Understanding energy transfer in aeroelastic flutter and exploiting free-play induced flutter for

76 Pages·2017·4.05 MB·English

Iowa State University Capstones, Theses and
Graduate Theses and Dissertations
Dissertations
2016
Understanding energy transfer in aeroelastic flutter
and exploiting free-play induced flutter for energy
harvesting
Prachi Deepak Deshpande
Iowa State University
Follow this and additional works at:https://lib.dr.iastate.edu/etd
Part of theMechanical Engineering Commons
Recommended Citation
Deshpande, Prachi Deepak, "Understanding energy transfer in aeroelastic flutter and exploiting free-play induced flutter for energy
harvesting" (2016).Graduate Theses and Dissertations. 15689.
https://lib.dr.iastate.edu/etd/15689
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Understanding energy transfer in aeroelastic flutter and exploiting free-play
induced flutter for energy harvesting
by
Prachi Deepak Deshpande
A thesis submitted to the graduate faculty
in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
Major: Mechanical Engineering
Program of Study Committee:
Atul Kelkar, Major Professor
Partha Sarkar
Ming-Chen Hsu
Iowa State University
Ames, Iowa
2016
Copyright (cid:13)c Prachi Deepak Deshpande, 2016. All rights reserved.
ii
DEDICATION
IwouldliketodedicatethisthesistomyfatherDeepakandmotherAparna. Theirunending
support, encouragement and motivation is the most integral part of the whole journey.
iii
TABLE OF CONTENTS
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
CHAPTER 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Background Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Aeroelasticity and Flutter . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 Free-play Nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.3 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
CHAPTER 2. TWO DIMENSIONAL SYSTEM DEVELOPMENT . . . . . . 10
2.1 Description of the 2D model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Modelling of free-play nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.1 Hyperbolic Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
CHAPTER 3. TWO DIMENSIONAL SYSTEM ANALYSIS . . . . . . . . . . 16
3.1 2D System simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 System response under LCO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 Energy analysis of 2D system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
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CHAPTER 4. THREE DIMENSIONAL MODEL DEVELOPMENT . . . . . 28
4.1 Revisiting experimental model development . . . . . . . . . . . . . . . . . . . . 28
4.2 Computational model development . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.3 Modal analysis of computational model . . . . . . . . . . . . . . . . . . . . . . 32
CHAPTER 5. THREE DIMENSIONAL SYSTEM ANALYSIS . . . . . . . . 35
5.1 Two way system coupling using Ansys Workbench . . . . . . . . . . . . . . . . 35
5.2 Steps in setting up Workbench interface . . . . . . . . . . . . . . . . . . . . . . 37
5.3 Energy analysis of 3D system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
CHAPTER 6. ENERGY HARNESSING ANALYSIS . . . . . . . . . . . . . . 49
6.1 Magnetostrictive Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
6.2 Use of Galfenol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.3 Energy harvesting concept for 2D system . . . . . . . . . . . . . . . . . . . . . 53
6.4 Energy harvesting concept for 3D system . . . . . . . . . . . . . . . . . . . . . 55
6.5 Key benefits of proposed concept . . . . . . . . . . . . . . . . . . . . . . . . . . 58
CHAPTER 7. CONCLUDING REMARKS AND FUTURE WORK . . . . . 59
7.1 Key Contributions: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
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LIST OF TABLES
Table 3.1 System parameters and initial condition . . . . . . . . . . . . . . . . . 17
Table 4.1 List of Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . 32
Table 6.1 List of Galfenol properties . . . . . . . . . . . . . . . . . . . . . . . . . 52
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LIST OF FIGURES
Figure 1.1 Aspects of Aeroelasticity . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Figure 1.2 System with nonlinearity in feedback interconnection . . . . . . . . . . 3
Figure 1.3 Flutter Velocity vs Free-play ∗ . . . . . . . . . . . . . . . . . . . . . . . 4
Figure 1.4 Hopf Bifurcation ∗ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Figure 1.5 Schematic of WADC model ∗ . . . . . . . . . . . . . . . . . . . . . . . 5
Figure 2.1 2D Airfoil System∗ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Figure 2.2 Hyperbolic Nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Figure 3.1 Displacement vs Time . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Figure 3.2 Angular Displacement vs Time . . . . . . . . . . . . . . . . . . . . . . 18
Figure 3.3 Lift vs Complete time . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Figure 3.4 Aerodynamic Moment vs Time . . . . . . . . . . . . . . . . . . . . . . 19
Figure 3.5 Lift vs Time in one cycle . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Figure 3.6 Aerodynamic Moment vs Time in one cycle . . . . . . . . . . . . . . . 20
Figure 3.7 Pitch Rate vs Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Figure 3.8 Plunge Rate vs Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Figure 3.9 Moment vs Pitch Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Figure 3.10 Lift vs Plunge Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Figure 3.11 Potential Energy vs Time in one cycle . . . . . . . . . . . . . . . . . . 24
Figure 3.12 Kinetic Energy vs Time in one cycle . . . . . . . . . . . . . . . . . . . 24
Figure 3.13 Acceleration vs Time in one cycle . . . . . . . . . . . . . . . . . . . . . 25
Figure 3.14 Total Energy vs Time in one cycle . . . . . . . . . . . . . . . . . . . . 26
Figure 3.15 Total Energy vs Time. . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
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Figure 4.1 Experimental Setup (front)∗ . . . . . . . . . . . . . . . . . . . . . . . . 29
Figure 4.2 Experimental Setup (side) ∗ . . . . . . . . . . . . . . . . . . . . . . . . 29
Figure 4.3 Individual Section ∗ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Figure 4.4 Internal Structure ∗ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Figure 4.5 Free-play Mechanism ∗ . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Figure 4.6 Computational Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Figure 4.7 3D Model Dimesions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Figure 4.8 Mode 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Figure 4.9 Mode 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Figure 4.10 Mode 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Figure 5.1 Two Way Data Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Figure 5.2 Short Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Figure 5.3 Steps in the Workbench set-up. . . . . . . . . . . . . . . . . . . . . . . 39
Figure 5.4 Data Transfer 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Figure 5.5 Data Transfer 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Figure 5.6 Two Way System Coupling Set-up . . . . . . . . . . . . . . . . . . . . 41
Figure 5.7 Lift vs Plunge Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Figure 5.8 FFT Result ∗ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Figure 5.9 Damped Response ∗ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Figure 5.10 Divergent Response ∗ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Figure 5.11 Stable LCO Region ∗ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Figure 5.12 Kinetic Energy in one cycle . . . . . . . . . . . . . . . . . . . . . . . . 46
Figure 5.13 Potential Energy in one cycle . . . . . . . . . . . . . . . . . . . . . . . 46
Figure 5.14 Total Energy in one cycle . . . . . . . . . . . . . . . . . . . . . . . . . 47
Figure 6.1 Magnetostriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Figure 6.2 Magnetostriction Effects . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Figure 6.3 Induced Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Figure 6.4 Induced voltage in One Cycle . . . . . . . . . . . . . . . . . . . . . . . 54
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Figure 6.5 LCO after changing δ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Figure 6.6 Voltage induced in one cycle . . . . . . . . . . . . . . . . . . . . . . . . 56
Figure 6.7 Design Concept-Galfenol Spar ∗ . . . . . . . . . . . . . . . . . . . . . . 56
Figure 6.8 Structure Array Concept ∗ . . . . . . . . . . . . . . . . . . . . . . . . . 56
Figure 6.9 Basic Quadruple Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Figure 6.10 Response with higher flutter frequency . . . . . . . . . . . . . . . . . . 57
Figure 6.11 Energy harvesting schematic block diagram . . . . . . . . . . . . . . . 58
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ACKNOWLEDGEMENTS
I would like to take this opportunity to express my heartfelt gratitude to all people who
helped me with various aspects of my masters program, conducting research and the writing
of this thesis.
First and foremost, I thank my advisor Dr. Atul Kelkar for his generous support, advices,
patience and continuous guidance at each and every step. He was very helpful throughout my
graduate program, research and the writing of this thesis. I greatly appreciate VSI Aerospace,
Inc., Ames, IA for sharing the data useful for this work.
Iwouldalsoliketothankmycommitteemembersfortheirefforts,insightsandcontributions
to this work. Dr. Ming-Chen Hsu and his group was really helpful whenever needed during
the project work. I am thankful to Dr. Sarkar for his guidance in the graduate program and
this work. Also, I am grateful to Dr. Dayal for his time and suggestions whenever required.
I extend my thanks to the Department of Mechanical Engineering for financial assistance
and all the support they provided throughout my graduate program.
I express my gratitude to my friends for their guidance, motivation, useful discussions and
confidence on me. My deepest thanks to my family, without their continuous encouragement
and unending support it was impossible for me to reach here. They are the strong pillars of
my foundation.