SPATIAL CHARACTERISTICS OF THE UNSTEADY DIFFERENTIAL PRESSURESON 16% F/A-18 VERTICAL TAILS
Robert W. Moses, Ph.D.AIAA Member
Aeroelasticity BranchNASA Langley Research Center
Hampton, VA
Holt Ashley, Professor EmeritusAIAA Honorary Fellow
Department of Aeronautics & AstronauticsStanford University
Stanford, CA
Abstract
Buffeting is an aeroelastic phenomenon whichplagues high performance aircraft at high angles ofattack. For the F/A-18 at high angles of attack,vortices emanating from wing/fuselage leadingedge extensions burst, immersing the vertical tailsin their turbulent wake. The resulting buffeting ofthe vertical tails is a concern from fatigue andinspection points of view.
Previous flight and wind-tunnel investigations todetermine the buffet loads on the tail did notprovide a complete description of the spatialcharacteristics of the unsteady differentialpressures. Consequently, the unsteady differentialpressures were considered to be fully correlated inthe analyses of buffet and buffeting. The use offully correlated pressures in estimating thegeneralized aerodynamic forces for the analysis ofbuffeting yielded responses that exceeded thosemeasured in flight and in the wind tunnel.
To learn more about the spatial characteristics ofthe unsteady differential pressures, an available16%, sting-mounted, F-18 wind-tunnel model wasmodified and tested in the Transonic Dynamics
Tunnel (TDT) at the NASA Langley ResearchCenter as part of the ACROBAT (ActivelyControlled Response Of Buffet-Affected Tails)program. Surface pressures were measured athigh angles of attack on flexible and rigid tails.Cross-correlation and cross-spectral analyses ofthe pressure time histories indicate that theunsteady differential pressures are not fullycorrelated. In fact, the unsteady differentialpressures resemble a wave that travels along thetail. At constant angle of attack, the pressurecorrelation varies with flight speed.
Introduction
Buffeting is an aeroelastic phenomenon whichplagues high performance aircraft, especially thosewith twin vertical tails. For aircraft of this type athigh angles of attack, vortices emanating fromwing/fuselage leading edge extensions burst,immersing the vertical tails in their wake, as shownin Figure 1. The resulting buffeting of the verticaltails is a concern from fatigue and inspectionpoints of view. Previous wind-tunnel and flighttests were conducted to quantify the buffet loadson the vertical tails.
The spectral aspects of the unsteady differentialpressures on the vertical tail caused by a burstLEX (leading edge extension) vortex are welldocumented.1 The results of Reference 1 illustratethe variations of the power spectral densities androot mean square (rms) values of the differentialpressures with flight speed, angle of attack (AOA),
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dynamic pressure, and tail coordinate using onlyfive differential pressure transducers.1 InReference 1, the worst case condition, defined bythe highest rms values of differential pressure atdesign limit load, occurs around 340 psf and 32degrees angle of attack. Other findings were thatthe root mean square value of the differentialpressure varies linearly with dynamic pressure,and that Strouhal scaling provides a means forcomparing model and flight data. Also, the highestrms values occurred at stations closest to theleading edge while the lowest rms values occurrednear the trailing edge with a gradual change in rmsvalues between these two regions of the tail. Thereasons for this gradual reduction in the rmsvalues with increase in chord coordinate were notexplained. During the investigation, the unsteadydifferential pressures were considered fullycorrelated (in phase) because their results of thepressures measured at only five stations did notindicate otherwise. The sampling rate used in thistest is not clearly reported.
Figure 1. Flow Visualization of Leading EdgeExtension (LEX) Vortex Burst,30 Degrees Angle of Attack
After the research of Reference 1 and prior to theresearch reported herein, wind-tunnel tests wereconducted to investigate the spatial characteristicsof the unsteady surface pressures on the tail.2Contour plots of the time delays on each surfacewere constructed using cross-correlation analysesof the unsteady pressures measured on each tailsurface of a 6% rigid F/A-18 model tested at Mach0.6. As shown in Figure 2 for 35 degrees angle ofattack, the contours for each surface are quitedifferent. The spatial characteristics of the
unsteady differential pressures are unclear fromexamination of these plots of the unsteadypressures on each surface. On the inboardsurface at 35 degrees angle of attack and Mach0.6, the time delay from a station near the leadingedge to a station near the trailing edge isapproximately 0.0006 seconds. The sampling rateis not clearly reported; however, a time delay of0.0006 seconds indicates that a high sampling rateis needed to capture the convection of the flow.
Because little information was known regardingtheir spatial correlation, the differential pressureson the tail were assumed to be zero- or fully-correlated during the computations of thegeneralized aerodynamic forces.3"5 Theseanalyses did not estimate the buffeting accurately.After further study, it was concluded that the issueof pressure correlation is the key to successfulbuffeting prediction and should be the subject ofmore research.4'5
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Figure 3. Cross-Spectral Density and CoherenceFunctions Between the Differential Pressures Nearthe Leading-Edge Tip and the Trailing-Edge Tip,
Full-Scale Tail, M=0.15, (From Reference 6)
To learn more about the pressure correlation, afull-scale F/A-18 was tested at high angles ofattack at a maximum speed of Mach 0.15 in a windtunnel. Plots of the magnitudes and phase delaysof the unsteady differential pressures wereconstructed using cross-spectral analyses of theunsteady pressures measured on each tail surfaceat Mach 0.15.6"7 As shown in Figure 3a for 20degrees AOA, the phase is approximately negative400 degrees (-360-40) at 45 Hz, which is thefrequency of the first torsion mode of the tail. Asshown in Figure 3b for 32 degrees angle of attack,the phase is approximately negative -180 degreesat 20 Hz. In Figure 3b, the phase values atfrequencies above 20 Hz are difficult to determinebecause of the wrapping used in plotting thephase. Although flight conditions were notmatched, the results of this wind-tunnel testindicate that the differential pressures acting on
the tail are not in phase. However, thedependencies of pressure correlation on flightconditions were not clearly understood from theseresults.
To better understand the pressure correlationduring buffet, an available 16%, sting-mounted, F-18 wind-tunnel model was modified and tested inthe Transonic Dynamics Tunnel (TDT) at theNASA Langley Research Center as part of theACROBAT (Actively Controlled Response OfBuffet-Affected Tails) program.8 Surfacepressures were measured for scaled flightconditions at high angles of attack on flexible andrigid tails. Pressure signals were sampled at 6538Hz for approximately 30 seconds. Cross-correlation and time-averaged cross-spectralanalyses 9 were performed for identifying anyconsistent spatial characteristics of the unsteadydifferential pressures. The results of theseanalyses indicate that the unsteady differentialpressures are not fully correlated. In fact, theunsteady differential pressures resemble a wavethat travels along the tail.
The purpose of this paper is to present some wind-tunnel results that illustrate the partial correlation ofthe unsteady differential buffet pressures on a rigidtail and a flexible tail of a 16% F/A-18 model.
Wind-Tunnel Model and Tunnel Conditions
An existing 16% (also referred to as 1/6-scale),rigid, full-span model of the F/A-18 A/B aircraft wasrefurbished, and three flexible and two rigid verticaltails were fabricated. This model was then sting-mounted in the Transonic Dynamics Tunnel (TDT)at the NASA Langley Research Center, as shownin Figure 4, where it underwent a series of tests todetermine buffet flowfield characteristics and toalleviate vertical tail buffeting using activecontrols.8
The three flexible tails were fabricated from a 1/8-inch thick aluminum plate and covered with balsawood. The aluminum plate thickness was chosensuch that the frequencies and shapes of the firstthree modes were close to those of the actual tailas determined by a finite element analysis. Allthree flexible tails were instrumented with a rootstrain gage aligned to measure bending momentand with two tip accelerometers near the leadingand trailing edges. The two rigid tails (one port,
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one starboard) were fabricated from a block ofaluminum and were geometrically identical to theflexible tails. Two of the flexible tails and both rigidtails were instrumented with unsteady pressuretransducers for measuring pressures on bothsurfaces of the tails, as shown in Figures 5 and 6,respectively. At each station, there are twotransducers, one on each side of the tail.
Figure 4. 1/6-Scale F/A-18 Model Mounted in theTransonic Dynamics Tunnel
For buffet, the Strouhal number is the primaryscaling relationship used in determining tunnelconditions.1 Shown in equation 1, the Strouhalnumber, n, is a nondimensional frequencyparameter that is proportional to reducedfrequency.
where f is frequency in Hz, c is characteristiclength, and U is velocity. A frequency ratiobetween model and aircraft structural modes andforcing function spectra of unity was chosen,leaving only two variables, c and U, to bedetermined. According to the Strouhal number, tomatch frequency content between aircraft modelsof different scales, the relationship of c divided byU must be identical. Since 1/6-scale model waschosen, only one variable, U, needed to bedetermined. According to Reference 1, thedynamic pressure where vertical tail buffetingappeared maximum was roughly 340 psf. Using avalue for air density at an altitude of approximately12,000 feet, velocity was determined. For the caseof a 1/6-scale wind-tunnel model that has afrequency ratio of one with the aircraft, the windspeed requirement is 1/6 of the flight speed of theaircraft. For the ACROBAT program, a tunnelspeed of 110 feet per second in atmospheric air(14 psf) was used.
General Buffet and Buffeting Characteristics of the16% F/A-18 Wind-Tunnel Model
Power spectral density plots of the unsteadydifferential pressures at one station on the tailillustrate the effect of angle of attack on themagnitude of buffet. The buffet at 20 degreesAOA, shown in Figure 7(a), appears broad bandcompared to the buffet at 34 degrees AOA, shownin Figure 7(b). At 34 degrees AOA, the magnitudeof the aerodynamic input (in the lower frequencies)has grown while its peak has shifted to a lowerfrequency value. These trends of the pressureswith angle of attack are consistent with otherexperimental data.1'6
The pressures, shown in Figure 7 (a)-(b), createdthe buffeting, or structural response to the buffet,shown in Figure 8 (a)-(b), respectively. At 34degrees angle of attack, the buffeting shown inFigure 8(b) around 15 Hz, which corresponds tothe first bending mode of the vertical tail, has
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intensified by 1.5 orders of magnitude above thelevel at 20 degrees AOA, shown in Figure 8(a).Since the buffet, or force input to the tail, hasshifted to a lower frequency with increased angleof attack, as indicated by Figure 7, the resultingvertical tail buffeting mainly consists of a responsein the first bending mode, as indicated bycomparing Figures 8 (a) and 8 (b). The responsein the mode around 58 Hz has not grownsignificantly with the increase in angle of attackbecause the magnitude of the pressures in thatportion of the spectrum has not increased withincreased angle of attack, as seen in Figure 7.These trends agree well with similar results ofother wind-tunnel tests.1l 6
(a) 20 Deg AOA (b) 34 Deg AOAFigure 8. Root Bending Moment Near Mid-Chord
Root, 1/6-Scale Flexible Tail
Chord-Wise Variation in Magnitude of TheUnsteady Differential Pressures
The magnitude of the unsteady differentialpressure varies with chord location, as seen inFigure 9 for the rigid tail at 34 degrees angle ofattack. The peak value and the rms value of thedifferential pressures near the leading edge arehighest, as seen in Figure 9c. As chord location is
3.5
3
2.5
2
1-5
1
0.5
0
Diff. P at Station 4
RMS: 0.024
20 40 60 80 100Frequency, Hz
a) Near Trailing Edge
Diff. P at Station 57
6
5
4
>. 3
1
0
XN
RMS: 0.031
0 20 40 60 80Frequency, Hz
b) Near Mid-Chord
Diff. P at Station 6
100
20 40 60 80 100Frequency, Hz
c) Near Leading Edge
Figure 9. Differential Pressures at Three Stationson the Rigid Tail Along The 75% Span Line, 34
Degrees AOA
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increased, the peak value and the rms value of theunsteady differential pressure drop, as seen inFigure 9, with the lowest values occurring near thetrailing edge. The shape of the power spectraldensity curves is similar regardless of chordlocation. Similar results were observed for theflexible tail.
Cross-Correlation Functions For The Rigid Tail
Cross-correlation functions were computed for thedifferential pressures acquired at the surfacestations of the rigid tail, shown in Figure 6. InFigures 10a, the time delays and coefficients areshown for the pressures between stations near thetip. The wave form changes more betweenstations 1 and 2 than between stations 2 and 3, asindicated by the maximum value of the coefficient(0.651 versus 0.777). Since the time delaybetween stations 1 and 2 is longer than the timedelay between stations 2 and 3 (-0.0031 secondsversus -0.0023 seconds, shown in Figure 10a), thetransport velocity between stations 1 and 2 isslower than the transport velocity between stations2 and 3.
Similar results are observed for the pressures at75% span, as shown in Figure 10b. However, thetransport velocities appear identical. In Figure 10c,the cross-correlation functions between trailingedge and leading edge stations are provided forthe two span locations just discussed. As a check,the maximum coefficients and their time delays ofthe two plots in Figure 10c should match theproduct and the summation of the individualcoefficients and time delays, respectively, ofFigures 10a and 10b.
The cross-correlation functions for the pressuresat lower stations on the tail are provided in Figures10d through 10f. Since the stations at the lowerspan are more highly separated than the stationsat the higher span, the time delays are longer.There is no noticeable difference in the transportvelocities between the stations at 40% span or25% span, as indicated by the time delays ofFigures 10d and 10e. In Figure 10f, the cross-correlation functions between trailing edge andleading edge stations are provided for the twospan locations just discussed. As a check, themaximum coefficients and their time delays of thetwo plots in Figure 10f should match the productand the summation of the individual coefficientsand time delays, respectively, of Figures 10d and10e.
Cross-Spectral Density Functions ForThe Rigid Tail
The cross-spectral densities between thepressures near the trailing edge with respect to thepressures near the leading edge are provided inFigure 11 for various span locations on the rigid tailshown in Figure 6. The cross-spectral densityfunctions provide similar information as the cross-correlation functions but in the frequency domain.The magnitude illustrates the frequencycomponents of the spectra that dominate thepressure signal, and the phase indicates thenumber of degrees that a particular frequencycomponent has turned upon reaching thedownstream station after passing the upstreamstation. For instance, the magnitude of(Diff_1)/Diff_3) indicates that the dominantfrequency component is around 23 Hz and turnsapproximately 48 degrees between stations 1 and3; or, at any time, the 23-Hz component at station1 lags the 23-Hz component at station 3 by 48degrees.
£0.-200 Frequency, HzFrequency, Hzb) Near Trailing Edge with respect to Near Leading
Edge, 40% Span and 25% Span
Figure 11. Cross-Spectral Density FunctionsBetween Differential Pressures at Stations on
Rigid Tail, 34 Deg AOA (See Figure 6 for StationLocations)
Cross-Correlation and Cross-Spectral DensityFunctions For The Flexible Tail
Cross-correlation and cross-spectral densityfunctions are shown for the flexible tail to illustratethat flexibility does not appear to affect time andphase delays. For instance, for the rigid tail(shown in Figure 6), the coefficient and time delayfor (Diff_5)/(Diff_6) are 0.773 and 0.0029,respectively, as shown in Figure 10b.
Corresponding to these stations on the flexible tail(shown in Figure 5), the coefficient and time delayfor (Diff_6)/(Diff_7) are 0.772 and 0.0026,respectively, as shown in Figure 12a. Similarcomparisons can be made among other cross-correlation and cross-spectral density functionsfound in Figures 10 through 13 for correspondingstations on the rigid and flexible tails shown inFigures 5 and 6.
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Figure 13. Cross-Spectral Density FunctionsBetween Differential Pressures at Stations onFlexible Tail, 34 Deg AOA (See Figure 5 for
Station Locations)
Comparing Time Delays With Phase Delays
The time delays can be verified using the distancebetween the two stations and the transportvelocity, as shown in Figure 14.
Figure 14. Visualization of Flow, Frequency, andDistance Between Stations
The transport velocity is expected to be less thanthe freestream velocity of 110 fps because theburst decelerates the flow local to the vertical tail.For the rigid tail at 34 degrees angle of attack, thetime delay, in Figure 10c, and phase delay at 23.1Hz, in Figure 11a for (Diff_4)/(Diff_6), are 0.0060seconds and 46 degrees, respectively. Stations 4and 6 are 6.1 inches apart. Using the separationdistance and freestream velocity, the time delay iscomputed using equation 2 as 0.0046 seconds.However, the freestream velocity is considerablyfaster than the transport velocity, which may becomputed as 85 fps using the 6.1-inchesseparation divided by the 0.0060-seconds timedelay. Using the time delay of 0.0060 seconds,the phase delay (at 23.1 Hz) is computed usingequation 3. The computed value of 49.8 degreesis close to the 46 degrees picked off the phase plotfor the cross-spectral density function shown inFigure 11 a.
t = d / U (2)= 6.1"/12ipf)/110fps= 0.0046 seconds
f = w t (3)= (2 rc f ) (d /U )= 49.8 degrees
Comparing Phase Delay Results Of DifferentModels and Tunnel Conditions
To verify the phase relationships of the partiallycorrelated unsteady differential pressures,comparisons were made with data from other
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tests. The time delays and phase delayscomputed for other wind-tunnel models werecompared to some of the results presented abovein the cross-correlation and cross-spectral densityfunctions. Using equation 2 above, the ratio of thetime delays for the two models may be written asfollows:
t|/6 _ "1/6 p 06(4)
0.06
Using d1/6= 2.66 do.06, and the U0.06 = 6 U1/6 (Mach0.6 / Mach 0.1), the time ratio is 16. As notedpreviously in Figure 2, the time delay between thepressures near the leading edge and the trailingedge on the inboard surface of the 6% rigid tail ofReference 2 is approximately 0.0006 seconds.The time delay for the 1/6-scale rigid tail, shown inFigure 10f for (Diff_10)/(Diff_12) is approximately0.009 seconds. These two time delays yield aratio of 15 which is close to the ratio of 16computed above.
Comparisons between the full-scale wind-tunneldata of Reference 6 and the 1/6-scale phasedelays further illustrate the scaling relationship.10
Using equation 3, the scaling relationship betweenthe phase of the 1/6-scale and the phase of thefull-scale cross-spectra is derived, as shown inequation 5. Using f1/6 = fF , d1/6= 6 dF, and UF = 1 .5U1/6 (Mach 0.15 / Mach 0.10), the phase ratio is0.25.
ri/6-Scale _
0Full-Scale fFdFU
,_.
l/6
Shown in Figure 15, the phase at 45 Hz in thecross-spectral density function for the 1/6-scale tailis approximately negative 100 degrees at 20degrees angle of attack. As shown in Figure 3a,the phase at 45 Hz in the cross-spectral densityfunction for the full-scale tail at 20 degrees angleof attack is approximately negative 400 degrees.The ratio of these two phase values is 0.25.Similarly, for the 1/6-scale model at 34 degreesangle of attack, the phase at 20 Hz in the cross-spectral density function shown in Figure 13a isapproximately negative 45 degrees. As shown inFigure 3b, the phase at 20 Hz in the cross-spectraldensity function for the full-scale tail isapproximately negative 180 degrees, which yieldsa ratio of 0.25.
0.01(Diff_1)/(Diff_3)
'cO)to
20 40 60 80 100200
o>30)U)(0
£-200
Frequency, HzFigure 15. Cross-Spectral Density Functions
Between Differential Pressures Near Trailing Edgeand Leading Edge, Near Tip, 1/6-Scale Flexible
Tail, 20 Degrees Angle of Attack
Conclusions
The unsteady differential pressures measured athigh angles of attack on rigid and flexible tails of a16% F/A-18 wind-tunnel model are not in phase.Cross-correlation and cross-spectral densityfunctions were presented which illustrate the timelags (in the time domain) and phase lags (in thefrequency domain) associated with the unsteadydifferential pressures at stations on vertical tails.The time lags and phase lags are characteristic ofa wave and were shown to be functions of thedistance between stations and the transportvelocity. At a given angle of attack, the partialcorrelation scales with flight speed, asdemonstrated through comparisons of time andphase lags from other wind-tunnel tests at differentconditions. For the 16% (1/6-scale) F/A-18 model,tail flexibility does not appear to affect the timedelays or the phase delays of the unsteadydifferential pressures since flexible-tail and rigid-tail results appeared similar. Comparisons withflight data are necessary for substantiating thepartial correlation presented herein and forexamining further the influence of tail flexibility onpressure correlation.
Acknowledgments
The authors wish to extend their gratitude to theNASA Langley Research Center, especially the
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engineers and technicians at the TransonicDynamics Tunnel, for the support of the 16% F/A-18 wind-tunnel tests mentioned herein. A specialpersonal thanks is extended to Mr. MichaelBanford of Wright Laboratory, Wright-Patterson AirForce Base for his staffing and maintaining thepressure data acquisition system used to recordthe pressures on the vertical tails. Special thanksare extended to Ms. Sheri Hoadley and Ms. CarolWieseman at NASA Langley Research Center fortheir analysis software that was used in computingand plotting .the 16% F/A-18 pressure resultsshown herein.
References
Zimmerman, N. H., and Ferman, M. A.,"Prediction of Tail Buffet Loads for DesignApplication," Vols. I and II, Rept. No. NADC-88043-60, July 1987.Lee, B. H. K., Brown, D., Zgela, M., and Poirel,D., "Wind Tunnel Investigation and FlightTests of Tail Buffet on the CF-18 Aircraft", inAircraft Dynamic Loads Due to FlowSeparation. AGARD-CP-483, NATO AdvisoryGroup for Aerospace Research andDevelopment, Sorrento, Italy, April 1990.Ashley, H., Rock, S. M., Digumarthi, R.,Chaney, K., and Eggers, A. J. Jr., "ActiveControl For Fin Buffet Alleviation," WL-TR-93-3099, January 1994.James, K. D. and Meyn, L. A., "Dependenceon Integrated Vertical-Tail Buffet Loads ForF/A-18 on Sensor Density," SAE TechnicalPaper 94110, Aerospace Atlantic Conferenceand Exposition, Dayton, Ohio, April 18-22,1994.Bean, D. E. and Lee, B. H. K., "Correlation ofWind Tunnel and Flight Test Data For F/A-18Vertical Tail Buffet," AIAA-94-1800-CP, 12th
AIAA Applied Aerodynamics Conference,Colorado Springs, CO, June 20-22, 1994.Pettit, C. L., Banford, M., Brown, D., andPendleton, E., "Pressure Measurements on anF/A-18 Twin Vertical Tail in Buffeting Flow,"Vols 1-4, United States Air Force, Wright Lab.,TM-94-3039, Wright Patterson AFB, OH,August 1994.Meyn, L. A. and James, K. D., "Full-ScaleWind-Tunnel Studies of F/A-18 Tail Buffet,"Journal of Aircraft. Vol. 33, No. 3, May-June1996.
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Moses, R. W., "Active Vertical Tail BuffetingAlleviation on a Twin-Tail Fighter ConfigurationIn a Wind Tunnel," presented at the CEASInternational Forum on Aeroelasticity andStructural Dynamics 1997, 17-20 June 1997,Rome, Italy.Bendat, J. S. and Piersol, A. G., EngineeringApplications of Correlation and SpectralAnalysis. Second Edition, John Wiley & Sons,Inc., 1993.Moses, R. W. and Pendleton, E., "AComparison of Pressure MeasurementsBetween a Full-Scale and a 1/6-Scale F/A-18Twin Tail During Buffet," presented at the 83rdMeeting of the Structures And Materials Panel(SMP) of the Advisory Group for AerospaceResearch and Development (AGARD),Florence, Italy, September 2-6,1996.
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