numerical and experimental investigations into the aerodynamics of dragonfly flight.

154 Pages·2009·6.35 MB·English

NUMERICAL AND EXPERIMENTAL
INVESTIGATIONS INTO THE AERODYNAMICS OF
DRAGONFLY FLIGHT.
A Dissertation
Presented to the Faculty of the Graduate School
of Cornell University
in Partial Ful(cid:12)llment of the Requirements for the Degree of
Doctor of Philosophy
by
David Baker Russell
August 2004
This document is in the public domain.
NUMERICAL AND EXPERIMENTAL INVESTIGATIONS INTO THE
AERODYNAMICS OF DRAGONFLY FLIGHT.
David Baker Russell, Ph.D.
Cornell University 2004
Dragon(cid:13)ies are one of the most manueverable of the insect (cid:13)yers. They are
capable of sustained gliding (cid:13)ight as well as hovering, and are able to change
direction very rapidly. Exactly how they use their wings to generate aerodynamic
forces remains unknown.
A new method was developed for solving 2D incompressible viscous (cid:13)ow prob-
lems [46] in order to numerically model the (cid:13)uid response and forces generated
by multiple (cid:13)apping wings. This (cid:12)nite di(cid:11)erence scheme uses the streamfunction-
vorticity formulation on a regular grid, and handles multiple moving irregular
boundaries.
To test the usefulness of this model, dragon(cid:13)ies were tethered to avertical force
sensor and (cid:12)lmed using high-speed digital video. This allowed the correlation
of speci(cid:12)c wing kinematics to the vertical force generated, so that when these
kinematics are modeled numerically the forces calculated can be compared with
experiment.
The results include detailed descriptions of two distinct wing kinematic pat-
terns, out of four observed. These kinematics resemble motions described by pre-
vious researchers in free (cid:13)ight conditions except for the phase between the fore and
hind wings. The forces calculated from applying the numeric method to a 2D ap-
proximation of these movements compare well to measured forces. The di(cid:11)erences
seen can be attributed to 3D e(cid:11)ects and to the simpli(cid:12)ed wing cross-section used
in the model.
We show that wing inertia is a large component of the instantaneous forces
experienced by a dragon(cid:13)y, and that the dragon(cid:13)y generates productive force
during both the downstroke and the upstroke. The counter-stroking behavior seen
infree(cid:13)ightisshowntorequirelesspowerthanthein-phasemotionobservedinthe
tethered dragon(cid:13)y, while producing the same average vertical force. We also show
evidence suggesting that during hovering (cid:13)ight wing rotation is passively driven
by (cid:13)uid forces, while during forward (cid:13)ight rotation at the end of the downstroke
is actively driven by the dragon(cid:13)y. Finally, the e(cid:11)ectiveness of applying such a 2D
model to the problem is examined, and suggestions are made for future research
to improve modeling ability.
BIOGRAPHICAL SKETCH
David Baker Russell was born on January 27, 1968 in Berkeley, California. He
was the third son of (cid:12)ve children. From the age of three he and his family lived
in Minneapolis, Minnesota. As a child, he was fascinated with (cid:13)ying things of all
kinds, and spent untold hours building and (cid:13)ying various airborne machines.
In 1987 he went to college at the University of Minnesota Institute of Tech-
nology, where he was enrolled in the Undergraduate Honors Program and ma-
jored in Aerospace Engineering. In the summer of 1988 he took an internship at
Itasca Consulting Group, acivil engineering (cid:12)rm, where he mostly helped tocreate
demonstrations that could be run on a computer to illustrate the software they
sold and the projects they had completed. This work helped rekindle a fascination
with computer programming (cid:12)rst aquired in high school, and soon he was helping
develop Itasca’s software as well as writing numerical simulations in the course of
his college work.
In 1992 he graduated from the University of Minnesota. Instead of going on
to graduate school as recommended by his coworkers and professors, he accepted
a full time position at Itasca Consulting. This allowed him to stay in Minneapolis
where he co-founded an income-sharing commune based on libertarian principles.
The commune failed a little more than a year later, leaving him the sole owner
of a house in the Uptown area of South Minneapolis. He continued to live there
and work for Itasca Consulting, eventually becoming a lead programmer of their
modeling software.
In 1998 his personal life left him feeling the need for a change, and at the same
time his lack of knowledge of math and theory was clearly limiting the work he
could do for Itasca. He decided to address the situation and enroll in graduate
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school. Eventually, he chose Cornell’s department of Theoretical and Applied
Mechanics under the advice of former co-workers.
Just a few months before leaving Minneapolis for Ithaca, he was introduced to
Jennifer Wall by mutual friends. They endured a long distance relationship for
the (cid:12)rst year of his graduate school, and Jennifer moved to Ithaca at the begining
of his second year. On September 15, 2001, just four days after the attack on
the World Trade Center, Jennifer and David were married. On July 1, 2003 they
celebrated the birth of their son Emory.
At Cornell David decided to avoid (cid:12)nding research that was strongly related
to his previous job, instead seeking something that would broaden his experience.
Remembering his former interest in all things (cid:13)ight related as well as a curiosity
aboutthe methods used in computational (cid:13)uid mechanics, he choose new professor
Jane Wang as his advisor.
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This work is dedicated to my wife Jennifer and my son Emory, who have made
my graduate school experience much di(cid:11)erent than I initially imagined, and
in(cid:12)nitely for the better.
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ACKNOWLEDGEMENTS
I am very grateful for the kind assistance of Professor James Marden at Penn
State University. Professor Marden generously o(cid:11)ered me his expertise in the
capture and handling of dragon(cid:13)ies, and he and his graduate student spent several
days assisting me in performing the experiment in his lab.
Professor Alan Zehnder, in a display of trust for someone with no experimental
experience and over which he had no direct supervision, graciously loaned me the
equipment necessary to perform the experiment.
I would like to thank the members of my committee, especially Tim Healey,
for providing me with sage advice over the years on the perils and bene(cid:12)ts of the
academic experience.
I am of course especially indebted to Jane Wang for having the trust to allow
me to pursue my interests, and for helping to guide those interests in a productive
direction.
Iwould alsolike tothanktheentire department ofTheoretical andApplied Me-
chanics for supplying an atmosphere of academic freedom that is rapidly becoming
extremely rare.
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TABLE OF CONTENTS
1 Overview and Introduction 1
1.1 Dragon(cid:13)y wing kinematics . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Wing Aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Numerical Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Numerical Method 13
2.1 Streamfunction-vorticity formulation . . . . . . . . . . . . . . . . . 13
2.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Underlying (cid:13)ow solver on the regular grid . . . . . . . . . . . . . . 17
2.4 Incorporating discontinuities into a Poisson equation solver . . . . . 20
2.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.2 A 1D Example . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.3 An e(cid:14)cient 2D implementation . . . . . . . . . . . . . . . . 23
2.4.4 Convergence Test . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5 Finding the velocity (cid:12)eld . . . . . . . . . . . . . . . . . . . . . . . . 27
2.5.1 Solving the Poisson equation . . . . . . . . . . . . . . . . . . 27
2.5.2 Satisfying no-penetration . . . . . . . . . . . . . . . . . . . . 30
2.6 Calculating boundary vorticity . . . . . . . . . . . . . . . . . . . . . 33
2.7 Integrating vorticity . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.8 Calculating forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.9 Summary and sequence . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.10 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.10.1 Flow past a stationary circular cylinder . . . . . . . . . . . . 46
2.10.2 Flow past a moving circular cylinder . . . . . . . . . . . . . 53
2.10.3 Flow past two cylinders moving with respect to each other . 56
3 Experimental setup and methods 61
3.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.2 3D Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.3 2D Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.4 Numerical simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.5 Inertial forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.6 Quasi-steady approximation . . . . . . . . . . . . . . . . . . . . . . 75
4 Dragon(cid:13)y Kinematics 78
4.1 The lift stroke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.2 The thrust stroke . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.3 Stroke analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
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5 Forces on Dragon(cid:13)y Wings 91
5.1 Calculated Lift Stroke Forces . . . . . . . . . . . . . . . . . . . . . 91
5.1.1 Comparison between computed by CFD and by ODE . . . . 95
5.1.2 Analysis of force trace features . . . . . . . . . . . . . . . . . 97
5.1.3 E(cid:11)ects of net downwash . . . . . . . . . . . . . . . . . . . . 100
5.1.4 Reynolds number dependencies . . . . . . . . . . . . . . . . 101
5.1.5 Fore-hind phase relationship . . . . . . . . . . . . . . . . . . 103
5.2 Calculated Thrust Stroke Forces . . . . . . . . . . . . . . . . . . . . 105
5.2.1 Analysis of force trace features . . . . . . . . . . . . . . . . . 109
5.2.2 E(cid:11)ects of net downwash . . . . . . . . . . . . . . . . . . . . 111
5.2.3 Reynolds number dependencies . . . . . . . . . . . . . . . . 113
5.3 Wing Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.4 Inertial Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.5 Comparison with Measured Forces . . . . . . . . . . . . . . . . . . . 120
5.5.1 Lift stroke comparison . . . . . . . . . . . . . . . . . . . . . 120
5.5.2 Thrust stroke comparison . . . . . . . . . . . . . . . . . . . 121
6 Conclusions 124
6.1 Numerical Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.2 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.3 Force Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
7 Future Work 128
7.1 Numerical Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
7.2 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.3 Force Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Bibliography 133
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