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oit ' ".`-

ti

^3A Technical, M, emorandum 833. 51 M ^ t

(NASA-TM-83351)CROSS SPECTRA BETWEEN 583-23116TEMPERATURE AND PRESSURE IN A CONSTANT AREADUCT DOWNSTREAM OF A COMBUSTOR (N AS A) 28 p

a .HC A03/NF A01 CSCb 20A Unclas03/7.1{979

Cross" Spectra "'Between. Tem eratu r. e andi

Pressure in a Cpnstant Area Duct JDownstream of a Combustor

0

4A,

J.: H. Miles, C. A. 'Wasserbauer, and - E. A, Krebs r'1. , . sj ewis'Research Center

Cleveland, Ohio a ^

r ,

Prepared for theEighth Aeroacoustics Conferences dnsored ^by, the American Institute of Aeronautics and AstrpnauticsAtlanta, Georgia, April 11-13, 1983

D.

PJA S-A

mb i snows` n

Center. In the study of core noise, the influenceof combustion must be considered because the com-bustion process is a major source of noise from aturbofan engine core. In a combustor, fluctua-

tions in the heat release rate can cause bathentropy and pressure perturbations. The prey-sure waves propagate through the engine and areradiated to the far field. The entropy variationsare not direct noise sources because they have noassociated pressure disturbance. However, as

the entropy convects through regions of velocitygradients they, too, generate acoustic waves.The resulting combustion noise represents acombination of waves due to both sources.

A model for predicting noise propagation in a

variable area core nozzle which included convectedentropy is discussed in Ref. 1. Using this model,calculations show that the noise level at a given

frequency can be related to the entropy auto-spectrum. Furthermore, the core nozzle transferfunction is affected by the entropy-pressure crossspectrum. The calculations show that if the

entropy and pressure are in phase at the inlet,the magnitude and phase of the transfer function

can have a rippled appearance. Consquently, inorder to describe certain characteristics of com-

bustion noise propagation, information about thecross-spectrum between the convected entropy andpressure and the entropy auto-spectrum are re-quired. However, no experimental entropy auto-spectra or entropy-pressure cross-spectra wereavailable to use in the model.

An entropy perturbation, S', is related to aperturbation in gas,pressure, p', and temperature,

Y

S' . T' +(I - r) L (1)c To r Po

Thus in order to obtain the entropy auto-spectrumand the entropy-pressure cross spectrum the tem-perature and pressure auto-spectra as well asthe temperature-pressure cross-spectrum must be

measured. The purpose of this paper is show thatit is feasible to measure temperature-pressurecross-spectra in a combustion rig over a rangeof frequencies of interest in combustion noisestudies, to obtain some baseline data, and todetermine if some non-random phase relationship,as hypothesized in Ref. 1, between pressure andtemperature calz exist.

Dynamic temperature and ppressure measurements

have been made in combustors Z-5 in order toobtain auto-spectra. In this paper an exploratorystudy investigating the measurement inside a com-bustion rig of pressure-temperature cross-spectraand coherence at a single point as well as tem-perature cross-spectra and coherence at spatially

separated points is presented. Pressure and tem-perature auto-spectra inside the combustion rigare also obtained. The engineering data acquired

R

r

0 R 10 1 NAL PA : I

OF POOR QUALITY

CROSS SPECTRA BETWEEN TEMPERATURE AND PRESSURE IN A CONSTANT AREADUCT DOWNSTREAM OF A COMBUSTOR

J. H. Miles, C. A. Wasserbauer and E. A. Krejsa

National Aeronautics and Space Administrationf

Lewis Research CenterCleveland, Ohio 44135

Abstract

Theory indicates that pressure-temperature

cross-spectra are necessary in predicting noisein regions of velocity gradients. In the presentstudy, the feasibility of measuring pressure-

temperature cross-spectra and coherence andtemperature-temperature cross-spectra and coher-

ence at spatially separated points along withpressure and temperature auto-spectra in a com-bustion rig was investigated. The measurementswere made near the inlet and exit of a 6.44 m longduct attached to a J-47 combustor. For this studythe fuel used was Jet A. The cross-spectra andcoherence measurements show the pressure and tem-perature fluctuations correlate best at low fre-quencies. At the inlet the phenomena controllingthe phase relationship between pressure and tem-

perature could not be identified. However, atthe duct exit the phase angle of the pressure isrelated to the phase angle of the temperature bythe convected flow time delay.

Nomenclature

co speed of sound

c specific heat at constant pressure

f frequency

Gii thermocouple auto-spectrumG ij thermocouple cross-spectrumH ii ratio of thermocouple auto-spectrum to

cross-spectrum, Gii/Gij

ik wavenumber, w/con integerp acoustic pressure

R duct exit reflection factorS entropy perturbationT temperature perturbationW mass flow rate

x displacement of point from combustorentrance

y ratio of specific heats

o square root of the variance of adistribution

t thermocouple time constantw angular frequency, 2nf

Superscripts:

* complex conjugate' perturbation

Subscripts:

g gas

m measured

1,2 thermocouple number3,4 duct locations

Introduction

A program to study turbofan engine core noise

has been conducted at the NASA Lewis Research

j This paper Is declared a work of the U.S.

i

Government and therefore is In the public domain.

.

000

W

CR8UMAL PArZ ,_. w1,71

OF POOR QUALI

can be used in models, such as that discussed inRef. 1, and compared with other published results.

The measurements to be described were made in

a long (6.44 m) constant area duct attached to .aJ-47 combustor. The rig was designed to operatewith no combustion in the long duct. However, forall the test conditions some combustion did occurat the duct inlet station where one set of pres-sure and temperature measurements were made.

Exoerimental Aaparatus

The temperature and pressure measurements were

made in the combustion rig shown in Fig. i whichconsisted of a J-47 can combustor (see Fig. 1(b))mounted in a 0.3 m diameter by 0.77 m long testsection and an attached 6.44 m long 0.3 m diameterstainless steel duct. The fuel used was .Jet A.

This paper discusses pressure and temperature mea-surmrnts at stations 3 and 4. The test conditionsare shown in Table I.

All tests were conducted in an outdoor acous-tic arena. The facility is shown, in Fig. 2.

Note that in all cases the duct exit tempera-

ture was greater than the duct inlet temperatureindicating some combustion was occuring in theduct. This was due to mechanical problems which

developed in the combustor during the test pro-gram. These problems make the test conditionsdifficult to duplicate and hinder the inter-pretation of the measurements. However, thecombustor mechanical problems have no bearing onthe examination of the feasibility of measuringtemperature—pressure cross spectra.

Pressure Measurements

The internal pressure transducers used were

conventional 0.635 cm microphones with pressureresponse cartridges. In order to avoid directexposure of the microphone to the combustiongases, they were mounted outside the ducted com-

bustion rig and the fluctuating pressure in therig was transmitted to the transducers by means ofa "semi—infinite" acoustic wave guide. Details onthese probes are given in Ref. 6.

Temperature Measurements

between the measured and theoretical values ofHll and H22 where

Gil 1 + W2 TiT2 + iw(Tl - T2)

and

G22 1 + W2 T 1 T2 + WT I. — T2)(3)H22 a

U1_1 =

1+W T2

where

i=

The temperature auto—spectra are Gil, and G22and the temperature—temperature cross spectrum is

G12. The model used assumes that the measuredtemperature, Tm, is related to the gas tempera-

ture, Tg by

TTm

= l +qiwc

in the frequency domain,. Futhermore, it is assumed

that the coherence between the two thermocouplesis high so that extraneous noise can be neglected.

Examination of the plots of the real andimaginary values of Hii can yield information onthe time constants since the imaginary value of

Hii has a maximum at w = 1/Ti. Furthermore

lim H11 = T2 / Ti (5)W+w

and

lim H22 = Tl1T2 (6)W+.

The time constant in all cases was determined

using the spectrum between 0 and 40 Hz.

(4)

0

The temperature fluctuations were measured

using chromel—alumel thermocouples. The twowire thermocouple probe design shown in Fig. 3was selected so"that the response time of thethermocouple could be determined based on theactual test data, as opposed to a separate pre—calibration. The procedure discussed in Ref. 7was used. The thermocouple chromel—alumel wirediameters were 76.2 and 25.4 Nm. The thermo-couples were inserted into the duct by actuatorsafter combustion started in order to prevent theirdestruction by the combustion start up transient.While the thermocouples were quite durable, theirlifetime was drastically reduced by operation atelevated temperatures (1115 K).

The approach used to determine the themocouple

time constants is based on the two thermocouplemethod described in Ref. 7 However, the actualtime constants were not found by examination ofthe plots as suggested in Ref. 7. Instead, a non-

linear minimization technique was used to find thetime constants to minimize the least square error

In order to demonstrate the procedure, typical

constant bandwidth (0.08 Hz) two wire thermocoupleauto—spe-etra, cross—spectra and coherence functionmeasurements are shown in Figs. 4 to 8. Note thatthe thermocouple coherence is high (Fig. 6). Thisis a necessary condition for application of thecalibration procedure since it means that extrane-ous noise is low. In addition, the measuredvalues of and H22 are shown in terms oftheir real and imaginary components along with the

least square curve fits used to find the time con-tants (Figs. 7 and 8). The W = 1/Ti points and

the high frequency asymptotic value of Hii arealso identified. Also, in Fig. 4 the gas tempera-ture ' Tg, auto—spectrum and cross—spectrum aftercorrection are shown. Table I gives the time con-stants used to correct the cases used herein.

Results and Discussion

This section discusses measurements of

pressure—pressure and temperature—temperaturecross—spectra between the inlet and the exit of

d

k ^

p

t°

2

41JYaNMMaiL.

OF POW

the long duct. Also, pressure-temperature cross-spectra at the inlet and the exit of the duct arediscussed Only a few typical results sufficientto establish definite trends are included here.

With each cross-spectrum, the corresponding

coherence function is presented. Note that a

coherence smaller than unity implies one or moreof the following conditiatfs exists:

1. Extraneous noise is present in the mea-surements.

2. The system relating the output to the inputis non-linear.

3. The output is due to more than one input.

Pressure Cross-Spectra and auto-Spectra

Typical constant bandwidth (2 Hz) pressure to

pressure cross-spectra and pressure auto-spectraare shown in Figs. 9 to 11. The cross-spectramagnitude plots and auto-spectra magnitude plots

have certain similarites since as the temperatureincreases, the frequency at which a particularspectral feature occurs increases in a proportionthat keeps the wave number constant. However, thevariation in temperature along the duct producesdistortions in the shape of the magnitude plotthat would not appear in a constant temperatureduct. The pressure auto-spectra are shown so that

they can be compared with the correspondingtemperature-pressure cross-spectra.

The cross-spectra phase relationships are due

to a longitudinal standing wave in the duct.The cross-spectra phase angle is intially zerocorresponding to a positive value of PA. The

phase angle switches by 180 degrees at approxi-mately 50 Hz intervals. The phase angle variatonwith frequency of the pressure cross spectra inthe duct is understandable in terms of a simple no

flow model for the acoustic pressure distribtionin the duct. Without flow the pressure in theduct is proportional to

p a eikx + R e-ikx (7)

Furthermore, at low frequencies the reflectionfactor is nearly - 1. Consequently, the pressureis approximately proportional to sin(kx ). Thusthe pressure cross-spectrum between station 3 and

4, p34 ► in a duct without flow is then propor-tional to

p 3p4 - sin(kx 3 )sin(kx 4 ) (8)

where x3 a 1.47 m and x4 - 6.91 m. This func-tion is either positive or negative and it changes

sign at frequencies n*f which are multiples ofthe first zero of p3p4. The phase angle devia-tions from this simple model are due to the pres-

ence of flow and the duct reflection and the ductreflection factor not being -1.

The corresponding coherence functions are

shown in Fig. 12. The coherences are quite largeabove 20 Hz. However, at multiples of the firstzero of p3p4 the coherence is zero.

Temperature-Temperature Cross-Spectra

Temperature-temperature constant bandwidth

(0.4 Hz) cross-spectra between the entrance andthe exit of the duct are shown for three cases in

Fig. 13. All temperature measurements are shownafter correction The cross-spectrum magnitude islargest at low frequencies.

At low frequencies (up to 50 Hz) the phase of

the cross spectra changes linearly with frequencywith slopes proportional to the time delay due to

convection of temperature in the duct. The timedel is about 125 ms for the data shown in Figs.13(aa and (b) where the mass flow rate, W,,is0.5 kg/s and 62.5 ms for the data shown in Fig.13(c) where the mass flow rate is 1.13 kg/s.

The corresponding coherence data are shown in

Fig. 14. At the higgher frequencies the coherenceis very low (Fly. 14) and no orderly relationship

between the temperatures is observed. Note also,from Fig. 14, that as the amount of burning in theduct increases the coherence is greatly reduced.

The thermocouple signals show the presence of

60 Hz and 110 Hz noise. The signal at station 4at the duct exit was more contaminated than thesignal at station 3 at the duct inlet.

Pressure-Temperature Cross Spectra

Duct inlet: Pressure-temperature constant

bandwidth 0.40 Hz) cross-spectra at the ductinlet (station 3) for three cases are shown itsFig. 15. The corresponding coherence fuctionsare shown in Fig. 16. The mechanical cut-off fre••quency of the microphone due to pressure equaliza-tiorb is abcut 5 Hz. Consequently, below thisfrequency the data are unreliable.

Above 50 Hz the shapes of the pressure-

temperature cross-spectra magnitude plots (Fig.15) resembles the shapes of the correspondingpressure auto-spectra magnitude plots shown inFig. 10. This indicates that the partof thetemperature perturbation coherent with the pres-sure perturbation has no strong spectral char-acteristics above 50 liz.

The phase angle variation shows distinct

patterns, indicating a systematic relationshipbetween pressure and temperature near the sourceregion. However, the physical phenomena producingthis pattern have not been identified.

Comparing, the pressure-temperature cross-

spectrum magnitude plots (Fig. 15) and coherenceplots(Fir, 16 ) with the pressure auto-spectraplots ((. Fig. 10) shows that the temperature per-turbation is weakly excited in certain frequencybands near ,particular duct resonant .frequencies.For inlet temperatures of 1115, 875 and 920 K notethe 110 Hz, 98 and 70 Hz regions respectively.

The systematic relationship between the pres-

sure and the temperature at the inlet is not a

strong one. Consequently, it is more visible inthe phase plots than the coherence plots.

Duct exit: Pressure,.temperature constant

bandwidth 0.40 Hz) cross-spectra at the ductexit (station 4) for three cases are shown inFig. 17. The corresponding coherence fuctions areshown in Fig. 18. Again the magnitude plots ofthe pressure-temperature cross spectra resemblethe magnitude plots of the corresponding pressure

auto-spectra shown in Fig. 11.

3

ORICUAL PACE' 10OF POOR QUALITY

\f

The phase of the cross spectra again show

linear dependence with slopes that are propor-tional to the time delay due to convection of

temperature in the long duct, Note, that sincethis is a phase measurement between two differentvariables, that is pressure and temperature, atthe same point, the time delay must be due to thedifference in travel times between a pressure andtemperature disturbance as they travel from the

same upstream source region. This shows that tem—perature and pressure fluctuations are related atthe combustion source point. Furthermor =e, anextrapolation of the cross—spectrum suggests thatthe two are in phase at low frequencies.

In view of these findings that pressure andtemperature are in in phase at the source in thiscombustion rig, it is possible that the entropy

and pressure in the JT15D nozzle might also be inphase at the nozzle inlet. Thus, some of theripple in the measured JT15D transfer functionpresented in Ref. 1 might be due to convectedentropy. This suggests that it might be ofinterest to obtain dynamic temperature measure-

ments along with acoustic pressure measurements inturbofan engine tests.

Temperature Auto—Spectra

Because plots of the gas temperature auto—

spectra resemble those presented in Fig. 5, addi-tional ones are not included. It can be seen thatmost of the fluctuations are at low frequencies.

The temperature standard deviations calculated byintegrating the temperature auto—spectra for afrequency range from 0 to 200 Hz are shown inTable I. the percent r.m.s. temperature fluctua-tions are also shown in Table I. At the inletwhere combustion is occuring they vary in a range

from 15 to 20 percent. At the duct exit the rangeis 2 to 4 percent. These results are similar tothose found at the exit of the gas turbine combus-for by Dils2 where the per cent r.m.s. temperaturefluctuations were 7 and 10 percent at a takeoffoperating condition where the average temperatures

were 1430 and 1438 K. The burner exit r.m.s.temperature fluctuations reported in Ref. 5 aregenerally lower than those observed by Dils.

Conclusions

From the results of this exploratory study,

the following conclusions were reached:

1. Pressure and temperature cross—spectra and

coherence functions can be measured in a combus-tion rig using a two—wire thermocouple probe andan infinite tube microphone over a range of fre-quencies of interest in combustion noise studies.

2. The temperature and pressure fluctuations

are related at the combustion source point and anextrapolation of the cross—spectrum phase suggeststhat the two are in phase at low frequencies.

3. At the duct exit the phase angle of the

pressure is related to the phase angle of thetemperature by the convected flow time delay.

These three conclusions, taken together,provide confidence that identifiable physical

relationships between temperature and pressurein a combustion system can be measured usingsophisticated data analysis techniques. Theserelationships are valuable either as inputs oras verification of outputs of theoreticalmodels describina combustion noise generationor propagation.

References

1. Miles, J. H., and Krejsa, E. A., "Pressure

Transfer Function of a JT15D Nozzle Due to Acous-tic and Convected Entropy Fluctuations," Journalof the Acoustical Society of America, Voles;

2. Dils, R. R., "Dynamics Gas Temperature

Measurements in a Gas Turbine Transtion DuctExit," Journal of En ineerinq for Power, Vol. 95,No. 3,W T s pp= _—_

3. Muthukrishnan, M., Strahle, W. C., andNeale, D. H., "Separation of Hydrodynamic,Entropy, and Combustion Noise in a Gas Turbine

Combustor," AIAA Journal, Vol. 16, No. 4, Apr.1978, pp. 3213-- 7—'

4. Sofrin, T. G., and Riloff, Jr., N.,

"Experimental Clean Combustor Program—NoiseStudy," Pratt and Whitney Aircraft, East Hartford,Conn., PWA-5458, Sept. 1976. (NASA CR-135106.)

Nagel, R. I•,Est' CombustionkNoiserinvestigation-Predicting Direct and Indirect Noise from AircraftEngines," Pratt and Whitney Aircraft Group,

PWA-5478, FAA4D-77-3, Feb. 1977,

6. Karchmer, A. M., and Reshotko, M., "Core

Noise Source Diagnostics on a Turbofan EngineUsing Correlation and Coherence Techniques,"NASA TM X-73535, 1976.

7. Strahle, W. C., and Muthukrishnan, M.,

"Thermocouple Time Constant Measurement by CrossPower Spectra," AIAA Journal, Vol. 14, No. 11,Nov. 1976, pp. 11x42--NT4'

4

k^L

C

L- c .^-%

OF POOR QUA, L Y

TABLE I. — THERMOCOUPLE TIME CONSTANTS, TEMPERATURE

STANDARD DEVIATION, AND RMS TEMPERATURE FLUCTUATION

Test Point 87 86 88

Texit' K 1135 990 1120

Tinlet, K1115 875 920

W, kg/s 0.5 0.5 1.13

Time constant

Station 4 (exit)

T1 (76.2 um diam), ms 41 79 49

T 2 (25.4 um diam), ms 20 34 22

Station 3 (inlet)

T1 (76.2 um diam), ms 61 67 42

T2 (25.4 um diam), ms 36 40 25

Standard temperature deviation, a

Station 4 (exit), K 35 40 25

Station 3 (inlet), K 170 150 170

Percent rms temperature fluctuation

Station 4 (exit) 3 4 2

Station 3 (inlet) 15 17 19

6.44m o a .:..

r-0.3 m

0.4 m-, r 0.77 m 0.4 m 0.3 m -n

J-47 0.203mDIAXa COMBUSTOR o 0 0.305 cm WALL

1 2 3S TAINLESS STEEL XPIPE 4

o INFINITE TUBE MICROPHONESX TWO WIRE PicOBE

(a) Rig schematic.

Figure 1. Schematic of ducted combustion system rig.

a

O^`^ICa66^G111. ^`E^OF POOR QUAL

q

t

QUENCHING

—, AND —MIXING ZONE

CONTINUINGCOMBUSTION

ZONE

IGNITION-REACTION ^--

ZONE

SECONDARY —"

AIR

COMBUSTION AIR FLOW

CAP Q Q UPRIMARY FLOW

AIR y \)^ c^-^FUEL NOZZLE

ii

t

3

I

(b) Injection scheme.

Figure 1. - Concluded,

Figure 2. - NASA Lewis combustion acoustics facility.

k

r

I

6.2 µm DIAMETER:HROMEL-ALUMEL

5.4µm DIAMETER;HROMEL-ALUMEL

OF POOR QUALITY

0.254 cm

0.305 cm

w

Figure 3. - Two wire thermocouple probe design.

120 TIME CONSTANT CORRECTEDcc

Li 1^N`r 100

z ^;

80

180

w 0

`-TIME CONSTANT CORRECTED

-90

-180 1

0 8 16 24 32

FREQUENCY, Hz

Figure 4. -Two wire chrome) alumel thermocouple timeconstant determination: temperature cross-spectrumbetween thick and thin thermocouples, G 12 (station 4,T^ _ET - 875 K, TEXIT ° 990 K. W = 0.5 kgls, band-width - 0.08 Hz).

TIME CONSTANTCORRECTED (T2 a 34 ms)

1

.60 8 16 24 32

FREQUENCY, Hz

Figure 6. -Two wire chromel alumel thermocoupletime constant determination: temperature coherencebetween thick and thin thermocouples (station 4,TINLET = 875 K. TEXIT = 990 K, W = 0.5 kgls, band-width = 0.08 Hz).

wUZw ,w $O

i

ii

ORIGINAL PAGE E5

TIME CONSTANTOF POOR QUALITY

CORRECTED (T1 -79 ms)

1'0'

120

100

80

60 (a)

120

100

80 (b)0 816 24

FREQUENCY, Hz(a)76.2pm diameter (G11)•(b)25.4µm diameter (G22).

Figure 5. - Two wire chromes alumel thermocoupletime constant determination: temperature auto-spectrum of thick and thin thermocouples (station4, TINLET ° 875 K, TEXIT = 990 K, W = 0.5 kg1s,bandwidth - 0.08 Hz).

32

1.00 2.60OF POOR QU,ALI` Y

, 93 2.43

.86 2.26

.79 2.09

,72 1.92

.65 1.75

.58 1.58

.51 1.41

.44 1.24

37 i im H Il • Tl • 0.43 1.07

.30(a) ( I w

.90C

• -'0 - f 1127rT 12.01 Hz

^.7

.26 .6

.22.5

.18 .4

.14 .3

.10 .2

.06 .1

.02 0

-.02 -,1

-.06 -.2

-.10 0) -.30 8 16 24 32

FREQUENCY, Hz

(a) Real part of till,(b) Imaginary part of Hll•

Figure 7, - Two wire chromel alumel thermocouple timeconstant determination: thick thermocouple ratio,H 11 - G11IG12 (station 4. TINT - 875 K. TEXIT990 K, W • 0.5 kg/s, bandw dth • 0.08 Hz).

0 8 16 24 32

FREQUENCY, Hz

(a) Real part of H22.

M Imaginary part of H22,

Figure 3. - Two wire chromel alumel thermocoupletime constant deter minatlort thin thermocoupleratio, H 22 G 1^I G 1 (station Q T NLET - 875 K,TEXIT 6940 K. W - 025 kg/s, bandwidth - 0.08 Hz).

^ `^is^arOF POO

160

2= 140

L

120

0C

Q100

80 (a)

180

9 90-ow 0 0NQ0. O

_,^pppp000^-90

d'-180 (a) 0

0 40 80 120 160 200

FREQUENCY, Hz

(a) TINLET' 1115 K. TEXIT ° 1135 K, W - 0.5 kgls.

Figure 9. - Pressure cross-spectra between duct Inlet(station 3) and duct exit (station 4). p4 p3 * (bandwidth- 2 Hz).

K

^i

ORIGINAL PACE [aOF PO()R OI&APVVI ITY

w

110—

100o =

90

80,

180 —

90 —

amo0a=10CP=

UrV) 00

cc 00

-90

-180

epapq=3:)00

120 —

va 100

1 (c)80

ISO —

an 90 —owwoowo

0W

6toowoma)o 0 0

0

0

0<

- vu

0

cp^

L(C) I

%D=COOOOOCD

-180 I 1 0 1 1

0 40 80 120 160 200FREQUENCY, Hz

(b) TINLET - 875 K, TEX rr n 990 K, W • 0.5 kg/s.

(c) TINLET - 920 K,IET Xrr n 1120 K, W • 1.13 kg/s.

Figure 9. - Concluded.

OF POOR QUALITY

150

130

110

^ MN 90

Nm 120

100

V))Uj 80a

130

1101

V \ / Y_

90 (c) I I I i0 40 80 120 160 200

FREQUENCY, Hz

(a) TINLET =1115 K. TEXIT = 1135 K, W = 0.5 kg/s.

0) TINLET ° 875 K. TEXIT ° 990 K. W = 0.5 kg/s.

(c) TINLET = 920 K. TEXIT - 1120 K, W = 1.13 kg/s.

Figure 10. - Pressure auto-spectra near duct inlet (sta-tion 3) , P3 P3* (bandwidth = 2 Hz).

ORICIVAL

OF Pt3 , )R QUALITY

150

130

110

90

m 120

J100

Lnvd^) vLn

80a

130 1--

110 J ^^

900 40 80 120 160 200

FREQUENCY, Hz(a) TINLEr 1115 K ^ TEXIT ° 1135 K, W - 0.5 kgls.

(b) TINLET a 875 K. TEXIT - 990 K, W - 0.5 kg/s.

(c) T INLET - 920 K. TEXIT -1120 K, W -1.13 kg/ s.

Figure 11. - Pressure auto-spectra near duct exit (sta-tion 4). P4 P4* (bandwidth - 2 Hz).

G

}

ri

Y

.&

6 .6zWGUW

OCJ d

r

t

a

ORI POOR01 P

QUALITY

0 40 80 120 1bu Mu

FREQUENCY, Hz

Figure 12. - Pressure coherence between duct Inlet (sta-tion 3) and duct exit (station 4), 1 p4 p3, 1 21 1 p3121

p " 1 2 (bandwidth • 2 Hz).

ORIGINAL FIRM ISOF POOR QUALITY

0FREQUENCY, Hz

N1 T INLET "` 875 K, TEXIT " 990 K, W - 0.5 kgls.

(c) TINLET " 920 K, TEXIT " 1120 K. W -1.13 k9/s.

Figure 12. - Concluded.

1.0

.8

.6

.Q

.2

u.,ca0

v1.0

.8

.6

.A

.2

ONIGIWAL PAM W

OF pooR QUALITY

130m_w^

110

^ v (a)90

180 $ c Ob 0 ° 0 cS^ OCS o0a 0(b o0 0 0

0% 66oa®oq0 ° o ° o

rn ZS%

p4hg0

o OO a 0 6 e% (^ U O° ^? a

0 °0 o 8 ° 0 0 0 od ° 0 0 0 `^ ° °A ° 00 o cb o d^

-g0 0co00

°000 80 q°

,to

^^

° R C6 O^

d'6 o08 88 e 4 ° °o ^ OLOn ^?of

-180 e a

0 32 64 96 128 160

FREQUENCY, Hz

(a) T INLET ° 1115 K. TEXIT -1135 K, W • 0.5 kg/s.

Figure 13. Temperature cross-spectra between duct inlet(station 3) and duct exit (station 4), T4T3* (bandwidth0.4Hz).

PAIM: is

3.

140—OP POOR QUALITY,

120—

Ljloo-

80 (b)

00 oo 0

180 —S o0 06 o08 0 0 C9%o

0-a

00 040 00 of gp 9 0 0 00

90:1— 0 0 '8 0 V(90 8 8 0

0110 0 0 %0 0 000-0 0

0 0 0 260 ^ 00 00 0 80 0 0 IV0 1

& 00 0 0 0 0

to 0< 0018 0 0 6^pE h

000 0 00 0 0 (go 00 %-0 0

o90(9 1 0

-90 00 0

200 0 0

0A o

t F CR-

0 0 6) 0 Cgo 0 00

0 0 000 0 0 0 - 01%

-180 -8008 o no on % 0 9 o on (b)

130

110

WWILa

90

70 (C)

180- 0iz) 00 10 o 0 0 8 b'

C O o 0 -%, 09? 9 0

0 (p 00 001 b 08

90 — (s 0 0 kcp 0 000 0

C%-08 o 00 t Ck (09, O§PLa 0 ^ 0 0 ep 0tn 0 00 0 C56

-

0< 0(68, °°" cb^ 'Ovo

(Z) 00

I G cp .0 0 0090 (1) 0 80Cb a 0 00 0'p

-180 (CM0 0 101%00 81 101%o 6^ 0

0 32 64 96 128 160

FREQUENCY, Hz

0) ) TINLET - 875 K. TEXIT - 990 K, W - 0.5 kg / s.

(c) TINLEET - 920 K. TEXIT - 1115 K. W -1.13 kg1s.

Figure 13. - Concluded.

• 4

ORIGINAL P^^L1,^`OF POOR Q

r

4

1.(

•8

w .6UZw

wZQ

.4

.2

U 32 64 46 128 160FREQUENCY, Hz

(a) TINLET = 1115 K, TEXIT =1135 K. W - 0.5 kg/s.

Figure 14. - Temperature coherence between duct inlet (sta-tion 3) and duct exit (station 4), I T4T3* I / ) Ty 1 2 1 T312thandwidth 0.4 Hz).

®^ c

n,

6

6R

r

L ,^

^p

RfM

'

1.0

.8

.6

.4

.2

0

0 1.0c^

.8

.6

.4

.2

OF c)ALITY

0 32 64 96 128 160FREQUENCY, Hz

(1) TINLET 875 K. TEXIT - 990 K. W - 0.5 kg/ S.(c) TINLET 920 K. TEXIT -1120 K, W . 1.13 kg/s.

Figure 14. - Concluded.

K-

a

F

f

A

l

^i

i

ORIGINAL

QUALITY,

. G'

^i/

0i= pOOR 4CUALI n

N

M

^ 140

N _

g 120

. 4

. 0

,100z

80

180

c90

n

w 0Lna

-90

-180

o9b^^ Q g3°p6 °°$o^a,, %p p

q, p ° 00"^•,'

g v o° p pp O° O p p C p° p°°p ° o^ p o p o p

0 CQ o Qfb

o ° -ca 0 8 00 `bo

p p O pp Cb

80p °o° 08°00Q o 0o pe

(al o$ ° o p ^0°o " 900 32 64 96 128 160

FREQUENCY, Hz

(a) TINLET " 1115 K. TEXIT "x.135 K; W " 0.5 kg/ S.

Figure 15. - Cross-spectra between pressure and temperatureat duct Inlet (station 3), We (bandwidth - 0.4 Hz).

q,

a

A

a

1

ORIGINAL PAu0`0 E3OF POOR Q, IALITY

120

CaCa

100

(b)80 —

j

1800 00 0 0 0 0

00(1*- 0

to

900000

(9

(9

La 0 09VC90 1, 00 0 0

(6 0 8000 0 00

%08 00

0 a 0 00vwi 0009

0 000 00

0."% 0 00% 0^

0 ^ -

09

00 0-90 ftc) (p 1 0 co o0

0go

0

cc)

-180 (b)

oo^ ao010% 'fa

120

Cn =LP. 100

goccl

180 0%-0, Co ^o 0 00

i90

w

Co 00OA, 0 ob%0

0 0 0 %000%9 .09

LLr co 0V) 0 OC8 Coo&0

CD 009 o ^.p

-90p0

0 0 0 ocb

00 0

-ISO L (c) -%o N-0 oa o A I

0 32 64 96 128 160

FREQUENCY, Hz

(b)TINLET 875 K, TEXIT 990 K, W • 0.5 k9fs.

(c)TINLET 920 K, TEXIT 1120 K, W • 1.13 kg1s.

Figure 15. - Concluded.

4

.4

.2

0

.4

.2

oRIGIOAL PAM 19OF POOR QUALITY

1.0

.8

.6

.4

.2

WUZw 0WZO

0 32 64 96 128 160FREQUENCY, Hz

(a)TINLET ° 1115 K, TEXIT ° 1135 K, W - 0.5 kg/s.

(b)TINLET ° 875 K, TEXIT R 990 K, W - 0.5 kg/s.(c)TINLET - 920 K, TEXIT ° 1120 K, W e 1.13 kg/s.

Figure 16. - Coherence between pressure and temperatureat duct inlet (station 3), I p 3 T 3* 1 2 1 I T3 12 I p3 1 2 (band-width - 0.4 Hz).

a

k

^I

fr

D

0MCaMAL E u

OF POOR QUALITY

130

N 110L

co

W 0LM

Z

70' • ,

180 0 0 0 0 0 0 °^ 0 0 000 bg° ° ° 0

C o90 O 0 0 °0

0 0 `O°D QO© a No cob ° °

a F" 0Ot^,° O 0 O p,_ 0P 0 %0 00 0 }O 0? ^O 0 O

N 0 O °° O 0 00 O OQ O O 8 Oq O 0000^i. 00 0 0 °0 0 O

(b O O °

-900 8 0 0 o o c90 "^° 00 %% 0 0 o° 99° o (a)

00 a)o o 0

-180 n 0 °1 8 0 ^no^° o 0

0 32 64 96 128 160

FREQUENCY, Hz(a)

TigLET -1115 K. TEXiT a 1135 K, W - 0.5 kg/s.

Figure 17. - Cross-spectra between pressure and temperatureat duct exit (station 4), polTe (bandwidth - 0.4 Hz).

1•

r

i

e'.

®RI pOOF POR QUALITY

i j 12000 .^

vo

100Z 0.

a° 80 (b)

180 ° 00 0 000 On

o 0° ^ o° ocz Ca

o0 °O O ®p ° 8 0 ^p °

CD

B °8°U'0 0o j

00 0 6 0 0 O^ 8 ° °° 08 90 0 8 0

w 0 00 o0o cb ° ^ o °

ti 0 0 o o i

O O ° O,t 04 p OCL 50

,,p-^ ° 8 0 000 °oo

8° ° 0 aQ) °°° p 8 W 80

-180 (b° 0 9 ° °W o 8g ° a o c °o ^^ 8 °^

110

u; `ro a! 90

70(c)

180 T ^ 000 0

0 0% 00 CP

00o0 0^ T

°^p^oo 0 0 °° 0

p p 08

000 O O p°

0g O 0 099° O

O O

U 0 ° p80

Op 0°°1$ 00^ OQ O)

a ZS °Q $ O 00 O Qp p ° 00 0 O-90 0 0 8 ^$ ° °^oSt o 8 0 0 p o

-180 0 (c) ° p

00

0(0 0 X00 0 co^o C^'

0 32 64 96 128 160

FREQUENCY, Hz

(b)TINLET - 875 K. TEXIT - 990 K. W - 0.5 kg/s.

(c)TINLEf - 920 K, TEXIT -1120 K, W -1.13 kg/s.

Figure 17. Concluded. R

1 ^ J

t

ORIGINAL 1,21OF POOR QUALITY

4

1.0

.8

W .6Uz

W

.4

.2

0 32 64 96 128 160FREQUENCY, Hz

(a) TINLET - 1115 K, TEXIT`1135K, W-0.5kgls.

Figure 18. - Coherence between pressure imd temperatureat duct exit (station 4), I p4 T4* 1 2 / I T4 12 1 p4 I 2 band-width - 0.4 Hz).

('F 'OOR QUALIV

}

1.0

.8

.6

.4

.2WUZWW0 0U

.8

.6

.4

.2

0 32 64 96 128 160FREQUENCY} Hz

0) TINLET ° 875 K. TEXIT ° 990 K. W e 0.5 kg/s.(c) T INLET = 920 K. TEXIT ° 1120 K, W -1.13 kg/s.

Figure 18. - Concluded.ji,s