -35.04 -34.44 -33.84 -33.24 -32.54 -31.84 -31.64 -31.24 -30.44

0.50 -41.64 -41.04 -40.44 -39.84 -39.24 -38.54 -37.84 -37.64 -37.24 -36.44

0.60 -47.64 -47.04 -46.44 -45.84 -45.24 -44.54 -43.84 -43.64 -43.24 -42.44

0.70 -53.64 -53.04 -52.44 -51.84 -51.24 -50.54 -49.84 -49.64 -49.24 -48.44

0.80 -59.64 -59.04 -58.44 -57.84 -57.24 -56.54 -55.84 -55.64 -55.24 -54.44

0.90 -65.64 -65.04 -64.44 -63.84 -63.24 -62.54 -61.84 -61.64 -61.24 -60.44

1.00 -71.64 -71.04 -70.44 -69.84 -69.24 -68.54 -67.84 -67.64 -67.24 -66.44

1.10 -77.64 -77.04 -76.44 -75.84 -75.24 -74.54 -73.84 -73.64 -73.24 -72.44

1.20 -83.64 -83.04 -82.44 -81.84 -81.24 -80.54 -79.84 -79.64 -79.24 -78.44

1.30 -89.64 -89.04 -88.44 -87.84 -87.24 -86.54 -85.84 -85.64 -85.24 -84.44

1.40 -95.64 -95.04 -94.44 -93.84 -93.24 -92.54 -91.84 -91.64 -91.24 -90.44

1.50 -101.64 -101.04 -100.44 -99.84 -99.24 -98.54 -97.84 -97.64 -97.24 -96.44

1.60 -107.64 -107.04 -106.44 -105.84 -105.24 -104.54 -103.84 -103.64 -103.24 -102.44

1.70 -113.64 -113.04 -112.44 -111.84 -111.24 -110.54 -109.84 -109.64 -109.24 -108.44

1.80 -119.64 -119.04 -118.44 -117.84 -117.24 -116.54 -115.84 -115.64 -115.24 -114.44

1.90 -125.64 -125.04 -124.44 -123.84 -123.24 -122.54 -121.84 -121.64 -121.24 -120.44

2.00 -131.64 -131.04 -130.44 -129.84 -129.24 -128.54 -127.84 -127.64 -127.24 -126.44

2.10 -137.64 -137.04 -136.44 -135.84 -135.24 -134.54 -133.84 -133.64 -133.24 -132.44

2.20 -143.64 -143.04 -142.44 -141.84 -141.24 -140.54 -139.84 -139.64 -139.24 -138.44

2.30 -149.64 -149.04 -148.44 -147.84 -147.24 -146.54 -145.84 -145.64 -145.24 -144.44

2.40 -155.64 -155.04 -154.44 -153.84 -153.24 -152.54 -151.84 -151.64 -151.24 -150.44

2.50 -161.64 -161.04 -160.44 -159.84 -159.24 -158.54 -157.84 -157.64 -157.24 -156.44

2.60 -167.64 -167.04 -166.44 -165.84 -165.24 -164.54 -163.84 -163.64 -163.24 -162.44

2.70 -173.64 -173.04 -172.44 -171.84 -171.24 -170.54 -169.84 -169.64 -169.24 -168.44

2.80 -179.64 -179.04 -178.44 -177.84 -177.24 -176.54 -175.84 -175.64 -175.24 -174.44

2.90 -185.64 -185.04 -184.44 -183.84 -183.24 -182.54 -181.84 -181.64 -181.24 -180.44

3.00 -191.64 -191.04 -190.44 -189.84 -189.24 -188.54 -187.84 -187.64 -187.24 -186.44

3.10 -197.64 -197.04 -196.44 -195.84 -195.24 -194.54 -193.84 -193.64 -193.24 -192.44

3.20 -203.64 -203.04 -202.44 -201.84 -201.24 -200.54 -199.84 -199.64 -199.24 -198.44

3.30 -209.64 -209.04 -208.44 -207.84 -207.24 -206.54 -205.84 -205.64 -205.24 -204.44

3.40 -215.64 -215.04 -214.44 -213.84 -213.24 -212.54 -211.84 -211.64 -211.24 -210.44

3.50 -221.64 -221.04 -220.44 -219.84 -219.24 -218.54 -217.84 -217.64 -217.24 -216.44

3.60 -227.64 -227.04 -226.44 -225.84 -225.24 -224.54 -223.84 -223.64 -223.24 -222.44

∆OASPL -5.200 -4.600 -4.000 -3.400 -2.800 -2.100 -1.400 -1.200 -0.800 0.000

NASA/TM—2012-217671 26
Table 4. Modified Stone et al30 High-Frequency Combustor-Noise Component (k=3) Distribution Index, continued (3)

log St3 θ = 90.0 100.0 110.0 120.0 130.0 140.0 150.0 160.0 170.0 180.0

0.00 -10.34 -8.84 -7.14 -5.34 -3.94 -7.44 -9.94 -11.94 -15.44 -17.44

0.10 -13.94 -12.44 -10.74 -8.94 -7.54 -11.04 -13.54 -15.54 -19.74 -21.74

0.20 -18.44 -16.94 -15.24 -13.44 -12.04 -15.54 -18.04 -20.04 -25.54 -27.54

0.30 -24.44 -22.94 -21.24 -19.44 -18.04 -21.54 -24.04 -26.04 -31.54 -33.54

0.40 -30.44 -28.94 -27.24 -25.44 -24.04 -27.54 -30.04 -32.04 -37.54 -39.54

0.50 -36.44 -34.94 -33.24 -31.44 -30.04 -33.54 -36.04 -38.04 -43.54 -45.54

0.60 -42.44 -40.94 -39.24 -37.44 -36.04 -39.54 -42.04 -44.04 -49.54 -51.54

0.70 -48.44 -46.94 -45.24 -43.44 -42.04 -45.54 -48.04 -50.04 -55.54 -57.54

0.80 -54.44 -52.94 -51.24 -49.44 -48.04 -51.54 -54.04 -56.04 -61.54 -63.54

0.90 -60.44 -58.94 -57.24 -55.44 -54.04 -57.54 -60.04 -62.04 -67.54 -69.54

1.00 -66.44 -64.94 -63.24 -61.44 -60.04 -63.54 -66.04 -68.04 -73.54 -75.54

1.10 -72.44 -70.94 -69.24 -67.44 -66.04 -69.54 -72.04 -74.04 -79.54 -81.54

1.20 -78.44 -76.94 -75.24 -73.44 -72.04 -75.54 -78.04 -80.04 -85.54 -87.54

1.30 -84.44 -82.94 -81.24 -79.44 -78.04 -81.54 -84.04 -86.04 -91.54 -93.54

1.40 -90.44 -88.94 -87.24 -85.44 -84.04 -87.54 -90.04 -92.04 -97.54 -99.54

1.50 -96.44 -94.94 -93.24 -91.44 -90.04 -93.54 -96.04 -98.04 -103.54 -105.54

1.60 -102.44 -100.94 -99.24 -97.44 -96.04 -99.54 -102.04 -104.04 -109.54 -111.54

1.70 -108.44 -106.94 -105.24 -103.44 -102.04 -105.54 -108.04 -110.04 -115.54 -117.54

1.80 -114.44 -112.94 -111.24 -109.44 -108.04 -111.54 -114.04 -116.04 -121.54 -123.54

1.90 -120.44 -118.94 -117.24 -115.44 -114.04 -117.54 -120.04 -122.04 -127.54 -129.54

2.00 -126.44 -124.94 -123.24 -121.44 -120.04 -123.54 -126.04 -128.04 -133.54 -135.54

2.10 -132.44 -130.94 -129.24 -127.44 -126.04 -129.54 -132.04 -134.04 -139.54 -141.54

2.20 -138.44 -136.94 -135.24 -133.44 -132.04 -135.54 -138.04 -140.04 -145.54 -147.54

2.30 -144.44 -142.94 -141.24 -139.44 -138.04 -141.54 -144.04 -146.04 -151.54 -153.54

2.40 -150.44 -148.94 -147.24 -145.44 -144.04 -147.54 -150.04 -152.04 -157.54 -159.54

2.50 -156.44 -154.94 -153.24 -151.44 -150.04 -153.54 -156.04 -158.04 -163.54 -165.54

2.60 -162.44 -160.94 -159.24 -157.44 -156.04 -159.54 -162.04 -164.04 -169.54 -171.54

2.70 -168.44 -166.94 -165.24 -163.44 -162.04 -165.54 -168.04 -170.04 -175.54 -177.54

2.80 -174.44 -172.94 -171.24 -169.44 -168.04 -171.54 -174.04 -176.04 -181.54 -183.54

2.90 -180.44 -178.94 -177.24 -175.44 -174.04 -177.54 -180.04 -182.04 -187.54 -189.54

3.00 -186.44 -184.94 -183.24 -181.44 -180.04 -183.54 -186.04 -188.04 -193.54 -195.54

3.10 -192.44 -190.94 -189.24 -187.44 -186.04 -189.54 -192.04 -194.04 -199.54 -201.54

3.20 -198.44 -196.94 -195.24 -193.44 -192.04 -195.54 -198.04 -200.04 -205.54 -207.54

3.30 -204.44 -202.94 -201.24 -199.44 -198.04 -201.54 -204.04 -206.04 -211.54 -213.54

3.40 -210.44 -208.94 -207.24 -205.44 -204.04 -207.54 -210.04 -212.04 -217.54 -219.54

3.50 -216.44 -214.94 -213.24 -211.44 -210.04 -213.54 -216.04 -218.04 -223.54 -225.54

3.60 -222.44 -220.94 -219.24 -217.44 -216.04 -219.54 -222.04 -224.04 -229.54 -231.54

∆OASPL 0.000 1.500 3.200 5.000 6.400 2.900 0.400 -1.600 -4.054 -6.054

NASA/TM—2012-217671 27
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4. TITLE AND SUBTITLE

A Comparison of Combustor-Noise Models 

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Hultgren, Lennart, S. 

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WBS 561581.02.08.03.45.02.01 

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John H. Glenn Research Center at Lewis Field 

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14. ABSTRACT

The current status of combustor-noise prediction in the NASA Aircraft Noise Prediction Program (ANOPP) for current-generation (N) 

turbofan engines is summarized. Best methods for near-term updates are reviewed. Long-term needs and challenges for the N+1 through 

N+3 timeframe are discussed. This work was carried out under the NASA Fundamental Aeronautics Program, Subsonic Fixed Wing Project, 

Quiet Aircraft Subproject. 

15. SUBJECT TERMS

Aeroacoustics; Turbomachinery noise; Core noise; Combustor noise 

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