computational modeling of unsteady aerodynamics in hummingbird flight

146 Pages·2016·7.8 MB·English

COMPUTATIONAL MODELING OF UNSTEADY
AERODYNAMICS IN HUMMINGBIRD FLIGHT
By
Jialei Song
Dissertation
Submittedto theFacultyofthe
GraduateSchool ofVanderbiltUniversity
in partialfulfillmentoftherequirements
forthedegreeof
DOCTOR OFPHILOSOPHY
in
Mechanical Engineering
May,2016
Nashville,Tennessee
Approved:
HaoxiangLuo,Ph.D.
CaglarOskay,Ph.D.
Robert Pitz, Ph.D.
DeyuLi, Ph.D.
Acknowledgments
Pursuing the doctorate degree is like running a marathon. It is a long and tough
journey,anditcan’tbesuccessfullyaccomplishedwithoutthehelpandsupportofmany
people. Here Isincerely thankallthesepeople.
First, I would like to owe the biggest thank you to my advisor, Dr. Haoxiang Luo,
who continuously gave me the insightful advice on the research and warmhearted care
on the life during the past five years. His great efforts and tremendous patience helped
me become well trained on scientific research methods and work productively. Aside
theresearch,Dr. Luoalsoofferedmeplentyofopportunitiesonthecareerdevelopment
and network-building. Overall, I have greatly improved in the last five years under the
supervisionofDr. Luo.
Second,IwouldliketogivemygreatthankstoDr. TysonHedrickattheUniversity
of North Carolina at Chapel Hill and Dr. Bret Tobalske at University of Montana. My
research is computational modeling of aerodynamics of hummingbird flight, and the
accurate description of the bird kinematics is of great importance. Dr. Hedrick kindly
provided us the data of the hummingbird hovering flight, and Dr. Tobalske provided
us the data of the fast forward flight. In addition, the discussions with them were re-
ally a pleasant experience since they offered many insightfulsuggestions and provided
numeroushelpfulinputsfrom thebiologyaspect.
Ialso want tothankmy Ph.D. committeemembers,Profs. Robert Pitzand DeyuLi
in the Department of Mechanical Engineering and Prof. Caglar Oskay in the Depart-
ment of Civil and Environmental Engineering, for their time and effort of serving on
mycommittee. Theygavemenotonlytheadvicefortherefinementofmyresearchand
ii
dissertation,butalso helpfuladviceontheacademiccareer.
Finally, thanks must be given to my family, friends and lab mates, Dr. Fangbao
Tian, Dr. Bo Yin, Dr. Hu Dai, Siyuan Chang, Chi Zhu, Casey Brock, Joshwa Webb,
Ye Chen and Yang Zhang for their love, their support and their help. Especially, Dr.
Fangbao Tian has selflessly given me advice and support from my undergraduate time
tothepresent.
IappreciatethatIhaveallthesepeopleinthislongjourneyandtheyhavemadethis
marathonjoyful,meaningfulandunforgettable.
iii
CONTENTS
Acknowledgments ii
ListofTables vi
ListofFigures vii
I Introduction 1
1.1 MAVsand aerodynamicsofflapping wings . . . . . . . . . . . . . . . 1
1.2 Aerodynamicsofhummingbirdflight . . . . . . . . . . . . . . . . . . 4
1.3 Thespecific objectivesofthisstudy . . . . . . . . . . . . . . . . . . . 7
II Numerical approach andModel reconstruction 9
2.1 Numericalapproach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 ModelReconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
III Three-dimensionalflowandliftcharacteristicsofahoveringruby-throated
hummingbird 19
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
(1) Experimentand reconstructionofthewingkinematics . . . . . 22
(2) Simulationsetupand modelvalidation . . . . . . . . . . . . . . 25
3.3 Resultsand discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 31
(1) Force, power,and efficiency . . . . . . . . . . . . . . . . . . . 31
(2) Circulation andwing rotation . . . . . . . . . . . . . . . . . . 35
(3) Asymmetricliftproduction . . . . . . . . . . . . . . . . . . . 37
(4) Drag-based vertical force . . . . . . . . . . . . . . . . . . . . . 38
(5) Wing speedand angleofattack . . . . . . . . . . . . . . . . . 41
(6) Wing-wakeinteraction . . . . . . . . . . . . . . . . . . . . . . 42
(7) Three-dimensionalvortexstructures . . . . . . . . . . . . . . . 47
(8) Full-bodysimulation . . . . . . . . . . . . . . . . . . . . . . . 48
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
IV Performance ofa quasi-steady model forhovering hummingbirds 53
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2 Modelingapproach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
V Wing-pitching mechanism ofa hovering ruby-throated Hummingbird 64
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.2 Modelingapproach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
(1) Thewingmodel . . . . . . . . . . . . . . . . . . . . . . . . . 66
(2) Descriptionoftherotationalvelocityofthewing . . . . . . . . 67
(3) Dynamicsofrotation . . . . . . . . . . . . . . . . . . . . . . . 70
iv
5.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
(1) Dynamicsofthedistalsection . . . . . . . . . . . . . . . . . . 74
(2) Dynamicsoftheproximalsection . . . . . . . . . . . . . . . . 79
(3) Dynamicsofflapping motion . . . . . . . . . . . . . . . . . . 83
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
VI Three-dimensional simulation for fast forward flight of a calliope hum-
mingbird 89
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.2 Modelconfigurationand simulationapproach . . . . . . . . . . . . . . 91
(1) Reconstruction ofthewingkinematics . . . . . . . . . . . . . . 91
(2) Wing kinematics . . . . . . . . . . . . . . . . . . . . . . . . . 95
(3) Simulationsetupand verification . . . . . . . . . . . . . . . . . 96
6.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
(1) Aerodynamicforces . . . . . . . . . . . . . . . . . . . . . . . 99
(2) Force productionmechanism . . . . . . . . . . . . . . . . . . . 102
(3) Vortex structures . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
(1) Forces on thebirdbody . . . . . . . . . . . . . . . . . . . . . . 106
(2) Comparisonofhummingbirds,insectsand otherbirds . . . . . 110
VIISummary andfuture work 114
7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
7.2 Futurestudy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
(1) Unsteady maneuversofhummingbirds . . . . . . . . . . . . . 117
(2) Further comparisonofhummingbirdsand otherflyinganimals . 120
(3) Fluid-structureinteractionoftheelasticflapping wings . . . . . 122
Appendix 124
References 127
v
LIST OFTABLES
3.1 Comparisonbetweentheruby-throatedhummingbirdmodelandtheex-
perimentaldatafor therufous hummingbird. . . . . . . . . . . . . . . . 26
3.2 Comparison of the downstroke and upstroke, where C¯′ and C¯′ are the
Z P
lift and power coefficients rescaled by the respective U¯ and S of either
downstrokeorupstroke. . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3 Theaerodynamiclift,drag,andtheirverticalcomponentforbothdown-
stroke and upstroke. All forces are normalized in the same way as de-
scribedearlier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.1 QuantitativecomparisonoftheforcecoefficientsbetweentheBEMand
CFD results,where“down”meansdownstrokeand “up”means upstroke. 60
4.2 Coefficients of forces due to the wing translation, rotation and acceler-
ation effects. The numbers in the parentheses represent the percentage
oftheforcewithinthetotalforce that includesthetranslation,rotation,
andacceleration effects. . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.1 Morphologicaldataofthehummingbirdused inthestudy. . . . . . . . 94
6.2 The comparison of the forces on both wing and body (unit: mN) from
thetwo differentmeshes. . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.3 Averagedverticalforcecoefficient,C ,thrustcoefficient,C ,andpower
Z T
coefficient, C of the wings, and averaged lift and drag coefficients of
P
thebody,C andC . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Z,b D,b
6.4 Liftcontributionfromthebodytoeweightsupportfordifferentspecies.
The measurement of the insects was done on isolated bodies and the
data for zebra finch was done using live birds with intact but folded
wingsand tails. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
vi
LIST OF FIGURES
2.1 A2Dillustrationofthesharp-interfaceimmersed-boundarymethodfor
thefluid–solidboundary. Flowfieldextrapolationisappliedattheghost
nodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Fourcamera viewsofa hummingbirdhoveringina transparentchamber. 16
2.3 Datacollectionfromhigh-speedvideos. (a)Thefirstmouseclickinone
view generates a line in the 3D space shown in the other views. (b) A
secondclickinanotherviewdeterminesthe3Dcoordinatesofthepoint.
Notethatinthisfigure, twosimultaeousX-ray viewsare alsoincluded,
which show the musculoskeletal structure of the bird (Hedrick et al.,
2012). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1 (a) Marker points on the outline of the wing. (b) Reconstructed wing
kinematics (shown for the right wing). (c) The triangle represents the
distalhalfofthewingsurface, based onwhichthechord angle,α , and
c
theangleofattack, α,are defined in thetext. . . . . . . . . . . . . . . . 22
3.2 Four camera views of the bird. A syringe of nectar is served for the
hummingbirdhovering. . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3 Comparisonofthereconstructedwingandthevideoimageduringearly
downstroke, around mid-downstroke, early upstroke, and around mid-
upstroke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.4 The baseline mesh around the bird (only one out of every 4 points in
each direction is shown). (b) Grid convergence study where the nor-
malizedverticalforce ofasinglewing,C ,is plotted. . . . . . . . . . . 27
Z
3.5 Comparison of the spanwise vorticity, ω , during middle downstroke
z
(theunitis1/s). (a,c,e,g)PIVimageadaptedfromWarricketal.(2009)
(image usage authorized); (b,d,f,h) current simulation. (a,b) middle
downstroke, (c,d) supination, (e,f) pronation, (g,h) begining of down-
stroke. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.6 ComparisonofthephaseaveragedboundcirculationΓbetweencurrent
simulation and the experimental measurement of Warrick et al. (2009)
(re-plotted to include the sign of Γ), where time t is normalized by the
periodT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.7 The three normalized force components C (a), C and C (b) in the
Z X Y
single-wingsimulation. (c)Thepowercoefficientnormalizedby 1rˆ3ρU¯3S,
2 3
andpositivepowermeans workdonetotheflow. . . . . . . . . . . . . 33
vii
3.8 The lift coefficient, the tip velocity in m/s, the chord angle in deg., and
thepitchingvelocity in deg./s in typical cycles (average datastill taken
fromall eightcycles). . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.9 (a)Theaveraged trajectoryoftherightwingtipinthe XZ-plane. Force
decomposition in terms of the aerodynamic lift and drag is illustrated.
Note that the actual decomposition depends on the orientations of the
wingaxisandtipvelocityvectorinthe3Dspace. (b)Theinstantaneous
(thinline)andcycle-averaged(thickline)strokeplaneangleβandangle
ofattack αin deg. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.10 (a) Normalized aerodynamic lift and drag for two typical cycles. (b)
Vertical components of C and C . Average data are calculated from
L D
alleightcycles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.11 Comparison of the wing tip velocity between the flapping wing of the
revolving wing. (a) downstroke; (b) upstroke. Note that for the flap-
ping wing, the wing tip never has a moment of ’zero’ velocity since
thevelocityvectoralwayshas anon-zero component. Theacceleration
periodoftherevolvingwingisapproximatedwithasinusoidalfunction. 43
3.12 The revolving wing versus the flapping wing in the production of lift.
(a) Downstrokeand (b) upstroke. Only one typical strokecycle is used
inthistest. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.13 Typical asymmetric wing-wake interaction shown in a spanwise slice
for (a) an early downstroke at Y = 70% wingspan and t/T = 0.1, and
(b) an early upstrokeat Y = 50% wingspan and t/T = 0.6. The dashed
lineindicatesthetiptrajectoryofthiscycle,and thecircleindicatesthe
oppositeflow caused by the preceding half stroke. The chord is shown
asathickline. Thebirdbodywasnotincludedintheactualsingle-wing
simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.14 Lift production of isolated wing strokes and continuous strokes. Aver-
agedataarecalculated from alleightcycles. . . . . . . . . . . . . . . . 46
3.15 Three-dimensional vortex structures in the flow during a stroke cycle,
wherethetimestampfrom(a)to(d)is0.37T,0.51T,0.58T,and0.78T.
The vortex loop from the downstroke is marked by a dashed line. The
thickarrowin (d)indicatesthelocationwheretheLEVispinched off. . 49
3.16 Three-dimensional vortex structures in the full-body simulation shown
foradownstroke(a) andupstroke(b). . . . . . . . . . . . . . . . . . . 51
viii
3.17 Comparison of the vertical force coefficient in typical cycles between
thefull-bodysimulationandsingle-wingsimulation. . . . . . . . . . . 52
4.1 Illustrationofawingchord intheblade-elementmodel. . . . . . . . . . 54
4.2 Translationalforce coefficient fitting from the revovlvingwing simula-
tions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3 (a) Sample chords used to determine the location of the wing axis. (b)
Illustration of calculation of the wing axis. V , V and V are the
le te loc
leading-edge velocity, trailing-edge velocity, and translational velocity
ofthechord. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.4 Pitching axis and the corresponding rotational force coefficient of se-
lectedchords. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.5 Normalizedverticalandhorizontalforces,C andC ,givenbytheBEM
v h
predictionand theCFD simulation. . . . . . . . . . . . . . . . . . . . . 60
4.6 Breakdown of forces predicted by the BEM. Use “Total, Translation,
Rotation,andAcceleration” inthelegend. . . . . . . . . . . . . . . . . 61
4.7 Historiesofthenormalizedrotationalforce,wingtipvelocityandpitch-
ingvelocityofthedistalwing. Useα˙ . . . . . . . . . . . . . . . . . . 62
d
5.1 Illustration of the hummingbird wing model and the wing-fixed coor-
dinate systems for the distal and proximal sections. The wing root and
thefinger tiparedenoted byO and F, respectively. . . . . . . . . . . . 67
5.2 Coordinatetransformationand definitionoftherotationangles. . . . . . 68
5.3 Pressure differential (unit: Pa) over the wing surface obtained from a
previous CFD study (Song et al., 2014) for (a) downstroke and (b) up-
stroke. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.4 Surface density of the hummingbird wing. The dashed line indicates
thetorsionalaxis,and thethick bar represents thebonystructureofthe
wing,whichhas additionalmass. . . . . . . . . . . . . . . . . . . . . . 74
5.5 Pitchingdynamicsofthedistalsection. (a)Thephase-averagedangular
velocities in terms of the Euler angles. (b) The corresponding angular
velocities in the wing-fixed coordinate system. (c) The inertial torque
terms. (d) The sum of all inertial torques, T , the twist torque, T ,
inertia F
the negativeof the aerodynamic torque, T , and the actuation torque
aero
attheroot,T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
O
ix
5.6 Rate of change in the pitching energy of the distal section, the power
contribution of the inertia, P , aerodynamic power, P , and tor-
inertia aera
sionalinput, P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
F
5.7 Pitchingdynamicsoftheproximalsection. (a)Comparisonofthephase-
averaged angular velocity, in terms of ψ˙, between the proximal section
anddistalsection. (b)Thecorrespondingangularvelocitiesinthewing-
fixedcoordinatesystemfortheproximalsection. (c)Theinertialtorque
terms for the proximal section. (d) The sum of all inertial torques,
T ,thetwisttorque,T ,andthenegativeoftheaerodynamictorque,
inertia F
T , fortheproximalsection. . . . . . . . . . . . . . . . . . . . . . . 81
aero
5.8 (a) Comparison of the power at the root, P and the torsional power to
O
the distal section, P . (b) Rate of change in the pitching energy of the
F
proximalsectionand thepowercontributions. . . . . . . . . . . . . . . 83
5.9 (a)Thephase-averaged actuationtorqueattheroot,inertialtorque,and
aerodynamic torque for flapping motion of the entire wing. (b) The
correspondingpowerforflappingmotionoftheentirewing. . . . . . . 85
6.1 Cameraviewsofthehummingbirdin thewindtunnel. . . . . . . . . . . 93
6.2 Reconstructed bird model and corresponding snapshots from the cam-
eraview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.3 Reconstructedwingpositionofthehummingbirdwithinonebeatcycle:
(a) downstroke, (b) upstroke, and (c) the wingtip trajectory as viewed
in a body-fixed coordinate system, where the thick line is the cycle-
averaged trajectoryand thinistheinstantaneoustrajectory. . . . . . . . 94
6.4 Instantaneouswingtipvelocity. . . . . . . . . . . . . . . . . . . . . . . 96
6.5 Thechord angleψ(a,b)andeffectiveangleofattack α(c,d)foraprox-
imalchordat rˆ = 0.15(a,c) and adistalchordat rˆ = 0.90(b,d). . . . . . 97
6.6 Wingtwistasmeasured usingthedifferencebetween twochord angles. 97
6.7 (a) The baselinemesh around the bird (only one out of every 10 points
ineachdirectionisshown). (b)Theforcecomparisonbetweenthebase-
linesimulationandfine meshsimulation. . . . . . . . . . . . . . . . . 99
6.8 Theforceproductionandaerodynamicpowerconsumptionofeachhum-
mingbird wing: (a) vertical force coefficient, (b) thrust coefficient, and
(c) power coefficient. In each case, the thin lines are the instantaneous
data,and thethicklineis thephase-averaged data. . . . . . . . . . . . . 101
x