Unsteady Aerodynamics for Aeroelastic Applications Using the Impulse Response Method Randal ...

219 Pages·2013·9.52 MB·English

-J
Unsteady Aerodynamics for Aeroelastic Applications Using
the Impulse Response Method
by
Randal Edmund Guendel
B.E., Vanderbilt University
(1998)
Submitted to the Department of Aeronautics and Astronautics
in partial fulfillment of the requirements for the degree of
Master of Science in Aeronautics and Astronautics
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2000
© Massachusetts Institute of Technology 2000. All rights reserved.
/' ) - ,-
A uthor ...........................
Department of Aeronautics and Astronautics
May 18, 2000
Certified by......................
II
Carlos E. S. Cesnik
Assistant Professor of Aeronautics and Astronautics
Thesis Supervisor
Accepted by ................................................... : ............
Nesbitt W. Hagood, IV
Professor of Aeronautics and Astronautics
Chair, Committee on Graduate Students
MASSACHUSETTS INSTITUTE
OFTECHNOLOGY
SEP 0 7 2000
LIBRARIES
Unsteady Aerodynamics for Aeroelastic Applications Using
the Impulse Response Method
by
Randal Edmund Guendel
Submitted to the Department of Aeronautics and Astronautics
on May 18, 2000, in partial fulfillment of the
requirements for the degree of
Master of Science in Aeronautics and Astronautics
Abstract
Aeroelasticity is a critical issue in the design of aircraft and other aerospace vehicles,
particularly those with highly flexible components. A reliable but efficient analysis
tool is required to aid decision-making in the preliminary design phase. This thesis
focuses on the unsteady aerodynamics component of the total aeroelastic system.
Classically unsteady aerodynamics has been grounded on the Theodorsen function,
which identifies the response of a 2-D wing section to harmonic pitch and plunge
oscillations. Recently, however, the Aerodynamic Impulse Response has emerged,
identifying a more fundamental aerodynamic response of a discrete-time system as
that to a unit impulse. With this response, the response to any motion in the time
domain can be easily predicted. This thesis examines the Aerodynamic Impulse
Response method using an aerodynamic panel code, PMARC, to obtain impulse
responses. The basic formulation of the method is limited to rigid-body analyses and
is thus of limited use to aeroelastic studies. To this end, the method is extended to
flexible-body responses by considering impulse distribution functions that are related
to structural mode shapes of the body. Both linear and nonlinear responses are
considered: the former uses convolution to generate arbitrary responses, the later
the Volterra series. Linear results for both rigid and flexible bodies are encouraging.
Predictions for a range of input motions closely match the unsteady response from
PMARC for the same motion. However, for harmonic motion accuracy erodes for
f/At < 0.05, limiting the frequency range over which the model is accurate. Nonlinear
responses are erratic and further study is required.
Thesis Supervisor: Carlos E. S. Cesnik
Title: Assistant Professor of Aeronautics and Astronautics
3
Acknowledgments
A project of this scale would have been impossible without the support and assistance
of a veritable army of friends and associates. Thanks go foremost to my advisor,
Prof. Carlos Cesnik. Without his guidance this project would never have come to
completion. I'm grateful for all his advice along the way, both with respect to my
thesis research and to my academic development.
I'm especially grateful to all the people at NASA Langley who have supported
my research endeavors over the past few years. The LARSS program was invaluable
in acquainting me with the research environment; I have many fond memories from
three summers at NASA Langley. Thanks to Rafaela Schwan and the others in the
Office of Education for making it all happen and, especially, for helping win the GEM
Fellowship. I'm grateful to each of my mentors at Langley: Dr. Mark Lake, Greg
Gatlin, and Dr. Keats Wilkie. Each gave me a tremendous opportunity to develop
myself as a researcher. In addition, I'd like to thank Dr. William Milholen, who first
introduced me to PMARC and who has provided willing support since then. Perhaps
most importantly, Dr. Walter Silva. Without Walt and the time he spent introducing
me to the Aerodynamic Impulse Response method, this project would have taken a
very different form. Thanks, Walt, for giving me that boost and for your support
along the way.
I also want to thank all the faculty, staff, and students of TELAC. Being the
only aerodynamicist in a structures lab was awkward at times, but you all made me
feel at home and offered valuable insight along the way. Special thanks go to Seth
Kessler, for all the advice and working out coding puzzles with me; Dennis Burianek,
for his words of wisdom as the lab's senior graduate student and for all his help with
LaTeX; and Barbara Huppe, for combing through my thesis with me and for lending
a willing ear on the occassions when my frustration exceeded my motivation. Outside
of TELAC, Tony Chobot and Chris Dunn also deserve sincere thanks for helping to
tame my computer system. And finally, grateful thanks go to Andrea Cook at Purdue
University for struggling with PMARC alongside of me-the frequency of the word
4
"PMARC" in our correspondence was certainly frighteningly high.
Further thanks are extended to those at my undergraduate institution, Vanderbilt
University, who have been instrumental in my development as a reseracher and
engineer. In particular, thanks go to Prof. Ephrahim Garcia and Dr. Joel Barnett.
Nor could I have done this without the support of friends to keep me sane and
(nearly) level-headed. Zac and Hootan, those tried and true souls met early at
Vanderbilt who have stuck with me through the years, have unfailingly helped keep
me afloat. Nothing brightens a weekend quite like a long discussion of music and
literature with Zac or of the latest Formula 1 race with Hootan. And the new friends
I've made here in Cambridge, thanks for everything. Memories of nights on the town
with Jeff, Tony, and Dan will never fade. Jamie I can't thank enough for her simple
optimism, her insistence that I need only to fix my "equation." And many thanks go
to Seth, my roommate and officemate, for everything that we've shared and for just
being there.
And of course none of this would have been possible without my loving and
supporting family. Thanks to my parents for pushing me hard, for always emphasizing
the value of a good education, and for always being behind me.
This research was partially supported by the Air Force Office of Scientific Research
under the subgrant E-16-N96-G1.
5
6
Contents
1 Introduction 19
2 Background 25
2.1 A eroelasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.1.1 Structural Dynamics . . . . . . . . . . . . . . . . . . . 28
2.1.2 Aerodynamics . . . . . . . . . . . . . . . . . . . . . . . 29
2.1.3 Aerodynamics and Structures Coupling . . . . . . . . . 30
2.1.4 Controls Coupling . . . . . . . . . . . . . . . . . . . . . 31
2.2 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.1 CFD Methods . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.2 Reduced-Order Methods . . . . . . . . . . . . . . . . . 33
2.2.3 Simplified Aerodynamics Models . . . . . . . . . . . . 40
2.2.4 Limitations Towards the Application to Highly Flexible Vehicles 49
3 The Aerodynamic Impulse Response Method 51
3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2 Mathematical Foundations . . . . . . . . . . . . . . . . . . . 52
3.2.1 Clasification of Mathematical Systems . . . . . . 52
3.2.2 The Linear Impulse Response Method . . . . . . 54
3.2.3 The Nonlinear Impulse Response Method . . . . . . . 56
3.3 The Aerodynamic Impulse Response Method . . . . . . . 60
4 An Overview of Aerodynamic Panel Methods 63
7
4.1 H istory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2 T heory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.3 Benefits of the Panel Method . . . . . . . . . . . . . . . . . . . . . . 70
4.4 PMARC . . . . . . . . . .. . .. . ..... . . . . . . . . .. . . . . . 72
5 PMARC Modifications and Other Coding 75
5.1 Linear PMARC/AIR for Rigid Bodies . . . . . . . . . . . . . . . . . . 76
5.2 Nonlinear PMARC/AIR for Rigid Bodies . . . . . . . . . . . . . . . . 79
5.3 Linear PMARC/AIR for Flexible Bodies . . . . . . . . . . . . . . . . 81
5.3.1 Modeling Complex Deformations . . . . . . . . . . . . . . . . 81
5.3.2 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.3.3 Two-Dimensional Lumped Vortex Model . . . . . . . . . . . . 84
5.3.4 PMARC Implementation . . . . . . . . . . . . . . . . . . . . . 89
5.4 Other Codes Developed . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.4.1 Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.4.2 Deflected Wing Generation . . . . . . . . . . . . . . . . . . . . 93
5.4.3 Sinusoidal Input Function Generator . . . . . . . . . . . . . . 94
6 Geometry Models 95
6.1 Highly Flexible, High Aspect Ratio Wings . . . . . . . . . . . . . . . 95
6.2 Geometry Modeling with PMARC . . . . . . . . . . . . . . . . . . . . 96
6.3 Simple High Aspect Ratio Wing . . . . . . . . . . . . . . . . . . . . . 99
6.4 BACT Wing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
7 Results and Discussion 103
7.1 Error Analysis Method . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.2 Preliminary Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
7.2.1 PMARC Unsteady Tests . . . . . . . . . . . . . . . . . . . . . 105
7.2.2 Nonplanar Wing Tests . . . . . . . . . . . . . . . . . . . . . . 108
7.3 Rigid-Body PMARC/AIR . . . . . . . . . . . . . . . . . . . . . . . . 115
7.3.1 Linear Impulse Responses . . . . . . . . . . . . . . . . . . . . 115
8
7.3.2 Linear Responses to Sinusoidal Motions . . . . . . . . . . 116
7.3.3 Linear Response to Step Input . . . . . . . . . . . . . . . 135
7.3.4 Linear Response to Arbitrary Input . . . . . . . . . . . . 137
7.3.5 Nonlinear Impulse Responses . . . . . . . . . . . . . . . 139
7.3.6 Nonlinear Responses to Sinusoidal Motions . . . . . . . . 142
7.3.7 Summary of Rigid-Body Results . . . . . . . . . . . . . . 142
7.4 Flexible-Body PMARC/AIR . . . . . . . . . . . . . . . . . . . . 143
7.4.1 Initial Testing . . . . . . . . . . . . . . . . . . . . . . . . 144
7.4.2 Linear Impulse Responses . . . . . . . . . . . . . . . . . 145
7.4.3 Linear Responses to Various Input Motions . . . . . . . 147
7.4.4 Summary of Flexible-Body Results . . . . . . . . . . . . 150
8 Concluding Remarks 151
8.1 C onclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
8.2 Recommendations for Future Study . . . . . . . . . . . . . . . . . . 153
Bibliography 157
A PMARC/AIR Code Listings 165
A.1 Linear Rigid-Body PMARC/AIR . . . . . . . . . . . . . . . . . . . 165
A.2 Linear Flexible-Body PMARC/AIR . . . . . . . . . . . . . . . . . . 169
A .3 Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
A.4 Volterra Series .................................... 175
A.5 Input Generation Program ........................... 179
B Other Code Listings 181
B.1 MATLAB Lumped Vortex Model . . . . . . . . . . . . . . . . . . . 181
B.2 Deflected Wing Generation Program . . . . . . . . . . . . . . . . . 185
C Input Files 191
C.1 SHAR1 PMARC Input File for 29% Bending . . . . . . . . . . . . . 191
C.2 SHAR2 PMARC Input File . . . . . . . . . . . . . . . . . . . . . . 215
9
C.3 BACT PMARC Input File ........................ 217
C.4 Flexible-Body Impulse Distribution File (IMPULSE) ......... 220
10
List of Figures
1-1 Aurora Flight Science's Theseus HALE UAV, with Endurance of 50
hrs at 88,000 ft [1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1-2 AeroVironment's Pathfinder HALE UAV, with Endurance of 16 hrs at
70,000 ft [1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2-1 Collar's Triangle of Aeroelastic Forces . . . . . . . . . . . . . . . . . . 27
2-2 Aero-Structural Coupling Through an Interface . . . . . . . . . . . . 31
2-3 Real and Imaginary Lift Components Using Eigenanalysis [2] . . . . 36
2-4 Comparison of POD and Arnoldi Models to the CFD Simulation of a
Pulse Response [3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2-5 Airfoil Coordinate System for Peters' Finite-State Inflow Model . . . 41
2-6 Comparison of Results Using the Peters Inflow Model with Theodorsen
T heory [4] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2-7 Flutter Speed Predicted with Various Models [5] . . . . . . . . . . . . 45
2-8 Spanwise Lift Predicted with Various Models [6] . . . . . . . . . . . . 47
2-9 Comparison of Theoretical Response Due to Wagner to the Response
Predicted Using the VSAERO Panel Code of 2-D and 3-D Wings to
Plunging M otions [7] . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3-1 Simple Example of the Discrete-Time Convolution Method . . . . . . 55
3-2 Block Diagram of the Linear Aerodynamic Impulse Response Method 56
3-3 Three-Dimensional View of the 2nd-Order Kernel of the Burgers
Equation [8] . . . . . . . . . . . . . . . . . . . . . . .. . ... . . . 58
3-4 Block Diagram of the Nonlinear Aerodynamic Impulse Response Method 59
11