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Aerodynamic and Structural Measurement of the Aerostructures Test Wing for Flutter Testing Arun S. Mangalam * Tao of Systems Integration, Inc., Hampton, VA 23666 Christine Jutte , and Marty Brenner NASA Dryden Flight Research Center, Edwards, California, 93523 One of the fundamental problems associated with flight control of flexible structures is that, unlike structural dynamics and control actuation, unsteady aerodynamic parameters are not directly measured as observables in real time. This paper describes an approach that addresses aspects of distributed sensing for control synthesis to actively compensate for aeroservoelastic dynamics. The second Aerostructures Test Wing (ATW2) provided a platform for flight validation of the approach. The ATW2 was instrumented with tor- sion/bending strain gauge bridges, accelerometers and hot-film sensors. The hot-film sen- sors were used to identify the unsteady aerodynamic flow characteristics on the test article at all the flight operating conditions and correlated with the ATW2 structural response. I. Introduction Aeroservoelasticity is an important concern for high-performance flight vehicles that must be considered for a rigorous stability analysis. The introduction of advanced materials and construction methods has led to vehicles that are lighter in weight and thus achieve rigid-body goals but unfortunately are also reduced in stiffness and thus may be more susceptible to problems with the structural dynamics. Additionally, high- bandwidth control systems are often essential to ensure rigid-body performance goals are met; yet these systems can interact with the structural dynamics and result in adverse flight properties. Aeroservoelastic (ASE) control of the wing can help in reducing aero-structural loads and avoid Helios- type failures, improve aircraft performance, and improve safety of flight. There are also concerns associated with analysis of distributed aeroelastic flight data. In conventional flight dynamics, the state variables are usually the overall aircraft normal accelerations, rotation rates, and control actuation parameters; they generally do not include any unsteady aerodynamic measurement variables other than those obtained with the airdata system (such as airspeed, angle-of-attack, sideslip angle, pressure, etc.), which usually appear only for the determination of overall system coefficients. The overall dynamics of the flight vehicle are generally defined in terms of state variables, which are derived from rigid body degrees of freedom (DOFs) of the aircraft and augmented with quasi-elastic DOFs for flexible structures. One of the fundamental problems associated with flight control of flexible structures is that, unlike structural dynamics and control actuation, unsteady aerodynamic parameters are not directly measured as observables in real time. While such an approach may be satisfactory for steady or quasi-steady flight of rigid wings, it is inadequate for the control of flexible structures due to significant global and local variations in both the unsteady aerodynamic forcing function and the structural dynamic response. A fundamental gap exists due to the almost complete absence of experimental tools that directly link the fundamental flow physics to the unsteady aerodynamic forces and moments generated by the lifting surface. Flight dynamics of flexible structures require distributed sensors and actuators to effectively define and monitor both global and local unsteady aerodynamic environment in real time. * Senior Scientist. Member AIAA. [email protected] Aerospace Engineer. Member AIAA. [email protected] Aerospace Engineer. Member AIAA. [email protected] 1 of 10 American Institute of Aeronautics and Astronautics AIAA Atmospheric Flight Mechanics Conference 2 - 5 August 2010, Toronto, Ontario Canada AIAA 2010-8113 Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. The U.S. Government has a royalty-free license to exercise all rights under the copyright claimed herein for Go
Transcript

Aerodynamic and Structural Measurement of the

Aerostructures Test Wing for Flutter Testing

Arun S. Mangalam�

Tao of Systems Integration, Inc., Hampton, VA 23666

Christine Jutte y, and Marty Brenner z

NASA Dryden Flight Research Center, Edwards, California, 93523

One of the fundamental problems associated with ight control of exible structures isthat, unlike structural dynamics and control actuation, unsteady aerodynamic parametersare not directly measured as observables in real time. This paper describes an approachthat addresses aspects of distributed sensing for control synthesis to actively compensatefor aeroservoelastic dynamics. The second Aerostructures Test Wing (ATW2) provideda platform for ight validation of the approach. The ATW2 was instrumented with tor-sion/bending strain gauge bridges, accelerometers and hot-�lm sensors. The hot-�lm sen-sors were used to identify the unsteady aerodynamic ow characteristics on the test articleat all the ight operating conditions and correlated with the ATW2 structural response.

I. Introduction

Aeroservoelasticity is an important concern for high-performance ight vehicles that must be consideredfor a rigorous stability analysis. The introduction of advanced materials and construction methods has ledto vehicles that are lighter in weight and thus achieve rigid-body goals but unfortunately are also reducedin sti�ness and thus may be more susceptible to problems with the structural dynamics. Additionally, high-bandwidth control systems are often essential to ensure rigid-body performance goals are met; yet thesesystems can interact with the structural dynamics and result in adverse ight properties.

Aeroservoelastic (ASE) control of the wing can help in reducing aero-structural loads and avoid Helios-type failures, improve aircraft performance, and improve safety of ight. There are also concerns associatedwith analysis of distributed aeroelastic ight data. In conventional ight dynamics, the state variables areusually the overall aircraft normal accelerations, rotation rates, and control actuation parameters; theygenerally do not include any unsteady aerodynamic measurement variables other than those obtained withthe airdata system (such as airspeed, angle-of-attack, sideslip angle, pressure, etc.), which usually appearonly for the determination of overall system coe�cients. The overall dynamics of the ight vehicle aregenerally de�ned in terms of state variables, which are derived from rigid body degrees of freedom (DOFs)of the aircraft and augmented with quasi-elastic DOFs for exible structures.

One of the fundamental problems associated with ight control of exible structures is that, unlikestructural dynamics and control actuation, unsteady aerodynamic parameters are not directly measured asobservables in real time. While such an approach may be satisfactory for steady or quasi-steady ight ofrigid wings, it is inadequate for the control of exible structures due to signi�cant global and local variationsin both the unsteady aerodynamic forcing function and the structural dynamic response. A fundamentalgap exists due to the almost complete absence of experimental tools that directly link the fundamental owphysics to the unsteady aerodynamic forces and moments generated by the lifting surface. Flight dynamicsof exible structures require distributed sensors and actuators to e�ectively de�ne and monitor both globaland local unsteady aerodynamic environment in real time.

�Senior Scientist. Member AIAA. [email protected] Engineer. Member AIAA. [email protected] Engineer. Member AIAA. [email protected]

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AIAA Atmospheric Flight Mechanics Conference2 - 5 August 2010, Toronto, Ontario Canada

AIAA 2010-8113

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. The U.S. Government has a royalty-free license to exercise all rights under the copyright claimed herein for Governmental purposes. All other rights are reserved by the copyright owner.

Recently, Tao Systems with support from NASA and AFRL, conducted wind tunnel and ight exper-iments to demonstrate the existence of a direct correlation between the unsteady aerodynamic forces andthe instantaneous spatial locations of a few critical aerodynamic ow feature indicators (CAFFIs), such asthe leading-edge stagnation point (LESP) and ow separation point (FSP) using ush-mounted, micron-thinhot-�lm sensor arrays.1{4 These experiments have demonstrated that CAFFIs can be used as an unsteadyaerodynamic observable in the same manner that strain gage and accelerometers are used to measure thestructural response. The CAFFI, such as LESP, laminar-to-turbulent transition, ow separation and reat-tachment, shock location, etc., are treated as state variables in the plant equation as well as unsteady aero-dynamic observable in the measurement equation of the aeroelastic state-space model. These observablescan be used to initiate control actuation to realize desired spatial aeroelastic load force distributions.

Figure 1. Aerostructures Test Wing (ATW) mounted on the side of the F-15B Flight Test Fixture

This paper describes an approach that addresses aspects of distributed sensor developments for controlsynthesis that actively compensate the aeroservoelastic dynamics. An ASE controller is a potentially missionenabling technology for gust alleviation, load control, morphing aircraft control, and body freedom utteravoidance on tailless aircraft. Active aeroelastic control is an area of focus for improvements in performance,e�ciency, and safety. The validation of newly proposed sensor-actuator schemes and controllers is thusan important consideration. Wind tunnels typically do not provide such an environment because they donot su�er from high levels of sensor noise, poor excitation, turbulence and gust, and time-varying ightcharacteristics. Therefore, a system that can be used on a ight test article must be utilized, and the secondAerostructures Test Wing 2 (ATW2) provided a platform for such a validation. ATW2 is a modi�ed versionof a previous ATW own in 20015 (see Fig. 1).

II. Aerostructures Test Wing

The Aerostructures Test Wing 2 (ATW2) is a testbed that serves the ight test community by demon-strating aeroservoelastic research concepts in a realistic ight environment. The ATW is a ight experimentdesigned to generate data to validate ight utter prediction techniques. Testing of the ATW is similar thatof a new or modi�ed aircraft, including ground vibration testing and ight envelope clearance ights. Toconduct ight tests with the ATW and ATW2, the wing was mounted on the NASA Dryden Flight TestFixture (FTF).6 The objective of this ATW2 test was to y the wing to the utter instability threshold,while acquiring aerodynamic and structural data that could be used to develop a control methodology for utter suppression.

The ATW2 has the following properties (see Fig. 2 for depiction):

� National Advisory Committee for Aeronautics (NACA) 65A004 airfoil

� wing area of 197 in2

� half-span of 18 in., root chord of 13.2 in. and a tip chord of 8.7 in.

The wing has a somewhat complicated structure in that it is composite and there are several internal ribsand spars, which provide dynamics that are more challenging than simpler solid or hollow models. The wingis attached to the FTF (see Fig. 1).

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Wing Instrumentation

Figure 3 shows the instrumentation layout for theATW, which included three accelerometers and fourteenstrain gages. The accelerometers provided the dynamicdata that tracked flutter stability. Seven of the straingages provided torque measurements and sevenprovided bending measurements. The strain gages werecalibrated during ground tests to develop bending, shear,and torque equations for flight-test monitoring. Thethree accelerometers were located in the wingtip boom.Each accelerometer had a range of ±50

g

, a sensitivity of100mV/

g

, and a frequency range of 0.3 Hz to12,000 Hz. The aircraft instrumentation systemprovided a sample rate of 800 and 200 samples per sec

for the accelerometers and strain gages. The straingages and accelerometers were monitored and recordedreal time during flight and ground tests.

Excitation System

The excitation system design was subjected to thefollowing system requirements or constraints:

1. The actuation system must be capable ofbroadband excitation, and sinusoidal sweeps anddwells, with a frequency bandwidth from 1 to100 Hz.

2. A single channel of piezoelectric actuators mustexcite the first wing-bending mode and the firsttorsion mode of the ATW.

3. Stiffness and mass of the piezoelectric actuatorsmust not change the first-bending mode andfirst-torsion mode frequencies by more than5 percent.

4. The design for this excitation system must befrangible.

The final excitation system design consisted of fourmain components, the piezoelectric actuators, theamplifier, and the control computer, with a pilotinterface box. A sketch of the system diagram is shownin figure 4 and photographs of the components areshown in figure 5.

Piezoelectric Actuators

Piezoelectric actuators undergo a dimensional changewhen electric voltage is applied. When properly bondedthese actutators can apply a strain to the surface. In this

010001

8.7

18.0

xz

y

13.2

Spar centerline at 30 percent cord

Center of gravity

Aerodynamic center

Elastic axis

Figure 1: Aerostructures test wing sketch.

24

36Chord, in.

020013

Span

, in.

Bending gagesTorque gagesAccelerometers

20

16

12

8

4

0 4 8 12 16 20 24 28 32

Figure 3: Instrumentation on the aerostructures testwing.

Figure 2: Aerostructures test wing on the flight testfixture.

Figure 2. Aerostructures test wing sketch5

A. Sensors, Instrumentation & Signal Processing

For aeroelastic applications, ideally, the aerodynamic loads and structural response should be experimentallydetermined to both assess actual wing aeroelastic performance. This entails instrumenting the turbine bladeswith both high-bandwidth ow sensors to measure the ow state and strain gauges and accelerometersto measure the structural state. Unfortunately, there are numerous factors that a�ect the measurementreliability of ow sensors in an operational environment: altitude, temperature, density, humidity, dust,vibration, electromagnetic and radio-frequency interference (EMI/RFI), among others.

The typical way of measuring aerodynamic loads is by instrumenting the blade with surface pressuresensors to obtain lift through integration of the pressure distribution over the wing surface. Consideringthis environment, pressure sensors must sense the pressure uctuations from the de ections of an inertialdiaphragm, which, to protect it from direct exposure to the environment, is layered with protective coatingor tubing, further damping the diaphragm structural response and increasing the latency. It is possible todeconvolve the pressure response to determine this latency, but this process will require considerable e�ortto calibrate and model the pressure sensor and its associated time lags, and these calibrations will changeover time. Lags happen to be critical for accurate aeroelastic modeling, since they impact the nonlinearrelationship between the aerodynamic forcing function and the lagged structural response. Thus, to improve utter testing methodology and productivity, new low-latency approaches should be explored to measureand correlate unsteady aerodynamic forces with structural response.

Thermal anemometry, in conjunction with non-intrusive hot-�lm sensors, can measure viscous e�ectslike shear stress with a relatively high frequency response and minimal lag. Hot-�lm sensing is based onindirectly calculating ow properties by measuring the amount of heat dissipated from a heated sensor to the ow. Unlike pressure sensors that primarily measure the normal forces, hot-�lm sensors primarily measurethe tangential forces, e.g. shear, without any delay-adding moving parts. However, accurately obtainingreliable shear stress measurements over a wide range of frequencies is a notoriously di�cult problem, as thefrequency and phase characteristics of the hot-�lm sensor depend on the relatively complex anemometer-speci�c heat transfer condition with the sensor substrate. Since hot-�lm sensors are directly exposed to the ow environment, they are also even more susceptible to adverse e�ects from the ambient ow environmentthan pressure sensors. For example, when embedded on wings, hot-�lm sensors are essentially long metallicantenna, picking up stray electromagnetic signals with hardly any way to shield the exposed heated resistor.Yet another severe problem with the use of thermal anemometry in the �eld is the inherent variability inambient temperature.

Figure 3 depicts the instrumentation layout for the ATW2, which included:

� Eight (8) torsion bridges

� Six (6) bending bridges

� Four (4) shear bridges

� Two (2) wingtip accelerometers in the wingtip boom and two (2) mid-span on the wing

� Eight (8) hot-�lm sensor elements around the leading-edge on the wing

� Four (4) hot-�lm sensor elements on the wingtip boom

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(a) Top View of the ATW2

(b) Bottom View of the ATW2

Figure 3. ATW2 instrumentation

The eight hot-�lm sensors are located at symmetrical locations on the top and bottom surfaces at 0.28,1.11, 1.95 and 3.3 % chord from the leading-edge along the surface (see 4). The chord length at theleading-edge sensor location is around 10.8 inches. The hot-�lm sensors are operated by a bank of constantvoltage anemometers (CVAs). The hot-�lm sensors were used to identify the unsteady aerodynamic owcharacteristics on the test article at all the ight operating conditions. The FTF also records Mach, altitudeairspeed, and angle-of-attack (F-15B and FTF) through the onboard airdata system. In addition, there wereseveral piezoelectric exciter patches,5 but they were not used in this experiment.

With respect to signal processing, if multiple sensor signals can be referenced with respect to each other,we could quantitatively determine crucial ow phenomena characteristics without depending on the absolutevalue of skin friction using phase-based signatures.7{9 These crucial ow phenomena might include owbifurcation points (FBPs) such as leading-edge stagnation point (LESP), ow separation point (FSP) and ow reattachment point. Previous ow measurement studies have shown the capability to extract, with

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!

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#$$%"&'(")*+$,-."

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(Not to scale)

Leading Edge

/"0$123'4%"5-67$+7"""

Figure 4. Hot-�lm sensor locations on the ATW2 wing and boom

sub-millisecond response time, FBPs on various airfoils and wing surfaces, for laminar/turbulent ows,at subsonic to supersonic speeds, using unique signal processing techniques in the time and/or frequencydomains,1{4,10 and even in the presence of severe plasma-generated EMI.11 All of these techniques dependon a high signal-to-noise ratio, so even with advanced signal processing techniques, instrumentation playsa vital role. It is important to note, with proper instrumentation and signal processing techniques, it ispossible to obtain FBP locations with absolute error bounds.12

III. Test Results

In this section, a brief description of the preliminary results of the tests conducted on the F-15B willbe given. The focus will be on correlating the hot-�lm sensors data with the co-located structural stateinformation collected simultaneously. We will also discuss the practical utilization and implementation ofthese new ow sensors for aeroservoelastic applications.

Figure 5. Flow bifurcation points near the leading-edge

Figure 5 shows the time series for several hot-�lm sensors near the leading-edge, an accelerometer andthe angle of attack of the FTF a few seconds before utter destroys the ATW2 wing. Notice that theangle of attack is always negative, so the LESP is on the pressure side which is the top surface, and theFSP is on the suction side, which is on the bottom surface. The positive s=c locations along the surface

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correspond to sensors on the top surface, and the negative s=c locations correspond to sensors on the bottomsurface. The two sensors nearest to the leading-edge, �0:3% s=c show a clear di�erence in phase. Thisphase signature implies that a ow bifurcation point, namely, LESP, is oscillating between the two sensors.Therefore, the LESP is essentially absolutely bounded between �0:3% s=c. Looking further downstreamon the lower surface, the two sensors at �1:1 and �2:0% s=c are also out-of-phase. The ow is oscillatingrapidly between ow attachment and separation. In fact, the duration of the peaks for the sensor located at�2:0% s=c corresponds to the duration of attached ow.

Flow separation is a very important phenomena especially in the case of utter. If the ow is separated,the downstream actuator becomes much less e�ective. This loss in e�ectiveness results in a nonlinearityin actuation that probably has not been accounted for in the control law development. These unmodelednonlinearities have the potential to destabilize the ASE system, and in the case of utter, cause prematuredestruction of the wing.

A. Phenomenological Approach to Unsteady Aerodynamics and Aeroelasticity

It can be shown that ow phenomena such as LESP and FSP are uniquely related to circulation for subsonicpotential ows.13 Streamline bifurcation occurs when the ow attaches to (LESP) or separates from thebody (FSP). Flow separation occurs when the ow is unable to negotiate positive pressure gradients. Incertain conditions, the separated ow could also reattach itself to the body. For fully attached ow, thecirculation around an airfoil can be determined through the application of the Kutta condition requiring therear stagnation point be located at the sharp trailing edge. Flow separation results in a signi�cant loss incirculation as the rear stagnation point moves upstream. As the LESP moves downstream on the pressureside with higher angle-of-attack (AoA), the aerodynamic lift continues to increase with AoA so long as FSPremains at the trailing edge. As the ow becomes unable to negotiate the positive pressure gradient at higherangles of attack, the ow separates and the FSP moves upstream, causing a loss in lift and an increase inpro�le drag. The results of a recent wind tunnel test describes the behavior of the LESP and FSP withchanges in lift, where we could observe that the estimated lift follows the actual aerodynamic lift throughoutthe range of angles, including post-stall.14

Figure 6. Envelope of the hot-�lm signal

For a given angle of attack and wing geometry, if the LESP is directly related to the lift, then the signalassociated with LESP should increase at the same rate as a force-type signal such as an accelerometer. Asthe wing oscillations increase due to utter, the magnitude rise of the LESP signal should correspond to themagnitude rise of an accelerometer signal. We could obtain the magnitude rise of the LE hot-�lm sensorsignal by obtaining the signal envelope or local extrema in the time series, as seen in Fig. 6.

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Figure 7. Comparison of the magnitude of a hot-�lm sensor near the leading-edge with an accelerometer

Figure 7 depicts the magnitude rise of the accelerometer signal envelope and LE hot-�lm sensor signalenvelope. Excepting the scale, the rate of increase is practically the same, demonstrating the LESP movementcorresponds to a force-type measurement. The di�erences between the signal lie in the local phase changesbetween the accelerometer and hot-�lm sensor as the aerodynamic damping decreases.

The phase di�erence between the time series of the aerodynamic and structural sensor is an importantdeterminant in how quickly the oscillation amplitude rises. Stability and performance of an aeroelastic controlsystem can be described using the energy relationships between the uid and structure. The following is anenergy balance for an aeroelastic system:

E0 = K:E: + P:E:�W = K:E: + P:E:�Z

(Pb + PL + PM + Pc) (1)

where E0 is constant initial energy, W is the sum of the work of the non-conservative forces, Pb is thepower dissipated by the structural damping, PL and PM are the powers dissipated by aerodynamic lift andmoment, respectively, Pc is the power dissipated or applied by the control system. If the net work by theaerodynamic forces equals the work done by the internal dissipative (damping) forces then the system isneutrally stable. If aerodynamic work exceeds that of the internal dissipation, then energy is being extractedfrom the airstream resulting in increasing structural deformation. If the energy extraction is at an increasingrate, then utter rapidly develops.

With the concept of aerodynamic work per cycle as a measure of the energy transferred from the uidto the structure in one period:

Waero =

I(PL + PM ) dt (2)

we can assess the aeroelastic stability. Aerodynamic work is composed of the bending and torsional termscorresponding to PL and PM , respectively. The aerodynamic damping is directly proportional to the negativeof the aerodynamic work. So, if the work per cycle is positive, then the aerodynamic damping is negativeand the system is consequently unstable, and if the work per cycle is negative then the aeroelastic system isstable.

In the energy framework, the energy exchanged between the uid and structure determines how muchenergy the structure must dissipate in order for the system to remain stable. In this report, we will concen-trate our analysis on the plunge term, i.e., PL; although the pitching moment is ignored in this analysis itcould be included in the future in a more detailed analysis of all energy terms. Moreover, in this preliminary

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analysis, we will provide order of magnitude estimates without engineering units to show the trends. Wecould estimate the work done by the aerodynamic lift using the following real-time integral

WL =

IL dh =

IL _h dt (3)

where WL is the aerodynamic work done by lift, L is the instantaneous aerodynamic lift, h is the verticalposition of wing, and _h is the vertical velocity or plunge (positive up). As previously mentioned, aerodynamiclift is a function of LESP, FSP, instantaneous wing geometry and local ow speed. Integrating over a cycle,we can obtain the aerodynamic work done. For every cycle, if the aerodynamic work done is increasingthen the uid is continuously transferring energy to the structure, potentially leading to structural failure ifthe energy is not dissipated or removed. Observing the integral, it is clear that with the appropriate phasedi�erence between the lift and plunge, the oscillation amplitude could be ampli�ed or attenuated.

Figure 8. Signals from a hot-�lm sensor, accelerometers and a calculated plunge parameter

Using a time integral of the two forward and aft accelerometers co-located with the hot-�lm sensors, wecould determine the pitch and plunge term. Figure 8 depicts the calculated plunge time series along witha hot-�lm sensor, two co-located accelerometers and Mach number. The local plunge rate along with a liftestimate will provide enough information to calculate the work done per cycle as a function of time. If thework done by the airstream is increasing then we know that the energy into the system is increasing and willresult in a corresponding increase in oscillation amplitude.

Figure 9 depicts the the aerodynamic work done on the structure along with an accelerometer time seriesand Mach number as the wing approaches utter. We see minor levels of aerodynamic work until around24 seconds corresponding to Mach 0.5. After 24 seconds, there is a relatively rapid rise in the work done.There is still enough aerodynamic damping to cause a reduction in aerodynamic work and a correspondingreduction in accelerometer amplitude. However, at 26 seconds as the aircraft continues to increase beyondMach 0.51, the system is unstable and there is a rapid rise in work done. Soon after, the ATW2 wing loadlimit is reached and the wing breaks due to bending-torsion utter. The ATW2 broke at approximatelymid-span, and the outer wing, including the ATW2 boom, separated from the root section of the wing (seeFig. 10).

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Figure 9. Calculated aerodynamic work done by lift on the structure along with an accelerometer signal asthe wing undergoes utter

!Figure 10. ATW2 wing before (left) and after (right) the utter ight test

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IV. Conclusion

We showed it is possible to instrument the leading edge with high-bandwidth ow sensors that correlateswell with co-located accelerometers. In previous papers it has been shown that it should be possible toobtain lift and moment coe�cient in real-time for that section along the span; this paper provided empiricalevidence of the claim that the LESP does indeed correspond to a force-type signal. Using the lift and momentcoe�cient, co-located accelerometers and local airspeed, an instantaneous estimate of the power expendedby the uid into the structure could be obtained. A cyclical integral of this power results in a quantitativefunction of the energy exchange of the uid with the structure as a function of time. For utter suppressionand gust load alleviation, the objective is to minimize this cyclical integral in real-time through the use ofactuators that appropriately phase the lift with the aeroelastic motion of the wing.

In this paper, we demonstrated a way to obtain that time integral of the work done by the airstream onthe wing structure using the ATW2 ight test data. In a future work, we could estimate the bounded liftcoe�cient using the bounded LESP locations, the pitch and plunge velocities, and �nally obtain an estimateof the work done on the structure by the uid in terms of engineering units. This will enable us to comparethe work done at various Mach numbers quantitatively.

References

1S. Mangalam, P. Flick, and M. Brenner, \Higher level aerodynamic input for aeroservoelastic control of exible aircraft,"AIAA 2007-6380, Hilton Head, SC, August 2007.

2A. Mangalam, S. Mangalam, and P. Flick, \Unsteady aerodynamic observable for gust load alleviation," AIAA 2008-1725,Schaumberg, IL, April 2008.

3A. Mangalam, S. Mangalam, and P. Flick, \Unsteady aerodynamic observable for gust load alleviation and uttersuppression," AIAA 2008-7187, Honolulu, HI, August 2008.

4A. Mangalam and M. Davis, \Ground/ ight correlation of aerodynamic loads with structural response," AIAA 2009-881,Orlando, FL, January 2009.

5D. Voracek, M. Reaves, L. Horta, and S. Potter, \Ground and ight test structural excitation using piezoelectric actua-tors," AIAA 2002-1349, 2002.

6D. Richwine, \F-15B/Flight Test Fixture II: a test bed for ight research," NASA TM 4782, December 1996.7S. Mangalam, \Real-time extraction of hydrodynamic ow characteristics using surface signatures," Journal of Oceano-

graphic Engineering, vol. 29, July 2004.8S. Mangalam, \Phenomena-based real-time aerodynamic measurement system (PRAMS)," in IEEE Aerospace Confer-

ence, vol. 7, pp. 3347{3356, March 2003.9S. Mangalam, G. Sarma, R. Pfouts, T. Kwa, J. Carper, M. Wallace, H. Moghadam, and R. Nigon, \Detection of

transition and ow bifurcation regions on a hydrofoil using hot-�lm constant voltage anemometry," in International Symposiumon Seawater Drag Reduction, (Newport, RI), July 1998.

10T. Moes, G. Sarma, and S. Mangalam, \Flight demonstration of a shock location sensor using constant voltage hot-�lmanemometry," TM-4806, NASA, August 1997.

11J. Poggie, C. Tilmann, P. Flick, J. Silkey, B. Osborne, G. Ervin, D. Maric, S. Mangalam, and A. Mangalam, \Closed-loopstall control on a morphing airfoil using hot-�lm sensors and DBD actuators," AIAA 2010-547, Orlando, FL, January 2010.

12A. Mangalam and T. Moes, \Real-time unsteady loads measurements using hot-�lm sensors," AIAA 2004-5371, Provi-dence, RI, January 2004.

13L. Woods, The Theory of Subsonic Plane Flow. Cambridge University, January 1961.14A. Mangalam, G. Moore, D. Berg, M. Blaylock, and M. Rumsey, \Real-time observable for wind turbine applications,"

AIAA 2010-2652, Orlando, FL, 2010.

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