FACILITY AND FLOW DEPENDENCE ISSUES INFLUENCING THE
EXPERIMENTAL CHARACTERIZATION OF A LAMINAR SEPARATION BUBBLE
AT LOW REYNOLDS NUMBER
By
David Arthur Olson

A THESIS
Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of
MASTER OF SCIENCE
Mechanical Engineering
2011

ABSTRACT
FACILITY AND FLOW DEPENDENCE ISSUES INFLUENCING THE
EXPERIMENTAL CHARACTERIZATION OF A LAMINAR SEPARATION
BUBBLE AT LOW REYNOLDS NUMBER
By
David Arthur Olson
There is an immediate and evolving need for Micro Air Vehicles (MAVs) in both the defense and civilian industry. The applications for these very small (bird and insect sized),
remotely operated or autonomous vehicles range from reconnaissance to remote hazardous
material identiﬁcation. The fundamental ﬂuid mechanics of these small aerial vehicles, operating at low speeds, are not yet fully understood. One particular issue is a documented
discrepancy in the characteristics of the laminar separation bubble on airfoils obtained from
various experimental and computational studies at Reynolds numbers typical of MAV operation. The inﬂuence of added freestream turbulence, among other facility-dependent issues,
is studied for a range of chord Reynolds numbers (2 × 104 − 6 × 104 ), and angles of attack
(0◦ − 11◦ ). The baseline ﬂow is compared against the ﬂow with added freestream turbulence using single-component Molecular Tagging Velocimetry (1c-MTV) with a cross-stream
spatial resolution of 52 µm. An increase in freestream turbulence is shown to decrease the
size of the separation bubble, both by delaying separation and triggering an earlier reattachment. Increased freestream turbulence is also characterized by a reduction in the height of
the reversed ﬂow region, and a decrease in the streamwise velocity ﬂuctuations downstream
of separation. The experimental characterization of the separation bubble is also found to
be sensitive to near-wall spatial resolution. The introduced bias error shortens the measured
bubble length and is dependent on the shape of the separation bubble.

Copyright by
DAVID ARTHUR OLSON
2011

ACKNOWLEDGMENTS

First and foremost, I would like to acknowledge my advisors Dr. Manooch Koochesfahani
and Dr. Ahmed Naguib for their continual support and guidance throughout the course
of project. And, I would like to thank the other members of my guidance committee: Dr.
Farhad Jaberi and from the Air Force Research Laboratory, Dr. Miguel Visbal.
I graciously thank Dr. Shahram Pouya for his endless patience and support in the early
stages of my research (and all the troubleshooting int the latter stages). I would like to
thank Rohit Nehe for our endless discussions, which ranged from the technical details to
recommendations for quality movies and television. I also greatly appreciated all of the
much needed ping-pong breaks at all hours of the day and night. And I would also like to
thank Dr. Bruno Monnier, who has provided good daily conversation over lunch and has
made Rohit and I step up our ping-pong game.
Lastly, I would like to thank my friends and family for attempting to keep me sane during
this entire process.

iv

TABLE OF CONTENTS

List of Tables

vii

List of Figures

viii

Nomenclature

xi

1 Introduction
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Experimental Methods
2.1 Facility . . . . . . . . . . . . . . . . . .
2.1.1 Flow Facility . . . . . . . . . .
2.1.2 Airfoil . . . . . . . . . . . . . .
2.1.3 Grid Generated Turbulence . .
2.2 Molecular Tagging Velocimetry (MTV)
2.2.1 Background . . . . . . . . . . .
2.2.2 Current Implementation . . . .
2.2.3 Error Quantiﬁcation of 1c-MTV
2.3 Quantifying the Freestream Turbulence
2.3.1 Background . . . . . . . . . . .
2.3.2 Technique . . . . . . . . . . . .
2.4 Data Acquisition . . . . . . . . . . . .
2.4.1 Imaging . . . . . . . . . . . . .
2.4.2 Image Processing . . . . . . . .
2.4.3 Alignment and Synchronization
2.5 Experiments . . . . . . . . . . . . . . .
2.5.1 Experimental Parameters . . .
2.5.2 Experimental Procedure . . . .

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over an Airfoil Surface
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3 Results and Discussion
3.1 Freestream Turbulence Characteristics . . . . . . . . . . . .
3.2 Representative Results . . . . . . . . . . . . . . . . . . . . .
3.2.1 Streamwise Velocity Contours: Mean and Fluctuation
3.2.2 Separation and Reattachment . . . . . . . . . . . . .
3.3 Characterizing the Laminar Separation Bubble . . . . . . . .
3.3.1 Inﬂuence of Added Freestream Turbulence . . . . . .
v

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4 Summary
4.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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A Freestream Turbulence
A.1 Freestream Turbulence Spectra . . . . . . . . . . . . . . . . . . . . . . . . .

69
69

B Mean and RMS Contours
B.1 Mean Flow ﬁeld Evolution by Angle of Attack . . . . . . . . . . . . . . . . .
B.2 RMS Flow ﬁeld Evolution by Angle of Attack . . . . . . . . . . . . . . . . .
B.3 Mean Flow ﬁeld Evolution by Reynolds Number . . . . . . . . . . . . . . . .

73
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81

C Compiled LSB Characteristics

86

D Miscellaneous
D.1 Test Section Photos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.2 Procedure of Simulated Experiments . . . . . . . . . . . . . . . . . . . . . .
D.3 Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88
88
90
92

Bibliography

96

3.4

3.5

3.3.2 Inﬂuence of Angle of Attack . . . .
3.3.3 Inﬂuence of Reynolds Number . . .
Comparisons of LSB Characteristics . . . .
3.4.1 Separation and Reattachment . . .
3.4.1.1 Reynolds Number 20,000 .
3.4.1.2 Reynolds Number 30,000 .
3.4.1.3 Reynolds Number 40,000 .
3.4.2 Bubble Length . . . . . . . . . . .
3.4.3 Summary of LSB Characteristics .
Facility and Flow Dependent Issues . . . .
3.5.1 Freestream Turbulence . . . . . . .
3.5.2 Flow Three-Dimensionatlity . . . .
3.5.3 Airfoil Shape . . . . . . . . . . . .
3.5.4 Near-wall Spatial Resolution . . . .
3.5.5 Uncertainty in Wall location . . . .
3.5.6 Angle of Attack Sensitivity . . . . .

vi

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LIST OF TABLES

2.1

Experimental test matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

3.1

Freestream characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36

C.1 Compiled LSB characteristics . . . . . . . . . . . . . . . . . . . . . . . . . .

87

vii

LIST OF FIGURES

1.1

A typical laminar separation bubble . . . . . . . . . . . . . . . . . . . . . . .

2

2.1

Flow facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

2.2

Test section schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

2.3

Airfoil proﬁle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

2.4

Error in airfoil proﬁle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

2.5

Airfoil camber line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

2.6

Airfoil pitching system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

2.7

Near-wall regions of airfoil surface . . . . . . . . . . . . . . . . . . . . . . . .

12

2.8

Experimental determination of surface location . . . . . . . . . . . . . . . . .

12

2.9

Turbulence-generating woven mesh screen . . . . . . . . . . . . . . . . . . .

13

2.10 Example of MTV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

2.11 Schematic representing the 1c-MTV error . . . . . . . . . . . . . . . . . . . .

16

2.12 Simulated experiment 1c-MTV error results . . . . . . . . . . . . . . . . . .

17

2.13 Enlarged view of simulated experiment 1c-MTV error results . . . . . . . . .

18

2.14 Sample spatial autocorrelation of the freestream . . . . . . . . . . . . . . . .

20

2.15 Sample spatial autocorrelation coeﬃcients of the freestream . . . . . . . . . .

21

2.16 Sample 2c-MTV image pair . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

viii

2.17 Sample 1c-MTV image pair . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

2.18 Sample FOV shift diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

2.19 Hardware diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

2.20 Timing diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

3.1

Freestream spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

3.2

Representative contour of streamwise velocity . . . . . . . . . . . . . . . . .

38

3.3

Representative contour of streamwise velocity ﬂuctuation . . . . . . . . . . .

38

3.4

Representative view of separation . . . . . . . . . . . . . . . . . . . . . . . .

40

3.5

Representative view reattachment . . . . . . . . . . . . . . . . . . . . . . . .

41

3.6

Inﬂuence of increased FSTI on u at Rec = 3 × 104 and moderate α . . . . .
¯

43

3.7

Inﬂuence of increased FSTI on u at Rec = 2 × 104 and high α . . . . . . . .
¯

44

3.8

Inﬂuence of increased FSTI on u at Rec = 4 × 104 and moderate α . . . . .
¯

45

3.9

Inﬂuence of increased FSTI on urms at Rec = 4 × 104 and moderate α . . .

46

3.10 Inﬂuence of increased FSTI on urms at Rec = 3 × 104 and moderate α . . .

47

3.11 Angle of attack eﬀect on separation and reattachment locations . . . . . . .

49

3.12 Reynolds number eﬀect on separation and reattachment locations . . . . . .

50

3.13 Separation and reattachment locations, Rec = 2 × 104

. . . . . . . . . . . .

52

3.14 Separation and reattachment locations, Rec = 3 × 104

. . . . . . . . . . . .

54

3.15 Separation and reattachment locations, Rec = 4 × 104

. . . . . . . . . . . .

56

3.16 Laminar separation bubble length . . . . . . . . . . . . . . . . . . . . . . . .

58

ix

3.17 Near-wall region of separation . . . . . . . . . . . . . . . . . . . . . . . . . .

62

A.1 Freestream PSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

A.2 Freestream PSD for each Reynolds number . . . . . . . . . . . . . . . . . . .

72

B.1 u for Rec = 2 × 104
¯

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74

B.2 u for Rec = 3 × 104
¯

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75

B.3 u for Rec = 4 × 104
¯

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

B.4 urms for Rec = 2 × 104 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

B.5 urms for Rec = 3 × 104 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

B.6 urms for Rec = 4 × 104 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80

B.7 Reynolds number eﬀect on baseline u, low α . . . . . . . . . . . . . . . . . .
¯

82

B.8 Reynolds number eﬀect on baseline u, medium α
¯

. . . . . . . . . . . . . . .

83

B.9 Reynolds number eﬀect on baseline u, high α . . . . . . . . . . . . . . . . . .
¯

84

B.10 Reynolds number eﬀect on increased FSTI u, high α . . . . . . . . . . . . . .
¯

85

D.1 Test section photos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

x

Nomenclature
α

Angle of attack

u
¯

Mean streamwise velocity

ν

Kinematic viscosity

c

Chord

Ly

Integral length scale

urms

Root mean square of the streamwise velocity

U∞

Magnitude of the freestream velocity

(X,Y)

Lab reference frame with X along the bottom of the tunnel

(x,y)

Airfoil reference frame, x is along the chordline and the leading edge is (x=0,y=0)

1c-MTV

Single-component MTV

2c-MTV

Two-component MTV

Rec

Chord Reynolds number, Rec = U∞ c
ν

FOV

Field of view
xi

FSTI

Freestream turbulence intensity

hp

Horsepower

LSB

Laminar separation bubble

mC

Milli-chord, 1 mC = 0.001c

MTV

Molecular Tagging Velocimetry

PSD

Power spectral density

RMS

Root mean square

SNR

Signal to noise ratio

u,u

The streamwise component of velocity along the X-direction

UV

Ultraviolet

v,v

The cross-stream component of velocity along the Y-direction

xii

Chapter 1
Introduction

1.1

Motivation

Low Reynolds number (104 − 105 ) aerodynamic ﬂows are found in applications ranging from
small wind turbines, model aircrafts, to bio-mimetic devices and Micro Air Vehicles (MAVs).
Developments in complementary technologies, such as microelectronics and lightweight power
supplies, have brought MAVs into focus recently for a variety of applications in both the civilian and defense industry. They are well suited for reconnaissance, search and rescue, remote
diagnostics, and other applications where human presence is not possible or hazardous.

1.2

Background

The boundary layer of airfoils in the low-Reynolds number regime tends to remain laminar,
at least for some portion of the airfoil. This renders the boundary layer susceptible to
separation while the ﬂow is still laminar, a process that is primarily dictated by the adverse
pressure gradient and is referred to as laminar separation. The separated shear layer will
1

typically transition into turbulence over the surface of the airfoil and will then reattach to
the surface, forming a laminar separation bubble, as depicted in Figure 1.1. If the separated
shear layer does not reattach to the surface, it is referred to as an open separation.

Figure 1.1: The general characteristics of a laminar separation bubble are shown.
In the mean ﬂow, separation is deﬁned by the location at which the wall shear
stress is zero, corresponding to the location where the dividing streamline between forward and reversed ﬂow region intersects the wall. Reattachment is also
deﬁned in the mean ﬂow where the wall shear stress returns to zero and the
diving streamline intersects the wall again.

The presence of a laminar separation bubble is typically associated with an increase in
drag and decrease in lift and is therefore, detrimental to the performance. The bursting
of a laminar separation bubble (i.e. an open separation) is not only detrimental to the
performance, but the stability of the aircraft. In the development of MAVs, it is important
that these ﬂow dynamics are understood so they may be properly modeled and resolved in
computational studies. The steady ﬂow around a stationary SD7003 airfoil has been used in
various studies (both experimental and computational) in the literature to investigate this
ﬂow phenomena.
There are however, discrepancies in the literature in the locations of separation and
reattachment (which deﬁne the laminar separation bubble) for this airfoil, e.g. see Ol et al.
(2005); Katz (2010); Olson et al. (2011). This presents a signiﬁcant challenge for validating
simulations. The discrepancies have previously been attributed to: diﬀerences in spatial
2

resolution by Ol et al. (2005), and diﬀerences in freestream turbulence by Burgmann and
Schr¨der (2008); although none of the studies examined these eﬀects systematically.
o
Freestream broadband turbulence acts as an excitation source for the boundary layer
instability upstream of separation and the Kelvin-Helmholtz instability of the separated
shear layer. Based on physical reasoning, increased freestream turbulence would be expected
to delay separation and trigger an earlier transition and subsequent reattachment.
In the present work, the characteristics of the laminar separation bubble on an SD7003
airfoil are studied experimentally for a range of angle of attack (α = 0◦ − 11◦ ) and chord
Reynolds number Rec = 2 6 × 104 . The measurements are carried out using single component Molecular Tagging Velocimetry over the entire suction side of the airfoil. The freestream
turbulence of the test facility is modiﬁed and the resulting ﬂow with increased freestream
turbulence is compared to the baseline case. The primary characteristics of interest are the
locations of separation and reattachment, the separation bubble thickness, and the characteristics of the streamwise velocity ﬂuctuations. The results of the current study are compared
to various other experimental and computational studies in the literature. The inherent
limitations of the experimental techniques and their impact on accurately characterizing the
laminar separation bubble are also discussed.

3

Chapter 2
Experimental Methods
The inﬂuence of added Freestream Turbulence Intensity (FSTI) on the mean ﬂow around
a stationary SD7003 airfoil was studied experimentally for a range of chord (c) Reynolds
number (Rec = 2 × 104 − 6 × 104 ) and angle of attack (α = 0◦ − 11◦ ). The baseline ﬂow
was compared against the ﬂow with added freestream turbulence using single-component
Molecular Tagging Velocimetry (1c-MTV) with a speciﬁc focus on the laminar separation
bubble (LSB) which may develop on the suction side of the airfoil.

2.1
2.1.1

Facility
Flow Facility

Experiments were performed in a 10,000 L close-loop water tunnel operating with a freesurface. The facility was designed and manufactured by Engineering Laboratory Design
and is located at Michigan State University’s Turbulent Mixing and Unsteady Aerodynamics Laboratory (TMUAL) in East Lansing, Michigan. The various ﬂow management de4

vices and their locations are illustrated in Figure 2.1 while a more detailed schematic of
the test section conﬁguration is shown in Figure 2.2. Photos of the test section may be
found in Figure D.1, located in Appendix D.1. The test section is 24 in. × 24 in. × 96 in.
(61 cm × 61 cm × 243 cm) and the polycarbonate coated Plexiglas walls provide full optical
access in the visible spectrum for unobstructed imaging of the measurement region. Quartz
windows are mounted in a ﬂat-bottom boat-shaped holders that skim the surface of the
water to permit the transmission of the UV photon source to the measurement region while
eliminating beam scatter due to water surface irregularities. The tunnel’s speed is adjusted
with a Toshiba Tosvert VT130H1U motor controller which powers a 20 hp motor connected
to the tunnel’s impeller. The ﬂuid temperature is measured for each experiment using a
VWR 61066-104 thermometer (with nominal accuracy of ±0.5◦ C) and is taken into account
in determining the viscosity for calculating the Reynolds number.
Two coordinate systems are used in these experiments. The ﬁrst, (X, Y), is relative to the
test section with X along the streamwise direction (aligned with the bottom of the tunnel)
and Y is in the cross-stream, which are depicted in the top of Figure 2.2. The streamwise
velocity, (u), and cross-stream velocity (v) are also deﬁned in this coordinate system with
the magnitude of the freestream is deﬁned as U∞ . The origin of this coordinate system is
not explicitly deﬁned.
The second coordinate system, which will be used to present velocity contours and discuss
locations along the airfoil (such as separation and reattachment), is shown near the bottom
of Figure 2.2 with the origin deﬁned at the leading edge of the airfoil with x along the
chordline and y normal to it. Note, both u and v are still deﬁned in (X, Y).

5

Figure 2.1: Flow Facility Schematic. The original drawing was created by Gendrich (1999) and has been updated accordingly.

6

Figure 2.2: Test Section Schematic. The relative position of the ﬂow management, turbulence generating screen, airfoil and measurement regions are shown
above. The upstream measurement location is located along the chordline at
a geometric angle of attack, α = 0◦ relative to the bottom of the tunnel. The
coordinate system (X,Y) is ﬁxed, with no explicitly deﬁned origin, and relative
to the test section. The coordinate system (x,y) rotates with the airfoil with
its origin deﬁned as the leading edge of the airfoil. The chord length, c, is also
indicated. The green arrows and lines represent the simpliﬁed laser beam path.
For interpretation of the references to color in this and all other ﬁgures, the
reader is referred to the electronic version of this thesis.

7

2.1.2

Airfoil

The theoretical airfoil proﬁle designated for testing was an SD7003, a low Reynolds number
airfoil that has a long separation bubble over a wide range of angle of attack and Reynolds
number; more detailed information may be found in Selig et al. (1995) on the airfoil’s performance and characteristics at various Reynolds numbers. This particular airfoil was chosen
due to the large number of recent comparisons in the literature, both experimental and computational, and the considerable amount of discrepancy in a number of these studies. The
physical airfoil model has a chord length, c = 7.959 in., a span of b ≈ 18 in., and was loaned
to TMUAL by Dr. Michael Ol of the Air Force Research Laboratory, Wright Patterson Air
Force Base, Ohio.

y/c [mC]

0.5

Proﬁle at Measurement Plane
Theoretical Proﬁle

0

−0.5
0

1

2

3

4
x/c [mC]

5

6

7

8

Figure 2.3: The theoretical proﬁle is plotted against the measured airfoil proﬁle
at the measurement plane (not to scale). The actual airfoil is clearly thicker
than the theoretical proﬁle with most of the added thickness from the bottom
surface.

8

10

y/c [mC]

8

6

4

2

0
0

0.1

0.2

0.3

0.4

0.5
0.6
x/c [mC]

0.7

0.8

0.9

1

Figure 2.4: The error in the proﬁle thickness as a function of chord. The error
in thickness is nearly constant over 70% of the chord at ∼ 8 mC (0.064 in.)

The airfoil’s actual shape was determined by GKS Global Services in Plymouth, MI with
a nominal accuracy of ±0.0015 in. using a triangulation 3D laser scanner. The measured
shape at the spanwise location of the measurement plane is compared to the theoretical
proﬁle in Figure 2.3 and is noticeably thicker, approximately a constant 8 mC (1 mC =
0.001c) over 70% of the chord, as shown in Figure 2.4. It was not possible to determine if
the previous study done by Katz (2010) at MSU, which used the same model, also had the
same proﬁle thickness. The measurement plane was chosen to be ∼ 2.6 in. oﬀ mid-span to
avoid surface anomalies that develop after prolonged underwater exposure.
Figure 2.5 shows the camber lines of both the theoretical and current airfoil proﬁle. The
current airfoil’s maximum camber was determined to be 1.36% compared to 1.46% in the
theoretical proﬁle. The location of maximum camber is farther upstream at 0.30 x/c compared to 0.35 x/c of the theoretical proﬁle. There is little visual devation in the camber lines
9

for x/c < 0.20, but a systematic decrease in the camber line is seen from 0.4 > x/c > 0.95.

Current Airfoil
Current Camber Line
Chord Line
SD7003 Airfoil
SD7003 Camber Line

0.06

y/c

0.04
1.46 %
1.31 %

0.02

0

−0.02

−0.04

0

0.1

0.2

0.3

0.4

0.5
x/c

0.6

0.7

0.8

0.9

1

Figure 2.5: The normalized proﬁles of the current and theoretical airfoil and
their respective camber lines (not to scale). The location of the peak camber is
identiﬁed by the square symbols with the percent camber indicated. The current
airfoil’s peak camber is less and is located farther upstream than the theoretical
SD7003 airfoil.

10

Deviation from two-dimensional ﬂow conditions were minimized by mounting the airfoil
between two acrylic plates since the airfoil’s span (∼18 in.) is not as wide as the test section
(24 in.). The airfoil’s angle of attack was adjusted using a Velmex A1506P40-S1.5 linear
traverse mounted to a lever arm 7 in. from the pitch axis as depicted in Figure 2.6. This
manual pitching system provided a relative angle change accuracy of ±0.05◦ , determined by
rotational correlation of images of the airfoil proﬁle.

Figure 2.6: A Velmex A1506P40-S1.5 Unislide traverse with a 0.001 in. graduated knob is connected via a lever arm to the pitch axis of the airfoil to change
the angle of attack of the airfoil. The blue arrows indicate the motion with the
black circles representing pin joints.

11

Figure 2.7: A small region (width = 170 pixels) of an average undelayed MTV
image (see Section 2.2.2 for more details) is shown above. The white arrows
indicate the manually determined surface locations. The image has been artiﬁcially colored green to resemble the emission wavelength. The large bright
spots beneath the surface are artifacts of the Pixelﬂy CCD and do not eﬀect the
measurements.

0.049
Laser Scan Surface
α = 4.50 ◦
α = 4.55 ◦
α = 4.45 ◦

0.048
0.047

y/c

0.046
0.045
0.044
0.043
0.042
0.041
0.04
0.52

0.54

0.56
x/c

0.58

0.6

0.62

Figure 2.8: The manually located surface locations are plotted for diﬀerent possible geometric angles of attack. The error in location of these points to the
laser scan surface was minimized to yield α = 4.5◦ for this case. It is easily seen
the accuracy of this technique is better than the ±0.05◦ shown here. Note, only
a very small portion of the suction side of the airfoil surface is shown.

12

The geometric angle of attack was determined by a least-squares minimization of the
error between airfoil surface location manually located from each laser line intersecting with
the surface (shown in Figure 2.7) and the surface proﬁle as measured by the laser scanning.
The repeatability of visually determining the surface was ±1 pixel. The uncertainty of this
technique is better than ±0.05◦ (estimated by the procedure shown in Figure 2.8) which
also accounts for all other angle alignment uncertainties.

2.1.3

Grid Generated Turbulence

The water tunnel’s freestream turbulence is modiﬁed during the current experiments by the
introduction of a mesh grid 4c upstream of the airfoil as depicted in the test section schematic
(Figure 2.2). The grid itself, shown in Figure 2.9, is a stainless steel woven wire screen with
a mesh size of 0.75 in. and a wire diameter of 0.120 in.

Figure 2.9: A small region of the stainless steel woven mesh screen is shown with
the mesh size and wire diameter indicated.

The freestream turbulence intensity (FSTI), based on the streamwise velocity component,
was measured from FOV #11 (see Figure 2.18), which extends over a range of 2.10 − 4.20 in.
(Y/c = 0.264 − 0.528) above the leading edge and a range of 0 − 1.09 in. (X/c = 0 − 0.14)
downstream of the leading edge of the airfoil. The baseline FSTI over a range of tunnel speed
13

U∞ ≈ 9 − 19 cm/s was 0.42 - 0.66%, which corresponds to (Rec ≈ 2 × 104 − 4 × 104 ). In the
presence of the grid, the FSTI was measured to be 0.95 - 1.47% over the same range of tunnel
speed. The details of the freestream turbulence measurements using single-component MTV
(1c-MTV) may be found in Section 2.3.

2.2
2.2.1

Molecular Tagging Velocimetry (MTV)
Background

Molecular Tagging Velocimetry (MTV) is a whole ﬁeld measurement technique in which
particular molecules of a homogenous solution are utilized as long lifetime tracers through
photon excitation. In the current application, a phosphorescent supramolecule, Gendrich
et al. (1997), is utilized as the tracer and is excited by a pulsed UV Excimer laser (Lambda
Physic XeCl 308 nm). The laser is ﬁred once to excite, or tag, molecules and the resulting
phosphorescent emission is interrogated twice with a prescribed time delay to form an image
pair. Features in the images, created by spatial gradients in intensity, are correlated to yield
an estimate of the displacement, and with the prescribed time delay, the velocity of the ﬂow
ﬁeld as shown in Figure 2.10. The reader is referred to Gendrich and Koochesfahani (1996);
Gendrich et al. (1997); Koochesfahani and Nocera (2007) for more details on the history,
applications, and photochemistry of MTV.

2.2.2

Current Implementation

The experiments utilized both single and two-component MTV. Two-component measurements were used to monitor freestream ﬂuctuations in the approach ﬂow 2c upstream of the
14

Figure 2.10: A typical 2c-MTV image pair and resulting 2-component velocity
vector ﬁeld. (a) The ﬂuid ﬂow of a vortex ring impinging on a ﬂat plate with
normal incidence is imaged ∼ 1 µs after the laser pulse. (b) The same tagged ﬂuid
is interrogated again 8 ms after the ﬁrst image. (c) The resulting 2-component
velocity vector ﬁeld is derived from correlating the undelayed (a) and delayed
(b) images. (Gendrich and Koochesfahani, 1996).

airfoil during the experiments and were also used for calibrating the tunnel speed. In the primary measurement region, the suction side of the airfoil, single component MTV (1c-MTV)
was employed to measure the streamwise component of velocity.

Single-component MTV is a highly attractive technique for the current study because
it captures the key features of interest, separation and reattachment, and provides highly
detailed velocity proﬁles for future comparisons to simulations. The very high resolution,
which is approximately 10 times that of recent PIV studies of this airfoil, Burgmann et al.
(2007); Burgmann and Schr¨der (2008), comes at the expense of a possible error due to the
o
unresolved velocity component in the measurement plane. The inherent error associated
with this technique and the implications on this type of ﬂow ﬁeld are discussed in the next
section, 2.2.3.
15

2.2.3

Error Quantiﬁcation of 1c-MTV over an Airfoil Surface

The inherent error in 1c-MTV, previously investigated by Hill and Klewicki (1996) is deﬁned
as follows in Koochesfahani and Nocera (2007). The error is most easily shown by the diagram in Figure 2.11 which shows the initial tagged line of ﬂuid and displaced ﬂuid molecules
at a later time. If there is a component of the velocity vector (V ) parallel to the tag line,
i.e. θ = 0, the error (∆u) is also non-zero.

Figure 2.11: The tagged ﬂuid at t0 (green) and t0 + ∆t (red) due to the velocity
vector V . The measured streamwise velocity u and its error ∆u is also shown.

The images are processed assuming the ﬂuid molecules have displaced normal to the tag
line (x-direction), which, in the presence of a v-component of velocity, is not generally a
good assumption. The error in the measured streamwise velocity component, as presented
in Koochesfahani and Nocera (2007), may be formally expressed as

∆u
v ∂u
=
∆t
u
u ∂y

(2.1)

where the error is deﬁned in terms of the ﬂow variables and ∆t, the time delay between
v
the image pair. From Equation 2.1, it is clear that ∆u → 0 near surfaces, where u → 0,
16

and in the freestream, where ∂u → 0. The error may be minimized by reducing the ∆t
∂y
between interrogations, but the latter cannot be set arbitrarily small in experiments because
the molecules must displace far enough to be accurately measured.
In order to determine the accuracy of 1c-MTV over the entire suction side of the airfoil,
“simulated experiments” were conducted using CFD simulations (performed by Galbraith
(2009)) of the mean ﬂow around an SD7003 at Rec = 4 × 104 and α = 4◦ . Other conditions
were also studied but have been excluded for brevity. The “simulated experiments” were
performed using the procedure outline in Appendix D.2, which match the assumptions and
parameters of the experiments.
|∆u|
The magnitude of the error, normalized by the freestream velocity ( U ), between the
∞
known ﬂow ﬁeld and the simulated experiment is shown in Figures 2.12 and 2.13 for ∆t =
5 ms (which is typical of the current experiments). Most of the ﬂow ﬁeld has a negligible
amount of error with the highest values occurring near the leading edge, as expected, due to
the very high velocity gradients and large v in this region. The error in the separated shear
layer, extending from ∼0.24c - 0.7c, is < 2%.

|∆u|
Figure 2.12: The error in the 1c-MTV estimate of u is shown as U × 100 over
∞
the entire suction side of the airfoil.

17

Figure 2.13: An enlarged view of Figure 2.12 over the leading edge.

2.3

2.3.1

Quantifying the Freestream Turbulence

Background

The freestream turbulence must be accurately quantiﬁed to enable future comparisons to
simulations. Previous measurements of the FSTI have varied in this facility: 0.3% (Gendrich (1999)), 1.5% (Bohl (2002)), and most recently, ∼ 2% (Katz (2010)) but the spectral
components and length scales have never been reported. The ﬂow management and tunnel
operating conditions were not necessarily the same between any of these investigations and
must be measured again for completeness.
Traditionally, LDV (Laser Doppler Velocimetry) and hot-wire anemometry (or hot-ﬁlm
anemometry) have been utilized for the measurement of turbulent quantities. Both techniques are nominally point measurements of high temporal resolution whereas MTV is a
whole ﬁeld technique with a high, user-conﬁgurable spatial resolution but a typically much
lower data rate. At the time of the current experiments neither LDV or hot-ﬁlm anemometry
was available for use, so the feasibility of using MTV for FSTI was investigated.
18

2.3.2

Technique

The two primary quantities in these experiments used to describe the freestream turbulence
are: the freestream turbulence intensity,

FSTI =

urms
U∞

(2.2)

and the integral length scale,
Ly =

ξ0
0

Ruu (ξ) dξ

(2.3)

where urms is the RMS (root mean square) of streamwise velocity ﬂuctuation, with ξ as
the spatial oﬀset in the cross-stream direction and ξ0 is the ﬁrst zero crossing of Ruu (ξ).
The autocorrelation function, ruu (∆ξ ), is obtained from measurements of the streamwise
velocity at Ny discrete spatial locations along y, ∆ξ , and time record (m), and is given by:
Ny −1−∆ξ
u(m, n) u(m, n − ∆ξ )
ruu (∆ξ ; m) =

n=0
Ny − ∆ξ

(2.4)

The autocorrelation coeﬃcient, Ruu (∆ξ ), is deﬁned as:

Ruu (∆ξ ) =

ruu (∆ξ ; m)
ruu (0; m)

(2.5)

and was averaged over all m. In practice however, these calculations were performed in the
frequency domain using periodic extensions of the spatial signals for ease and computational
eﬃciency. The high spatial resolution of 1c-MTV in the y-direction, i.e. u(y), allowed the
computation of Ly to be performed relatively easily and was proven to be a robust and
19

consistent measurement, which is described in Section 3.1.
The computation of FSTI, requires an accurate measure of both U∞ (a mean quantity)
and urms (the RMS of velocity). Even in measurements with high levels of random uncertainty the mean quantities can still be known with a high degree of certainty (depending on
the number of samples). The RMS, however, is signiﬁcantly higher than the actual value
due to the contribution of noise. If the noise is purely random, it may be removed by using
the autocorrelation function, as shown in Figure 2.14. Since white noise only correlates with
−3

7 x 10

u2
rms

r uu(ξ ) [cm 2 /s 2 Hz]

6
5

u2
rms

4

total

noise

3
2

u2
rms

1

turbulence

0
−1
−4

−2

0
ξ [cm]

2

4

Figure 2.14: The autocorrelation (ruu (ξ)) obtained from a a single tag line of 1cMTV data. The autocorrelation function at zero-lag is equal to u2
rms (ruu (0) =
2 ) and may be used, as shown, to obtain the fraction of u2
urms
rms that is due to
turbulence only.

20

1
0.8
0.6
R uu(ξ)

0.4
ξ0

0.2
0
−0.2
−0.4
−0.6
−4

−2

0
ξ [cm]

2

4

Figure 2.15: The autocorrelation coeﬃcient is shown after the white noise has
been removed. The integral length scale, Ly is calculated from this curve by
integrating from ξ = 0 to ξ0 .

itself at zero spatial and temporal oﬀset it will only have a non-zero contribution to the
autocorrelation at zero oﬀset, i.e. Ruu (0). Once removed, a “noise-free” autocorrelation can
be obtained, as shown in Figure 2.15, which is used in conjunction with Equation 2.3 for the
computation of Ly .

21

The Power Spectral Density (PSD) is also computed to characterize the freestream data.
The PSD is computed from each 300 s time series from a single row of pixels from a single
tag line by splitting the time series into 10 records each of length 600 to compute the mean
PSD. The overall mean PSD, which is described and shown for both the baseline and ﬂow
with increased FSTI in Section 3.1, is the average PSD from all of the rows and tag lines in
FOV #11 (see Figure 2.18 for location of FOV).

2.4
2.4.1

Data Acquisition
Imaging

The upstream measurement region, located 2c upstream of the airfoil, is imaged using a
12 bit 1280 × 1024 pixel PCO DiCam Pro camera paired with a Micro-Nikkor 105mm f/2.8D
lens. This camera is capable of taking two images with a short time delay between images
to form the MTV image pair. The ﬁrst image is acquired at ∼ 3 µs after the laser has ﬁred
with a 0.7 ms exposure and the second image is acquired 10.7 ms after the beginning of the
ﬁrst image, also with a 0.7 ms exposure. A 336 × 512 pixel region of the CCD array is used
to record the images, this reduces the data size while also increasing the maximum frame
rate of the camera.
The images are recorded directly to disk on a 32 bit Windows XP PC using PCO Camware
v3.02 and a set of sample instantaneous images are shown in Figure 2.16. The image scale
was determined to be 102.6 ± 0.2 px/cm, using a subpixel accurate, 2D cross-correlation
routine applied to an image of a target that was placed in the measurement plane. The
target, as described in Bohl (2002), consists rectangular intersections of a known spacing.
22

For each ﬁeld of view (FOV) in the primary measurement area, a sequence of 1500 image
pairs recorded at 5 frames per second, (5 minutes), was taken simultaneously at the upstream
location to monitor the approach ﬂow.

(a) Sample Instantaneous Undelayed
Freestream Image

(b) Sample Instantaneous Delayed
Freestream Image

Figure 2.16: Representative instantaneous undelayed (a) and delayed (b) upstream images. The images are artiﬁcially colored and the look up table (LUT)
has been adjusted for clarity. Only high quality intersections are used for correlation to ensure the highest possible subpixel accuracy.

The primary measurement region was imaged using a 12bit 1392×1024 pixel PCO Pixelﬂy
QE camera paired with a Nikkor 50mm f/1.2 lens. This camera does not have the capability
of recording two images in short succession, therefore, there are no longer individual image
pairs but two sequences of images recorded at two diﬀerent time delays relative to the laser
pule. The ﬁrst undelayed image sequence is ∼ 30 µs after the laser pulse and the second
23

delayed image sequence, is at t = t2 after the laser pulse, which is typically varied in the
range of 0.5 ms - 6.8 ms for diﬀerent ﬁelds of view over the airfoil surface. The FOVs used
for computing freestream turbulence characteristics typically used a 12 ms delay. A sample
image pair may be seen in Figure 2.17. The time delay and exposure (typically 0.2 ms 0.8 ms) was optimized for each FOV based on ﬂow conditions to maximize the accuracy of
the technique.

Figure 2.17: Representative average undelayed (left) and average delayed (right)
images are shown near where separation occurs. Only ∼ 1/4 of the height of the
image is shown so the shear layer may be seen.

Each FOV in the primary measurement region is 1024px × 1392px and contains 19 lines
equally spaced at ∼ 30 pixels in the streamwise direction with an eﬀective measurement area
of ∼ 1024 × 530 pixels. The scale factor of this imaging setup is 192.9 ± 0.2 px/cm resulting
in an eﬀective measurement region of 2.76 cm × 5.31 cm or (137 mC × 528 mC), a line
spacing of 0.16 cm or 8 mC, and a cross-stream resolution of 51.8 µm or 0.26 mC in the X
and Y directions respectively. Each undelayed image sequence contains 500 images recorded
at 10 frames per second, which was determined to be suﬃcient by studying the convergence
of the subpixel noise characteristics of correlating the mean image with its instantaneous
images. Each delayed image sequence is comprised of 3000 images (also recorded at 10
frames per second for an acquisition time of 5 minutes). In the case of FOVs used for
24

computing freestream turbulence characteristics, the images are recorded at 20 frames per
second by sacriﬁcing the vertical resolution by a factor of 2. The length of time series was
determined by Katz (2010) to ensure statistical convergence in the separated shear layer over
the same airfoil and under similar ﬂow conditions.

Clearly, at the relatively small size of the ﬁeld of view needed to obtain high spatial
resolution, multiple FOVs are needed to image the entire suction side of the airfoil. This was
accomplished using a set of linear traverses along the streamwise and wall normal directions
to move the imaging system relative to the test section to image the entire airfoil. The
accuracy of the traverse motions were found to be ±0.008 in. (1 mC) in the streamwise
direction and ±0.004 in. (0.5 mC) in the cross-stream direction. The UV optics are attached
to the streamwise traverse such that the camera and tagged ﬂuid region move together. This
setup can be seen in the test section schematic seen in Figure 2.2 and the pictures in Figure
D.1. A sample shift pattern, showing the relative motion between each FOV is shown in
Figure 2.18 for a geometric angle of attack of α = 8◦ .

There are 8 FOVs over the suction side of the airfoil and two additional FOVs to record
data immediately upstream and downstream of the airfoil. The two FOVs located above
the airfoil (FOV # 11,12) are utilized for turbulence measurements; it was found from CFD
simulations and previous experiments that the velocity ﬂuctuations (u and v ) in these
regions were representative of freestream conditions (assuming an open separation did not
occur). For improved temporal resolution, in these two FOVs the spatial resolution was
reduced by a factor of 2 and the acquisition rate increased to 20 Hz to yield 6000 images in
the delayed sequence.
25

0.7
0.6
FOV
11
Shift ↑
2.151
Shift→
1.027

0.5
0.4

y/c

0.3
0.2
0.1

FOV
10

FOV
9

FOV
12
Shift→
8.160

FOV
8

0
−0.1
−0.2

All
Shift ←
1.020

−0.3
−0.4

−0.2

FOV
FOV
6
FOV
FOV
FOV
Shift ↑ 5
7
Shift ↑ 4
FOV FOV
3
0.225
0.240 Shift ↑ Shift ↑ 2
1
0.250
0.255 Shift ↑ T E S
0.145 67

0

0.2
x/c

0.4

0.6

0.8

Figure 2.18: The shift diagram for a geometric angle of 8◦ is shown. All units
are in inches unless noted. All shifts to the left are 1.020 in. The dotted line
represents the airfoil proﬁle 0.20c above the surface, beneath which (in all but
a few cases), all of the interesting ﬂow features are contained. The TEs in FOV
#1 indicates the height of the trailing edge, in pixels, from the bottom of the
image to ensure the chordline, if extended past the trailing edge, is still imaged
on the right hand side of the image.

26

2.4.2

Image Processing

The upstream measurements (2c-MTV) are processed using in-house processing programs
previously developed and described in detail in Gendrich and Koochesfahani (1996). The
1c-MTV data is also processed using an in-house processing program described in Katz
(2010). As part of the current work, the 1c-MTV code has since undergone a signiﬁcant
amount of optimization and parallelization to allow all of the current experiments to be
completely processed in a reasonable about of time. The speed of the original processing
code was ∼ 230 displacement vectors per second (refereed to as nodes/second). After the
initial parallelization and speed enhancements it was capable of 730 nodes/second on dualcore machines. After suﬃcient performance testing, two Apple Mac Pro machines with
(2) 6-core 2.66 GHz Intel Xeon 5650 processors and 12 GB of 1333 MHz ECC RAM were
purchased for data processing. Additional optimizations were made to take advantage of the
new machines which are capable of processing at ∼ 20, 000 nodes/second. Using the original
code, processing the data would have taken ∼ 11, 000 hours (∼ 150 weeks), whereas with
the new processing code it was reduced to ∼ 300 hours or just under 2 weeks.
In the current experiments, the undelayed and delayed 1c-MTV images are not acquired
from the same laser pulse (i.e. the molecules tagged in the ﬁrst image are not the same as
those in the second). The average of the undelayed images is correlated to each instantaneous
delayed image to form image pairs. This technique is acceptable if the ﬂuid can be assumed
to be steady over the exposure time period of the ﬁrst image and laser jitter is small. Any
deviation from steady ﬂow (or changes in tag line location) will manifest as an increase in
the RMS of the mean ﬂow. This increase in RMS associated with this technique may be
estimated by examining the correlations of the mean undelayed image with each instanta27

neous undelayed image. If all of the assumptions made above are correct and there is no
noise due to processing, both the mean and displacement RMS should be zero. The mean
will be non-zero if there is an asymmetric distribution in the displacement ﬂuctuations. The
displacement RMS is however, non-zero and serves as an estimate for the combined eﬀect
of both the processing noise and due to correlating the average undelayed image to each
instantaneous delayed image.
The data presented have been remapped onto a regularly spaced grid, with an x and
y spacing approximately equivalent to the original data spacing to facilitate plotting. The
urms has been spatially ﬁltered along the tag line in order to remove noisy pixels. The ﬁlter
uses the deviation from the local mean to identify bad pixels and replaces it with a linear
interpolation of the region. In general, less than 20 pixels per line (< 3%) were modiﬁed.
The spatially non-uniform background u2 has been removed from the data as well. This
rms
was necessary to account for large variations in SNR across a FOV. There is virtually no
diﬀerence in the background u2
rms values subtracted between the baseline and increased
FSTI cases and therefore, does not impact any conclusions regarding the eﬀect of FSTI of
either u or urms .
¯

2.4.3

Alignment and Synchronization

The alignment of the two diﬀerent imaging systems, the stationary upstream DiCamPro and
the translating Pixelfy QE, was achieved by directing the beam of a HeNe Laser through
the end view of the test section such that it passed through both camera’s FOV in the
measurement plane. The scatter of the HeNe beam produces images of a straight line passing
through the entire FOV. The angle of this line relative to each camera’s pixel coordinates
28

is found, providing the rotational alignment required between the imaging systems. The
alignment of translational axis of the imaging system and the bottom of the tunnel was
determined with an accuracy of ±0.03◦ by correlating the images of an object placed on
the bottom of tunnel at two diﬀerent positions to ﬁnd the vertical displacement for a known
travel distance of the imaging system.
The synchronization of the two diﬀerent imaging systems and laser was achieved using
two Stanford Research Systems DG535 Digital Delay Generators as indicated in the hardware
diagram in Figure 2.19 and the timing diagram in Figure 2.20.

29

Figure 2.19: The diagram above indicates the hardware, synchronization, and
data ﬂow for the current experiments. The ﬁrst digital delay generator provides
the sync signal to the second delay generator and triggers the laser and Pixelﬂy
Camera at 10 or 20 Hz depending on the FOV. The Pixelﬂy either records the
ﬁrst or second image which are ∆t1 apart and sends the images to PC #1 where
it is written to hard disk. The second digital delay generator uses this sync
signal and outputs a 5 Hz signal to the DiCam Pro, which records two images
(∆t2 apart) and sends the images to PC #2 where it is written to hard disk.
Both PC #1 and PC #2 use Camware v3.02 provided by PCO to control and
record images.

30

Figure 2.20: The timing diagrams of the experiments (not to scale). It should
be noted that CCD # 2, the Pixelﬂy QE, only records one exposure at a time,
the second exposure is recorded during a diﬀerent sequence of images.

31

2.5
2.5.1

Experiments
Experimental Parameters

The chord Reynolds number and angle of attack for both the baseline and increased FSTI
conﬁguration for each case in the current study are listed in Table 2.1. The chord Reynolds
numbers shown are mostly slightly less than the objective: 20,000, 30,000 and 40,000, because
the airfoil was originally thought to be 8.000 in., but was later found to be 7.959 in. from the
laser scanning measurements. And, although extreme care was taken to ensure the angles
of attack would be very close to other experimental and computational studies (i.e. 2, 4, 6,
8, and 12 degrees), a minor issue was uncovered after the experiments had been performed
leading to the geometric angles of attack listed (relative to the bottom of the tunnel). Data
were also taken at a Reynolds number of 60,000 but has been excluded since only the baseline
case was performed.

2.5.2

Experimental Procedure

The time required to take all 12 FOVs for each case angle of attack was approximately 2
hours, which permitted a single Reynolds number (for either the baseline or increased FSTI)
to be studied in each day of data taking. As described previously, the day-to-day ﬂuctuations
of the tunnel operating parameters where monitored and taken into consideration. The
typical procedure used for conducting the experiments is given in Appendix D.3. The total
hard disk space required for each case, a single angle of attack for a single Reynolds number
for a single freestream condition, after processing is ∼180 GB, for a total size of 5.4 TB for
all of the experiments.

32

Rec
20120
19880
19940
19900
19900
29740
29760
29760
29820
29820
39340
39420
39280
39300
39360

±
±
±
±
±
±
±
±
±
±
±
±
±
±
±

Baseline
Geometric α
40
0.5 ± 0.1
20
2.5 ± 0.1
60
4.5 ± 0.2
120
6.1 ± 0.1
80
10.0 ± 0.2
60
0.5 ± 0.2
120
2.3 ± 0.1
40
4.4 ± 0.0
140
6.4 ± 0.1
60
10.7 ± 0.1
240
0.4 ± 0.1
300
2.4 ± 0.0
140
4.6 ± 0.1
20
6.8 ± 0.1
100
10.8 ± 0.1

Increased FSTI
Rec
Geometric α
19720 ± 60
-0.3 ± 0.3
19780 ± 20
1.5 ± 0.2
19800 ± 80
3.5 ± 0.2
19820 ± 80
5.8 ± 0.1
19780 ± 60
10.0 ± 0.1
29820 ± 60
0.7 ± 0.1
29820 ± 120
2.4 ± 0.1
29860 ± 100
4.6 ± 0.0
29900 ± 100
6.4 ± 0.0
29900 ± 120
10.6 ± 0.1
39740 ± 20
0.4 ± 0.1
39900 ± 240
2.4 ± 0.1
39840 ± 100
4.5 ± 0.2
39840 ± 60
6.6 ± 0.1
39800 ± 60
10.7 ± 0.1

Table 2.1: The Reynolds number and angle of attack for each case studied is
shown in the table with the uncertainty of each value. The freestream velocity
for each of the three Reynolds number shown above are approximately: 9.3 cm/s,
14.2 cm/s, and 18.3 cm/s.

33

Chapter 3
Results and Discussion

3.1

Freestream Turbulence Characteristics

The velocity ﬂuctuations in the freestream of the water tunnel facility is predominately
produced by very low frequency oscillations (f < 0.2 Hz) which may be seen in the power
spectral density (PSD) in Figure 3.1a. These frequencies are suspected to be from ‘U-Tube’
oscillations that develop and are allowed to propagate due to the exposed free surface along
the entire length of the tunnel (as discussed in Katz (2010)). These oscillations manifest in
the test section as spatially uniform velocity ﬂuctuations of very low frequencies.
Fluctuations of this type may, however, be removed by subtracting the spatial mean
velocity at each instance in time. The spectra for both the baseline and increased FSTI
conﬁgurations are shown in Figure 3.1b after the spatial mean was removed. The removal of
the spatial mean is warranted for two reasons: (1) to characterize the broadband ‘random’
ﬂuctuations in both space and time (i.e. what is typically considered turbulence); (2) it is
hypothesized that these very low frequencies do not signiﬁcantly inﬂuence the ﬂow physics of
34

separation and reattachment, and should simply be considered as a ﬂuctuation in Reynolds
number rather than an increased turbulence level. It is not, however, possible from the
current experiments to completely determine if this hypothesis is correct and should be
considered for future work.
(b) Spatial-Mean Removed

(a) Original

Figure 3.1: The original (a) and spatial-mean removed (b) freestream power
spectral density (PSD) for each Reynolds number and conﬁguration. The baseline conﬁguration is represented by solid lines and dashed lines represent the
increased FSTI conﬁguration in both plots. The color of the line corresponds to
the Reynolds number. The PSD is computed from the average of 12, 500-point
records of the time series from each pixel of each line.

35

The addition of the woven mesh grid increases the freestream turbulence for all Reynolds
numbers but its inﬂuence on the spectra changes as a function of Reynolds number. The
inﬂuence of the grid at low frequencies degrades as the Reynolds number increases while the
impact on high frequencies increases with an increasing Reynolds number. A more detailed
comparison of the spectra at each Reynolds number may be found in Appendix A.
The turbulence characteristics described in Section 2.3, Ly and FSTI, are calculated from
the spatial mean removed velocity data for each case in the current study. The FSTI and
Ly for both the baseline and increased FSTI conﬁgurations are compared in Table 3.1 for
each Reynolds number. The value shown is the mean computed from ∼ 15 tag lines in FOV
# 11 for each angle of attack (approximately 75 samples in total). The uncertainty listed as
the RMS of those 75 samples. For reference, the FSTI computed from the raw time series
at Rec = 2 × 104 is 1.82% (baseline) and 2.15% (increased FSTI conﬁguration).
Table 3.1: Freestream Characteristics

Rec
2 × 104
3 × 104
4 × 104

Baseline
Increased FSTI
FSTI [%]
Ly [cm]
FSTI [%]
Ly [cm]
0.45 ± 0.04 0.59 ± 0.01 1.43 ± 0.03 0.44 ± 0.01
0.52 ± 0.01 0.53 ± 0.02 1.23 ± 0.01 0.38 ± 0.01
0.65 ± 0.03 0.48 ± 0.01 1.29 ± 0.02 0.36 ± 0.01

There is little variation in both the FSTI and Ly for diﬀerent angles of attack (α).
This provides conﬁdence in the ﬂow facility and its ability to provide repeatable boundary
conditions since the minimum time between measurements was ∼3 hours and some were as
much as 24 hours. With this conﬁdence, changes in LSB characteristics should be correlated
to the addition of the mesh screen, and not day-to-day changes in the ﬂow facility.
In the baseline conﬁguration, the FSTI increases slightly with increased tunnel speed. The
36

integral length scale however, decreases slightly with increased tunnel speed. The presence
of the grid increases the FSTI of the tunnel by a factor of ∼ 2 − 3 and decreases the integral
length scale by ∼25%. The Reynolds number dependencies, described above for the baseline
conﬁguration, are reduced by the presence of the grid.
The freestream turbulence characteristics presented in this section provide a complete
description of how the freestream was modiﬁed by the grid.

3.2
3.2.1

Representative Results
Streamwise Velocity Contours: Mean and Fluctuation

Representative contours of the mean streamwise velocity and streamwise velocity RMS are
described in this section. The separation location is deﬁned with respect to the mean ﬂow
ﬁeld as the surface location above which the sign of the velocity reverses from positive to
negative in the data closest to the wall. Similarly, the reattachment location is deﬁned width
respect to the mean ﬂow ﬁeld as the location where the sign of the velocity reverses from
negative to positive. The determination of separation and reattachment from the data is
described in more detail in the next section. All colormaps shown of the mean streamwise
¯
velocity utilize the same color scale of −0.18 ≤ Uu ≤ 1.74 with any velocities above or
∞
¯
below these values are saturated. There is a step change at Uu = 0, such that all negative
∞
velocities are pink to facilitate the identiﬁcation reversed ﬂow.
The primary features of interest in the mean streamwise velocity contour shown in Figure 3.2 are the separation and reattachment locations, which are indicated. The length and
height of the reversed ﬂow region changes with both Reynolds number and angle of attack.
37

Figure 3.2: A representative mean streamwise velocity contour at Rec = 2 × 104
and α = 6.1◦ . Separation, reattachment, and the laminar separation bubble has
been indicated. The pink to purple colors represent reversed ﬂow.

The primary features of interest in Figure 3.3 are the long slender region of gradually increasing urms in the separated shear layer and its abrupt increase in height, quickly extending
back to the surface of the airfoil, after which the ﬂow becomes highly unsteady characterized
by a non-canonical boundary layer underneath the unsteady ﬂow structure emerging from
the separated region.

Figure 3.3: A representative contour plot of the RMS streamwise velocity at
Rec = 2 × 104 and α = 6.1◦ . The are primary feature of the urms is a long thin
region of increased urms initially tracking the separated shear layer and gradually increasing in magnitude. At some downstream location, the thin band of
increased urms extends from the separated shear layer to the surface; downstream of which an elongated region of much higher urms is found and gradually
decreases in magnitude along the x-direction.

The slight discontinuities in the u or urms contour plots (as seen in Figures 3.3 and 3.2
¯
and others) may be attributed to the following: uncertainties or error in FOV alignment, the
38

accuracy of the laser sheet alignment relative to the CCD array, optical distortions, changes
in laser sheet location (quantiﬁed to cause < 1% spatial non-uniformity in magniﬁcation),
and slight changes in ﬂow from the time one FOV is recorded to the next. In the distribution
of urms , the spatial non-uniformity of the signal to noise ratio (SNR) also contributes to the
discontinuity of the results. Although corrective measures were implemented (see Section
2.4.2) to account for most spatial non-uniformity in urms , clearly, some may still exist.

3.2.2

Separation and Reattachment

As discussed previously, separation is determined by locating ﬂow reversal at the ﬁrst available velocity data above the surface in the mean ﬂow. In this study, due to near wall imaging
issues, the ﬁrst 4 or 5 pixels (1.0 - 1.3 mC) above the wall are excluded. It was shown in Olson
et al. (2011) from computational results at Rec = 4×104 and α = 4◦ that excluding the ﬁrst
2 mC of data above the surface, separation would be improperly identiﬁed 100 mC farther
downstream than its actual location as determined by the closet computational point above
the surface. The growth in height of the reversed ﬂow above the surface is nearly linear for
this simulation, and therefore, it is reasonable to estimate that by excluding 1 mC of above
the surface, separation would be identiﬁed ∼50 mC farther downstream than its actual value.
Clearly, since this analysis was performed only at Rec = 4 × 104 and α = 4◦ , this conclusion
relies on the shape of the separated bubble to be uniform across both Rec and α, and also
assumes the shape of the bubble in these simulations is the same as experiments, which is
generally not the case. It does however, yield a useful estimate of the bias introduced by
using velocity vectors 1 mC above the surface of the airfoil.
Another possible alternative for estimating both the actual separation point and/or the
39

error by excluding the near wall region is by following the change in sign of velocity as
a function of both x/c and y/c and extrapolating this locus to the surface. This may be
visualized in Figure 3.4 by following the dark band (i.e. zero velocity) above the clearly
reversed region in the upstream direction and locating its intersection with the surface.
This technique has been proposed for future work. The shape of the reversed ﬂow region
near reattachment is typically not as sensitive to this issue but, a bias does still exist. Its
magnitude however, should be less and results in identifying reattachment farther upstream
than its actual location.

Figure 3.4: Representative view of separation for the baseline conﬁguration,
Rec = 2 × 104 , and α = 6.1◦ (not to scale). The regions of clearly forward and
reversed ﬂow are indicated. The separation location is x/c = 0.18 ± 0.02.

40

The process of determining separation is depicted in Figure 3.4 with the regions of the
ﬂow that are “clearly forward”, and “clearly reversed” indicated. Separation must occur
between these two regions and is recorded as midpoint between the ﬁrst “clearly forward”
velocity vector and the ﬁrst “clearly reversed” vector. The uncertainty is listed as the
distance between these two clearly deﬁned regions, which is typically 1 or 2 line spacings
(8 mC or 16 mC). The same procedure is used for determining the reattachment location as
shown in Figure 3.5.

Figure 3.5: Representative view of reattachment for the baseline conﬁguration,
Rec = 2 × 104 , and α = 6.1◦ (not to scale). The regions of clearly forward and
reversed ﬂow are indicated. The reattachment location is x/c = 0.74 ± 0.02

41

3.3

Characterizing the Laminar Separation Bubble

In this section the inﬂuences of increased freestream turbulence intensity, Reynolds number,
and angle of attack, on the laminar separation bubble are discussed. The eﬀects of these
parameters on separation location, reattachment location, and the overall bubble length
are presented with the primary focus on the inﬂuence of FSTI. Most eﬀects are discussed
qualitatively, but separation and reattachment location are quantitatively compared, when
available in the literature, between the baseline and increased FSTI conﬁgurations as well
as other experiments and computations.

3.3.1

Inﬂuence of Added Freestream Turbulence

Qualitatively, the inﬂuence of increased freestream turbulence intensity on the mean ﬂow has
the eﬀect of suppressing the laminar separation bubble: separation moves downstream and
reattachment moves upstream making the bubble shorter in length and thinner in height.
This eﬀect can be seen across all Reynolds numbers studied and all angles of attack, although
its extent reduced at both high and low angles. These eﬀects can be seen by comparing the
mean streamwise velocity shown in Figure 3.6 for both the baseline and increased FSTI
conﬁguration for Rec = 3 × 104 and α = 6.4◦ . The reversed ﬂow region in the baseline case
is clearly visible, while in the increased FSTI case the reversed ﬂow region is barely visible
at this scale. Quantitative results for all other cases are presented later in Section 3.4.1 and
the contours of mean and RMS for all cases are provided in Appendix B.
In some cases, the increased FSTI conﬁguration is drastically diﬀerent from the baseline
conﬁguration as seen at Rec = 2 × 104 and α = 10.0◦ in Figure 3.7. At these conditions the
baseline case is characterized by an open separation, i.e. the ﬂow has a fully separated shear
42

(a) Baseline u
¯

(b) Increased FSTI u
¯

Figure 3.6: The mean ﬂow is compared for the baseline (top) and increased
FSTI (bottom) conﬁguration at Rec = 3 × 104 and α = 6.4◦ . In the increased
FSTI conﬁguration, separation has been delayed, reattachment occurs earlier,
the reversed ﬂow region is shorter in length, and is much thinner in height
(barely visible at this resolution.

43

layer which does not reattach over the surface of the airfoil (the ﬂow is much more indicative
of a leading edge separation/stall). On the other hand, the ﬂow with increased FSTI has
clearly deﬁned closed separation bubble. This observation indicates increased FSTI may
delay stall.
(a) Baseline u
¯

(b) Increased FSTI u
¯

Figure 3.7: The mean ﬂow is compared for the baseline (top) and increased
FSTI (bottom) conﬁguration at Rec = 2 × 104 and α = 10◦ . The baseline ﬂow is
indicative of stall whereas the ﬂow with increased FSTI the has a well behaved
LSB.

Figure 3.8 compares the baseline ﬂow to the ﬂow with increased FSTI at Rec = 4 × 104
and α ≈ 6.7◦ . At these conditions, the LSB has been suppressed to the point where it can
no longer be detected in the ﬂow with increased FSTI. This may either be because there is
no longer a reversed ﬂow in the mean, or the current near wall spatial resolution is not high
enough to detect the reversed ﬂow.

44

(a) Baseline u
¯

(b) Increased FSTI u
¯

Figure 3.8: The mean ﬂow is compared for the baseline (top) and increased FSTI
(bottom) conﬁguration at Rec = 4 × 104 and α ≈ 6.7◦ . The baseline ﬂow has
a thin, but clearly deﬁned separation bubble whereas there is no reverse ﬂow
detected in the case with increased FSTI.

45

In general, however, the contours of the RMS for both baseline and increased FSTI have
similar features for these conditions however, as seen in Figure 3.9. The location of peak
RMS occurs farther upstream for the increased FSTI case and the thin band of increased
RMS extending upstream from the peak occurs closer to the surface. These observations may
also be seen when at other conditions when reversed ﬂow is detected in both conﬁgurations.
This may support the argument for the reversed ﬂow region has simply become too thin to
detect, or, as observed in this case by examining instantaneous results (not depicted), the
ﬂow experiences periods in which there is a well deﬁned reversed ﬂow region, that is not seen
in the mean velocity.
(a) Baseline u
¯

(b) Increased FSTI u
¯

Figure 3.9: The streamwise ﬂuctuations are compared for the baseline (top) and
increased FSTI (bottom) conﬁguration for Rec = 4 × 104 and α ≈ 6.7◦ . Both
contours are qualitatively similar even though there is no reversed ﬂow detected
in the increased FSTI conﬁguration.

46

Increased freestream turbulence intensity also has the qualitative eﬀect of decreasing
streamwise velocity ﬂuctuation (urms ) in the separated shear layer and near reattachment.
The ﬂow downstream of reattachment is also characterized by a lower urms . This may be
seen by comparing the contour maps of urms at Rec = 3 × 104 and α = 6.4◦ in Figure 3.10.
(a) Baseline urms

(b) Increased FSTI urms

Figure 3.10: The streamwise ﬂuctuations are compared for the baseline (top)
and increased FSTI (bottom) conﬁguration for Rec = 3 × 104 and α = 6.4◦ . The
primary eﬀect of increased FSTI is the overall reduction in urms , indicating a
more ‘gentle’ reattachment process.

The bias error in determining the separation and reattachment location discussed in
Section 3.2.2 regarding near-wall spatial resolution, has the tendency of shortening the LSB
due to delayed detection of separation and an early identiﬁcation of reattachment. The bias
is also inversely proportional to the height of reversed ﬂow region, which increased FSTI
decreases, so the bias error is expected to be higher in the increased FSTI conﬁguration
that the baseline. Quantiﬁcation of the bias error for both baseline and increased FSTI
conﬁguration should are suggested for future work.
47

3.3.2

Inﬂuence of Angle of Attack

Typically, as the angle of attack of an airfoil is increased, the peak adverse pressure gradient
increases in magnitude and also moves upstream. At the low Reynolds numbers of the current
study, laminar separation is dictated by the adverse pressure gradient, and is expected to
also move upstream as the angle of attack is increased. This trend is observed in the current
experiments for both the baseline and ﬂow with added freestream turbulence. The evolution
of the ﬂow ﬁeld as a function of angle of attack for the baseline conﬁguration and a Reynolds
number of 3 × 104 is shown in Figure 3.11, all other cases and conﬁgurations may be found
in Appendix B.1. As the angle of attack is increased the peak streamwise velocity increases
and the separation bubble increases in height as it moves upstream.

3.3.3

Inﬂuence of Reynolds Number

The primary eﬀect of the Reynolds number can be seen as a thinning of the reversed ﬂow
region i.e. the LSB is shorter in height as Rec increases. Additionally, the separation
location moves downstream slightly, and reattachment occurs farther upstream. This eﬀect
is seen equally in both the baseline and increased FSTI conﬁgurations. The baseline cases at
α ≈ 2.4◦ are shown in Figure 3.12. At high angles of attack (such as ∼10◦ as shown for both
conﬁgurations in Appendix B.3), the separation location is not signiﬁcantly impacted by
the Reynolds number, but the LSB becomes shorter (by the reattachment location moving
upstream) and thinner with increasing Rec . The Reynolds number is also very important in
determining the bubble length, which may be seen later in Figure 3.16.
48

(a) α = 2.3◦

(b) α = 6.4◦

(c) α = 10.7◦

Figure 3.11: The mean ﬂow ﬁeld is shown for Rec = 3 × 104 with increasing α
top to bottom. The location of the reversed ﬂow region moves upstream as the
angle is increased. The baseline cases are shown here, all other cases may be
found in Appendix B.1

49

(a) Rec = 2 × 104 , α = 2.5◦

(b) Rec = 3 × 104 , α = 2.3◦

(c) Rec = 4 × 104 , α = 2.4◦

Figure 3.12: The mean ﬂow ﬁeld is shown for an increasing Rec top to bottom
for an α ≈ 2.4◦ . The baseline cases are shown here, all other cases may be found
in Appendix B.3. The primary eﬀect of the Reynolds number is a thinning of
the reversed ﬂow region i.e. the LSB is shorter in height as Rec increases. Also
with increased Rec the separation is delayed slightly and reattachment occurs
farther upstream.

50

3.4

Comparisons of LSB Characteristics

The locations of separation, reattachment, and the bubble length between the baseline and
added freestream turbulence conﬁgurations are compared in this section. The available data
in the literature, namely Burgmann and Schr¨der (2008); Burgmann et al. (2007); Galbraith
o
(2009), and the previous study at MSU, Katz (2010), are also presented for comparison.

3.4.1

Separation and Reattachment

The separation and reattachment locations for each Reynolds number studied are presented
along with a discussion of the results. Each Reynolds number will be ﬁrst discussed separately, with the results shown in Figures 3.13 for Rec = 2 × 104 , 3.14 for Rec = 3 × 104 , and
3.15 for Rec = 4 × 104 . The primary features that are discussed and compared between different investigations in the following are: the general trends of separation and reattachment,
the separation and the reattachment locations.

3.4.1.1

Reynolds Number 20,000

In Figure 3.13 the separation and reattachment locations are plotted versus angle of attack for
both the baseline and added freestream turbulence conﬁguration. The separation locations
move downstream, relative to the baseline case, for the increased FSTI cases. The exception
is at α = 10◦ ; where, at this angle, the baseline ﬂow has stalled, whereas the increased FSTI
case has a closed separation bubble. The drastically diﬀerent ﬂow conditions may explain
why the separation location does not ﬁt the trend (of delayed separation due to increased
FSTI) for this case. The strong adverse pressure gradient at this high angle of attack would
dominate, making the boundary layer less receptive to freestream disturbances.
51

Rec = 2 × 104

1
0.9
0.8
0.7

x/c

0.6
0.5
0.4
0.3
0.2
0.1
0

Olson (2011), Baseline
Olson (2011), Added FSTI
Katz (2010)
Burgmann & Schr¨ der (2008)
o
Burgmann et al. (2007)

0

2

4
6
8
Angle of Attack, α - Deg.

10

12

Figure 3.13: Separation (circles) and Reattachment (squares) locations are compared for Rec = 2 × 104 . The square symbols with a white face color indicate an
open separation. The error bars for the current experiments have been excluded
from this and subsequent ﬁgures because the random uncertainty is typically less
than the symbol size, however, this does not include the systematic error which
is discussed later regarding the identiﬁcation of separation and reattachment
location.

52

The reattachment locations also change with increased FSTI, moving upstream relative
to the baseline case. This is constant with the idea of the freestream disturbances exciting
the Kelvin-Helmholtz instability, transporting higher momentum ﬂuid towards the surface.
At the lowest angles, where open separations occur, ﬂow with increased FSTI has the eﬀect
of shortening the reversed ﬂow region extending past the trailing edge (which may be seen
in the contours at this Reynolds number of Figure B.1 located in Appendix B.1).
There is good qualitative agreement between the current study and previous MSU study,
with open separation occurring in the baseline case at both low and high angles of attack.
The disagreements in separation location appear to fall within the uncertainty of the measurements (the α uncertainty in the pervious experiments was ±0.4◦ ).
The actual locations of reattachment are slightly diﬀerent between the two studies at
MSU, but, the overall eﬀect appears to be consistent with the previous study having a lower
FSTI than the current study. The freestream turbulence is however, not well known from
the previous study and future work should attempt to quantify the FSTI of the previous
MSU study utilizing the techniques described in Section 2.3 but applying them to the old
data sets.
Comparing the reattachment locations of current data sets with those of Burgmann and
Schr¨der (2008); Burgmann et al. (2007) also supports the hypothesis that the primary difo
ferences may be explained by the Burgmann studies having higher FSTI. The reattachment
locations of these two studies by the Burgmann also agree very well with the cases with increased FSTI of the current study. The earlier Burgmann study (2007), however, had a FSTI
of 1.5% whereas, in the 2008 study it had been reduced to 1.0%, The separation locations
did move upstream as expected by increased freestream turbulence, but the reattachment
53

points actually moved downstream with increased FSTI. It is not entirely clear why this
is the case, but as it has been shown, accurate characterization of the these ﬂow features
are highly sensitive to a variety of issues, which have not all been quantiﬁed in previous
investigations.

3.4.1.2

Reynolds Number 30,000
Rec = 3 × 104

1
0.9
0.8
0.7

x/c

0.6
0.5
0.4
0.3
0.2
0.1
0

Olson (2011), Baseline
Olson (2011), Added FSTI
Katz (2010)
Galbraith (2009)

0

2

4
6
8
Angle of Attack, α - Deg.

10

12

Figure 3.14: Separation (circles) and Reattachment (squares) locations are compared for Rec = 3 × 104 . The square symbols with a white face color indicate an
open separation.

54

At a Reynolds number of 3 × 104 , the eﬀect of freestream turbulence and angle of attack
are also observed (see Figure 3.14). Separation is delayed and an earlier reattachment is
observed with increased FSTI. The inﬂuence of freestream turbulence on separation degrades
at both high and low angles of attack (as observed at Rec = 2 × 104 ). The inﬂuence of FSTI
on reattachment is similar at all angles, with , except in the case at Rec = 2 × 104 where
stall was delayed.
There is good agreement between the previous MSU study and the current study. The
same systematic diﬀerence in FSTI discussed at Rec = 2 × 104 can be applied to this
data set as well. The other comparison at this Reynolds number, Galbraith (2009), is
a simulation which has no freestream turbulence. With its location of separation farther
upstream and reattachment farther downstream than the experimental data, the lack of
FSTI in the simulations could potentially explain the diﬀerences observed.

55

3.4.1.3

Reynolds Number 40,000
Rec = 4 × 104

1

Olson (2011), Baseline
Olson (2011), Added FSTI
Katz (2010)
Burgmann & Schr¨ der (2008)
o
Rizzetta & Visbal (2011)

0.9
0.8
0.7

x/c

0.6
0.5
0.4
0.3
0.2
0.1
0

0

2

4
6
8
Angle of Attack, α - Deg.

10

12

Figure 3.15: Separation (circles) and Reattachment (squares) locations are compared for Rec = 4 × 104 . The square symbols with a white face color indicate an
open separation.

The data shown in Figure 3.15 is the separation and reattachment locations for the
current study and several other experimental (Katz, 2010; Burgmann and Schr¨der, 2008)
o
and computational (Rizzetta and Visbal, 2011) studies. The same inﬂuence of increased
FSTI, by delaying separation and an earlier reattachment relative to the baseline case, is
observed. The shortening in height of the reversed ﬂow region due to increased FSTI makes
it diﬃcult to discern if the bubble is either non-existent or too thin to detect at α ≈ 7◦ . At
56

this Reynolds number, the decreasing inﬂuence of FSTI on separation location at both high
and low angles of attack is observed.
There is more scatter when comparing the data at this Reynolds number among the different studies. There is relatively good agreement between the MSU studies in reattachment
locations. However, there is a diﬀerent slope in the separation curve between the MSU studies. The slope of the separation curve of the earlier MSU study (Katz, 2010) does, however,
more closely match that of Burgmann and Schr¨der (2008).
o
With respect to the computations, there is poor agreement in separation location at
α = 4◦ although the agreement is much better at α = 8◦ . The better agreement at the
high angle may be due to the larger pressure gradient at this angle of attack dominating
the separation location. The bubble geometry is not as sensitive to the near-wall spatial
resolution bias discussed below and also in Section 3.2.2. However, the opposite is true for
reattachment, with the lower angle closer to the experiments than the higher angle. The
systematic diﬀerences in numerical results of separation location may be explained in part
by FSTI with both its eﬀect on separation and reattachment locations and its eﬀect on the
bubble height.
The bias error in the detection of separation location due to bubble geometry, discussed
in Olson et al. (2011) and also in Section 3.2.2, is estimated to be 0.05c for Rec = 4 × 104 and
α = 4◦ from the numerical results. Since this error estimate relies on the bubble geometry,
which has been shown to change signiﬁcantly for diﬀerent Reynolds numbers and angles of
attack, is also expected to change for each case. Less bias error is expected at α = 8◦ due
to the diﬀerences in bubble geometry, which may explain, in part, why separation agrees
decently in the simulations to the experiments at this angle.
57

3.4.2

Bubble Length
Re c = 2 × 10 4 ,
Re c = 2 × 10 4 ,
Re c = 2 × 10 4 ,
Re c = 2 × 10 4 ,
Re c = 2 × 10 4 ,
Re c = 3 × 10 4 ,
Re c = 3 × 10 4 ,
Re c = 3 × 10 4 ,
Re c = 3 × 10 4 ,
Re c = 4 × 10 4 ,
Re c = 4 × 10 4 ,
Re c = 4 × 10 4 ,
Re c = 4 × 10 4 ,
Re c = 4 × 10 4 ,

0.8

0.7

Bubble Length - x/c

0.6

0.5

0.4

Olson (2011) Basline
Olson (2011) Added FSTI
Katz (2010)
Burgmann & Schr¨ der (2008)
o
Burgmann et al. (2007)
Olson (2011) Baseline
Olson (2011) Added FSTI
Katz (2010)
Galbraith (2009)
Olson (2011), Baseline
Olson (2011), Added FSTI
Katz (2010)
Burgmann & Schr¨ der (2008)
o
Rizzetta & Visbal (2011)

0.3

0.2

0.1

0
2

4

6

8

10

12

Angle of Attack, α - Deg.

Figure 3.16: The compiled separation bubble length for diﬀerent conditions and
diﬀerent studies. Each color represents a Reynolds number, and each symbol a
particular study. The symbols with a black edge represent the increased FSTI
cases with its face color indicating the Reynolds number.

The eﬀect of increased FSTI has been shown to decrease the size of the laminar separation
bubble in both length and height. Figure 3.16 show the length of the LSB for various
Reynolds numbers versus angle of attack for all the studies discussed in this chapter.
The ﬁrst observation from the ﬁgure is the amount of scatter in the data. There are
58

however, a few trends that can still be discerned. The eﬀect of freestream turbulence is
signiﬁcant relative to the other inﬂuences of Reynolds number and angle of attack. In the
Burgmann studies, contrary to all of the other studies, there is little dependency of the
bubble length on angle of attack. In the case of all of the computational studies, the bubble
length is considerably longer than experiments, which is expected from when the inherent
experimental bias in determining the length of the LSB is considered and the inﬂuence of
freestream turbulence.
For 2◦ < α < 7◦ the length of the LSB has been shown to be reduced by 60±11% between
the baseline and increased FSTI conﬁgurations of the current experiments at Rec = 2 × 104
and Rec = 3 × 104 . At Rec = 4 × 104 , the length of the LSB is reduced by ∼ 95% for the
same range of angles. At the highest angle of attack in the current measurements, α ≈ 10◦ ,
the length of the LSB was reduceded by ∼ 18 ± 4%.

3.4.3

Summary of LSB Characteristics

The separation location, reattachment location, and corresponding laminar separation bubble length have been measured for a range of α and Rec for both the baseline and increased
FSTI conﬁgurations. Theses characteristics have been presented in the preceding sections
and have been tabulated in in Table C.1, in Appendix C.

59

3.5

Facility and Flow Dependent Issues

There are many factors that oﬀer explanations for the diﬀerences in the measured separation and reattachment locations among the current study and the literature. Several of
these eﬀects have been described in the previous sections, such as, freestream turbulence,
near-wall resolution, and the geometry of the reversed ﬂow region. Some of these factors
cause diﬀerences in the actual ﬂow while others are inherent limitations of the experimental
technique. The following sections are presented as potential explanations for diﬀerences in
the literature.

3.5.1

Freestream Turbulence

The turbulence characteristics of the freestream have been shown to alter the ﬂow around a
stationary airfoil at 2×104 < Rec < 4×104 . This is expected as freestream turbulence acts as
excitation source to the boundary layer upstream of separation and also the separated shear
layer downstream of separation. It is not clear which aspect(s) of the freestream turbulence
inﬂuences the laminar separation bubble, whether it be the FSTI, integral length scale, or
spectral content, but it is a signiﬁcant contributing factor to diﬀerences in the measured LSB
characteristics from diﬀerent ﬂow facilities. The lack of freestream turbulence in simulations
is clearly problematic for comparisons to the ﬂow obtained from experiments. The tendency
of simulations to separate earlier and reattach later are consistent with the eﬀect of freestream
turbulence and can account for at least some of the discrepancies between simulations and
experiments.
60

3.5.2

Flow Three-Dimensionatlity

The current experiments and those compared to in the literature all attempt to recreate
nominal 2D ﬂow conditions through the use of end walls, however, Burgmann and Schr¨der
o
(2008) observed a signiﬁcant amount of 3-dimensional ﬂow over this airfoil. The diﬀerences
in 3-dimensional ﬂow structures for diﬀerent levels of FSTI were studied in Burgmann and
Schr¨der (2008) and was concluded to be small. The inﬂuence of ﬁnite aspect ratio, and
o
blockage eﬀects will both contribute to changes in the 3-dimensional structure of the ﬂow,
which were not he same between all the studies. It is not known what inﬂuences these
eﬀects will have on the separation and reattachment locations that are compared in the
current study.

3.5.3

Airfoil Shape

This is a relatively obvious source of error when comparing studies conducted at diﬀerent
facilities and in computations. The actual shape of the current airfoil, described in Section
2.1.2, is approximately 1% thicker than the theoretical proﬁle, with most of the added
thickness occurring below the chordline. The decrease in camber compared to the theoretical
proﬁle would indicate, from thin airfoil theory estimates of the inﬂuence of camber (see
Currie, 1993), a slight decrease in the eﬀective angle of attack of ∼ 0.11◦ is expected. This
change in eﬀective angle of attack due to the diﬀerences in camber is small and therefore,
is not expected to eﬀect the results, trends, and conclusions presented. Other studies in
the literature do not report the actual shape of their model, which makes it impossible to
compare actual proﬁle shapes. The impact the slight deviations in airfoil shape is unknown,
but, is easily investigated with inexpensive potential ﬂow simulations.
61

3.5.4

Near-wall Spatial Resolution

In the current experiments, a region of 4-5 pixels is excluded near the wall due to surface
imaging issues. It was seen from the current experiments (and computations found in the
literature) that the LSB is very thin near separation, as shown in Figure 3.17. Identifying

Figure 3.17: The region around separation from simulations (performed by
Rizzeta & Visbal (2011)) at Rec = 4 × 104 and α = 4◦ Olson et al. (2011).
The arrows indicate where separation would be detected with the nearest velocity vector at ∼ 0 (CFD), 3 mC, or 6 mC above the wall.

separation and reattachment from velocity data at some distance above the surface will introduce a bias in determining these locations. Separation will be identiﬁed farther downstream,
estimated to be 0.05c at Rec = 4 × 104 and α = 4◦ , than compared to where the wall-shear
stress is zero. The reattachment will be identiﬁed farther upstream than their real locations,
by slightly less than the separation error, and is also highly dependent on the separation
bubble geometry. The combined eﬀect of these biases is such that the LSB will be measured
to be shorter than it really is.
62

3.5.5

Uncertainty in Wall location

The experimental uncertainty in identifying the wall location in the current experiments is
±2 pixels, which also contributes to the same type of error described in the previous section.
Since the surface locations are used to determine the geometric angle of attack, one would
be inclined to believe that this would also produce error in determining the angle of attack,
but it does not. There is no increased error in determining α because if the error is purely
random, it will not inﬂuence the mean surface result.
If there is a ﬁxed bias, i.e. the surface is consistently selected above or below its physical
location, the second degree of freedom in the optimization routine, used to determine the
geometric angle, will account for this bias. The ﬁrst degree of freedom is the airfoil angle of
attack, while the second is the vertical location of the axis of rotation while its horizontal
location is ﬁxed due to the high degree of certainty of the streamwise location of the trailing
edge. The only error that would contribute to an incorrect angle of attack would be one that
systematically varied the surface identiﬁcation location from the trailing to leading edge (or
visa-versa). This was determined to not be the case by locating the same surface locations
on diﬀerent days and comparing the results.

3.5.6

Angle of Attack Sensitivity

The sensitivity of the separation location to the angle of attack can be seen from the current
study and in the literature. The sensitivity at low angles of attack, α < 4◦ , was determined to
∂xsep
≈ 0.1cdeg−1 (where xsep is the location of separation) from both simulations and
∂α
experiments in Olson et al. (2011) and the current experiments at Rec = 4 × 104 . Clearly,

be

with separation location moving ∼ 10% of the chord per degree at low α, a considerable
63

amount of conﬁdence in the angle of attack is required. Measuring the angle of attack is
however, a nontrivial task experimentally: both the geometric orientation of the airfoil must
be known as well as the angle of the freestream, which is non-zero due to the boundary layer
growth along the test section walls.
The angle of attack listed for all the current experiments is relative to the bottom of the
tunnel, which does not take into account the angle of the freestream. The freestream angle
is expected to be small and its exclusion in the current experiments does not impact the
trends and observations presented; for reference Katz (2010) measured (at ∼4 c upstream
of the airfoil) 0.25◦ at Rec = 2 × 104 and 0.14◦ at Rec = 4 × 104 . The ﬂow management
between the current and this previous study was not the same and therefore, the freestream
angles may not be the same. In the other literature, no detailed information is provided to
clarify or quantify the freestream angle when computing the angle of attack.

64

Chapter 4
Summary

4.1

Summary

The inﬂuence of added Freestream Turbulence Intensity (FSTI) on the mean ﬂow around a
stationary SD7003 airfoil was studied experimentally for a range of chord Reynolds number
(Rec = 2 × 104 − 4 × 104 ) and angle of attack (α = 0◦ − 11◦ ).
The mean and RMS ﬂuctuation of the streamwise velocity of the baseline ﬂow were
compared against the ﬂow with added freestream turbulence using high resolution singlecomponent Molecular Tagging Velocimetry with speciﬁc focus on the laminar separation
bubble on the suction side of the airfoil. The locations of separation and reattachment, and
the bubble length are quantitatively compared. Qualitative results regarding the height of
the separation bubble and the diﬀerences in the streamwise velocity RMS ﬂuctuations are
discussed.
The inﬂuence of increased freestream turbulence was shown to move the separation location downstream and move the reattachment point upstream from where it occurs in the
65

baseline ﬂow. The increased freestream turbulence has the eﬀect of suppressing the separation bubble by both shortening it in length and in height. In some cases, the increase in
freestream turbulence is associated with delaying stall, or even eliminating the reversed ﬂow
region in the mean ﬂow (within the resolution of the measurements).
The inﬂuence of freestream turbulence, and other experimental parameters, such as near
wall spatial resolution, and angle of attack sensitivity, have been expired to explain most of
the discrepancies in separation and reattachment locations in the literature.

4.2

Future Work

There are many diﬀerent aspects of the current work than can be expanded upon and others
that can be immediately addressed from the current data sets.
The inﬂuence of increased FSTI should be quantiﬁed in terms of: laminar separation
bubble height, the value and location of peak RMS of the ﬂuctuating streamwise velocity.
The observation of decreased streamwise ﬂuctuation, (which should be correlated to the
turbulent kinetic energy, although the current single component data prohibits making a
comprehensive conclusion), should be quantiﬁed.
The near surface imaging issues, caused by the surface of the model absorbing the incident
UV radiation and subsequently phosphorescing with a lifetime on the order of the MTV
tracer needs to be addressed. This will enable future measurements of this type to have high
quality data near the wall.
The extrapolation of the separation and reattachment location based on bubble geometry
should be explored to yield better estimates of separation and reattachment. The technique
should be ﬁrst explored with computational data at various angles of attack and Reynolds
66

numbers (i.e. for diﬀerent bubble geometries).
In regards to the inﬂuence of freestream turbulence on the laminar separation bubble,
additional fundamental research is warranted in the receptivity of shear layer instabilities
to freestream turbulence near a wall. It is also recommended that high ﬁdelity simulations
are performed that match the freestream conditions used in the present study such that the
experiment may be compared directly to simulation results.

4.3

Conclusions

The discrepancies found in the literature regarding the locations of separation and reattachment can be mostly explained by the work presented. The basic ﬂow around the stationary
airfoil, in the range of Reynolds number investigated, are highly sensitive to both freestream
conditions and the conﬁguration parameters (such as Reynolds number and angle of attack).
It has been shown that a high degree of precision and accuracy is required to properly characterize these ﬂows. Luckily, much of the future work of MAV aerodynamics lies in fully
unsteady motions, which tend to be less sensitive to these small details.

67

APPENDICES

68

Appendix A
Freestream Turbulence

A.1

Freestream Turbulence Spectra

The following Figures show the power spectral density for the freestream. Figure A.1 shows
both the raw PSD and after the spatial mean has been removed for both the baseline and
increased FSTI conﬁgurations. It is clear that the spatial mean, caused by the low frequency
oscillations, make up a signiﬁcant portion of the total ﬂuctuation energy.
Referring to Figures A.1 (c) and (d), the shape of the PSD for each conﬁguration are
not signiﬁcantly altered due to Reynolds number. It is the magnitude that changes with
respect to Reynolds number. The Reynolds number eﬀect on the magnitude of the PSD in
the increased FSTI conﬁguration is signiﬁcantly less at low frequencies, and it is the high
frequencies that tend to have the greater variation in magnitude. In the baseline case, the
opposite is true of the Reynolds number eﬀect, i.e. similar magnitudes at higher frequencies
with the low frequencies varying in magnitude as a function of Reynolds number.

69

(a) Baseline

(b) Increased FSTI

(c) Spatial Mean Removed

(d) Spatial Mean Removed

Figure A.1: The power spectral density for both the baseline and increased FSTI
conﬁgurations are shown. In (a) and (b) the raw PSD are calculated and the low
frequencies dominate the spectrum. By removing the oscillatory components
due to spatially uniform ﬂuctuations in velocity (the spatial mean velocity from
each tag line is removed), the PSD shown in (c) and (d) are computed.

70

The inﬂuence of the grid at each Reynolds number may be seen in Figure A.2. At low
Reynolds number, 2 × 104 , the increase in PSD is over a broad range of frequencies, while
trailing oﬀ at high frequencies. At the higher Reynolds numbers of 3 × 104 and 4 × 104 , the
inﬂuence of the grid is minimal for frequencies up to 0.3 Hz (3 × 104 ) and 0.9 Hz (4 × 104 ).
The diﬀerences in the spectra as a function of Reynolds number could be signiﬁcant.
At higher Reynolds number, it appears that it is primarily small scales of turbulence that
are introduced, whereas as lower Reynolds number, it is larger scales are primarily introduced. However, since the overall trends observed in this study are consistent across diﬀerent
Reynolds numbers, it is likely that the eﬀect observed can be related to the changes in FSTI
and not requiring entire turbulence spectra to describe the changes in LSB characteristics
between the baseline ﬂow and the ﬂow in the presence of the grid.

71

(a) Rec = 2 × 104

(b) Rec = 3 × 104

(c) Rec = 4 × 104

Figure A.2: The power spectral density for Rec = 2×104 , 3×104 , and 4×104 are
shown comparing the two conﬁguration at each Reynolds number. The addition
of the grid increases the broadband freestream turbulence across all Reynolds
numbers however, its impact on low frequencies degrades as Reynolds number
increases and its impact on high frequencies increases as the Reynolds number
increases.

72

Appendix B
Mean and RMS Contours

B.1

Mean Flow ﬁeld Evolution by Angle of Attack

The proceeding three pages compare the mean baseline ﬂow to the ﬂow with increased FSTI
as a function of Reynolds number and angle of attack. Each page is dedicated to a single
Reynolds number, with the baseline cases in the left column and the increased FSTI cases
in the right column and an increasing angle of attack top to bottom. All of the colormaps
¯
are the same, −0.18 ≤ Uu ≤ 1.74. The colormap has been created with a step change
∞
at 0 with an increasing intensity of ‘pink’ representing higher negative velocity. Velocities
outside this range are saturated.

73

Baseline

Increased FSTI

(a) α = 0.5◦

(b) α = −0.3◦

(c) α = 2.5◦

(d) α = 1.5◦

(e) α = 4.5◦

(f ) α = 3.5◦

(g) α = 6.1◦

(h) α = 5.8◦

(i) α = 10.0◦

(j) α = 10.0◦

Figure B.1: The mean ﬂow ﬁeld is shown for Rec = 2 × 104 with increasing α top
to bottom. Added freestream turbulence is on the right column.

74

Baseline

Increased FSTI

(a) α = 0.5◦

(b) α = 0.7◦

(c) α = 2.3◦

(d) α = 2.4◦

(e) α = 4.4◦

(f ) α = 4.6◦

(g) α = 6.4◦

(h) α = 6.4◦

(i) α = 10.7◦

(j) α = 10.6◦

Figure B.2: The mean ﬂow ﬁeld is shown for Rec = 3 × 104 with increasing α top
to bottom. Added freestream turbulence is on the right column.

75

Baseline

Increased FSTI

(a) α = 0.4◦

(b) α = 0.4◦

(c) α = 2.4◦

(d) α = 2.4◦

(e) α = 4.6◦

(f ) α = 4.5◦

(g) α = 6.8◦

(h) α = 6.6◦

(i) α = 10.8◦

(j) α = 10.7◦

Figure B.3: The mean ﬂow ﬁeld is shown for Rec = 4 × 104 with increasing α top
to bottom. Added freestream turbulence is on the right column.

76

B.2

RMS Flow ﬁeld Evolution by Angle of Attack

The following three pages compare the streamwise RMS ﬂuctuation of the baseline ﬂow to
the ﬂow with increased FSTI as a function of Reynolds number and angle of attack. Each
page is dedicated to a single Reynolds number, with the baseline cases in the left column and
the increased FSTI cases in the right column and an increasing angle of attack top to bottom.
There are two color scales; the ﬁrst for Rec = 2 × 104 and 3 × 104 is 0.02 ≤ urms ≤ 0.40 and
U∞
the second, for Rec = 4 × 104 , is 0.02 ≤ urms ≤ 0.30. In almost all cases, the ﬂoor level of
U∞
urms < 0.02 yields no appreciable ﬂow information, and is made up mostly of non-uniform
U∞
background noise. The exception is the Rec = 2 × 104 at the lowest α, where one can see a
very slight increase in RMS above the trailing edge location. With a more appropriate color
scale, one would see a slender band of increased RMS over the aft end of the airfoil, similar
to the next higher angle.
The background RMS has been subtracted from each line to account for the spatial nonuniformities in the SNR of each tag line, which greatly inﬂuence the RMS as SNR drops.
The background RMS that is subtracted is simply the mean urms 2 from the ﬁrst 100 pixels
in the tag line with no appreciable diﬀerence between the removed background between the
baseline and increased FSTI cases were found.

77

Baseline

Increased FSTI

(a) α = 0.5◦

(b) α = −0.3◦

(c) α = 2.5◦

(d) α = 1.5◦

(e) α = 4.5◦

(f ) α = 3.5◦

(g) α = 6.1◦

(h) α = 5.8◦

(i) α = 10.0◦

(j) α = 10.0◦

Figure B.4: The RMS ﬂow ﬁeld is shown for Rec = 2 × 104 with increasing α top
to bottom. Added freestream turbulence is on the right column.

78

Baseline

Increased FSTI

(a) α = 0.5◦

(b) α = 0.7◦

(c) α = 2.3◦

(d) α = 2.4◦

(e) α = 4.4◦

(f ) α = 4.6◦

(g) α = 6.4◦

(h) α = 6.4◦

(i) α = 10.7◦

(j) α = 10.6◦

Figure B.5: The RMS ﬂow ﬁeld is shown for Rec = 3 × 104 with increasing α top
to bottom. Added freestream turbulence is on the right column.

79

Baseline

Increased FSTI

(a) α = 0.4◦

(b) α = 0.4◦

(c) α = 2.4◦

(d) α = 2.4◦

(e) α = 4.6◦

(f ) α = 4.5◦

(g) α = 6.8◦

(h) α = 6.6◦

(i) α = 10.8◦

(j) α = 10.7◦

Figure B.6: The RMS ﬂow ﬁeld is shown for Rec = 4 × 104 with increasing α top
to bottom. Added freestream turbulence is on the right column.

80

B.3

Mean Flow ﬁeld Evolution by Reynolds Number

The proceeding section compares the mean ﬂow as a function of Reynolds number at simliar
angles of attack. Each page is dedicated to a single angle of attack, with an increasing
Reynolds number top to bottom.
There is little eﬀect of Reynolds number at very low angles of attack, α ≈ 0.5◦ as seen in
Figure B.7. However, increasing the angle of attack to α ≈ 2.5◦ , shown in Figure B.8, both
the length and height of the reversed ﬂow region can be seen to decrease with increasing
Reynolds number. The location of separation appears to not be signiﬁcantly eﬀect at this
angle of attack. At a much higher angle, α ≈ 10.5◦ , which may be seen in Figure B.9, the
eﬀect of Reynolds number is even more drastic than at the lower angle, but the eﬀects are
the same: reversed ﬂow region thins and shortens with increasing Reynolds number, with
the reattachment location moving upstream considerably with Reynolds number.
The same trends are observed between both the baseline and increased FSTI conﬁgurations. The increased FSTI conﬁguration for α ≈ 10.5◦ is shown in Figure B.10 to demonstrate the simliar Reynolds number eﬀects between both levels of freestream turbulence.

81

(a) Rec = 2 × 104 , α = 0.5◦

(b) Rec = 3 × 104 , α = 0.5◦

(c) Rec = 4 × 104 , α = 0.4◦
Figure B.7: The baseline conﬁguration mean ﬂow ﬁelds are shown for an increasing Rec top to bottom for an α ≈ 0.5◦ .

82

(a) Rec = 2 × 104 , α = 2.5◦

(b) Rec = 3 × 104 , α = 2.3◦

(c) Rec = 4 × 104 , α = 2.4◦
Figure B.8: The baseline conﬁguration mean ﬂow ﬁelds are shown for an increasing Rec top to bottom for an α ≈ 2.4◦ .

83

(a) Rec = 2 × 104 , α = 10.0◦

(b) Rec = 3 × 104 , α = 10.7◦

(c) Rec = 4 × 104 , α = 10.8◦
Figure B.9: The baseline conﬁguration mean ﬂow ﬁelds are shown for an increasing Rec top to bottom for an α ≈ 10.5◦ .

84

(a) Rec = 2 × 104 , α = 10.0◦

(b) Rec = 3 × 104 , α = 10.7◦

(c) Rec = 4 × 104 , α = 10.8◦
Figure B.10: The increased FSTI conﬁguration mean ﬂow ﬁelds are shown for
an increasing Rec top to bottom for an α ≈ 10.4◦ .

85

Appendix C
Compiled LSB Characteristics
The following table lists the separation and reattachment locations and the LSB bubble
length from the current experiments. The Reynolds number referenced is the nominal
Reynolds number, the precise Rec and the angle of attack uncertainty may be found in
Table 2.1 on 33.

86

Table C.1: Separation location, reattachment location, and bubble length are
tabulated for each case. All values are determined from a location ∼2.69 mm
(0.0013c) above the airfoil surface. If the ﬂow does not reattach, the reattachment location is listed as ‘open’. If ﬂow separation is not detected, the separation
location is listed as N/A.

Baseline
Rec = 2 × 104

Baseline
Rec = 3 × 104

Baseline
Rec = 4 × 104

Added FSTI
Rec = 2 × 104

Added FSTI
Rec = 3 × 104

Added FSTI
Rec = 4 × 104

α
[deg]
0.5
2.5
4.5
6.1
10.0
0.5
2.3
4.4
6.4
10.7
0.5
2.5
4.5
6.8
10.8
-0.3
1.5
3.5
5.8
10.0
0.7
2.4
4.6
6.4
10.6
0.4
2.4
4.5
6.6
10.7

Separation
Location
[x/c]
0.81 ± 0.01
0.47 ± 0.02
0.28 ± 0.01
0.18 ± 0.02
0.06 ± 0.01
0.70 ± 0.05
0.51 ± 0.01
0.27 ± 0.01
0.15 ± 0.02
0.03 ± 0.01
0.80 ± 0.01
0.51 ± 0.01
0.32 ± 0.01
0.19 ± 0.01
0.03 ± 0.02
0.98 ± 0.01
0.70 ± 0.01
0.47 ± 0.01
0.28 ± 0.02
0.05 ± 0.02
0.76 ± 0.02
0.57 ± 0.01
0.40 ± 0.01
0.26 ± 0.01
0.03 ± 0.01
0.82 ± 0.01
0.59 ± 0.02
0.44 ± 0.02
N/A
0.03 ± 0.02

87

Reattachment
Location
[x/c]
open
open
0.86 ± 0.01
0.74 ± 0.02
open
open
0.95 ± 0.01
0.71 ± 0.01
0.55 ± 0.01
0.27 ± 0.01
open
0.86 ± 0.01
0.60 ± 0.01
0.38 ± 0.01
0.20 ± 0.01
open
open
0.81 ± 0.01
0.55 ± 0.02
0.25 ± 0.01
open
0.77 ± 0.02
0.54 ± 0.01
0.36 ± 0.02
0.18 ± 0.01
open
0.61 ± 0.02
0.47 ± 0.02
N/A
0.15 ± 0.01

Bubble
Length
[x/c]
N/A
N/A
0.57 ± 0.01
0.28 ± 0.02
N/A
N/A
0.45 ± 0.01
0.44 ± 0.01
0.40 ± 0.02
0.24 ± 0.01
N/A
0.35 ± 0.01
0.27 ± 0.01
0.19 ± 0.01
0.16 ± 0.01
N/A
N/A
0.34 ± 0.01
0.27 ± 0.02
0.20 ± 0.02
N/A
0.20 ± 0.02
0.14 ± 0.01
0.09 ± 0.02
0.15 ± 0.01
N/A
0.02 ± 0.02
0.03 ± 0.02
N/A
0.12 ± 0.01

Appendix D
Miscellaneous

D.1

Test Section Photos

88

(a) View Looking Downstream

(b) View Looking Upstream
Figure D.1: Photos of the test section. The primary imaging system and the
translating UV optics attached to the streamwise linear traverse.

89

D.2

Procedure of Simulated Experiments

The following procedure outlines the simulated experiments that were performed to validate using the 1c-MTV technique over the surface of an airfoil under the conditions of the
experiments.

1. “Known Flow Field”
The mean velocity ﬁeld from CFD simulations are utilized to provide the ﬂow ﬁeld in
which the “experiments” will be performed. This ﬂow ﬁeld is assumed to be indicative
of the ﬂow ﬁelds to be examined during the actual experiments of this study.

2. Coordinate Transformations
The coordinate systems of CFD simulations place the chordline of the airfoil along the
x-axis and the freestream u and v are adjusted to achieve the desired angle of attack.
The experiments on the other hand, move the airfoil relative to a freestream that has
(nearly) zero v. So, coordinate system of the CFD simulation is transformed into the
experimental reference frame.

3. Tag Lines
The Lagrangian displacement of prescribed ﬂuid locations, with a spatial resolution in
the cross stream and line spacing indicative of the current experiments, are tracked in
time.

4. Displacement
Each ﬂuid element is displaced using the known ﬂow ﬁeld for a time period of ∆t using
10 intermediate time steps between t = 0 and t = ∆t.
90

5. Measurement
The displaced ﬂuid elements are remapped (via liner interpolation) such that the ypositions of original ﬂuid locations are found. This yields a displaced lines of ﬂuid
whose Y-locations are the same as the initially prescribed ﬂuid. The displacement if
found from subtracting the originally prescribed ﬂuid location from the location of the
ﬂuid with the same y-value. This accurately simulates the processing technique used
for 1c-MTV without considering a ﬁnite line thickness or signal to noise of images,
i.e. it is the best possible estimate of velocity using this technique. The velocity is
calculated by dividing by ∆t.
6. Comparision
The know ﬂow ﬁeld (CFD) is remapped onto the simulated experiment’s originally
prescribed ﬂuid data locations to allow the error in u be calculated for each location.

91

D.3

Experimental Procedure

The following procedure outlines the experiments that were performed in this study.

1. Tunnel Speed Adjustment
At the beginning of each session the freestream speed is adjusted to the correct speed
for the desired Rec using the 2c-MTV measurements upstream of the airfoil. The
temperature is measured at the beginning of each case and is used for computing the
viscosity term in the Reynolds number.
2. Airfoil Angle of Attack
The upstream measurements also provide the angle of the freestream, which was utilized for setting the geometric angle of attack such that the freestream angle plus the
geometric angle of attack would yield the desired α = 2, 4, 6, 8 or 12 degrees. It was
later found that the v component of velocity at a location 2c upstream of the airfoil has
not been suﬃciently reduced to a level representative of the freestream. The initial α
was determined with a rotational correlation routine using an image of the proﬁle of the
airfoil and the theoretical proﬁle. After setting the initial angle all subsequent angle
changes were achieved using the traversing mechanism (but also, incorrectly, utilized
a new freestream angle, hence why not all ∆α’s are precisely 2◦ or 4◦ ).
3. Image Acquisition, FOV #1-10
For the ﬁrst FOV, an undelayed image sequence is recorded, then immediately the
delayed image sequence and upstream images are recorded at the same time. To
reduce the number of times settings needed to be changed, in the second FOV the
delayed image sequence and upstream images are recorded ﬁrst, immediately followed
92

by the undelayed image sequence. This pattern was repeated until each FOV had
been completed. Each delayed image sequence is 5 minutes, and each undelayed image
sequence is 1.5 minutes in length. The ﬂow was observed for several seconds prior to
recording the the images and the exposure and time delay were optimized for each
FOV. The traverse motion between each FOV was determined from one of the eleven
diﬀerent shift patterns developed to maximize the measurement domain.
4. Image Acquisition, FOV #11 & 12
For FOV #11 and #12, the laser repetition rate was increased from 10 Hz to 20 Hz.
To achieve the higher frame rate, the Pixelﬂy was binned in the cross-stream direction.
This yielded a resolution of 512 × 1392 pixels for the same physical FOV size, i.e. the
scale factor in the Y-direction has reduced by a factor of 2. In these FOVs, the delay
time was typically 12 ms, which was determined to be the optimum delay time for
measuring ﬂuctuating quantities in the freestream based on the relationship between
subpixel accuracy and the ﬂuid displacement.
5. Repeat
The procedure listed above is repeated for each angle of attack at the current Reynolds
number. The intra-day temperature ﬂuctuations were typically negligible, but could
vary signiﬁcantly day-to-day since the building’s ambient temperature ﬂuctuated considerably depending on the weather and building cooling schedule. The ﬁnal set of
experiments were taken over an approximately 2.5 week time period.

93

BIBLIOGRAPHY

94

BIBLIOGRAPHY
Bohl, D. G. (2002). Experimental Study of the 2-D and 3-D Structure of a Concentrated
Line Vortex Array. PhD thesis, Michigan State University.
Burgmann, S., Dannemann, J., and Schr¨der, W. (2007). Time-resolved and volumetric PIV
o
measurements of a transitional separation bubble on an SD7003 airfoil. Experiments in
Fluids, 44:609–622.
Burgmann, S. and Schr¨der, W. (2008). Investigation of the vortex induced unsteadiness of
o
a separation bubble via time-resolved and scanning PIV measurements. Experiments in
Fluids, 45:675–691.
Currie, I. G. (1993). Fundamental Mechanics of Fluids. McGrawl-Hill, 2nd edition.
Galbraith, M. C. (2009). Implicit large eddy simulation of low-reynolds-number transitional
ﬂow past the SD7003 airfoil. Master’s thesis, University of Cincinnati.
Gendrich, C. P. (1999). Dynamic Stall of Rapidly Pitching Airfoils: MTV Experiments and
Naiver-Stokes Simulations. PhD thesis, Michigan State University.
Gendrich, C. P. and Koochesfahani, M. M. (1996). A spatial correlation technique for
estimating velocity ﬁelds using molecular tagging velocimetry (MTV). Experiments in
Fluids, 22:67–77.
Gendrich, C. P., Koochesfahani, M. M., and Nocera, D. G. (1997). Molecular tagging velocimetry and other novel applications of a new phosphorescent supramolecule. Experiments in Fluids, 23:361–372.
Hill, R. B. and Klewicki, J. C. (1996). Data reduction methods for ﬂow tagging velocity
measurements. Experiments in Fluids, 20:142–152.
Katz, A. W. (2010). Molecular tagging velocimetry measurements of the low-reynoldsnumber ﬂow around an SD7003 airfoil. Master’s thesis, Michigan State University.
Koochesfahani, M. M. and Nocera, D. G. (2007). Molecular tagging velocimetry. In Tropea,
C., Yarin, A., and Foss, J. F., editors, Handbook of Experimental Fluid Dynamics, volume
XXVIII, chapter 5.4. Springer-Verlag.
Ol, M. V., McAuliﬀe, B. R., Hanﬀ, E. S., Scholz, U., and K¨hler, C. (2005). Comparison
a
of laminar separation bubble measurements on a low reynolds number airfoil in three
facilities. In 35th AIAA Fluid Dynamics Conference and Exhibit, number AIAA 20055149.
Olson, D. A., Katz, A. W., Naguib, A. M., Koochesfahani, M. M., Rizzetta, D. P., and
Visbal, M. R. (2011). An investigation of the eﬀect of freestream turbulence on the
laminar separation bubble on an SD7003 airfoil. In 49th AIAA Aerospace Sciences Meeting
including the New Horizons Forum and Aerospace Exposition 4 - 7 January 2011, Orlando,
Florida, number AIAA 2011-395.
95

Selig, M. S., Guglielmo, J. J., Broeren, A. P., and Giguere, P. (1995). Summary of Low-Speed
Airfoil Data, volume 1. Soartech Publications.

96