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OL2010.pdf
AFRL-RB-WP-TR-2010-3013
UNSTEADY LOW REYNOLDS NUMBER
AERODYNAMICS FOR MICRO AIR VEHICLES (MAVs)
Michael V. OL
Low-Speed Aerodynamic Configuration Branch
Aeronautical Sciences Division
MAY 2010
Final Report
Approved for public release; distribution unlimited.
See additional restrictions described on inside pages
AIR FORCE RESEARCH LABORATORY
AIR VEHICLES DIRECTORATE
WRIGHT-PATTERSON AIR FORCE BASE, OH 45433-7542
AIR FORCE MATERIEL COMMAND
UNITED STATES AIR FORCE
NOTICE AND SIGNATURE PAGE
Using Government drawings, specifications, or other data included in this document for any
purpose other than Government procurement does not in any way obligate the U.S.
Government. The fact that the Government formulated or supplied the drawings, specifications,
or other data does not license the holder or any other person or corporation; or convey any
rights or permission to manufacture, use, or sell any patented invention that may relate to them.
This report was cleared for public release by the USAF 88th Air Base Wing (88 ABW) Public
Affairs Office (PAO) and is available to the general public, including foreign nationals. Copies
may be obtained from the Defense Technical Information Center (DTIC) (http://www.dtic.mil).
AFRL-RB-WP-TR-2010-3013 HAS BEEN REVIEWED AND IS APPROVED FOR
PUBLICATION IN ACCORDANCE WITH THE ASSIGNED DISTRIBUTION STATEMENT.
*//signature//
_______________________________________
//signature//
______________________________________
MICHAEL V. OL
Project Engineer
Low-Speed Aerodynamic Configuration
Branch
Aeronautical Sciences Division
CHRISTOPHER P. GREEK
Chief
Low-Speed Aerodynamic Configuration
Branch
Aeronautical Sciences Division
//signature//
______________________________________
DIETER MULTHOPP
Technical Advisor
Low-Speed Aerodynamic Configuration
Branch
Aeronautical Sciences Division
This report is published in the interest of scientific and technical information exchange and its
publication does not constitute the Government’s approval or disapproval of its ideas or
findings.
*Disseminated copies will show “//signature//” stamped or typed above the signature blocks.
Form Approved
OMB No. 0704-0188
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1. REPORT DATE (DD-MM-YY)
2. REPORT TYPE
May 2010
3. DATES COVERED (From - To)
01 June 2002 – 01 December 2009
Final
4. TITLE AND SUBTITLE
5a. CONTRACT NUMBER
UNSTEADY LOW REYNOLDS NUMBER AERODYNAMICS FOR MICRO
AIR VEHICLES (MAVs)
IN HOUSE
5b. GRANT NUMBER
5c. PROGRAM ELEMENT NUMBER
0602201
6. AUTHOR(S)
5d. PROJECT NUMBER
Michael V. OL
A07C
5e. TASK NUMBER
5f. WORK UNIT NUMBER
A07C0B
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
8. PERFORMING ORGANIZATION
REPORT NUMBER
Low-Speed Aerodynamic Configuration Branch (AFRL/RBAA)
Aeronautical Sciences Division
Air Vehicles Directorate, Air Force Research Laboratory
Wright-Patterson Air Force Base, OH 45433-7542
Air Force Materiel Command, United States Air Force
AFRL-RB-WP-TR-2010-3013
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)
10. SPONSORING/MONITORING
AGENCY ACRONYM(S)
Air Force Research Laboratory
Air Vehicles Directorate
Wright-Patterson Air Force Base, OH 45433-7542
Air Force Materiel Command
United States Air Force
AFRL/RBAA
11. SPONSORING/MONITORING
AGENCY REPORT NUMBER(S)
AFRL-RB-WP-TR-2010-3013
12. DISTRIBUTION/AVAILABILITY STATEMENT
Approved for public release; distribution unlimited.
13. SUPPLEMENTARY NOTES
PAO Case Number: 88ABW 2010-0446, cleared 02 February 2010. Report contains color.
14. ABSTRACT
This work introduces the Micro Air Vehicle (MAV) problem from the viewpoint of aerodynamics. Water tunnels are assessed as
tools for MAV aerodynamics. The design, construction and instrumentation of RB’s “Horizontal Free-surface Water Tunnel” is
documented. Experiments in steady aerodynamics at low Reynolds number for airfoils, plates and wings of various planforms are
mentioned, with focus on laminar to turbulent transition and documentation of how Reynolds number, flowfield conditions and
model geometry interplay to affect laminar separation and possible turbulent reattachment, and how planform effects impact lift
generation. Passing to the unsteady aerodynamics problem, the HFWT’s “High-Intensity Pitch-Plunge Oscillator” Rig is described.
Then, the bulk of the report focuses on experiments in unsteady aerodynamics. A broad range of periodic and transient problems is
covered, anchored in traditional problems of airfoil dynamic stall, and expanding to MAV applications of perching and flapping.
New knowledge includes elucidation of the surprisingly broad limits of linear superposition in markedly nonlinear problems, and
notes on the relative importance of laminar to turbulent transition in a broad range of unsteady problems.
15. SUBJECT TERMS
Unsteady Aerodynamics, Micro Air Vehicle, Vortex Dynamics, Dynamic Stall
16. SECURITY CLASSIFICATION OF:
a. REPORT
b. ABSTRACT
Unclassified Unclassified
c. THIS PAGE
Unclassified
17. LIMITATION
18. NUMBER
OF ABSTRACT:
OF PAGES
SAR
150
19a. NAME OF RESPONSIBLE PERSON (Monitor)
Michael V. OL
19b. TELEPHONE NUMBER (Include Area Code)
N/A
Standard Form 298 (Rev. 8-98)
Prescribed by ANSI Std. Z39-18
i
Table of Contents
List of Figures
List of Tables
Acknowledgements
1.
Summary
2.
Introduction: Philosophy, Scope, and Approach
2.1.
General Musings on MAVs
2.1.1. Opinions on Benefits and Drawbacks of Flapping Wings
2.1.2.
Unsteady Aerodynamics in Two Dimensions
2.1.3.
Rectilinear vs. Nonrectilinear Motions
2.2.
Canonical Problems
3.
The Water Tunnel as a Research Tool in Low-Speed Aerodynamics
3.1.
The Case for Water Tunnels for Low-Speed Aerodynamic Research
3.1.1.
Introductory Remarks
3.1.2.
Reynolds Number Effects
3.1.3.
Laser-Based Distributed Flowfield-Diagnostic Methods
3.1.4.
Rapid Prototyping of Water Tunnel Models
3.1.5.
Dynamic Testing
3.1.6.
Example: Forced Airfoil Oscillation in Pure Plunge
3.1.7.
Example: Particle Image Velocimetry for a UCAV Configuration
3.1.8.
Summarizing the Case for Water Tunnels
3.2.
AFRL/RB’s “Horizontal Free-surface Water Tunnel” (HFWT)
3.2.1.
The HFWT’s Origin and Installation History
3.2.2.
Flow Quality Measurements and Instrumentation Suite of the HFWT
3.2.3.
Dye Injection
3.2.4.
Force Balances
3.2.5. Summarizing the HFWT
4.
Experiments in Steady Aerodynamics at Low Reynolds Number
4.1.
Laminar Separation Bubbles for the SD7003 Airfoil
4.2.
Aspect Ratio = 2 Flat Plates of Various Planform
5.
Establishing a Capability for Unsteady Aerodynamics Experiments
5.1.
A Scheme for Pitch and Plunge Motions
5.1.1. Rig Performance
5.2.
Extension of HIPPO to 3-DOF
6.
Experiments in Unsteady Aerodynamics using the HIPPO rig
6.1.
High-Frequency Pure-Plunge
6.1.1. Introduction
6.1.2. Frequency and Reynolds Number Effects
6.1.3. Plunge at k = 3.93, Re=40,000 and Re = 60,000
6.1.4. Strouhal Number and Reduced Amplitude
6.1.5. Start-up and Relaxation to Periodicity
6.1.6. Nonzero Mean Angle of Attack
iii
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6.1.7. Summary
6.2.
Sinusoidal, Trapezoidal and Triangular Pitch; and Pitch-Plunge Comparison
6.2.1. Introduction and Problem Statement
6.2.2. Flowfield History from Startup: Dye Injection Results
6.2.3. Established Flowfields: PIV Measurements
6.2.4. Discussion: Pitch-Plunge Comparison and Other Observations
6.3.
Further Observations of High-Frequency Sinusoidal Pitch
6.3.1. Dye Injection Results
6.3.2.
PIV Results
6.4.
Low-Frequency Pure-Plunge and the Role of Transition for Deep Stall Problems
6.4.1. Introduction and Problem Definition
6.4.2. Re = 60,000 Results
6.4.3. Reynolds Number Effects
6.4.4. Aerodynamic Force Coefficients
6.5.
Low-Frequency Pitch-Plunge and the Role of Transition for Shallow Stall Problems
6.5.1. Introduction and Problem Definition
6.5.2. Re = 60,000 Results
6.5.3. Thoughts on the Role of Transition
6.5.4. Reynolds Number Effects
6.5.5. Aerodynamic Force Coefficients
6.6.
Sinusoidal Pitch and Plunge of a Flat Plate
6.6.1. Pitch-Plunge Case
6.6.2. Pure-Plunge Case
6.6.3. Lift Coefficient Comparison
6.7.
Sinusoidal Pitch and Plunge of an AR=2 Flat Plate
6.7.1. Introduction and Motivations
6.7.2. Flowfield Results
6.8.
Mixed-Frequency Problems, where Pitch and Plunge Frequency Differ
6.8.1. Problem Definition
6.8.2. Flowfield Results
6.9.
Pitch Ramp-and-Return
6.9.1. Introduction
6.9.2. Experimental Parameter Study with Dye Injection
6.9.3. Qualitative vs. Quantitative Flow Visualization
6.9.4. Removing Parasitic Surge
6.9.5. Pitch Ramp and Return, 2nd Sequence
6.10. Perching: an Extension of the Linear Pitch Ramp
6.10.1.
Motion Definition
6.10.2.
Dye Injection, PIV and Direct Force Measurement
6.10.3.
Summary
6.11. Flapping
6.11.1.
Motivations and Motion Definition
6.11.2.
Dye Injection Results
7.
Conclusion
iv
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7.1
General Musings
7.2
Resume of Results
7.3
Toward Future Work
LIST OF ACRONYMS, ABBREVIATIONS, AND SYMBOLS
Appendix A. The Fiber-Bragg Grating Force Balance
A.1.
FBG Theory of Operation
A.2.
Load Cell Mechanical Design
A.3.
Load Cell Calibration
A.4.
Data Processing
Appendix B. Resume of Publications Supporting the Present Work
Appendix C. Listing of Research Collaborators
8.
References
v
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124
126
128
129
List of Figures
Figure 1. Notional estimate of airfoil performance vs. Re. From Horten, as reported by Mueller.
8
Figure 2. Eppler E387 airfoil drag polar, Re = 60K to 500K, collected from wind tunnel data at the
University of Illinois, Urbana-Champaign.
9
Figure 3. Comparison of out-of-plane vorticity contours from experiment in the water tunnel (left
column), 2D computation using the commercial code CFL3D, and 2D immersed boundary-method
computation, at various phases of motion; Re=40,000, SD7003 airfoil pure-plunge.
13
Figure 4. The 1303 UCAV configuration: 5’-span model installed in QinetiQ 5m wind tunnel, and 3Dprinted (plastic) installed in water tunnel test section.
14
Figure 5. 1303 UCAV water tunnel PIV, contours of Reynolds stress u’v’: 30% semispan, α = 6 º (top);
30% semispan, α = 4º (bottom-left); and 30% semispan, α = 6º (bottom-right).
14
Figure 6. The HFWT installed at Caltech, as originally built by the PI (1997).
16
Figure 7. Schematic of the HFWT as installed in Building 24C, Wright-Patterson.
16
Figure 8. HFWT installation history: site preparation, including excavation for sewer drain (top left);
mockup of main components on support frame, without connecting plumbing and test section glass walls
(top right), and tunnel operational (above).
17
Figure 9. Pitot-manometer-derived HFWT calibration curve; test section free-stream speed vs. pump
controller setting.
18
Figure 10. 1-component hot film probe installed in HFWT test section.
18
Figure 11. Typical hot wire time-traces, constant mean streamwise velocity of ~15 cm/s; voltage drift
with time (left) and fluctuating velocity vs. time, after subtracting moving-average of mean signal.
19
Figure 12. Fluctuating u-component of velocity vs. PIV ensemble point, cm/s; mean is 15 cm/s.
20
Figure 13. Contour plot of streamwise velocity distribution in the HFWT, over 400 (nominally) shots,
using PIV; nominal speed is 15 cm/s, and the PIV light sheet is at the test section centerplane.
21
Figure 14. 50º-sweep delta wing with port-panel of leeward side instrumented with S3Ffilm, in
collaboration with ISSI, to measure skin friction field: model about to be lowered into the HFWT test
section (top left), view of metric side of model (top right), and typical result of skin friction intensity
(bottom).
22
Figure 15. SD7003 airfoil installed inside test section, showing smooth suction-side of airfoil (top left)
and plunge rod coupling on pressure-side of airfoil (bottom left). Black arrow in bottom image points to
dye injection exit port location. Middle: injector tube attached to flat-plate model leading edge, firing
spanwise outboard. Right: flat plate model with no internal dye passages, showing position of externallyfed dye at the leading edge.
23
Figure 16. SD7003 airfoil mounted upside-down, below Rolling Hills Research Corporation 5component waterproof force balance; lifted from the test section for model installation.
24
Figure 17. 3-component force balance based on Fibre Bragg grating (FBG) sensors, integrated with
airfoil mount; photo shows the HIPPO plunge rods bushed into the inner frame of the balance, and a lock
plate bridging the inner and outer frames, to lock the two safely during model installation.
25
Figure 18. SD7003 airfoil static lift coefficient vs. angle of attack, Re = 60K: XFOIL results at
amplification factor N = 9 (black line), wind tunnel data of Selig et al., and water tunnel data (blue line),
with error bars at 95% confidence intervals. Mean angle of attack for oscillatory motions discussed in a
later chapter of this report, 8°, labeled by the dashed red line.
26
vi
Figure 19. Schematic of PIV interrogation window tessellation on SD7003 airfoil (left), and photo of
airfoil mounted in the water tunnel test section (right).
29
Figure 20. Contours of SD7003 LSB mean streamwise velocity component, α=4°.
29
Figure 21. Contours of SD7003 LSB normalized Reynolds stress, α=4°, together with LSB dividing
streamline.
30
Figure 22. Contours of SD7003 LSB mean streamwise velocity component, α=8°.
30
Figure 23. Contours of SD7003 LSB normalized Reynolds stress, α=8°.
30
Figure 24. Contours of SD7003 LSB mean streamwise velocity component, α=11°.
31
Figure 25. Contours of SD7003 LSB normalized Reynolds stress, α=11°; not the higher magnitude of
Reynolds stresses in the contour levels.
31
Figure 26. AR=2 planforms: rectangle (left), semicircle (middle) and delta wing (right).
33
Figure 27. In-plane velocity magnitude and out-of-plane vorticity; α= 10°; downstream X/C = 1; U∞ = 9
cm/s; Re = 8,000.
34
Figure 28. Vorticity evolution vs. distance downstream from trailing edge, α=10°; semi-ellipse (left) and
rectangle (right); note difference in vorticity contour levels.
35
Figure 29. Normalized circulation vs. contour radius; X/C = 0.1 (left), X/C = 1.0 (center) and X/C = 2.0
(right).
35
Figure 30. CL vs. X/C Comparison for rectangle (left) and semi-ellipse (right).
36
Figure 31. CL vs. α; rectangle (top left), comparison of rectangle data with aspect-ratio scaled results of
Laitone (top right), delta wing (bottom left) and semi-ellipse (bottom right).
37
Figure 32. Examples of 2-degree-of-freedom rigs in water tow-tanks and water tunnels: (a) Paquet,
Parker et al., Anderson et al., Hanff, Kurtulus et al.
38
Figure 33. "High-Intensity Pitch/Plunge Oscillator" Rig: (top left) schematic, (top right) installed atop
water tunnel test section, (middle left) with plates to damp free-surface oscillations caused by model
motion, (middle right) schematic of SD7003 airfoil mount and plunge rods, with rod endpoints interior to
the model; and (bottom) side view of test section with rig and airfoil model installed.
39
Figure 34. Time-traces and FFTs of plunge-rod commanded position, attained position and relative
difference (error).
41
Figure 35. k = 0.80 pure-plunge, contours of phase-averaged (230 realizations) normalized streamwise
component of velocity (left) and Reynolds shear stress (right), after periodic conditions established; φ = 0,
1/4, 1/2 and 3/4.
42
Figure 36. Full longitudinal 3-DOF motion capability; view of full linear motor setup above HFWT test
section (left), and detail of linear motor enabling streamwise-direction motion (right).
42
Figure 37. Schematic of airfoil pitch and plunge oscillation.
43
Figure 38. Dye Visualization, Re = 60,000, mean α = 4°, h = 0.05: k = 0.080, 1.31, 1.96 and 2.62, at the
top (right-hand-side of page; φ = whole number) and bottom (left-hand-side; φ = n/2).
45
Figure 39. Re = 10,000 to 60,000, mean α = 4°, h = 0.05: k = 3.93, established flow, top of the plunge
stroke.
46
Figure 40. k =3.93, Re = 10,000: near-wake (left) and over the airfoil suction-side (right); top of stroke
(upper two images) and bottom of stroke (lower two images).
46
Figure 41. Re = 10,000 to 60,000, mean α = 4°, h = 0.05: k = 3.93, established flow, top of the plunge
stroke.
47
Figure 42. Vorticity contours based on single image pairs for four phases within the cycle. k= 3.93, Re =
40,000.
48
vii
Figure 43. Pure-plunge, Re = 20,000, mean α = 4°; three cases of kh = 0.196, and three motion phases: φ
= 0.5 after start-up (bottom of stroke), bottom of stroke in established flow, top of stroke in established
flow.
49
Figure 44. Pure-plunge, Re = 20,000, mean α = 4°; three cases of kh = 0.591, and three motion phases: φ
=1 after start-up (top of stroke), bottom of stroke in established flow, top of stroke in established flow. 49
Figure 45. Dye streaklines for near-wake, h = 0.05 k = 3.93 plunge; evolution of starting-flow across 10
periods of motion. Re = 60,000.
50
Figure 46. Pure-plunge, Re = 20,000, mean α = 21° (top row), 4° (middle row) and 0° (bottom row); h =
0.05, k = 3.93; left column: φ =1 after start-up (top of stroke); middle column: bottom of stroke in
established flow; right column: top of stroke in established flow.
51
Figure 47. Sinusoidal (green), trapezoidal (black) and triangular (blue) time traces of pitch angle; and
sinusoidal plunge-induce angle of attack (orange). “a” – “h” mark phases where data were taken.
54
Figure 48. 8 periods of trapezoidal pitch: dye injection at phases a (left column), b (middle column) and c
(right column); time from motion onset is from top to bottom. Top row is first period, second row is
second period, and so forth, down to the 8th period. Double trailing vortex system is circled.
55
Figure 49. 8 periods of trapezoidal pitch, continued: sampling at phases e, f and g.
56
Figure 50. Sinusoidal pitch dye injection: phases a (left column), b (middle column) and c (right
column). Top row is 1st period, 2nd row is 2nd period,…, bottom row is 8th period.
57
Figure 51. Sinusoidal pitch dye injection, continued: phases e, f and g.
58
Figure 52. Triangular (linear ramp) pitch dye injection: phases a, b and d.
59
Figure 53. Triangular (linear ramp) pitch dye injection, continued: phases e, f and h.
60
Figure 54. Sinusoidal plunge dye injection, 5 periods of motion, phases a, b and d.
61
Figure 55. Sinusoidal plunge dye injection continued, phases e, f and h.
61
Figure 56. PIV phase-averaged vorticity contours for trapezoidal (left) and sinusoidal (right) pitch, Re =
10,000; 8 phases of motion (trapezoidal) and 4 phases (sinusoidal).
63
Figure 57. Dye injection for 4 different starting phases of pure-pitch motion; k = 3.93, pivot about x/c =
0.25, Re = 10K, dye injected at trailing edge; periods of oscillation as marked, from start of motion.
67
Figure 58. Instantaneous vorticity PIV images; phase “a” (1st column), “b” (2nd column), “c” (3rd column)
and “d” (4th column); periods, in rows from top to bottom, are: 1, 2, 3, 5, 10, 20, 30, 50 and 100.
68
Figure 59. Motion kinematics and effective angle of attack time history for pure-plunge and combined
pitch-plunge.
70
Figure 60. PIV entry #1; phases phi = 0, 90, 180 and 270.
71
Figure 61. entry #2; phases phi = 0, 90, 120, 150, 180, 210, and 270.
72
Figure 62. Planform view of dye streaks, over one period of motion; dye injected at ¾ span location, near
nominal spanwise position of PIV light sheet. Re = 60K
73
Figure 63. AFRL water tunnel Dye injection for pure-plunge, Re = 20K (left column), 30K (middle
column) and 60K (right).
74
Figure 64. Lift coefficient time history, SD7003 pure-plunge, Re = 60K; plotted vs. motion phase (left)
and effective angle of attack (right).
75
Figure 65. PIV, first data series, phases phi = 0, 90, 180 and 270.
77
Figure 66. PIV, second data series, phases phi = 0, 45, 90, 135, 180, 225, 270 and 315.
78
Figure 67. PIV, third data series, phases phi = 0, 90, 120, 150, 180, 210 and 270.
79
Figure 68. PIV-derived planar turbulent kinetic energy contours, AFRL data sets, phase phi = 180
(bottom of plunge downstroke): “small” separation (left) and “large” separation (right).
80
viii
Figure 69. Planform view of dye streaks for pitch-plunge, over one period of motion; dye injected at ¾
span location, near nominal spanwise position of PIV light sheet. Re = 60K.
80
Figure 70. dye injection, Re = 10K (left column), 30K (middle column) and 60K (right column; phases
phi = 0, 90, 120, 180 and 270.
81
Figure 71. Lift coefficient time history, SD7003 pitch-plunge, Re = 60K; plotted vs. motion phase (left)
and effective angle of attack (right).
82
Figure 72. PIV, phases phi = 0, 90, 180 and 270 degrees.
84
Figure 73. Dye injection for pitching-plunging flat plate, Re = 20K (left column) and Re = 60K (right
column); phases phi = 0, 45, 90, 120, 150, 180, 210 and 270.
84
Figure 74. Dye injection, flat plate in pure-plunge, Re = 20K (left column) and 60K (right column.
Snapshots from phases of motion as noted.
86
Figure 75. Lift coefficient for pitch-plunge (left) and pure-plunge (right) flat plate, Re = 60K; various
computations, and FBG force balance data (blue curve).
86
Figure 76. PIV, AR=2 plate in pure plunge, phases phi = 0, 90, 120, 150, 180, 210 and 270.
88
Figure 77. PIV results for AR=2 plate pitch-plunge.
89
Figure 78. Commanded vs. attained angle of attack history for sinusoidal pitch frequency double that of
sinusoidal plunge.
90
Figure 79. PIV (left), averaged over 10 instantiations per phase, and dye injection (right), Re = 10,000,
mixed-frequency pitch-plunge; phases of motion as marked.
94
Figure 80. Time-trace of pitch angle and plunge position. Flow visualization frames correspond to
position in time denoted by the black line segments; the fifth line segment is one ramp-motion’s time after
motion cessation.
97
Figure 81. Flat-plate pitch for various reduced frequencies: K = 0.1 (top row), 0.2 (row 2), 0.35 (row 3),
0.70 (row 4), and 1.4 (row 5).
98
Figure 82. Comparison of highest-rate-motion and lowest-rate-motion flowfield evolution with respect to
convective time; t* after motion cessation as marked. K = 1.4 (top row) and 0.1 (bottom row).
98
Figure 83. K = 0.70, 0º-40º-0º pitch (top row), “equivalent” pure-plunge (row 2), combined pitch-plunge
(row 3); and combined pitch-plunge with trailing edge dye injection (bottom row). Re = 10K.
99
Figure 84. Flat-plate 0º-40º-0º pitch, K = 0.70, Re = 10K; parameter study of role of pitch pivot point.
x/c = 0.0 (top row), 0.25, 0.50, 0.75 and 1.0 (bottom row).
100
Figure 85. K =0.70, Re =10K; dye injection (left column), phase-averaged velocity (middle column),
phase-averaged vorticity (right column) and samples of computed vorticity (also right column).
101
Figure 86. K =0.20, Re =10K; dye injection (left column), phase-averaged velocity (middle column),
phase-averaged vorticity (right column) and samples of computed vorticity (also right column).
102
Figure 87. α = 0º-45º linear ramp-hold-return, K = 0.7, pivoting about x/c = 1.0. Without removal of
parasitic surge (left) and with removal of parasitic surge using the third linear motor (right).
103
Figure 88. Sinusoidal ramp, angle of attack (top, angle of attack rate (middle) and accelerations (bottom)
for pitch-hold-return maneuver.
105
Figure 89. Smoothed linear ramp, angle of attack (top, angle of attack rate (middle) and accelerations
(bottom) for pitch-hold-return maneuver.
106
Figure 90. Dye injection results at Re = 5K, smoothed ramp and sinusoid, with pitch pivot location as
marked.
107
ix
Figure 91. CL for a = 2 (sinusoidal, left) and a = 11 (smoothed ramp, right), from Garmann and Visbal
computation (Re = 5000), Eldredge et al. computation (Re = 5000), and Ol et al. experiment (Re =
40,000).
108
Figure 92. Flow visualization by dye injection of 5 linear pitch ramp-and-hold cases for wall to wall flat
plates and airfoils. First column: SD7003 airfoil, 0-45º, constant free-stream, Re = 50K. Second column:
SD7003, 0-85º, constant free-stream, Re = 15K. Third column: flat plate, 0-85º, constant free-stream, Re
= 15K. Fourth column: flat plate, 0-85º, decelerating, Re = 15K based on tunnel speed. Fifth column:
SD7003 airfoil, 0-85º, decelerating, Re = 15K based on tunnel speed. Each row is a sampling at the same
angle of attack for all cases: 0.6º, 5.5º, 11.2º, 16.8º, 22.5º, 28.1º, 33.7º, 39.2º, 45.0º, 50.7º, 56.3º, 61.9º,
67.6º, 73.2º, 78.9º, and 84.5º.
111
Figure 93. PIV single-shot vorticity contours, SD7003, 0-45º, constant free-stream, Re = 50K. Reading
across each row and then down the next column, shots are at α = 0.6 º, 5.5º, 11.2º, 16.8º, 22.5º, 28.1º,
33.7º, 39.2º, 44.3º, 45.0º, and thereafter at 45.0º; samples are spaced 1.32 convective times, or 0.76
seconds in physical time.
112
Figure 94. Lift and drag coefficients for the SD7003 airfoil pitching 0-45 degrees angle of attack, plotted
vs. physical time in seconds.
113
Figure 95. Phase lag between prescribed plunge and passive pitch, “light” plate.
114
Figure 96. Phase lag between prescribed plunge and passive pitch, “light” plate.
115
Figure 97. Trailing edge dye injection indicating (in the scalar sense) TEV development. Phases of
plunge motion, from top left corner: 0, 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, and 330.
115
Figure 98. Drawing of the mounting plate showing the optical fiber path and the location of the flexures
and FBG sensors on the top surface of the plate. Another two FBG sensors are placed on the bottom side
of the flexures.
122
Figure 99. Typical powers spectra of a FBG sensor output. (a) Spectra of the raw data for a typical run,
(b) Spectra after low pass filter.
125
List of Tables
Table 1. Measured and computed SD7003 LSB Properties, Re=60,000, α=4°
Table 2. PIV test conditions (left) and flow visualization test conditions (right).
Table A1. Location and Wavelength of FBG Sensors in Load Cell
Table A2. Load Cell Calibration Standard Error
x
31
33
123
124
Acknowledgements
While the present report has only one author, it would be ludicrously pompous and unfair to fail
to mention the contributions of a long list of students and visiting associates who conducted experiments
in the HFWT and/or materially contributed to d evelopment of test articles, who wrote software and
developed algorithms, and so forth. These include:
•
•
•
•
•
•
•
•
•
•
•
•
•
Mr. Robert Downs, for conducting hot-wire and freestream PIV measurements to characterize
HFWT flow quality, for conclusively reporting on h ot wire limitations in the present s etup,
and for running a detailed parameter study of airfoil wake momentum losses using PIV.
Lt. (at the time) Deepak Peter, for conducting a different series of hot-wire measurements.
Lt. (at the time) Sergey Kaplan, for running PIV experiments on the AR=2 tip-vortex st atic
aerodynamics.
Prof. A aron A ltman, f or c alibration a nd e xperiments w ith t he R olling H ills R esearch
Corporation f orce b alance, f or a l ong ser ies o f m utual r esearch co nsultations, an d f or
supporting a steady stream of graduate students from the University of Dayton to participate
in HFWT research.
Prof. L uis B ernal, for de veloping t he F iber B ragg G rating f orce ba lance, for de signing t he
various iterations of the balance, and for developing the balance initial calibration procedure.
Mr. Jonathan R ausch a nd Mr. D an S tanley, f or r unning a s eries o f P IV a nd d ye i njection
experiments on plunging flat plate (not reported here, but materially influencing concepts of
vorticity transport cited in related projects).
Dr. Craig Cox, for writing essentially all of the motion control routines for the HIPPO rig, for
developing th e e lectrical installation o f the 3 rd HIPPO l inear m otor, for i mproving the
calibration process of the FBG balance, and for general automation of data reduction in the
HFWT.
Mr. Doug Szczublewski, for running a long series of dye injection experiments in the HFWT,
developing several data reduction routines, and general assistance in lab operation.
Lt. (at the time) Daniel Fredberg, for running airfoil plunge PIV experiments.
Ms. Meredith Almoney and Ms. Jeanette Aukerman, for developing a hydrogen bubble flow
visualization capability in the HFWT (not reported here) and for initial debugging of the 2motor version of the HIPPO rig.
Dr. S ergey F onov a nd D r. J im C rafton, for introducing t he S urface S hear S tress S ensitive
film t echnique i n the H FWT, a nd f or p roviding a steady s tream of a dvice o n opt ics a nd
electronics equipment.
Dr. Ernest Hanff, for suggesting the idea of a two vertical motor, two plunge-rod concept for
pitch/plunge actuation, and for extensive exchange of ideas in the aerodynamics of separated
flows.
Profs. Rolf Radespiel, Cam Tropea, Holger Babinsky, Jeff Eldredge, David Williams, Haibo
Dong, Don Rockwell, Ashok Gopalarathnam, Mark Reeder, Haibo Dong, Yongsheng Lian,
and Wei Shyy, for the many insightful discussions, collaborations, and general exchange of
ideas.
The author apologizes to all those who have been involved with HFWT experiments and
collaborations, but w ho for w hatever reason ha ve no t be en included h ere, o r whose c ontributions a re
inadequately not ed. O ne can on ly r emember s uch t hings i n w istful reminiscing – not i n t he f ury of
clerical hustle required to finish a long technical report!
xi
1.
Summary
Work under t he pr esent p roject, and therefore t his report, c an be s omewhat a rtificially bu t
nevertheless usefully segmented into the following:
1.
Introducing the Micro Air Vehicle (MAV) problem, and the relevance of low Reynolds number
aerodynamics – especially unsteady low Reynolds number aerodynamics – to performance, stability and
control, and the overall problem of flight of MAVs.
2.
Assessment of water tunnels as tools in aerodynamic research, for MAVs and for incompressible
configuration aerodynamics in general. We document the design, relocation from its original installation,
reconstruction a nd s hakedown of A FRL/RB’s “ Horizontal F ree-surface W ater T unnel” (HFWT), t o
include instrumentation for flowfield measurements and force measurements.
3.
Experiments i n st eady aerodynamics at l ow R eynolds num ber: a irfoils, and wings o f va rious
planforms. Here t he focus i s on l aminar to t urbulent transition and documentation of how R eynolds
number, f lowfield co nditions an d m odel g eometry i nterplay t o a ffect laminar s eparation and possible
turbulent reattachment, and how planform effects impact lift generation.
4.
Passing t o t he u nsteady aer odynamics p roblem, w e r ecite the requirements de finition, design,
installation and shakedown of t he H FWT’s “ High-Intensity Pitch-Plunge O scillator” Rig, or HIPPO,
which in its first configuration performs a broad range of two-degree-of-freedom longitudinal oscillations,
and a subsequent upgrade added a third degree of freedom.
5.
Experiments in Unsteady Aerodynamics using the HIPPO rig, first in two degrees of freedom of
motion, and then in three – to include airfoils, flat-plates and wings. We cover a broad range of periodic
and transient problems, anchored in traditional problems of airfoil dynamic stall, and expanding to MAV
applications of perching and flapping. New knowledge, or what passes for knew knowledge in a mature
field, i ncludes e lucidation of the s urprisingly br oad limits of linear superposition i n markedly nonlinear
problems, a nd not es on t he r elative i mportance o f l aminar t o t urbulent transition i n a br oad r ange of
unsteady problems.
The experiments d etailed he re p arallel num erous r elated c omputational a nd e xperimental
investigations. For example, “canonical problems” in pitch and plunge of airfoils were identified by the
PI and studied by several research groups to compare methodology and hierarchy of methods. However,
generally the results reported herein are limited to those obtained in the Principal Investigator’s lab.
1
2.
Introduction: Philosophy, Scope, and Approach
This report covers in-house experimental work on aerodynamics with applications primarily, but
not exclusively, directed towards the so-called Micro Air Vehicles, or MAVs. The period 2002 through
2009 is covered.
2.1.
General Musings on MAVs
Writing in 2010, it seems fair to remark that principal problems in aerodynamics remaining at the
research-level are at the extremes of very fast and very slow. Very fast problems – hypersonics and the
like – involve pr oblems of c ompressibility a nd heat t ransfer. I n c ontrast, v ery s low pr oblems – low
speeds and small scales – are incompressible and non-thermodynamic, but rife with complications from
the effects of v iscosity an d co nsequent flow s eparation. I n t he op inion o f the P I, t hese are t he m ost
celebrated a nd m ost intriguing pr oblems a t the juncture be tween fluid m echanics and flight v ehicle
engineering. And they form the subject of this report.
But w hat ar e t he ap plications? H ere w e co nsider MA Vs. MAVs are not onl y a t opical
application in modern t imes, but are also an intriguing pr oblem of fundamental interest to the fluid
mechanicist, the aeronautical designer and the biologist, as the relation between flight of natural creatures
and MAVs is not merely a metaphorical motivation, but is quite literally true. The definition of MAVs is
somewhat a morphous, de pending on t he b iases o f t he de finer. L oosely f ollowing McMichael a nd
Francis 1, Pines and Bohorquez 2, Shyy et al. 3, and Mueller 4, we can “define” MAVs for present purposes
as flyers in the Reynolds number range of 104 to 10 5 based on the relevant length scale (typically wing
chord) an d velocity scal e (typically f light sp eed), w hich t ranslates into vehicle maximal d imensions on
the order of 10-30 cm, or possibly somewhat less. Truly insect-scale vehicles are not excluded, but the
concomitant Reynolds number range is not studied in the following work, which has a lower bound of Re
~ 5000, stemming from the operating limits of the available experimental facility.
Most MA V-relevant f lows a re f undamentally uns teady. E ven i n approximately s teady-level
flight, the vehicle is subject to ambient gusts and other disturbances, such as passage through the wakes of
buildings. L ow flight s peed a nd s mall m oments of i nertia i mply t hat e ven nom inally qui escent
atmospheric conditions introduce palpable disturbances. Maneuvering flight, such as in making turns and
altitude changes, c ourse c hanges t o avoid o bstacles, l anding ap proaches a nd t he l ike, a re a n ob vious
source unsteadiness, where angle of attack variations are large in amplitude and relatively fast in terms of
convective time. This is an essential difference between MAV flight and the flight of larger aircraft. Yet
another di fference, c oupling i nto t he f irst, i s l ow-Reynolds n umber ef fects, w here b oundary l ayers ar e
generally l aminar an d t hus st rongly su sceptible t o f low sep aration. The a mount of f low s eparation
depends on R eynolds number ( and i n t urn on flight s peed) a nd other factors. F low s eparation d irectly
affects flight mechanics, and vice versa. S o we find a tightly coupled problem between fluid dynamics
and flight mechanics, fed by both low Reynolds number and small vehicle mass/inertia/speed. The result
is m assive u nsteadiness – and t his i s be fore w e e ven c onsider the i mportant pr oblem of s tructural
flexibility and fluid-structure interaction for MAVs 5. And for flapping-wing MAV configurations, which
attempt to follow examples of bird flight 6,7 or insect flight 8,9, unsteady aerodynamics and time-varying
flow separation are obviously dispostive factors.
But how unsteady is the aerodynamic force time history for even obviously unsteady flow fields?
The q uestion is n ot t rite o r r hetorical. The s implest f lows – the one s m ost am enable t o c losed-form
analysis – are potential flows. Lift curve slope is 2π, stall does not occur, and streamlines can negotiate
curved p aths w ith arbitrarily l arge ad verse pressure gradients w ithout separating, ex cept for p ossibly at
discrete p oints of i nfinite curvature. T he latter describes t he trailing-edge K utta condition, which fixes
separation a nd t ogether w ith the no -through-flow bounda ry c ondition a lso f ixes t he c irculation. This
“bound” circulation, t ogether with the s o-called noncirculatory l ift or a pparent-mass effects, determines
the lift and pitch time history for a broad class of flows where separation is limited to the trailing edge
region. I n t he w ork pr esently de scribed, w e s tudy v arious g eometric a nd k inematic a bstractions of
2
unsteady aerodynamics, with at least the preliminary assessment that quasi-steady models may be suited
to MAV conceptual design for even massively separated and unsteady flows.
Recent r eviews o n t he s ubject o f MA V flight a re g iven b y Shyy e t a l. 10 and M ueller4, a mong
many ot hers. H ere w e will not dwell on the conceptualization o f M AVs, be yond m aking s ome
philosophical obs ervations about the now -fashionable s ubject of flapping f light, a nd how f lapping –
besides o ther MA V aerodynamics p roblems – maps t o the m ore a bstract problems in unsteady
aerodynamics, r eminiscent o f t he c lassical p roblems o f d ynamic st all an d i mpulsive st art. T hese a re
among the threads justifying the present work.
2.1.1. Opinions on Benefits and Drawbacks of Flapping Wings
It is perhaps appropriate here to journalize some musings on the attractive and bewildering field
of f lapping-wing MA Vs, a nd t he a erodynamics ch allenges t hat t hese v ehicles pose. Why s hould any
manmade v ehicles u se f lapping w ings? We h ave spent over a cen tury o n spectacularly su ccessful
development of fixed-wing aircraft, where propulsion and lift are explicitly separated, and the better part
of a century developing rotary-wing aircraft, where lift/propulsion/control are combined. Flapping-flight
failed in the early 20th century in essence because the mass/power/area/speed relationships for flapping
fliers scale poorly to craft large enough to carry humans or human-sized cargo. And we know this from
observing birds. Larger birds fly more like fixed-wing aircraft, while smaller birds flap more vigorously
in frequency and amplitude relative to their wingspan. Does this mean that at extremely small scales, say
that of insects, flappers are more efficient than fixed-wing or rotary-wing craft? Is this statement further
strengthened if to the simple geometric scaling we add low-Reynolds number effects?
So far one c an not s ay. There are many w ays t o f lap i n nature, with seemingly very d isparate
solutions to broadly similar flight problems, such as the hovering of insects vs. hummingbirds11. If there
is no one p referred solution, t hen how do e ngineers pursue bi o-inspiration f or de signing a n “ optimal”
flapper? But f rom th e s cientific v iewpoint, as o pposed t o t hat o f pr actical e ngineering, what m akes
flapping so interesting is that it combines the nonlinearities of aerodynamics, structures and controls. I t
speaks t o s ome of t he m ost c elebrated pr oblems i n c ontinuum dy namics, i n a w ay t hat onl y now i s
becoming amenable to our computational methods and our experimental tools. And it rests on intriguing
parallels between pe rformance ob jectives i n na ture (perching, hov ering, pr ecision m aneuver, pr edator
evasion, p rey c apture, a nd on a nd on) a nd de sired p erformance f or u rban-type m ilitary f light v ehicles.
We do not, however, have any definitive evidence that a flapping vehicle is somehow superior to a rotary
vehicle.
But w e c an o ffer s ome s peculations about t he po ssible s uperiority of f lapping i n p roblems i n
maneuverability. Two examples are flight near rigid walls (obstacle avoidance) and gust tolerance. Both
are crucial for MAV applications.
All s chemes of g enerating l ift and p ropulsion by f luid m echanics involve m omentum t ransfer.
This is t rue fo r rotorcraft, f lapping c raft, o r rockets, o r f ixed-wing a ircraft. F lapping f light i s n ot
incomparably different from rotary flight, but there are potential advantages. In hover, there is a net high
momentum jet underneath the aircraft, and to some extent this will result in wall suck-in. W e speculate
that for flapping craft this may be less deleterious than for rotorcraft, for at least two reasons: weaker tip
vortices f or f lappers (and possible f urther i nboard o f t he w ing t ip), a nd f lappers' g reater c apacity t o
articulate and therefore to roll away from the wall.
Gust tolerance is governed by wing loading, moments of inertia and other quantities ineluctably
related to physical scale; but also by lift curve slope (lower is better!) and in particular by the distinction
between separated and attached flow. Attached incompressible flow responds quickly. B ound vorticity
changes instantaneously, and shed vorticity decays according to well-known theoretical descriptions - in
most cases also quickly. But separated flows, we speculate, respond more slowly to abrupt inputs.
Obviously separated flows are less efficient than attached flows, but attraction of operating in separation
3
is potentially smoother gust response. T his is not a proven fact, but is sufficiently compelling to justify
the requisite research and flight test of flappers.
Flappers o perating in m ostly a ttached f low are q uite s imilar to r otorcraft, e specially i f t he
dynamics of f lipping t he w ing a t t he s troke e ndpoints a re f ast, a nd t he w ings a re r elatively r igid. T he
main d ifferences are in ac tuation, structural dynamics an d aeroelaticity - not in a erodynamics or t hrust
production. In both cases t here i s a n ef fective airspeed at each b lade section, which f orms a d ynamic
pressure; there i s t he s ectional chord, the k inematic angle o f i ncidence, an d t hus t he s ectional l ift a nd
drag, resolving in to thrust and rotational resistance (power absorbed by the wings/blades).
The a erodynamic di fference be tween f lapping a nd r otorcraft comes f rom m anagement of
separated f low. A t s cales ab ove MA Vs, d ynamic-stall literature a ttests th at r otorcraft o perating in
regimes of large flow separation suffer an almost completely unmitigated penalty. L eading edge vortex
production is parasitic, not beneficial. C lassical aerodynamic intuition suggests that a rotor operating at
large effective angle of attack is a horrible idea, because massive disorganized separation will lead to both
high drag and low lift. But some recent experiments on revolving wings at MAV Reynolds numbers and
large i ncidence suggest r etention of the LEV and therefore a lift benefit, though possibly at t he c ost of
poor L/D. Other experiments give contradictory results for revolving wings41. In any case, no rotorcraft,
to our knowledge, has been developed to explicitly use managed separated flow at high blade effective
angle of attack.
For f lappers, h owever, L EV retention an d l arge l ift coefficients in s eparated f low a re w ell
documented8. As with rotorcraft, flappers operating in separated flow would suffer an efficiency penalty.
But unlike rotorcraft, we speculate, the management of flow separation, by attached LEVs or otherwise,
offers both high lift coefficients and a "slow" response to mitigate gusts. Rigorous substantiation of these
conjectures is a huge fundamental research task, but the attraction of a viable flapping-wing flight article
is that it motivates such research by anchoring in practical demonstration.
In summary, insect-type flapping at large effective angles of attack is perhaps not an efficient way
to fly, but it may be a maneuverable and gust-tolerant way to fly. The question now is, to what extent is
the time history of aerodynamic forces quasi-steady (with a possible phase lag or lead) with the effective
angle of attack, and/or other kinematic parameters of the motion? That is, we seek a closed-form solution
such as C L = f (α , α , α,...) , w here the r educed f requency, a mplitude a nd s o f orth are p arameters
subsumed i n t he pr oper choice of i ndependent variables. D oes such a solution exist, f or l ow Reynolds
numbers, for high rates, for aggressive motions, in closed-form? C learly such a solution is possible for
small-amplitude motions87 in 2D. In attempting to bridge from this to the full problem of flapping, we
consider a hierarchy of abstractions.
2.1.2. Unsteady Aerodynamics in Two Dimensions
2D problems are the natural starting point for more complex investigations. H ere, by “2D” we
mean not only airfoil-type problems, but problems of 3D wing planforms where the motion is limited to
the rectilinear case – that is, pitch, plunge and fore-aft motion (surge).
Despite the geometric and kinematic complexity of flapping wings in nature or even in manmade
vehicles, unsteady aerodynamics in two dimensions remains a c ritical area for Micro Air Vehicle flight,
with applications including perching, gust response, maneuvering flight and flapping wings. The central
question concerns the relation between time history of relative motion kinematics and aerodynamic loads
production. The maneuver of pe rching i s related t o the c lassical-pitch up p roblem, w here t he a ngle of
attack varies fairly quickly over a large amplitude 12. For all of its complexity, the f ully-articulated
flapping-wing f light of ba ts, i nvolving v arious g eometric rotations, t ranslations a nd p lanform c hanges,
shows ev idence t hat i nviscid an d “w ake-only” methods can st ill ap proximate f airly-well th e l ift
coefficient tim e-history 13. The pos sibility of us efulness o f qua si-steady se ctional ae rodynamic m odels
and strip-theory-type of 3D generalizations for maneuvering i nsect flight 14 and potential applications to
bio-inspired f light vehicles 15 implies a n eed to v alidate an d t o g eneralize the co nstituent a ssumptions
4
using a progress of well-defined abstractions, from simple classical problems to more geometrically-rich
cases c loser to MAV ap plications. F or g eometrically si mple p roblems su ch as sinusoidally o scillating
airfoils, w here there i s al ways an acceleration, i ndications a re t hat at h igh r educed f requency,
noncirculatory e ffects do minate 16,105, th us s implifying th e f orce m odeling. This contrasts w ith the
complexity of the dynamic stall problem at more moderate rates 17. In sum, it would be advantageous in
applied pr oblems i f full resolution o f v ortex shedding a nd t he resulting f lowfield e volution w ere n ot
strictly necessary to obtain reasonable accuracy of aerodynamic loads time history.
The problem can be divided into periodic and nonperiodic motions. Periodic motions – typically
sinusoidal – are more thoroughly studied 18, but are more applicable to cruise-type of MAV applications,
where one is p rimarily interested in f lapping-wing p ropulsion. N onperiodic m otions a re a rguably t he
richer problem, as t here is no forcing function to give a r epeatable bulk flowfield response, and because
such motions are closer analogues of maneuver and gust interaction. P itch-ramps of airfoils are perhaps
the m ost of t-studied nonpe riodic m otion. T his w as, evidently, a s ubject of i ntense i nterest in t he m id
1980’s to mid 1990’s, for applications to maneuvering fixed-wing manned aircraft. Typically the airfoil
was the NACA0012 or 0015, but the Re range was 104 to 105 – that is, not far removed from MAVs A
brief survey includes the experiments of Graham et al. 19,20,21, Chandrasekhara et al. 22,23, Walker et al.24,25,
Daley and Jumper 26, Ramaprian et al. 27,28, Acharya et al. 29,30, Koochesfahani and Vanco 31, and Schreck et
al 32. Typical measurement techniques were flow visualization, such as by dye injection in water; surface
pressure measurements and f orce-balance measurements. F or i nstance, G raham an d Y eow19 visualized
the linear pitch-ramp LEV s tructure in w ater, a t higher a ngle of a ttack excursions bu t lower rates than
those p resently co nsidered. S hih e t a l. 33 and C risler et a l 34. ap plied particle i mage v elocimetry t o the
airfoil pitch-ramp problem. C omputational examples include Ghosh Choudhuri and Knight 35, Okongo’o
and Knight 36, and Visbal et al. 37,38,39. Visbal and Shang37, for example, computed in 2D the linear pitchup of a N ACA0015 a irfoil a t R e = 10 4, f inding t hat l ags be tween e volution o f le ading-edge f low
separation and the airfoil motion kinematics should increase with increasing reduced frequency.
2.1.3. Rectilinear vs. Nonrectilinear Motions
The experimental facilities pursued i n the subject research accommodate primarily “rectilinear”
motions – oscillations in the longitudinal plane, consisting of pitch or rotation, plunge or heave, and surge
or fore-aft motions. Non-rectilinear motions, such a rotation in the sense of a m apleseed or most insect
wings 40, are excluded – with one except at the very end of this report. H ow important is the distinction
between rectilinear and nonrectilinear motions? If the latter can be analyzed in a strip-theory approach as
a c ollection of 2D s ections l inked by s panwise l ocation a nd l ocal dynamic pressure, t hen evidently the
distinction s hould b e s mall. H ere there i s c onsiderable c ontroversy. F or e xample, D ickinson a nd h is
various colleagues (see for example Lentink and Dickinson40 for a recent summary), f ind evidence t hat
rotation stabilizes the leading edge vortex forming at high angle of attack as the wings moves about each
half-stroke. This L EV i s i mportant in regularizing t he s eparated f low, maintaining hi gh l ift coefficient
and therefore producing sufficient lift/thrust for aggressive maneuver – which, ultimately, is asserted to be
the whole point of flapping. On the other hand, Babinsky and Jones 41 found very little difference in either
lift c oefficient h istory o r f lowfield e volution for im pulsive-start p roblems in r ectilinear m otion
(translation at a fixed angle of incidence) or non-rectilinear motion (wing impulsively revolving from rest,
at a f ixed an gle o f i ncidence). F urther, B abinsky an d J ones f ound q ualitatively si milar l ift h istories to
those of Dickinson et al.9. So we have to ask…
1. Do r ectilinear a nd no nrectilinear m otions, a t the s ame no minal R e, r educed f requency,
acceleration p rofile a nd so f orth, p roduce f undamentally di fferent f lowfields, in p articular
regarding LEV formation, retention and shedding?
2. Do nonrectilinear motions produce similar flowfields along the span, except possible near the root
and tip?
3. Do nonrectilinear and rectilinear motions produce similar lift coefficient time histories?
5
4. Can lift coefficient histories be similar, despite large differences in the flowfield?
5. Is the role of noncirculatory force the same in rectilinear and nonrectilinear motions?
6. Do large accelerations at motion onset effectively make “all flows look alike”?
So t here a re m any q uestions. The nonrectilinear p roblem i s esp ecially d ifficult b ecause i t is
kinematically co mplex, an d so u nlike t he c lassical dynamic st all problems that naturally em anate from
steady ai rfoil a erodynamics. H ere w e therefore co ncentrate o n t he l atter. O f p articular i nterest i s t he
establishment of c ommon problems, a bstracted a nd phrased to be of general interest, to benchmark t he
various methods and to suggest points of departure for parameter studies. If we are going to build motion
rigs, w hat kinematic pr operties should they possess? T he question i s i nformed by pur suit of canonical
problems.
2.2.
Canonical Problems
A l arge por tion o f t he s ubject w ork i n t he p ast 7 years, of ten l ed by t he P I, ha s be en the
suggestion, delineation and promulgation of “canonical problems” in steady and unsteady aerodynamics
at l ow sp eed. B y “can onical p roblems” o ne m eans abstracted test c ases o f g eneral ap peal, with cl ear
parameter de finitions, which ar e t o b e s tudied b y s everal c omputational and e xperimental efforts, by
different research g roups working towards a common reporting g oal. Objectives include: ( 1) crossvalidation of the various methods, (2) baselining the state of the art, (3) engendering interest in the subject
amongst r esearchers w ith affinity t owards t his a rea but o therwise lack o f c onnection t o t he s pecific
subject, (4) es tablishment o f a k nown t est c ase for archival r eference, and ( 5) p roviding a p oint of
departure for individual researchers to run parameter studies. The idea is that once a common baseline is
achieved, t he subsequent parameter studies have b etter contextual motivation and ar e o n f irmer ground
because the “correct” answer was found for the canonical case. Examples of such canonical problems in
the past 7 years have been:
- Airfoil laminar separation bubbles (LSBs) under NATO RTO Task Group AVT-101
- Various unsteady aerodynamics problems under NATO RTO Task Group AVT-149
- Pitch ramp-hold-return maneuvers proposed in the AIAA Fluid Dynamics Technical Committee’s “Low
Reynolds Number Aerodynamics Discussion Group”
- High-frequency l ow-amplitude a irfoil pitch a nd pl unge s inusoidal periodic motions, studied by t he P I
and a range of academic collaborators.
These a re e ach documented t hroughout the report. The evolving t heme i s pu rsuit of
experimental-computational agreement as basis of commencing future parameter studies. Therefore, the
present focus i s l ess on exposition of p hysical t rends, t han on e stablishment of t he a ssertion t hat o ur
various tools are adequate for quantitative study of such trends.
6
3.
The Water Tunnel as a Research Tool in Low-Speed
Aerodynamics
Aeronautical engineering, or at least external aerodynamics, is concerned with the flow of gasses,
not liquids. S ome motivation for the use of experimentation in water is therefore incumbent. H ere we
describe t he philosophical underpinnings of w ater t unnel experiments f or low-speed aerodynamics, an d
then describe Air Force Research Lab, Air Vehicles Directorate (AFRL/RB) water tunnel.
3.1.
The Case for Water Tunnels for Low-Speed Aerodynamic Research
3.1.1. Introductory Remarks
In al l o f ex perimental s cience t here is a t ension b etween sm all/cheap/simple/readily-accessible
experimental apparatus on the one hand, and elaborate/detailed/complex/expensive apparatus on the other
hand. It is specious to claim that the one is better than the other, as each enjoys its proper place in the
spectrum f rom exploratory investigation of f undamentals to de tailed e ngineering de sign. B ut it is
possible t o devise a metric of return on e ffort, or v alue for money. B y s uch m etric one can f ind v ery
favorable result from water tunnels.
Water t unnels d efinitely b elong t o t he f irst ca tegory i n ex perimental ae rodynamics, as al most
universally they are of scale and scheme commensurate with what one finds in university labs, rather than
showpieces of government or industry installations. They can generally be operated and maintained by 12 e ngineers w ith no s pecial p roficiency in m achine o peration, e lectronics and t he l ike, beyond g eneral
familiarity with fluid mechanics measurements. Environmental impact and electrical power requirements
are small ( power use i s rarely > 5 0 KW), safety co ncerns are minimal ( and generally o verwhelmed b y
concerns for constituent equipment, such as lasers, rather than the facility itself), and facility availability
is essentially continuous. There are complications in dealing with water – corrosion, leaks, requirements
for w ater filtering a nd s o f orth; bu t t hese r emain i n-scope f or sm all f acilities i n g eneral. In s ome
situations w ater t unnels compare f avorably w ith similarly-sized w ind t unnels. I n ot hers, c hiefly w here
Reynolds number scaling is important, water tunnels compare unfavorably.
Water tunnels, like any facility, are not a panacea for low-cost solutions to complex engineering
problems. Their key strengths in recent years have been twofold:
- The explosive growth i n l aser-based d istributed flowfield-diagnostic methods provides a r eady
and powerful means of c omparison with the equally fast-growing power of computational fluid
dynamics. Most such methods are easier to apply in water than in air.
- The high density a nd low dy namic viscosity o f w ater c an p otentially g reatly s implify
measurements i n u nsteady aer odynamics an d in dynamic t esting of a eronautical c onfigurations
and abstracted shapes such as airfoils.
But w ater tunnel testing i s s ubject t o s evere l imitations, principally due to u navoidably l ow
Reynolds num bers and s trictly i ncompressible f low. The t rue p romise of w ater tunnels c an best b e
fulfilled w hen w ater t unnel us ers work t ogether w ith t he C FD c ommunity a nd t he l arge-wind-tunnel
community, for example in the areas of CFD validation and development of test matrices for large Test
and Evaluation wind tunnels.
3.1.2. Reynolds Number Effects
The f irst i mpediment in usefulness o f w ater tunnels f or a erodynamic a pplications is from
Reynolds num ber s caling. C hord-based R eynolds n umbers f or airfoils, w ings an d ai rcraft m odels are
typically limited in water tunnels to an upper-bound of 100,000. For whole-airplane configurations, Re
based on m ean a erodynamic c hord c an be limited t o 10,000 for t he s maller w ater t unnels. For a irfoil
performance, and therefore airplane performance measurements even at the conceptual-design level, this
7
is a devastating and likely unacceptable flaw, since below Re = 100,000 most airfoils evince large laminar
separations wholly unrepresentative of flight conditions or even large wind tunnel conditions, and at Re ~
10,000 all airfoils operate in separated flow at all angles of attack. For Re ~ 50,000 – 250,000, Reynolds
numbers will be s ubcritical, a nd l aminar separation bubbles will either be very large or will be “open”,
resulting i n t he a irfoil be having s omething l ike a bl uff body . This t o s ome e xtent de pends on the
smoothness o f the a irfoil su rface; “r ough” a irfoils ar e l ess R e-sensitive; r efer t o t he cl assic a irfoil
performance cartoon by Horten4 (Figure 1), which compares airfoil maximum lift to drag ratio across the
Re r ange, down t o t he r ange f or i nsects. Drastic f all of m aximum L /D is concurrent w ith l arge, ope n
separations.
Figure 1. Notional estimate of airfoil performance vs. Re. From Horten, as reported by Mueller.4
A more quantitative rendition of prototypical decline in airfoil performance is given in Figure 2,
which shows w hat h appens t o a irfoil d rag pol ars i n going f rom R e = 500 K down t o 60K. While C Do
doubles in g oing f rom R e = 200 K t o 500 K, and certainly t his i s a pr oblem f or pe rformance-type of
aerodynamic testing, the far greater problem is the explosive growth in drag in going below Re = 200K.
Thus w e ha ve a qua litative, a nd not just a qua ntitative di sparity be tween w ater t unnel test
condition a nd f light (or l arge w ind tunnel). There a re o ther pr oblems be sides de cline o f a irfoil
performance at low-Re. C ontrol surface performance will be anomalous, so for example for a c lassical
airplane co nfiguration t he Cm_delta_e w ill be w rong. T he st all d ynamics w ill also be q uite d ifferent.
Wind tunnels of similar size (say, test section diameter of order 0.5m) have an advantage of ~5X increase
in airfoil se ctional Re, w hich i s enough to e xceed t he critical R e an d t herefore t o at least qualitatively
match the flight-like scenario, at least for angles of attack below stall. Referring t o Figure 2, the small
wind t unnel w ill s till g ive a pa lpably ov erestimated C Do, but s hould a t l east q ualitatively c apture t he
“correct” gross flowfield – whereas the water tunnel may not. Of course, for laminar-flow airfoils all of
these conclusions must be attenuated, and the better approach for performance testing would be to avoid
small tunnels entirely, be they wind or water.
The s econd d isadvantage of w ater tunnels i s the c onductivity a nd c orrosive p roperty of w ater.
This makes strain gauge force balance design quite troublesome, as gauges need to be waterproofed. The
waterproofing courts the possibility of balance fouling, and in any case is never robust. Optical methods,
such as fiber-Bragg l oad cells, are a p romising al ternative to conventional strain gauge b alances, albeit
immature at this stage. C orrosion, meanwhile, implies that models must be made from stainless steel or
water-resistant plastics. The latter shows good potential from the viewpoint of rapid prototyping and 3D
printing – of which more below.
Thirdly, b ecause a t al l practical test sp eeds w ater i s i ncompressible, those ae ronautical
applications w here co mpressibility i s important, su ch as sh ock-boundary l ayer i nteractions, w ill f ail i n
water tunnel testing. But this point is generally obvious and is unlikely to cause error in practice.
8
1.2
1.1
1
0.9
0.8
CL
0.7
0.6
0.5
60K
100K
200K
300K
500K
0.4
0.3
0.2
0.1
0
-0.1
0
0.02
0.04
0.06
0.08
CD
Figure 2. Eppler E387 airfoil drag polar, Re = 60K to 500K, collected from wind tunnel data at the
University of Illinois, Urbana-Champaign.71
It would therefore be foolish to employ a water tunnel for airplane performance testing, for data
such as lift curve slope, stall angle, elevator control power, trim angle of attack range, CDo, and so forth,
even at the conceptual design level. Instead, given the modern state of things, one should do pot entialflow computations with viscous corrections (such as XFOIL), and if necessary run RANS computations
for C Do a nd s tall b ehavior. One w ould appeal t o e xperiment in water tunnels either u pon f inding
anomalies o r am biguities in t he c omputations, o r i n doing f undamental r esearch pr ior t o i nvestigating
applications to airplanes. And water tunnels could be used as “pilot” facilities to guide test planning in
larger wind tunnels, later in the design cycle.
Broadly, water tunnels are a powerful tool for basic discoveries in fluid mechanics; problems of
bluff bodies, jets/wakes/shear layers, cavities, oscillating bodies and plates, boundary layers and so forth.
Where R eynolds num ber is m atched be tween w ind t unnel a nd w ater tunnel, w ater t unnels pe rform
admirably; an example is laminar separation bubble and boundary layer transition experiments on a Selig
SD7003 airfoil, where water tunnel, wind tunnel and tow tank produced similar results 42. Water tunnels
do have particular strengths in some practical aeronautical engineering applications even at the detaileddesign level. These are principally those cases where the full-scale Reynolds number is itself low or is
otherwise unimportant. For the former, two examples are some cases in turbine blades, and the emerging
area o f Mi cro A ir Vehicles. F or the l atter, s harp-edged sw ept w ings a re p erhaps the m ost ce lebrated
example, though not without controversy. Dynamic stall is another example.
A simple but convincing steady-aerodynamics example is water tunnel testing of an aspect ratio =
2 t hin rectangular flat p late 43, w hich i s de scribed in further de tail in i ts ow n section o f t his R eport.
Between the low aspect ratio and the “sharp” leading edge, Re-effects are attenuated to the point where
the measured l ift co efficient co mports very w ell w ith cl assical inviscid theory. Further, l ift c oefficient
from direct m easurement via a f orce balance compares well with lift derived f rom Kutta-Joukowski
treatment of the tip-vortex circulation in the Trefftz plane, obtained from particle image velocimetry. The
three-way comparison with theory holds well, up to stall. This implies that the term “Reynolds number
insensitive” is neither a t rite platitude nor a r are exception in flows of interest in applied aerodynamics.
But certainly one must use caution!
9
It should also be noted that in any small-scale facility, water or air, the small size of models will
result i n i nferior m anufacturing t olerances a nd i nability t o c apture configuration f eatures i n d etail. F or
detail-sensitive f lowfields, su ch as separation f rom some ai rcraft an d m issile forebodies, the l oss of
geometric fidelity i ncurred w ith s mall m odels m ay have pr ofound i mpact on t he r esulting f lowfield,
possibly l eading to e rroneous c onclusions. It i s t herefore c rucial t o a pproach water t unnel m ethods i n
consultation be tween t unnel pr actitioners a nd the a irplane d esign c ommunity, and not t o s chedule t he
water test campaign as an ancillary process to be fitted-in ad hoc.
3.1.3. Laser-Based Distributed Flowfield-Diagnostic Methods
For a ll of water t unnels’ disadvantages vs. w ind tunnels f or aerodynamic t esting, w ater t unnels
merit vociferous v indication whenever the research objective is o btaining flowfield d ata, rather than
integrated f orce/moment on t he m odel. P article Image velocimetry, or P IV, i s t oday’s pr inciple
experimental technique f or o btaining tim e-resolved, di stributed f lowfield velocity da ta 44. PIV i s
considerably e asier in w ater (and i n liquids i n g eneral) than i n air. W ater’s large d ensity m akes
distribution a nd s uspension of P IV t racer pa rticles much e asier than i n a ir, w hereby s eeding density is
improved, a nd c oncomitantly P IV da ta qua lity. P articles i n w ater a re m uch m ore l ikely t o f ollow t he
local flow trajectory, especially in high-gradient locales such as vortex cores, than would be the case in
wind t unnels. Thus, one o ccasionally f inds P IV w ind t unnel da ta w ith v oids of no -data i nside vo rtex
cores, whereas such is demonstrably not the case for water tunnels. Thus one has to carefully weigh the
disadvantages of Re-scaling in water tunnels vs. the advantages in PIV.
3.1.4. Rapid Prototyping of Water Tunnel Models
The cost and time sav ings of water tunnels can o nly be realized if every test component is
inexpensive, i ncluding t he model. W ood or a luminum models a re c ommon i n s mall w ind t unnels, but
create problems in water due to absorption of water, oxidation, and deterioration of surface finish, which
result in flaws in outer mold lines and therefore unreliable aerodynamic results. Sometimes these are no
great p roblem f or s hort te sts ( < 1 d ay o f total im mersion time), but t he c ulture o f small w ater t unnel
testing generally implies that a model is installed and the researcher revisits the experiment sporadically,
at his/her leisure, rather than undertaking a time-constrained concerted test campaign of short duration, as
is generally necessary in large facilities. Thus, durable models are imperative. The alternative – stainless
steel – is expensive to machine. A better al ternative i s r apid pr ototyping of plastic models. A s of this
writing (2008), for $200K USD one can obtain a “3D printer” capable of 0.0006” build-layer (0.15mm),
in a build volume of 12” cubed. Assuming a good 3D input file, the cost per model is <<$1000 USD, and
involving perhaps one man-day of setup and post-finishing. And a “good” 3D input file is identical to the
input file for a viscous-CFD 3D mesh. Thus, one obtains the former for free, upon building the latter. Of
course, the same sort of model is suitable for a small wind tunnel as well as a small water tunnel, provided
that the dynamic pressures are not too high.
3.1.5. Dynamic Testing
“Dynamic t esting” i s a br oad a nd a morphous term, c onnoting m otion of t he test a rticle w ith
respect to the lab-frame of reference. A detailed list of dynamic-testing subtopics may be:
1. Standard m easurement o f dynamic st ability d erivatives for r elatively conventional ai rplanes in
assumed linear conditions. These a re typically the roll, p itch and yaw damping d erivatives,
measured by forced sinusoidal oscillation about a trim point. The application would be building
the flight dynamic model and control laws.
2. Spin-tests an d o ther f orced o r f ree oscillations, w here the o bjective is to assess d eparturecharacteristics of t he a irplane, pr esumably i n c onditions pe ripheral t o t he nor mal pe rformance
envelope, but important for safety certification.
3. High-alpha/high-rate t ests, w here o ne i s i nterested i n h elicopter b lade d ynamic st all, o r
maneuvers for aerobatic/combat aircraft. Large flow separations and concomitant nonlinearities
10
4.
5.
6.
7.
8.
9.
are expected. Here one is interested in both the 6DOF aerodynamic loads and flowfield
measurements to elucidate the causes behind those loads. This area also includes (a) leading edge
vortices of sh arp-edged hi ghly-swept c onfigurations, a nd ( b) the v ortical structures emanating
from missiles, forebodies and after-bodies at high angle of attack.
Aeroelastic t ests, w here an i ntentionally f lexible m odel undergoes measurable t ime-dependent
deflections, and may be tested to destruction, to ascertain flutter limits and other fluid-structure
interaction problems. Problems i nclude safeguarding t he t unnel from damage by model de bris,
and time-resolved measurements of structure and flowfield.
Micro Air V ehicles (MAVs) and r elated small U AVs, which a re capable of violent m aneuvers
and a re e xpected t o e ncounter s trong w ind g usts, r elative t o t heir f light s peed. T his i ncludes
flapping-wing MAVs, which always operate in an unsteady flowfield. For this application there
is little distinction between basic research and engineering testing.
Store-separation tests, such as with a cap tive-trajectory system, involving relative motion of two
or more bodies. Typical problems are at high flight speeds, involving compressibility.
Wind-engineering t ests, i ncluding f ixed g round structures, g round-vehicles, aircraft in la nding
scenarios, etc., where a high-turbulence environment is simulated together with ground-effect.
Gust tests, where the tunnel is shuttered or otherwise the free-stream is modified from steady, to
assess aircraft response to transient flowfield conditions.
Free-flight tests, where the aircraft is tethered or completely free, and is “flown” in the tunnel test
section, thus combining testing of aerodynamics and flight dynamics.
The advantage of water tunnels in dynamic testing is that for a given reduced frequency of motion
(scaled by model length scale and tunnel free-stream velocity) the physical rate of motion is much smaller
in w ater th an in a ir. T his makes d ata acq uisition m uch eas ier. D ynamic t ares t o r emove t he m odel
inertial forces, a re e ither v ery easy o r so metimes co mpletely u nnecessary, i n co ntradistinction t o w ind
tunnel testing, where dynamic tares are difficult and the inertial load dominates the total measured load48.
Flow visualization is made easier by the slower physical rates of motion. Mechanism design and model
construction are much easier, since models can be heavier and internal loads in the forced-oscillation rig
will be much lower.
However, some dynamic tests are either impossible or very difficult in water. (6) Is beyond to
scope o f w ater t unnels w henever co mpressibility i s i mportant, su ch as in cav ity aco ustics. ( 9) I s n ot
amenable to water tunnels because of the tunnels’ small size, and because of the difficulty of propelling a
“flight” article in water (the exception is flapping-wing MAVs). Froude scaling, necessary for free-flight
tests, becomes p roblematic b ecause o f the d ensity of w ater. ( 2) I s i n principle pos sible, but a gain i s
awkward because of water tunnels’ small size and Froude scaling. This is best done in an open-jet wind
tunnel.
(4) Aeroelastic sc aling i s both problematic and pr omising i n w ater tunnels. It is p roblematic
because i t i s i mpossible t o match t he d ensity r atio b etween t he m odel m aterial an d w ater. A ny t est
requiring high model surface fidelity is unlikely to be successful, for t he s ame reasons as for static
problems. A nd t he a forementioned p roblems w ith force ba lances a lso hol d f or dy namic t ests, t hough
again the low motion rates in water offer much advantage. However, the mechanics of aeroelastic testing
in water are easier because broken models are easily contained before parts go downstream to potential
damage the pump – a huge concern in wind tunnel testing. And the slow rates make recording of model
vibration easier.
(7) Is us ually r eserved f or large wind tunnels, owing t o a need for proper separation of lengths
scales of the desired ambient turbulence environment, and the need for relatively large models with fine
structure. The chief obstacle in running such tests in water tunnels is difficulty in obtaining the “right”
turbulence environment. This raises the larger question, of how does one characterize water tunnel test
section flow quality. It is not a trivial topic, since hot wires and Pitot tubes perform marginally in water,
requiring alternative or at least improved techniques.
11
(8) Shuttering a wind tunnel is a convenient means of producing well-defined gusts 45, f or gu stresponse testing, and for producing disturbances in general, for system identification tests. S huttering a
water tunnel is difficult because of the density of water, the resulting pressures (waterhammer), and risk
of s pillage. H owever, for t he sam e r eason that h igh-rate t esting i n w ater t unnels i s s traightforward,
impulsive-start testing, such as to validate classical models such as Wagner’s, is readily possible in water
tunnels, but very difficult in wind tunnels. One example is use of a piston-driven water tunnel, producing
very rapid acceleration of the free-stream, for studying impulsive-start problems for airfoils at high angle
of attack 46. Such an experiment is impossible wind tunnels. For water tunnels with a long test section,
such as the US AFRL water tunnel, it is possible to run the tunnel as a tow tank, with the model carriage
translated on rails i n t he f ree-stream di rection, m odeling a “gust” by m oving t he m odel, o r m odeling
impulsive-start by violent acceleration. It should in principle be possible to run close approximations to
indicial m otions, t hus e xplicitly c onstructing t he i ndicial r esponse i ntegral47, ope ning ne w v istas i n
massively-unsteady aerodynamics. But this is a niche area, of interest at present primarily to just MAVs.
(1) I s t he m ain-line dy namic t est i n a eronautical engineering. Its out look f or swept-wing
configurations i n water tunnels i s discussed b y K ramer 48, w ho p oints o ut r emarkable s imilarity in
dynamic-derivative data b etween water tunnels, wind t unnels an d flight t est, b ut also notes the ea se of
obtaining such da ta i n water t unnels. It r emains h owever t o systematically assess t he o utlook f or l owsweep configurations lacking sharp leading edges, such as transport aircraft. Again the crux o f the
problem i s R e-scaling. The a uthors w ould l ike t o r efrain f rom de finitive recommendations, pe nding a
systematic comparison between wind tunnel and water tunnel tests on a common configuration.
Water tunnels perform brilliantly for items (3) and (5): for high-rate testing, especially for MAVs,
where it is essentially impossible to produce the requisite motion dynamics in air, but straightforward to
do so in water. This is the overarching justification for our research.
3.1.6. Example: Forced Airfoil Oscillation in Pure Plunge
The test case is sinusoidal pure-plunge of a Selig SD7003 airfoil, and Reynolds number 40,000
based on airfoil c hord a nd f ree-stream flow speed (~26 cm/s). The reduced frequency i s the very high
value of 3.93, but the physical frequency is only 0.54 Hz! The reduced amplitude of plunge oscillation is
0.05. B ecause the motion is periodic, we are interested in phase-averages of the flowfield response. I n
Figure 3, the top row of vorticity contours is taken at the phase of motion corresponding to the top of the
plunge s troke; t he second row i s at ha lfway dow n the p lunge s troke, w here motion-induced a ngle o f
attack is maximum positive; the third row is at the bottom of the plunge stroke; and the four and final row
is a t ha lfway ba ck up t he plunge s troke, w here m otion-induced an gle o f a ttack i s m aximum n egative.
Experiment ( particle i mage v elocimetry) i s c ompared w ith t wo di fferent c omputations. A part from
dissipative e ffects in t he c omputation, the m utual c omparison i s s triking. T his s ort o f e xperiment i s
crucial f or f lapping-wing m icro ai r v ehicles – and essentially i mpossible i n wind t unnels, w here the
required high physical frequency of motion would likely destroy the motion rig, or at least make the data
acquisition very problematic.
Exp, φ=0
CFL3D, φ=0
12
IB, φ=0
Exp, φ=1/4
CFL3D, φ=1/4
IB, φ=1/4
Exp, φ=1/2
CFL3D, φ=1/2
IB, φ=1/2
Exp, φ=3/4
CFL3D, φ=3/4
IB, φ=3/4
Figure 3. Comparison of out-of-plane vorticity contours from experiment in the water tunnel (left column),
2D computation using the commercial code CFL3D, and 2D immersed boundary-method computation, at
various phases of motion; Re=40,000, SD7003 airfoil pure-plunge.
As Micro Air Vehicle applications emerge from a niche area into more regular aeronautical
engineering practice, the relevance and importance of water tunnels promises to increase. The one word
of caution is regarding aeroelastic scaling; most MAV configurations are structurally flexible, and
structural scaling in water can be problematic. Rigid abstract shapes – airfoils, plates and the like,
undergoing high-rate motions – are easiest to test in water tunnels. Full configurations are harder – which
is precisely the same scenario as for static testing.
3.1.7. Example: Particle Image Velocimetry for a UCAV Configuration
Here the m otivation w as t o c onduct flowfield v elocimetry t o unde rstand the fluid m echanics
behind f orce/moment/surface-pressure results o btained in a high-quality t est en try i n a l arge i ndustrialtype wind tunnel 49. PIV was not possible for this test, because of complexity of seeding, of laser power
required for such large scales, required alternations to model surface finish (to minimize laser reflection),
and of t he intractable burdens of e quipment s etup a nd da ta r eduction. P ressure-tap d ata ju st aft of th e
wing l eading e dge on t he s uction s ide s howed l oss of L E-suction a t ou tboard stations of t he w ing, a t
angles of attack commensurate with the so-called “pitch break”. Was this due to tip stall, or to formation
of LEVs a t the m odel a pex or wing/body “ juncture”? The h ypothesis is that the wingtips stall, losing
loading, resulting in a nose-up pitching moment due to sweepback. To verify or to refute this, we need
knowledge on w hether the wingtips indeed stall at the pitch-break angle of attack, while further inboard
the flow r emains attached. This requires flowfield i nformation, a nd w as pursued i n a w ater t unnel
experiment on a 12”-span 3D-printed model of the 1303 UCAV configuration in a water tunnel ( Figure
4) 50. The model leading edge was “sharp”, as far as possible given the manufacturing process.
13
Figure 4. The 1303 UCAV configuration: 5’-span model installed in QinetiQ 5m wind tunnel49, and 3Dprinted (plastic) installed in water tunnel test section50.
Sectional R e of the 1303 c onfiguration varied from ~ 10,000 to 32,000, depending on s panwise
station. T his is clearly in the regime of large flow separations. I f fully attached flow is not possible at
any angle of attack, then how could one possibly reach conclusion on presence or absence of tip stall, and
regarding stall at the tips vs. further inboard? The answer lies in making reasoned qualitative distinction
between a large but closed separation, and an open separation. This is seen from comparison of Reynolds
Stress contours, u’v’. F or a closed separation, even where the closure occurs in the near-wake, the u’v’
distribution w ill be a characteristic “ lobe” pa ttern just d ownstream of t he trailing e dge, w ith l obes of
opposite sign. This i s w hat one s ees a t t he 30% s emispan s panwise station a t t he p itch-break a ngle of
attack, α = 6º. In fact here the u’v’ contour is characteristic of a usual airfoil laminar separation bubble,
terminating with free shear-layer transition and reattachment just ahead of the trailing edge. At the 90%
semispan sp anwise s tation, at α = 6º t he f low i s i n contrast s een t o be f ully s eparated, w ith a n op en
separation. But at α = 4º at the same location, one sees a closed separation, evinced by the u’v’ double lobes. This i s convincing e vidence that t he w ingtips unde rgo s tall b etween α = 4º and α = 6º, w hile
further i nboard the flow remains at tached. S imilar results ( not sh own h ere) s uggest t he ab sence o f a
discernable LEV structure, whence we conclude that the pitch-break is due to loss of lift outboard on this
highly-tapered c ranked-wing c onfiguration, and t hat a vortex-related p rocess is n ot a p rimary cause.
Thus, d espite t he h uge di sparity i n R eynolds num ber be tween w ind tunnel a nd water t unnel, the latter
gives good qualitative explanation for flowfield phenomena speculated but not measured in the former.
Figure 5. 1303 UCAV water tunnel PIV, contours of Reynolds stress u’v’: 30% semispan, α = 6º (top); 30%
semispan, α = 4º (bottom-left); and 30% semispan, α = 6º (bottom-right).
3.1.8. Summarizing the Case for Water Tunnels
Water tunnels will not obviate large-scale, high-precision industrial-type testing, and are at most
marginally useful f or p roducing r eliable r esults i n co nfiguration aer odynamics, ev en i n t he co nceptual
design s tage. For conventional aircraft co nfiguration t esting, su ch a s d rag p olar m easurement, they
14
compare u nfavorably t o s imilar-sized w ind t unnels, b ecause t he latter pr oduce much larger ope rating
Reynolds numbers at the same model scale. Water tunnels are more of a fundamental research tool than
an applied aerodynamics tool. However, they are eminently useful as part of a larger solution space, by
focusing the test matrix in large wind tunnels and providing validation for CFD. This is especially true
when equipped with modern optical flowfield velocimetry techniques, such as PIV, which is much easier
to implement in water tunnels than in wind tunnels.
In problems insensitive to Reynolds number, or where Reynolds number between the application
and t he w ater tunnel test article are closely matched, water tunnels sh ould be r egarded as t he p rincipal
tool of experimental a erodynamics. Examples i nclude Micro Air V ehicles, ve ry high-rate d ynamic
testing, and high-sweep sharp-edge configurations.
Dynamic t esting h as b een su ggested as an ap plication p articularly am enable t o w ater t unnel
testing, because of the f avorable s caling of physical motion frequencies i n liquid flows. While th is is
broadly true, the conclusion must be qualified by the kind of dynamic testing that one has in mind. For
high-rate and/or high angle of attack problems, the utility of water tunnels is demonstrably obvious. But
for conventional dynamic-derivative m easurements f or airplane configurations, w e r ecommend
withholding judgment until a definitive test is conducted. This would be a common experiment in a water
tunnel an d a l arge w ind t unnel, r unning t he same configuration at t he same r ates and t he same motion
kinematics.
The focus of the subject work is Micro Air Vehicles, whence the advantages of water tunnels are
palpably evident. This ha s be en the motivation f or AFRL/RB’s Horizontal Free-surface Water Tunnel,
built in 2002 and described in the following section.
3.2.
AFRL/RB’s “Horizontal Free-surface Water Tunnel” (HFWT)
Here w e o utline the evolution o f the p rincipal facilities in w hich the s ubject r esearch w as
conducted. This includes construction of the water tunnel and synopsis of its operations, and resume of
diagnostics tools available in the HFWT.
3.2.1. The HFWT’s Origin and Installation History
The H FWT w as or iginally ba sed o n the “ Student Water C hannel” at the C alifornia I nstitute o f
Technology (Caltech). The tunnel was rebuilt in 1997 at Caltech by the PI, as part of his Ph.D. research.
The 1997-2001 installation is shown in Figure 6. This entailed removing the test section from the Student
Water Channel, and mating it with new semi-custom fiberglass intake and exit plena. The exit plenum is
essentially a rectangular box that accept outflow from the test section, turns it with vertical and horizontal
vanes, and dumps it into a holding vessel, which connects to a 8”-diameter schedule-40 PVC return pipe.
The intake plenum is rather akin to a wind tunnel contraction. The contraction ratio is about 4:1 (small
for wind tunnels, but typical for water tunnels). The entry to the intake plenum is a vertical perforated 8”diameter PVC pipe, designed to ensure vertical uniformity of inflow speed. The uneven and turbulent jet
efflux then goes through a series of perforated plates, followed by two screen-honeycomb combinations
and a final screen, before entering the contraction section. Driving the whole circuit is a 12” single-stage
axial-flow impeller. The design and shakedown of the tunnel are covered in detail by Ol 51.
In 2001-2002, t he t unnel was m oved t o A FRL a nd rebuilt i n B uilding 24C , i n t he A FRL/RB
facilities complex. I nstallation a nd s hakedown o f the H FWT w ere the first portion o f the p resentlyreported research.
In t he A FRL r ebuild, t he HFWT’s recirculation c ircuit w as r evised, a nd t he d rive pum p w as
switched from vertical to horizontal installation. Otherwise the setup was largely a reproduction of that at
Caltech. A schematic of the r ebuild i s given i n Figure 7, w hile a c hronology o f t he i nstallation of t he
HFWT in Building 24C, from site preparation to tunnel operational condition, is given in Figure 8.
15
Figure 6. The HFWT installed at Caltech, as originally built by the PI (1997).
14.00
3" SQ. ST. TUBE
L3" X 2" X 3/8"
3" SQ. ST TUBE
3" SQ. ST TUBE
3" SQ. ST TUBE
76.27
3" SQ. ST TUBE
L3" X 2" X 3/8"
FLOW SURFACE
L3" X 2" X 3/8"
3" SQ. ST TUBE
L3" X 2" X 3/8"
3" SQ. ST TUBE
21.25
I-BEAM 3" X 2.5" X 3/16"
BOTTOM FLOW SURFACE
42.88
W8 X 10 WIDE FLANGE BEAM
72.00
Figure 7. Schematic of the HFWT as installed in Building 24C, Wright-Patterson.
A key f eature of the present i nstallation i s the placement of t he entire tunnel on a steel I-beam
frame, which can be elevated and placed on rollers for moving. This feature was deemed useful in 2001,
when it was surmised that Building 24C would undergo comprehensive renovation. W hile this has not
happened, the steel frame has arguably been useful for vibration isolation.
16
Figure 8. HFWT installation history: site preparation, including excavation for sewer drain (top left);
mockup of main components on support frame, without connecting plumbing and test section glass walls (top
right), and tunnel operational (above).
3.2.2. Flow Quality Measurements and Instrumentation Suite of the HFWT
The essential property of any aerodynamics ground test facility is flow quality. One seeks a
uniform, low-turbulence flow that is representative of free-flight conditions. Detailed flow
characterization is beyond the scope of the present report, but a rendition of instruments and their main
results is given herewith.
3.2.2.1.
Pitot-Manometer Measurements
The simplest experiment for a new facility is to calibrate bulk flow speed in the test section, with
settings for the tunnel controller. Any of a number of flow velocimetry schemes is possible, including of
course particle image v elocimetry ( PIV). But partly out of c ultural deference, and before PIV was
available in the HFWT, an experiment was run with a conventional inclined manometer and Pitot-static
tube, with the dynamic and static lines of the Pitot tube connected to opposite ends of the manometer. For
manometers in a water tunnel, one of course can not use water as the manometer working fluid. Instead, a
special oil im miscible with water, w ith specific g ravity 1.7, was used. A t the l ow he ad d ifferences in
HFWT operational speeds, care is required to measure manometer variations, whence signal to noise ratio
is no t hi gh. F urther, c are i s r equired t o pur ge t he m anometer of bub bles, l est t he readings i n he ad
difference b e g rossly i naccurate. The f inal results w ere c ross-checked by a n e ven c ruder m ethod:
injection of a clump of dye into the test section, and timing its convection over a known run length, say 2
17
meters. A summary of results for flow speed vs. controller setting (from a low of around 3.5 to a high of
60; controller setting times 30 = pump RPM) is given in Figure 9.
0.45
test section speed, m/s
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0
10
20
30
controller setting
40
50
60
Figure 9. Pitot-manometer-derived HFWT calibration curve; test section free-stream speed vs. pump
controller setting.
3.2.2.2.
Hot Film Measurements
Knowing the bulk free-stream flow speed in the test section, the next measurement of interest is
flow quality: spatial flow uniformity (quality of mean velocity profile), angularity (presence of parasitic
vertical and lateral velocity components), slow temporal variation (sloshing, thermal gradients), mediumspeed temporal a nd s patial variations (secondary f low due t o t he contraction section and corners of t he
test section) and fast temporal variation (“turbulence”). By way of context, specifications for a competing
water tunnel de sign of 24 ”x36” t est s ection, f rom R olling H ills R esearch C orporation52, t he pr incipal
provider o f re search-grade w ater t unnels t oday, are l isted as: < 0.1% RMS t urbulence i ntensity, < ± 2%
velocity uni formity, and < ± 1° m ean flow a ngularity. T he HFWT a ims to exceed t hese s tandards. In
practice, one is often only concerned with velocity profile uniformity and the free-stream component of
temporal variations, or “turbulence intensity”. Both quantities can be measured by a hot wire or hot film,
at le ast i n principle. Figure 10 shows a single-component ho t f ilm s etup i n t he H FWT test s ection53,
mounted to an older rig rendered obsolete by the pitch-plunge rig described elsewhere in this report.
Figure 10. 1-component hot film probe installed in HFWT test section.
We define, in the usual sense, the fluctuating streamwise velocity component as subtraction of the
mean from the time-varying signal:
u i' = U (t i ) −
1 n
∑U (t i )
n i =1
And then the root mean square streamwise velocity component is
18
u
'
rms
1  n ' 2
=
 ∑ (u i ) 
n  i =1

1/ 2
The turbulence intensity is then the ratio of the RMS streamwise component to the mean.
Unfortunately hot-film experiments were plagued by (1) formation of bubbles at the probe, and
(2) dr ift of the s ensor r eading in s teady conditions 54. B ubble formation is related b ut not ne cessarily
caused buy local boiling. I t is somewhat improved by using “old” water – that is, not draining/refilling
the water for months. D rift, on the ot her ha nd, has no s olution. I t c omes f rom t he hot w ire operating
more l ike a t hermometer t han a v elocimeter. The r eason i s t he l ow ov erheat ratio w hen ope rating in
water. R oughly, a 3° C t emperature d ifference i s c omparable to 100% v elocity e rror a t typical H FWT
operating speeds. Since some fraction of °C variation happens often, not only as a function of time but
from place to place in the test section, the resulting drift – even if no bubbles form on the instrument – is
unacceptable for spatial surveys with a traverse. The hot wire was however used for a few single-point
streamwise-component t urbulence m easurements, b y su btracting t he “m ean” d rifting v elocity f rom th e
time-trace, instead of the mean-proper. T hat is, one uses a moving-average with a w indow much larger
than t he t emporal v ariations asso ciated w ith t urbulence. T ypical r esults a re s hown i n Figure 11, f or
nominal tunnel speed of 15 cm/s. The resulting fluctuations equate to a RMS speed of 0.0867 cm/s, or a
turbulence intensity of 0.58%.
Figure 11. Typical hot wire time-traces, constant mean streamwise velocity of ~15 cm/s; voltage drift with
time (left) and fluctuating velocity vs. time, after subtracting moving-average of mean signal.
We briefly note in passing that besides hot film/hot wires, laser Doppler velocimetry is another
obvious s ingle-point t echnique. The H FWT do es not ha ve a n LDV permanent c apability, but a
backscatter p ortable system f rom Measu rement S cience E nterprises, I nc 55 was demonstrated, f inding a
turbulence i ntensity of 0.4% a t flow s peeds f rom 15 through 40 c m/s. But the L DV al most assu redly
samples a t a lower t emporal r esolution t han t he hot wire – and t hus t he a pparently l ower t urbulence
intensity.
3.2.2.3.
Free-Stream Flow Quality Measurements by PIV
Particle i mage velocimetry does no t g ive s ufficient temporal r esolution for studying t emporal
statistics of turbulence with the present equipment, where the sampling rate is 15 image pairs per second.
But the “ergodic hypothesis” – that turbulence spatially is akin to turbulence temporally – allows use of
spatial statistics from PIV to study not only spatial uniformity, but to quote turbulence intensity proper. A
given PIV interrogation window is selected, and the velocity values for each shot stored as a string, much
19
akin to the approach for hot wire velocimetry, but with a much lower temporal frequency content. This
gives an R MS velocity an d t hus a t urbulence intensity. O ne can al so p lot t he sp atial v ariation o f
turbulence intensity, as it were. But this “turbulence” intensity is limited to the PIV sampling frequency –
or more properly, to half of the sampling frequency. The alternative is to step window-by-window across
one PIV image, gathering the individual velocity vectors into a string, as if they were temporal records.
This is the ergodic hypothesis. U nfortunately one must subtract the spatial variation from the image, in
the sense of how the bulk flow, not associated with turbulence proper, varies across the test section. This
amounts t o a s moothing o r l ow-pass f iltering o f t he PIV i mage, an d subtraction o f t he r esult f rom t he
original. C are, or artful enterprise, is required in determining how to filter, lest one artificially drive the
reported t urbulence intensity t oo low, bu t s ubtracting s patial v ariation ( the filtered data) from s patial
variation (the unfiltered) and arrive at, well, low spatial variation. Therefore here we revert to the earliermentioned approach and merely report the ensemble-variation for one selected PIV window in a sequence
of i mages. Figure 13 plots a t ime t race f or a n ominal sp eed set ting o f 1 5 cm /s, w here t he m ean i s
subtracted from e ach da ta point t o produce a f luctuating v alue. This q ualitatively r ecalls the h ot w ire
signal i n Figure 11. Calling t his a t urbulence i ntensity r esults in Tu ~ 0.35% - close t o the
aforementioned L DV-derived v alue. T his i s s lightly l ower t han the L DV-derived value, as b efits t he
lower temporal resolution of the PIV. S o we are gratified by 3-way consistency between hot wire, LDV
and PIV.
Figure 12. Fluctuating u-component of velocity vs. PIV ensemble point, cm/s; mean is 15 cm/s.
Of course, there is no artifice in using PIV to study spatial variation of mean velocity; a sam ple
result, a t nominal s etting of 15 c m/s (normalized by t his num ber), i s s hown in Figure 13, f or t he u component.
20
Figure 13. Contour plot of streamwise velocity distribution in the HFWT, over 400 (nominally) shots, using
PIV; nominal speed is 15 cm/s, and the PIV light sheet is at the test section centerplane.
3.2.2.4.
Surface Skin Friction Measurements
Besides flowfield data (velocity and vorticity) it is desirable to characterize on-surface properties,
namely the pressure and skin friction field. This is all the more desirable if one has field data, instead of
merely discrete-point data. The pressure field can be integrated to calculate lift, while the skin friction
field, not directly useful for performance calculations at low-Re because so much of the drag is pressuredrag, n evertheless gives invaluable i nsights i nto time-dependent f low s eparation. Skin f riction a nd
pressure are hard to measure for the usual signal-to-noise reasons; at low speeds, stresses are low, while
model supports are generally flimsy, whence vibrations can easily overwhelm the desired measurements,
if a displacement-based measurement technique is used.
The proposed approach was a “shear stress sensitive film”, or S3F. The details of S3F chemistry,
principles of operation, data reduction and limitations are covered by Fonov et al. 56 In brief, a polymer
doped w ith a fluorescent filler i s ap plied t o t he ar ea of i nterest, and i ts surface is sprinkled w ith t racer
particles. T ypically t he polymer i s 0.1mm-1mm t hickness, with very l arge r ange of possible shear and
bulk m odulus, de pending on t he e xpected r ange of a erodynamic l oads. A s t he pol ymer i s ne arly
incompressible, it does not r espond to pressure distribution directly, but it does respond to pr essure
gradient through local changes in thickness. It also responds to shear stress by locally deforming in shear,
with a l inear d istribution o f de formation, f rom z ero a t t he w all to f ull-range at t he outer s urface. T he
thickness change is interrogated as a change in fluorescence, while the shear deflection is interrogated by
what amounts to PIV, taking the statistically most likely displacement of a w indow of surface particles.
Thus one compares wind-off and wind-on polymer deformation states, to obtain both pressure and skin
friction. There is the issue of crosstalk: a pressure gradient will cause outward shear-like displacement of
the polymer away from the point of maximum pressure, while a shear will cause a thickness change too,
because t he p olymer i s i ncompressible. F onov et a l.56 describe m athematical methods f or cr osstalk
attenuation; essentially, this is a calibration matrix. The result of the shear stress measurements is lines of
skin friction, akin to streamlines from PIV.
21
The c hallenge of u sing S 3F i s t o a rrive at polymer pr operties w here sensitivity is high, but t he
flow does not c ause w aves or ot her undulations i n the pol ymer. T hickness should be kept a s small a s
possible, in the spirit of non-intrusive diagnostics. Failing that, an indentation can be milled in the body,
and filled with t he S3F polymer. This produces erroneous r eadings at the periphery of t he indentation,
and may materially affect the overall skin friction field, but is the simplest proof-of-concept approach. A
candidate f low suited t o S3F p reliminary m easurements i s the sharp-edged de lta wing, with its
concentrated L EVs an d resulting w ell-known s kin f riction a nd pr essure signatures on the suction side.
Accordingly, a delta wing with 50-degree leading edge sweep (reminiscent of the PI’s Ph.D. thesis) was
instrumented with a S3F patch inside a milled indentation, and the mean skin friction field was measured
(Figure 14). The LEV contribution to skin friction is quite clear.
Figure 14. 50º-sweep delta wing with port-panel of leeward side instrumented with S3Ffilm, in collaboration
with ISSI, to measure skin friction field: model about to be lowered into the HFWT test section (top left),
view of metric side of model (top right), and typical result of skin friction intensity (bottom).
Many o bstacles r emain. One i s t he t emporal r esponse o f the S 3F. A nother i s b alancing
sensitivity (needs to be down to 0.1 Pa) with robustness. T he experiments on which Figure 14 is based
were taken at a t ime w hen S 3F ch emistry w as s till i n i ts infancy, an d progress w as curtailed b y t he
aforementioned obstacles. S3F proved to be very successful in water at dynamic pressures much higher
than those normally obtained in the HFWT, but these are not of interest for MAV applications. In future
22
work, we intend to revisit S3F in the HFWT, taking advantage of the developments in chemistry in recent
years, and perhaps using stereo PIV-type of techniques to infer both pressure and skin friction from the
surface particle displacement, instead of pressure separately from ratioing fluorescence intensity.
3.2.3. Dye Injection
The q uintessential d istinction o f f luid m echanics, f rom all o ther engineering d isciplines, is that
things move large distances relative to each other, in complex and intriguing ways. Perhaps no other field
of study i s s o visual a nd s o i nfused w ith the i mportance of visually pe rceiving where things move a nd
how they evolve over time. Wh ile applied aerodynamics is more concerned with measuring total forces
on bodi es ( lift, drag a nd so f orth), a nd the actual flowfield is o f s econdary i nterest unl ess there a re
anomalies in t he f orce measurements, f low v isualization i s t he foundation of e xperimental f luid
mechanics. By far the most accessible scheme of flow visualization is qualitative methods of tagging the
flow an d o bserving t he t ags. T hese can b e rendered q uantitative b y si mple m eans ( time-stamping t he
position of traces, such as by pulsing hydrogen bubbles or dye clumps) or elaborate means (particle image
velocimetry). Here we consider the simplest means. And as mentioned above, water tunnels are ideally
suited to such means.
We assume t hat t he passive scalar of dye concentration is an adequate surrogate f or the out -ofplane component of vorticity, at least for qualitative assessment of attached vs. separated flow. A 1k x
1k-pix digital c amera ( UniqVision UP-1830) at 30 frames/second was used in m ost e xperiments for
imaging, ope rating uns huttered. I n so me cases this is s ufficiently f ast t o “freeze” t he m otion o f t he
model, while in others it causes blurring. F or k = 0.25 reduced-frequency oscillation of an airfoil model
of 152.4mm chord (typical) at Re = 60K, one motion period corresponds approximately to 158 frames at
30 frames/second, giving temporal resolution of ~2.3 degrees of motion phase per video frame.
A w and w ith 0.5m m i nternal d iameter, i njecting c oncentrated blue f ood c oloring, i s typically
used. F or models with sufficient internal volume, such as airfoils, the dye wand can be fitted inside the
model a nd e xits f lush w ith t he out er mold l ines, firing a pproximately w all-normal. A n e xample i s t he
SD7003 airfoil model in Figure 15.
Figure 15. SD7003 airfoil installed inside test section, showing smooth suction-side of airfoil (top left) and
plunge rod coupling on pressure-side of airfoil (bottom left). Black arrow in bottom image points to dye
injection exit port location. Middle: injector tube attached to flat-plate model leading edge, firing spanwise
outboard. Right: flat plate model with no internal dye passages, showing position of externally-fed dye at the
leading edge.
The dy e exit l ocation i s not v isible i n Figure 15, bu t i s m arked by t he bl ack a rrowhead i n the
bottom-right-hand por tion of Figure 15. D ye i s en trained towards t he su ction side a t t hose p hases o f
airfoil injected by a “New Era” NE-1000 syringe pump 57, with infusion volumetric flow rate programmed
to attain desired flow speed. For wall-normal firing this is typically ~0.25U∞ at the probe exit. Dye flow
streaklines tend to be independent of dye exit rate for rates less than ~0.5U∞, and the value of 0.25U∞ was
selected t o attain r easonable f low v isualization image co ntrast w hile f urther r educing l ikelihood o f
23
flowfield disturbance. F or thin models, such as flat plates, the dye wand is epoxied to the model outer
mold lines. A typical location is a downstream-firing wand on the model pressure-side, or a wand
running along the leading edge, firing spanwise outboard. For the former, typically the dye exit velocity
is matched to free-stream velocity.
3.2.4. Force Balances
3.2.4.1. Rolling Hills Research Corporation 5-Component Force Balance
The f irst f orce b alance c onsidered u nder the p resent st udy w as an o ff-the-shelf m odel built by
Rolling Hills Research Corporation (RHRC). This is a 5-component balance – missing only a drag link –
consisting of 5 single-channel stages ganged in series, with a common waterproofing and interfacing with
a conventional aft-mount sting. A photo of the installation for a wall-to-wall airfoil model is shown in
Figure 16.
Figure 16. SD7003 airfoil mounted upside-down, below Rolling Hills Research Corporation 5-component
waterproof force balance; lifted from the test section for model installation.
The RHRC balance was used for static force measurements on the SD7003 airfoil 58 and a series
of aspect ratio = 2 flat plate planforms43. As this device suffered mechanical failure and gauge
delamination in two successive iterations, and is no longer in use, we will limit ourselves to reporting a
summary of the measurement results. Details of balance calibration, software development, and operating
procedure are given by Altman58.
3.2.4.2. Fiber-Bragg Grating Custom Balance
The RHRC force balance, even if operating robustly, can not be directly integrated into the pitchplunge r ig us ed in the u nsteady ex periments, as d etailed i n sections b elow. This r equires a cu stom
geometry of ba lance, t hough not ne cessarily a n u nconventional de sign. H owever, t o c ircumvent
difficulties associated with electrical strain gauges in water – waterproofing, routing of wires, drift, gauge
delamination and so forth – an optical approach, using fibre-Bragg gratings (FBGs) 59, was used. This is
not s trictly s peaking a nov elty, a s F BGs a re us ed w idely f or e xample i n c ivil engineering; bu t t o this
author, the present instance is the first use of FBGs in aerodynamic applications.
Coherent light is sent through the fibre and through gratings written onto the fibre. Each grating
reflects light of very narrow bandwidth. I f the segment of the fibre containing a grating is strained, the
reflected light wavelength shifts proportionately. Strain of the fibre could be due to mechanical strain of
the underlying substrate ( the flexure j oint i n t he f orce balance) and t o t hermal effects, which must b e
removed though a ppropriate c ompensation. In t he present application, a s ingle fibre w ith 4 grating
elements was integrated into a two-flexure-joint airfoil mount, thus serving as an integrated force balance
24
(Figure 17). The balance can resolve axial force, normal force and pitching moment, though only the lift
is reported here.
Path of optical fiber
Lock plate
FBG sensing element
Figure 17. 3-component force balance based on Fibre Bragg grating (FBG) sensors, integrated with airfoil
mount; photo shows the HIPPO plunge rods bushed into the inner frame of the balance, and a lock plate
bridging the inner and outer frames, to lock the two safely during model installation.
Like hot wires, the FBGs are sensitive to temperature as well as the desired measurement quality
(mechanical strain). To circumvent thermal crosstalk, a later iteration of the balance had a 5th, unstrained
FBG element, whose signal assisted in the calibration to remove temperature response of the whole unit.
To f urther r educe t hermal r esponse, t he b alance w as calibrated in-situ, m ounted on t he H IPPO
plunge rods with the test section filled. Weights were hung from several points along the balance length,
at 0° and ±45°, and angles in between. These data were used to compute the load cell calibration matrix.
The s tandard e rror of t he c alibration m atrix f or the l ift f orce i s 0.16N , w hich c orresponds t o a l ift
coefficient standard error of 0.03.
The FBG signal was interrogated via a Micron Optics sm130 instrument 60, with sampling ranging
from 250Hz t o t he i nstrument’s m aximum r ate of 1Khz, t ypically ov er 100 periods o f os cillation for
periodic motions. Data were ensemble-averaged and further smoothed with a moving average, a nd the
first 5 periods removed from the sample. Inertial tares were conducted by draining the water tunnel and
repeating the airfoil motion. More details on the theory and implementation of the balance are given in
Appendix 1. An example o f l ift measurements for an ai rfoil heavily f eatured in t his r eport i s given i n
Figure 18, w here co mparison i s al so m ade w ith r esults o f S elig71 and w ith t he cl assical 2 πα. The
favourable c omparison implies b oth th at the b alance is w orking a cceptably w ell, a nd th at the s tatic
behaviour of t he a irfoil is ne arly c ommensurate with 2D; a lternatively, i t c ould imply a pe rfect
cancellation of errors, but we discount this possibility because at heart we are optimists.
The main drawback of the FBG balance is that loads sensed by the flexures include not only the
directly measured nor mal force, axial f orce a nd pitching moment, but also l oads imparted t o t he outer
frame of the balance, from torquing the bolts connecting the balance to the model. These loads result in a
DC offset from zero. If this offset remains constant on time intervals comparable to a typical dynamic
test sequence, then the offset can be removed through a t are procedure. A nd if the offset begins to vary
significantly, that is indication that the FBGs are beginning to delaminate from the flexures, and it is time
to renew the b alance. This h as h appened at l east twice in the p eriod t hat an FBG b alance has been in
operation in the HFWT (2008-2010).
25
1.25
1
CL
0.75
0.5
0.25
Selig
XFOIL
FBG
2πα
0
-0.25
-0.5
-0.75
-10
-5
0
5
α
10
15
20
Figure 18. SD7003 airfoil static lift coefficient vs. angle of attack, Re = 60K: XFOIL results at amplification
factor N = 9 (black line), wind tunnel data of Selig et al.71, and water tunnel data (blue line), with error bars
at 95% confidence intervals. Mean angle of attack for oscillatory motions discussed in a later chapter of this
report, 8°, labeled by the dashed red line.
3.2.4.3.
ATI Nano Balance
The second balance currently (as of January 2010) in operation in the HFWT is an off-the-shelf 6component internal, integrated w ith t he H IPPO pl unge r od non -metric c oupler, a nd de signed to b e
mounted as a co nventional af t s ting. A s r esults u sing t hat b alance are s till in the d evelopment st age,
details will be l imited to t he cursory observation that where both t he A TI and FBG balances ha ve full
functionality, they return comparable lift time traces.
3.2.5. Summarizing the HFWT
Looking a head t o o ther s ections o f t his R eport, it is pe rhaps f itting he re t o s ummarize t he
operating conditions and capabilities of the HFWT and of its concomitant instrumentation suite:
-
-
-
Main parameters of the Horizontal Free-surface Water Tunnel (HFWT)
o Tu ~ 0.4 %, 18” w ide x 2 4” hi gh x 108” l ong t est s ection, 3 cm/s – 45 c m/s f low
speed.
o Supports range o f experiments i n ab stracted-configuration a nd v ehicle e xternal
aerodynamics, f undamental f lows such as bluff bodies an d p lates, unsteady
aerodynamics and vortical flows.
o Free-surface terminated b y s plitter pl ate da mps s loshing w hile allowing user
interaction with the test article during the test.
High-Intensity Pitch-Plunge Oscillator (HIPPO Rig)
o 3DOF sinusoidal and nonsinusoidal oscillation capability (8” vertical stroke, max 48deg pitch, 48” streamwise stroke).
o Can su pport perching ex periments w here the m odel ch anges an gle of a ttack an d
comes to relative rest (with respect to free stream) upon maneuver completion.
o Can s upport flapping e xperiments w ith p rescribed o r f ree-to-pivot m otions, t aking
advantage of favorable temporal and dynamic scaling in water vs. air.
Particle Image Velocimetry system
26
Pair of PCO 11 Mp ix CCD cam eras and 120mJ/pulse laser allows for LES-type
resolution (for validation) near boundary layers and beyond-DNS resolution in bulk
flow
o Synchronized to HIPPO at user-selectable phase, for phase-averaged data, first order
and second order flowfield statistics, and instantaneous PIV.
o Complements dye injection system for rapid visualization of flow separation and
qualitative tagging of vorticity transport.
Fiber-Bragg Grating force balance
o 3-component balance supports instantaneous and pha se-averaged d ata for lift, pi tch
and drag/thrust.
ATI 3/6-component internal balance
o Integrated with aft-sting arrangement for 3D models in rectilinear motions
o
-
We n ow turn t o a s election o f results i n s tatic aerodynamics at l ow R eynolds number, b efore
describing the HIPPO rig, and then moving to the unsteady aerodynamics results, which are the core of
this report.
27
4.
Experiments in Steady Aerodynamics at Low Reynolds Number
While the principal objective of the underlying r esearch is in unsteady aerodynamics, one must
first a pproach t he st eady p roblem, t o asses s t he s tate o f t he ar t an d to asc ertain o pportunities w here
unsteady problems are most pressing. Here we consider three core areas:
- Laminar s eparation bubb les of c onventional airfoils a t l ow R eynolds n umber: f low phy sics,
flowfield properties, force measurements, and implication for flight vehicle performance in this
Reynolds number range.
- Lift production by low aspect ratio wings of various planforms. Since MAV configurations tend
to be low a spect ratio, t he na tural point of departure i s the steady pr oblem, w here w e c ompare
classical theories to several different measurements.
4.1.
Laminar Separation Bubbles for the SD7003 Airfoil
The formation, presence and burst of laminar separation bubbles (LSBs) has long been known as
a de triment t o the pe rformance o f a irfoils a t low R eynolds num ber, di rectly a ffecting not on ly M AV
endurance – an issue conceivably ameliorated by improvements in system components such as b atteries
and multifunctional materials – but, more importantly, degrading vehicle handling and stability, due to the
time-dependency o f sep arated s tructures sen sitive t o di sturbances e ncountered i n f light4. B etter
understanding and ultimately management of LSBs is therefore useful for improving the flight mechanics
of MAVs. The LSB is a classical topic in laminar to turbulent transition, h aving b een ex tensively
examined both from the viewpoint of fundamental fluid mechanics (see for example Tani 61, Watmuff 62,
Bao and Dallmann 63) and i n t he context of a erodynamics of a irfoils and w ings ( Arena and Mu eller 64
Roberts 65; Bastedo and Mueller 66, Gopalarathnam et al.67; Biber et al. 68, and McAuliffe and Yaras 69).
The present st udy seeks t o t rack t he d evelopment o f the L SB o ver a r ange o f angles o f attack,
from l ow a ngles w here t he bubb le i s s table and w ell-defined, t o hi gher a ngles, w here bu rst e ventually
occurs. O f primary interest is to produce a data set suitable for validation of computations. Therefore,
emphasis is o n r esolving t he velocity field and i ts statistics, r ather than o btaining i ntegrated forces and
moments. The near-wall velocity distribution can be compared with the results of commonly-used airfoil
analysis codes, for example XFOIL 70, by looking at the predicted vs. the measured shape of the LSB for a
given cr itical am plification f actor. The co de i s ex pected to b e r eliable f or t hose c onditions w here t he
bubble i s s table a nd c loses w ell upstream of t he airfoil trailing e dge. The secondary ob jective of this
study i s t o b enchmark an d co mpare three recently co nstructed experimental facilities o f v ery d ifferent
type; a w ater t ow t ank, a wind t unnel a nd a w ater t unnel, by t esting a common geometry a t nominally
identical experimental conditions: matching the model, the Reynolds number and the angle of attack.
The S D7003 a irfoil 71 was c hosen b ecause of the l ong, stable L SB t hat i t e xhibits o ver a broad
range of angle of attack, at Reynolds numbers below 100,000. Here the Reynolds number of interest is
60,000.
The work pursued here was paralleled in two other facilities: at water towing tank at the Canadian
Institute for A erospace R esearch, N ational R esearch C ouncil, O ttawa, C anada; and t he Technical
University of Braunschweig, Institute of Fluid Mechanics, Braunschweig, Germany. Snapshots of LSB
results for all three facilities are compared, but details are only reported for the AFRL experiments.
PIV measurements were taken at α=4°, where the LSB is long, thin and well-behaved; at α=8°,
where the L SB i s sh ort o r p ossibly ab sent, an d i n a ny case is c lose to the airfoil leading ed ge; and at
α=11°, near stall, where there is a small LSB near the leading edge underneath a largely open separation.
At α=4°, r ecirculating p rojected t ime-averaged “st reamlines” ar e w ell-resolved i nside t he L SB, but a t
α=8°, they are no longer resolved. E vidently, this is due to comparative lack of resolution, either due to
the t hinness of t he bubbl e a nd hence t he d ecrease o f P IV v elocity v ector d ensity i n t he w all-normal
28
direction, relative to the bubble thickness; or greater flow unsteadiness, requiring more PIV image pairs
for the flow statistics to be adequately converged; or both. T he problem of insufficient convergence of
flow statistics becomes progressively worse at α=11°, where mismatch in both mean velocity and
Reynolds stress contours, in going from PIV interrogation field to field, is quite clear.
To ob tain r easonable resolution, t he a irfoil was i maged pi ecewise, i n s ix ov erlapping f ields o f
view, s kipping the a ft ~30% of t he chord (Figure 19). The av eraged v elocity data w ere b ased on 840
images (420 velocity fields) in the two upstream fields, and 1176 images (588 velocity fields) in the four
downstream fields, with 28.9mm x 28.9mm field size. The PIV algorithm was two-pass, (locally adapted
window t ranslation in t he second pa ss, bu t no w indow r esizing) w ith 32x3 2 p ixel w indows a nd 50 %
overlap. The l arge w indow si ze w as c hosen to m inimize t he num ber of P IV out liers, a t the po tential
expense of r educed s patial r esolution. Mean velocity c ontours for α=4° are s hown i n Figure 20.
Contours o f R eynolds stress a re s hown in Figure 21. Normalization i s w ith r espect t o free-stream
velocity a nd chord length, so t hat a s peed of “1” equals free-stream. Similarly, mean velocity and
Reynolds stress are plotted for α=8° in Figure 22 and Figure 23, respectively. This is continued for mean
velocity and Reynolds stress for α=11° in Figure 24 and Figure 25, respectively.
Figure 19. Schematic of PIV interrogation window tessellation on SD7003 airfoil (left), and photo of airfoil
mounted in the water tunnel test section (right).
Figure 20. Contours of SD7003 LSB mean streamwise velocity component, α=4°.
The cross-prime Reynolds stress, u’v’, in Figure 21 and subsequent related figures is normalized
by free-stream speed squared. The value of -0.001 is taken as the “cutoff” value beyond which transition
to turbulence is posited to occur.
29
Figure 21. Contours of SD7003 LSB normalized Reynolds stress, α=4°, together with LSB dividing
streamline.
Figure 22. Contours of SD7003 LSB mean streamwise velocity component, α=8°.
Figure 23. Contours of SD7003 LSB normalized Reynolds stress, α=8°.
For α=11° the Reynolds stress levels are much higher than for the lower angles of attack,
evidently because large-scale separation is accompanied by turbulent mixing. That is, unlike the mostly
attached-flow case, it is not the case that there is a large run of laminar separation followed by transition
in a free shear layer and turbulent reattachment. Stall, perhaps trivially, is turbulent in this Reynolds
number range.
30
Figure 24. Contours of SD7003 LSB mean streamwise velocity component, α=11°.
Figure 25. Contours of SD7003 LSB normalized Reynolds stress, α=11°; not the higher magnitude of
Reynolds stresses in the contour levels.
The l ocations of L SB s eparation, transition o nset, time-averaged r eattachment, an d ma ximum
bubble h eight for t he three s ets o f r esults a re listed i n Table 1, along w ith th e e stimated facility
turbulence intensity. R espective l ocations predicted by X FOIL f or the disturbance amplification factor
N= 9 ar e a lso g iven, w ith separation and reattachment i nferred f rom st reamwise co ordinates w here the
skin f riction coefficient first reaches zero declining from pos itive (separation) and returning back to
positive (reattachment). I AR and TU-BS data on t he LSB separation, reattachment and transition points
agree quite well. I n t he AFRL data set, the bubble forms considerably f urther upstream and reattaches
further upstream, t hough its l ength is somewhat longer than in the I AR and TU-BS results (~40%c
compared t o ~ 30%c). Transition i s dom inated by t he K elvin-Helmholtz in stability m echanism w hich
leads to the r oll-up, pa iring, a nd s ubsequent s hedding of l arge-scale v ortices69, a s opposed to turbulent
spot-based t ransition in which b ursting of s mall-scale t urbulence o ccurs d irectly w ithin t he sep arated
shear layer (as observed by Roberts and Yaras 72, for example). Therefore the locations of transition onset
listed in Table 1 are reliable measurements and are probably not affected by spatial resolution errors.
Data
Set
IAR
TU-BS
AFRL
XFOIL
Table 1. Measured and computed SD7003 LSB Properties, Re=60,000, α=4°
Freestream
Separation, Transition, Reattachment,
Max Bubble
Turbulence, Tu [%]
xS/c
xTR/c
xR/c
Height*, hb/c
0*
0.33
0.57
0.63
0.027
0.1
0.30
0.53
0.62
0.028
~0.1
0.18
0.47
0.58
0.029
0.070 (N = 9)
0.21
0.57
0.59
31
*thickness of entire boundary layer at maximum bubble thickness
We can therefore c onclude t hat m odern, y et c onventional o ff-the-shelf 2 D p article image
velocimetry i s capable of resolving averaged velocity f ields in an airfoil laminar separation bubble at a
Reynolds num ber o f 60, 000. C omparison o f nom inally i dentical e xperiments i n t hree v ery di fferent
facilities – a water tow tank, a wind tunnel and a water tunnel – shows encouraging qualitative similarity
in the bubble shape and velocity fields, as well as Reynolds stress distributions. However, discrepancies
in the measured location and f low s tructure of the bubble remain. The f ormer is perhaps due to minor
variations in angle of attack or ambient turbulence intensity; the latter being a result of inadequate spatial
(magnification t oo l ow) or t emporal (insufficient number of PIV samples) resolution. Results from t he
present s tudy f orm a pr omising da tabase f or v alidation of l ow R eynolds n umber a irfoil num erical
solutions. At even lower Reynolds numbers, separation bubbles are larger and the interplay between LSB
physics a nd g lobal a erodynamic pr operties s uch a s t he dr ag pol ar w ould be come more s ignificant.
Research c ontinues. A t horough c omputational s tudy, motivated by t he pr esent w ork, w as r ecently
conducted by Galbraith and Visbal 73, generally confirming the experimental findings.
4.2.
Aspect Ratio = 2 Flat Plates of Various Planform
Here we shelve the problem of 2D airfoil aerodynamics and transition, and instead consider thin
flat-plate sections, where presumably transition is “forced” by the square leading edge. Evidence for such
a c laim i ncludes for ex ample G ursul et al.74, w ho found R e-insensitivity f or v arious l ow aspect r atio
planforms with s harp-edges sections, at least f or Reynolds numbers above approximately 20,000. T his
can be counterintuitive i n t he c ontext o f c onventional a erodynamics. N ormally, s harp l eading e dges
produce a small pocket of separation that closes by turbulent reattachment – not really a LSB, but a flow
structure that can be thought of as such. A s compared with rounded-edge airfoils, in moderate and high
Re applications the peak L/D is attenuated. B ut for low-Re applications one might find the reverse; for
instance, Spedding et al 75 report that at Re = 12,000 a nd AR=6, flat-plate airfoils produced higher lift to
drag ratio and more gentle stall than some low-Re optimized airfoil sections. U se of such thin flat-plate
“airfoils” allows for the isolation of planform ef fects, r ather than airfoil sectional effects. Our f ocus i s
therefore on p lanform ef fects on l ift c urve s lope, and h ow well d irect lift m easurements c orrelate with
inferences from the vorticity convected into the wake.
Laitone 76 studied r ectangular p lanform w ings a t R eynolds num bers n ear 20,0 00, t aking f orce
balance l ift an d drag measurements f or flat an d cambered plates i n a wind t unnel. His r esults for a
rectangular flat plate wing of aspect ratio of 2.18 were used to validate results in the present study. Other
examples i n t he r ecent literature are C osyn a nd V ierendeels 77, w ho c onducted fully-turbulent
computations on rectangular wings at Re = 100,000, finding close agreement with lift predicted by lifting
surface theory with Polhamus’s leading-edge suction analogy 78. In looking at numerous planform shapes
in an aspect ratio range from 0.5 to 2, at Reynolds numbers from 70,000 to 140,000, Torres and Mueller79
showed increasing nonlinearity in the lift curve slope and an increase in stall angle of attack as the aspect
ratio decreased. Zuhal and Gharib 80 studied tip vortex meandering for a NACA 0012 A R~4.6 wing in a
wind t unnel a t R eynolds n umbers c lose t o 9,000, w ith s tereoscopic P IV; t his is us eful for identifying
vortex core location for wake-based inferences of lift coefficient.
The pr esent study f ocuses on t he c onnection b etween t he c oefficients of l ift, e xperimentally
obtained from s tudying t railing v ortex s tructure ( and c irculation) at R e 8, 000 - 24,000, e xperimentally
obtained t hrough f orce m easurement, a nd t heoretical i nviscid p redictions. Trailing v ortex r oll-up a nd
formation is also obs erved w ith the he lp o f f low visualization. L ift is c alculated f rom t he K uttaJoukowski theorem, L = ρ ∞V∞ Γb ′ , using peak circulation from area integrations of the vorticity field in
the cross-flow plane as measured with digital particle image velocimetry. b' is taken as the effective span
– namely, twice the distance between the observable core of the trailing vortex and the wing centerplane.
32
For s lender w ings, t he i nviscid a pproximation C L = 12 πARα (e.g., T hwaites 81) ha ppens t o
2π 
coincide w ith l ifting-line theory, C L = α 
for A R= 2. S o AR= 2 i s a convenient prototypical
1 + 2 / AR 
low aspect ratio for general study, especially because it also fits well in the water tunnel at Re ~ 10,000
with m inimal b lockage. Effects o f l eading-edge s weep c an be m odeled w ith t he a pproximation81


4
, or with Lamar’s 82 extension of Polhamus’ leading-edge suction analogy,
C L = 12 πARα 

 2 + AR tan(ϕ1 / 2 c ) 
C L = K P sin(α ) cos 2 (α ) + K V sin 2 (α ) cos(α ) , w here KP, accounting for attached f low, i s a pproximately
2.5 at AR = 2, while KV, accounting for the vortical contribution is very close to π82.
Models used in the experiment are shown schematically in Figure 26, the test matrix is given in
Table 2. The u ncertainty i n t he m easurements o f t he v elocity v ectors and the c alculation o f the
coefficient of lift is within 5%, which results from averaging 90 sets of individual velocity vector fields
for each test in Table 2. The inaccuracy in the calculation of vortex position relative to the wing tip is on
the order of 2 pixels, resulting in an uncertainty of ~ 2% based on the mean aerodynamic chord.
Table 2. PIV test conditions (left) and flow visualization test conditions (right).
Figure 26. AR=2 planforms: rectangle (left), semicircle (middle) and delta wing (right).
Typical v elocity an d v orticity co ntour levels are given i n Figure 27, and a n e xample o f
downstream variations of vorticity is given in Figure 28. Variations with downstream l ocation and
Reynolds number were slight to negligible; full details are given in Kaplan et al.43.
Circulation is calculated by integrating vorticity about a circular area centered at the vortex core.
The vortex core location is obtained from dye injection, and confirmed by comparison with the vorticity
peak in the contour plots. Results of circulation magnitude vs. circular contour radius are given in Figure
33
29 for all of the examined cases. There is a peak circulation, achieved at that radius from the vortex core,
such that at subsequently larger radii vorticity of opposite sign is captured. This peak circulation is then
used in the modified Kutta-Joukouski theorem to calculate lift.
Figure 27. In-plane velocity magnitude and out-of-plane vorticity; α= 10°; downstream X/C = 1; U∞ = 9 cm/s;
Re = 8,000.
34
Figure 28. Vorticity evolution vs. distance downstream from trailing edge, α=10°; semi-ellipse (left) and
rectangle (right); note difference in vorticity contour levels.
0.25
0.2
Γ/bU∞
0.15
0.1
0.05
X/C = 1.0
X/C = 0.1
0
0
0.05
0.1
r/b
0.15
0.2 0
0.05
0.1
r/b
Rect α=5° Re = 8000
Rect α=5° Re = 24000
Rect α=10° Re = 8000
Rect α=10° Re = 24000
Rect α=15° Re = 8000
Rect α=15° Re = 24000
Delta α=10° Re = 8000
Delta α=10° Re = 24000
X/C = 2.0
0.15
0.2 0
0.05
0.1
r/b
0.15
Delta α=15° Re = 8000
Delta α=15° Re = 24000
Ellipse α=10° Re = 8000
Ellipse α=10° Re = 24000
Ellipse α=15° Re = 8000
Ellipse α=15° Re = 24000
Figure 29. Normalized circulation vs. contour radius; X/C = 0.1 (left), X/C = 1.0 (center) and X/C = 2.0
(right).
35
0.2
An example of lift calculation using the Kutta-Joukouski relation and the effective vortex span is
given in Figure 30, which shows that in all cases except for the near-stall case of the semi-ellipse, there is
very little variation in predicted lift coefficient with respect to wake streamwise sampling station.
Figure 30. CL vs. X/C Comparison for rectangle (left) and semi-ellipse (right).
Finally, the PIV-derived lift, the f orce balance m easurement, and the v arious t heoretical
predictions of lift are compared for the rectangle, delta wing and semi-ellipse, together with comparison
with Laitone’s data for the rectangle76 (rescaled using slender-body theory from the original aspect ratio
of 2.18 to the present case of 2.0), in Figure 31. Mutual agreement is generally good, which is surprising
given that the theories are developed for inviscid flow, and the PIV-derived circulation is likely plagued
with errors due to dissipation and discretization. The only significant outlying cases are for the delta wing
and l ow angles of attack, where LEVs and tip vortices may i nteract to cancel some of t he wake-vortex
circulation, thus underpredicting the lift.
36
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
CL
L
0.5
0.4
0.4
rectangle, Re = 8K FB
rectangle, Re = 24K FB
rectangle, slender theory
rectangle, suction analogy
rectangle, PIV, Re = 24K
rectangle, PIV, Re = 8K
0.3
0.2
0.1
rectangle, AR rescaled, Re = 20K
rectangle, AR rescaled, Re = 24K
Laitone, AR = 2.18, Re = 20K
AR = 2.18, slender theory
0.3
0.2
0.1
0
0
-0.1
-0.1
0
5
α
10
15
delta, Re = 8K FB
delta, Re = 24K FB
delta, slender theory
delta, suction analogy
delta, PIV, Re = 24K, b'
delta, PIV, Re = 24K
delta, PIV, Re = 8K, b'
delta, PIV, Re = 8K
1.6
1.4
1.2
1
0
5
α
20
10
15
20
0.9
0.8
0.7
0.6
0.5
L
CL
0.8
0.4
0.6
semi-ellipse, Re = 8K FB
semi-ellipse, Re = 24K FB
semi-ellipse, slender theory
semi-ellipse, suction analogy
semi-ellipse, PIV, Re = 24K
semi-ellipse, PIV, Re = 8K
0.3
0.4
0.2
0.2
0.1
0
0
0
5
10
15
α
20
25
30-0.1
0
5
α
10
15
20
Figure 31. CL vs. α; rectangle (top left), comparison of rectangle data with aspect-ratio scaled results of
Laitone76 (top right), delta wing (bottom left) and semi-ellipse (bottom right).
We conclude this section with the simple observation that viscous effects – that is low Reynolds
number effects – are not necessarily present at low Reynolds number, at least for problems focusing on
lift coefficient. The reason is a combination of low aspect ratio and sharp leading edges, which together
produce a sort of forcing, that overwhelms viscous effects.
A different sort of forcing occurs in the unsteady case, which is the subject of the remainder of
this report.
37
5.
Establishing a Capability for Unsteady Aerodynamics
Experiments
Having examined a range of nominally steady low Reynolds number aerodynamics problems, we
now turn to the much broader question of unsteady flows. I n this chapter, we document the design and
construction of a mechanism f or a ccurately pr oducing h igh-speed, hi gh displacement motions – first in
two degrees of freedom, and then in three.
5.1.
A Scheme for Pitch and Plunge Motions
We are i nterested as a baseline i n t he cl assical motions of unsteady aerodynamics, which ar e
vertical translation (normal to the free stream) of an airfoil, and pitch about a fixed axis somewhere along
the a irfoil c hord. T his i s a t wo de gree of m otion ( 2DOF) motion. S everal s chemes ar e p ossible f or
achieving t his, and a few selected ex amples are briefly r eviewed. D esigns i nclude (Figure 32) i nclude
those of Paquet 83 (top mount, t wo-component actuation at model end, with wing pi ercing free-surface),
Parker, Soria and von Ellenrieder 84( top mount with pitch and plunge on separate carriages), Anderson et
al. 85 (end-mounts, model horizontal with pitch and plunge on separate stages), Hanff83 (center mount, pair
of hydraulic actuators, similar to the present design), and Kurtulus et al.86 (end-mount, separate pitch and
plunge carriages).
(a)
(b)
(c)
(d)
(e)
Figure 32. Examples of 2-degree-of-freedom rigs in water tow-tanks and water tunnels: (a) Paquet83, Parker
et al.84, Anderson et al.85, Hanff83, Kurtulus et al.86
One 2DOF airfoil oscillation system design trade is supporting a v ertically-hanging model from
one tip, with the other free or abutting the test section floor; or, connecting to both tips, with the model
horizontal; or, a center-mount system with struts connecting to the centerline of a horizontal model. The
first has advantages of placing t he force balance above the water line and thus solving the balance
waterproofing i ssues, an d h as t he l east i nterference b etween t he r ig st ruts a nd t he m odel flowfield.
However, it makes free-surface effects largely unavoidable. The model mass (physical mass and motioninduced apparent m ass) p roduces an u nbalanced load on t he m odel s upports, w hich is e specially
troublesome for large models oscillating at high speeds in liquids. The second is limited to rigid airfoil
models spanning the tunnel test section. The third keeps model loads balanced and allows for both wallto-wall models and wings of various planform, but has large disadvantages of rig strut interference with
the f lowfield. T his, how ever, i s t o s ome e xtent of secondary i mportance i f pa rticle i mage velocimetry
data are taken in planar slices well-away from the model centerline. Assuming that this assertion is true, a
center-mounted arrangement was selected.
38
Figure 33. "High-Intensity Pitch/Plunge Oscillator" Rig: (top left) schematic, (top right) installed atop water
tunnel test section, (middle left) with plates to damp free-surface oscillations caused by model motion,
(middle right) schematic of SD7003 airfoil mount and plunge rods, with rod endpoints interior to the model;
and (bottom) side view of test section with rig and airfoil model installed.
39
Actuation op tions include rotary s ervo ( or s tepper) motors, l inear s ervomotors a nd hydraulics.
Rotary m otors are t he m ost common c hoice a nd could pr ovide l arge m otion a ngles, bu t ha ve the
disadvantage of linkage backlash in motions with aggressive starts and stops. Also, the model pivot point
would n ot b e a djustable purely in s oftware. T his f avors d irect linear a ctuation. E lectric linear motors
were selected in favor of hydraulics, on account of the small rig scale and the savings in required support
equipment. Linear motors mounted vertically have the disadvantage that unless current is flowing, model
weight is unsupported, and the apparatus falls to its lower bump-stops. The start of every experiment thus
requires a homing sequence. Also, the mass of the linear motors’ moving-stages becomes part of the load
that the motors need to support.
Aerodynamic l oads that the m otion r ig m ust s upport c an be e stimated f or e xample by
Theodorsen’s method87, or just the simple 2πα(t), where the effective angle of attack is the combination of
pitch a nd pl unge. A s a lready mentioned a bove, f or water tunnels i t i s no t t he c ase t he i nertial l oads
dominate aerodynamic loads; in fact, quite the opposite. H owever, for mechanism design purposes one
can estimate the various masses involved, and the desired accelerations, to calculate overall loads. This
can be important for abrupt motions with large transient accelerations, such as ramps and steps.
The present m echanism w as d esign w ith large, he avy “ plunge r ods” – not o nly f or i mproved
stiffness, b ut al so so t hat changing m odels w ould n ot g reatly af fect t he t otal mass o f t he m echanism,
whence the same controller coefficients (PID constants) could be used for all models.
The first iteration of the “High Intensity Pitch-Plunge Oscillator” Rig, affectionately dubbed with
the acronym “HIPPO”, consists of a pair of electric linear motors mounted vertically on a plate above the
tunnel t est s ection. E ach motor a ctuates a v ertical “ plunge r od”, w hich c onnects v ia a bus hing t o t he
airfoil a t a f ixed p ivot poi nt on t he a irfoil c hord, i n t he t est s ection v ertical pl ane of s ymmetry. T he
upstream pl unge r od i s c onstrained t o m ove pur ely vertically, w hereas t he do wnstream pl unge r od i s
allowed t o pivot in the t est se ction v ertical p lane of sy mmetry. Mo tion t rajectory o f e ach rod i s
programmed independently, such that the desired angle of attack and vertical position time history of the
airfoil a re c onverted t o po sition c ommands f or e ach l inear m otor. This a llows f or s ingle de gree-offreedom motions s uch a s pur e-pitch about a pr escribed f ixed p ivot poi nt, o r pure-plunge. P itch a nd
plunge c an be c ombined, a nd t he pi tch pi vot po int c an be v aried by s uitable c hoice of ph ase a nd
amplitude difference in trajectory of front or rear plunge rod. For all cases where the pitch pivot point is
not co incident w ith t he b ushed en d o f t he f ront p lunge r od, t here w ill b e a sm all p arasitic st reamwise
displacement of the model, which would be unavoidable unless the front plunge rod were to be allowed to
pivot similarly to the downstream one. The first functional configuration of HIPPO is depicted in Figure
33.
5.1.1. Rig Performance
We will refer to the time-history of the difference between commanded (ideal) position of the two
linear motors, and the attained position, as dynamic following error. Of course, error in positioning of the
model depends also on s tructural behavior of t he model and the connection between model and pl unge
rods, but upon ignoring those two factors, the dynamic following error implies directly the error in angle
of attack, acceleration and so forth. The commanded motion of the two motors is translated in software
from the desired pitch and plunge history, while the attained motion is sampled from an optical encoder
on each motor track. Dynamic following error is shown f or the representative case o f sinusoidal pureplunge with h = 0.05, k = 3.93, in Figure 34. For all pure-plunge cases that follow the motion is a cosine
wave, so that velocity is continuous from rest. In the example in Figure 34 the motion is a cosine wave,
showing the smoothing transient on startup. One half of a period after startup, dynamic following error is
seen to be < 0.5% of the motion amplitude. Error peaks at phase locations of maximal acceleration in the
sine wave; the frequency content of the error signal shows a peak at the actuation frequency, followed by
harmonics. T wo sets o f d ata are g iven – for t he f orward pl unge r od ( green) a nd t he aft ( black). T he
position t ime h istories o f t he two d iffer because the mean an gle o f attack o f t he m odel i s 4 °; with the
40
error normalized by h0
model mounted ups ide do wn ( pressure-side o f t he ai rfoil t owards the t est se ction f ree-surface), t he
inclination of the model causes relative elevation of aft plunge rod.
0.005
3.5E+06
0
3E+06
aft error
fwd error
2.5E+06
-0.005
2E+06
aft error
fwd error
-0.01
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
1.8E+13
1.5E+06
1.6E+13
1E+06
1.4E+13
500000
1.2E+13
0
t
fwd_C
fwd_A
aft_C
aft_A
0.04
0.02
0
1E+13
8E+12
h(t)
10
20
Hz
aft_A
aft_C
aft error
fwd error
0
6E+12
-0.02
4E+12
-0.04
2E+12
-0.06
0
0.25
0.5
0.75
1
1.25
1.5
1.75
t
2
0
0
1
2
3
4
5
Hz
Figure 34. Time-traces and FFTs of plunge-rod commanded position, attained position and relative
difference (error).
As an example of a classical, low-frequency, low angle of attack oscillation at the upper extreme
of what is accessible in wind tunnels, we consider a k = 0.80 pure –plunge of the SD7003 airfoil at Re =
60,000 (Figure 35), where contours of streamwise velocity and out-of-plane vorticity are shown. This can
be compared with the static results for the SD7003 in the previous chapter.
φ = 0, αT = 4°
φ = 1/4, αT = 8.55°
41
φ = 1/2, αT = 4°
φ = 3/4, αT = -0.55°
Figure 35. k = 0.80 pure-plunge, contours of phase-averaged (230 realizations) normalized streamwise
component of velocity (left) and Reynolds shear stress (right), after periodic conditions established; φ = 0, 1/4,
1/2 and 3/4.
5.2.
Extension of HIPPO to 3-DOF
Recognizing t hat l ongitudinal m otions a re s panned b y t hree de grees of f reedom ( fore-aft, up down, and rotation), a third linear motor was added to HIPPO in 2009. Since it was impractical to modify
the existing pair of motors and the carriage on which they rest, it was necessary to size the third motor to
be large enough t o move t he e ntire t wo-motor carriage as a single unit. This was accomplished with a
220V linear motor of 48” stroke, also from H2W. Taking advantage of the unusually long test section of
the HFWT, the new motor sits on an aluminum plate over the downstream half of the test section and the
exit plenum. Photographs of the three linear motors are given in Figure 36. It the latest iteration, all three
motors w ere r ewired w ith a G alil D MC-4040 E thernet-based c ontroller, w ith which a l aptop c an be
plugged into an Ethernet junction box t o issue commands and to receive encoder signals. This obviates
the need for a dedicated lab computer – a large advantage for modularity.
Figure 36. Full longitudinal 3-DOF motion capability; view of full linear motor setup above HFWT test
section (left), and detail of linear motor enabling streamwise-direction motion (right).
42
6.
Experiments in Unsteady Aerodynamics using the HIPPO rig
As a resume of research conducted in the past 7 years using the HFWT and HIPPO, we consider
the following cases:
1. high-frequency pure-plunge
2. high-frequency pitch: sinusoidal and non-sinusoidal; and pitch-plunge comparison
3. further observations of relaxation from startup for high-frequency pitch
4. airfoil low-frequency pure-plunge and the role of transition for deep stall problems
5. airfoil low-frequency pitch-plunge and the role of transition for shallow stall problems
6. configurational effects in low-frequency motions; repeat of (4) and (5) for a flat plate
7. mixed-frequency problems, where pitch and plunge frequency differ
8. the nonperiodic problem of pitch ramp-hold-return
9. perching, or a generalized form or linear pitch ramp, with varying free-stream speed
10. flapping, here akin to the so-called “normal hover”, but with the pitching angle free
Many of the below-mentioned experiments use the SD700371 airfoil. The first variant of HFWT
model of t he S D7003 had 8” or nominally 200m m chord, and w as c onstructed f rom f iberglass. The
second v ariant ha d 152.4mm c hord a nd w as c onstructed from 0.030” -thick s tainless st eel. T he latter
model consisted of 5 butt-welded segments each burned by wire-EDM from a block of 316 stainless steel.
Both models were nominally 457mm span, leaving approximately 1mm (or less) gap from tip to tunnel
test s ection s idewall, a nd were thus d eemed “2 D” o r w all-to-wall”. I n m ost c ases t he m ean a ngle o f
incidence was 4°. The airfoil and schematic of geometry are shown in Figure 37, for a typical Reynolds
number of 10,000, and nominal values of pitch and plunge amplitude.
U∞~ 6.6 cm/s
A=21.5º
Offset
α0 = 4º
c=15.24 cm
xp
h+↑ =0.092c
Figure 37. Schematic of airfoil pitch and plunge oscillation.
6.1.
High-Frequency Pure-Plunge
6.1.1. Introduction
Plunging airfoils are useful and common abstractions in unsteady aerodynamics for a wide range
of a pplications i n l ow-speed f light, su ch as h elicopter r otors 87. MAV-related m otivations of all t hree
types – fixed-wing, r otary-wing, and f lapping-wing – to s ome e xtent r equire departure f rom cl assical
unsteady airfoil theory 88 and classical dynamic stall 89, in nontrivial and qualitatively important ways. The
small size and low flight speed of MAVs necessarily leads to high dimensionless rates of motion, either
intentional (aggressive m aneuver, w ing r otation f or “perching”, w ing f lapping in hov er a nd loiter) or
unavoidable ( response to gusts o f h igh a mplitude r elative to the v ehicle f light s peed). The d esired
underlying knowledge set is how the flowfield and integrated aerodynamic coefficients – lift, drag/thrust,
and pitch – vary with angle of attack time history. P eriodic, and in particular sinusoidal angle of attack
variation i s th e most a ttainable and most c ommonly studied realization in practical l aboratory settings.
43
One can ask how the flowfield relaxes to periodicity upon ons et of the forced oscillation90, and how the
flowfield varies from period-to-period once nominal periodicity i s attained. E ven i n t he case of strong
periodicity, t he que stion i s how a erodynamic r esponse l ags motion kinematics – that is, t o w hat extent
does t his response depart from quasi-steady. Matters ar e f urther complicated by l aminar separations at
low R eynolds num ber, w here ev en in steady airfoil a erodynamic one f inds un usual be havior in CL =
f(α) 91.
The MAV application, where CL>0 is important, suggests a cambered airfoil with good on-design
performance at MAV-relevant Reynolds numbers; the Selig SD7003 airfoil was chosen because of prior
work on t he static case42. Pure-plunge of the SD7003 airfoil71 at Re = 60,000 at reduced frequency k≤
0.80 was studied by Radespiel et al. 92, to compare the suction-side boundary layer transition and laminar
separation bubb le b etween weakly-unsteady an d static c ases. A n extensive s tudy o f h igh-frequency
NACA 0012 plunge cases was conducted by Lai and Platzer 93 and Jones et al. 94, where the focus was on
thrust-production a nd w ake s tructure for v arious combinations o f reduced frequency a nd r educed
amplitude.
Plunging m otion is defined a s
with r esulting a ngle o f a ttack tim e h istory
and maximal extent of angle of attack of
. Following a plunge-case studied by Lai and Platzer93, we take k = 3.93 (note the
factor of 2 difference in definition of k between the present definition and that of ref.93) and h = 0.05.
6.1.2. Frequency and Reynolds Number Effects
We first consider a qualitative attempt to connect the low-frequency plunge studied by Radespiel
et al., with the high-frequency cases considered by Platzer et al. Questions include how the near-wake
passes from planar, in the quasi-steady case, to nonplanar and reverse-Karman vortex street93; what is the
role of leading-edge vortex shedding and its coupling into the wake topology; and how the various flow
separations depend on Reynolds number.
Figure 38 shows development of the near-wake for k = 0.80 through k = 2.62, for cosine-wave
plunge with h = 0.05. Figure 40 extends the reduced-frequency range to k = 3.93. In both figures,
snapshots are at the top and bottom of the plunge stroke. Figure 40 includes both the near-wake and the
flowfield over the suction side of the airfoil. Figure 38 is at Re = 60,000, and Figure 40 is at 10,000. In
all cases the mean angle of attack is α0 = 4º, and snapshots were taken at least 5 periods after motion
onset, to give good confidence that startup transients have relaxed. Substantiation of this assertion is
given further below.
k = 0.80, bottom of plunge
k = 0.80, top of plunge
k = 1.31, bottom of plunge
k = 1.31, top of plunge
44
k = 1.96, bottom of plunge
k = 1.96, top of plunge
k = 2.62, bottom of plunge
k = 2.62, top of plunge
Figure 38. Dye Visualization, Re = 60,000, mean α = 4°, h = 0.05: k = 0.080, 1.31, 1.96 and 2.62, at the top
(right-hand-side of page; φ = whole number) and bottom (left-hand-side; φ = n/2).
In Figure 39 the near-wake is rolling up i nto a reverse-Karman vortex street, much akin to that
reported i n R ef. 93 and 95, despite t he l arge di fference i n R eynolds num ber a nd a irfoil s hape, a nd t he
nonzero mean angle of attack. Visualization of the flow over the suction-side of the airfoil is by injection
just downstream of the leading edge. On the pressure side, visualization of the near-wake is by injection
at the trailing ed ge, al so o n t he pressure s ide. W hile f or the l atter t he d ye s tream i s thinner and more
coherent, qua litatively t he ne ar-wake as r esolved b y t he t wo i njection m ethods l ooks si milar. We
observe, therefore, t hat the d ye i njection is not i ntrusive, d espite t he o bvious p resence o f t he i njection
probe.
On the suction side of the airfoil, the formation of a small dynamic-stall vortex 96 is discernable,
shortly before the bottom of the plunge stroke. This vortex is not shed into the bulk flow, but convects
along the airfoil surface essentially at the free-stream velocity. The same vortex from the previous period
of oscillation is visible further downstream just ahead of the trailing edge. It does not, however, appear to
strongly interact w ith vorticity shed from the trailing edge, in the form of a merged trailing-edge –
leading-edge vortex pair.
Returning to Figure 38, at k = 2.62, the wake is akin to a reverse Karman street, but does not yet
evince strong vortex rollup. At k = 1.96 there is still strong wake curvature, but no discernable rollup at
all. By k = 0.80, t he ne ar-wake a ppears a lmost pl anar, a lthough a t a pproximately 10 c hord lengths
downstream of the trailing e dge, a sinusoidal dy e s treak ( not s hown) is v isible. I nterestingly, a t l ow
reduced frequency t here i s no r egular Karman v ortex s treet, akin to a bl uff b ody. T his is e vidently
because of the comparatively high Reynolds number (60,000), which is near the on-design condition of
this airfoil. In contrast, a NACA 0012 will have clearly discernable Karman-type shedding at conditions
where bluff-body-type behavior overwhelms the motion-induced shedding. 97
It ap pears, t hen, t o b e b roadly t he case that as r educed f requency i ncreases – while r educed
amplitude is held constant – that “Reynolds number effects” become more benign. I ndeed, comparing
Re = 10,000 – 20,000 – 40,000 – 60,000 for k = 3.93, h = 0.05 at the bottom of the plunge stroke (Figure
41), t he near-wake i s essentially i ndistinguishable o ver t his R eynolds n umber r ange. O f co urse, at t he
higher Re there will be more mass-diffusion, whence the dye streaks will be of lower contrast. There may
also be viscous-effects in regions of high shear, such as interior to vortex cores and in the feeding-sheets
connecting shed vortices.
45
Re = 60,000
Re = 40,000
Re = 20,000
Re = 10,000
Figure 39. Re = 10,000 to 60,000, mean α = 4°, h = 0.05: k = 3.93, established flow, top of the plunge stroke.
Figure 40. k =3.93, Re = 10,000: near-wake (left) and over the airfoil suction-side (right); top of stroke (upper
two images) and bottom of stroke (lower two images).
Re = 60,000
Re = 40,000
46
Re = 20,000
Re = 10,000
Figure 41. Re = 10,000 to 60,000, mean α = 4°, h = 0.05: k = 3.93, established flow, top of the plunge stroke.
6.1.3. Plunge at k = 3.93, Re=40,000 and Re = 60,000
We now consider PIV velocity and vorticity results, for the representative high-frequency case of
k = 3.93, h = 0.05. R esults a re reported f or f our p hases o f m otion: top of the plunge s troke ( φ=0),
halfway on t he downstroke (φ=1/4), bottom of the plunge stroke (φ=1/2), and halfway on the upstroke
(φ=3/4). At the two halfway phases, the effective angle of attack is just the mean angle of attack – again,
αT = α0 = 4º . A t φ=0, αT = α0 + a tan( h /U∞) = 21.5º, while at φ=1/2, αT = α0 + at an( h /U∞) = -17.5º.
Static stall for this airfoil, meanwhile, occurs at approximately α = 11º107 at Re = 60,000.
Figure 42 compares instantaneous PIV vorticity contour plots with phase-averages, based on 120
image pairs for each, at Re = 40,000. Vorticity was normalized by airfoil chord and freestream velocity,
with the near-zero levels blanked off for clarity, and limits set somewhat arbitrarily at ± 36. The region
below the pressure-side of the airfoil is also blanked, as it is in the shadow of the PIV light sheet.
While spurious vorticity (“noise”) is apparent in the instantaneous images and absent in the phase
averages, rendition of concentrated vorticity – over the airfoil suction-side and in the near-wake – is very
close between instantaneous and phase-averaged, suggesting strong periodicity. This holds even for the
discretization of vorticity concentrations in feeding sheets, especially at φ=1/2.
φ=0
φ=1/
φ=1/
47
φ=3/
Figure 42. Vorticity contours based on single image pairs for four phases within the cycle. k= 3.93, Re =
40,000.
6.1.4. Strouhal Number and Reduced Amplitude
Lai and Platzer93 point out for a NACA0012 airfoil in plunge that the production of net wake-like
or j et-like m omentum af t o f t he trailing ed ge v aries w ith t he p roduct kh (proportional t o Strouhal
number), and not k or h individually. H owever, h individually seems to govern the size of shed vortices
in t he near-wake. T he c onclusion i s br oadly t he s ame f or t he S D7003 w ith mean α = 4°, investigated
here. Figure 43 and Figure 44 cover t hree realizations of ( k, h) e ach; the fo rmer fo r kh = 0.196 (St =
0.125) and the l atter f or kh = 0.591 ( St = 0.376). In Figure 43 the starting-flow l ooks di fferent f or t he
different values of k, while qualitatively the established flow – as instantiated at the top and at the bottom
of the plunge stroke – looks broadly invariant; the difference is linear scaling of vortex size, vertical and
horizontal separation, which is essentially linear with h. In Figure 44 even the starting-flows for different
k look qualitatively alike, with the same linear scaling of feature size with respect to h. In Figure 44 there
is evidence of nonzero mean angle of the wake trajectory, akin to observations made by Jones et al.94 for
the NACA0012 a t zero mean angle of attack. While a cambered airfoil a t n onzero angle of attack
intuitively suggests a nonzero wake trajectory angle, this happens only for sufficiently high St. Evidently,
the wake follows the Strouhal number criteria identified by Jones et al. below a St threshold (~0.3, in the
present notation) the wake will be symmetric, and vice versa.
k = 1.96, h = 0.1, φ = 0.5
k =1.96, h = 0.1, φ = n*0.5
48
k = 1.96, h = 0.1, φ = n
k = 3.93, h = 0.05, φ = 0.5
k =3.93, h = 0.05, φ = n*0.5
k = 7.85, h = 0.025, φ = 0.5
k =7.85, h = 0.025, φ = n*0.5
k = 3.93, h = 0.05, φ = n
k = 7.85, h = 0.025, φ = n
Figure 43. Pure-plunge, Re = 20,000, mean α = 4°; three cases of kh = 0.196, and three motion phases: φ = 0.5
after start-up (bottom of stroke), bottom of stroke in established flow, top of stroke in established flow.
k = 5.91, h = 0.1, φ = 1
k =5.91, h = 0.1, φ = n*0.5
k = 5.91, h = 0.1, φ = n
k = 11.81, h =0.05, φ = 1
k =11.81, h = 0.05, φ = n*0.5
k = 11.81, h = 0.05, φ = n
k = 23.62, h = 0.025, φ = 1
k =23.62, h = 0.025, φ = n*0.5 k = 23.62, h = 0.025, φ = n
Figure 44. Pure-plunge, Re = 20,000, mean α = 4°; three cases of kh = 0.591, and three motion phases: φ =1
after start-up (top of stroke), bottom of stroke in established flow, top of stroke in established flow.
49
6.1.5. Start-up and Relaxation to Periodicity
While f avorable c omparison between pha se-averages an d i nstantaneous P IV su ggests r eliable
relaxation to pe riodicity a t s ome t ime a fter m otion o nset, i t r emains t o t rack how l ong t his r elaxation
process takes. Figure 45 shows the evolution of the near-wake from motion onset through 10 periods of
oscillation, again for k = 3.93, h = 0.05, R e = 60,000. The starting vortex is clearly visible at φ = ½. It
convects downstream away from the trailing edge at approximately the free-stream velocity; at φ = 1 after
motion onset, its core is ~0.8c downstream of the trailing edge. The starting transient dissipates (the flow
relaxes to periodic) by φ ~ 2. This is evidenced by the similarity of the wake at φ = 2 and φ =10.
Comparing φ = 3/2 and φ = 3/2, the first vortex pair upstream of the starting vortex – that is, φ = 3/2 – is
very similar to its companion pair at φ = 3/2. E vidently, all vortex shedding subsequent to the starting
vortex i s essentially pe riodic. T his c ontrasts with the much l onger r elaxation to periodicity f or hi gheramplitude motions at the same reduced frequency, implying a S trouhal number dependency as w ell as a
reduced-frequency dependency.
(a) φ = 0
(b) φ = 1/4
(c) φ = 1/2
(d) φ = 3/4
(e) φ = 1
(f) φ = 3/2
(g) φ = 2
(h) φ = 5/2
(i) φ = 10
Figure 45. Dye streaklines for near-wake, h = 0.05 k = 3.93 plunge; evolution of starting-flow across 10
periods of motion. Re = 60,000.
6.1.6. Nonzero Mean Angle of Attack
The present st udy w as in part an ou tgrowth o f w ork on steady-state ai rfoil la minar separation
bubbles, focusing on a cruise-type angle of attack of α = 4° 42. Most pitching/plunging studies have been
for mean α = 0° and for symmetric airfoils (NACA0012 is justifiably popular). The principal pure-plunge
case, k = 3.93 and h = 0.05, is revisited at Re = 20,000 for mean α = 0°, 4° and 21.5° (Figure 46) – the
latter being the increment of induced- α from the plunge itself, at the point of maximal vertical velocity.
The α = 0° and 4° cases are similar, with the exception that dye streaks are rather finer for α = 0°. The α
= 21.5° case shows strong interaction between the vortex shedding and the viscous wake of the airfoil, in
the bluff-body sense.
50
α=21.5º, φ = 1
α=21.5º, φ = n*0.5
α=4º, φ = 1
α=4º, φ = n*0.5
α=0º, φ = 1
α=0º, φ = n*0.5
α=21.5º, φ = n
α=4º, φ = n
α=0º, φ = n
Figure 46. Pure-plunge, Re = 20,000, mean α = 21° (top row), 4° (middle row) and 0° (bottom row); h = 0.05,
k = 3.93; left column: φ =1 after start-up (top of stroke); middle column: bottom of stroke in established flow;
right column: top of stroke in established flow.
6.1.7. Summary
The presently-reported results for a SD7003 airfoil are in good accord with results given i n t he
literature f or the v enerable NACA 0012. T his gives reason t o believe t hat t he effects o f a r elatively
intrusive model mounting, where the support rods bisect the pressure-side of the airfoil, does not greatly
detract from a f low state commensurate with 2D expectations. Small nonzero mean angle of attack and
airfoil nonzero camber do not cause significant departure from established results for NACA0012 plunge
at k = 3.93, h = 0.05. However, for the Reynolds numbers studied here, no Karman vortex street was seen
at l ow r educed frequencies, w here v iscous s hedding dom inates m otion-induced s hedding. O nce the
flowfield response has relaxed to periodicity, th ere is little d ifference in either t he n ear-wake o r in t he
flow over the airfoil suction side, between instantaneous PIV and phase-averages. R elaxation to
periodicity for k = 3.93 and h = 0.05 is quite fast, taking less than two periods of oscillation.
This fundamental study leads to important and useful conclusions for MAV designers. First, this
combined experimental and computational study serves as a step toward the ultimate goal of accurately
predicting uns teady f low f ields, a nd he nce un steady f orces a nd m oments, f or a n a ircraft w ith f lapping
wings. V erification u sing r elatively si mple test c ases i s n ecessary i n o rder t o b uild c onfidence i n new
computational methods and, verification in this instance, applies specifically to an airfoil operated in pure
plunge within the regime where the wake is symmetric. The asymmetric wake at large kh, which is also
consistent with t he l iterature, s uggests a flow pa ttern w hich i s q uite c omplex, e ven w hen t he airfoil
motion is quite simple. Second, the results clearly illustrate that the flow field for an airfoil undergoing
pure plunge, the vortex dynamics are not significantly altered by Reynolds number, within the range of
Re = 10,000 t o 60,000 . A s i n m ost t raditional a pplications, t he e stablishment of R eynolds num ber
independence in trends r elated t o t he f low field, an d h ence t he p ressure d istribution o n t he a ircraft, i s
important because the scale of a test article and fluid media may be different from that of the actual flight
vehicle operating in air. In the case of MAVs, there may be instances where a larger model might perhaps
51
be simpler to build and more convenient to use in experiments. These results show that valuable testing
might be conducted for a scaled-up, rather than scaled-down, model as long as the reduced frequency is
taken into account.
52
6.2.
Sinusoidal, Trapezoidal and Triangular Pitch; and Pitch-Plunge Comparison
6.2.1. Introduction and Problem Statement
Flapping i n nature t ends t o be n onsinusoidal, and in a ny c ase, pu rely s inusoidal m otions h ave
limited frequency c ontent. A m ore g eneral s tudy of p itch a nd pl unge i n t wo d imensions begs
consideration of nonsinusoidal motions, and fortunately this is easy to achieve with the HIPPO apparatus.
One example of nonsinusoidal motions is skewed sinusoidal time trace of pitch angle of attack, studied by
Koochesfahani97.; this produced various interesting wake vortex pairings not seen for sinusoidal motions.
An alternative a pproach, pursued here, is t o consider an amalgamation between r amp-type motions a nd
sinusoidal periodic m otions, w here t he m otion has sharp corners a nd linear s egments of v elocity, but
remains p eriodic. T he i dea i s t hat d iscontinuities i n accel eration – or a t l east, p ractically r ealizable
approximations t hereto – may result in significant departures from s inusoidal motions with identical
reduced f requency a nd e xtremes of a ngle o f a ttack, b ut w here p osition t ime h istory in finitely
differentiable. As a secondary objective we consider similarities in leading edge vortex shedding between
pure-pitch and pure-plunge oscillations. Such comparisons are not new to the dynamic-stall literature (for
example, Fukushima a nd Dadone 98), but the subject can be extended to Micro Air Vehicle applications
with more detailed information on shed vorticity, enabled by ease of flow visualization in water at high
reduced frequencies.
We p resent a sequence of ex periments at the same r educed frequency an d an gle o f a ttack
amplitude, but differing in kinematics:
1. Sinusoidal pitch, pivoting about xp = 0.25, α (t ) = α 0 + A cos(2πft + ϕ ) .
2. Trapezoidal pitch, xp = 0.25.
3. Linear-ramp or triangular pitch, xp = 0.25.
4. Sinusoidal plunge, h(t) = h0 cos(2πft), h0 =0.092, with offset angle α0 =4º.
All p itch m otions commence w ith t he a irfoil at i ts maximum a ngle of i ncidence (= 25.5º), for
continuity of pitch speed from rest. Thus the first half of the first period of motion can be considered in
isolation as a return-from-stall ramp motion.
Idealized t ime-traces of t he pi tch a ngle of a ttack f or s inusoidal, t rapezoidal a nd l inear-ramp
motions are shown in Figure 47, including the phases of motion at which PIV and/or dye-injection data
are presented; values of geometric incidence for pitch are with respect to the left-side vertical axis. T he
choice of phases at which to take data is motivated by the trapezoidal pitch, where phases “a”, “c”, “e”
and “g” are at the vertices of the trapezoid, while “b” and “f” are halfway on the downgoing and upgoing
strokes, respectively.
phase
a
b
c
d
e
f
g
h
a
α, deg
20
b
10
t/T =
0.091
0.25
0.409
0.50
0.591
0.75
0.909
1 or 0
0
g
h
35
25
15
5
-5
-15
-25
-35
f
-10
-20
c
0
0.2
e
0.4
d
phase, t/T
53
0.6
0.8
1
Figure 47. Sinusoidal (green), trapezoidal (black) and triangular (blue) time traces of pitch angle; and
sinusoidal plunge-induce angle of attack (orange). “a” – “h” mark phases where data were taken.
For the sinusoidal plunge, the quasi-steady motion-induced angle of attack is shown as the orange
curve in Figure 47, denoted with respect to the right-hand vertical axis. The quasi-steady motion-induced
angle o f a ttack a mplitude w ith h0 = 0.092 i s αe = - arctan(h U ∞ ) = 36.0º ; v s. 21.5 º pi tch geometric
incidence amplitude. h0 =0.092 is equal to the airfoil leading edge peak displacement with 21.5º pitch and
xp = 0.25. It is 90º out of phase with the pitch motions, as the plunge motion begins with the airfoil at rest
at t he t op o f the stroke; t he an gles of attack ar e w ith r espect to the r ight-side vertical axis. The p hase
difference be tween pitch a nd pl unge ha s a significant e ffect on t he startup conditions and r elaxation to
time-periodicity, but not on the time-periodic flow. Also, we note that the time trace of angle of attack for
plunge with sinusoidal variation of elevation is itself not strictly sinusoidal.
The triangular motion or linear ramp simply connects peak positive and negative pitch angles in
the sinusoid, while the trapezoidal motion matches the maximum positive and negative pitch rates of the
sinusoid. T he m otivation of t he t rapezoidal m otion i s t hat by matching t he s inusoid’s a ngle of a ttack
limits and peak rates, the principal terms of the circulatory lift in quasi-steady airfoil theory look identical
– suggesting that f lowfield v elocity and vorticity history should look s imilar, if linear c oncepts r emain
valid. The triangular pitch, on t he other hand, has a lower pitch rate of nominally constant magnitude,
with an “instantaneous” switch of direction at upper and lower extremes of angle of attack.
6.2.2. Flowfield History from Startup: Dye Injection Results
We first consider dye injection for the four classes of motion, showing evolution from startup for
8 pe riods of m otion f or t he pi tch c ases, a nd 5 pe riods of m otion f or t he pl unge. T rapezoidal pi tch i s
shown in Figure 48 and continued in Figure 49; sinusoidal pitch is shown in Figure 50 and continued in
Figure 51; and triangular pitch is shown in Figure 52 and continued in Figure 53.
In a n e ffort to m inimize the n umber o f p ictures w hile ad equately r esolving salient f eatures,
formatting of these figures is as follows: the trapezoidal and sinusoidal pitch cases are shown in phases
“a”, “b”, “c”, “e”, “f”, and “g”. P hase “d” is similar to “c” a nd “h” is similar to “g”, especially for the
trapezoidal case, where theoretically there is no motion between those respective phases. T he triangular
pitch case is shown in phases “a”, “b”, “d”, “e”, “f” and “h”, retaining the extremes of motion at “d” and
“h”. For all of the pitch cases, commencement of oscillation from a deep-stall incidence angle requires 45 pe riods t o r each t ime-periodicity; t hat is, w here s napshots of the n+ 1st cycle ar e n ot su bstantively
distinguishable from the nth. The physical period of oscillation is 1.846s, or 0.8 convective times. Thus,
relaxation to periodicity takes as many as 4 convective times. But as will be discussed in the subsequent
section, l arge-amplitude l arge-frequency pi tch ramps ha ve a subtle r elationship of flowfield e volution
with starting conditions, which is ultimately related to Strouhal number.
Dye i njection results f or 5 pe riods after s tartup for the pl unge c ase a re g iven i n Figure 54 for
phases “ a”, “ b” a nd “ d”, and c ontinued i n Figure 55 for pha ses “ e”, “ f” a nd “ h”. N ot surprisingly,
because t he motion co mmences from α0 = 4º a nd not f rom de ep-stall, t he relaxation t o t ime-periodicity
takes f ewer pe riods of o scillation than reported f or t he pi tch c ases a bove; by t he f ourth p eriod, if no t
sooner, the flow has reached periodicity.
The tw o m otions w ith d iscontinuity in angle o f a ttack r ate – trapezoid a nd t riangle – evince a
concentrated vortex shedding just downstream of the trailing edge, in phase a and especially phase f. This
is most pronounced f or the t riangle, w hich has the l argest alpha r ate discontinuity. T he sinusoid has a
more ambiguous TE vortex formation, and a strong vortex is not evident until phases b and f, where pitch
rate i s m aximum. The pr incipal distinction b etween th e trapezoidal p itch th e other tw o cases i s th e
former’s double-formation of shed vortices twice per stroke. This is clear in the dye injection images in
phase “f” (circled in red in period-8, phase-f of Figure 49), and to a lesser extent in phase “b” (circled in
red in period-8, phase-b of Figure 48. The greater clarity of vortex-doubling in phase f vs. b is ascribed to
54
the camber of the airfoil and positive offset, α0 = 4º. Vortex-doubling is apparent as early as the second
period, at least for phase f.
Figure 48. 8 periods of trapezoidal pitch: dye injection at phases a (left column), b (middle column) and c
(right column); time from motion onset is from top to bottom. Top row is first period, second row is second
period, and so forth, down to the 8th period. Double trailing vortex system is circled.
55
Figure 49. 8 periods of trapezoidal pitch, continued: sampling at phases e, f and g.
56
Figure 50. Sinusoidal pitch dye injection: phases a (left column), b (middle column) and c (right column).
Top row is 1st period, 2nd row is 2nd period,…, bottom row is 8th period.
57
Figure 51. Sinusoidal pitch dye injection, continued: phases e, f and g.
58
Figure 52. Triangular (linear ramp) pitch dye injection: phases a, b and d.
59
Figure 53. Triangular (linear ramp) pitch dye injection, continued: phases e, f and h.
60
Figure 54. Sinusoidal plunge dye injection, 5 periods of motion, phases a, b and d.
Figure 55. Sinusoidal plunge dye injection continued, phases e, f and h.
61
6.2.3. Established Flowfields: PIV Measurements
We n ext consider the sinusoidal and trapezoidal pitch cases af ter the flowfield response h as
relaxed to time-periodicity. P IV data were taken in sequences of 120 image pairs per motion phase (“a”
through “h” for trapezoidal, “b”, “d”, “f” and “h” for sinusoidal), with the first 5 pairs disregarded and the
remaining 115 ensemble-averaged for each phase (Figure 56). T he aforementioned vortex doubling for
the trapezoidal pitch is also clear from the phase-averages in the respective phases in the PIV, suggesting
that the phenomenon is strongly periodic. Evidently, the two “shoulders” at the angle of attack extremes
of the trapezoid are responsible for a shedding akin to that of a starting-vortex in impulse start. All of the
pitch cases evince a LEV forming at or near the top of the pitch stroke. From the dye injection results, the
strength of this LEV is somewhat greater in the trapezoidal than the sinusoidal, and in turn appreciably
greater t han for the t riangular pitch. The t riangular pitch’s w eaker L EV i s intuitively a ttributable to a
lower peak pitch rate. More properly, for the trapezoidal pitch one should speak of a LEV pair rather than
a single vortex, albeit the positive-signed concentration of vorticity is much weaker than the negative. It
is r easonable t o su rmise that f or the trapezoid an d sinusoid the L EV remains su fficiently co herent t o
interact w ith th e trailing v ortex s ystem b y th e tim e th at i t a rrives a t the t railing e dge. T he tr iangular
pitch’s LEV, being weaker, does not have such an obvious relationship with the TE vortex system.
Phase a
Phase b
Phase c
62
Phase d
Phase e
Phase f
Phase g
Phase h
Figure 56. PIV phase-averaged vorticity contours for trapezoidal (left) and sinusoidal (right) pitch, Re =
10,000; 8 phases of motion (trapezoidal) and 4 phases (sinusoidal).
63
6.2.4. Discussion: Pitch-Plunge Comparison and Other Observations
Next, we turn to comparison of sinusoidal pitch and sinusoidal plunge. Pitch-plunge comparison
is us eful i n t he c ontext of e xtending qua si-steady c oncepts. P erhaps through de eper unde rstanding of
pitch and plunge as canonical motions, it will be possible to “explain” all 2DOF airfoil oscillations, in the
sense o f pi tch a nd p lunge s panning t he s pace of a ll pos sible 2D OF os cillations. W hile i t remains
premature to justify such lofty ambition, a preliminary extension relevant to massively-separated cases is
assessment of what plunge amplitude i s r equired t o pr oduce LEV s trength s imilar t o t hat observed in
pitch. Matching plunge-induced and pitch-geometric angle of attack was shown to fail to give matching
leading edge separation105, but matching displacement of the airfoil leading edge between the pitch and
plunge oscillations shows promise. As noted in Figure 47, the resulting induced angle of attack in plunge
is far larger than the geometric angle of attack in pitch, nor does sinusoidal variation of plunge position
produce truly sinusoidal angle of attack variation at these high motion rates.
Comparing pha se “ d” of the pl unge, which corresponds l oosely t o phase “b” of t he pitch c ases
(referring to the angle of attack time traces in Figure 47), it is evident that the LEV is very similar to that
of the sinusoidal pitch, as shown in Figure 50. This holds for all phases where the LEV has not convected
far from the leading edge, and breaks down as the LEV progresses further downstream. The wakes are in
fact entirely di fferent be tween t he p lunge a nd a ny of t he p itch c ases. F or t he pl unge, t he w ake i s a
reverse-Karman st reet95 with p ositive an d n egative c oncentrations of v orticity. The idea of L EV
downstream convection and interaction with the TE vortex system resembles the “shear layer vortex” of
McAlister and Carr96, and Walker et al 99. H owever, the shear layer vortex and LEV (or more properly,
dynamic stall vortex) form essen tially simultaneously, whereas in t he present work we find that t he
vorticity concentration on the airfoil suction side just upstream of the TE is the leading edge vortex from a
prior cycle of oscillation.
We c onclude w ith a brief m ention o f lift coefficient c omparability between t he f our cases.
Because HFWT force balance results were not available for these cases, the discussion would be limited
to the parallel computational results, as reported in Ol et al.106 But this is not shown for brevity and for
purposes of limiting this report to in-house experiments only, wherever possible. We mention in passing
that ( 1) the s inusoidal-trapezoidal-triangular p itch m otions evince differences i n l ift co efficient m ostly
limited to spikes associated with noncirculatory force; these are discussed in detail in a subsequent section
on nonperiodic motion. Also, (2) the sinusoidal pitch and sinusoidal plunge show roughly comparable lift
coefficient time h istories, su ggesting – but no t p roving! – that similarity o f L EV d evelopment has
correlation with similarity of lift coefficient time history.
We ne xt t urn t o a k inematically s imilar s et o f m otions, but a t m uch l ower r educed f requency,
where noncirculatory forces are negligible, quasi-steady approximations are tantalizingly at tractive, and
both wind tunnels and water tunnels can accommodate the subject motions.
64
6.3.
Further Observations of High-Frequency Sinusoidal Pitch
In t he pr evious s ection, sinusoidal pitch o scillation was s tudied i n onset f rom m otion s tartup,
through r elaxation to pe riodicity. R oughly 8 pe riods ( or l ess) w ere n ecessary t o r elax t o p eriodicity.
Does this always happen, and how does the startup transient vary with the starting position of the airfoil?
Largely by accident, we discovered that the starting phase makes no difference in the eventual geometry
of the wake, but it does make a large difference in how long it takes to reach that wake form, and how the
evolution from startup to final periodicity unfolds. We first document this with dye injection, and then
with PIV.
6.3.1. Dye Injection Results
Flowfield de velopment f rom s tartup is seen f rom t he systematic d ye i njection i n Figure 57, f or
four different phases of motion (0 degrees, 90 d egrees, 180 degrees and 270 degrees of phase). For the
third column in Figure 57, the skewed up-going wake with trailing edge vortex pairing is evident as early
as the 10th period of oscillation, if not sooner. F or the second column, such a wake is not attained until
the 15 th or 20 th period. For the first column, the skewed wake becomes evident at around the 25th period.
Finally, for the fourth column, the skewed wake is not evinced until the 55th period. Until then, there is an
intermediate form of wake – a fairly symmetric r everse K arman vortex st reet, with no clear upwash or
downwash. That is, there is a starting transient that takes about 2 periods to relax to periodicity, which is
the reverse Karman wake. Thereafter there is a second time scale, on the order of 50 periods, before the
skewed wake is manifested.
Period 0
Period 1
Period 2
Period 3
Period 4
65
Period 5
Period 6
Period 10
Period 15
Period 20
Period 25
Period 30
Period 40
Period 50
66
Period 55
Figure 57. Dye injection for 4 different starting phases of pure-pitch motion; k = 3.93, pivot about x/c = 0.25,
Re = 10K, dye injected at trailing edge; periods of oscillation as marked, from start of motion.
6.3.2. PIV Results
Particle image v elocimetry co nfirms the ab ove assertions. Figure 58 shows instantaneous P IV
vorticity contours (level is -36 to +36) – that is, with no ensemble- or phase-averaging – for one starting
condition, b ut sampled at f our phases p er pe riod. Each r ow of Figure 58 is on e pe riod; 1st period, 2nd
period, a nd s o forth, dow n t o t he 100 th period. In t he f irst period, one sees the evolution of the staring
vortex, the first vortex of the stroke reversal, and so forth. A t this point an LEV is forming (rightmost
column) but is not convecting downstream. This situation changes by the 20th or 30th period, where there
is a definite LEV-type of vortical structure on the airfoil suction side. It is also by around the 30th period
that the reverse Karman vortex street has finally given way to the upswept paired-vortex wake.
P1
P2
P3
P5
P 10
P 20
67
P 30
P 50
P 100
Figure 58. Instantaneous vorticity PIV images; phase “a” (1st column), “b” (2nd column), “c” (3rd column)
and “d” (4th column); periods, in rows from top to bottom, are: 1, 2, 3, 5, 10, 20, 30, 50 and 100.
What causes the switching from reverse Karman vortex street to skewed paired vortex wake, and
how is the starting phase (see previous subsection) responsible for the number of periods required before
this wake switching? And why would the wake be upswept, when the airfoil is cambered and has a mean
positive angle of attack, implying positive mean lift and therefore a necessary downwash in the wake? At
present these questions have not been answered. We also know (not reported here) that for a flat plate,
the eventual flowfield history does depend on the starting phase of motion, in the sense that the wake may
become downswept or upswept. B ut the pairing of TE vortices does seem to be universal regardless of
the airfoil sectional shape. A r everse-Karman vortex s treet a t high S trouhal number i s but a t ransitory
phenomenon.
Arguably, t hese are academic q uestions. MA Vs d o not f lap at such h igh f requency, an d h ighfrequency f lappers have a m uch more co mplicated st roke kinematics, w hich i s p robably n onsinusoidal,
and which probably extends to much larger angles of attack. Aeroelastic problems, which can be at this
reduced f requency or h igher, a re likely of m uch s maller amplitude. W e t herefore now t urn to l ower
frequencies and higher amplitudes in our study of periodic sinusoidal oscillations.
68
6.4. Low-Frequency Pure-Plunge and the Role of Transition for Deep Stall
Problems
We leave for now the high-frequency problems that can really only be studied in liquid flows, and
turn t o lower-frequencies, w here both w ind t unnels and w ater tunnels can c ontribute. T he objective i s
cross-facility comparison by means of canonical pr oblems; o f course, t his a lso includes c omparison
between experiment and computation; we are interested in seeing how standard off-the-shelf codes might
cope w ith t he r ole o f t ransition, l ess so i n m odeling bounda ry l ayer phy sics itself, than i n s eeing how
transition p rediction a ffects t he ov erall f low separation pr ediction. The num erical results, a nd results
from other experiments, are not presented in this report, as we focus only on the HFWT. However, the
different iterations o f th e same e xperiment in th e H FWT g ive in sight in to the r ole o f t ransition. F ull
coverage of experimental-computational comparison for these problems is reported by Ol et al 100.
6.4.1. Introduction and Problem Definition
We consider the following general kinematics for combined pitch and plunge:
plunge: h(t ) h=
=
0.5 c cos(0.5U ∞ t / c)
0 c cos(2π ft )
pitch: α (t ) = α 0 + A cos(2π ( ft + ϕ )) = 8° + 8.42° cos(0.5U ∞ t / c + π / 2)
The time t races o f effective an gle o f attack f or co mbined pitch-plunge a nd f or pure plunge a re
given in Figure 59, which is the output of the HIPPO motor encoder tape – not theoretical prescription of
motion. Our choice of reduced frequency, k = 0.25 =ωc/2U∞ = πfc/U∞, was motivated in part by cruisetype conditions for flapping flight of birds. Although the Strouhal number, St = 0.08, is below the range
for m aximum pr opulsive efficiency for m ost f lyers in na ture 101, t he pr esent f low c onditions a re on t he
upper-end of t he dy namic-stall l iterature f or h elicopter b lade a pplications102, f or w hich t he t raditional
analytical o r phe nomenological m odels in aeronautics t end t o f ocus. A s is o ften t aken i n applications
motivated by pr opulsive e fficiency of pi tch-plunge85, pi tch l eads p lunge by one qua rter of phase (φ =
0.25) and thus the airfoil “f eathers”, w ith t he g eometric p itch angle p artially can celling t he p lungeinduced a ngle o f a ttack, arctan(h U ∞ ) . T he amplitude of p itch, A = 8.42º , w as c hosen from t he
expression λ ≡
A
. λ is the ratio of pitch angle amplitude to the peak angle of attack induced

arctan(hmax U ∞ )
by the plunge motion; we chose λ= 0.6,which as will be shown below, leads to shallow dynamic stall. λ
=0, on the other hand, is a pure plunge, which produces a strong leading edge vortex, and is more akin to
deep dynamic stall.. Variation of λ is an option for parameter studies (not pursued here) for search for lift
and t hrust efficiency, w hile keeping S trouhal number c onstant. Alternatively, S trouhal number c an be
varied (by changing reduced frequency or reduced amplitude) and λ varied such that the effective angle of
attack history, when disregarding pitch rate effects, is kept constant.
Figure 59 shows the plunge trajectory (green curve), total effective angle of attack in pure-plunge
(black curve), pitch geometric angle of attack (purple curve) and total effective total angle of attack for
combined pitch-plunge (blue curves). F or pitch-plunge, the total effective angle of attack time-trace, αe,
straddles the s tatic stall v alue of ~ 11 º; t his i s just t he s um of t he pi tch a nd pl unge cosines w ith
appropriate pha se s hift. B ut αe, c an be taken t o include t he e ffect of pi tch rate, w hich depends on t he
pitch pi vot p oint l ocation, by s umming al l o f the c omponents i nside t he b rackets in t he t hird t erm o f
Equation 1; this is the dashed blue curve in Figure 59. The difference, vs. disregarding the effect of pitch
pivot point location (solid blue curve) is a phase shift of ~0.05t/T. With inclusion of the pivot effect, the
limits on αe become 2.03º < αe < 14.03º, whereas for pure-plunge they are -6.0º < αe < 22.0º.
69
h(t)
plunge αe
geometric pitch α
pitch-plunge αe
pitch-plunge αe with pivot eff
20
0.5
h(t)
0.4
α, deg
0.3
15
0.2
0.1
10
0
-0.1
5
-0.2
0
-0.3
-0.4
-5
-0.5
0
0.25
0.5
t/T
0.75
1
Figure 59. Motion kinematics and effective angle of attack time history for pure-plunge and
combined pitch-plunge.
6.4.2. Re = 60,000 Results
Velocity and vorticity contour plots from PIV in the HFWT are shown in Figure 60 and Figure
61. Figure 60 is an o lder d ata se t, an d Figure 61 is a n upda te. For v elocity, we u se t he n ormalized
streamwise component, u/U, as the metric of choice. Vorticity is limited to the out-of-plane component,
and normalization is by free-stream velocity, U, and airfoil chord, c. For velocity the contour levels are 0
to 1.5, while for vorticity they are -36 to +36.
70
Figure 60. PIV entry #1; phases phi = 0, 90, 180 and 270.
71
Figure 61. entry #2; phases phi = 0, 90, 120, 150, 180, 210, and 270.
The reason for having two data sets is the implications of other experiments and computations run
by pa rtners s tudying t he s ame c anonical pr oblem, under t he N ATO R TO T ask G roup A VT-149,
“Unsteady Aerodynamics for MAVs”. The various experiments all largely agreed in how and when the
LEV forms on the downstoke, but disagreed in subsequent flowfield evolution. Indeed, this is exactly the
observation for the above two data sets. The later data set shows suction-side separation washing away
earlier i n t he p lunge st roke, w hile t he o lder data se t sh ows a large l ow-speed r egion l ingering l onger.
Why? Both data sets have the PIV light sheet nominally at the ¾ span location, to be equidistant from
two so urces o f disturbances: t he H IPPO p lunge r ods, an d the test section s idewalls. H owever, the
position of the light sheet may have been somewhat different between the two, and that small difference,
deemed i nsignificant a t t he t ime, c ould h ave be en r esponsible f or t he a forementioned f lowfield
differences. Other e xperiments, w hose r esults are not s hown in t he t his report, s how e ven m ore
separation a t t he dow nstroke b ottom; b ut i n al l o f t hese ca ses t he P IV l ight sh eet w as a t t he m odel
centerplane, not the ¾ span location. W e conclude, at least tentatively, that the HIPPO plunge rods are
not t he culprit, b ut t hat there is a spanwise v ariation i n f low se paration e ven f or w all-to-wall models.
That is, large flow separations are never truly 2D. T his is further illustrated by t he spanwise-view d ye
injection in Figure 62. At the top of the plunge stroke, phase t/T = 0, the dye streak is thin and of minimal
spanwise e xtent, but s panwise e ruption a ccompanies f ormation o f t he L EV a t t /T = 0.25, br oadening
further as the L EV l oses c oherence a nd c onvects downstream. L EV f ormation, l et alone shedding a nd
downstream convection, is seen to be a 3D process. By t/T ~ 0.5 the spanwise extent of the dye streak is
larger than o ne ch ord-length. T his i s not , in i tself, p roof that m inor s panwise r elocation o f t he
interrogation plane accounts for large changes in the evinced flow at t/T = 0.5 between one PIV data set
and another, but it does illustrate the strongly 3D nature of the flow. R eattachment at the leading edge
brings r eturn t o nom inal t wo-dimensionality upon commencement of t he ups troke. B y t /T = 0.75, t he
dye-tagged flowfield region over the suction side is again nominally 2D.
We mention he re w ithout proof (see O l e t al.100) t hat b oundary l ayer t ransition p lays at most a
minor role in this flow. Much akin to classical dynamic stall, there is a strong LEV formed halfway down
the p lunge s troke. B ut s ince c lassical d ynamic st all r esearch i s m otivated by m uch h igher R eynolds
number applications, before considering lift time histories – which of course matter more for applications
than do niceties of flowfield details – we consider, at least in a limited sense, Reynolds number effects.
72
t/T=0.333
t/T=0
t/T=0.125
t/T=0.417
t/T=0.5
t/T=0.583
t/T=0.75
t/T=0.25
Figure 62. Planform view of dye streaks, over one period of motion; dye injected at ¾ span location, near
nominal spanwise position of PIV light sheet. Re = 60K
6.4.3. Reynolds Number Effects
Figure 63 compares Re = 20K, 30K and 60K dye injection. To lower the operating Re, the tunnel
is run more slowly, and the rig and the dye discharge rate are proportionately slower.
t/T=0
t/T=0.125
t/T=0.25
t/T=0.333
t/T=0.375
73
t/T=0.417
t/T=0.5
t/T=0.583
t/T=0.75
Figure 63. AFRL water tunnel Dye injection for pure-plunge, Re = 20K (left column), 30K
(middle column) and 60K (right).
At the trailing edge, at Re = 30K and especially at Re = 20K there is a discernable trailing edge vortex at
t/T = 0.375-0.417, with a region of reverse flow just ahead of the trailing edge. At Re = 60K, no TEV is
clearly visible in the dye injection, but it was strongly apparent at t/T = 0.417 in the PIV. The near-wake
at the top of the plunge stroke also shows a discernable Re-effect, with coherent vortices seen for Re =
20K. In going from t/T = 0 to 0.125 to 0.25, the suction-side dye concentrations splits, as it were, into a
leading-edge and trailing-edge portion, the former coagulating into the LEV at t/T = 0.25. Towards the
bottom of the plunge stroke, the pocket of dye lacuna just aft of the leading edge is smaller for higher Re,
further suggesting that this region can be thought of as a laminar separation bubble.
6.4.4. Aerodynamic Force Coefficients
For p ractical MAV ap plications w e are m ore i nterested in a erodynamic f orce coefficients t han
necessarily in the details of the flowfield; but we must know the flowfield well enough to predict force
coefficients accurately a nd on a s ound p hysical basis, r ather than from he uristics or curve fits. I n t his
section, experimental measurements of lift coefficient in the water tunnel are compared with theory and
with a large set o f co mputations f rom t he P I’s v arious co llaborators. These i nclude L arge E ddy
Simulations from elsewhere in AFRL/RB and from the Canadian National Research Council; Reynoldsaveraged N avier Stokes from t he U niversity o f Michigan, Middle E ast Technical University, T echnical
University o f D armstadt; an d sem i-empirical m ethods f rom U niversity of T oronto. H FWT f orce
measurements use the FBG balance.
74
The most basic quantity of interest is lift coefficient, and indeed one hopes to obtain reasonably
correct l ift c oefficient time h istory a t R e = 60K a cross t he f ull r ange o f a nalytical and c omputational
methods, including the lower-order methods. Figure 64 shows computational and measured lift coefficient
time history at Re = 60K. The encouraging result is that all curves qualitatively follow the same trend.
Also i nteresting i s that the l ift time history i s essentially si nusoidal, despite t he obvious presence of an
LEV and its putative dynamic-stall effects on lift, which ought to manifest itself as a large hysteresis for
lift plotted vs. angle of attack. Qualitatively the behaviour is surprisingly not far from the inviscid 2πα,
despite the fact that peak effective angle of attack is more than twice that of static stall.
The present experiment and A FRL 3 D LES a re v ery cl ose, as w ould b e expected f rom a h ighfidelity computation. NRC 2D LES essentially splits the difference between AFRL LES and RANS, as is
to be e xpected from t he r esolution o f t he N RC c omputation. B ut t he m ost r emarkable f act is that
Theodorsen’s f ormula (dashed b lack cu rve i n Figure 64) also f ollows v ery cl osely w ith t he 3 D L ES
computations, slightly underpredicting dynamic lift at the max effective angle of attack (t/T = 0.25) and in
turn o verpredicting lift o n t he f irst ha lf o f t he upstroke ( t/T = 0.5 t o 0.75) . Thus t he two extremes of
calculation fidelity ap pear to p erform comparably well! R ANS co mputations a re also in reasonable
agreement, though they tend to overpredict loss of lift at the plunge downstroke (t/T = 0.5), and in general
show a slightly stronger dynamic stall than does the LES; in other words, a fuller hysteresis loop. The
vortex particle method, on the other hand, overpredicts retention of lift during the upstroke. C uriously,
the large difference in velocity/vorticity contour plots between the AFRL 2D and 3D LES and between
AFRL and NRC LES does not correspond to much difference in the lift time history.
Figure 64. Lift coefficient time history, SD7003 pure-plunge, Re = 60K; plotted vs. motion phase (left)
and effective angle of attack (right).
It i s o f c ourse p ossible t hat p eriod-to-period v ariations i n t he ex periment a re sm eared in t he
ensemble average, in the sense that dynamic-stall peaks and troughs in the lift coefficient time history in
any one period are attenuated in the average because they vary randomly from period to period. This is
disappointing f rom t he v iewpoint of fundamental f luid m echanics, bu t f rom t he v iewpoint of applied
engineering one concludes that dynamic stall effects are uncorrelated and therefore unimportant, and the
lift time history is quite sinusoidal, with small phase lag.
We ne xt turn t o t he p itch-plunge pr oblem, w here angles of a ttack a re lower, a nd laminar to
turbulent transition matters significantly more.
75
6.5. Low-Frequency Pitch-Plunge and the Role of Transition for Shallow Stall
Problems
6.5.1. Introduction and Problem Definition
Here we generalize the motion from the previous section to consider a combination of pitch and
plunge. In t he context of Figure 59, this is the b lue an gle o f a ttack cu rve. Whereas t he p ure-plunge
motion was motivated by the desire to observe a dynamic-stall case and a strong LEV, the pitch-plunge
case is m otivate b y co nsiderations o f ef ficient f lapping-wing pr opulsion. T hus, t he e ffective a ngle of
attack should never venture into too deep of a stall.
6.5.2. Re = 60,000 Results
Particle i mage v elocimetry r esults for m ean st reamwise v elocity co mponent and out -of-plane
vorticity c omponent a re shown f or three successive d ata sets, i n Figure 65, Figure 66, a nd Figure 67,
respectively. The motivation for three data sets was again the desire to better compare with other labs’
experiments. B ut a nother r eason w as t he s trange d isparities i n d ye i njection r esults, sometimes f rom
adjacent runs. Why would in one run the separation even towards the bottom of the downstroke be well
aft of the leading edge, while in a run taken literally minutes later, the separation would commence almost
at the leading edge? To be sure, in no cases is there a LEV. All results are topologically identical. But in
the context of boundary-layer-type measurements, where one is interested in precise data and regions of
large f lowfield g radients a re t hin an d close t o the m odel w all, the ev inced d ifferences in su ction-side
separation were significant.
76
Figure 65. PIV, first data series, phases phi = 0, 90, 180 and 270.
77
Figure 66. PIV, second data series, phases phi = 0, 45, 90, 135, 180, 225, 270 and 315.
78
Figure 67. PIV, third data series, phases phi = 0, 90, 120, 150, 180, 210 and 270.
6.5.3. Thoughts on the Role of Transition
Another means of assessing the role of turbulence and transition is to plot turbulent kinetic energy
contours. It is reasonable to surmise that for Re ~ 60,000, separation should lead to turbulence. Attached
boundary layers may be laminar, but if there is large region of separated flow, it can not remain laminar
for long. Indeed, in Figure 68, the comparison of turbulent kinetic energy contours in one realization of
the flowfield vs. another – both at t/T – shows significant variation. The one with larger separation shows
larger tu rbulent kinetic e nergy inside t he sep arated region, b ut t hat m eans t hat t he o verall f low i s l ess
turbulent, for o therwise t he sep aration w ould h ave b een sm aller. M eanwhile outside of the sep arated
region, turbulent kinetic energy is comparable, and small – so there is not an obvious source of ambient
79
disturbances in the one case and not in the other, at least not at the amplitude discernable from the contour
plot. This does not explain why one realization shows more separation than other, but does show that two
identical m otions w ith t he sam e model i n t he sam e f acility can h ave l arge v ariation, an d t hat su ch
variation is not a fluke.
Unlike i n the p ure-pitch c ase, there is good r eason to di scount t he role of s panwise v ariations.
Figure 69 is the analog of Figure 62 shown earlier for pure plunge. For pitch-plunge, there is no LEV and
no large spanwise extent of dye spread, until the bottom of the downstroke; and even that only occurs at
x/c = 0.5 a nd further aft. I t thus seems reasonable that the apparent spanwise extent of separtion would
not de pend strongly on s panwise l ocation, and therefore t he v airous d isparities f rom r un t o run a re
unlikley to be due from slight variation of PIV light sheet location.
Figure 68. PIV-derived planar turbulent kinetic energy contours, AFRL data sets, phase phi = 180
(bottom of plunge downstroke): “small” separation (left) and “large” separation (right).
t/T=0.25
t/T=0.333
t/T=0.375
t/T=0.5
t/T=0.583
t/T=0.75
t/T=0
Figure 69. Planform view of dye streaks for pitch-plunge, over one period of motion; dye injected at ¾ span
location, near nominal spanwise position of PIV light sheet. Re = 60K.
As a further check on the role of transition vs. other possible causes for explaining the differences
in PIV contour plots, we turn to examination of Reynolds number effects.
6.5.4. Reynolds Number Effects
Figure 70 compares dye injection results at Re = 10K, 30K and 60K. Care was taken to select the
“small” version of flow separation at Re – 60K. A t Re = 30K and below, no r un-to-run variation was
observed.
t/T=0
80
t/T=0.25
t/T=0.333
t/T=0.5
t/T=0.75
Figure 70. dye injection, Re = 10K (left column), 30K (middle column) and 60K (right column; phases
phi = 0, 90, 120, 180 and 270.
At Re = 10K, the flow over the airfoil suction side is never fully attached. Towards the top of the
plunge stroke, the dye streakline smoothly bounds an open region of separation, as opposed to a laminar
separation bubble; but care is required in interpretation, since the dye is slightly heavier than water, and
drift dow n ( down i n t he l ab f rame i s up i n t he a irfoil f rame). B y t /T = 0.25, w here effective a ngle of
attack is m aximum, la rge d isturbances a kin to Kelvin-Helmholtz r ollers a re v isible, bo unding a br oad
separated region. By t/T = 0.5 the loss of coherence of such structures suggests shear-layer transition. By
t/T = 0.75 a well-organized streakline bounds the separation region all to way to the trailing edge. At Re
= 20K (not shown), the suction-side flow separation is thinner and the aforementioned rollers at t/T = 0.25
are no longer discrete, but fully attached flow is still not present at any time. By Re = 30K, the separation
at 0.75 < t/T <0 (or 1.0) closes into what might be termed a laminar separation bubble (LSB). The LSB is
much smaller but still present at Re = 60K.
The Re = 30K=40K region is a qualitative divide, below which flow separation is largely “open”,
and above which, the boundary layer varies from attached turbulent to LSB-dominated, to mild separation
in the second half of the downstroke. T he extent of this separation at Re = 60K is a strong function of
transition processes – perhaps ambient turbulence, perhaps some other source. How separation develops
in this region d epends, in all l ikelihood, not on ly on a mbient c onditions a t the t ime, bu t o n incipient
instabilities in t he bo undary l ayer e arlier i n t he do wnstroke. I n s um, i t i s ha rd t o say how i mposed
dynamics couples with boundary layer physics t o affect t he f low separation history. T hinking towards
MAV applications, the disturbance environment is likely to be stronger than in the water tunnel, because
of propwash, flexible surfaces and so forth. So rather than attempting to delve deeper into boundary layer
physics, let us turn to estimation of lift coefficient.
6.5.5. Aerodynamic Force Coefficients
Force data (Figure 71) were co llected f rom a br oad range of c omputations – and f rom H FWT
experiments. Lift coefficient time history is compared in Figure 71. The quasi-steady approximation and
81
Theodorsen’s formula are the simplest models, followed by the vortex-particle method, then by the two
RANS computations, from the University of Michigan and METU, and finally by the LES computation
(NRC). It is here that the argument about sensitivity to transition comes fully to the fore. T he METU
RANS c omputation ( details n ot sh own) is “ laminar” an d p redicts a l arge se paration; i ndeed, ev en a n
LEV. The UM computation is fully-turbulent. The present measurements, using the FBG balance, fall
somewhere in between.
Another i mportant que stion i s t he r ole of classical i nviscid p redictions. The qua si-steady
approximation performs fairly well on the upstroke, but poorly on the downstroke. Theodorsen’s formula
does better. It overpredicts lift in t/T < 0.25 < 0.75, and interestingly enough, it appears to be worse for
pitch-plunge than for pure-plunge! This is counterintuitive, because pure-plunge has the less planar wake,
and much l arger separation. T he resolution to this dilemma i s t o realize that LEVs regularize the flow
separation and result in behavior more akin to attached flow. But this explanation should not be taken too
far, for otherwise the quasi-steady approximation would have performed better on the downstroke.
Figure 71. Lift coefficient time history, SD7003 pitch-plunge, Re = 60K; plotted vs. motion phase (left)
and effective angle of attack (right).
In su m, t he ca se o f m oderate dynamic st all, h ere realized through λ=0.6 pitch-plunge, e vinces
largely attached flow, but is quite complex because of t he coupling with laminar t o turbulent transition
and the forcing f rom t he motion dynamics. O f course, further work is merited, i n parameter studies of
different values of λ, frequency and so forth. In particular one needs to assess whether the same effective
angle of attack history, produced by different combinations of λ, k and h, produces similar lift history.
Preliminary ass essment shows t hat t he f lowfields ar e i ndeed very si milar, b ut h ave a difference
relationship of vortex formation vs. phase of motion.103
We n ext t urn t o co nsideration o f different sectional g eometry – perhaps t he more fundamental
case of a flat plate, with the same kinematics as from the above two sections.
82
6.6.
Sinusoidal Pitch and Plunge of a Flat Plate
Our s econd s et of low-frequency case s i s for flat p lates, n ominally o f 3 % t hickness an d r ound
(semicircular) edges. In some sense the flat plate is a more fundamental problem than the airfoil, because
apart f rom t he i mmediate vicinity o f t he l eading ed ge, t here i s n o p ressure g radient d ue t o t he m odel
geometry itself. Plates are also easy to manufacture f or experiments, while the round trailing ed ge
somewhat s implifies the computational grid. And plates are a c loser analog t o membrane-type a irfoils
and other thin airfoils more likely to be encountered in flight articles in the Re ~ 10K range, but camber
As with the airfoil, the plate geometry is nominally 2D, with the model tip gaps of less than 1mm.
The airfoil cases are deeply concerned with understanding the role of boundary layer transition in
unsteady a erodynamics, bu t i n m any M AV a pplications t ransition i s pe rhaps of s econdary i mportance.
Wings tend to be thin, with sharp edges; and transition only occurs in the wake, or in the late evolution of
large separated structures. For a flat plate with round leading edge (as opposed to say a “super-ellipse”),
presumably t ransition w ould oc cur ne ar t he l eading e dge, a nd w ould be fixed across a br oad range of
cases. This indeed turned out to be true.
6.6.1. Pitch-Plunge Case
PIV velocity and vorticity contours at Re = 60K for the pitch-plunge case are shown in Figure 72,
while dye injection results for Re = 20K and 60K are in Figure 73.
83
Figure 72. PIV, phases phi = 0, 90, 180 and 270 degrees.
Figure 73. Dye injection for pitching-plunging flat plate, Re = 20K (left column) and Re = 60K (right
column); phases phi = 0, 45, 90, 120, 150, 180, 210 and 270.
84
6.6.2. Pure-Plunge Case
We next turn to the pure-plunge case. Unfortunately only dye injection is available for this case,
and i t is s hown i n Figure 74 (Re = 20 K a nd 60 K, analogous t o Figure 73). As e xpected, R eynolds
number effects are benign. The Re = 20K evinces discrete rollers in the near-wake at t/T = 0.25, whereas
in the Re = 60K a continuous mixed wake is apparent. In general the lower-Re case h as clearly defined
dye st reaklines, w hile the h igher-Re case has mixing. It is n ot entirely c lear whether th is is p artially a
figment of the flow visualization technique (diffusivity of dye), or is entirely a statement about turbulent.
In any case, there is no discernable effect on the LEV or the overall extent of flow separation.
t/T=0
t/T=0.25
t/T=0.25
t/T=0.333
t/T=0.375
t/T=0.417
t/T=0.5
t/T=0.583
85
t/T=0.75
Figure 74. Dye injection, flat plate in pure-plunge, Re = 20K (left column) and 60K (right column. Snapshots
from phases of motion as noted.
As c ompared t o t he S D7003 a irfoil in pur e-plunge, t he d ifferences a re n ot g reat; t he f lat-plate
LEV is s omewhat larger a nd more diffuse t han f or the airfoil, a nd t he low-speed r egion on the s uction
side towards the bottom of the downstroke persists less. This may mean (but has not been shown!) that
the flat plate has less spanwise variation than the airfoil.
6.6.3. Lift Coefficient Comparison
As w ith t he ai rfoil, w e co mpare t he F BG b alance m easurements f rom t he H FWT w ith a w ide
range of computational results. Unfortunately by the time that these FBG measurements were taken, the
balance w as n o longer b ehaving w ithin sp ecifications, w hence the r eported d ata a re t o b e t aken w ith
rather more scepticism than is normally appropriate for such things. The results, such as they are, are in
Figure 75. F or t he pitch-plunge cas e, t he F BG m easurement t racks cl osely with t he v arious R ANS
computations, but for the pure-plunge case, the FBG measurement has an overshoot. The basic trends are
similar to those of the airfoil: sinusoidal lift (even more so than for the airfoil, as expected); unlike for the
airfoil, the “laminar” and “turbulent” RANS computations agree closely, suggesting even further that for
the flat-plate, Re dependency is absent.
Figure 75. Lift coefficient for pitch-plunge (left) and pure-plunge (right) flat plate, Re = 60K; various
computations, and FBG force balance data (blue curve).
86
6.7.
Sinusoidal Pitch and Plunge of an AR=2 Flat Plate
6.7.1. Introduction and Motivations
Perhaps the most natural generalization from wall-to-wall models (in experimental facilities) and
spanwise-periodic boundary conditions ( in computations) i s t he f inite-wing of hi gh a spect ratio. B y
systematically reducing aspect ratio from so me l arge but f inite value, towards ever smaller values, it is
possible t o co nstruct a co nsistent p assage i nto 3 D f rom 2D . T his i s s ensible, f or e xample, i n terms of
understanding the f lapping-flight of large b irds (see Chapter 1 ), w hich tend t o be of hi gh a spect ratio.
However, in an experimental facility this introduces t he p roblem of blockage or very low Reynolds
number. To avoid blockage, the wingspan needs to be some fraction of the test section width, and at high
aspect ratio this severely limits the chord. I n turn the Reynolds number, based on chord, becomes very
low. B ut v ery l ow R eynolds num ber pr oblems, be sides be ing i nconsistent w ith t he f ocus of e arlier
chapters, tend to be of comparatively low aspect ratio, as is the case for most insects. In computation, full
resolution of high aspect ratio means a grid much longer in the spanwise than in the streamwise direction,
which r aises problems of c omputational size, if we w ish t o maintain hi gh resolution i n t he s treamwise
direction.
The alternative is to consider low aspect ratios. This is more amenable to investigation, but more
importantly, i t i s esp ecially interesting b ecause o f the st rong i nteraction ex pected at low a spect ratio
between l eading ed ge v ortices and w ingtip v ortices, w here f or ex ample t he l atter m ight st abilize t he
former t hrough s panwise p ressure g radients. L ow a spect ratio w ings unde rgoing various l ongitudinalplane manoeuvres are expected t o evince a q ualitatively d ifferent flow structure an d l oads t ime h istory
from those of the same sectional geometry, but in 2D. A full treatment of the problem requires detailed
3D v elocimetry, w hich un fortunately i s b eyond t he scope of this s tudy. I n ke eping w ith the abovereported r esults, f lowfield d ata ar e p resented i n s treamwise-parallel p lanes, typically at t he ¾ -span
location of the model. The featured configuration is the rectangular-planform flat plate of aspect ratio 2,
with round edges on its entire periphery. Both the pure-plunge and the pitch-plunge case are considered.
The c anonical R eynolds n umber i s now 40, 000 r ather t han the 6 0,000 for the w all-to-wall cases, a s
blockage problems are reduced with a smaller model, and thus a smaller chord.
The sectional geometry of a thin flat plate with round edges was selected to deemphasize the role
of boundary layer transition and to at least partially solve the problem of how to treat the airfoil section at
the wingtips. Such shapes are also easy t o manufacture, and i n general easy to grid. Looking t owards
future work, they are amenable to generalization to flexible structures, such as membranes.
6.7.2. Flowfield Results
Pure p lunge a nd pi tch-plunge PIV-derived st reamwise v elocity an d v orticity c ontours for t he
AR=2 rectangular plate are given in Figure 76 and Figure 77, respectively. PIV data in all cases are at the
¾-span location. The most striking difference between these results and the corresponding motions of the
wall-to-wall plate are the absence of a discernable LEV in the pure-plunge case. In general the extent of
flow separation f or t he A R= 2 p late i s sm aller t han f or t he w all-to-wall p late, ev idently b ecause o f
“spanwise relief”, or a spanwise pressure gradient. Alternatively, we can revert to thoughts developed for
the A R= 2 s tatic ex periment m entioned ab ove; t he e ffective q uasi-steady an gle o f at tack for the A R= 2
plate is h alf o f th at o f th e w all-to-wall pl ate, bo th a ccording t o l ifting l ine a nd s lender body t heories.
Accordingly, the flow separation for the AR=2 plate should be attenuated. This is basically the case here.
As w e w ill see i n a su bsequent s ection on hi gher-rate p roblems, as t he r educed f requency i ncreases,
appeal to quasi-steady concepts becomes more tenuous – consistent with intuition.
87
t/T=0
t/T=0.25
t/T=0.333
t/T=0.417
t/T=0.5
t/T=0.583
t/T=0.75
Figure 76. PIV, AR=2 plate in pure plunge, phases phi = 0, 90, 120, 150, 180, 210 and 270.
88
t/T=0
t/T=0.25
t/T=0.333
t/T=0.417
t/T=0.5
t/T=0.583
t/T=0.75
Figure 77. PIV results for AR=2 plate pitch-plunge.
89
6.8.
Mixed-Frequency Problems, where Pitch and Plunge Frequency Differ
6.8.1. Problem Definition
In our f inal s egment on pe riodic motions, w e c onsider a problem w here the frequency of pitch
differs from the frequency of plunge by some multiple, while both are sinusoids. Of what relevance is
such an exercise? Loosely, it could be a proxy for gust response of flapping-wing vehicles, where the fast
frequency m odels t he wing f lapping, w hile the s low frequency models t he g ust. S ometimes pitch a nd
plunge i nduced a ngle o f a ttack a re i n opp osition, r esulting i n a ne t l ow a ngle; ot her t imes, t hey a dd
constructively, with very large excursions in effective angle of attack. Thus such motions are useful for
producing large alpha variations without requiring very aggressive motions.
We consider a pitch amplitude of 15°, plunge amplitude of 0.1, Re = 10,000, mean angle of attack
of 4°, and reduced frequency based on plunge of 3.93. As usual, pitch leads plunge by a phase difference
of φ=0º. From he re, w e vary t he r atio of pi tch t o pl unge f requency as f ollows: 0.25, 0. 75, 1, 2 a nd 4.
Pitch pivot points at x/c = 0, 0.25, 0.5, 0.75 and 1.0 are considered. The main case of interest has pivot
point at the midchord and pitch frequency twice that of plunge frequency. T he model was started from
rest at φ=0º, and begins motion by pitching nose-down and plunging down. The effective angle of attack,
superimposed on the pitch angle, is shown in Figure 78. Commanded and attained values are compared;
the l atter sh ows o scillations asso ciated w ith d ynamic st artup t ransients i n the l inear m otors, w hich
presumably respond as a second-order system to a step input in velocity.
60
40
α, deg
20
0
-20
θ commanded
θ attained
αT commanded
αT attained
-40
-60
0
0.5
T
1
1.5
Figure 78. Commanded vs. attained angle of attack history for sinusoidal pitch frequency double that of
sinusoidal plunge.
6.8.2. Flowfield Results
Figure 79 is a detailed tracing of the history of flow evolution from PIV and dye injection, at φ =
0º, 45º, 90 º, 135º, 180º, 225º, 270º, 315º, 360º, 405º, 450º, 495º, 540º, 585º, 630º, 675º, 720º, 1080º, and
1440º. φ = 360º c ompletes one pe riod o f pl ung e o scillation a fter m otion ons et, 720 º c ompletes t wo
periods, and so forth. P IV resolution was 88 pixels/cm. F or 32x32 pixel windows with 16x16 overlap,
90
this results in 84 velocity vectors per the 152mm chord length. As usual, laser reflections from the model
surface limit boundary-layer resolution, and the pressure-side of the airfoil is in t he shadow of t he PIV
light sheet. It would eventually be desirable to have an optically transparent model to acquire PIV data on
the suction and pressure sides simultaneously, but even then, parallax would result in a void of data in the
immediate model periphery, because the near-edge of the model would block said periphery in the plane
of the light sheet. Of course, for more detailed boundary layer physics one can turn to CFD.
φ=0°
φ=45°
φ=90°
φ=135°
91
φ=180°
φ=225°
φ=270°
φ=315°
φ=360°
φ=405°
92
φ=450°
φ=495°
φ=540°
φ=585°
φ=630°
93
φ=675°
φ=720°
φ=1080°
φ=1440°
Figure 79. PIV (left), averaged over 10 instantiations per phase, and dye injection (right), Re = 10,000,
mixed-frequency pitch-plunge; phases of motion as marked.
94
The final two frames of Figure 79 illustrate the limitations of dye injection. That is, through the
first one and a half periods of motion, agreement between PIV vorticity and intensity of dye concentration
is excellent. By two periods of motion, this agreement has declined, as dye is becoming more diffuse. By
three periods of motion, agreement i s very poor. We can argue towards the general statement that dye
flow visualization is an excellent marker for how vortices form and grow, but is less useful for following
how v orticity i s t ransported, be cause t he m ixing o f dy e a nd the stretching/folding of v orticity a re
different. Of course, this is not a new concept, but it is useful to assess dye vs. more quantitative methods
in the general context of low Reynolds number unsteady aerodynamics, as dye visualization is broadly –
and unfairly! – denigrated for its crudeness and putative tendency to give dubious results.
Comparing φ = 720º, 1080º a nd 1440º, t he PIV shows strong repeatability. T herefore t he flow
appears to relax to periodicity – if the ensemble average is to be believed – by two periods of plunge after
motion onset. We also see the curious phenomenon of shedding a vortex pair upstream from the leading
edge, for example at φ = 450º. The wake behind the trailing edge is not parallel to the free stream but is
biased t owards the d ownwash d irection. S uch wake b ias r ecalls the h igh-frequency pur e-pitch
oscillations reported earlier.
We mention onl y br iefly t he r ole of pi tch pi vot point l ocation, a s t his w ill be covered i n more
detail in the sections o n n onperiodic motion, and the ef fect is m uch t he same a s in the p eriodic cases.
Namely, moving the pivot point further aft delays the LEV formation, but results in a stronger LEV when
it does e ventually f orm. We a lso no te that the m ixed-frequency ca se i s a challenging l itmus t est for
experimental-computational c omparison104, at l east f or 2D c omputations, as p resumably t he s ame 3D
stretching/folding effects that plague dye vs. PIV comparison also affect the computation. That is, in the
first 1 -1½ pe riods of m otion, c omputational-experimental ag reement i s q uite g ood, ev en ac ross a large
mismatch between the two in Reynolds number. But thereafter the agreement decays. This suggests that
impulsive or non -periodic p roblems ar e m ore p romising, at l east i n some case s, f or ex perimentalcomputational agreement. And this is where we turn next.
95
6.9.
Pitch Ramp-and-Return
6.9.1. Introduction
While most of the preceding work related to MAVs was motivated by problems of flapping, here
we return to the second major application – perching. Several approaches are possible. One approach is
direct p erching, w here the a ngle of a ttack v aries f rom s ome l ow t o hi gh v alue, a nd s tays t here. A n
alternative is a motion of pitch ramp, followed by steady hold at high angle of attack, followed by return
to the original angle of attack. Here we consider a parameter range similar to that studied by Visbal and
Shang37, a nd c ontinue t o much hi gher r educed r ates. T he h igher r ates w ere of m inimal i nterest for
dynamic-stall applications, prior to the advent of MAVs.
The o bjectives o f this sec tion ar e t o (1) c onduct a p arameter-study of R eynolds num ber, pi tch
pivot poi nt l ocation, reduced f requency and pitch-plunge comparison (the latter to extend sinusoidal
pitch-plunge c omparisons 105,106 to linear r amps); ( 2) to m utually-validate a 2 D h igh-resolution
computation and a water tunnel experiment, in the sense that the latter is inevitably plagued by tunnel test
section wall effects and blockage; and (3) to computationally explore trends in lift coefficient time history
for a parameter s tudy of r educed frequency. In de parture from m ost of t he above-cited l iterature, we
consider p itch r amp-hold-return, w here the pl ate r eturns to z ero i ncidence a ngle, i nstead of p ure pi tch
ramp-hold. T his is motivated by the impression that the return problem has the more complex flowfield
transients, and is therefore a richer test case for modeling lift coefficient time histories departing from the
simplest abstractions. Subjects (2) and (3) are reported in publications currently in-print, with extramural
collaborators; the present report will focus strictly on the in-house research.
6.9.2. Experimental Parameter Study with Dye Injection
The typical motion time history is shown in Figure 80. “Time” is convective time, or number of
chords traveled by the free-stream. The baseline case is pitch about x/c = 0.25 at K = cθ
= 0.70 and Re
2U ∞
= 10K, from an initial incidence of 0º to a final incidence of 40º. The hold at the top of the ramp motion
lasts f or 0.05c convective t ime. T he “eq uivalent” p lunge, i n t he sen se o f h (t) su ch t hat
 h(t ) 
 = α (t ) matches that of the pitch (ignoring the pitch-rate effect), is shown as the green curve in
arctan

 U∞ 
Figure 80. Plunge time history is parabolic concave-up to compare with linear pitch-up, linear to compare
with pitch-hold, and parabolic concave-down to compare with linear pitch-down. S tarting and stopping
transients are smoothed by cubic splines, set for an upper bound of acceleration of 10 m/s2. Comparison
between c ommanded a nd attained p lunge rod position s hows a m aximum de viation of a bout 0.1m m,
corresponding to an angular error of ~0.13º in the plane of the airfoil chord, had the airfoil been a rigid
body. H owever, a s m entioned b elow, t he v arious m odels s uffered from e lastic v ibrations, resulting in
angular e xcursions a t the t op a nd bot tom of t he pi tch s troke, w hich w ith p resent m ethods c an no t be
reliably quantified.
In this section, a l arge but rather superficial survey of flows from various motion parameters is
presented, in all cases by dye injection from the plate leading or trailing edge at approximately the ¾-span
location. I n m ost c ases, snapshots of t he f lowfield a re s hown w hen the m odel is halfway up to i ts
maximum an gle o f at tack; u pon r eaching m aximum angle of a ttack; ha lfway o n t he d ownstroke; up on
returning back to the zero angle; and one ramp’s worth of time after returning to the zero angle. These
are denoted with black line segments in Figure 80.
96
θ
40
h
35
0.4
0.35
30
0.3
25
0.25
20
0.2
15
0.15
10
0.1
5
0.05
0
0
0.5
t
1
1.5
0
Figure 80. Time-trace of pitch angle and plunge position. Flow visualization frames correspond to position
in time denoted by the black line segments; the fifth line segment is one ramp-motion’s time after motion
cessation.
In Figure 81 the pitch ramp-hold-return is examined across a range of reduced frequency from K
= 0.1 through 1.4, keeping the pivot point at x/c = 0.25. All cases show a large leading edge vortex, and
all show an interaction between the bluff-body-type Karman vortex street prior to motion onset, with the
motion-induced t railing v ortex sy stem af ter m otion onset. A s K increases, t he L EV b ecomes m ore
compact and is better able to retain its integrity as it eventually convects downstream. H igher K means
not only stronger vorticity transport into what becomes the LEV, but also that the LEV has had less time
to form, and therefore is less advanced at the same snapshot of model position, relative what happens at
lower K. Higher K also results in a pair of vortices in the near-wake, aft and below the plate. This is
discussed i n m ore de tail i n S ection 2 below. A small v ortex i s formed upon return to z ero a ngle o f
incidence. F inally, t he e ventual c onvection of the L EV p ast the t railing ed ge r esults i n shedding o f a
trailing-edge v ortex of op posite s ign, t o ob serve c onservation o f c irculation, en r oute to r eturn t o the
flowfield state seen prior to motion onset. A s K increases, the strength of this final TEV also increases.
But in all cases, return of the wake to its shape before the motion onset occurs 3-4 convective times after
motion completion. This can be seen from Figure 82, which shows the extremes of K = 1.4 and 0.1, with
snapshots p resented at i nteger values of convective t ime af ter motion cessation. T his su ggests that the
aggregate of flowfield features such as shed v ortices convects with the free-stream. Exceptions are
vortex-on-vortex interactions, such a s in t he t railing vortex pa ir, for the higher reduced frequencies.
These may be r esponsible for transients in lift and especially i n pitching moment – a conjecture whose
verification is beyond the scope of the present study.
K=0.10, Re 10K
K=0.20, Re 10K
97
K=0.35, Re 10K
K=0.70, Re 10K
K=1.4, Re 10K
Figure 81. Flat-plate pitch for various reduced frequencies: K = 0.1 (top row), 0.2 (row 2), 0.35 (row 3), 0.70
(row 4), and 1.4 (row 5).
K=1.4, t* = 0
K=0.1, t* = 0
K=1.4, t* = 1
K=0.1, t* = 1
K=1.4, t* = 2
K=0.1, t* = 2
K=1.4, t* = 3
K=0.1, t* = 3
K=1.4, t* = 4
K=0.1, t* = 4
Figure 82. Comparison of highest-rate-motion and lowest-rate-motion flowfield evolution with respect to
convective time; t* after motion cessation as marked. K = 1.4 (top row) and 0.1 (bottom row).
Returning t o Figure 81, t he f lowfields f or t he S D7003 a irfoil a nd f lat pl ate at K = 0.7 a re
reasonably s imilar, suggesting th at m otion-induced e ffects dominate those o f t he m odel c ross-section.
With its sharper trailing edge, the airfoil has much stronger dye c oncentration in the trailing vortex
system, e specially i n t he v ortex s hed d uring t he ups troke, but t he s hape a nd c onvective h istory of t he
vortex system ar e si milar t o t he p late’s. The p late’s L EV i s so mewhat st ronger, more offset from t he
model s uction-side a nd m ore coherent in g oing dow nstream. It is not c lear whether th is is due to th e
difference in the models’ leading edge radii or the camber/thickness distributions.
Figure 83 compares pitch and “ equivalent” plunge. Also, pitch and equivalent negative plunge
are s uperimposed i n a c ombined motion, i n a n effort t o discern t o w hat e xtent t he c ombination, w hich
gives quasi-steady identically zero angle of attack, comes close to producing a vorticity-free flowfield.
Wakes o f p itch and p lunge ar e seen t o b e entirely d ifferent, w ith t he l atter sh owing a sm ooth
separation from the trailing edge followed by roll-up into a vortex pair. In the combined pitch-plunge, the
flowfield lo oks s imilar to that f or pure-pitch. Thus p itch-plunge eq uivalence o r cancellation f ail
completely in regards to the trailing vortex system. On the other hand, the LEV of the plunge is similar in
appearance to that of the pitch. And for the combined motion, the LEV is largely vestigial
As w ith pi tch a t K = 0.7, plunge f or the airfoil v s. t he f lat-plate h ave s imilar flowfields – even
more so for plunge than pitch, as in the latter the trialing edge motion is small, and thus the airfoil’s sharp
trialing edge has less of a role in the overall vorticity production budget. And, as with pitch, in plunge the
flat-plate’s LEV is somewhat larger than the airfoil’s – probably again because of edge radius.
98
Figure 83. K = 0.70, 0º-40º-0º pitch (top row), “equivalent” pure-plunge (row 2), combined pitch-plunge (row
3); and combined pitch-plunge with trailing edge dye injection (bottom row). Re = 10K.
The above comparison of pitch vs. plunge ignores the effect of pitch-rate, which enters the quasisteady expression for C L(t) whenever the pitch pivot point is not x/c = 0.75 87, and which is increasingly
important w ith l arger K. While the p resent w ork h as n ot ex tended t o linear ramps t he p itch-plunge
equivalence based on Theodorsen’s formula, as considered by McGowan et al105., the role of pivot-point
changes is considered qualitatively. Figure 84 shows 0-40-0 pitch with pivot point locations x/c = 0, 0.25,
0.5, 0.75 and 1.0. With pivot point further aft, the vertical extent of the near-wake becomes smaller. For
pitch about x/c = 1.0, the near-wake begins to resemble that of plunge, from Figure 83. For pivot at x/c =
0.25 and 1.0, dye injection was conducted at both leading and trailing edge, and close agreement between
the two implies that the injection method can be deemed to be non-intrusive – or, to be pedantic, equally
intrusive. In going towards further-aft pitch pivot point, the LEV on the plate suction-side at peak angle
of incidence becomes more concentrated, and during the downstroke the LEV lifts further off of the plate
surface. Flow along the vortex axis also becomes stronger, akin to the trailing vortex system reported by
Ol for high-frequency sinusoidal pure-plunge 107. On the plate pressure side, a companion LEV forms for
the further-aft pi vot point locations. I t i s subsumed by t he suction-side LEV on t he downstroke. The
larger p ressure-side L EV for t he fu rther-aft pi vot locations s tands t o reason, as s uch a m otion looks
locally to the LE as a pure-plunge, and the “LEV” is the trailing vortex behind a locally plunging plate.
x/c = 0.0
x/c = 0.25
99
x/c = 0.50
x/c = 0.75
x/c = 1.0
Figure 84. Flat-plate 0º-40º-0º pitch, K = 0.70, Re = 10K; parameter study of role of pitch pivot point. x/c =
0.0 (top row), 0.25, 0.50, 0.75 and 1.0 (bottom row).
6.9.3. Qualitative vs. Quantitative Flow Visualization
PIV and dye injection results from the water tunnel are compared in Figure 85 for K = 0.70, and
in Figure 86 for K = 0.20. Figure 85 and Figure 86 also include the computed vorticity field at θ = 20º
and θ = 40º on the upstroke for K = 0.70 and 0.20, respectively. All results are at Re = 10,000.
To reiterate, the dye injection is “instantaneous”, while the PIV is phase-averaged. B ecause the
pre-motion Karman s hedding i s unc orrelated w ith t he pi tch-ramp motion, t he Karman v ortex s treet so
visible i n t he dy e i njection i s absent in the P IV vor ticity c ontours. O therwise, the c orrespondence
between concentrations of dye and peaks of vorticity is quite close, in the sense that high-contrast regions
of dye nearly coincide with high-amplitude ensemble-averages of vorticity. PIV data consist of 50 pairs,
acquired in a sequence where each ramp-hold-return event was separated from the previous event by ~6
convective times.
The K = 0.7 c ase ha s a c ounter-rotating v ortex pa ir i n t he ne ar-wake, j ust d ownstream o f t he
trailing edge at motion cessation. I t consists of a co unter-clockwise vortex formed during the upstroke,
and a c lockwise v ortex i n t he dow nstroke. B oth v ortices a re c onnected by f eeding s heets, w hose
constituents t hemselves r oll up into d iscrete vortices u nder self-induction. This s tructure s urvives t he
phase-average without smearing. At the leading edge, there is a dynamic stall vortex system akin to what
was observed for high-frequency sinusoidal pitch by McGowan et al105.
The K = 0.2 case, in contrast, has a strongly coherent trail of counter-clockwise discrete vortices
shed all the way until the model reaches maximum pitch angle. At the top of the pitch stroke, or shortly
after downgoing motion commences, a weak vortex of opposite sign is shed.
θ = 20º, upstroke
100
θ = 40º, end of upstroke
θ = 20º, downstroke
θ = 0º, downstroke
θ = 0º, 1 ramp-time
post downstroke
velocity contour levels
vorticity contour levels
Figure 85. K =0.70, Re =10K; dye injection (left column), phase-averaged velocity (middle column), phaseaveraged vorticity (right column) and samples of computed vorticity (also right column).
θ = 20º, upstroke
101
θ = 40º, end of upstroke
θ = 20º, downstroke
θ = 0º, downstroke
Figure 86. K =0.20, Re =10K; dye injection (left column), phase-averaged velocity (middle column), phaseaveraged vorticity (right column) and samples of computed vorticity (also right column).
6.9.4. Removing Parasitic Surge
One of the drawbacks of the original 2-motor installation was an undesired but inevitable fore-aft
motion w henever t he p rescribed p itch pi vot p oint w as not coincident with t he f ront l ower p lunge r od
bushing. This is because the front plunge rod was constrained to move up and down, with no provision to
swing ( otherwise t he r ig w ould be f limsy). H aving t he t hird l inear m otor, a f ore-aft m otion c an be
programmed to negate the parasitic motion. F or example, in the following there is a pitch from 0 t o 45
degrees, about the trailing edge of the model. A sequence with no surge correction is compared with a
corrected sequence. B ecause in the f ormer t he t railing ed ge i s in undesired motion, t he ne ar-wake i s
different, with stronger trailing edge vortex shedding (Figure 87).
No surge removal
with surge removal
11.25, upstroke
22.5, upstroke
33.75 upstoke
102
max, no surge
33.75 on downstroke
22.5 on downstroke
11.25 downstroke
End of ramp
Figure 87. α = 0º-45º linear ramp-hold-return, K = 0.7, pivoting about x/c = 1.0. Without removal of
parasitic surge (left) and with removal of parasitic surge using the third linear motor (right).
6.9.5. Pitch Ramp and Return, 2nd Sequence
The previously-described problem is revisited upon gleaning more experience, and was proposed
as a “canonical problem”. This was the subject of several results reported at the AIAA Aerospace
Sciences Meeting in Orlando, FL, January 2010.
6.9.5.1. New Motion Definitions
We define a family of motions with shared angle of attack range and peak angle of attack rate, but
in one case with nominally sinusoidal (nearly one-minus-cosine function) angle of attack history, and in
103
another o f t rapezoidal hi story, w here a ccelerations are l imited to na rrow regions of time, a nd are zero
otherwise. The unsmoothed trapezoidal motion has an upgoing and downgoing linear ramp in angle of
attack, defined nondimensionally as K = cθ
= 0.20 , with pivot about the leading edge.
2U ∞
To a void model vibration in e xperiments a nd num erical i nstabilities i n t he c omputations, and
delta-function spikes in calculated noncirculatory force, considerable care is taken to smooth all motions.
For a r amp i n g oing f rom 0 de grees a ngle o f a ttack t o 45 de grees, t he f irst 1 0% ( 4.5 de grees) can be
replaced with a sinusoid tangent to the baseline ramp, and similarly in approaching the “hold” portion at
the peak angle of attack, and again on the downstroke. The result is a piecewise sinusoidal and piecewise
linear fit. T his u nfortunately h as d iscontinuities in the angle o f at tack sec ond d erivative, an d w as
therefore replaced b y an a lternative C∞ smoothing f unction developed by E ldredge 108. The s moothing
function G(t) is defined as:
 cosh(aU ∞ (t − t1 ) / c) cosh(aU ∞ (t − t 4 ) / c) 
G (t ) = ln 

 cosh(aU ∞ (t − t 2 ) / c) cosh(aU ∞ (t − t 3 ) / c) 
where a is a free parameter, c is the chord, and the times t1 through t4 are:
t1 = time from reference 0 until when the sharp corner of the unsmoothed ramp would start
t2 = t1 + duration of the pitch upstroke, until the sharp corner where the hold would have begun
t3 = t2 + the unsmoothed hold time at maximum alpha
t4 = t3 + the unsmoothed pitch downstroke duration
Then, with the pitch amplitude A = 45 deg, the smoothed motion becomes
α (t ) = A
G (t )
max(G (t ))
By varying the parameter a, G(t) becomes a parametrization of smoothing from true trapezoid all
the way t o approximate sinusoid. A l arge v alue of a leads t o an abrupt a cceleration, p resumably w ith
large spikes in noncirculatory lift and pitch (but not drag/thrust, which has no noncirculatory portion).
The r elation be tween linear ramp and sinusoid, i n Figure 88, is c onstrained by matching t he
amplitude and peak pitch rate between the two. S o for a linear ramp with dimensional pitch rate θ , the
, and the length of
duration of the linear ramp relates to the frequency of the sinusoid as t 2 − t1 = 1
2πf
1
1
the linear ramp’s hold time becomes t 3 − t 2 =
− . S etting a = 2 produces a close fit between the
2 f πf
sinusoid, θ (t ) = A(1 − cos(2πft ) ), w hile a = 11 i s i n turn a c lose a pproximation t o t he 10 % s inusoidal
smoothing of an otherwise linear ramp (Figure 89).
Physically, the pitch ramp-hold-return motions in the K range of 0.2-0.7 and Re range of O(104)
feature the growth of a large leading edge vortex (LEV) that does not pinch off until the pitching motion
ends. T he hold at maximum angle of attack lasts roughly as l ong as i t would take the LEV to convect
from leading to trailing edge at free-stream speed. The downstroke is proposed as a prototypical motion
to study flow “memory” effects, where upon returning to zero angle of attack the flow is still recovering
from m assive sep aration. We sp eculated, at this p oint, t hat a q uasi-steady m odel w ith the a ppropriate
tuning can account for lift coefficient time history over the entire upstroke (other than for noncirculatory
effects), b ut w ill fail on the dow nstroke. F or a pplications such a s i nsect f lapping, t here r eally i s no
downstroke in the sense of the present case, as the motion essentially starts afresh on every half-stroke. It
is perhaps for this reason that quasi-steady models for insect-type flapping are successful 109.
Thus, t here a re f our m ain c ases: t wo R eynolds n umbers a nd t wo v alues of t he s moothing
parameter a, of 2 and 11.
104
45.0
pitch values, degrees
40.0
35.0
alpha, deg
ramp
piecewise sin
smoothed_a(t)
30.0
25.0
20.0
15.0
10.0
5.0
convective times
0.0
-1
0
1
2
6
3
4
5
6
first derivatives
deriv ramp
4
deriv piece sin
smoothed_a(t)
2
0
-1
0
1
2
3
4
5
6
-2
-4
-6
1.5
2nd derivative
1
2nd deriv comp
smoothed_dot^2
0.5
0
-2
-1
0
1
2
3
4
5
6
7
-0.5
-1
-1.5
Figure 88. Sinusoidal ramp, angle of attack (top, angle of attack rate (middle) and accelerations (bottom) for
pitch-hold-return maneuver.
45.0
pitch values, degrees
40.0
35.0
alpha, deg
ramp
30.0
piecewise sin
smoothed_a(t)
25.0
20.0
15.0
10.0
5.0
convective times
0.0
-1
0
1
2
3
105
4
5
6
6
first derivatives
deriv ramp
4
deriv piece sin
smoothed_a(t)
2
0
-1
0
1
2
3
4
5
6
4
5
6
-2
-4
-6
6
2nd derivative
4
2nd deriv comp
smoothed_dot^2
2
0
-1
0
1
2
3
-2
-4
-6
Figure 89. Smoothed linear ramp, angle of attack (top, angle of attack rate (middle) and accelerations
(bottom) for pitch-hold-return maneuver.
6.9.5.2. Dye injection results
Dye injection results for Re = 5000 a re given in Figure 90. A gain there is a parameter study of
pitch pivot point location. On the upstroke, growth of the LEV is faster, the closer the pivot point is to
the leading edge. The starting vortex from pitch-ramp onset is also weaker. Thus, on the upstroke at least
until around α~30º, one can state that the closer to pivot point to the leading edge, the more benign the
flow separation overall. B ut in the s ubsequent motion hi story, t he r ole of pi vot poi nt diminishes, s uch
that by halfway on the downstroke, LE-pivot and TE-pivot are hard to distinguish.
Sinusoidal vs. ramp motions, both pivoting at the LE, show very little difference on the upstroke,
through the hold. T he main difference is that the sinusoidal motion, being less abrupt, has a smaller TE
starting vortex. L ate into the downstoke some differences appear in what remains of the LEV; namely,
for the sinusoid there is a longer route towards flow reattachment after returning to zero angle of attack.
But overall the sinusoidal and ramp flowfields are similar.
LE pivot
0.25c pivot
TE pivot
α=11.25º↑
α=22.5º↑
α=33.75º↑
106
LE sinusoid
α=45º
α=33.75º↓
α=22.5º↓
α=11.25º↓
α= end
Figure 90. Dye injection results at Re = 5K, smoothed ramp and sinusoid, with pitch pivot location as
marked.
6.9.5.4. Lift Coefficient History
Force data using the FBG balance is compared to two computations: implicit Large-Eddy
Simulation and Vortex Particle Method (Figure 91). Angle of attack is scaled such that if the lift curve
were 2πα, the angle of attack and lift time traces would coincide. To save embarrassment of the
experimentalists, t he e xperimental lift c oefficient is di vided by 1.5. T he i dea comes f rom Lian110, i n a
computational s tudy of dom ain s ize. If one us es a 2D do main w ith up per a nd l ower bound s
corresponding t o t he r atio of p late c hord to the height o f t he water t unnel t est s ection, t hen o ne f inds
approximately 1.5X increase in peak lift coefficient. In the absence of more sophisticated reasoning or
experimental data from other facilities, we will call this scaling of 1.5X a d ynamic blockage correction.
With this r escaling, t he t hree data s ets c oincide on the ups troke a nd hold, a nd a lmost coincide on t he
downstroke. To save computational costs, the numerical results are at the lower of the two canonical Re,
while to increase balance signal to noise ratio, the experimental results are at the higher Re.
107
5
CL
4.5
sinusoid
Eldredge a 2
Garmann a2 Re 5K
Ol a = 2 /1.5
4
3.5
α
3
45
5
40
4.5
45
CL
ramp
Eldredge a 11
Garmann a11 Re 5K
Ol a = 11 /1.5
4
35
3.5
30
α
3
25
2.5
40
35
30
25
2.5
20
2
20
2
15
1.5
10
1
15
1.5
10
1
0.5
5
0.5
5
0
0
0
0
-0.5
-0.5
-5
0
2
4
6
-5
2
t*
4
6
t*
Figure 91. CL for a = 2 (sinusoidal, left) and a = 11 (smoothed ramp, right), from Garmann and Visbal
computation (Re = 5000), Eldredge et al. computation (Re = 5000), and Ol et al. experiment (Re = 40,000).
6.9.5.5. Summary
Both sinusoid and ramp appear to have a phase lead between lift time history and angle of attack
time history. How can the aerodynamic force lead the motion? The answer comes from considering the
noncirculatory portion of the lift, which is in phase with the pitch acceleration. As seen in Figure 89 for
the ramp ( the sinusoid i s similar), t he p eak acceleration ap pears at the very st art o f the angle o f attack
ramp, and then quickly drops. The noncirculatory lift therefore has a strong jump at motion onset. When
added to the circulatory portion, the combined manifestation is a phase lead and a spike at every “corner”
of the ramp motion – thus, four spikes total. F or the sinusoid, the noncirculatory lift, when added to the
circulatory, does not produce any apparent spikes because the acceleration is smooth; instead the
noncirculatory contribution appears as a phase lead in an otherwise sinusoidal response. This behavior is
seen in two very different computations and in experiment. A ll capture the same phase response. And
Reynolds number appears to have a very weak influence at most, responsible perhaps for variations in lift
oscillation towards the bottom of the downstroke.
We also note the advantage of specific prescription for smoothing the ramp. In the water tunnel
experiment of Ol et al., the structural vibration of the model, in spanwise bending, is at approximately 13
Hz, w hereas the dominant f requency of t he non circulatory l ift s pikes i s a pproximately 6 H z. This
separation i n f requency allows low-pass f iltering to r emove s tructural v ibration in lift t ime h istory,
without significantly attenuating the noncirculatory spikes.
The next challenge is, first, closed-form modeling of the lift (and eventually pitch) response for
the entire motion, in its three parts – upstroke, hold, and downstroke; and second, extension of wall-towall plate (or nominally 2D) results to finite aspect ratios. A lso, it remains to see whether the trends in
lift coefficient, such are general independence of Reynolds number, conveys to other quantities, such as
pitching m oment co efficient. We s peculate t hat aerodynamic f orce co efficient m odeling o n t he
downstroke w ill be t he m ost c hallenging, but a re s anguine a bout t he r eliability of c omputation a nd
experimental data.
108
6.10. Perching: an Extension of the Linear Pitch Ramp
Perching was mentioned as one of the core MAV unsteady aerodynamics problems at the start of
this report. At a first approximation the maneuver of perching is related to the classical-pitch up problem,
where t he angle of at tack v aries f airly q uickly o ver a large amplitude. The key d ifference b etween
perching and ramp motions in classical unsteady aerodynamics is that in the latter the free-stream velocity
is constant during the maneuver, while in perching there is a flight trajectory beginning from a cruise-like
condition and terminating in landing. To properly model this in a ground test facility, one needs to reduce
the effective free stream by the end of the maneuver to zero – and this is what the surge motor of HIPPO
allows.
6.10.1. Motion Definition
All runs are at nominal reduced frequency K = cθ 2U ∞ = 0.03. We consider 5 cases, all with linear
pitch ramp and sinusoidal smoothing of starting/stopping motion transients:
1. SD7003 a irfoil, R e = 50 K, c onstant relative free-stream, a ngle of a ttack f rom 0 t hrough 45
degrees.
2. SD7003 a irfoil, R e = 15 K, c onstant relative f ree-stream, a ngle of a ttack f rom 0 t hrough 85
degrees.
3. Flat plate of ~2% t hickness and r ound edges, Re = 15K, constant relative f ree-stream, angle of
attack from 0 through 85 degrees.
4. Flat plate of ~2% thickness a nd round edges, nom inal R e = 15 K ba sed o n t unnel free-stream
velocity, varying tow speeed, angle of attack from 0 through 85 degrees.
5. SD7003 a irfoil, nom inal R e = 15K ba sed on t unnel free-stream velocity, v arying t ow sp eeed,
angle of attack from 0 through 85 degrees.
6.10.2. Dye Injection, PIV and Direct Force Measurement
Dye i njection results f or a ll 5 c ases are sh own i n Figure 92, w ith e ach ca se i n its r espective
column. PIV results, presently limited to the first case, are shown in Figure 93. These are instantaneous
shots – not phase averages. Data in Figure 93 were taken from motion onset through several convective
times after motion completion, and thus reveal the Karman vortex shedding, in the bluff-body sense, of
the most-maneuver flowfield.
In all cases in Figure 92, a leading edge vortex (LEV) is formed at an angle of attack of around 20
degrees, and in no case is the LEV long-lived. Indeed, in the lift and drag time trace for the first case,
shown in Figure 94, there is no dynamic-stall peak associable with LEV formation. There is, however, a
very large p eak lift coefficient – which r apidly collapses as t he f low d egenerates to Karman shedding.
Therefore, approximately the first half of the motion time history for all cases is quite similar, but in the
second half of the motion time history the effect of decelerating relative free-stream manifests itself.
109
110
Figure 92. Flow visualization by dye injection of 5 linear pitch ramp-and-hold cases for wall to wall flat
plates and airfoils. First column: SD7003 airfoil, 0-45º, constant free-stream, Re = 50K. Second column:
SD7003, 0-85º, constant free-stream, Re = 15K. Third column: flat plate, 0-85º, constant free-stream, Re =
15K. Fourth column: flat plate, 0-85º, decelerating, Re = 15K based on tunnel speed. Fifth column: SD7003
airfoil, 0-85º, decelerating, Re = 15K based on tunnel speed. Each row is a sampling at the same angle of
attack for all cases: 0.6º, 5.5º, 11.2º, 16.8º, 22.5º, 28.1º, 33.7º, 39.2º, 45.0º, 50.7º, 56.3º, 61.9º, 67.6º, 73.2º, 78.9º,
and 84.5º.
111
Figure 93. PIV single-shot vorticity contours, SD7003, 0-45º, constant free-stream, Re = 50K. Reading across
each row and then down the next column, shots are at α = 0.6º, 5.5º, 11.2º, 16.8º, 22.5º, 28.1º, 33.7º, 39.2º, 44.3º,
45.0º, and thereafter at 45.0º; samples are spaced 1.32 convective times, or 0.76 seconds in physical time.
112
Figure 94. Lift and drag coefficients for the SD7003 airfoil pitching 0-45 degrees angle of attack, plotted vs.
physical time in seconds.
As of this writing, work in progress involves selection of “optimal” perching trajectories, which are a
combination of elevation change, angle of attack time history and relative forward speed history, chosen
for example to minimize energy over the trajectory.
6.10.3. Summary
Perching is a fundamental unsteady motion elucidating the difference between truly quasi-steady
aerodynamic r esponse an d r ate-dependent o r acc eleration-dependent e ffects. F ollow-on w ork will
focusing on de tailed p arameter s tudies o f p ivot p oint an d p itch r ate. S o far we can ascertain t hat the
presence of absence of deceleration i n t he streamwise direction during t he perching maneuver has little
effect on the flowfield evolution, and that Reynolds number effects appear to be benign in this deep-stall
problem – as in most deep-stall problems.
113
6.11. Flapping
6.11.1. Motivations and Motion Definition
Our final application is flapping in hover. The water tunnel is turned into a tow tank, with the
third linear motor as the towing mechanism. Doman et al. 111, proposed a flight control scheme based on
the f lapping-wing c onfiguration de veloped by W ood e t a l.112, w here t he w ing l eading e dge i s di rectly
actuated in a sinusoidal sweeping motion, but the wing incidence angle is free to float between limiters.
The i dea is t o minimize t he number of a ctuators. The in cidence a ngle is g enerally r ight at t he l imiter
throughout the “translation” phase of each half-stroke, with a rapid rotation from one limiter side to the
other, at or near the extrema of each half-stroke. Doman et al.111 assume in their analysis a quasi-steady
lift coefficient hi story t hroughout t he t ranslation s troke, a nd a no n-lifting instantaneous rotation phase.
The former assumption is probably j ustified for conceptual-design purposes based on our earlier results
for sinusoidal periodic pl unge, where one finds remarkable robustness of the simple CL = 2πα even for
large in cidence a ngles. But th e la tter assumption is only valid if th e stroke f raction oc cupied by t he
rotation is small, and post-rotation transients dye out quickly. And, since the incidence angle time history
during rotation is passively accepted from the combination of body dynamics (wing mass and moment of
inertia, hinge dynamics, etc.) and aerodynamic loads (time history of pressure distribution on t he wing),
the actual incidence angle history is not known a priori. One may find various lags between rotation and
translation, and asymmetries between start and end of each stroke endpoint rotation.
90
attained pitch angle vs.
phase of motion
ABS(pitch angle), deg
85
80
75
70
65
60
55
50
phase, t/T
45
40
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figure 95. Phase lag between prescribed plunge and passive pitch, “light” plate.
90
85
80
75
70
65
60
55
50
45
40
0
60
120
180
240
plunge phase, deg
114
300
360
Figure 96. Phase lag between prescribed plunge and passive pitch, “light” plate.
Instead of sw eeping motion, w hich i s non rectilinear, w e us e a rectilinear m otion – simple
sinusoidal translation. T he problem reduced to a form of “normal hover” with imposed translation and
rotation history, except that pitch is free to float, instead of being prescribed. The p rescribed-pitch
problem i s v ery w ell s tudied; Milano an d G harib113, K urtulus e t al. 114, S hyy e t a l 115; among ot hers, a ll
considered it, generally with an upper bound of Re < 1000. H FWT data so far are limited to two cases
with pa ssive pi tch a nd pr escribed sinusoidal pl unge of 10c m ( = 2 c hords) a mplitude a nd f requency of
0.5Hz, which corresponds to Re ~ 16,000 and max translation speed of ~31 cm/s.
Figure 95 shows that indeed the angle of attack of the plate settles at nearly 45° on t he fore and
aft stroke, but that there is an approximately 20 de gree phase lag between instantaneous 90° orientation
(plates hangs vertically) and the extremum of the fore-aft translation sinusoid. Figure 96 shows that for a
heavier plate, the phase lag is essentially double - 40°.
6.11.2. Dye Injection Results
We next turn to dye injection as a preliminary scheme for understanding the flowfield evolution.
Figure 97 traces the history of vortex evolution using trailing-edge dye injection, in 30-degree increments
of phase of the fore-aft translation, for the plate considered in Figure 96. A strong trailing edge vortex
forms shortly after translation stroke reversal, but is quickly shed. On the rotation at the extremum of the
opposite stroke, a n opp osite-sign vortex forms from t he p late trailing ed ge. These f orm an al ternating
vortex pair, akin to the reverse vortex street identified by Freymuth 116.
Figure 97. Trailing edge dye injection indicating (in the scalar sense) TEV development. Phases of plunge
motion, from top left corner: 0, 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, and 330.
As of t his w riting ( January 2010) , w e h ave onl y be gun t o s tudy t o r ectilinear free-to-pivot
problem. T he HIPPO rig can easily handle the nonrectilinear version too, by mounting a desired aspect
ratio plate in th e with its span along w hat w ould b e t he s treamwise di rection, and c alling t he “ pitch”
115
degree of f reedom of t he H IPPO r ig, t he s weeping m otion. H owever, t his is a t ask f or the f ollow-on
project. Our work here is already good enough for government work.
116
7.
7.1
Conclusion
General Musings
The literature i n un steady a erodynamics a t l ow Reynolds num ber i s v ast a nd g rowing.
University-type o f w ind tunnels an d w ater t unnels easily l end themselves to l ow-Re experiments, an d
low-Re i s a n atural choice f or ei ther resource-limited c omputations, or high-resolution c omputations at
any r esources sc ale. O n t he ap plied a erodynamics s ide, Micro A ir Vehicles a re a natural ch oice f or
aircraft construction, flight test and experimentation, because of low cost and relative ease of transitioning
from t he l ab t o the flight line. N either i s research in l ow-Reynolds num ber a erodynamics l imited t o
applications t o M icro A ir Vehicles o r n atural f lyers; i t ex tends to ai rfoils in g eneral, f or aerodynamic
testing of aerospace configurations in small-scale facilities where the Reynolds number happens to be low
not by intention but by necessity, for fundamental studies such as oscillating circular cylinders, for flowcontrol experiments and on and on. The field is breathtakingly broad.
In this humble work, our objectives have been (1) to extend to dynamic problems the recent work
on static low Reynolds number airfoils, such as laminar separation bubbles and separations in general; (2)
to explore how the Reynolds number, f requency and amplitude range f or MAV-relevant problems may
differ from t hose o f cl assical d ynamic st all; (3) to co nsider h ow c lassical an alytical m ethods for
aerodynamic f orce pr ediction, s uch a s Theodorsen’s f ormula, m ight a pply f or m assively uns teady
conditions; (4) to explore the limitations of linear superposition, and the presence of phase lags between
force r esponse a nd motion pr escription; ( 5) t o s urvey c onditions f or c oncentrated-vortex f ormation a nd
shedding, and (6) to build a path from abstract unsteady problems to MAV applications such as perching
and flapping. We ignored important problems such as fluid-structure interaction, non-rectilinear motions,
very low Re (below 5,000), gust and other unsteady external forcing effects, and on and on.
The a erodynamics of flapping w ings is u ltimately c oncerned w ith the relation between m otion
kinematics an d t he t ime-history of a erodynamic f orces a nd m oments. B ut a n i mportant i ntermediate
quantity is the evolution of the flowfield – and in particular of flow separation. Nature’s solution to large
time-varying pressure gradients, for example those due to aggressive motions, is to form and eventually to
shed vortices. We are interested in understanding and exploiting these vortices – for example, in delaying
vortex s hedding t o pr omote l ift i n s ituations w here flow sep aration i s i n an y case i nevitable; an d i n
surveying how vortex s hedding doe s or do es no t l ead t o non linearities. O nce t he m ain t rends i n
aerodynamic f orce hi story a re u nderstood, w e b ecome e quipped to r un l arge pa rameter studies a nd
optimizations, first c onfined to force/energy/power in aerodynamics, and then in a multi-disciplinary
sense, including for example considerations of structure and actuation.
7.2
Resume of Results
Summarizing the findings of research covered by this report, we have:
-
-
As i s w ell known, t he f low s eparation a nd aerodynamic f orce history of l ow-Reynolds number
airfoils (Re of ~60,000) depends strongly on l aminar to turbulent transition, and therefore on the
facility f low qua lity. I n t he dy namic case, w here t he a irfoil i s pi tching/plunging, t he role o f
transition is more subtle. At moderate Reynolds number (10,000 – 60,000) and n ear-stall peak
effective angle of attack, as results from a combined pitch-plunge motion, lift and flow separation
are again strongly sensitive to boundary layer transition effects. On the other hand, high effective
angle of attack, well beyond stall, means that effects of transition are of secondary importance.
Flat plates with round edges have much lower sensitivity to either Reynolds number or boundary
layer transition effects, whether in static or dynamic conditions.
117
-
-
-
7.3
For static problems, flat plates of low aspect ratio have lift coefficient behavior in almost exact
accordance w ith p redictions o f c lassical slender-wing t heory, a nd w ake v orticity measurement
gives accurate estimate of lift, relative to direct force measurement with a balance.
On the ot her hand, i n t he dynamic case, s mall aspect ratio p lates ( AR = 2 ) evince f lowfield
features irreducible to infinite aspect ratio, but the lift and drag history of the AR=2 plate is more
quasi-steady and more similar to simple theoretical prediction than what one finds for a wall-towall or 2D plate.
Lift c oefficient time h istory is m uch m ore q uasi-steady t han t he ev olution of f low s eparation
would purport, suggesting that low-level engineering methods still have good potential for MAV
aerodynamics p rediction. This is e ssentially a c orollary o f the f inding th at flow separation,
especially leading edge vortices, has relatively benign effect on lift coefficient history. It appears
that the role of LEVs is more to extend quasi-steady lift curve slopes to post-stall angle of attack,
than necessarily to provide “vortex lift”.
Lift pr oduction i n h igh-frequency l ow-amplitude o scillations i s dom inated by nonc irculatory
effects, w hence cl assical planar-wake models ha ve good pr edictive ut ility de spite not r esolving
the flowfield features even to first order.
Circulatory a nd noncirculatory f orce c ontributions a re additive, i n the s ense of l inear
superposition, e ven f or m assively nonl inear p roblems, s uch a s hi gh-rate hi gh a ngle-of –attack
pitch ramps.
The specific type of motion profile – sinusoidal, linear sawtooth, and so forth – has very much a
secondary role in flowfield evolution for high-rate periodic or transient problems.
Some hi gh-rate h igh-amplitude (that i s, h igh S trouhal num ber) m otions h ave n onunique w ake
states, and the route towards achieving this or that wake flowfield depends on starting conditions.
No rectilinear motions, whether for low-aspect ratio or wall-to-wall models, was found where the
leading edge vortex is retained for any significant amount of dimensionless time; vortex shedding
invariably follows vortex formation.
Toward Future Work
The main emerging theme of t his w ork i s t he e xtent t o w hich uns teady, l ow R eynolds number
aerodynamics is really quasi-steady. Unsteadiness comes from viscous effects – separation and so forth;
and from u nsteadiness, where n either f low st ate n or aerodynamic forces a re reducible to instantaneous
position information. We have given many ex amples o f u nsteadiness and surprising cases w here large
unsteadiness is to be expected, but was not evinced; or, for example in the case of high-rate pitch ramps,
where circulatory and noncirculatory forces superimpose, although superposition should fail in massively
nonlinear pr oblems. T he most obv ious e xtension o f work c onducted s o f ar is more pa rameter studies.
These include:
-
-
Variations of the pi tch-plunge parameter λ, plunge amplitude h, pl unge f requency h, pi tch
amplitude, m ean i ncidence a ngle, a nd pi tch p ivot po int. One co uld s elect v arious sch emes t o
further s tudy p itch-plunge e quivalence, t he r ole of S trouhal num ber, the br eakdown o f
Theodorsen’s l ift f ormula for s ufficiently a ggressive motions ( which must ha ppen e ventually!),
and the f ormation of v ortex-on-vortex i nteractions w hich m ust, on e w ould think, a lso oc cur in
fast e nough m otions – as i ncipiently ha ppened i n t he mixed-frequency pr oblems, w here L EVs
formed into pairs and swam upstream. How do these various flowfield curiosities translate into
tangible integrated aerodynamic force effects?
Impulsive-start p roblems, w here the w ater t unnel is r un as a t ow-tank u sing the s treamwiseoriented l inear m otor. E xamples i nclude W agner-type m otions t o s tudy i ndicial r esponse, a nd
more complex motions to compare convolution of indicial response with the motion history, vs.
118
directly-measured lift. This is yet another test of superposition/linearity, and can be studied at a
wide range of geometric conditions (aspect ratio, set angle of incidence, etc.).
In a ddition, on e c ould study pr oblems m ore r elevant t o M AV a pplications, a nd m ore
interdisciplinary, beyond strictly aerodynamics. Just a few thoughts include:
- Generalization to f lexible plates/wings/airfoils, and the pr oblem of f luid-structure interaction.
Does a chordwise-flexible plate b end to o rient itself to attenuate sep aration? D oes a spanwise
flexible p late, in r ectilinear p itch/plunge, h ave a w ingtip d eflection h istory th at te nds t owards
producing a spanwise pressure gradient stabilizing a particular kind of flow separation (such as a
stable LEV)? And how does structural flexibility couple into the concept of fluid apparent mass?
- How c an g usts encountered i n flight s ituations be m odeled i n a g round t est facility? F or a n
accelerating m odel, t here i s a n oncirculatory f orce d ue t o acc eleration. B ut i n an acce lerating
flow about a m odel s tationary i n t he l ab-frame, t here i s p ressure g radient n ecessary to su pport
said acceleration, which also manifests itself as a f orce on the model. T o what extent do these
issues matter for gust modeling? A nd what is the relevant gust spectrum which we ought to be
modeling?
- Generalizing t o richer k inematics, including bot h r ectilinear a nd n onrectilinear, how doe s on e
begin t o s earch for the “optimum” k inematics of f lapping, a ssuming f or the sake of di scussion
that we have settled on the appropriate definition of “optimal”?
- And finally, to close with a discussion that commenced this report: what really is it about flapping
that o ffers a nd a dvantage over rotary f light… especially if both c an be a dequately m odeled by
quasi-steady methods, and it turns out that neither really exploits spectacular nonlinearities for lift
enhancement?
There are indeed many questions to address. Let us hope that the grant money remains forthcoming!
119
LIST OF ACRONYMS, ABBREVIATIONS, AND SYMBOLS
ACRONYM/
SYMBOL
MAV
LEV
TEV
PIV
LSB
RTO
NATO
TTCP
HIPPO
HFWT
CFD
EFD
LES
RANS
FBG
ω
Γ
ν
St
k
CL
CD
CM
U∞
c
f
h
h0
α0
t/T
λ
φ
xp
αe
A
Re
K
°
DESCRIPTION
Micro Air Vehicle
Leading Edge Vortex
Trailing Edge Vortex
Particle Image Velocimetry
Laminar Separation Bubble
Research and Technology Organization
North Atlantic Treaty Organization
The Technical Cooperation Program
High-Intensity Pitch-Plunge Oscillator Rig
Horizontal Free-surface Water Tunnel
Computational Fluid Dynamics
Experimental Fluid Dynamics
Large Eddy Simulation
Reynolds-Averaged Navier Stokes Simulation
Fiber Bragg Grating Load Cell
Vorticity, out-of-plane component
Circulation
Kinematic viscosity of water
Strouhal Number
Reduced Frequency of Sinusoidal Oscillation
Lift coefficient
Drag (or thrust) coefficient
Pitching moment coefficient, about the quarter-chord
Free-stream speed, typically cm/s
Airfoil, plate or wing reference chord
Sinusoidal oscillation frequency of pitch, plunge or surge, in Hz
Plunge position as function of time
Nondimensional plunge amplitude
Mean angle of attack (the constant pitch angle offset from zero)
Dimensionless time
Ratio of pitch-amplitude to plunge-induced angle of attack
Phase difference between pitching and plunging; positive → pitch leads
Pitch pivot point: fraction of chord aft airfoil leading edge
Total angle of attack from trigonometric combination of pitch and plunge
Pitch amplitude (in degrees)
Reynolds number, Re = c U∞/ν
Dimensionless pitch rate in linear pitching motion
Degrees (angle of attack, etc.)
120
Appendix A. The Fiber-Bragg Grating Force Balance
Here we provide a brief summary of the Fiber-Bragg Grating (FBG) custom force balance as used
in the above-mentioned experiments. The methodology is not new, but the design of the balance is oneoff, i n t he s ense t hat a c onventional ba lance w ould not i nterface w ith t he p itch-plunge o scillation r ig,
whence a custom solution was necessary.
A.1.
FBG Theory of Operation
A FBG sensor is a single-mode optical fiber in which a periodic index-of-refraction modulation
along the fiber direction (grating) is introduced in a short section of the fiber. Light propagating along the
fiber refracts in the grating resulting in a reflected signal of very narrow wavelength determined by the
period of the refractive index modulation. The wavelength of the reflected signal is given by
λ=
2 n eff Λ
B
(Eqn. A1)
where n eff is the e ffective r efractive in dex of th e single-mode opt ical fiber, a nd Λ is the period o f th e
refractive index modulation. In t ypical i mplementations of the technology, t he gr atings are 8 to 20 m m
long and several can be placed along the same fiber spaced from centimeters to a few meters apart.
FBG sensors measure strain by detecting very small changes in the wavelength of the reflected light.
The change in wavelength, ∆λ B is a function of the strain and the temperature change in the fiber,
∆λ B
= Pe ∆ε +  Pe ( α s − α f ) + ς  ∆T
λB
(Eqn. A2)
where P e is t he st rain-optic c oefficient, ∆ε is the s train a cting on t he f iber, αs and αf are t he t hermal
expansion coefficients of the fiber bonding material and the fiber, respectively, and ζ is the thermo-optic
coefficient. The normalized constant temperature strain response is,
∆λ B
=
0.78 × 10−6 1/ micro − strain
λ B ∆ε
and the normalized thermal response at constant strain is,
∆λ B
−1
= 6.678 × 10−6 ( °C ) .
λ B ∆T
(Eqn. A3)
(Eqn. A4)
For t ypical co mmercial F BS sen sors t he w avelength sh ifts a re ~ 1 p m/micro-strain a nd 10 pm /°C
(1 pm = 10-12 m).
The second important element of an FBG system is the wavelength reading instrument or optical sensor
interrogator. A typical commercial system has t he capability to sam ple multiple channels ( 4), each
having multiple SBG sensors (100s) with resolution as small as 0.1 pm and sampling frequency up t o a
few kHz. These performance metrics make the technology very attractive for the present application. Key
features that are particularly relevant are: 1) the sensing element is optical and should be immune to emradiation and other noise sources; 2) very small sensors (the size of the optical fiber) that could be easily
integrates i nto t he load c ell s tructure. I mportant c hallenges f or t he t echnology a re: 1) hi gh t emperature
sensitivity that will require temperature compensation, and 2) fiber optic bending radius should be larger
1-inch w hich may r epresent a p roblem f or v ery s mall sy stems. T hese ch allenges must b e ad equately
addressed in the design of the load cell to achieve the high sensitivity and balance stiffness required for
the present application.
A.2.
Load Cell Mechanical Design
FBGs measure strain at a s pecific location in an optical fiber by detecting the spectrum of reflected
light. The f iber r eflection spectrum has a m aximum at a w avelength w hich i s proportional t o t he l ocal
strain at the location of a FBG sensor. As noted above the main advantages of the technology relevant to
121
the present application are: 1 – It is an optical sensing technique and therefore immune to electronic noise,
which i s p articularly p roblematic f or e lectronic sensors i n w ater an d i n p roximity t o t he hi gh c urrent
linear motors used to drive the model; 2 – Several FBG strain sensors can be placed in the same fiber at
precise locations and, therefore, only a single fiber is needed for a multi component force sensor. For the
present research the mounting plate was instrumented with 4 (1st generation) or 5 ( 2nd generation) F BG
sensors to measure the l ift, drag and p itching moment acting on t he a irfoil. The ba sic g eometry of t he
mounting plate is the same as the original mounting plate. The plunge rods pivot locations, airfoil model
attachment p oints an d thickness ar e t he sam e. T he f lexures an d fiber o ptic paths are m achined to
accommodate the FBG sensors. A drawing of the 1st generation instrumented mounting plate is shown in
Figure 98. There a re t wo parts i n t he m odified a ttachment pl ate, r elative t o t he or iginal de sign of t he
HIPPO airfoil installation, which was uninstrumented. The plunge rods are attached to the center part of
the plate at the pivot points, while the airfoil model is attached to the outer part of the plate. Thin flexures
instrumented w ith F BG s train sen sors join t he t wo parts o f t he p late. The l ocations o f the F BGs ar e
designed to provide temperature compensation as well as decoupling between the lift, drag and pitching
moment component measurements as discussed below.
Flow
Flexure
FBG location
Optical fiber path
Forward pivot point
Flexure
Aft pivot
Figure 98. Drawing of the mounting plate showing the optical fiber path and the location of the flexures and
FBG sensors on the top surface of the plate. Another two FBG sensors are placed on the bottom side of the
flexures.
A commercial CAD package with FEM analysis (SolidWorks, http://www.solidworks.com/) was used to
size t he flexures a nd t o o btain pr eliminary e stimates o f th e lo ad c ell calibration m atrix a nd s tiffness
characteristics. The primary design parameters are the flexures length and cross section dimensions; and
the spacing between the two attachment points of the load cell center section to the flexures. For the data
reported here the f lexure lengths are 0 .75”, t he cross sections are 0.033”× 0.140” and the distances
between c enter s ection a ttachment poi nts a re 0.3 75”. T he resonance f requency of t he load cell m odel
combination with the SD7003 model mounted was estimated using FEM analysis and is approximately 60
Hz.
122
A.3.
Load Cell Calibration
The load cell is designed to measure the force components normal to the mounting plate, parallel to
the plate (that is, the axial force) and the pitching moment. T his is achieved with 5 gauges – two are at
the front flexure of the load cell, two are at the aft flexure, and the fifth gauge is unstrained, being used as
a temperature co mpensation d evice. Locations an d s pecifications of the f our l oad-sensing g ratings a re
given i n Table A1. During installation the FBG sensors are pre-strained before bonding to the flexures.
The resulting shift in wavelength for no load is also given in Table A1.
Table A1. Location and Wavelength of FBG Sensors in Load Cell.
FBG
#
1
2
3
4
Location
Wavelength (nm)
Bottom Aft
Bottom Forward
Top Aft
Top Forward
1526
1536
1546
1556
No Load
(nm)
1526.833
1536.765
1546.788
1556.607
Wavelength
Load cell sensor outputs can be combined to decouple the three force components and a temperature
output. A pos itive nor mal force (towards t he s uction s ide of t he a irfoil) produces positive s train in the
FBGs mounted on the top of the sensor bars and negative strain on the FBGs mounted on the bottom of
the sensor bars. Similarly positive axial force (downstream) produces positive strain in the FBG mounted
on t he forward sensor bar a nd negative strain in the F BG m ounted on t he a ft s ensor ba r. A po sitive
pitching moment (forward up) produces positive strain in top forward and bottom aft FBGs and negative
strain in t he bottom f orward and top aft FBGs. And a n increase in temperature produces a positive
increase of the wavelength of all the FBG sensors. Hence, for the purpose of calibration we define,
∆λ N = −∆λ1 − ∆λ 2 + ∆λ 3 + ∆λ 4
∆λ A = ∆λ1 − ∆λ 2 + ∆λ 3 − ∆λ 4
∆λ M = ∆λ1 − ∆λ 2 − ∆λ 3 + ∆λ 4
(Eqn. A5)
∆λ T = ∆λ1 + ∆λ 2 + ∆λ 3 + ∆λ 4
or in matrix form,
 ∆λ N   −1 −1 1

 
 ∆λ A  =  −1 1 −1
 ∆λ M   1 −1 −1

 
 ∆λ T   1 1 1
1  ∆λ1 


1  ∆λ 2 
1  ∆λ 3 


1  ∆λ 4 
(Eqn. A6)
C14   ∆λ N   N o 


 
C24   ∆λ A   A o 
+
C34   ∆λ M   M o 


 
C44   ∆λ T   To 
(Eqn. A7)
Then, in the calibration matrix is
N
 
A
=
M
 
T
 C11

 C 21
 C31

 C 41
C12
C 22
C32
C 42
C13
C23
C33
C43
The calibration matrix is expected to be almost diagonal, and off-diagonal terms attempt to account for
sensor cross-talk. Of course, since compensation and calibration is just successive matrix multiplication,
the two can be combined in one step.
Calibrations are in-situ inside the water tunnel, using the water’s large thermal inertia to minimize
temperature e ffects. A lo ading f ixture is a ttached t o the load c ell, a nd weights are hung f rom s pecific
points on t he fixture. The p itch/plunge r ig i s pr ogrammed t o s lowly s tep t hrough a s eries of a ngles of
attack in semi-random fashion, typically from -45° to +45°, in 5° increments, in upgoing and downgoing
123
directions (to control for possibility of hysteresis). Applied loads are from 0 to 5 lbf. The whole process
is repeated for at least two nominal values of water temperature, in attempt to build a calibration resulting
in load sensing insensitive to temperature. F resh water introduced into the HFWT is typically at around
57°F, but after 1-2 days the temperature equilibrates to around 68°F. Thus an adequate spread in ambient
temperature is achieved by running a l oading sequence in water that has been resident for several days,
followed by a new sequence after draining and refilling the tunnel.
At each load condition the wavelength shifts ∆λ i , i = 1 − 4 are measured and t he values of ∆λ N ,
∆λ A , ∆λ M , and ∆λ T are calculated. A least squares fit to the data gives the calibration matrix, for which a
typical value would be
N
 
A
=
M
 
T
7.457
4.457
0   ∆λ N   0.030 
 58.477
 



0   ∆λ A   0.011 
 1.251 137.009 1.190
.
+
 0.141
2.965 104.960
0   ∆λ M   -0.022 
 



−9.235 8.813   ∆λ T   50.854 
 −2.413 −3.4
(Eqn. A8)
where the wavelength shift are expressed in nm, the physical variables (N – normal force, A – axial force,
M - pitching moment and T - temperature) are expressed in imperial units.
Standard error for the force and temperature calibration results are given in Table A2. The calibration
matrix diagonal elements for the force components are very large compared to the off diagonal elements
indicating good decoupling between the measured force components and good temperature compensation.
This is also shown by the plots which show excellent correlation between the force applied and
component wavelength shift.
Table A2. Load Cell Calibration Standard Error.
N (lbf)
A (lbf)
M (in-lbf)
T (K)
A.4.
Standard Error
0.11
0.15
0.07
0.34
Data Processing
A Mi cron O ptics s m130 4-channel 1000H z-samping “ Optical S ensor Interrogator” was u sed t o
record the FBG’s wavelength time-history. The instrument recorded the output of all 5 FBG sensors in the
fiber, so metimes at t he maximum sa mpling r ate, an d so metimes su bsampled (down t o 2 50 Hz o r less)
with m oving-averages ap plied. Even 250H z much higher t han n ecessary f or the p resent ex periments
where typical motion physical frequency is of the order of 1 Hz or less. The data were smoothed using a
recursive low pass filter with a cut-off frequency of 6.5 Hz (-3 dB point), which is well above the airfoil
motion frequency and the characteristic flow frequency U/c ~ 2.7 s -1. This filter effectively averages data
50 co nsecutive d ata p oints w ith w eight factors d esigned t o o ptimize h igh-frequency r oll off a nd i t is
implemented with symmetric impulse response to eliminate phase distortion. The frequency cut-off of the
filter w as determined ba sed on m easurements of the power s pectra of t he F BG out puts. Typical pow er
spectra before and after filtering a re plotted in Figure 99. Figure 99(a) shows the power spectra of the
output data from a typical unsteady run. At low frequency (i.e. < 5 Hz) there well-defined spectral peaks
associated with the airfoil motion. There is also a very strong peak at 25 Hz. It was determine that this
spectral peak is associated with the water channel pump rotational speed. Examination of the flow with
flow v isualization revealed no e vidence o f f low s tructure at t his frequency. T he pow er s pectrum a fter
filtering t he da ta is s hown i n Figure 99(b), the p eak a t 2 5 H z is s till p resent b ut th e m agnitude i s
significantly reduced, to a value comparable to the noise floor of the present measurements (~ -5 dB/Hz).
124
50
Power Spectral Density (dB/Hz)
0
-50
-100
-150
0
5
10
15
Frequency (Hz)
20
25
30
20
25
30
(a)
50
Power Spectral Density (dB/Hz)
0
-50
-100
-150
0
5
10
15
Frequency (Hz)
(b)
Figure 99. Typical powers spectra of a FBG sensor output. (a) Spectra of the raw data for a typical run, (b)
Spectra after low pass filter.
Critical to successful design of the FBG balance – and for that matter, any balance – is ensuring
that the strain in the flexure is much larger than the strain in the non-metric portions of the balance, such
as the interior piece connecting to the pitch/plunge rig’s plunge rods, and the exterior frame connecting to
the model. One attempts to design this using finite-elements, but in practice the geometry of the balance
evolves from trial and error, such as episodes where one observes that removing and replacing the model
– involving torquing and untorquing bolts connecting the model and the balance – causes drift in the FBG
wavelength s hifts. S uch observations a re ong oing, w hence e volutions o f ne w i terations of the F BG
balance are also ongoing.
125
Appendix B. Resume of Publications Supporting the Present Work
Self-referentially, this report is based on a series of conference papers and journal articles in
2002-2010, of which the PI was author or co-author. These are listed as follows:
11. OL, M.V. and Gharib, M. “Leading Edge Vortex Structure Of Nonslender Delta Wings
At Low Reynolds Number”. AIAA Journal, Vol. 41, No.1, pp 16-26. Jan 2003.
12. Biber, K., OL. M.V., and Tilmann, C.P. “Some Examples of Airfoil Design For Future
UAV Concepts”. AIAA-2004-1050.
13. Khrabrov, A., and OL, M. “Effects of Flow Separation on Aerodynamic Loads in
Linearized Thin Airfoil Theory”. Journal of Aircraft, Vol. 41, No. 4, pp. 944-949, JulyAugust 2004.
14. OL, M.V., McAuliffe, B. R., Hanff, E. S., Scholz, U., Kaehler, Ch., “Comparison of
Laminar Separation Bubble Measurements on a Low Reynolds Number Airfoil in Three
Facilities", AIAA 2005-5149.
15. Fonov, S., Goss, L., Jones, G., Crafton, J., Fonov, V., and OL, M.V. “New Method for
Surface Pressure Measurements”. AIAA-2005-1029.
16. Kaplan, S., Altman, A., and OL, M.V. “Wake Vorticity Measurements for Low Aspect
Ratio Wings at Low Reynolds Number”. J. Aircraft, Vol. 44, No. 1, pp. 241-251, 2007.
17. OL, M.V. "Water Tunnel Velocimetry Results for the 1303 UCAV Configuration".
AIAA-2006-2990.
18. OL, M.V. “Vortical Structures in High Frequency Pitch and Plunge at Low Reynolds
Number”. AIAA-2007-4233.
19. Lian, Y., OL, M.V., and Shyy, W. "Comparative Study of Pitch-Plunge Airfoil
Aerodynamics at Transitional Reynolds Number". AIAA-2008-652, 2008.
20. Dong, H., Webb, C., and OL, M.V. "Effects of Unequal Pitch and Plunge Airfoil Motion
Frequency on Aerodynamic Response". AIAA-2008-582, 2008.
21. McGowan, G., Gopalarathnam, A., OL, M.V., and Fredberg, D. "Computation vs.
Experiment for High-Frequency Low-Reynolds Number Airfoil Pitch and Plunge".
AIAA-2008-653, 2008.
22. OL, M.V., Dong, H., and Webb, C. "Motion Kinematics vs. Angle of Attack Effects in
High-Frequency Airfoil Pitch/Plunge". AIAA-2008-3822
23. Abate, G., OL, M.V., and Shyy, W. "Introduction: Biologically Inspired
Aerodynamics". AIAA Journal, Vol.46 no.9, pp. 2113-2114, 2008
24. OL, M.V., Parker, G., Abate, G., and Evers, J. "Flight Controls and Performance
Challenges for MAVs in Complex Environments". AIAA-2008-6508
25. Chabalko, C., Snyder, S., Beran, P., OL, M.V., and Dong, H. "Study of Deflected Wake
Phenomena by 2D Unsteady Vortex Lattice". AIAA-2009-2475
26. McGowan, G., Gopalarathnam, A., OL. M.V., and Edwards, J. "Analytical,
Computational, and Experimental Investigations of Equivalence Between Pitch and
Plunge Motions for Airfoils at Low Reynolds Numbers". AIAA-2009-535
27. OL, M.V., Bernal, L., Kang, C.-K., and Shyy, W. “Shallow and Deep Dynamic Stall for
Flapping Low Reynolds Number Airfoils”. Experiments in Fluids, Vol. 46, No. 5, May
2009.
28. Bernal, L.P., OL, M.V., Szczublewski, D., and Cox, C. "Unsteady Force Measurements
in Pitching-Plunging Airfoils". AIAA-2009-4031
29. Eldredge, J., Wang, C., and OL, M.V. "A Computational Study of a Canonical Pitch-Up,
Pitch-Down Wing Maneuver". AIAA-2009-3687
30. Alam, M., Suzen, Y.D., and OL, M.V. "Numerical Simulations of Pitching Airfoil
Flowfields for MAV Applications". AIAA-2009-4029
126
31. OL, M.V., Reeder, M., Fredberg, D., McGowan, G., Gopalarathnam, A., and Edwards, J.
"Computation vs. Experiment for High-Frequency Low-Reynolds Number Airfoil
Plunge". International J. of MAVs, Vol. 1, No. 2, 2009.
32. OL, M.V., Eldredge, J.D., and Wang, C. “High-Amplitude Pitch of a Flat Plate: an
Abstraction of Perching and Flapping”. International J. of MAVs, Vol. 1, No. 3, 2009.
33. Rausch, J., Baik, Y.S., Bernal, L., and Ol, M. "Fluid Dynamics of Rigid and Flexible
Lifting Flat Plates in Pitch-Plunge Motion at Low Reynolds Numbers". AIAA-2010-389
34. Baik, Y.S., Rausch, J., Bernal, L., Shyy, W., and Ol, M. "Experimental Study of
Governing Parameters in Pitching and Plunging Airfoil at Low Reynolds Number".
AIAA-2010-0388
35. OL, M., Altman, A., Eldredge, J., Garmann, D., and Lian, Y. "Summary of Progress on
Pitching Plates: Canonical Problems in Low-Re Unsteady Aerodynamics". AIAA-20101085
36. Lian, Y., and Ol, M.V. “Computation and Experiment on a Low Aspect Ratio Pitching
Flat Plate”. AIAA 2010-0385.
127
Appendix C. Listing of Research Collaborators
The work described in this report would have been impossible to conceive or to execute as sole
and individual effort. C ross-pollination of ideas has been invaluable, both amongst experimentalists and
with t heoreticians a nd c omputationalists. In t he c ase of c omputations, w ater tunnel e xperiments h ave
provided validation, and computation has yielded force data where none was available in the experiment.
Computation can also reverse-validate experiment, for example to help understand the role of blockage or
ambient turbulence intensity. Theory has guided test matrix definition in the water tunnel, and has been a
baseline c heck on e xperiment a nd computation a like. A nd ot her e xperiments h ave l ent s upport t o t he
present results, f or e xample c onfirming t he r ole of model v ibrations i n f orce balance t ime-traces, o r
particle image velocimetry resolution in tracking the evolution of Reynolds stresses in laminar separation
bubbles. In brief, principal collaborations over the past 7 years have been:
Prof. Haibo Dong, W right S tate U niversity. C omputations ( immersed bounda ry methods) o n
airfoils and flat plates undergoing various motions, including sinusoidal pitch and plunge oscillations and
linear ramps.
Prof. Ashok Gopalarathnam, N orth C arolina S tate U niversity. T heory ( classical m ethods) an d
Reynolds-Averaged N avier S tokes c omputations on airfoil pitch-plunge e quivalence and l ift coefficient
time history vs. motion time history.
Prof. Altman, University of D ayton. A daptation o f R olling H ills R esearch C ompany’s w ater
force balance in the HFWT, HFWT test campaign on static Aspect Ratio = 2 wings, and experiments on
flat-plate plunge in hover.
Dr. M iguel Visbal, A FRL/RBAC. High-order 2D a nd 3D c omputations us ing Implicit L arge
Eddy S imulation o n a r ange of a irfoil plunge, p itch a nd “perching” pr oblems, pa ralleling H FWT
experiments.
Prof. Jeff Eldredge, University of California, Los Angeles. C omputations (Immersed Boundary
Method) on canonical problem of pitch-hold-return of a flat plate, identifying trends in lift coefficient vs.
motion reduced frequency; and theoretical modeling of unsteady loads.
Prof. Wei Shyy, University of Michigan. R eynolds-Averaged Navier Stokes computations on a
range o f oscillating ai rfoil and flat plate ca ses, co mparing computed vortex-formation and time hi story
with HFWT experiments.
Prof. Luis Bernal, University of Michigan. Water tunnel experiments paralleling experiments in
the HFWT, and development of Fiber-Bragg Grating force balance for the HFWT.
Prof. Holger Babinsky, Cambridge University, United Kingdom. Water tow tank experiments on
rectilinear vs. n on r ectilinear motion o f f lat plates, t o assess r ole of sp anwise f low an d stability o f the
leading edge vortex, paralleling HFWT experiments limited to the rectilinear case.
Prof. Rolf Radespiel, Technical University of Braunschweig, Germany. Wind tunnel experiments
on sinusoidally oscillating airfoils and low aspect ratio flat plates, comparing laminar separation bubble
physics vs. facility flow quality, relative to HFWT experiments.
Prof. Y ongsheng L ian, U niversity o f L ouisville. R eynolds-Averaged N avier-Stokes
computations of periodic and aperiodic unsteady problems, compared with water tunnel experiments on
the same configuration, with a focus on the role of water tunnel test sectional blockage and other groundtesting corrections.
128
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