Unsteady aerodynamics in the gust and manoeuvre response of flexible aircraft

108 Pages·2016·10.7 MB·English

by  D. Westerveld

Unsteady aerodynamics in
the gust and manoeuvre re-
sponse of flexible aircraft
Thesis report
D. Westerveld
elft
D
eit
sit
r
e
v
ni
U
e
h
c
s
ni
h
c
e
T

Unsteady aerodynamics in the
gust and manoeuvre response
of flexible aircraft
Thesis report
by
D. Westerveld
toobtainthedegreeofMasterofScience
attheDelftUniversityofTechnology,
tobedefendedpubliclyon7October2016,at13:00.
Studentnumber: 41060332
Projectduration: September4,2015–October7,2016
Thesisregistrationnumber: 089#16#MT#FPP
Thesiswordcount: 36706
Thesiscommittee: Prof.dr.ir.L.L.M.Veldhuis, TUDelft,chairman
Dr.ir.M.Voskuijl, TUDelft,supervisor
Dr.A.Elham, TUDelft,supervisor
Dr.-ing.R.Schmehl TUDelft,externalcommitteemember
Anelectronicversionofthisthesisisavailableathttp://repository.tudelft.nl/.

Summary
In the strive for ever decreasing fuel consumption, aircraft wings have become more slender and, in
turn,moreflexible. Thisbringswithitachangeinaircrafthandlingqualities,anditcanhaveaneffect
onthestructuraldesignofthewing. Italsobringsthepossibilityofharnessingthisstructuralflexibility
for beneficial effects like load alleviation control. For optimal results this structural flexibility needs
to be taken into account from the start of the aircraft design, which calls for an aeroelastic design
framework. Inthisworkpartofsuchadesignframeworkisconstructed. Theobjectiveofthisstudyis
aninvestigationintotheeffectofunsteadyaerodynamicsonthegustresponseofflexibleaircraft. This
is realised by implementing an unsteady aerodynamic model, a gust model and a coupling of these
modelstoanaeroelasticflightmechanicstool.
First, the aerodynamic model used as a comparison to the developed unsteady aerodynamic model
was discussed. This is a quasi-steady aerodynamic model, based on Theodorsen’s work under con-
sideration of zero frequency motion. This model is included in the flight mechanics tool. Next to this,
theadaptionofthegustmodelexistingintheaeroelasticflightmechanicstoolboxwasdiscussed. This
adapted gust model is based on the 1−cos gust model defined in regulations and is able to model
gusts in space, meaning that a time-delay effect can be modelled. This time-delay effect implies that
thefrontoftheaircraftseesthegustatanearliertimethantherearoftheaircraft. Withthisgustmodel,
thesimulationcasesusedinthisworkweredefined. Thesecasesweredefinedforatypicalshort-haul
passengeraircraft,flyingatcruisealtitude. Theusedgustsrangedfrom10to200metersinlength. The
simulations were performed with the developed unsteady aerodynamic model, and the quasi-steady
aerodynamicmodelasreference.
Theunsteadyaerodynamicmodeldevelopedforthisworkistheunsteadyvortexlatticemethod. This
potentialflowmethodallowsformodellingtime-varyingaerodynamicsaroundliftingsurfaces,including
themovementofthewakebehindthisliftingsurface. ThemodelhasbeenimplementedasaMATLAB
program,andisverifiedtoworkcorrectlyforwingswithsweepanglessmallerthan30∘. Aslightoffset
in the aerodynamic center is predicted by the model, as well as an underprediction of induced drag.
Theliftwasfoundtobepredictedcorrectly,includingitstime-dependentbehaviour.
Theaerodynamicmodelhasbeencoupledtoaflightmechanicstool,thatcansimulateflexibleaircraft.
This flight mechanics tool works by means of a rigid aircraft specifying the flight mechanics motion,
andamodeshaperepresentationoftheaircraftwingsthatspecifytheflexiblewingbendingandmove-
ment. The coupling required some coordinate transformations to make both models consistent with
each other. These transformations were shown to be implemented correctly. Next to this, the trim
algorithm included in the flight mechanics tool has been adapted to work with the new aerodynamic
model. Thisadaptionhasbeenperformedbyincludingatrimobjectiveontheunsteadyaerodynamics,
in the form of the change of bound vortex strength over time. Next to this, the original trim algorithm
hasbeenextendedbymeansofalongitudinalautopilottrimfunctionthatcanflytheaircrafttoasteady
state.
Several results have been generated in this work. First of all, the original and adapted gust model
werecompared. Itwasfoundthatthegusttime-delayeffectcanhaveaprofoundeffectontheaircraft
gustbehaviour,especiallyforshort(highfrequency)gusts. Itwasfoundthattheoverallloadpeakson
the aircraft increase in duration, due to being engulfed in the gust for a longer time. Moreover, it was
seenthatthereisatendencyoftheaircrafttopitchupatfirst,onceonlythefrontoftheaircrafthitsthe
gust. Secondly,theresultsoftrimwithbothaerodynamicmodelswerecompared. Itwasfoundthatthe
unsteadyaerodynamicmodelrequireslessthrustfortrimmedflight,andabout10degreeslesselevator
deflection. This is attributed to an underprediction of pitching moment in the unsteady aerodynamic
model. Afterthis,thegustresponsesimulationhavebeencarriedout. Theresultsofthesesimulations
showed a phase shift in the response of the aircraft modelled with unsteady aerodynamics. This is
due to the modelling of the time-history of the flow with unsteady aerodynamics. While the overall
reactions of the aircraft with unsteady aerodynamics were found to be slower, the aircraft reacted
iii
iv 0.Summary
earlier to a gust. This is due to the gust model that, in combination with the unsteady aerodynamic
model, takes into account the total wing geometry. No differences in behaviour other than the phase
shift were found between the two aerodynamic models. What was found is larger forces predicted
by the unsteady aerodynamic model. Due to uncertainty in the modelling capability of the unsteady
aerodynamic model no conclusion could be drawn whether this stemmed from the actual unsteady
behaviour,orjustadifferenceinforcemodelling. Finally,theaircraftbehaviourafteranelevatorimpulse
has been simulated. This proves that manoeuvre loads can also be simulated with the current work.
The elevator impulse simulation showed that the unsteady aerodynamics led to an increase of 18%
in the period of the short period motion. This is due to the delay between angle of attack and force
changeinunsteadyaerodynamics.
Overall, it is concluded that the influence of unsteady aerodynamics in the gust response of flexible
aircraft is not significant. The relative differences between the models were small. Together with the
factthatthecomputationtimeoftheunsteadyaerodynamicmodelismuchlargerthanthequasi-steady
model,itisconcludedthatunsteadyaerodynamicsshouldnotbeusedformodellingthegustresponse
ofconventionalflexibleaircraft. However,resultshaveindicatedthatunsteadyaerodynamicscanlead
to a response difference for flexible wings, compared to rigid wings. Finally, while not performed in
this work, the current model allows for simulating the aircraft in longitudinal and lateral motions with
wings of variable structural flexibility. This allows for control law design and modelling with unsteady
aerodynamicsasapotentialapplication.
Contents
Summary iii
Preface vii
Nomenclature ix
ListofFigures xiii
ListofTables xvii
1 Introductionandbackground 1
1.1 Unsteadyaerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Flightmechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Aeroelasticflightmechanics . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Loadprediction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.1 Flightenvelope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.2 Gustsandturbulence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Aeroservoelasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Thesisobjective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.6 Thesisoutline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Simulationcases 11
2.1 Quasi-steadyaerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Gustanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 Gustmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.2 Gustimplementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Simulationcases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.1 Aircraftchoice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.2 Flightparameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.3 Gustprofiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.4 Outputfromthecases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3 Aerodynamicmodel 19
3.1 Potentialflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.1 Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.1.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.3 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 UnsteadyVortexLatticeMethod. . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.1 Referenceframes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2.2 Calculationoftheflowfield . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2.3 Calculationoftheaerodynamicforcesandmoments. . . . . . . . . . . . . 25
3.3 Verificationandvalidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3.1 Gridconvergence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3.2 Computationtime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3.3 Steadyflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.4 Unsteadyflow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4 Aeroelasticflightmechanics 33
4.1 Aeroelasticflightmechanicstoolbox. . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.1.1 Aircraftmodel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.1.2 Structuralmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
v
vi Contents
4.1.3 OutputsoftheFMT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2 Connectingtheunsteadyaerodynamics . . . . . . . . . . . . . . . . . . . . . . . 35
4.2.1 ChangestotheSimMechanicsmodel. . . . . . . . . . . . . . . . . . . . . 36
4.2.2 FMTtoUVLM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2.3 UVLMtoFMT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.3 Trim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.3.1 Quasi-steadyaerodynamictrim . . . . . . . . . . . . . . . . . . . . . . . . 40
4.3.2 UVLMtrim. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3.3 Finishingtrimming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.4 Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.4.1 Wingshape. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.4.2 Fightpath. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.4.3 Aerodynamicforces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5 Resultsanddiscussion 49
5.1 Effectoftime-delayingustvelocities . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.2 Trimresults. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.3 Gustresponse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.3.1 Aircraftloads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.3.2 Aircraftflightmechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.3.3 Wingtipdeflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.4 Elevatorpulseresponse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6 Conclusionsandrecommendations 63
6.1 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Bibliography 69
A UVLMImplementation 73
A.1 Theunsteadyvortexlatticemethod . . . . . . . . . . . . . . . . . . . . . . . . . . 73
A.1.1 Geometryandflightpathdefinition. . . . . . . . . . . . . . . . . . . . . . . 73
A.1.2 Calculationofvorticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
A.1.3 Calculationofaerodynamicproperties . . . . . . . . . . . . . . . . . . . . 74
A.1.4 Solvingthewake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
A.2 Usermanual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
B Additionstoflightmechanicstoolbox 79
B.1 Addedfunctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
B.2 Addedblocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
C Gustsimulations 83
C.1 Loadfactorandwingrootbendingmoment. . . . . . . . . . . . . . . . . . . . . . 83
C.2 Flightmechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
C.3 Wingtipdeflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
C.4 Airspeedandaltitude. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
D Wakeshapes 87
Preface
This report marks the end of my time as a student at Delft University of Technology after six years.
During this time I’ve learned a lot about engineering, aircraft, spacecraft and myself. I’ll always look
backfondlyonmytimeinDelft.
Ifirstwanttothankmysupervisors,MarkVoskuijlandAliElham. Mark,thisisthesecondtimeyou’ve
been my supervisor and again it was very helpful to have you as supervisor. Thanks for motivating
me,andsettingmeontrackaftereverymeeting. Ali,intheoriginalgoalofthisthesistherewasapart
dedicatedtoflutterandoptimisation. ThispartI’vedroppedoverthecourseofthethesisasitwasabit
toomuchtochew,butI’dliketothankyouforstickingwithmeevenafterdroppingmostofyourtopic.
Finally, I would like to thank Leo Veldhuis for being the chair of my committee, and Roland Schmehl
foracceptingtobemyexternalcommitteemember.
IwillalsoliketothankthepeopleinKamertje1. You’vemadetheworkoverthepastyearalotmore
enjoyable. It was very nice to always have someone to discuss results with, to help people with their
work,tohavecoffeebreaks,anddrinksduringtheweekends. ThelunchissomethingI’mgoingtomiss
most. Jelle,thanksforproofreadingthisreport!
Finally, these years in Delft would not be possible if it was not for my parents. Thanks for supporting
meduringalltheseyears. Ifitwasn’tforyou,IwouldnotbewhereIamtoday.
DaanWesterveld
21September2016
vii