NASA Technical Memorandum 105936 AIAA-93-0599 Acoustic Mode Measurements in the Inlet of a Model Turbofan Using a Continuously Rotating Rake: Data Collection/ Analysis Techniques David G. Hall Sverdrup Technology, Inc. Brook Park, Ohio and Laurence Heidelberg and Kevin Konno Lewis Research Center Cleveland, Ohio Prepared for the 31st Aerospace Sciences Meeting sponsored by the American Institute of Aeronautics and Astronautics Reno, Nevada, January 11-14, 1993 NASA https://ntrs.nasa.gov/search.jsp?R=19930006214 2020-05-08T00:50:21+00:00Z
Transcript
NASA Technical Memorandum 105936AIAA-93-0599
Acoustic Mode Measurements in the Inlet ofa Model Turbofan Using a ContinuouslyRotating Rake: Data Collection/Analysis Techniques
David G. HallSverdrup Technology, Inc.Brook Park, Ohio
and
Laurence Heidelberg and Kevin KonnoLewis Research CenterCleveland, Ohio
Prepared for the31st Aerospace Sciences Meetingsponsored by the American Institute of Aeronautics and AstronauticsReno, Nevada, January 11-14, 1993
ACOUSTIC MODE MEASUREMENTS IN THE INLET OF A MODEL TURBOFAN USING A
CONTINUOUSLY ROTATING RAKE: DATA COLLECTION/ ANALYSIS TECHNIQUES
David G. HallSverdrup Technology, Inc.
Lewis Research Center GroupBrook Park, Ohio 44142
Laurence Heidelberg and Kevin KonnoNational Aeronautics and Space Administration
Lewis Research CenterCleveland, Ohio 44135
A hctrart.
This paper documents the rotating microphonemeasurement technique and data analysis proceduresused to determine circumferential and radial acousticmode content in the inlet of the Advanced Ducted Pro-peller (ADP) model. Circumferential acoustic mode lev-els were measured at a series of radial locations usingthe Doppler frequency shift produced by a rotating inletmicrophone probe. Radial mode content was then com-puted using a least-squares curve fit with the measuredradial distribution for each circumferential mode. Therotating microphone technique is superior to fixed-probetechniques because it results in minimal interferencewith the acoustic modes generated by rotor-stator inter-action. This effort represents the first experimentalimplementation of a measuring technique developed byT.G. Sofrin. Testing was performed in the NASA LewisLow Speed Anechoic Wind Tunnel at a simulated take-off condition of Mach 0.2. This paper includes thedesign of the data analysis software and the performanceof the rotating rake apparatus. The effect of experimen-tal errors is also discussed. The ADP model wasdesigned and built by the Pratt & Whitney Division ofUnited Technologies.
Introduction
Acoustic testing of the ADP model was conductedbetween October 1990 and April 1991 in the NASALewis Low Speed Anechoic Wind Tunnel. Woodward,et al. l documented this testing, concentrating on far-field noise measurements with some results from therotating rake. The present report will provide moredetail on the rotating rake measurement technique. Arelated publication provides a detailed description ofthe rotating rake test results.
The ducted propeller represents a hybrid technology,providing the structural and acoustic benefits of the highbypass ratio turbofan while retaining much of the
efficiency and aero-acoustic performance of the unductedpropeller. In particular, the ADP engine is designed toallow in-flight adjustment of rotor blade pitch angles toprovide reverse thrust. This eliminates the weight anddrag penalties inherent in conventional thrust reverserhardware. Engine fan tones are an important compo-nent in overall aircraft noise. These tones are a result ofthe interaction between rotor blade wakes and the fixedstator vanes. A typical analysis of the spinning pressurefield in the duct proceeds by evaluating the periodic(modal) variations in the circumferential and radialdirections.3
Attempts to measure the modal content of thediscrete, coherent sound in a fan inlet duct have beenmade in the past with limited success. The rotatingrake method employed in this test was developed byT.G. Sofrin and previously documented in Ref. 4.
This method is unique because accurate measure-ment of the modal content is possible despite thecontaminating effect of the wake created by the presenceof the pressure measurement rake directly upstream ofthe rotor. The acoustic signal resulting from rake-rotorinteraction appears as a circumferential mode with orderequal to the number of rotor blades (the rotor-lockedmode. This mode becomes cut-on in a ducted fan onlywhen the rotor blade tip speed becomes supersonic. Theanalysis for a fan with subsonic tip speed (such as theADP model) proceeds by ignoring the rotor-lockedmode. During the NASA Lewis ADP tests, rotatingrake measurements were made with three different inletgeometries and two stator vane configurations. Sometesting was also performed with fixed inlet rods togenerate a known inlet distortion pattern (and thereforea predictable modal content.
Processing of the pressure data was performed in twosteps. First, a high resolution spectral analysis was usedwith time domain averaging to obtain the circumferen-tial modal content at a series of radial locations. Then,these circumferential results were used as the input to a
1
program which calculated radial modes from a least-squares curve fit having eigenfunctions composed fromY and J type Bessel functions. This program also hadthe capability to simulate the inlet pressure field withuser-selected modal coefficients and add random noise topermit analysis of the effect of experimental errors onthe rotating rake method.
The main body of this paper is divided up into sixmajor sections following this introduction. The firstsection presents background information on the rotatingrake technique. The second section describes the experi-mental apparatus and procedures. The third sectionprovides a mathematical basis for radial and circum-ferential mode decomposition. The fourth sectiondiscusses experimental errors and their impact on thedata analysis. The fifth section documents "lessonslearned" and presents recommendations for futureresearch. The sixth and final section contains conclud-ing remarks.
Background
The material in the following section is intended toprovide the reader with a detailed understanding of thepressure measured by a rotating microphone in the inletof a ducted fan. In concept, the rotating pressure probeuses doppler shift physics to separate circumferentialrotating mode orders. This analysis, which was origin-ally published in Ref. 4, is presented below for the sakeof completeness.
First, the mathematical expression for the acousticpressure at a fixed point in the duct will be developedfrom a modal viewpoint. This description will then beextended to describe the pressure measured at a pointwhich rotates, with speed proportional to the fanrotation. It will be shown that each active circumfer-ential mode induces a signal at a unique frequency. Theeffect of the rake wake contamination will then bediscussed. A mathematical analysis will be presented toshow that the contamination produces a spuriouscircumferential mode with order equal to the number offan blades. This rotor-locked mode can not exist forfans with subsonic tip speed (such as the ADP model).The spectral signal corresponding to this mode, whichoccurs at a distinct frequency, is simply ignored in thefinal modal analysis.
General Concept
The acoustic pressure, at a fixed radial location in aplane which is perpendicular to the duct axis, may bedescribed as follows. B is the angular location in thecircumferential direction:
P(0,t)
Re Cm exp i * (in B — n *W *t )n=0 m =- -
where
P pressure
t time
w fan shaft speedin wave order
n shaft speed harmonic number
C mode coefficient
The complex circumferential mode coefficient (C)gives amplitude and phase at a frequency equal to aharmonic of the fan speed w. For a fan with B evenlyspaced, symmetric blades and subsonic tip speed, thesignificant values for n are 13,213,313. . . . Positivevalues for in modes which are rotating in thesame direction as the fan, while negative values indicaterotation in the opposite direction.
Now consider the pressure measured at a point whichis rotating in the circumferential direction. The termB in Eq. (1) is replaced by Q * t, where Q is theangular speed of rotation:
p(0,t)
Re Cm exp —i * [(n * w — in Q * t]n=0 in---
(2)
The frequency of this signal for a given m-number(circumferential mode) at the blade passing frequency(n = B) is thus:
freq=B *w — m *Q (3)
In the nonrotating case, the circumferential (m)modes produce signals only at the blade passing fre-quency (BPF) and its harmonics. In the rotating case,the frequency of the signal produced by a given m-modeis shifted away from the BPF. The degree of shiftdepends on the order of the in-mode and the angularvelocity of the measuring device. For example, supposewe are completing one 360° survey of the duct duringthe time it takes for the fan to complete 100 revolutions.Thus, w = 100 * Q, and Eq. (3) may be rewritten as:
freq = w (B — m/100) (4)
2
In this case, the probe is rotating at a speed whichis directly proportional to the fan speed. This propor-tionality is critical. The frequency of the signal pro-duced by the in 1 circumferential mode will appearwith a frequency shift of 0.01 shaft orders. The m = 2mode will have a frequency shift of 0.02 and so forth.Furthermore, m-modes with negative numbers will haveunique frequency shifts in the opposite sense. A typicalspectrum (from a test with the ADP model) is shown inFig. 1. This spectrum contains clusters of closely spacedtones, centered at frequencies of 13,213,313..., etc. Theblade passing frequency for this case was 2880 Hz.
Contamination Due to the Wake of theRotating Microphone
The above discussion ignores the effect of the wakegenerated by the presence of the microphone in the duct.This section will analyze the effect of that wake andshow that it does not interfere with mode measurementsin most cases.
The interaction noise field generated by the presenceof a fixed inlet distortion may be expressed as a super-position of frequency harmonic terms as follows:
PL(B,t)
Re (CL exp —i * ^(n±L) * B — n * w * tI
(5)
where
P pressure
B angular location of the distortion in the circum-ferential direction
L circumferential spatial harmonic number for thewake
w fan speed, rad/sec
n 13,213,313...
If the distortion rotates slowly, with speed 0, thefrequency at which the rotor cuts through the distortion-induced wake changes by an additive factor of (L * Q)and the noise field may be written as follows:
PL (B,t() _
lRe j CL exp i * [(nfL) * B (n * w±L * 0) * t] 1
To determine the time signal sensed by a microphonewhich rotates with the distortion, we make the substitu-tion B = 0 * t. After cancelling like terms, the result-
ing expression for the time signal generated by the rakewake distortion is:
PL(t) = Re[CL exp i — n(w — Q)tJ(7)
where
n 13,213,313...
This implies that the signal generated by the rotat-ing microphone disturbance appears only at a single fre-quency, equal to the blade passing tone minus B timesthe microphone speed. It is also important to note thatthis frequency is not a function of L, the wake spatialharmonic number. This is a critical result. The inter-pretation given to a signal at this frequency in the"tonal cluster" of a rotating microphone measurement isa circumferential mode of order B (equal to the numberof fan blades). This mode, corresponding to the directrotor field, cannot propagate in a ducted fan with sub-sonic tip speed (such as the ADP model). During anal-ysis of the rotating measurement data from such a fan,the signal component at the frequency corresponding toin B is simply ignored. In cases with supersonic fantip speed, the analysis is contaminated by the spuriousmicrophone wake only for the in B mode, whichmay propagate.
Apparatus
The rotating rake assembly provided a precisecircumferential drive for the microphone rake. A photo-graph of the rotating pressure probe installed on theADP model in the NASA Lewis 9- by 15-Foot AnechoicWind Tunnel is shown in Fig. 2. As shown in the cross-sectional sketch of Fig. 3, this was accomplished bymounting the rake, facing inward, from a large ringgear. The ring gear was driven by a stepping type elec-tric motor coupled through a pinion gear. The ring gearhad a sufficient diameter to assure that only the trans-ducer rake interacted with the fan inflow. The ring gearrevolved on a precison ball bearing track which was, inturn, secured to the test model. The pinion/ring gearratio was 16:110. The rake was equipped with five pres-sure transducers acting as microphones. These transduc-ers, model 8507C-5, were supplied by the Endevco/Allied Signal Company with a nominal sensitivity of8.7 uV/Pa (0.060 V/psi), an operating range of 0 to34 482 Pa (0 to 5 psi), and a nominal diameter of2.34 mm (0.092 in.).
Telemetry and signal conditioning electronics wereattached to the rotating rake/gear. The telemetrysystem used FM encoding to transmit the rake pressuresignals to an adjacent antenna. The five rake transducer
signals were demodulated using standard telemetryreceivers and recorded on FM analog tape using IRIGWide Band Group I format at a speed of 30 in./sec.The fan and ring gear were each equipped with l/revtachometer pickups which were recorded on the analogtape along with an IRIG B time code signal. Infor-mation from these tachometer pickups was used toprecisely control the rake rotational speed as a fractionof the fan rotor speed.
The ADP model was configured with three differentinlets and two different stator vane numbers duringrotating rake testing. The rake was operated at two dif-ferent radial immersions for each model configuration,requiring a total of 10 test runs. Shim pieces of varyingthickness were inserted between the rake arm and thering gear to adjust the radial location of the rake.These shims were designed to insure that when the rakewas changed from inner to outer immersion, transducer#1 occupied the location vacated by transducer #2.During the initial data analysis, the results from thesetwo transducers were carefully examined to verify thatmodel operating conditions were comparable. Duringfinal data analysis, the data from the inner and outerimmersion runs were merged prior to circumferential(spectral) analysis, giving nine independent radial meas-urement locations. The data for the repeated radiallocation (#1 Inner#2 Outer) were determined bytaking a complex average of the two spectra.
A block diagram of the rake contol system is shownin Fig. 4. Testing was conducted by first bringing theADP model up to operating speed. The ring gear drivemotor was then activated and manually brought up toa speed near the desired operating speed. The automaticspeed control system was then engaged to establish atight synchronization between fan and rake. The initialdesign of the rake control system included a fan/rakespeed ratio of 200:1. This was modified to 250:1 duringdevelopment because the stepper motor tended to stallat high fan speeds.
During development of the apparatus, the fan/rakesynchronization requirement was stated as follows:With a fan/rake speed ratio of 250:1, the fan would(ideally) rotate through 90 000° while the rake rotatedthrough 360'. The control system was designed toprovide an actual fan revolution of 90 000±15° whilethe rake rotated once. This was accomplished bymodulating the speed of the rake drive motor. TheADP model was powered by a NASA air turbine drivemotor, operating from the NASA Lewis 450-psi airsupply system. Air turbine speed was set using a systemof pneumatic regulators and valves. The fan speedtended to vary randomly over a small range (approxi-mately f0.2 percent) during testing. This variation hadto be tracked precisely by the rotating rake control
system in order to implement corresponding changes inrake speed. Details may be found in Ref. 5.
Data Processing Algorithms
This following section describes the data processingfunction for this experiment in detail. First, the circum-ferential modal decomposition is discussed. A high reso-lution spectrum analysis was used to compute the mag-nitude and phase of each circumferential mode at aseries of radial locations. The radial mode analysis wasperformed using the radial distribution data for each cir-cumferential mode as the input to a least-squares curvefitting program. Bessel eigenfunctions were used in cal-culating the radial coefficients.
Circumferential Mode Analysis
The pressure measurement data was digitized usingan angle clock to generate 128 samples for each fanrevolution. Fan set speed varied from 6600 to12 000 rpm, so the actual sample rate varied from14 080 to 25 600 Hz. The requirement for this experi-ment was to attempt to analyze the tone clusters cen-tered at the BPF frequency as well as those at 2 * BPFand 3 * BPF. With 16 fan blades, 3 * BPF equates toa center frequency of 9600 Hz for the maximum speedcase of 12 000 rpm. Analog low pass anti-aliasing filterswere used with cutoffs set to 10 kHz during digitizing.
The length of each time averaged pressure ensemblewas selected according to the required spectral resolu-tion. The frequency spread between adjacent tones inthe tone cluster centered at BPF was determined fromthe fan/rake speed ratio to be (fan speed)/250. Thiscorresponds to a frequency spread of 0.8 Hz at the high-est fan speed and to a spread of 0.56 Hz at the lowestspeed. It was decided that at least two to three fre-quency points were required between adjacent tones. Afurther requirement was to form the averaged pressureensembles from an integral number of rake revolutions.An ensemble consisiting of five rake revolutions waschosen. This provided a frequency resolution varyingfrom 0.2 Hz (at 12 000 rpm) to 0.112 Hz (at 8400 rpm).The use of the angle clock, with a constant 128 samplesper fan revolution, resulted in a constant spectralresolution of 0.0078 shaft orders. The number of sam-ples in a single ensemble was calculated as follows:
# samples = (# samples/fan rev) * (# fan revs/rake
X rev) * (# rake revs/ensemble)
= 128 * 250 * 5 = 160 000 (8)
4
Time domain data was collected in files correspond-ing to 20 consecutive rake revolutions, yielding 640Kdata points per channel. From this, 16 overlappingensembles were extracted (each ensemble containing 5rake revolutions) and averaged. The once-per-revolutiontachometer pickups from the rake and fan were digitizedalong with the microphone signals.
The time domain ensembles were extracted, usingthe tachometer channels, so as to be syncronous with therotation of the fan and with the rotation of the rake.Each ensemble was defined to start at the beginning ofthe fan revolution closest to the beginning of the corre-sponding rake revolution. Ensemble number 1 containedrake revolutions 1 to 5. Ensemble number 2 containedrake revolutions 2 to 6, and so on. These ensembleswere then averaged together to improve the signal tonoise ratio. A Hanning window function was appliedafter averaging.
The data storage requirements for this experimentbecame burdensome quite rapidly. Each test conditionrequired storage of 640K samples (1.280 Mbytes perdata channel. There were five rake transducers, twotachometer channels and two rake immersions, giving atotal data storage requirement for each test condition of17.92 Mbytes (1.280 Mbytes * 7 channels * 2 immer-sions). Over 50 test conditions were run, resulting indata storage exceeding 900 Mbytes for raw files alone.
The spectral analysis for this data required compu-tation of a Discrete Fourier Transform (DFT) with160 000 points. This analysis does not allow directapplication of the classic FFT algorithm, since 160 000is not a power of 2. Instead, a chirp-Z transform wasused. This technique allows for calculation of a complexspectrum more quickly than the "brute force" methodemploying the definition of the DFT. Even so, eachchirp-Z transform required computation of three 256K-point FFTs. The computer used to perform this analy-sis was the TRADAR-3 system at NASA Lewis. Thechirp-Z transform algorithm was taken from Ref. 6 andmodified to use the TRADAR-3 vector acceleratorhardware for FFT calculations.
Figure 1 shows a typical spectrum from the circum-ferential analysis. As discussed previously, eachm-mode generates a tone at a distinct frequency. Thespectrum in the figure, centered at the blade passingtone (16 shaft orders), contains 6 peaks. These peaksrepresent the magnitudes of circumferential modes oforder —8,-4,0,+4,+8, and +12. These modes are allmultiples of 4, as expected for this configuration, whichhad four inlet rods. The extraneous tone due to thewake rake is located at mode +16.
Radial Mode Analysis
The algorithm used to compute the radial modecoefficients was originally developed in Ref. 7. Theresults are summarized here for convenience. The out-put from the circumferential analysis consists of a com-plex pressure value for each m-mode at nine differentradial locations. The basic task performed by the radialanalysis program is to calculate a least-squares curve fitusing Bessel eigenfunctions to match this data. Thisyields the (complex) radial mode coefficients.
In an annular duct with uniform axial flow, thefollowing expression may be derived from the separatedacoustic wave equation to describe the modal shape ofthe sound f°ield:7
p(B,r,x,t) _
Pm,njEmn(kmn) exp [i * (2 * IT * f * t + m * 0f7mn * x)]
(9)where
f temporal frequency
B circumferential anglein mode number
n radial mode number
7 axial wave number
r radial distance normalized on outer duct radius
x axial location
kmn eigenvalue (see below)
E(kmnr) is the radial mode function formed from Jand Y type Bessel functions:
E(kmnr) = Cmn[Jm(kmnr) + Q mnYm( k mnr )1 (10)
Values for Qmn and kmn are determined by the ductinner and outer boundary conditions. With a hardwalled duct, there must be a zero radial gradient at thewall, so:
Jm ( k mn) + Q mjY ( k mn) = 0 (Outer wall) (11)
and
J m( k mna) + Q mnYm( k mn a) = 0 (Inner wall) (12)
Where v is the ratio between inner and outer ductwall radius. The factor Cmn above is a normaliz-ing constant which insures that the integral of power
5
squared across the duct is unity. The value of C mn isgiven by:
21 = ir * 1 —
in
(Cmn)22 kmn
* [Jmn(k mn) + Q mnYm( k mn) ]
2 121m
— * [Jmn( Q * kmn) + gmnYm( Q * kmn)kmn
(13)
The general form of the mode pressure phasor in oneaxial plane is given by the following, where n is theradial mode order:
PM,r,f = Pm,n,i * Emn(kmnr) (14)n=0
In the case being considered here, a finite number ofradial modes are assumed to exist, placing an upperbound on the value of n in the above. The outputfrom the circumferential decomposition corresponds tothe left hand side of Eq. (14). Calculation of the Pm,n,iterms may be performed using a least-squares curve fit,minimizing the total mean square error, which is definedas follows:
zNP N_
errorz = E E Pm,n,t * Emn(kmnri) — Pm,ri,ii=1 n =0
(15)
where
Nmmaximum radial mode order to compute
NP number of radial measurement locations
m circumferential mode number
Matrix algebra is used to compute values for theradial mode coefficients such that the mean square erroracross all of the radial measurement locations is mini-mized. The results can be substituted back into a modi-fied form of Eq. (14) to obtain an overall curve fit foreach circumferential mode. Figure 5 shows a plot of themagnitude of the experimental data from a typical testcondition together with corresponding results from thecurve fit.
Figure 6 shows a three-dimensional magnitude plotof all the active radial/circumferential modes for onemodel configuration (one particular combination ofinlet length and stator vane number) at a speed of11 400 rpm. Plots of this type were used to evaluate therelative signifigance of various modes and to develop abetter appreciation of the complexity of the modal con-tent of the ADP model.
Analysis of Experimental Errors
The data measured using the rotating rake methodcontains both desired (signal) and undesired (noise)components. The desired signal is the true acousticpressure generated by the fan. The undesired noise con-sists of all other unsteady pressures, such as turbulence,and/or electronic noise. The following section will dis-cuss the development of procedures to choose the maxi-mum radial mode during curve fitting, and the effect ofnoise contamination on the circumferential/radial modeanalysis. Finally, the effect of the rake speed controlsystem will be discussed.
Selectin¢ the Number of Radial Modes
When performing the curve fit to obtain the radialcoefficients, some method must be found to determine acorrect upper limit on the number of radial modes. Themaximum radial mode which can actually propagate islimited by the duct dimensions and flow conditions.8,9In the ideal case, the circumferential decomposition willcontain only signal and no noise. The mean square errordefined in Eq. (15) will then become zero when the cor-rect number of radial modes is used. In reality, thecircumferential decomposition will contain some noise.This noise will require the use of extraneous, highordered radial mode coefficients to obtain a low valuefor mean square error. Mean square error may be madearbitrarily close to zero if the number of radial modes ismade equal to the number of radial pressure measure-ment locations. During the development of the dataanalysis software, some of the early attempts at curvefitting did use the maximum number of radial modes.
Table 1 shows the radial mode coefficients for atypical test case using actual experimental data. Thecurve fitting program was used, with the number ofradial modes varying from 2 to 8. It appears that the'A correct" solution would include radial modes 0, 1, and2 (this conclusion is based partly on cutoff ratio, whichis described below). The data for trials with five ormore radials shows that the magnitude of some of thehigher ordered coefficients became quite large. Thisincorrect result, which was typical for cases run using alarge number of radials, prompted some further analysis.
6
The curve fitting program was modified to accept userinputs for radial mode coefficients and compute a pres-sure profile for the desired circumferential mode. Thisis the inverse of the normal operation for this program(given a circumferential distribution, compute the radialcoefficients). The radial coefficients computed using thenine standard transducer locations were fed in. Circum-ferential pressures were computed for 50 evenly spacedradial distances, spanning the full radius of the duct.Thus, the radial coefficients determined by curve fittingthrough the nine transducer locations were used to pre-dict the modal pressure shape across the entire duct.
Figure 7 shows the magnitude of the 9-point experi-mental data together with three 50-point curve fits. Inthe case using five radials, curve fit results for locationsoutside the standard transducer positions were reason-able, i.e., the magnitude did not show any large excur-sions. Results using eight radials were questionable,showing a large increase in predicted pressure near thehub. The results with nine radials were quite erroneous.While the curve fit was an exact match for the experi-mental data at the transducer locations, the predictedpressure near the hub became very large and unrealistic.
Calculation of Cutoff Ratio
Analysis of several cases like the one described abovelead to a requirement to predict the "best" number ofradial modes to use for curve fitting each case. Analgorithm was developed to calculate a duct cutoff ratiofor each potential mode. The basis for this calculationmay be found in Ref. 9. The final form of the equationis as follows:
radial coefficient is small (roughly one-half the size orsmaller) compared to the other coefficients, the curve fitis acceptable. Other factors were considered as well.The normalized relative vector error (phase/magnitude)at each transducer location was calculated and examinedas well. In general, the selection of the proper numberof radial modes requires the application of some engi-neering judgement.
Quantitative Effect of Random Noise in Spectral Results
The technique described above for selecting thenumber of radial modes was developed using various testcases, such as the one to be described here. An artificialpressure profile was generated using the curve fit pro-gram with in 8. These numbers are approximatelythe same as one of the experimental cases. The artificalpressure profile was distorted using various levels ofadditive white noise. The Signal to Noise Ratio (SNR)varied from X20 to —3 dB. For each case, a curve fitwas computed using the first three radials. The result-ing radial coefficients are shown in Table 2.
Figures 8 and 9 show the magnitudes of the resultingcurve fits. These results (and others not documentedhere) suggest that SNR values in the 6 to 10 dB rangeare a minimum requirement to obtain an accurate curvefit. During analysis of the experimental data, the ratiobetween background level and tone peak level wasexamined to estimate actual SNR for each circumfer-ential mode. Cases that were used to attempt to predictfar field acoustic levels were selected using a minimumSNR of approximately 6 dB.
n * B * M t 2 I 1^2CR = * (1 — Md! (16) Rake Control System and Digitizing Errors
kmn
Two additional error sources that required moni-where toring were rake/fan position variations and digitizing
clock rate.
n BPF harmonic
B number of blades
Mt rotor tip Mach number
kmn eigenvalue for a particular circumferential (m)and radial (n) mode
Md Mach number at the duct wall, at the axiallocation of the rotating rake
The following procedure was developed for analyzingexperimental results; Let Q equal the highest radialmode number where the cutoff ratio is equal to orgreater than 1. Then calculate a curve fit using Q + 1radial modes. If the magnitude of the Q + 1 order
During testing, speed variations in the fan weredetected by the rake control system and compensatorychanges in rake speed occurred automatically. Thesespeed adjustments were not instantaneous, and not al-ways 100 percent effective. The actual performance wasmonitored during data analysis. The rake and fan wereeach equipped with once-per-revolution tachometer pick-ups. These signals were digitized, along with the pres-sure transducers, using the angle clock. The number ofsamples between the occurrence of the rake once-per-revolution and the nearest fan once-per-revolution wascalculated for each rake revolution. Ideally, this timedifferential would be constant, indicating tight syn-chronization (the fan should return to the same angular
position at the start of each rake revolution). Caseswhere the synchronization was poor were either redigi-tized from analog tape, or not used for radial modedecomposition.
When the data were digitized using the angle clock,the fan speed variations would sometimes cause theangle clock to generate 127 or 129 pulses per fan revolu-tion instead of the desired 128. The data analysissoftware had a feature to count the number of samplesbetween each fan once-per-revolution tachometer pulse.The number of samples between each rake tachometerpulse was also counted. During the analysis, thesoftware generated a report on these counts to warn theoperator of loss-of-sync events. Usage of rake data withserious loss-of-sync was minimized based on thesereports.
The detection of data with more or less than thedesired number of samples per revolution (128) is asimplistic check on synchronous digitizer performance.A better method would be to sample at a rate severaltimes higher than the minimum of 128 samples perrevolution. This would allow more accurate detection ofloss-of-sync. One drawback to this approach would belarger data file storage requirements. Tachometersystems generating more than one pulse per revolutionwould also be helpful.
Lessons Learned/ Recommendations forFuture Research
Two difficulties that were encountered duringrotating rake testing with the ADP model could beaddressed in future experiments. The first difficulty wasrelated to data acquisition and processing. The seconddifficulty involves the characteristics of the ducted fanmodel itself. This section concludes with some generalcomments on the selection of rake transducer locationsand fan/rake speed ratio.
Rotating rake data from the ADP model wasrecorded on analog tape and played back later using anangle clock to control digitizing. This procedure wastedious and inefficient. It is recommended that futureprograms provide for on-line digitizing of the transducersignals during testing, assuming no adverse impact onthe time required for data acquistion. A high speed/multichannel A/D computer system would be required.In place of the angle clock, the model should be designedto provide the digitizing control signal. For example,the fan shaft could be provided with an encoding deviceto generate 128 or more pulses per revolution. Thissignal could then be conditioned and used to drive theA/D converter directly.
The use of a fan having many propagating modesresults in a complicated far field acoustic directivity.This does not detract from the validity of the rotatingrake measurements, however, one goal in the develop-ment of computational aero-acoustics is to predict farfield acoustic radiation given the in-duct modal coeffi-cients. The rotating rake experimental data will be usedto verify computational aero-acoustic results and/orimprove computational models. The comparisonbetween measured and predicted data becomes moredifficult when many modes are propagating. A futuretest could be conducted where the fan is designed toallow only a few selected modes to propagate. Thiswould simplify the near-field to far-field comparison taskconsiderably.
Selection of the number and location for the raketransducers has, in the past, been done empirically.Reference 4 (Cicon, Sofrin, and Mathews) suggests theuse of a number of transducers equal to twice thehighest radial order that is expected. Reference 7(Moore, JS and V) recommends that transducers bespaced in equal increments of duct radius squared, thusproviding equal coverage of duct area. The rotatingrake apparatus for this test provided nine radial meas-urements as described above. Analysis of the test casesat BPF were, for the most part, successful. If the radialcontent at higher harmonics of the blade passing fre-quency is of interest, more resolution is needed. Duringthe ADP experiment, some analysis of data at 2 * BPFwas performed. It was limited (typically) to cases whereradial modes of order 4 or less were present.
Experience gained in the ADP test program suggeststhat the best method is an iterative process. The initialestimate for the number of transducers should be basedon Ref. 4, with initial locations based on Ref. 7. Thisconfiguration would then be evaluated by simulating thein-duct pressure variations, inputting modal coefficientsand additive noise. The sensitivity of the curve fittingprocess to noise level would be evaluated, and changesin microphone number and/or location could be pro-posed. Further simulation studies would then beconducted to optimize the rake design. The samecomputer program which was used to analyze the ADPdata has the capability to perform this analysis.
The rake/fan speed ratio is another importantparameter in the design of a rotating rake experiment.Rake speeds which are high compared to the fan speedare desirable to provide a greater frequency spreadbetween adjacent tones. In some cases, the rake drivemotor will be the limiting factor. Another limit existsas well. Referring back to Eq. (3), consider the frequen-cies of the following two tones (B = number of blades):
8
(1) One caused by a circumferential mode of order+13 at BPF. This is the highest-frequency tone in thecluster near BPF for subsonic tip speed.
facilitate the verification of computational aero-acousticpredictions.
(2) One caused by a circumferential mode of order—213 at 2BPF. This is the lowest-frequency tone in thecluster near 2BPF for subsonic tip speed.
As rake speed is increased, a point will be reachedwhere these two tones interfere with each other. Thisspeed is the maximum upper limit for the case of sub-sonic tip speed. In cases with supersonic tip speed,modes of order greater than B may propagate. Themaximum rake speed must be decreased accordingly.
Concluding Remarks
Testing of the ADP model in the NASA Lewis 9- by15-Foot Low Speed Wind Tunnel included the first suc-cessful attempt to measure the inlet acoustic modes of aducted fan using a rotating rake apparatus. This tech-nology is significant for the following reasons:
1. The mechanisms controlling the generation ofducted fan acoustic modes can be investigated in an effi-cient manner, with rake intrusion effects minimized. Abetter understanding of these mechanisms can be used todevelop more accurate computational models to predictthe modal content.
2. The computational models describing acousticmode propagation can be improved by performing acomparison between actual and predicted results forfar-field acoustic levels.
The improved computational models can then beused to predict the acoustic performance of new aircraftengine systems during the early design phase, thusshortening development time and minimizing develop-ment costs.
The following improvements are recommended forfuture rotating rake experiments:
1. Use on-line digital data acquisition to analyze therake pressures rather than analog tape recording. Ifdata is to be digitized at a rate of 128 samples per fanrevolution (for example, then install a 128-per-revolution shaft encoder on the fan.
2. Use a ducted fan with a simple acoustic mode sig-nature, i.e., only one or two modes active at any time.A large, low speed fan rig is suggested, with inlet rodsas needed to select the cut-on modes. This change will
3. Select the rotating rake drive motor to allowoperation at maximum rake speed, subject to the limitimposed by interference between adjacent BPF harmon-ics. This will reduce the requirement for extremely finespectral resolution and large computer data files.
References
1. Woodward, R.P., Bock, L.A., Heidelberg, L.J., andHall, D.G., "Far-Field Noise and Internal ModesFrom a Ducted Propeller at Simulated AircraftTakeoff Conditions," AIAA Paper 92-0371, Jan.1992. (Also, NASA TM-105369, 1992).
2. Heidelberg, L., and Hall, D., "Acoustic Mode Meas-urements in the Inlet of a Model Turbofan Using aContinuously Rotating Rake," to be published asAIAA Paper 93-0598, 1993.
3. Sofrin, T.G., "Some Modal-Frequency Spectra of FanNoise," AIAA Paper 81-1990, Oct. 1981.
4. Cicon, D.E., Sofrin, T.G., and Mathews, D.C.,"Investigation of Continuously Traversing Micro-phone System for Mode Measurement," NASACR-168040, 1982.
5. Konno, K.E., and Hausmann, C.R., "Rotating RateDesign for Unique Measurement of Fan-GeneratedSpinning Acoustic Modes." NASA TM-105946, Jan.1993.
6. Stearns, S.D., and David, R.A., Signal ProcessingAlgorithms, Prentice-Hall, Inc., Englewood Cliffs,NJ, 1988.
7. Moore, C.J., "Measurement of Radial And Circum-ferential Modes in Annular and Circular Fan Ducts,"Journal of Sound and Vibration, Vol. 2, Jan. 1979,pp. 235-256.
9. Rice, E.J., Heidmann, M.F., and Sofrin, T.G.,"Modal Propagation Angles in a Cylindrical Ductwith Flow and Their Relation to Sound Radiation,"AIAA Paper 79-0183, Jan. 1979. (Also, NASATM-79030, 1979.
Figure 2.—Photograph of the ADP model in the 9X15 LSWT withrotating rake hardware installed.
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Figure 3.—Details of fan mode measurement rake.
11
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speed/conditionco
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'Manual control basedon oscilloscope Rake/ring gear
Figure 4.—Rotating rake system block diagram.
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qa
8N
a
4 O Curve fit resultsq Experimental
045 .55 .65 .75 .85 .95
Normalized radial location, 1.0 = duct
Figure 5.--Curve fit results, circum. mode 4, 3 radial.
80
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circumferential mode numberFigure 6.—Modal content for ADP model with long inlet and 22-vane stator at
11 400 RPM.
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70
60
50
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20
10
0.3 .4 .5 .6 .7 .8 .9 1.0
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Figure 7.--Curve fit comparison.
70 q No noiseO SNR =20 dB
60 10 SNR =14 dB0 SNR=10dB O
50
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30
20
10
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Normalized radial location, 1.0 = duct
Figure 8.—Magitude vs. SNR, curve fit results, m = 8.
160
q No noiseO SNR=6dB0 SNR=3dB4 SNR=OdB
120
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80O 8 OIL
40
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Radial location, 1.0 = duct wall
Figure 9.—Magitude vs. SNR, curve fit results, m = 8.
13
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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3_ REPORT TYPE AND DATES COVERED
January 1993 Techmol l Memorandum4. TITLE AND SUBTITLE 5. FUNDING NUMBERS
Acoustic Mode Measurements in the Inlet of a Model Turbofan Using aContinuously Rotating Rake: Data Collection/Analysis Techniques
WU-535- 03-106. AUTHOR(S)
David G. Hall, Laurence Heidelberg and Kevin Konno
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATIONREPORT NUMBER
National Aeronautics and Space AdministrationLewis Research Center E-7452Cleveland, Ohio 44135-3191
9. SPONSORING/MONITORING AGENCY NAMES(S) AND ADDRESS(ES) 10. SPONSORING/MONITORINGAGENCY REPORT NUMBER
National Aeronautics and Space AdministrationWashington, D.C. 20546-0001 NASA TM-105936
AIAA-934599
11. SUPPLEMENTARY NOTES
Prepared for the 31st Aerospace Sciences Meeting sponsored by the American Institute of Aeronautics and Astronautics, Reno, Nevada,January 11-14, 1993. David G. Hall, Sverdrup Technology, Inc., Lewis Research Center Group, 2001 Aerospace Parkway, Brook Park, Ohio44142; Laurence Heidelberg and Kevin Konno, NASA Lewis Research Center. Responsible person, David G. Hall. (216) 433-3392.
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Unclassified -UnlimitedSubject Category 71, 7
13. ABSTRACT (Maximum 200 words)
This paper documents the rotating microphone measurement technique and data analysis procedures used to determinecircumferential and radial acoustic mode content in the inlet of the Advanced Ducted Propeller (ADP) model. Circum-ferential acoustic mode levels were measured at a series of radial locations using the Doppler frequency shift produced bya rotating inlet microphone probe. Radial mode content was then computed using a least squares curve fit with themeasured radial distribution for each circumferential mode. The rotating microphone technique is superior to fixed-probetechniques because it results in minimal interference with the acoustic modes generated by rotor-stator interaction. Thiseffort represents the first experimental implementation of a measuring technique developed by T.G.Sofrin. Testing wasperformed in the NASA Lewis Low Speed Anechoic Wind Tunnel at a simulated takeoff condition of Mach 0.2. Thispaper includes the design of the data analysis software and the performance of the rotating rake apparatus. The effect ofexperimental errors is also discussed. The ADP model was designed and built by the Pratt & Whitney Division of UnitedTechnologies.
14. SUBJECT TERMS 15. NUMBER OF PAGES
Coherent fan noise; Acoustics; Measuring techniques 1416. PRICE CODE
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