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Aerodynamics at low Re: separation, reattachment, and control

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Aerodynamics at low Re: separation, reattachment, and control

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Aerodynamics at Low Re: Separation,
Reattachment, and Control

by

Joe Tank

A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(AEROSPACE ENGINERING)

December 2018

iii

Dedication

To my parents and sister, who have always been supportive

And to my fiancé Chelsey, who I am lucky to have found

iv
v
Abstract

In recent years, the reduction in the size and weight of electronics has allowed for the
development of small scale, fixed wing flying devices that operate at Reynolds numbers (Re)
below 5 × 10
5
. These vehicles, which include small scale UAVs and MAVs, are comparable in
both size and speed to birds and model airplanes. At these “low” Re, smooth airfoil performance
is generally poor (i.e. low lift, high drag) compared to that seen at the higher Re due to laminar
boundary layer separation that often occurs, even at small angles of attack. There have been
numerous experimental studies that have focused on the lift and drag generated by airfoils at low
Re, but even carefully run tests on the same airfoil shape in different facilities have produced
conflicting data sets. This will become an increasingly important issue as interest in low Re
vehicles increases, and high quality airfoil performance data is needed. Experimental data is also
needed to establish baseline agreements with computations, including three-dimensional direct
numerical simulations (DNS) which have recently become available for airfoils at Re > 10
4
. The
lack of agreement in low Re experimental data is primarily due to two factors: 1) the sensitivity of
lift and drag to experimental conditions that are highly facility dependent, such as free stream
turbulence level, surface finish, model mounting technique, and acoustic environment, and 2) the
difficulties associated with measuring the small aerodynamic forces generated at low Re,
especially drag, with acceptable uncertainties. The increased sensitivity to experimental conditions
at low Re is due to the increased impact these conditions can have on the boundary layer over the
airfoil.
The boundary layer behaviors seen over airfoils at low Re have a significant impact on
performance and can differ significantly from those seen at higher Re. Laminar boundary layer
separation can lead to either a large, recirculating region behind the airfoil, or the formation of a
laminar separation bubble (LSB) that covers a significant portion of the airfoil surface. An LSB
forms when laminar separation is quickly followed by a transition to a turbulent state, allowing for
boundary layer reattachment to the surface in a time-averaged sense. The boundary layer
separation location, the location of transition to turbulence, and whether or not the boundary layer
reattaches to the surface after separation to form an LSB can change the effective shape of the
airfoil, and cause the aerodynamic performance to differ significantly from the classical potential
flow theory predictions in often unexpected ways. More high quality experimental data is needed
vi
to better understand the effects of these different boundary layer behaviors on airfoil performance.
In addition, a better understanding of the transition process over airfoils at low Re will assist in the
development of better models to predict the boundary layer behavior.
In the current study, two airfoils shapes, one symmetric and one cambered, were
investigated in order to gain a better understanding of airfoil behavior at low Re: the NACA 0012
(Re = 5×10
4
) and the NACA 65(1)-412 (2×10
4
≤ Re ≤ 9×10
4
). Well resolved lift and drag data
were collected with a force balance, and explanations for behaviors that differ from those seen at
high Re (e.g. changing lift slope before stall, negative lift at positive angles of attack, a sudden
jump to a high lift/low drag state) were given based on time-averaged PIV flow fields. Dye-
injection flow visualization images were then collected in a water channel for the NACA 65(1)-
412 to investigate time-dependent boundary layer characteristics and wake vortex shedding
frequencies. The insights gained from this study can help in the future design of low Re fliers and
the development of flow control systems. The high quality lift and drag data can also be used as
reference data for future low Re experimental or computational studies.
Once the boundary layer behavior and its impact on performance is better understood, it
can be manipulated to improve aerodynamic performance. Increasing performance is especially
important at these low Re, where the maximum lift to drag ratios (L/D) for smooth airfoils are
known to be much lower than at Re > 10
6
. Previous studies have suggested that the flow is most
sensitive to forcing near the boundary layer separation point, which can be approximated in
unsteady flows by identifying the location at which an attracting Lagrangian coherent structure
(LCS) approaches the airfoil surface. Therefore, a flow control technique that leverages insights
from LCS fields is suggested. If a measurable signature of the separation location can be identified,
this information can be fed back to a controller, so that the forcing location can be adjusted
depending on the changing flow field to optimize performance (i.e. maximize L/D). Additional,
perhaps unintuitive, forcing locations may be identified based on the locations of prominent LCS,
as LCS are dynamically important structures that play a role in organizing the flow field, and a
flow control technique that aims to manipulate the behavior of LCS to alter the flow field is
currently under development by collaborators at the University of Minnesota. A closed loop flow
control system would be able to respond to changes in the flow field in a way that the current open
loop flow control techniques with fixed forcing locations cannot.
vii
Time-averaged force and flow field data for the NACA 65(1)-412 at Re = 2 × 10
4
have
been compared with direct numerical simulations provided by collaborators at San Diego State
University, and the agreement has been found to be satisfactory. This clears the way for the
development of reduced Navier-Stokes or data driven flow control models based on the high
resolution computational data. The lift and drag curves for the NACA 65(1)-412 have been shown
experimentally to remain qualitatively similar as Re is increased from 2 × 10
4
to 9 × 10
4
, which
suggests that flow control models developed using computations at Re = 2 × 10
4
may be effective
at a higher Re, where a model size/free stream velocity balance can be struck that allows for
accurate time-resolved pressure measurements at the airfoil surface. A novel closed loop flow
control system will be tested as part of a proposed continuation of this work.
viii
Acknowledgments

Thank you to my mom, dad, and sister for always supporting me and for stressing the
importance of a good education. My family has always worked hard to put me in positions where
I can be successful, and without them I would not be where I am at today.
Thank you to Chelsey for sharing the last five years with me. She has been a wonderful
partner, and my life would not be nearly as fun without her.
Thank you to Dr. Spedding for accepting me as a student and for guiding my research. I
am lucky to have been able to work in the Dryden Wind Tunnel lab.
Thank you to my labmates Yohanna, Saakar, Michael, and James, for always being easy
to work with and willing to discuss problems I was having in the lab or in the classroom. I want
to especially thank Yohanna, who was with me from the beginning and who is always friendly
and helpful, no matter what type of mood I am in.
Thank you to Rod Yates for helped me machine many parts for my tests and teaching me
a lot about the machine shop. His work saved me a lot of time and I am very thankful for that.
Thank you to all of the undergraduate students for helped out in the lab, including Jack,
Ana, Ara, and Ethan. The work that they did made my life much easier.
Thank you to our collaborators, Dr. Jacobs and Bjoern at San Diego State University and
Dr. Hemati and Debraj at the University of Minnesota, who I have enjoyed working with and
learning from.
Thank you to Dr. Luhar and his students Christoph, Andrew, and Mark for allowed me to
use the water channel and for helping me set up tests.

ix
Table of Contents

Dedication iii
Abstract v
Acknowledgments viii
1 Introduction 1
1.1 Motivation ........................................................................................................ 1
1.2 Airfoil aerodynamics at low Reynolds numbers .............................................. 2
1.3 Boundary layer behavior .................................................................................. 6
1.4 Boundary layer control .................................................................................... 12
1.5 Lagrangian coherent structures ........................................................................ 17
1.6 Objectives ........................................................................................................ 19
1.6.1 NACA 0012 .......................................................................... 20
1.6.2 NACA 65(1)-412 .................................................................. 20
2 Materials and Methods 22
2.1 Testing at low Reynolds numbers .................................................................... 22
2.1.1 Force balance measurements ................................................ 22
2.1.2 Wake measurements ............................................................. 22
2.1.3 Approximation of 2D geometries with endplates ................. 23
2.1.4 Flow sensitivity ..................................................................... 25
2.2 Dryden Wind Tunnel ........................................................................................ 26
2.3 USC Water Channel ......................................................................................... 27
2.4 Models .............................................................................................................. 28
2.4.1 NACA 0012 .......................................................................... 28
2.4.2 NACA 65(1)-412 .................................................................. 29
2.5 Force balance measurements ........................................................................... 30
2.6 Time-averaged particle image velocimetry (PIV) ........................................... 32
2.6.1 NACA 0012 .......................................................................... 34
2.6.2 NACA 65(1)-412 .................................................................. 34
2.7 Water channel flow visualization ........................................................................ 35
2.7.1 Boundary layer images ......................................................... 36
x
2.7.2 Wake images ......................................................................... 36
2.8 Hot-wire .............................................................................................................. 37
2.8.1 Test setup .............................................................................. 37
2.8.2 Turbulence measurements .................................................... 39
2.8.3 Post processing of turbulence intensity time traces .............. 41
3 Wind Tunnel Free Stream Turbulence 42
3.1 Motivation ........................................................................................................ 42
3.2 Turbulence intensity definition and assumptions ............................................ 42
3.3 Results of turbulence measurements ................................................................ 43
4 NACA 0012 47
4.1 Time-averaged lift and drag .............................................................................. 47
4.2 Time-averaged PIV ........................................................................................... 50
4.3 Comparison with literature and computations .................................................. 55
5 NACA 65(1)-412 59
5.1 Re = 2 × 10
4
..................................................................................................... 59
5.1.1 Time-averaged lift and drag ................................................... 59
5.1.2 Time-averaged PIV: α <

α
crit
................................................. 62
5.1.3 Time-averaged PIV: α =

α
crit
................................................. 69
5.1.4 Time-averaged PIV: α >

α
crit
................................................. 72
5.1.5 Water channel flow visualization: boundary layer behavior 76

5.1.6 Water channel flow visualization: wake vortex shedding .... 79
5.2 Increasing Re

.................................................................................................... 83
5.2.1 Change in 𝛼
#$%
and 𝑐
',)
........................................................ 84
5.2.2 Re = 5 × 10
4
– 9 × 10
4
......................................................... 87
6 Conclusions 91
6.1 NACA 0012 ..................................................................................................... 91
6.2 NACA 65(1)-412 ............................................................................................. 92
6.3 Future Work

..................................................................................................... 93
References 94
Appendix A: Blockage Effects in Dryden Wind Tunnel 108
Appendix B: Water Channel Equipment Drawings 110
1
1 Introduction

1.1 Motivation
The aerodynamic properties of flying objects are largely dependent on the Reynolds
number (Re) at which they operate. The Re is the ratio of inertial to viscous effects in a flow, and
can be calculated using equation (1.1), where U is a characteristic flow speed, l is a characteristic
length scale, and 𝜌, 𝜇, and 𝜐 are the density, dynamic viscosity, and kinematic viscosity of the
fluid. In this work, U and l are taken as the free stream velocity and the airfoil chord (c) unless
otherwise specified.

Re=
1'2
3
=
1'
4
(1.1)

Historically, aeronautical engineers have been primarily interested in flying objects that
operate at Re > 10
6
. This is the Re regime of airplanes that fly at high speeds and are large enough
to carry people and cargo long distances quickly. Until recently, the aerodynamics of fixed wing
flying vehicles that operate at 10
4
< Re < 5 × 10
5
(hereafter referred to as “low Re”) have mainly
only been of interest to model airplane enthusiasts. As can be seen in figure 1.1 adapted from
Lissaman (1983), this is the Re range in which birds and model airplanes fly.

Figure 1.1: Reynolds number spectrum (Lissaman, 1983)

2
With the reduction in the size and weight of electronics in recent years, it is now possible
to produce low Re fliers – small unmanned aerial vehicles (UAVs) or micro air vehicles (MAVs)
– that can serve a variety of purposes, including surveillance, search and rescue, communication,
sensing of dangerous biological, chemical, or nuclear materials, or placement of sensors (Mueller,
1999). Examples of UAVs currently used by the US military include AeroVironment’s Wasp ($27
million contract with US Marine Corps in 2014), which operates near Re = 1.3 × 10
5
, and the
Raven and Puma ($47 million contract with US Army in 2015), both of which operate near Re =
2.5 × 10
5
. Other low Re applications include small wind turbines, sailplanes, high altitude and
ultralight aircraft, high altitude jet engine fans, compressors, turbine blades, and aircraft designed
to operate in a Martian atmosphere (Mueller, 1985).
With the increase in demand for slower, smaller, fixed wing flying devices, there is a need
for a better understanding of the aerodynamic properties of airfoils and wings at low Re. Although
experimental data do exist for select airfoils at these Re (Selig et al., 1995; Selig et al., 1996; Lyon
et al., 1998; Selig & McGranahan, 2004; Williamson et al., 2012), there is no comprehensive
database of airfoil data for this Re regime, especially for Re < 10
5
. The Dryden Wind Tunnel at
the University of Southern California, with its free stream turbulence intensity (T) < 0.035% is
especially well suited for testing at low Re.

1.2 Airfoil aerodynamics at low Reynolds numbers
Reducing Re into the low Re regime can change the aerodynamic performance of airfoils
in important and sometimes surprising ways. Non-linear lift curves prior to stall and hysteresis in
lift and drag curves are often seen at low Re (e.g. Mueller & Batill, 1982; Mueller et al., 1983),
and several common low Re drag polar shapes that differ from those seen at high Re have been
identified by Carmichael (1981). It is well known that the aerodynamic efficiency of airfoils is
reduced significantly as the Re drops below a critical value near 10
5
. An often cited figure from
McMasters & Henderson (1980), found in figure 1.2, shows this large drop in the lift over drag
ratio (L/D), a measure of airfoil effectiveness, for smooth airfoils with a reduction in Re. There is
also a more gradual decrease in performance for rough airfoils.

3

Figure 1.2: Change in airfoil performance with Re (McMasters & Henderson, 1980)

At the lower end of the 10
4
< Re < 5 × 10
5
range, the boundary layer over the suction
surface of the airfoil often remains laminar into the adverse pressure gradient region. The boundary
layer typically cannot overcome this adverse pressure gradient while in a laminar state, and so this
often results in boundary layer separation from the surface of the airfoil (a definition of the
separation point is given in section 1.5) far from the trailing edge, even at low angles of attack (𝛼).
Boundary layer separation is accompanied by an increase in drag and a decrease in lift, which leads
to the decrease in L/D seen in figure 1.2. After separation, the flow will transition to a turbulent
state, and if this occurs early enough, the separated boundary layer can reattach to the airfoil
surface due to increased mixing and momentum transfer from the outer flow toward the airfoil
surface. This reattachment leads to the formation of a closed, recirculating region in a time-
averaged sense called a laminar separation bubble (LSB) – sometimes also referred to as a
“transitional separation bubble”. At low Re, laminar separation without reattachment is generally
seen over airfoils at small 𝛼, followed by LSB formation at moderate 𝛼, and then bubble bursting
and stall at high 𝛼 (Huang et al., 1996). However, the 𝛼 at which an LSB first forms will decrease
as Re increases, due to the larger amplification rates of unstable frequencies at the higher Re
(Huang et al., 1996; Yarusevych et al., 2006,2009). An illustration of an LSB can be found in
figure 1.3. A more detailed description of the LSB will be given in the next section.

4

Figure 1.3: Laminar separation bubble illustration (Horton, 1968)

The separation of the boundary layer and the possible formation of an LSB, which can
cover a significant portion of the airfoil surface at low Re (often > 15% as pointed out by Brendel
& Mueller (1988)), has a significant impact on the outer streamlines patterns around the airfoil.
This leads to what can be thought of as a change in the effective shape of the airfoil. Because of
the increased size of the viscous region over the airfoil due to the early boundary layer separation,
potential flow theories (thin airfoil theory, lifting line theory, etc.) which give valuable
performance predictions at high Re but neglect viscous forces are less applicable. The presence of
the bubble has a large impact on the mean pressure distribution, and therefore the lift production.
To complicate things further, the boundary layer separation location and the LSB size and position
when reattachment occurs, and therefore the effective shape of the airfoil, can change significantly
with changes in 𝛼 or Re.
As the Re decreases, it becomes more difficult to address performance issues through
airfoil design, as the boundary layer will remain laminar over a larger portion of the airfoil, and it
is therefore harder to deflect the flow downwards, which is necessary to create lift, without causing
separation. In their brief summary of airfoil design principles, McMasters & Henderson (1979)
state that, in order to achieve high lift, an orderly transition to turbulence before the adverse
pressure gradient region becomes an important consideration at low Re to avoid separation.
However, the skin friction drag may increase significantly if transition is forced too far upstream.
Therefore, an active flow control system that can manipulate the transition location to minimize
skin friction drag, while at the same time preventing separation, is sought.
5
Computational simulations often give aerodynamic performance predictions that do not
agree with experimental measurements at low Re (Tank et al., 2016). A major difficulty for RANS
computations is the lack of reliable turbulence and transition models to predict the boundary layer
separation location and the transition location of the separated shear layer, and successful LES of
LSBs over curved geometries often use nearly DNS level resolution, which is still computationally
expensive in the Re regime of interest (Castiglioni, 2015). As pointed out by Jones et al. (2008),
even fully resolved DNS of separation bubbles can produce conflicting results. For example, they
point out that separate DNS studies of LSB over a flat plate have identified different instability
mechanisms leading to transition. Significant differences between three-dimensional DNS and
more computationally inexpensive two-dimensional DNS of LSBs over a flat plate have also been
observed (Marxen & Henningson, 2011; Marxen et al., 2013).
There have also been difficulties in producing consistent experimental data at low Re
(Carmichael, 1981; Marchman, 1987; McArthur, 2008; Olson, 2011; Tank et al., 2016). This has
been attributed in large part to the extreme sensitivity of airfoil performance to experimental
conditions, the difficulty in accurately measuring the small aerodynamic forces generated at low
Re, and the difficulty in producing a close approximation of a two-dimensional geometry. Several
of the difficulties associated with conducting low Re experiments will be discussed in more detail
in section 2.1. The decrease in consistency of data sets generated in different facilities as the Re
decreases is illustrated in figure 1.4.

6

Figure 1.4: Drag polar data for the Eppler 387 generated at several different facilities for Re =
[3,2,1,0.6] × 10
5
(McArthur, 2008)

1.3 Boundary layer behavior
When transition to turbulence occurs in the boundary layer before separation, it is generally
caused by either the amplification of viscous Tollmien-Schlichting (T-S) waves, leading to
nonlinear interactions and a breakdown to turbulence when disturbances in the free stream
environment are small, or by bypass transition when disturbances in the free stream environment
are large (Kachanov, 1994). As previously mentioned, the boundary layers over smooth airfoils at
low Re often remain laminar into the adverse pressure gradient region, which can lead to separation
and the formation of a separated shear layer with a mean velocity profile with an inflection point.
When this occurs, the streamwise amplification of disturbances due to the inviscid Kelvin-
Helmholtz instability often leads to the formation of large scale, spanwise roll-up vortices in the
shear layer over the airfoil that are shed at frequencies that match those of the most amplified
disturbances (McAuliffe & Yaras, 2005; Yarusevych et al., 2006,2008,2009; Hain et al., 2009;
Kirk & Yarusevych, 2017). An example of roll-up vortices in the separated shear layer above an
airfoil can be seen in figure 1.5. However, the roll-up location depends on Re and 𝛼, and if both
are sufficiently low, the separated shear layer can remain laminar, with no vortex roll-up, past the
trailing edge. When the shear layer does roll up before the trailing edge, the resulting vortices
7
travel downstream at approximately 0.5U (Yarusevych et al., 2006,2008). These vortices can
merge, and will often break down to small scale turbulence before they reach the wake, but
coherent vortices shed from the shear layer persist further downstream without breaking up as Re
is reduced. At low enough Re, they can reach the trailing edge or beyond, possibly interacting with
vortices shed into the wake, which are formed in the near wake region and shed at a lower
frequency than those shed from the separated shear layer (Yarusevych et al., 2006,2009).

Figure 1.5: Smoke wire flow visualization illustrating the roll-up vortices in the separated shear
layer over a NACA 0025 at 𝛼 = 5
o
, Re = 5.5 × 10
4
(Yarusevych et al., 2008)

If Re and 𝛼 are both sufficiently high, the roll-up vortices will form early enough so that,
before the boundary layer separates too far from the airfoil, they entrain a significant amount of
high momentum fluid from the outer flow, leading to time-averaged reattachment and the
formation of an LSB. In the case of LSB formation, the roll-up vortices travel downstream at
approximately 0.4𝑈
6
, where 𝑈
6
is the edge velocity, (Haggmark et al., 2000; Boutilier &
Yarusevych, 2012a; Kurelek et al., 2016; Kirk & Yarusevych, 2017; Lambert & Yarusevych,
2017). The reattachment of the boundary layer when an LSB is formed has been shown to be
primarily due to the enhanced mixing caused by these large scale roll-up vortices, as opposed to
the smaller scale turbulence after vortex breakdown (Lin & Pauley, 1996; Marxen & Henningson,
2011; Lambert & Yarusevych, 2017; Kirk & Yarusevych, 2017), and in the case of LSB formation,
the breakdown of the vortices occurs after the mean reattachment point. Further increases in 𝛼
after LSB formation will eventually lead to stall when the bubble “bursts” and large scale
separation occurs. Marxen & Henningson (2011) suggest that this bursting may be due to the rapid
8
breakdown of the separated shear layer to smaller scale turbulence without the formation of large
scale roll-up vortices, which does not allow for significant momentum transfer from the outer flow.
When an LSB forms, the breakdown of the spanwise vortices has been shown to begin with
the development of spanwise undulations that lead to portions of the vortices orienting themselves
in the streamwise direction, as can be seen in figure 1.6 (Haggmark, 2000; Burgmann & Schroder,
2008; Kurelek et al., 2016; Kirk & Yarusevych, 2017; Lambert & Yarusevych, 2017). Jones et al.
(2008) suggests that this production of streamwise vorticity is linked to a hyperbolic instability in
the braid region (the layers of vorticity between consecutive spanwise vortices) and an elliptic
instability in the vortex cores. Marxen et al. (2013) also linked vortex breakdown to secondary
instabilities in the braid region and vortex core in their numerical study of an LSB over a flat plate.
Michelis et al. (2018) performed a linear stability analysis on PIV data (for the LSB) and the
numerically solved boundary layer equations based on the measured pressure distribution (for the
boundary layer upstream of separation) and attributed the initial spanwise perturbations of roll-up
vortices to the superposition of normal and oblique modes initiated upstream of separation. The
authors suggested that the initial amplitude of spanwise perturbations will depend on the impact
experimental conditions have on the relative amplitudes of the different modes. The same study
found that increasing the relative amplitude of the normal mode (e.g. by applying two-dimensional
forcing) will increase the spanwise uniformity of rollup vortices. The spanwise undulations lead
to more complex vortex interactions, resulting in the rapid breakdown to smaller scales. The later
stages of the transition to turbulence of the boundary layer during LSB formation are still not fully
understood, however, Jones et al. (2010) suggest that, since the amplification of primary modes
takes place over a larger length scale than the final, nonlinear breakdown, understanding the
growth of the initial modes is more important when it comes to the approximation of the transition
location. The remainder of this section will discuss boundary layer behavior when an LSB is
formed.

9

Figure 1.6: Smoke wire flow visualization over the suction surface of a NACA 0018 airfoil at
𝛼 = 5
o
, Re = 10
5
in the vicinity of an LSB. The z-coordinate is in the spanwise direction, and the
x-coordinate is in the streamwise direction. 𝑥
8
/c and 𝑥
9
/c identify the chord normalized mean
transition and reattachment points respectively (Kurelek et al., 2016)

The process of vortex formation, shedding, and breakdown in the boundary layer varies
somewhat from cycle to cycle. Occasional pairing of vortices shed by the separated shear layer has
been observed in several studies due to a slower vortex near the surface being overtaken by a faster
vortex further from the surface, but this is not believed to be a strongly periodic phenomenon
(McAuliffe & Yaras, 2005; Kurelek et al., 2016; Lambert & Yarusevych, 2017). Variations in
vortex shedding frequency in time have been linked to variations in the most amplified frequency
within an unstable band of frequencies in the separated shear layer in natural transition (Kirk &
Yarusevych, 2017; Yarusevych & Kotsonis, 2017; Lambert & Yarusevych, 2017), and significant
differences in vortex roll-up location (>0.08c) between cycles have been observed (Kirk &
Yarusevych, 2017; Lambert & Yarusevych, 2017). It should be noted that previously reported
results having to do with the transition to turbulence in the LSB have been generated in facilities
with T ranging from ≈ 0 (in tow-tanks) to O(1%) (in water channels), and T is expected to impact
the formation and evolution of the structures in an LSB. Istvan & Yarusevych (2018) showed that
increases in T (0.06 – 1.99%) caused earlier shear layer roll-up, and leads to less spanwise
10
coherence in roll-up vortices. The same study found signs of bypass transition for T > 0.5% which
may eliminate the LSB at higher T.
The base (time-averaged) flow in the front half of an LSB is nearly parallel (Diwan &
Ramesh, 2012), and viscous and inviscid linear stability theory predictions of the spatial
amplification rates of unstable frequencies in the separated shear layer during the initial stages of
transition, obtained by solving the Orr-Sommerfeld and Rayleigh equations respectively, have
been shown to agree well with experiments (LeBlanc et al., 1989; Yarusevych et al., 2006,2008;
Boutilier & Yarusevych, 2012a; Michelis et al., 2018). The Orr-Sommerfeld and Rayleigh
equations can be found in equations (1.2) and (1.3) respectively, where 𝜙 is the amplitude of the
perturbation streamfunction mode, 𝑈
<
is the steady state velocity profile, 𝜔 is the angular
frequency (assumed to be real for disturbances growing in space), 𝑘 is the wave numbers (𝑘 =
𝑘
?
+𝑖𝑘
B
where –𝑘
B
is the spatial amplification rate) and primes denote differentiation in the wall
normal direction. For a given Re, 𝑈
<
, and 𝑘, the equations are polynomial eigenvalue problems,
where 𝜔/𝑘 is the complex eigenvalue and 𝜙 is the eigenfunction. The prediction of the stability
characteristics of the boundary layer can be useful for flow control purposes, as will be discussed
in the next section.

𝜙
DDDD
−2𝑘
G
𝜙
DD
+𝑘
H
𝜙 =𝑖𝑘𝑅𝑒 𝑈
<
−
𝜔
𝑘
𝜙
DD
−𝑘
G
𝜙 −𝑈
<
DD
𝜙 (1.2)

𝑈
<
−
𝜔
𝑘
𝜙′′−𝑘
G
𝜙 −𝑈
<
DD
𝜙 =0 (1.3)

Vortex shedding, transition, and reattachment are unsteady phenomena, and the LSB grows
and shrinks in both streamwise and wall-normal directions with time in a process known as “bubble
flapping” (Brendel & Mueller, 1988; Burgmann & Schroder, 2008; Zhang et al., 2008; Hain et al.,
2009; Istvan & Yarusevych, 2018), though the LSB is often thought of in a time-averaged sense,
where there is a single reattachment point. The time-averaged properties of the LSB are easier to
measure (via time-averaged particle image velocimetry, pressure, and hot-wire methods) and are
better understood. The location and length of the LSB are often determined using time-averaged
surface pressure measurements. An illustration of the typical evolution of an LSB with 𝛼 can be
seen in figure 1.7, where the location and length of the nearly constant pressure region mark the
11
location and length of the laminar portion of the LSB, and the rapid pressure recovery region marks
the transition and reattachment of the boundary layer. Although transition to turbulence does not
occur suddenly at one location, a transition “point” is often identified as the end of the plateau in
the chordwise pressure distribution, and has been found to approximately coincide with the
beginning of shear layer roll-up, the location of maximum boundary layer displacement thickness
(i.e. bubble height), and the location where there is an abrupt change from frequency-centered
energy content to broadband energy content in boundary layer hot-wire measurements (Brendel &
Mueller, 1988; Boutilier & Yarusevych, 2012a; Kurelek et al., 2016; Kirk & Yarusevych, 2017;
Yarusevych & Kotsonis, 2017; Istvan & Yarusevych, 2018). The LSB moves forward and
decreases in length with increased Re or 𝛼 (Huang et al., 1996; Boutilier & Yarusevych, 2012b;
Tank et al., 2016; Kirk & Yarusevych, 2017), and increasing free stream disturbance levels leads
to later boundary layer separation and earlier transition, and therefore the shortening or elimination
of the LSB (Huang & Lee, 1999; Marxen & Henningson, 2011; Olson et al., 2013; Istvan &
Yarusevych, 2018). Increasing Re or T have also been shown to decrease the height of the LSB,
while increasing 𝛼 increases the height (Olson, 2011). According to Boutilier & Yarusevych
(2012b), the decrease in length of the separation bubble with an increase in Re or 𝛼 is due to an
increase in spatial amplification rates for unstable frequencies in the separated shear layer, whereas
Istvan & Yarusevych, (2018) attributed the decrease in length with increase in T to the larger initial
amplitudes of the disturbances. Predictions of time-averaged LSB properties from boundary layer
characteristics at the point of separation, such as shape factors (the ratio of displacement thickness
to momentum thickness or energy thickness to momentum thickness) or Re based on displacement
thickness or momentum thickness, have been attempted with limited success (O’Meara & Mueller,
1987; Brendel & Mueller, 1988; McAuliffe & Yaras, 2005).

12

Figure 1.7: Time-averaged surface pressure distributions over a NACA 0018 airfoil at Re = 10
5

for a) 𝛼 = [0
o
, 5
o
, 8
o
, 10
o
] and b) 𝛼 = 5
o
alone. The evolution of the LSB with changes in α can
be seen in a), where the separation, transition, and reattachment locations (𝑥
M
, 𝑥
8
, 𝑥
9
) can be
approximated from the curves as shown in b) (Kirk & Yarusevych, 2017).

1.4 Boundary layer control
The extreme sensitivity of the boundary layer to even small scale disturbances at low Re
can be exploited for flow control purposes, and several passive and active flow control techniques
have been used to effectively manipulate boundary layer behavior at low Re. These techniques
involve perturbing the flow using, for example, external acoustic forcing (Collins & Zelenevitz,
1975; Mueller & Batill, 1982; Zaman et al., 1987; Zaman & McKinzie, 1991; Yarusevych et al.,
2003,2005,2007; Yang & Spedding, 2013b), internal acoustic forcing (Huang et al., 1987; Hsiao
et al., 1989a; Yang & Spedding, 2014), passive acoustic resonance (Yang & Spedding, 2013a),
surface roughness boundary layer trips (Mueller & Batill, 1982), suction or blowing (Haggmark
et al., 2000; Haggmark, 2000), plasma actuators (Yarusevych & Kotsonis, 2017), oscillating flaps
or wires, vortex generators, and surface heating. Many of these techniques are discussed in Gad-
el-Hak (1990). Flow control at low Re is generally used to hasten the transition to turbulence in
the separated (or attached) boundary layer, which allows it to reattach (or remain attached) to the
wing’s surface, increasing lift and decreasing drag. The size and shape of the LSB can also be
altered if reattachment has already occurred, and Haggmark (2000), in his study on pressure
induced LSBs over flat plates, showed that active forcing at appropriate frequencies can reduced
both the length and height of the LSB. These changes would most likely further increase airfoil
13
performance, even if the boundary layer reattaches naturally. The same work also demonstrated
that appropriate forcing in the presence of an LSB will reduce the unsteadiness of the bubble by
reducing the amplitude of velocity fluctuations at unforced frequencies. A similar reduction in
unforced frequency amplitudes was noted by Dovgal et al. (1994), who attributed the phenomenon
to the upstream influence of the transition process, which was altered by the forcing. Active control
methods are preferred over passive methods because they can be made to adapt to the changing
flow conditions encountered by maneuvering flying devices, and they can be designed to maintain
a laminar boundary layer on the front part of the airfoil, which will reduce skin friction drag. Note
that whereas the reattachment of the boundary layer to form a LSB can increase performance at
these lower Re, the opposite is generally true at higher Re. The present study will focus on acoustic
forcing.
It has been known since at least the 1940’s that acoustic waves can affect the transition
process in boundary layers (Schubauer & Skramstad, 1947). By the 1970’s it had been shown that
external acoustic forcing can increase the aerodynamic performance of airfoils, especially near
stall (Collins & Zelenevitz, 1975). Since then, boundary layer control over airfoils by acoustic
forcing has been shown to be effective for frequency and amplitude combinations that depend on
airfoil geometry, Re, and 𝛼.
The most effective forcing frequencies that increase airfoil performance correspond to a
band of frequencies around the most unstable frequency in the separated shear layer, 𝑓
O
. This
frequency can be identified from the amplitude spectra of hot-wire measurements in the separated
shear layer or surface pressure fluctuations measured at the airfoil surface (Gerakopulos &
Yarusevych, 2012; Boutilier & Yarusevych 2012a), or, as mentioned in the previous section, it can
be approximated using linear stability theory, given a time-averaged velocity profile directly
downstream of separation. Forcing at frequencies near 𝑓
O
leads to more coherent rollup vortices in
the separated shear layer that form earlier, which can result in either time-averaged reattachment
for flows where there was previously no reattachment, or an earlier reattachment when an LSB
was already present (Yarusevych & Kotsonis, 2017). The values of the most amplified frequencies
have been shown to increase with Re and 𝛼 for a given airfoil in a given flow state (e.g. separated
flow or LSB) (Yarusevych et al., 2009; Boutilier & Yarusevych, 2012b; Kirk & Yarusevych,
2017), and the range of effective forcing frequencies expands with increasing Re (Zaman et al.,
1987; Zaman & McKinzie, 1991; Yarusevych et al., 2003; Yang & Spedding, 2013b, 2014).
14
Yarusevych et al. (2009) found that, for a given airfoil at a given 𝛼, 𝑓
O
varies as 𝑅𝑒
P
, where 0.9 <
n < 1.9, and Boutilier & Yarusevych (2012b) compiled low Re data from several airfoils at multiple
𝛼 and found that the relationship 𝑅𝑜 =0.0023𝑅𝑒
T.UV
gives an order of magnitude estimate for 𝑓
O
,
expressed as the non-dimensional Roshko number (𝑅𝑜 =𝑓
O
𝑐
G
/𝜈). Note that Yang & Spedding
(2014) found that the range of effective frequencies that resulted in L/D >1/2 (L/D)
max
was nearly
1400 Hz wide when internal acoustic forcing was applied at an appropriate chordwise location,
which suggests that an order of magnitude estimate may be good enough to realize significant
increases in performance. Yarusevych & Kotsonis (2017) suggested that 𝑓
O
and disturbance growth
rates increase linearly with the boundary layer shape factor. It has been suggested by Kirk &
Yarusevych (2017) that expressing the shear layer vortex shedding frequency, 𝑓
M
, which
corresponds with 𝑓
O
, as 𝑆𝑡
M
/𝑅𝑒, where 𝑆𝑡
M
=𝑓
M
𝑐/𝑈 is the Strouhal number based on 𝑓
M
, decreased
the variability of data from different airfoils and Re at a given 𝛼. Zaman & McKinzie (1991) found
that the excitation frequency, 𝑓
6
, that led to the largest increase in lift, expressed as the modified
Strouhal number 𝑆𝑡
∗
=𝑆𝑡
6
/𝑅𝑒
T/G
, where 𝑆𝑡
6
=𝑓
6
𝑐/𝑈, will fall between 0.02 and 0.03 at low Re
and 𝛼. Data from Yarusevych et al. (2003) fell within this range as well, but other studies have
found that 𝑆𝑡
∗
may depend on 𝛼 or Re (e.g., Yang & Spedding, 2013b,2014).
Increasing the forcing amplitude can increase Δ(L/D) and the range of α affected by a
single forcing frequency until some maximum value, at which point there is no longer an
improvement with increased amplitude (Yang & Spedding, 2013b; Yarusevych et al, 2007).
Yarusevych et al. (2007) found that the increased Δ(L/D) was due to the delayed separation and
earlier boundary layer reattachment seen at higher forcing amplitudes that reduced the LSB size
(i.e. an increase in forcing amplitude has a similar effect as an increase in Re). Yarusevych et al.
(2003) showed that the range of effective forcing frequencies increases with acoustic forcing
amplitude.
It was demonstrated by Hsiao et al. (1989a) that a much smaller sound pressure level could
be used to effectively control the boundary layer when internal acoustic forcing was used as
opposed to external acoustic forcing. While the internal acoustic forcing studies of Hsiao et al.
(1989a) and Huang et al. (1987) emitted sound from a spanwise slot in the airfoil, Yang &
Spedding (2014) emitted sound locally from 0.5 mm diameter holes distributed over the suction
surface of a wing. It should be noted that forcing from an open slot or hole can introduce additional,
unaccounted for forcing modes due to acoustic resonance that depend on the cavity properties
15
(Yang & Spedding, 2013a). Because of this, the cavities should be designed with their resonance
properties in mind, or diaphragms should be use to cover any openings. Yang & Spedding (2014)
showed that the forcing location with the largest increase in performance and widest effective
frequency range is just upstream of separation, and both Hsiao et al. (1989a) and Huang et al.
(1987) concluded that the best forcing location is near the boundary layer separation point.
Kamphuis et al. (2018) also found that the largest response in the lift coefficient to a pulse actuation
occurred when the actuation was applied at or just upstream of the separation point. An example
of the increase in L/D for an airfoil at two Re < 10
5
when internal acoustic forcing is applied at an
appropriate frequency, amplitude, and chordwise location can be seen in figure 1.8.

Figure 1.8: A demonstration of the increase in L/D with acoustic forcing at a) Re = 4×10
4
and b)
6×10
4
(Yang & Spedding, 2014)

While there are many studies on the effects of external acoustic forcing, Yang & Spedding
(2013b) point out that it is difficult to draw conclusions about the effectiveness of certain
frequencies and amplitudes when there are complicated constructive and destructive acoustic wave
interactions due to the reflection of waves off wind tunnel walls. These interactions change with
tunnel size and geometry, making it hard to compare results from different facilities. Real world
devices operate outside of wind tunnels, where the acoustic environment will most likely be much
different, and with less significant reflections. Furthermore, the range of effective frequencies has
been shown to be different for local internal forcing than it is for external forcing (Yang &
Spedding, 2014). Internal acoustic forcing appears to be more promising, both because of the
16
reduced energy consumption and the increased applicability to flying devices operating outside of
a wind tunnel.
All of the studies previously mentioned have focused on stationary wings with steady flow
field conditions, and have used open loop flow control with forcing that is confined to a fixed
location and frequency for a given test. If the flow controller can not respond to the changes in the
flow field that occur often in real world flights, it will be far less effective. Even the presence of
forcing itself can change the flow field in ways that may change the effectiveness of an open loop
flow controller. Marxen & Henningson (2011) and Yarusevych & Kotsonis (2017) showed that
forcing that reduces LSB size can change the stability characteristics (growth rates and most
amplified frequencies) of the LSB. It stands to reason that forcing which causes a separated
boundary layer to reattach – a more drastic change in the flow field – could have an even larger
impact on stability characteristics. Therefore, it would be beneficial to use closed loop flow control
so that the forcing frequency and location can respond to changes in the flow field. The question
then becomes what flow field variable should be monitored and fed back to the controller to track
these changes. One of the more useful parameters to track would be the boundary layer separation
location, given that it has been shown to be particularly sensitive to forcing, and therefore should
be targeted by the flow control system. Sears & Telionis (1975) suggest that boundary layer
separation can be identified as the location where the assumptions upon which the boundary layer
equations are based break down, causing the solution to these equations to become singular.
Although the separation location is commonly identified in steady flows as the location where the
skin friction goes to zero at a surface, this does not necessarily indicate unsteady flow separation
(Sears & Telionis, 1975; Taneda, 1977; Williams, 1977; Gad-el-Hak, 1987; Weldon et al., 2008),
and Sears & Telionis (1975) identified unsteady flows where reverse flow is observed in the
boundary layer upstream of the separation singularity. Unsteady separation can be found using the
Moore-Rott-Sears model, which identifies the unsteady separation point as the point in the
boundary layer where both the shear and velocity vanish in a field of reference that is moving at
the same velocity as the separation point (Williams, 1977; Gad-el-Hak, 1987). Unfortunately, the
velocity of the separation point must be known ahead of time in order for this model to be useful.
However, Lagrangian coherent structures near the airfoil surface have been used to identify the
unsteady separation location over airfoils, and a variable that would allow for the tracking of these
structures would be an ideal feedback variable. Much of the work presented here is part of a
17
collaborative project with San Diego State University and the University of Minnesota that is
attempting to design a novel flow control system that manipulates these structures in order to
increase airfoil performance. The significance of Lagrangian coherent structures is discussed in
more detail in the next section.

1.5 Lagrangian coherent structures
Fluid flows are often thought of from an Eulerian point of view, where at time t the fluid
is described in terms of properties (F) at fixed points (𝑥) throughout the flow: 𝐹(𝑥,𝑡). On the other
hand, a Lagrangian description of the flow field tracks the properties of specific fluid elements,
located at positions 𝑟 𝑡;𝑟
O
,𝑡
O
, where 𝑟
O
was the position of the fluid element at time 𝑡
O
, as they
move through the flow field: 𝐹(𝑟 𝑡;𝑟
O
,𝑡
O
,𝑡). One tool that can be used to analyze an unsteady
flow field from a Lagrangian point of view is a Lagrangian coherent structure (LCS) field. An LCS
in two-dimensions is a zero-flux material line that organizes the rest of the flow field. More
specifically, the LCSs are the material lines that attract and repel fluid at the highest local rate over
a fixed time interval (Haller & Peacock, 2013), and can be thought of as finite time approximations
of stable and unstable manifolds in dynamical systems (Shadden, 2005). Prominent LCS generally
separate dynamically distinct regions of the flow (Shadden, 2012). These Lagrangian structures
are useful because they are frame-invariant descriptions of the flow field, and can therefore be
used to identify structures such as vortices regardless of reference frame (Peacock & Dabiri, 2010).
LCSs can be identified as ridges in the finite time Lyapunov exponent (FTLE) field, which
is found by integrating particle trajectories in a velocity field forward (for repelling LCSs) and
backward (for attracting LCSs) in time, as FTLEs are measures of the sensitivity of a fluid
particle’s behavior to its initial position (Haller & Peacock, 2013). If the position of a particle
released at time 𝑡
O
at position 𝑥
O
is denoted by 𝑥(𝑡;𝑥
O
,𝑡
O
), then the flow map that gives the location
of the particle after time T can be defined as: Φ
a
b
a
b
c8
𝑥 =𝑥
O
+ 𝑢 𝑥 𝑡;𝑥
O
,𝑡
O
,𝑡 𝑑𝑡
a
b
c8
a
b
. The
right Cauchy-Green tensor, ∆, can be calculated as: ∆=
gh
i
b
i
b
jk
(l)
gl
∗
gh
i
b
i
b
jk
(l)
gl
, where ()
∗
denotes
the matrix transpose. The largest eigenvalue, 𝜆
nol
, of ∆ can then be used to calculate the FTLE
field at time 𝑡
O
with integration time T: 𝜎
a
b
8
𝑥 =
T
8
𝑙𝑛 𝜆
nol
(Shadden, 2005; Gonzalez et al.,
2016).
18
Haller (2004) points out that, since the separation point over a solid boundary is the point
from which a material line (the separation profile) attracts and ejects particles from near the
boundary, as illustrated in figure 1.9, prominent LCSs should coincide with unsteady boundary
layer separation (attracting LCS) and reattachment (repelling LCS) lines. However, due to the no-
slip boundary condition, an LCS cannot intersect with a surface because particles at the surface
cannot be repelled or attracted, and therefore the LCS will deviate from the actual separation line
close to the surface (Kamphuis et al., 2018). Still, the LCS will come near the surface and therefore
may give useful approximations of the separation and attachment locations. Shadden et al. (2005)
argued that extrapolating LCS identified from FTLE fields to the boundary can give a reasonable
estimate of the separation location, and LCS have also been used to identify the separation location
over an airfoil by Lipinski et al. (2008). Shadden et al. (2005) showed how an attracting LCS can
be used to estimate the time dependent separation location and illustrate the behavior of the
separation profile over an airfoil in an unsteady flow, which can be seen in figure 1.10.

Figure 1.9: Time dependent material line, 𝑀(𝑡), whose intersection with a surface marks an
instantaneous separation point (Haller, 2004)

As mentioned in the previous section, the boundary layer separation point over the suction
surface of an airfoil appears to be a location where the flow is particularly sensitive to forcing, and
therefore forcing should be targeted at the location where the most prominent attracting LCS
approaches the airfoil surface, as this can give a good estimate of the separation point. The ability
to track this separation location in real time as it moves (e.g. due to changing free stream conditions
or wing orientation) would allow for effective closed loop flow control where the forcing location
can follow the moving separation location. Robust, closed loop flow control has the potential to
19
greatly increase the efficiency of airfoils at these low Re, as discussed in the previous section.
Additionally, since LCSs are dynamically important structures in the flow, manipulating their
behavior should have a large impact on the global flow field, and therefore the aerodynamic
performance, and so the locations of prominent LCSs other than the LCS that marks the separation
profile could suggest additional effective, although maybe unintuitive, forcing locations (Cardwell
& Mohseni, 2008; Lipinski et al., 2008). Similarly, the magnitude of the response of an LCS to
forcing should give an idea of how effective that type of forcing is at altering the flow field.

Figure 1.10: Time dependent separation profile behavior illustrated with LCS identified from
FTLE fields. The attracting LCS is highlighted in red, black tracers mark recirculating flow,
green tracers mark the outer flow. (Shadden et al., 2005)

1.6 Objectives
The two main objectives of this work are to 1) link aerodynamic performance to boundary
layer behaviors for two airfoil shapes, the NACA 0012 and NACA 65(1)-412, at Re = 5 × 10
4
and
Re = 2 × 10
4
- 9 × 10
4
respectively, in the low turbulence Dryden Wind Tunnel and the USC
water channel using force balance measurements, time-averaged PIV, and dye-injection flow
20
visualization, and 2) compare the experimental data for the NACA 65(1)-412 with DNS data that
will be used in the future to develop a closed loop flow control system to improve the performance
of airfoils at low Re.

1.6.1 NACA 0012

Re = 5 × 10
4
was chosen for NACA 0012 tests so that comparisons could be made with
DNS data in the literature (Jones et al., 2008). Time-averaged force measurements are made at -5
o

< 𝛼 < 9
o
and distinct regions in the lift curve are linked to boundary layer behaviors using time-
averaged PIV at 𝛼 = [0
o
, 0.5
o
, 2
o
, 4
o
, 6
o
, 8
o
]. The lift and drag curves are compared with
experimental and computational data sets from the literature.

1.6.2 NACA 65(1)-412

The NACA 65(1)-412 is first tested at Re = 2 × 10
4
, chosen so that comparisons could be
made with DNS from collaborators at San Diego State University. Time-averaged force balance
measurements are made at -5
o
< 𝛼 < 11
o
, and time-averaged PIV data at 𝛼 = [0
o
, 2
o
, 4
o
, 6
o
, 8
o
, 10
o
,
10.1
o
, 10.2
o
, 10.3
o
, 10.4
o
, 10.5
o
] are used to identify boundary layer behaviors that have a large
impact on the airfoil performance. Dye-injection flow visualization tests are conducted in the USC
water channel to investigate time-dependent boundary layer characteristics. PIV and dye injection
tests are expected to show a separated shear layer that becomes increasingly unstable, and therefore
susceptible to flow control by acoustic forcing, with an increase in 𝛼. Experimental time-averaged
force coefficients and flow fields are compared with DNS at 𝛼 = [4
o
, 8
o
, 10
o
]. These comparisons
are made to verify that the DNS data closely matches measurements in the wind tunnel and can
therefore be used as the basis for the development of a closed loop flow control system that will
be tested in the wind tunnel. Time-averaged force measurements are then made for 2 × 10
4
< Re
< 9 × 10
4
to determine if increasing Re has a significant impact on the qualitative performance of
the airfoil. If the lift and drag curves are qualitatively similar for this Re range, it will suggest that
the basic flow field characteristics remain the same, and a closed loop flow control system
developed for Re = 2 × 10
4
may be effective at a higher Re where accurate surface pressure
measurements can be made and fed back to the controller. Testing with multiple models in two
21
facilities using several experimental techniques highlights the sensitivities of boundary layer
behavior and airfoil performance to experimental conditions.

22
2 Materials and Methods

2.1 Testing at low Reynolds numbers
There are many difficulties associated with collecting flow field and force data for airfoils
at low Re that contribute to the previously noted discrepancies in data from different facilities. It
is important to understand the pros and cons of each experimental method before choosing one
that is appropriate. Even carefully run tests can produce different results if the experimental setups
or measurement techniques are different. It is therefore important to carefully describe the setup
and methods when presenting low Re data, so that others can take this into consideration. The
following is an incomplete list of issues associated with low Re airfoil testing.

2.1.1 Force balance measurements

Perhaps the simplest type of test, direct measurement of aerodynamic forces with a force
balance, is complicated by the fact that the aerodynamic forces are much smaller at low Re for a
given model size. Therefore, a highly accurate, high resolution force balance is needed for these
measurements. A strain gauge force balance that measures small forces with high accuracy
necessarily lacks stiffness, and therefore unsteady loads lead to significant model vibrations. This
makes force balance measurements past stall, where the aerodynamic loads are relatively large and
unsteady, particularly difficult. It is important that the model used is sized correctly with an
appropriate aspect ratio (AR = b/c, where b is span length, c is the chord length) to produce forces
in an appropriate range for the balance.

2.1.2 Wake measurements

A second method for measuring drag is to calculate the wake momentum deficit. It has
been shown that in the low Re regime there is often a spanwise variation in the profile drag
calculated with this method (Guglielmo & Selig, 1996; Yang & Spedding, 2013c). Because of this,
measurements should be taken at many spanwise locations and averaged in order to improve
accuracy. An example of the spanwise drag variation of an Eppler 387 airfoil at several 𝛼 can be
23
seen in figure 2.1. Pressure and single-wire hot-wire measurements in the wake may lead to
underestimates of the true drag when the flow is separated, which is often the case for airfoils at
low Re, due to the presence of large scale vortices (Mueller & Jansen, 1982; Barlow et al., 1999).
Multi-wire hot-wires that can simultaneously measure multiple velocity components are more
appropriate for these measurements.

Figure 2.1: Spanwise drag variation for Eppler 387 airfoil at several 𝛼. Variations in 𝑐
g
in the
central portion of the span (-0.4 < y/b < 0.4) exceed measurement uncertainty (Yang &
Spedding, 2013c)

2.1.3 Approximation of 2D geometries with endplates

Endplates are often used to eliminate wingtip vortices and approximate a two-dimensional
geometry with a three-dimensional model. A small gap between the endplates and wingtips is
generally used to isolate the model from the endplates during force balance measurements. Barlow
et al. (1999) suggests keeping the endplates within 0.005b of the wingtips, but several studies have
24
shown that corner flows that develop where the wingtips approach endplates and airflow through
the gap between the endplates and wingtips can both have a significant impact on force balance
measurements at low Re, even when the gap is kept extremely small. An illustration of the corner
flows that can develop near the wing tips can be seen in figure 2.2.
Barber (1978) found that a horseshoe vortex will form at the intersection of a strut and a
wall, and that the size of the vortex depends on the size of the boundary layer on the wall. These
vortices can effect drag measurements. Thick boundary layers result in large horseshoe vortices
and a small increase in drag, whereas thin boundary layers result in small horseshoe vortices and
a large increase in drag. Using surface oil flow visualizations, Galbraith (1985) was able to observe
an early separation of the corner boundary layer and the formation of a strong standing vortex
where an airfoil meets a tunnel wall. Mueller & Jansen (1982) and Pelletier & Mueller (2001) tried
to eliminate the effect of corner flows at the endplates by creating three-piece models where only
the center piece, which is not exposed to the corner flows, is attached to the force balance. Mueller
& Jansen (1982) found that the minimum drag for the three-piece model was reduced by 10-16%
compared to a one-piece model for an AR = 1.6 wing when 6×10
4
< Re < 3 × 10
5
, and Pelletier &
Mueller (2001) found that the drag was reduced and the lift was increased for an AR = 2.4 wing
for 3 × 10
4
≲ Re ≲ 1 × 10
5
when the three-piece model was used. However, when Jacobs (1980)
used a three-piece model, he found that drag coefficients from force balance measurements were
larger than those calculated using wake pressure measurements at mid-span due to a three-
dimensional flow near the gaps between the end pieces and the center section at Re = 3.3 × 10
5
.
After a correction factor was applied, drag coefficients calculated using both force measurement
techniques agreed. The same author also tested a one-piece model and found that normalized drag
values measured by a force balance were up to 30% higher than those calculated with pressure
measurements in the wake at mid-span for angles of attack where significant lift was generated.
However, when considering the results of Jacobs (1980), it should be kept in mind that determining
airfoil drag from wake measurements is difficult at low Re, as was previously discussed.
Marchman et al. (1998) found that the zero lift angle of attack (𝛼
#$%
) increased when there
was a gap between the endplate and wingtips for a cambered, low AR, semi-span model at low Re
(< 5 × 10
5
), and attributed this to the leakage of air through the gap, which alters the pressure
distribution over both sides of the model and changes the “effective camber” of the wing. This
effect is reduced as the AR of the wing is increased. This same study found that hysteresis near
25
stall is reduced or eliminated as the AR decreases. Burns & Mueller (1982) found no measureable
changes in lift or drag when the gap between the model and endplate (λ) was varied between 0.02%
< λ/b < 0.33%, and Kuppa & Marchman (1987) found that lift curves for a semi-span model were
shifted by the same amount when 0.04% < λ/b < 0.79% for 10
5
< Re < 2 × 10
5
due to flow through
the gap. The flow through the gap was observed by Kuppa & Marchman (1987) using an oil flow
visualization technique for λ/b = 0.4%, Re = 10
5
. These findings indicate that minimizing the size
of the gap does not change the effect of the gap. Kuppa & Marchman (1987) also observed that
when the gap was below λ/b = 0.2%, 𝑐
',)
remained constant when Re was reduced from 2 × 10
5
to
1.5 × 10
5
, but

decreased when Re was reduced from 1.5 × 10
5
to 1 × 10
5
.
Regardless of how endplates alter the forces measured on a wing at low Re (corner flows,
flow through the gap, or a combination of both), increasing the model AR should bring
measurements closer to the true two-dimensional values.

Figure 2.2: Corner flow over an endplate near wing tip (Mueller & Jansen, 1982a)

2.1.4 Flow sensitivity

As mentioned before, the test environment and model quality can have a large impact on
low Re measurements, due to their potential impact on the transition of the boundary layer
(Mueller & Batill, 1982; Mueller et al., 1983; Huang & Lee, 1999; Olson, 2011). Care should be
taken to create a smooth model surface, minimize vibrations, and minimize T. All of these
factors have been shown to affect measurements, and may, for example, eliminate hysteresis in
26
lift and drag curves (Mueller et al., 1983). Non-invasive measurement techniques should be used
whenever possible, as a poorly designed test that involves inserting a probe (hot-wire, pitot tube,
etc.) into the boundary layer may alter the flow. No experiment can remove all disturbances, and
this should be kept in mind when comparing with computations, where disturbances can be
controlled to a greater extent.

2.2 Dryden Wind Tunnel
Force balance and PIV tests were carried out in the Dryden Wind Tunnel, located at the
University of Southern California. The tunnel has an octagonal test section that measures 1.37 m
wall-to-wall (1.56 m
2
cross section). There is a 7:1 contraction immediately upstream of the test
section, and 11 anti-turbulence screens immediately upstream of the contraction. The turbulence
in the tunnel has been measured and found to be < 0.035% of the free stream velocity for 10 Hz <
f < 1000 Hz in the velocity range 4 < U < 20 m/s (see chapter 3). The coordinate system used has
the origin at mid-span on the leading edge of the model, with the x-, y-, and z-directions illustrated
in figure 2.3, adapted from Yang & Spedding (2013a). Three-dimensional wings can be positioned
between adjustable endplates to eliminate wingtip vortices. Endplates were aligned with a bubble
level and held within 2 mm of either end of the model. Blockage effects were calculated (see
Appendix A) and were found to be negligible.

Figure 2.3: Wind tunnel coordinate system (Yang & Spedding, 2013a)

27
For all tests, the model was aligned with the free stream by eye using a camera above the
wind tunnel. The camera was first aligned with the wind tunnel wall, and then the model was
aligned with the camera. If it is assumed that the free stream is aligned with the walls of the wind
tunnel, this process will align the model with the free stream. The resulting 𝛼
#$%
measured with
the force balance was repeatable to within ~0.5
o
for the NACA 0012 and ~0.2
o
for the NACA
65(1)-412. Based on this, the uncertainty in 𝛼 is believed to be < 0.5
o
. The better accuracy with
the NACA 65(1)-412 is due to the more pronounced leading and trailing edge of that model, which
makes alignment by eye easier.

2.3 USC Water Channel
A flow visualization study was conducted in the closed loop, horizontal, University of
Southern California water channel. The channel has a rectangular test section that measures 762
cm × 89 cm × 61 cm. The walls and floor of the channel are clear, allowing visual access to the
test section. The turbulence in the tunnel was measured to be < 1.7% using a Laser Doppler
Velocimeter (LDV) during all tests. In order to eliminate free surface and end effects, the model
was positioned between the bottom of the channel and an acrylic endplate. A small gap (< 0.007b)
was left between the model and the endplate and between the model and the wall to allow for
changes in 𝛼.
The model 𝛼 was set using a device that can rotate the model and fix the position in 0.5
o

increments. This device is made up of a fixed bottom plate with a pattern of holes and a rotating
top plate with two thin slots. The pattern of holes in the bottom plate were positioned so that a pin
could be inserted through the slots in the rotating top plate and into a specific pair of holes in the
bottom plate for each 𝛼-setting. The pin would lock the position of the model. The rotating plate
was connected with a pin or set screw to a hollow support rod that was in turn connected to the
model with set screws. The set screws were tightened onto flats that were aligned with the model
chord. Model alignment was checked by eye before each test by setting 𝛼 = 0
o
and translating the
model in the streamwise direction to verify that the leading and trailing edge passed over the same
position. The uncertainty associated with setting 𝛼 using this method was estimated to be 0.5
o
. The
test setup and coordinate system with origin at the model leading edge, center span is illustrated in
figure 2.4. Drawings for the wing, endplate, and the angle of attack setting device can be found in
Appendix B.
28

Figure 2.4: Water channel test setup, with tunnel walls not shown. Upstream injection is shown.

2.4 Models
All models used to generate the data in this report have been milled out of aluminum or
acrylic by the on-campus Kaprielian Hall machine shop. The mill used can produce parts with a
precision of 0.0005 inch (0.013 mm).

2.4.1 NACA 0012

The NACA 0012 wing used for both force balance and PIV tests has a 7.5 cm chord and a
48 cm span, giving AR = 6.4. The wing was first force balance tested, then painted matte black for
PIV testing. A force balance test after painting verified that the aerodynamic properties were not
altered. The NACA 0012 airfoil is symmetric with a maximum thickness of 0.12c at 30% chord,
has been used in various conventional aircraft wings, helicopter blades, and wind turbines, and is
illustrated in figure 2.5.

29

Figure 2.5: NACA 0012 airfoil

2.4.2 NACA 65(1)-412

The NACA 65(1)-412 airfoil, illustrated in figure 2.6, has a maximum thickness of 0.12c
at 39.9% chord and a maximum camber of 2.2% at 50% chord. NACA 6-series airfoils were
designed to delay the transition of the boundary layer as long as possible. This airfoil is generally
used for compressor blades, but experiences problems common to many types of airfoils at low
Re. Four NACA 65(1)-412 models were created: one for force balance testing, two for PIV testing,
and one for water channel flow visualization tests.
The force balance wing is solid aluminum with a 5.5 cm chord and a 71 cm span, giving
AR = 12.9. The large AR was chosen to give aerodynamic forces at Re = 2 × 10
4
that can be
measured by the force balance with high accuracy. There were several noticeable grooves in the
suction surface, and these were filled in with bondo body filler and sanded. The entire wing was
sanded to a finish that is smooth to the touch (i.e. smoother than the machined surface).
Two PIV wings were also made of aluminum with a 7.5 cm chord and 22.5 cm span (AR =
3). The chord length was chosen to be as large as possible to achieve a Re = 2 × 10
4
while keeping
the free stream velocity in the normal operating range for the Dryden Wind Tunnel (4 m/s < U <
20 m/s), in order to maximize the spatial resolution of the PIV. The span length was chosen to be
small enough so that the wingtips would not obscure the particles near the wing surface when the
camera was focused at mid-span during PIV tests. Because the location of the laser was fixed with
respect to the tunnel, the models were made to be mirror images of each other. One was used to
capture data over the suction surface of the wing while the other was used to capture data over the
pressure surface of the wing.
The water channel wing was made of clear acrylic with a chord of 14.4 cm and a span of
45 cm (AR = 3.1). The large chord was chosen to maximize resolution while staying within the
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
y/c
x/c
30
normal operating range of the water channel for tests at Re = 2 × 10
4
. An AR of 3.1 is sufficient to
generate a largely two-dimensional flow at the mid-span location. A 0.635 cm diameter reservoir
hole spans the entire length of the model at x = 0.26c. A hollow support rod was inserted partially
into this hole, and dye was injected through the support rod into the reservoir hole. Four, 1.6 mm
diameter injection holes were drilled between the leading edge of the model and the reservoir hole
at y/b = -[0, 0.15, 0.30, 0.46] to allow for dye injection into the boundary layer at the leading edge.
Drawings of the wing can be found in Appendix B.

Figure 2.6: NACA 65(1)-412 airfoil

2.5 Force Balance Measurements
Lift and drag data were collected for both airfoils using a custom, three-component,
cruciform-shaped, strain gauge force balance with a parallel plate structure design. A planform
drawing of the force balance can be seen in figure 2.7, and a detailed description of the design can
be found in Zabat et al. (1994). A new calibration was performed before each test, generating a
3x4 calibration matrix which converts voltage outputs to force units. The three most recent
calibration matrices were then averaged to generate the final calibration matrix that was used
during the test. Because the force balance is mounted on top of the rotary table that controls 𝛼, the
model normal and axial forces are directly measured and then converted to lift and drag. A study
was carried out in order to quantify the uncertainty associated with the force balance. In this study,
known loads were applied to the force balance with ratios of normal to axial force typical of a
NACA 0012 at Re = 5 × 10
4
. The difference between the resulting axial and normal force outputs
from the force balance and the known loads increased with the magnitude of the load, and was less
than 5 mN in the axial direction for applied loads less than 1 N. Differences in the normal direction
were always a small percentage of the true load (< 1.2%). It is estimated that a large portion of the
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
y/c
x/c
31
difference was due to uncertainties in load application angle, so these uncertainty estimates are
believed to be conservative.

Figure 2.7: Planform drawing of force balance showing strain gauge placement. Adapted from
Zabat et al. (1994)

After each test, lift and drag measurements were zeroed with forces corresponding to the
empty sting, the weight of the model, and free stream flow interaction with the sting. The empty
sting force was needed to prevent the subtraction of the same force twice, and the formula used for
zeroing the measurements is: 𝐹
u
=𝐹−𝐹
M
− 𝐹
n
−𝐹
M
− 𝐹
vM
−𝐹
M
, where 𝐹
u
is the zeroed force,
𝐹 is the un-zeroed force, 𝐹
n
is the zeroing force associated with the model weight, 𝐹
M
is the zeroing
force associated with the empty sting, and 𝐹
vM
is the zeroing force associated with the free stream
flow interaction with the sting. Because the sting was shielded by a shroud (and the bottom
endplate in two-dimensional tests), the free stream flow interaction component, 𝐹
vM
−𝐹
M
, was
found to be negligible during NACA 0012 tests. Therefore, for the later NACA 65(1)-412 tests,
this zeroing force was no longer recorded, and the zeroing formula simplifies to: 𝐹
u
=𝐹−𝐹
M
−
𝐹
n
−𝐹
M
=𝐹−𝐹
n
. For three-dimensional tests, the model support rod was also exposed to the
free stream. To account for this, the forces on a rod of the same size were also measured and
subtracted from the test data. The zeroing formula for three-dimensional tests is then: 𝐹
u
=𝐹−
32
𝐹
M
− 𝐹
n
−𝐹
M
− 𝐹
?
−𝐹
M
, where 𝐹
?
is the zeroing force associated with the drag force on the
support rod.
Each force balance test consisted of five sweeps, forward and backward, through the entire
range of 𝛼 in increments of 0.5
o
(or 0.2
o
for the high resolution portion of the NACA 0012 plots).
After each 𝛼 step, the flow was allowed to settle for ten seconds before ten seconds of data were
collected at 1kHz (NACA 0012) or 5kHz (NACA 65(1)-412) and averaged. The higher sampling
rate was chosen for the later (NACA 65(1)-412) tests to increase the range of frequencies that
could be analyzed from the resulting time traces. The five sweeps produced ten time-averaged
measurements for each 𝛼, which were averaged to obtain a single time-averaged value. The
uncertainty of each resulting force value was taken as the standard deviation of the ten
measurements or the estimated uncertainty of the force balance (5 mN in drag and 15 mN in lift
when the total aerodynamic force is less than 1 N), whichever was largest. The uncertainty
associated with the force balance was not taken into account for NACA 0012 test, where the
uncertainty was always taken as the standard deviation of the ten time-averaged measurements, as
the force balance uncertainty estimates are believed to be dominated by the uncertainty associated
with balance alignment, and small alignment errors could be removed after the test by setting 𝛼 =
0
o
as the angle where the lift curve passed through the origin (because the airfoil is symmetric).
Estimated uncertainties for span and chord (0.5 mm), density (0.0081 kg/m
3
, corresponding to the
change in density due to changes in temperature between 22
o
C and 24
o
C, the normal range of
temperatures seen during testing), and free stream velocity (0.1 m/s) were also taken into account
when calculating force coefficient uncertainties. The entire test procedure was repeated at least
three times to test for day to day repeatability. After stall, the model would typically begin to
oscillate considerably, so measurements were not taken for post-stall 𝛼.

2.6 Time-averaged particle image velocimetry (PIV)
Time-averaged boundary layer and wake properties were investigated using PIV. While
performing PIV tests, the tunnel is filled with glycerin-based smoke with a typical particle diameter
of 0.2-0.3 µm and a laser sheet parallel to the flow direction (in (x, z)) was generated using a
Quantel EverGreen double-pulsed Nd:YAG laser. An Image Pro X 2M CCD camera (1600 x 1200
pixel, 14 bit) imaged particle fields on a cross-section at mid-span (for the NACA 65(1)-412 test)
or 2.5 cm (0.05b) above mid-span (for the NACA 0012 tests), with a Nikon 70 – 210mm f/4-5.6
33
NIKKOR AF lens. Because the images were taken far from the wing tips for the large AR NACA
0012 wing, endplates were not used. The lower AR NACA 65(1)-412 wings were positioned
between endplates to eliminate the effects of wing tip vortices. Previously discussed results from
the literature suggest that force balance measurements of wings between endplates may be affected
by three-dimensional flows that form at the intersection of the wing and the endplate, but several
studies have shown spanwise uniformity near the center of the wing, even for smaller AR models.
Mueller & Batill (1980) showed that the flow over an AR = 1.6 model at Re = 5 × 10
4
between
endplates was essentially uniform except for within approximately 0.06b of the endplates.
Boutilier & Yarusevych (2012c) showed that installing endplates improves spanwise uniformity,
and that surface pressure distributions were least sensitive to endplate spacing when b/c > 2. This
was true when a laminar separation bubble was formed as well as when there was boundary layer
separation without reattachment. Therefore, it was assumed that end effects are not important at
the mid-span location of the NACA 65(1)-412 wing, where PIV measurements are made, despite
the small AR. As will be discussed in chapter 5, this is no longer believed to be true.
In order to increase spatial resolution, the flow field was split into several, slightly
overlapping sub-regions that were imaged in separate tests. A set of image pairs were captured for
each sub-region at a sampling rate of 9.6 Hz, and the time delay between image pairs (δt) was
carefully tuned to maximize the dynamic range of observable displacements while minimizing
peak locking. δt was also limited by the need to minimize the amount of shear within each
interrogation box near the airfoil surface. The images were processed with LaVision’s DaVis
software to produce velocity field estimates (u, w) in the streamwise and vertical directions (x, z),
on a uniform grid using a multi-pass algorithm. A 50% interrogation box overlap was used to
increase resolution.
All of the instantaneous velocity fields were averaged to produce one time-averaged
velocity field for each sub-region. A built in Matlab thin-plate smoothing spline function (“tpaps”)
with a single smoothing parameter that could vary from 0 (smoothing maximized – least squares
approximation to the data by a linear polynomial) to 1 (no smoothing– thin plate spline interpolant
to the data), similar to the smoothing spline used in Spedding & Rignot (1993), was applied to the
time-averaged fields in order to reduce random noise. Different smoothing parameter values were
tested on typical velocity fields from PIV data, and it was found that changing the smoothing
parameter from 0.1 to 0.9 changed all u measurements in the boundary layer, where velocity
34
gradients were largest, by less than 5% of the free stream velocity for the typical test case. The
changes in velocity due to smoothing are much smaller outside of the boundary layer, where
velocity gradients were smaller. A smoothing parameter value of 0.3 was chosen for all of the
results discussed, which is expected to result in changes in the u- and w-velocity that are always
less than 3% of the free stream velocity. The spanwise component of vorticity, 𝜔
w
=
𝜕𝑤
𝜕𝑥
−
𝜕𝑢
𝜕𝑧
, was calculated at each grid location from the derivatives of the smoothing spline
coefficients, and the smoothing is expected to result in changes in the vorticity over the airfoil that
were less than 10% of the maximum vorticity value. All averaged and smoothed sub-region
velocity/vorticity fields were finally combined to form one composite velocity/vorticity field for
each 𝛼.

2.6.1 NACA 0012

PIV tests were carried out for the NACA 0012 at 𝛼 = [0
o
, 0.5
o
, 2
o
, 4
o
, 6
o
, 8
o
]. Because the
model was symmetric, images of the suction and pressure sides were captured by rotating the
model in positive and negative 𝛼 respectively. The flow field on each side of the airfoil was split
into two sub-regions, and 200 image pairs were captured for each sub-region. Interrogation
windows were reduced to 16 × 16 pixels by the final processing pass for each sub-region. The 50%
overlap gave a final spatial resolution of 8 pixels, which is 0.27 mm. This is 0.23𝛿
'on
or 0.15𝛿
a|?}
,
where 𝛿
'on
=
Vl
96
and 𝛿
a|?}
=
%.~Ul
96
/
are the laminar and turbulent boundry layer thickness at 0.5c
of a flat plate with the same chord length as the model used.

2.6.2 NACA 65(1)-412

PIV data for the NACA 65(1)-412 were collected at 𝛼 = [0
o
, 2
o
, 4
o
, 6
o
, 8
o
, 10
o
, 10.1
o
, 10.2
o
,
10.3
o
, 10.4
o
, 10.5
o
]. The two mirror image NACA 65(1)-412 PIV models were used to collect data
from the suction and pressure sides of the airfoil. The flow field was split into five (for 𝛼 = [0
o
, 2
o
,
4
o
, 6
o
, 8
o
, 10
o
]) or two (for 𝛼 = [10
o
, 10.1
o
, 10.2
o
, 10.3
o
, 10.4
o
, 10.5
o
]) overlapping sub-regions.
When two sub-regions were used, they correspond to the front half and the back half of the suction
side of the airfoil. When five sub-regions were used, they correspond to the front half and back
35
half of both the suction and the pressure sides of the airfoil, and the wake. 1000 image pairs were
captured for each sub-region. The interrogation windows were reduced to either 16 × 16, 8 × 8, or
6 × 6 pixels for the final processing pass. The 8 × 8 pixel resolution was usually used in the wake
and over the suction surface of the airfoil in order to generate more data points for velocity and
vorticity profiles, but the 6 × 6 pixel resolution was used over the suction surface of the airfoil for
𝛼 = 10.2
o
and 10.3
o
to increase the resolution when the LSB was particularly thin. Smaller
interrogation windows were found to give poor results (i.e. low correlation coefficients). A 50%
interrogation box overlap gave a final spatial resolution of [3, 4, 8] pixels, which is [0.11, 0.14,
0.28] mm. This is [0.06, 0.07, 0.15]𝛿
'on
or [0.05, 0.06, 0.13]𝛿
a|?}
.

2.7 Water channel flow visualization
Dye-injection flow visualization tests were carried out in the USC water channel in order
to investigate the time-dependent properties of the boundary layer and wake of the NACA 65(1)-
412 airfoil at Re = 2 × 10
4
. Dye was either injected into the boundary layer at the leading edge of
the model through injection holes or through an injector (L-shaped probe with 1 mm outer
diameter) positioned upstream of the model. The rate of injection was carefully adjusted so that it
would not alter the natural properties of the boundary layer (for leading edge injection) or so that
the dye was injected at the same speed as the surrounding flow (for upstream injection). Both
injection locations gave equivalent results.
Milk was chosen for the dye in most tests because of its reflective properties and because
the fat in the milk allows for longer lasting filaments that diffuse slowly into the water. Isopropyl
alcohol was mixed with the milk to make the dye neutrally buoyant. The milk mixture was found
to not mix well with the boundary layer when injected close to the leading edge, and fluorescent
water tracer red dye was therefore also used in several wake tests because it would easily mix with
the boundary layer, even when injected very close to the leading edge, allowing for more control
over the dye trace.
A 5.14 W, 532 nm wavelength CNI continuous wave laser was spread into a sheet in an (x,
z)-plane and aligned in the y-direction to illuminate the dye trace. A Mako U-130 camera (1280 ×
1024 pixel, 10 bit) with an Edmund Optics 25 mm C series fixed focal length lens collected images
at a frame rate of 20 fps from below the model through the clear floor of the channel.

36
2.7.1 Boundary layer images

A series of 400 images were taken for each 𝛼 over the suction surface of the airfoil to
visualize the boundary layer behavior. Leading edge injection could not be used at low 𝛼 because
the holes were positioned such that the dye would travel over the pressure surface of the airfoil.
Instead, dye was injected approximately 10 cm upstream of the leading edge in order to capture
images of the separated boundary layer. For these images, the injector was carefully positioned so
that a thick stream of dye would enter the boundary layer and travel over the suction surface,
making clear the separation point and onset of vortex roll-up. At higher 𝛼, where the separated
boundary layer would reattach to form a separation bubble, leading edge injection from the mid-
span leading edge hole was found to produce the clearest images. Both instantaneous and time-
averaged images were compared with PIV.

2.7.2 Wake images

A series of 800 images taken in the wake of the airfoil for several 𝛼 were analyzed to
determine the vortex shedding frequency as a function of 𝛼. To generate these images, dye was
injected from the mid-span leading edge hole in the model or from an injector approximately 1 cm
upstream from the leading edge. Both injection techniques gave equivalent results. A Matlab code
was used to estimate the frequency at which vortex structures were shed into the wake. The dye
injected into the boundary layer would mark these structures, and so the images were analyzed to
determine how often patches of dye passed through the wake. This was done by selecting a grid
of pixels (20 pixel × 20 pixel grid spacing) from an interrogation box in the wake images and
determining their intensity as a function of time. A spike in the pixel intensity would indicate that
a patch of dye (marking a vortex structure) was passing over that pixel location. The fast Fourier
transform was then used to generate an amplitude spectrum for each pixel, and the spectra from
all pixels were averaged to determine the dominant frequencies in the wake. This method generally
produced sharp, distinct peaks in the spectra at low 𝛼, where individual vortices could be easily
identified in the images, but less distinct peaks at the higher 𝛼, where the wake became more
turbulent, leading to rapid diffusion of the dye into the water. The difference between low- and
high-𝛼 wake images can be seen in figure 2.8. Several interrogation boxes where analyzed in each
37
wake image to verify that the measured dominant frequencies did not depend on the location of
the interrogation box in the wake. When there was no obvious dominant frequency for a particular
image set, or when the dominant frequency would change with the location of the interrogation
box, that image set was discarded.

Figure 2.8: Wake behind the wing at 𝛼 = 0.5
o
(top) and 𝛼 = 5.5
o
(bottom)

2.8 Hot-wire

2.8.1 Test setup

Velocity measurements were made with a Dantec Dynamics MiniCTA and single wire hot-
wire probe (55P16). The MiniCTA has a bandwidth of ~10 kHz. No offset was applied to the data,
and the gain was kept equal to 1. Tests were run at a constant overheat ratio (𝑅

𝑅
o
, where 𝑅

is
the hot resistance of the sensor and 𝑅
o
is the resistance of the sensor at the fluid temperature) of
1.8, as was suggested by Brunn (1995). The hot-wire probe, which has a built-in support and was
connected to the MiniCTA with a 4 m long BNC cable, has a 1.25 mm long platinum-plated
tungsten wire with a diameter of 5 𝜇m. The MiniCTA was connected to the computer through a
24 bit, NI 9234 DAQ card (input range: +/- 5 V, resolution: 0.596 µV). Test section temperature
data were also collected with a 4-wire RTD and OMEGA DP41-RTD temperature indicator which
38
were connected to the computer through a 16 bit, NI 6353 DAQ card. A schematic of the entire
test setup can be found in figure 2.9.

Figure 2.9: Hot-wire test setup

Equation (2.1) was used to correct voltage readings for changes in temperature between
calibration and test, where 𝐸
o
is the acquired voltage, 𝑇

is the sensor hot temperature (242.24
o
C), 𝑇
O
is the ambient reference temperature (temperature at calibration), and 𝑇
o
is the acquisition
ambient temperature (Jorgensen, 2002).

𝐸
O??
=𝐸
o
8

8
b
8

8

(2.1)

Calibrations were performed in the Dryden Wind Tunnel using a pitot tube to set the free
stream velocity. Ten calibration points were collected (4 m/s < U < 20 m/s) for each calibration,
where the average of 10 seconds of data sampled at 10.24 kHz were used for each point. The
calibration points were distributed logarithmically between the minimum and maximum
calibration velocity. Because the temperature in the test section could rise several degrees during
calibration, the calibration voltages were also corrected with equation (2.1) before calculating
coefficients for the calibration equation. The 𝑇
O
value used was that of the first calibration point,
and this was also the value used when correcting test data. A calibration equation in the form of
equation (2.2) was used to convert from corrected voltage to an effective velocity (𝑉
6
), where A,
B, and n are determined based on the calibration.
39
An expression for 𝑉
6
in terms of the normal (𝑈

), tangential (𝑈
8
), and binormal (𝑈

)
velocity components, illustrated in figure 2.10, is given in equation (2.3), where typically 𝑘 ≈ 0.2
and ℎ ≈ 1.1 for unplated, single wire, normal probes (Brunn, 1995). The ℎ value is associated with
the interaction of the flow with the prongs, and in general only varies slightly with β (Brunn, 1995).

𝑉
6
=
𝐸
O??
G
−𝐴
𝐵
T/P
(2.2)

𝑉
6
= 𝑈

G
+𝑘
G
𝑈
8
G
+ℎ
G
𝑈

G
(2.3)

Figure 2.10: Velocity decomposition from (Brunn, 1995)

2.8.2 Turbulence measurements

Before conducting turbulence intensity tests, the flow speed was set and the tunnel was
allowed to settle for at least 15 minutes. Nine flow speeds between U = 4 m/s and 20 m/s were
tested (U ~ [4, 6, 8, 10, 12, 14, 16, 18, 20] m/s). The probe was attached to a two axis traverse with
a 78 cm arm so that the sensor was approximately 85 cm in front of the traverse. Velocity time
traces were gathered on a 27cm × 27cm grid with a grid spacing of 1 cm (729 total locations).
Diagrams of the experimental setup can be found in figure 2.11. The size of the grid was limited
by the size of the traverses used to move the probe. The position of the probe was controlled by a
40
LabView VI which would take 10 seconds of data at a sampling rate of 10.24 kHz, move the probe,
wait 5 seconds for the flow to settle, and repeat until time traces had been collected at all grid
points. The mean flow speed would drift slightly, but this was not an issue as T is normalized with
the mean velocity from each time trace. One second of temperature data was taken at 1 kHz and
averaged directly after each time trace was collected. The average temperature value was output
into a separate file and used to make temperature corrections during post processing. An
illustration of the time trace numbering convention and traverse path can be found in figure 2.12.

a) b)
Figure 2.11: a) Traverse setup and b) survey box location

Figure 2.12: Traverse path and time trace numbering convention. Each circle represents the
location of one time trace

41
2.8.3 Post processing of turbulence intensity time traces

The voltage time traces were first temperature corrected using equation (2.1). The corrected
voltages were then converted to 𝑉
6
using equation (2.2), and the velocity fluctuations were obtained
by subtracting the mean value from each time trace. T was then calculated after removing
frequencies outside the range 10 Hz < f < 1 kHz with a digital 8
th
order butterworth band pass
filter. The range of modified Strouhal numbers, 𝑆𝑡
∗
=𝑆𝑡
6
/𝑅𝑒
T/G
, that this frequency range
represents for all wind tunnel tests is given in table 2.1. Zaman & McKinzie (1991) and
Yarusevych et al. (2003) found that the frequencies that had the largest impact on airfoil
performance generally fell between 0.02 < 𝑆𝑡
∗
< 0.03, and this range is covered by the unfiltered
frequencies for all wind tunnel tests. The energy content decreases at higher frequencies in typical
turbulent flows, so the fact that a decrease in energy is not seen with an increase in frequencies
higher than 1 kHz suggests that frequencies higher than 1 kHz in the hot-wire signal are most likely
dominated by electrical noise. Frequencies less than 10 Hz correspond to fluctuations that are slow
when compared to the convective time scales of the wind tunnel tests and are not believed to have
a large impact on the flow over the airfoils.

Table 2.1: Range of 𝑆𝑡
∗
associated with 10 Hz < f < 1 kHz for wind tunnel tests
Airfoil Test Re 𝑆𝑡
nBP
∗

𝑆𝑡
nol
∗

NACA 0012
PIV,FB 5 × 10
4
0.0003 0.033
NACA 65(1)-412
FB 2 × 10
4
0.0007

0.070
NACA 65(1)-412 PIV 2 × 10
4
0.0013 0.130

42
3 Wind Tunnel Free Stream Turbulence

3.1 Motivation
Previously publications report T in the Dryden Wind Tunnel of less than 0.03% (unknown
frequency range) (McArthur, 2008), 0.025% for 2 Hz < f < 200 Hz (Yang, 2013), and ~ 0.1% for
f > 10 Hz (Zabat et al., 1994). Because of the previously noted impact T can have on low Re wind
tunnel tests, it is important to quantify the free stream turbulence levels when performing low Re
tests. At the beginning of the Fall 2016 semester, the Dryden Wind Tunnel was sealed to prevent
the leaking of smoke during PIV tests. It was not known if the sealing had an effect on T in the test
section, so tests were carried out to re-measure T with a hot-wire probe. A hot-wire probe was used
because of its excellent temporal resolution.

3.2 Turbulence intensity definition and assumptions
The T in a wind tunnel test section can be calculated with equations (3.1) and (3.2), where
the velocity is defined in terms of its mean 𝑈
B
and fluctuating 𝑢
B
components as described in
equation (3.3).

𝑇 =
|
1
(3.1)

𝑢 =
T
~
𝑢
l
G
+𝑢
w
G
+𝑢
u
G
(3.2)

𝑈 = 𝑈
l
,𝑈
w
,𝑈
u
(3.3)
= 𝑈
l
+𝑢
l
,𝑈
w
+𝑢
w
,𝑈
u
+𝑢
u

= 𝑈
l
,𝑈
w
,𝑈
u
+ 𝑢
l
,𝑢
w
,𝑢
u

=𝑈+𝑢′

If the assumption is made that the turbulence is homogeneous and isotropic
𝑢
l
G
=𝑢
w
G
=𝑢
u
G
, then equation (3.1) will simplify to:
43

𝑇 =
|

1

(3.4)

Therefore, a single wire hot-wire is sufficient to measure T in a wind tunnel.

3.3 Results of turbulence measurements
T was found to vary randomly within the survey box. A typical T-distribution across the
survey box is given in figure 3.1.

Figure 3.1: T-distribution across survey box for U ~ 14 m/s

T was averaged over the survey box and plotted against the average U of each test in figure
3.2. The uncertainty bars represent the standard deviation of the T and U values measured during
one test. The uncertainty bars for U are smaller than the size of the markers, and therefore cannot
be seen. T is seen to generally increase with U, with one noticeable exception being between U =
10 and 12 m/s, where the average T decreases by an amount that exceeds uncertainty estimates.
The power spectrum was calculated for each time trace and averaged over the entire survey box
for each U. Average power spectrum results are plotted in figure 3.3, where each spectrum is offset
from the previous spectrum by three orders of magnitude for clarity.

0
10
20
30
0
10
20
30
0.01
0.015
0.02
0.025
0.03
0.035
0.04
x [cm]
z [cm]
T [%]
44

Figure 3.2: T variation with U

Figure 3.3: Averaged velocity fluctuation power spectrum for all U tested. Each spectrum is
offset three orders of magnitude from the previous spectrum for clarity

From figure 3.2 it is clear that T < 0.035 in the Dryden Wind Tunnel for 4 m/s < U < 20
m/s in the frequency range 10 Hz < f < 1 kHz. It can be seen from figure 3.3 that there is a
significant T for f < 10 Hz, but it is assumed that these frequencies do not have a large impact on
0.01
0.015
0.02
0.025
0.03
0.035
3 5 7 9 11 13 15 17 19 21
T [%U]
U [m/s]
45
low Re tests, as fluctuations at these frequencies are slow in comparison to convective time scales
(t
c
= c/U). The t
c
information for all wind tunnel tests and the ratio of the period (𝜏
T% u
)
corresponding to the highest removed frequency (less than 1 kHz) to t
c
can be found in table 3.1.
In all cases 𝜏
T% u
is at least five times larger than the convective time scale. The largest consistent
peak in the power spectrum for every U is at f = 0.2 Hz. There are also large peaks at f = 0.5 Hz
and 0.7 Hz for U = 14 m/s and 16 m/s respectively that correspond to large, periodic fluctuations
in the free stream that can be clearly seen in the fluctuation velocity (𝑈−𝑈) time traces. These
fluctuations may be caused by a problem with the wind tunnel motor controller or a vibration in
the fan blades, but are not seen at any of the free stream velocities used for tests in this work. No
prominent peaks other than the harmonics of the utility frequency (discussed below) are seen for f
> 1 kHz.

Table 3.1: Convective time scale information for past and planned tests
Airfoil Test Re c [m] U [m/s] t
c
[ms] 𝜏
T% u
/t
c
NACA 0012 PIV,FB 5 × 10
4
0.075 10.2 7 13.6
NACA 65(1)-412
FB 2 × 10
4
0.055 5.5 10 10.1
NACA 65(1)-412 PIV 2 × 10
4
0.075 4.1 18 5.4

There are several features of the power spectra between 10 Hz < f < 1 kHz that deserve
mentioning. As pointed out by Brendel & Mueller (1988), the location of peaks in the free stream
turbulence power spectrum can be more important than the overall turbulence intensity as it relates
to transition to turbulence. Prominent spikes in this region that correspond to 60 Hz (the utility
frequency) and its harmonics and subharmonics are due to interference from surrounding electrical
equipment, and therefore do not correspond to turbulence features in the free stream. These
frequencies were removed before calculating T. There is a peak near f = 12.2 Hz for the U = 4 m/s
spectrum that shifts to higher frequencies as U increases. The increase in the frequency of this peak
with U may be due to the increase in frequency of the fan blades or unsteady boundary layer
motions. This peak could potentially hasten transition if it corresponds to instabilities in the
boundary layer or separated shear layer over the wing being tested, although it corresponds to 𝑆𝑡
∗

< 0.008 for all NACA 0012 and NACA 65(1)-412 wind tunnel tests, which is well outside the
range of 𝑆𝑡
∗
associated with frequencies that have a large impact on airfoil behavior identified by
Zaman & McKinzie (1991) and Yarusevych et al. (2003). The decrease in magnitude of this
46
prominent peak between U = 10 m/s and 12 m/s may explain the decrease in T between these two
flow speeds.
This investigation of the turbulence intensity of the Dryden Wind Tunnel confirms the
generally low T. This characteristic makes the Dryden Wind Tunnel especially well suited for low
Re testing, as results at low Re can be altered significantly by high T in the free stream.
47
4 NACA 0012

A series of tests were carried out for the NACA 0012 at Re = 5 × 10
4
so that comparisons
could be made with the DNS of Jones et al. (2008) – one of the few publications to date with DNS
data for an airfoil in the low Re regime of interest. Jones et al. (2008) performed two- and three-
dimensional simulations at 𝛼 = 5
o
. Their three-dimensional forced simulation (3DF) had a domain
that extended 0.2c in the spanwise direction and was initialized with the flow field from their two-
dimensional simulation (2D). Disturbances were added to the 3DF simulation through volume
forcing in the boundary layer at frequencies chosen based on a linear stability analysis of time-
averaged velocity profiles from the 2D simulation. Their three-dimensional unforced simulation
(3DU) was a continuation of the 3DF simulation with all forcing removed. Force balance
measurements revealed lift curve behaviors that differ significantly from what is seen at higher
Re, and these behaviors were linked to boundary layer behaviors using time-averaged PIV.

4.1 Time-averaged lift and drag
The time-averaged lift and drag curves for the NACA 0012 at Re = 5 × 10
4
can be seen in
figure 4.1, where the lift and drag coefficients are defined as follows: 𝑐
'
=
#
%.V21

}
, 𝑐
g
=

%.V21

}
,
where L and D are the measured lift and drag forces. There are several interesting features of the
lift curve. The slope of the lift curve (𝑐
',)
) is negative at 𝛼 = 0
o
, resulting in negative lift at small
positive 𝛼 for the symmetric airfoil. This is not consistent with any theoretical prediction. Near 𝛼
= 0.5
o
, 𝑐
',)
increases to above the thin airfoil theory prediction of 2𝜋, and remains relatively
constant until approximately 𝛼 = 3
o
. At this point, the lift generated by the airfoil is larger than the
theoretical prediction, represented by the straight black line in the figure. From 𝛼 = 3
o
until stall
after 𝛼 = 9
o
, 𝑐
',)
again decreases below 2𝜋. The inset plot shows the curve in higher resolution
(Δ𝛼 = 0.2
o
) near 𝛼 = 0
o
. The nonlinearities in the lift curve that occur over small 𝛼-ranges illustrate
the need for high 𝛼-resolution in force measurements. The 1
o
increments that are typically used
will not capture the details of all of the nonlinearities that can be seen at low Re. Table 4.1 gives
𝑐
',)
for the three distinct regions of the lift curve, estimated by fitting a straight line to the data in
each region. The drag curve is shaped similar to that of a typical symmetric airfoil at high Re, with
48
a minimum near 0.015 at 𝛼 = 0
o
. Both curves are symmetric, as is expected with a symmetric
airfoil.

Figure 4.1: Time-averaged a) 𝑐
'
𝛼 and b) 𝑐
g
𝛼 for the NACA 0012 at Re = 5 × 10
4
. The
straight black line in the 𝑐
'
𝛼 plot represents the thin airfoil theory prediction for two-
dimensional airfoils: 𝑐
'
=2𝜋𝛼.

Table 4.1: Lift slope values for NACA 0012
Region Range in 𝛼 (
o
) Lift slope (𝜋/rad)
1 0.0 – 0.5 -1.4
2 0.5 – 3.0 3.4
3 3.0 – 8.5 1.4

Plots of L/D(𝛼) and 𝑐
'
𝑐
g
can be found in figure 4.2. The L/D(𝛼) curve has a distinct
nonlinearity near 𝛼 = 0
o
due to the shape of the lift curve. There is a broad peak between 3
o
< 𝛼 <
8
o
with a maximum value near 15. The drag polar shows a loop where the curve intersects the
abscissa. This is again due to the lift curve behavior near 𝛼 = 0
o
. All of the previously noted
characteristics are also present in the AR = 6.4 test results (where endplates are removed), as can
be seen in figures 4.3 and 4.4. The loop in the drag polar in figure 4.4b is clear, even when taking
into account the uncertainty of the measurements. Based on this, the flow field over the model is
not expected to change significantly when the endplates were removed during PIV tests.
49

Figure 4.2: Time-averaged a) L/D(𝛼) and b) 𝑐
'
𝑐
g
for the NACA 0012 at Re = 5 × 10
4

Figure 4.3: Time-averaged a) 𝑐
#
𝛼 and b) 𝑐

𝛼 for the AR = 6.4 NACA 0012 at Re = 5 × 10
4

The straight black line in the 𝑐
#
𝛼 figure represents the lifting line theory prediction for three-
dimensional wings: 𝑐
#
=2𝜋𝛼
𝐴𝑅
𝐴𝑅+2
.

50

Figure 4.4: Time-averaged a) L/D(𝛼) and b) 𝑐
#
𝑐

for AR = 6.4 NACA 0012 at Re = 5 × 10
4

4.2 Time-averaged PIV
The unexpected shapes in the time-averaged force coefficient plots can be linked to
boundary layer behaviors using time-averaged PIV. Velocity magnitude (𝑞 = 𝑢
G
+𝑤
G
) and
spanwise vorticity (𝜔
w
) fields can be found in figure 4.5, and streamwise velocity (u) and vertical
velocity (w) fields can be found in figure 4.6. Discontinuities where the sub-regions from separate
PIV acquisition windows meet are noticeable in several images, and are due to small differences
in the free stream velocity between tests. At 𝛼 = 0
o
(row 1) a symmetric flow field is generated
with boundary layer separation approximately 1/3c before the trailing edge. At 𝛼 = 0.5
o
, the
separation point has moved forward over the suction (top) surface and aft over the pressure
(bottom) surface. At this 𝛼, the lowest part of the airfoil is forward of the bottom separation point
and below the trailing edge, and so fluid leaving the bottom surface is given a significant positive
w. At the same time, the separation over a significant portion of the top of the airfoil deflects the
flow upward, decreasing the magnitude of the negative w of the fluid leaving the top of the airfoil.
This leads to a net upwash at the trailing edge, resulting in negative lift at 𝛼 = 0.5
o
. At this 𝛼, the
airfoil has an effective negative camber due to the boundary layer separation.
1

1
During the writing of this thesis, a description of this behavior was found in a textbook by Houghton &
Carpenter (2003), who described “lift reversal” that occurs at small α for thick surfaces with large trailing
edge angles due to boundary layer separation over the suction surface while the flow over the pressure
surface remains attached.
51
As 𝛼 is increased further to 2
o
(row 3), the separation point continues to move forward over
the top surface and the flow is fully attached over the bottom surface. At this point, there is no
longer a net positive w (upwash) at the trailing edge, and the lift has become positive. The large
𝑐
',)
can be explained by the separation streamline behavior. As is the case when a LSB is formed
(see figure 1.3), after the separated boundary layer begins to roll-up, high momentum fluid is pulled
towards the airfoil surface due to the increased mixing, and the time-averaged separation
streamline turns back towards the airfoil. Between 0.5
o
< 𝛼 < 3
o
this occurs in the vicinity of the
trailing edge, increasing the average downwash and therefore the amount of lift generated. This is
supported by figure 4.6 (row 3) where an increase in w in the negative direction is seen near the
trailing edge, indicating an increase in downwash. In this region, the boundary layer separation
leads to an increasing effective positive camber. Although not done here, the wake deflection and
negative lift could be verified with PIV data using a control volume or circulation analysis.
At 𝛼 = 4
o
(row 4), an LSB, marked by a large region of near zero total velocity, can be
clearly seen in figure 4.5a over the top of the airfoil. This is accompanied by strong negative 𝜔
w

at the location of the bubble in figure 4.5b and a large negative w near the surface of the airfoil
where the boundary layer reattaches in figure 4.6b. As 𝛼 increases to 6
o
(row 5) and 8
o
(row 6),
the bubble moves forward and decreases in length. This is consistent with the bubble behavior
reported for wings and airfoils at low Re in previous studies (e.g., Bastedo & Mueller, 1986;
McGhee et al., 1988; Hsiao et al., 1989b; Huang et al., 1996; Hain et al., 2009; Boutilier &
Yarusevych, 2012a). The vorticity becomes more negative in the bubble region as the bubble
decreases in size. A bubble over the airfoil in the three-dimensional simulations of Jones et al.
(2008) at 𝛼 = 5
o
is found between 0.13 < x/c < 0.5 (3DF) and 0.1 < x/c < 0.6 (3DU). It is difficult
to determine the exact separation and reattachment points of the LSB from the time-averaged PIV
due to the resolution near the airfoil surface, but if the “location” of a bubble is taken as the point
directly between the mean separation and reattachment points, then the locations of the 3DF (x/c
= 0.315) and 3DU (x/c = 0.35) bubbles at 𝛼 = 5
o
appear to fall between those of the PIV bubbles
at 𝛼 = 6
o
and 8
o
. Therefore, the experimental bubble location will most likely pass through the
DNS bubble location between 6
o
< 𝛼 < 8
o
.
The slope of the lift curve decreases with the formation of the LSB, but the increased
effective camber is associated with lift values that exceed theoretical predictions for 1.5
o
< 𝛼 <
4.5
o
. A change in lift curve slope at the 𝛼 where the bubble forms has been noted in Carmichael
52
(1981) and Mueller & Batill (1982) (for Re = 1.3 × 10
5
) , and Boutilier & Yarusevych (2012b)
suggest that the decrease in the lift slope as the bubble moves towards the leading edge is due to
the decrease in the suction peak near the leading edge of the airfoil. It should be noted that the
presence of an LSB is generally associated with a decrease in airfoil performance at higher Re,
though the present findings show that it can increase the amount of lift produced at low Re due to
its impact on the effective shape of the airfoil. This effective airfoil shape is sometimes
approximated by increasing the thickness of the airfoil at each location along the chord by an
amount equal to the boundary layer displacement thickness, including in the XFOIL software (Rao
et al., 1980; Drela, 2001; Lian & Shyy, 2007). However, Selig et al. (1996) suggests that changes
to the velocity distribution around the airfoil caused by flow separation can not be attributed solely
to the effects of displacement thickness. The idea of an effective airfoil shape will be discussed in
more detail in chapter 5.
It is clear from the PIV that the negative lift value observed at small, positive 𝛼 is due to
the inability of the airfoil to impart a strong negative w on the fluid moving over the top surface to
overcome the positive w of the fluid being turned upward by the bottom surface. It is likely that
this same phenomenon will be seen for many thick, symmetric airfoils at low Re and small 𝛼 where:
1) the boundary layer separates early over the top surface, deflecting the flow upward (increasing
w over the top surface), and 2) the lowest point of the airfoil surface is below the trailing edge and
forward of the bottom separation point, allowing for a significant positive w to be imparted on the
fluid moving over the bottom surface. Yarusevych et al. (2004) measured negative lift for a NACA
0025 at 𝛼 = 5
o
for Re < 1.35 × 10
5
(i.e. a thick, symmetric airfoil at low Re and small 𝛼), where
the boundary layer is separated over the suction surface, supporting this hypothesis. Figure 4.7
taken from Yarusevych et al. (2007) shows a smoke wire flow visualization in the wake behind
the same airfoil at 𝛼 = 5
o
and Re = 10
5
, and it is clear that the wake is leaving the trailing edge in
a net upward direction. The positive w of the fluid leaving the pressure surface and decreased w of
the fluid leaving the suction surface due to separation can also be seen from the streaklines. Mueller
& Batill (1982) measured negative lift at positive 𝛼 for another thick, symmetric airfoil, the NACA
66(3)-018, at Re = 1.3 × 10
5
. Smoke wire flow visualization images from that study also showed
the separation point moving forward over the suction surface and aft over the pressure surface
from their 𝛼 = 0
o
(i.e. zero lift) positions as 𝛼 was increased to the value where negative lift was
53
measured. This behavior was eliminated when a trip strip was placed at the wings leading edge as
well as when acoustic forcing was applied, which significantly alters the boundary layer behavior.

Figure 4.5: PIV generated fields for a) 𝑢 =𝑞 = 𝑢
G
+𝑤
G
and b) 𝜔
w
for, from top to bottom,
𝛼 = [0
o
, 0.5
o
, 2
o
, 4
o
, 6
o
, 8
o
]
54

Figure 4.6: PIV generated fields for a) u and b) w for, from top to bottom, 𝛼 = [0
o
, 0.5
o
, 2
o
, 4
o
,
6
o
, 8
o
]

55

Figure 4.7: Smoke wire flow visualization of wake behind NACA 0025 at 𝛼 = 5
o
showing wake
leaving in upward direction, resulting in negative lift (Yarusevych et al., 2007)

4.3 Comparison with literature and computations
Figure 4.8 shows a comparison of the current lift and drag curves along with several
experimental data sets from the literature. Uncertainty bands for the current study are shown in
red, but uncertainty estimates were not given for any other data set. It is clear from the plots that
any agreement in 𝑐
'
is coincidental, except, perhaps, for the agreement seen between the current
study and Tsuchiya et al. (2013) for 4
o
< 𝛼 < 8
o
. At 𝛼 = 0.5
o
, the reported 𝑐
'
values (or the
interpolated values) vary by a considerable amount: ∆𝑐
'
~ 0.25, which is over 5 times larger than
the magnitude of 𝑐
'
seen in the current experiment at this 𝛼. Several of the lift curves show similar
trends, such as a reduction in 𝑐
',)
before 𝛼 = 3
o
. All of the data except those from Lee & Su (2012)
show regions where 𝑐
',)
is larger than the theoretical value, and for these same data sets there are
regions where 𝑐
'
exceeds theory, as is seen in the curve from the current study. However, none of
the previous studies found negative 𝑐
'
at positive 𝛼. This may be due in part to insufficient 𝛼-
resolution, but it is likely also due to the differences in force measurement method and free stream
T, which are summarized in table 4.2. As has been discussed, larger T can lead to later boundary
layer separation and earlier boundary layer transition, which could eliminate the conditions that
lead to negative 𝑐
'
at positive 𝛼. Differences in the drag curves are also large, and again, any
agreement appears to be coincidental.
56

Figure 4.8: Comparison of current 𝑐
'
𝛼 and 𝑐
g
𝛼 curves with results from the literature for Re
at or near 5 × 10
4
(Huang et al., 1996; Kim et al., 2011; Lee & Su, 2012; Tsuchiya et al., 2013)

Table 4.2: Data collection methods and turbulence intensity information for presented data
Reference Re (×10
3
) Measurement method T [%]
Huang et al, 1996 50.8 Force balance 0.2
Kim et al., 2011 48 Integrate pressure distribution < 0.4
Lee & Su, 2012 54 PIV/circulation estimate Not given
Tsuchiya et al., 2013 47 Force balance 0.5
DWT 50 Force balance < 0.3

A comparison of the current experimental data with computational data sets can be seen in
figure 4.9. Details of the RANS simulations can be found in Tank et al. (2016). Although 𝑐
'

predictions from the RANS simulations agree well with the experimental curve between 4
o
< 𝛼 <
8
o
(all 𝛼 at which an LSB forms), there is no other 𝛼-range with consistent agreement. The RANS
data also lack symmetry about the y-axis, which leads to questions about the accuracy of the
predictions, given the fact that the airfoil is symmetric.
XFOIL predicts negative lift at positive 𝛼 and three distinct regions of nearly constant 𝑐
',)
,
but either overestimates or underestimates 𝑐
'
(compared to the experimental curve) for nearly
every 𝛼. The locations where the XFOIL curve crosses the x-axis at positive and negative 𝛼 were
found to change as the effective turbulence level, controlled by the “Ncrit” parameter, is changed
(Ncrit = 9 is used for the plotted data). The fact that the XFOIL and experimental curves are
57
qualitatively similar suggests the XFOIL viscous boundary layer model does a decent job of
predicting the boundary layer behavior and that using the displacement thickness to estimate the
effective airfoil shape, as is done in XFOIL, may be appropriate when the separated region remains
relatively small. As the Re is reduced, the separated region behind the airfoils increases in size
(see the flow fields over the NACA 65(1)-412 at Re = 2 × 10
4
in the next chapter), and the accuracy
of XFOIL lift and drag predictions is expected to decrease.
The 2D DNS from Jones et al. (2008) predicts a 𝑐
'
at 𝛼 = 5
o
that falls below the
experimental curve, whereas the 3DF and 3DU simulations predict larger 𝑐
'
. The 𝑐
'
predictions
from the 3DU and 3DF simulations agree closely with the experimental value at 𝛼 = 6
o
, which can
be explained by the forward location of the bubble in the simulations: a similar flow field (i.e. a
bubble between approximately 0.1 < x/c < 0.6) will not be seen until a later 𝛼 in experiments (6
o

< 𝛼 < 8
o
). Differences between the DNS and experiments may be due to differences in the free
stream conditions (e.g. T) that can impact separation and transition locations. In addition, the three-
dimensional DNS used a domain that only extended 0.2c in the spanwise direction, which may not
allow for the formation of large, three-dimensional structures, possibly affecting the transition
process. A computational study by Almutairi et al. (2010) found LSB formation when the spanwise
length of the domain was 0.5c, but no LSB when this length was decreased to 0.2c, and therefore
concluded that the LSB is sensitive to the spanwise length of the domain, which should be at least
0.5c.
All computations except the 3DU DNS at 𝛼 = 5
o
and the RANS simulations at 𝛼 = 7
o
and
8
o
predict 𝑐
g
values that fall below the experimental curve. There is essentially zero agreement
between the experimental curve and any 𝑐
g
data from computations, with the only exception being
the 3DU value from Jones et al. (2008). XFOIL predicts 𝑐
g
values that are closer to experiments
than the RANS simulation for most 𝛼, and the extremely small 𝑐
g
values predicted by the RANS
simulations at 𝛼 = +/- 3
o
and 4
o
are most likely not realistic given the fact that the flow is separated
at these 𝛼.
Based on the comparisons made here, it appears that there is very little meaningful
agreement in the published experimental or computational 𝑐
'
and 𝑐
g
data for this simple,
symmetric airfoil at Re = 5 × 10
4
. More work is needed to determine the experimental and
computational factors that lead to the observed differences.

58

Figure 4.9: Comparison of current 𝑐
'
𝛼 and 𝑐
g
𝛼 results with computations for NACA 0012
at Re = 5 × 10
4
(Jones et al., 2008; Tank et al., 2016). FP laminar and FP turbulent correspond to
the drag on a flat plate, assuming a laminar or turbulent boundary layer respectively.

59
5 NACA 65(1)-412

Force balance, PIV, and flow visualization tests were carried out for the NACA 65(1)-412
to investigate the boundary layer behavior and airfoil performance at Re = 2 × 10
4
. Comparisons
were made to DNS data (Re = 2 × 10
4
, Mach number M = 0.3) generated by collaborators at San
Diego State University. The DNS used a discontinuous-Galerkin spectral element method with
12
th
-order orthogonal polynomials as basis functions on unstructured meshes (Nelson, 2015).
Nelson (2015) states that this method is naturally suited for the analysis of flows over curved
geometries, and its low dispersion and diffusion characteristics make it well suited for DNS. The
governing equations were integrated in time using a low-dispersion, 4
th
-order explicit, Runge-
Kutta scheme, and data were collected averaged over at least 2.5 convective time units. For three-
dimensional simulations, the domain was extended 0.5c in the spanwise direction and periodic
boundary conditions were applied to model an infinite wing. Three-dimensional computations
were initialized using the two-dimensional fully developed flow result, with a local perturbation
added to help the transition to three-dimensional flow. Details of the simulations can be found in
Klose et al. (2018), and additional details of the method and how it is used to efficiently generate
accurate LCS fields are given in Nelson & Jacobs (2015, 2016) and Nelson et al. (2016).
Force balance tests were carried out for 2 × 10
4
< Re < 9 × 10
4
in order to determine how
lift curve characteristics, such as 𝛼
#$%
, 𝑐
',)
, and 𝛼
?Ba
, change with Re, where 𝛼
?Ba
is defined as
the 𝛼 at which the separated boundary layer reattaches to the airfoil surface, forming an LSB and
causing a jump from a low lift/high drag state to a high lift/low drag state.

5.1 Re = 2 × 10
4

5.1.1 Time-averaged lift and drag

Two-dimensional time-averaged lift and drag curves for -5
o
< 𝛼 < 11
o
, generated with the
force balance in the Dryden Wind Tunnel, are shown in figures 5.1 and 5.2. Time-averaged lift
and drag from DNS are also plotted for 𝛼 = [4
o
, 8
o
, 10
o
], and the thin airfoil theory lift curve
60
prediction, assuming the 𝛼
#$%
found in the experiment, is plotted as a black line. The uncertainty
estimates for the DNS data points are calculated as the standard deviation of the fluctuations about
the mean value. The experimental 𝑐
',)
matches closely with the thin airfoil theory prediction
(𝑐
',)
=2𝜋) from approximately 𝛼 = -1.5
o
– 4
o
. Experimental lift and drag values were both found
to match the DNS within experimental uncertainty at 𝛼 = 4
o
, where the modest lift suggests that
the airfoil is still in the low lift state (i.e. 𝛼 < 𝛼
?Ba
). From 𝛼 = 6
o
– 8.5
o
, directly before 𝛼
?Ba
, 𝑐
',)

of the experimental lift curve decreases considerably. The 𝛼
?Ba
value can be identified from the
time-averaged lift curve as the 𝛼 at which there is a sudden and significant increase in lift, and the
force balance measurements in figure 5.1 show that 8.5
o
< 𝛼
?Ba
< 9
o
. The jump to the high lift
state occurs at a smaller 𝛼 for the DNS, as evidenced by the fact that the time-averaged lift is
already well above the thin airfoil theory prediction at 𝛼 = 8
o
. The experimental lift at 𝛼 = 10
o

matches that of the DNS within experimental uncertainty, and 𝑐
'
from both data sets suggest the
airfoil is in the high lift state at this 𝛼. The experimental lift begins to decrease with increasing 𝛼
after the initial jump in lift. Although hysteresis is often seen for airfoils in this Re regime, none
was found in the present test. However, the same model did show hysteresis when the Re was
increased, as will be seen in section 5.1.3. One unexpected characteristic of the lift curve at this
Re is the 𝛼
#$%
value, which is positive. Because the NACA 65(1)-412 is cambered, it is expected
that it would have a negative 𝛼
#$%
value. This is investigated further in section 5.2.1. Similar post-
𝛼
#$%
lift curve behavior was seen for another 6-series airfoil, the NACA 66(3)-018, at Re = 4 ×
10
4
in Mueller & Batill (1982), with a jump at 𝛼
?Ba
due to sudden boundary layer reattachment
followed by a decrease in lift with a further increase in 𝛼.
The drag curve has a minimum value of approximately 0.03 near 𝛼 = -1.5
o
, and increases
gradually with 𝛼 until 𝛼
?Ba
. The jump to the high lift state at 𝛼
?Ba
is accompanied by a decrease
in drag, which creates a kink in the drag curve at 𝛼 = 8.5
o
. After 𝛼
?Ba
, the drag curve rises quickly.
The experimental drag is slightly higher than that of the DNS at 𝛼 = 10
o
.
The L/D plot in figure 5.2 has a broad maximum around 8 between 4
o
< 𝛼 < 9
o
, but jumps
to near 13 at 𝛼 = 9.5
o
due to the switch to the high lift/low drag state. After α = 9.5
o
, L/D decreases
quickly due to the rapid increase in drag and the moderate decrease in lift with increasing 𝛼. The
switch to the high lift/low drag state also creates a large jump in the drag polar. The characteristics
61
of these curves will be investigated further with time-averaged PIV and DNS flow-fields, as well
as dye-injection images.

Figure 5.1: Time-averaged a) 𝑐
'
𝛼 with thin airfoil theory prediction and b) 𝑐
g
𝛼 for the 2D
NACA 65(1)-412 at Re = 2 × 10
4

Figure 5.2: Time-averaged a) 𝑐
'
𝑐
g
and b) L/D(𝛼) for the 2D NACA 65(1)-412 at Re = 2 × 10
4

62
5.1.2 Time-averaged PIV: 𝛼 <

𝛼
?Ba

Time-averaged u, w, 𝜔
w
, and 𝑢
G
+𝑤
G
PIV flow fields for 𝛼 <

𝛼
?Ba
can be found in
figures 5.3 and 5.4. For all 𝛼 <

𝛼
?Ba
, the boundary layer separates early from the suction surface
of the airfoil and does not reattach, creating a region of slow, recirculating fluid behind the airfoil.
A thin layer of high 𝜔
w
marks the separated shear layer that is created for all 𝛼 shown when the
boundary layer separates in figure 5.3b. An earlier dissipation of 𝜔
w
near the trailing edge at higher
𝛼 (see row 6) is associated with the upstream movement of the shear layer roll-up location with
increasing 𝛼, as will be seen in section 5.1.5. The slow, recirculating region behind the airfoil
grows rapidly after 𝛼 = 6
o
(rows 5 and 6 of figures 5.3a and 5.4a), extending significantly further
into the wake. The growth of this recirculating region has a negative effect on airfoil performance,
and is associated with the decrease in 𝑐
',)
directly before 𝛼
?Ba
seen in the lift curve. Similar to
what was seen for the NACA 0012 at small, positive 𝛼, the positive w of the fluid leaving the
pressure surface is larger in magnitude than the negative w of the fluid leaving the suction surface
after the trailing edge at 𝛼 = 0
o
(see row 1 of figure 5.4b), which leads to a net upwash and slightly
negative lift generation despite the airfoil’s positive camber.
Boundary layer separation angles were estimated by applying a linear least squares fit to
curves connecting the u = 0 m/s points from time-averaged u-velocity profiles, below which is
reversed flow. The separation angle increases with 𝛼, as can be seen from figure 5.5c, which plots
separation angle as a function of 𝛼. The separation location moves forward, towards the leading
edge, with an increase in 𝛼. Note that the boundary layer remains separated from the airfoil at 𝛼 =
10
o
, which is after the 𝛼
?Ba
value identified from the time-averaged force balance curves of the
previous section. This will be discussed further in section 5.1.3.

63

a) b)
Figure 5.3: a) Velocity magnitude ( 𝑢
G
+𝑤
G
) field and b) 𝜔
w
field from PIV for
𝛼 = [0
o
, 2
o
, 4
o
, 6
o
, 8
o
, 10
o
]

64

a) b)
Figure 5.4: a) u-velocity field and b) w-velocity field from PIV for 𝛼 = [0
o
, 2
o
, 4
o
, 6
o
, 8
o
, 10
o
]

65

Figure 5.5: a) u = 0 m/s contour b) separation streamline positions (PIV and DNS streamlines at
𝛼 = 4
o
are marked by blue and purple diamonds respectively), and c) boundary layer separation
angles. 𝑥
<
runs parallel to the airfoil chord and is measured from the leading edge and 𝑧
P,M
is
perpendicular to the airfoil chord and is measured from the airfoil surface.

The streamline patterns around the airfoil, calculated using time-averaged PIV velocity
fields, can be found in figure 5.6. The evolution of two, time-averaged vortices in the separated
flow region can be seen as 𝛼 increases from 0
o
to 10
o
. When 𝛼 = 0
o
, the core of a large clockwise
rotating vortex (v1) is located above the core of a smaller counterclockwise rotating vortex (v2)
near the trailing edge of the airfoil in the separated region. When 𝛼 is increased to 2
o
, v1 moves
forward while v2 remains directly off the trailing edge. As 𝛼 is increased to 6
o
, the core of v2
slowly moves away from the trailing edge while v1 remains in approximately the same location.
The more rapid growth of the recirculating region after 𝛼 = 8
o
is accompanied by a change in the
relative positions of v1 and v2, when the core of v1 moves up and aft of the trailing edge, so that
66
it is again above the core of v2, which is being stretched. As 𝛼 increases to 10
o
and the roll-up of
the separated shear layer moves upstream, v2 grows significantly and becomes more rounded, and
its core again drifts back over the trailing edge of the airfoil.
The region of slowly recirculating fluid under the separated shear layer grows with an
increase in 𝛼 and has a cross section that has approximately the size and thickness of the airfoil by
𝛼 = 8
o
. The global flow field can be thought of as being induced by an effective airfoil shape,
which is made up of both the airfoil and this slow recirculating region where viscous forces are
significant. This effective airfoil shape deflects the streamlines of the outer flow, which behaves
as if it were inviscid. The effective airfoil shape has been approximated with a blue curve for 𝛼 =
10
o
in figure 5.6. The changes in the effective airfoil shape (and the effective camber) with 𝛼 lead
to changes in lift and drag curve behavior. The most abrupt change in the effective airfoil shape
occurs when the separated boundary layer reattaches to form an LSB at 𝛼
?Ba
. This abrupt change
results in the abrupt jump in lift and drag curves. Large, recirculating regions generally do not
form behind airfoils at high Re, where the effective airfoil shape is made up almost entirely of the
airfoil and does not change significantly with 𝛼. This is why the changes in slope and large jumps
in the lift curve commonly seen at the lower Re are not seen at the high Re, where the lift curve
instead generally has a constant slope until stall.
The fact that the outer streamline patterns are heavily influenced by the shape of the large,
recirculating region renders the shape of the airfoil essentially useless – it is no longer redirecting
the air in the way that it was designed to. In order for the airfoil to behave as it was designed to,
boundary layer separation must be minimized as much as possible. An effective closed loop control
system will do just this.

67

Figure 5.6: Streamline patterns for 𝛼 = [0
o
, 2
o
, 4
o
, 6
o
, 8
o
, 10
o
]

At 𝛼 = 4
o
, both the PIV and DNS show that the airfoil has not yet reached 𝛼
?Ba
. Velocity
and vorticity profiles over the suction surface of the airfoil and in the wake from both sets of data
have been plotted together in figures 5.7 and 5.8. Although the resolution of the PIV does not allow
for good comparisons of the boundary layer before mid-chord, it appears that both sets of data
show boundary layer separation at approximately the minimum pressure location (~0.5c, identified
from DNS) on the suction side of the airfoil. The boundary layer thickness grows faster and the
peak vorticity value moves away from the airfoil surface faster as the trailing edge is approached
for the DNS profiles, agreeing with the finding that the boundary layer separation angle is slightly
68
larger for the DNS (see figure 5.5c). There is less agreement in the wake of the airfoil, where the
momentum deficit appears to be larger for the DNS, and where the DNS wake is shifted slightly
upward, due to the larger separation angle at the airfoil surface, indicating that the DNS airfoil is
experiencing more drag and producing less downwash (and therefore less lift). However, these
differences do not appear to be dynamically significant, and the time-averaged lift and drag forces
from the DNS agree with force balance measurements at this 𝛼 within measurement uncertainty,
as was noted in the previous section.

Figure 5.7: u-profile (top) and 𝜔
w
-profile (bottom) comparison between DNS and PIV over the
suction surface at 𝛼 = 4
o
. 𝑥
<
runs parallel to the airfoil chord and is measured from the leading
edge and 𝑧
P,M
is perpendicular to the airfoil chord and is measured from the airfoil surface.

69

Figure 5.8: u-profile (top) and 𝜔
w
-profile (bottom) comparison between DNS and PIV in the
wake at 𝛼 = 4
o
. 𝑥
<
runs parallel to the airfoil chord and is measured from the leading edge and
𝑧
P,M
is perpendicular to the airfoil chord and is measured from the chord line extended into the
wake.

5.1.3 Time-averaged PIV: 𝛼 =

𝛼
?Ba

Although the lift and drag curves in figure 5.1 show 8.5
o
< 𝛼
?Ba
≤

9
o
for the experimental
NACA 65(1)-412 at Re = 2 × 10
4
, time-averaged PIV flow fields plotted in figure 5.9 show 10
o
<
𝛼
?Ba
≤

10.1
o
. The difference is at least in part due to the fact that the PIV data were generated with
the AR = 3 model, while the force balance data were generated with the AR = 12.9 model (both
positioned between endplates). Ideally, the AR of the model would not impact 𝛼
?Ba
as the purpose
of the endplates is to eliminate three-dimensional flows at the wing tips, allowing a three-
dimensional wing to behave like a two-dimensional airfoil. However, time-averaged force balance
70
data for both wings at Re = 4 × 10
4
(chosen so that both wings would generate forces in the
appropriate range for the force balance used) in figure 5.10 show that there were several differences
between the curves from the different AR wings. The wing with the smaller AR had a smaller 𝑐
',)

before 𝛼
?Ba
, a more negative 𝛼
#$%
, and a later 𝛼
?Ba
. The large uncertainty in the lift and drag
curves for the AR = 12.9 wing at 𝛼 = 7
o
is due to the fact that the wing experiences hysteresis at
this 𝛼 for Re = 4 × 10
4
, where it is switching between lift states. This hysteresis can be seen in
figure 5.11, where data from forward and backward sweeps have been separated. No hysteresis is
seen for the smaller AR wing, consistent with the findings of Marchman et al. (1998), who noted
a significant reduction in hysteresis near stall for a cantilevered wing with a decrease in AR from
2 to 1.

Figure 5.9: Time-averaged streamline patterns for α = 10
o
and 10.1
o

71

Figure 5.10: Time-averaged experimental a) 𝑐
'
𝛼 and b) 𝑐
g
𝛼 curves for the NACA 65(1)-412
airfoil at Re = 4×10
4
. The blue curve shows the results for an AR = 12.9 wing, the black curve
shows the result for the AR = 3 wing

Figure 5.11: A hysteresis loop is visible in the AR = 12.9 NACA 65(1)-412 𝑐
'
𝛼 curve between
6.5
o
< 𝛼 < 7.5
o
at Re = 4×10
4

72
The difficulties of using endplates to approximate a two-dimensional geometry at low Re
has been discussed in section 2.1.3. Huang et al. (1995) found that the presence of a wall at one
wingtip would alter the flow field up to one chord length away from the wall when there was
laminar separation without reattachment over a NACA 0012 at Re = 8 × 10
4
. It is clear from the
illustrations of the surface oil patterns in the same study that the influence of the wall is felt up to
one chord length away when an LSB is formed as well. If the same held true for the current tests,
the flow over a much more significant portion of the AR = 3 wing would be impacted by the
presence of endplates compared to the AR = 12.9 wing. Obviously, the AR = 3 wing between
endplates would be a far worse approximation of a two-dimensional geometry, which would
explain the differences seen in the lift curves in figure 5.10. This would call into question force
balance data from the low AR wing. Although the force balance measures the integrated force over
the entire model, PIV data is only taken at the mid-span location, where the flow remains largely
two-dimensional (assuming the “wall effect” extends no more than one chord length away from
the wall and AR ≳ 2.5). This is not to say, however, that the shear layer roll-up location in this
largely two-dimensional flow region near mid-span is not affected by the “wall effect”, and in fact,
the differences in 𝛼
?Ba
suggest that, when AR = 3, it is. The fact that 𝛼
?Ba
appears to be delayed
when the wall effect is more prominent may also explain the difference between the force balance
and DNS values at Re = 4 × 10
4
, as wall effects are present in the force balance tests but not in the
DNS.

5.1.4 Time-averaged PIV: : 𝛼 >

𝛼
?Ba

The evolution of the LSB over the model for 𝛼 >

𝛼
?Ba
can be seen in the time-averaged
PIV streamline plots in figure 5.12. Between 10
o
< 𝛼 < 10.1
o
the boundary layer abruptly reattaches
to form the LSB over the middle third of the airfoil. The bubble then moves forward with an
increase in 𝛼 until it reaches the leading edge at approximately 𝛼 = 10.4
o
. The bubble thickness
decreases significantly directly after it forms, but increases again as it moves forward.

73

Figure 5.12: Time-averaged streamline results from PIV. The thinner bubbles may extend further
upstream, even if it is not evident in these images, due to the limited resolution of the PIV.

The boundary layer separation angle and the shear layer roll-up location vary with time, to
some degree, at all of the 𝛼 >

𝛼
?Ba
. This is especially noticeable for 𝛼 = 10.2
o
and 10.3
o
, where
the time-averaged bubble is thin and moving forward over the airfoil surface rapidly with
74
increasing 𝛼. A large separation angle and early shear layer roll-up, like that seen at 𝛼 = 10.5
o
in
figure 5.13, are associated with shorter, thicker bubbles near the leading edge. A small separation
angle and later shear layer roll-up like that seen at 𝛼 = 10.1
o
in figure 5.13, are associated with
longer, thinner bubbles located further aft. It appears that a separated shear layer that travels further
away from the airfoil surface tends to transition earlier. This is consistent with the findings of
Marxen & Henningson (2011), who noted that changes in the distance of the shear layer from the
wall can change the stability characteristics of an LSB that forms over a flat plate. Specifically,
they found that a shear layer that was further from the wall had larger disturbance amplification
rates due to a decrease in viscous damping. In general, larger amplification rates lead to earlier
vortex roll-up. Examples of a small separation angle with late transition location and a large
separation angle with early transition can both be found at different instances for 𝛼 = 10.3
o
, as seen
in figure 5.14. Variations in bubble length (i.e. roll-up location) and thickness at a single 𝛼 with
time is often referred to as bubble flapping.

Figure 5.13: A small boundary layer separation angle and late transition location is seen in the
instantaneous u-velocity field at 𝛼 = 10.1
o
, and a large boundary layer separation angle and early
transition location is seen in the instantaneous u-velocity field at α = 10.5
o

75

Figure 5.14: A small boundary layer separation angle and late transition location (time t = 1.1s)
and a large boundary layer separation angle and early transition location (time t = 4.0s) are both
seen in separate instantaneous u-velocity fields at α = 10.3
o
. (time t = 0.0s is associated with the
first instantaneous field of the 1000 instantaneous fields taken at this α)

Similar to the experimental data, the DNS shows a thin bubble initially forming behind the
mid-chord point and then moving forward until becoming fixed at the leading edge. DNS
streamlines can be found in figure 5.15. The size, location, and shape of the DNS bubbles at 𝛼 =
8
o
and 10
o
is similar to that for experiments at 𝛼 = 10.1
o
and 10.4
o
respectively. The 𝛼 at which
the thin bubble forms is earlier for the DNS, as was predicted based on the time-averaged force
coefficients.

76

Figure 5.15: DNS streamlines for 𝛼 = 8
o
(top) and 𝛼 = 10
o
(bottom)

5.1.5 Water channel flow visualization: boundary layer behavior

Dye was injected into the boundary layer of the water channel wing in order to identify the
boundary layer separation point as well as the rollup location of the separated shear layer. As
pointed out by Taneda (1977), streakline data, which is generated in dye injection tests, is valuable
because “the point at which the streakline is separated from the wall is thought to be a meaningful
definition of the separation point”. Streaklines do not change according to reference frame (unlike
streamlines), and streaklines injected into the boundary layer are a useful tool to track vorticity, as
all vorticity in the flow field around an airfoil is generated at the surface of the airfoil.
Three distinct types of flow field were identified in the analysis of instantaneous PIV and
dye injection images: type 1) laminar separation with vortex rollup beginning after the trailing
edge, type 2) laminar separation with vortex rollup beginning before the trailing edge but no
reattachment, and type 3) laminar separation with reattachment. The forward movement of the
shear layer roll-up location with an increase in 𝛼 indicates that the separated shear layer is
becoming increasingly unstable. This agrees with the findings of Boutilier & Yarusevych (2012b),
which showed that the disturbance amplification rates in the separated shear layer increase with 𝛼.
Flow fields of type 1 and 2 occur before 𝛼
?Ba
, whereas type 3 occurs after 𝛼
?Ba
. Examples of time-
averaged and instantaneous flow fields of type 1, 2, and 3 can be found in the top, middle, and
bottom row respectively of figure 5.16. Note that the same field of view is shown for both PIV and
dye injection images. PIV and dye injection images of the same flow type look very similar, and
77
the separation locations and angles are nearly identical when both sets of image show type 1 flow
fields over the airfoil at the same (low) 𝛼. The main difference between PIV and dye injection
images is that the dye injection images show a transition from flow field type 1 to type 2 and from
flow field type 2 to type 3 at smaller 𝛼. Type 1 and type 3 flow fields can also be seen over a
NACA 66(3)-018 airfoil at Re = 4 × 10
4
before and after the 𝛼
?Ba
respectively, where 𝛼
?Ba
was
identified from force balance measurements in in smoke wire flow visualization tests by Mueller
& Batill (1982).

Figure 5.16: a) time-averaged 𝜔
w
from PIV, b) instantaneous 𝜔
w
from PIV, c) time-averaged and
d) instantaneous dye flow visualization images for 𝛼

= 𝛼

= 4
o
(top), 𝛼

= 9
o
𝛼

= 6
o

(middle), and 𝛼

= 𝛼

= 11
o
(bottom).

78
Analysis of dye injection videos and images revealed a steady separation location when 𝛼
is held constant. The slowly recirculating flow under the laminar portion of the separated boundary
layer is relatively steady in type 1 and type 2 flow fields, and appears very similar to the time-
averaged streamlines in the same region in figure 5.6. A switch from a type 2 flow field to a type
3 flow field with an LSB near the leading edge occurred with just a 0.5
o
increase in 𝛼 (the smallest
allowable increment of the 𝛼 – setting device). This agrees with the 𝛼 – range over which the LSB
forms and moves to the leading edge in the time-averaged PIV images in figure 5.12.
Although both the wing used for PIV and the wing used for the dye injection tests have
approximately the same AR, the 𝛼
?Ba
value found in the water channel tests was approximately
1.5
o
lower than that observed in PIV tests. This is not surprising, as the turbulence levels in the
water channel were approximately two orders of magnitude larger than those in the wind tunnel.
Larger fluctuations in the flow field, whether they are caused by artificial forcing or a more
turbulent free stream, as is the case here, can lead to an earlier shear layer roll-up and transition to
turbulence. This has been shown by Istvan & Yarusevych (2018), who found that the mean
transition location in an LSB, which corresponds to the location of shear layer roll-up, moves
upstream when T was increased due to the larger initial amplitude of disturbances (as opposed to
increased amplification rates). In addition, both Istvan & Yarusevych (2018) and Hosseinverdi &
Fasel (2015) found streamwise streaks developing upstream of an LSB when T was > 0.5%, which
interact with the Kelvin-Helmholtz instability during transition, resulting in less spanwise
coherence in the shear layer roll-up vortices. The earlier roll-up may increase mixing while the
shear layer is nearer to the airfoil surface, causing an earlier boundary layer reattachment. In fact,
Mueller et al. (1983) found just this while investigating hysteresis in the lift and drag curves of an
airfoil at Re = 1.5 × 10
5
. It was shown that, when T was minimized, an airfoil that had stalled
while 𝛼 was increasing would remain stalled even when 𝛼 was reduced past the original stall angle.
However, when T was increased, the stall angle observed in backwards sweeps increased, moving
it closer to the value observed in forward sweeps and reducing the amount of hysteresis. The
reduction in hysteresis was linked to the extreme sensitivity of the boundary layer to free stream
disturbances – larger turbulence intensities would lead to an earlier roll-up of the separated shear
layer, which would in turn allow for boundary layer reattachment at a higher 𝛼 during backward
sweeps. This is analogous to what is believed to be happening in the current study; an increase in
T causes a separated boundary layer to reattach, increasing lift and decreasing drag. Marchman et
79
al. (1986) found a similar result to Mueller et al. (1983), and pointed out that lift and drag curves
are more sensitive to T as Re decreases.

5.1.6 Water channel flow visualization: wake vortex shedding

The shedding of vortices into the wake of the airfoil can produce noise and leads to
unsteady lift and drag forces on the wing, which are important to consider from a structural point
of view when designing an aircraft. The wake of the wing will also dictate the flow over any
downstream objects, which could include propellers or vertical and horizontal stabilizers. The
dependence of the wake vortex shedding frequency, 𝑓

(not to be confused with the shear layer
shedding frequency, 𝑓
M
), expressed as the non-dimensional Strouhal number 𝑆𝑡 =
v

1
was
measured using wake images from seven tests and can be found in figure 5.17. St remains between
3 and 3.3 for 0
o
< 𝛼 < 3.5
o
, before dropping to approximately 2.6 by 𝛼 = 4.5
o
. At 𝛼 = 5
o
, St jumps
back to approximately 3.25 and remains nearly constant until 𝛼 = 8
o
. Reliable measurements at
higher 𝛼 could not be made because of the formation of an LSB after 𝛼 = 8
o
, which greatly
increases the diffusion of dye before the trailing edge due to the increased mixing in the turbulent
boundary layer after reattachment. One data point each from 𝛼 = 6
o
, 6.5
o
, and 7
o
was found to be
between 1.5 and 1.62, which is approximately half the value measured from all other tests.
Prominent peaks at these lower frequencies may be due to frequent vortex pairing for these
individual tests.
The shedding of vortices into the wake of the airfoil causes oscillations in lift and drag
forces, and so St can be estimated based on DNS force time traces. At 𝛼 = 0
o
and 4
o
, the St
estimated in this way from two-dimensional DNS falls within the bounds of the experimental data.
At 𝛼 = 6
o
, DNS gives St = 1.9, which is significantly lower than most experimental measurements,
and lies near a straight line extrapolated from the experimental data for 𝛼 = 3.5
o
, 4
o
, and 4.5
o
. The
differences between the St from experiments and DNS at this 𝛼 may be due to the fact that the
variations in force are caused by vortex behavior at the trailing edge. At 𝛼 = 6
o
, the roll-up location
of the separated shear layer has moved upstream of the trailing edge, and this vortex behavior may
change rapidly as the vortices shed from the shear layer move into the wake. At higher 𝛼 where
DNS data was generated, the flow states from the simulations and experiments differ, and therefore
no fair comparisons can be made.
80

Figure 5.17: St variation with 𝛼

The abrupt jump in St between 𝛼 = 4.5
o
and 5
o
roughly coincides with the vortex roll-up
location moving upstream of the trailing edge, which occurs at approximately 𝛼 = 5.5
o
(note that
the estimated uncertainty in 𝛼 is 0.5
o
). This suggests that the jump in St may be due to a wake
instability being replaced by a separated shear layer instability as the dominant instability mode
that leads to wake vortex shedding. However, several points should be kept in mind when
interpreting the current data. First, an upstream perturbation of the dye filament can create a pattern
in the filament that persists far downstream, even after the initial perturbation has died out. This
means that patterns in the wake can be contaminated with the signatures of structures that may no
longer exist, such as roll-up vortices that form over the airfoil surface. Second, it is unknown how
large the vortex formation region is in the wake, and making measurements within this region may
impact the data. Yarusevych et al. (2006,2009) identify a wake formation region of 1 ≤ x/c ≤ 1.8
for a NACA 0025 airfoil at 𝛼 = 5
o
and Re = 10
5
, which corresponds to a flow field with a separated
boundary layer without reattachment. The end of the formation region was defined as the
streamwise location with the largest wake vortex-associated peak in a hot-wire frequency
spectrum. The same studies found evidence of the persistence of vortices shed from the shear layer
in hot-wire frequency spectra as far downstream as x/c = 1.5 at 5.5 × 10
4
, although the peak
associated with the wake vortices is clearly dominant by x/c = 1.25. All measurements in the
81
current study were made for x/c ≤ 1.8 to minimize dye diffusion and to assure that the endplate
extended over the measurement region. This was important because there was a sudden, significant
deformation of vortices once they moved downstream of the endplate. Finally, the diffusion of dye
as the wake becomes more turbulent makes it harder to make accurate measurements using the
current methods. This problem is more pronounced at higher 𝛼. A more detailed study using wake
and boundary layer hot-wire measurements is suggested to further investigate the instabilities that
lead to the vortex shedding in the wake.
Few studies have examined how 𝑓

varies with 𝛼 for airfoils at low Re. It has been shown
that for Re > 5 × 10
4
, shear layer roll-up vortices, which are shed at a higher frequency than the
wake vortices, generally break down before reaching the trailing edge, and vortices shed into the
wake form due to a global instability in the near wake region (Yarusevych et al., 2006,2009).
However, in the current study, the Re is low enough so that the boundary layer remains separated
until a relatively high 𝛼, and shear layer roll-up was not observed before the trailing edge for 𝛼 <
5.5
o
. This almost certainly leads to significant interaction between the separated shear layer or the
shear layer roll-up vortices (depending on 𝛼) with the wake. Huang & Lin (1995) investigated
vortex shedding behind a cantilevered wing at Re as low as 10
4
, and found that 𝑓

decreases with
increasing 𝛼 at a given Re, although the change in 𝑓

with 𝛼 is less significant at smaller Re.
However, this same trend could not be clearly seen in the data presented by Yarusevych et al.
(2009), where 𝑓

increases approximately linearly with Re, with the slope of the curve increasing
significantly after an LSB forms.
It is common to define the Strouhal number using the length of the airfoil projected in the
cross-stream plane, d, as the characteristic length scale: 𝑆𝑡
c
=
v

g
1
. For a NACA 0012 at Re = 2
× 10
4
, Huang & Lin (1995) found that 𝑆𝑡
c
fell between approximately 0.3 and 0.45 at small 𝛼 (0
o
,
2
o
, 5
o
). This matches closely with the 𝑆𝑡
c
range seen in the current study (~ 0.29 - 0.39), where
the thickness of the airfoil was the same. Yarusevych et al. (2006) found little variation in 𝑆𝑡
c

with Re for a single 𝛼 when the boundary layer remains separated, as can be seen in figure 5.18
taken from Yarusevych et al. (2006) which also includes data from Huang & Lin (1995). A large
jump in 𝑆𝑡
c
can be seen when an LSB forms after Re = 1.4 × 10
5
. The same study noted that
thinner airfoils produced higher 𝑆𝑡
c
(~0.2 - 0.3 for NACA 0025 vs. ~0.25 - 0.375 for NACA 0012
for 2 × 10
4
< Re < 1.4 × 10
5
, 𝛼 = 5
o
). Huang & Lee (2000) found that 𝑆𝑡
c
did not vary significantly
82
with 𝛼 for a given 𝑅𝑒
g
=
1g

when there was laminar separation without roll-up before the trailing
edge (~ 0.38 for a NACA 0012 at 𝛼 = [0
o
, 2
o
, 3
o
, 3.75
o
] and the mean 𝑅𝑒
g
of the current test), and
then dropped when roll-up occurred before the trailing edge. Neither of these trends are seen in
the current data.

Figure 5.18: Variations in 𝑆𝑡
c
with Re for a NACA 0025 (“Wake data”) and a NACA 0012
(“Huang & Lin”) at 𝛼 = 5
o
(Yarusevych et al., 2006)

Several studies have also nondimensionalized 𝑓

using the Roshko number 𝐹

=
v

g

,
which is a product of 𝑅𝑒
g
and 𝑆𝑡
c
. Yarusevych et al. (2006) found that 𝐹

varies linearly with Re,
with the slope depending on whether or not an LSB has formed. However, Yarusevych & Boutilier
(2011) found the the slope of the curves depend on airfoil geometry.
Although 𝑓

has been shown to vary with Re, with the dependence on Re increasing
significantly when an LSB forms, Yarusevych et al. (2009) found that using the wake thickness,
defined as the distance between peaks in the rms-velocity profiles, as the characteristic length scale
collapsed the nondimensionalized 𝑓

data for a NACA 0025 at 𝛼 = [0
o
, 5
o
, 10
o
] to approximately
0.17 for 5.5 × 10
4
< Re < 2.1 × 10
5
, regardless of whether or not an LSB has formed. Yarusevych
& Boutilier (2011) applied this same scaling to data for a NACA 0018 at 𝛼 = 10
o
and found a
collapse to approximately the same value (~ 0.18) for the same Re range. This suggests that a
83
measure of the wake thickness would be more appropriate scaling length than the airfoil chord. It
would also explain the large jump in 𝑆𝑡
c
seen when an LSB forms (which increases 𝑓

while
decreasing wake thickness dramatically), as well as the fact that Yarusevych et al. (2006) found a
thinner airfoil, which will generally produce a thinner wakes, had slightly higher 𝑆𝑡
c
. The
relatively small variation in 𝑆𝑡
c
with Re when there is laminar separation without reattachment
can now be explained by the fact that d is a decent approximation for the wake width in this flow
state. It can then be concluded that, by preventing significant boundary layer separation that leads
to thick wakes before 𝛼
?Ba
, a flow controller will increase 𝑓

at low 𝛼 and prevent abrupt jumps
in the shedding frequency caused by sudden boundary layer reattachment at 𝛼
?Ba
.

5.2 Increasing Re
The close agreement between DNS and experiments at Re = 2×10
4
and 𝛼 = [4
o
, 10
o
], along
with the similarities in the evolution of the LSB with increasing 𝛼 after 𝛼
?Ba
found in the previous
section, give confidence in the ability of the DNS to accurately simulate the flow. It is therefore
appropriate to use the high resolution data generated by the DNS to design a closed loop flow
control system. Gerakopulos & Yarusevych (2012) and Boutilier & Yarusevych (2012a) have
shown that pressure sensors can be used as a substitute for hot-wires to measure velocity
fluctuations near the airfoil surface, and can therefore be used to identify stability characteristics
of the separated shear layer. The same studies showed that the time-resolved pressure
measurements could also be used to determine whether or not the boundary layer reattaches and
to estimate the location and size of the LSB if it does. The current flow control system may feed
similar time resolved surface pressure measurements from an array of sensors along the chord of
the wing into physics-based reduced Navier-Stokes (RNS) models or data driven models in order
to determine the most appropriate forcing frequency and location in real time. Taira et al. (2017)
and Rowley & Dawson (2017) give two recent reviews of modeling techniques for fluid flow
control purposes that may prove useful for this application. However, the small variations in the
static pressure generated over the airfoil chord at the Re of the DNS present a problem for pressure
measurements if both time-averaged pressure distributions and time-resolved fluctuations are
needed.
Ideally, the pressure sensors should be small enough to fit inside the wing and have a
response time that is quick enough to make at least 10 measurements per convective time unit. The
84
minimum chord length of the wing used to test the flow control system will be limited to
approximately 10 cm by the fact that the wing must be large enough to fit sensors and acoustic
actuators inside. Because of this, the free stream velocity will need to be less than or equal to 3.05
m/s to achieve a Re = 2×10
4
. This limits the magnitude of the variations in surface pressure in both
time and space over the wing to levels that can not be measured accurately using any pressure
sensors known to the author that have an appropriate size and response time. Increasing the Re of
the DNS to a value that would allow for accurate wind tunnel pressure measurements would be
too computationally expensive. However, if the flow controller works at the design Re (2 × 10
4
),
then it may be reasonable to expect that the same controller, possibly with some minor
modifications, will work at higher Re where the wing still experiences laminar separation without
reattachment at moderate 𝛼. That is, the flow control models may still be useful at a higher Re that
would allow for accurate pressure measurements if the flow over the wing at that Re is qualitatively
similar to the flow that the control models are based on. After all, any useful control system will
need to work for a range of Re, as real world flying devices do not always fly at the same speed.
Wind tunnel tests of the closed loop flow control system could then be performed at a higher Re
that produces measureable pressure values.
Insight into the behavior of the flow can be drawn from time-averaged force data. It has
been shown that at Re = 2 × 10
4
, the NACA 65(1)-412 has a lift curve with an abrupt increase in
lift accompanied by a sharp decrease in drag at an 𝛼
?Ba
, indicating that the flow remains separated
at low 𝛼 before suddenly reattaching to form an LSB at higher 𝛼. Force balance tests were
conducted at 2 × 10
4
< Re < 9 × 10
4
in order to determine if there are significant qualitative changes
in this airfoil behavior with increasing Re that would indicate significant changes in the flow field
evolution.

5.2.1 Change in 𝛼
#$%
and 𝑐
',)

As was previously noted, 𝛼
#$%
is greater than zero for Re = 2 × 10
4
. As all cambered airfoils
generate positive lift at 𝛼 = 0
o
at high Re, this implies that 𝛼
#$%
(Re) for some low Re range. In
order to better understand this relationship, 𝑐
'
𝛼 curves were generated for Re = [2, 3, 4, 5] × 10
4

at small 𝛼 using the AR = 12.9 wing. All Re were tested on the same day, using the same calibration
matrix, and without altering the test setup between tests. Figure 5.19 shows that 𝛼
#$%
shifts nearly
85
a full degree to the left as Re increases from 2 × 10
4
to 5 × 10
4
. 𝛼
#$%
is most sensitive to Re between
3 × 10
4
< Re < 4 × 10
4
, and the Re where 𝛼
#$%
= 0 also falls in this Re range. The average 𝛼
#$%

from three different tests for each Re can be found in figure 5.21a. The shift in 𝛼
#$%
is most likely
due to the dependence of the separation location over the suction surface of the airfoil on Re, as
lift generation is sensitive to this parameter. The separation location is expected to move
downstream with an increase in Re, decreasing the size of the recirculating region behind the
airfoil. This will change the effective airfoil shape, and therefore the effective camber, which will
change 𝛼
#$%
. As previously noted, endplate effects have also been shown to impact 𝛼
#$%
, although
these effects are expected to be small in the current tests due to the large AR of the wing used, and
are therefore not believed to be the cause of the trend in figure 5.19.

Figure 5.19: 𝑐
'
𝛼 for Re = [2, 3, 4, 5] × 10
4
at small 𝛼

It is clear from figure 5.19 that 𝑐
',)
at low 𝛼 is also a function of Re. To better illustrate the
change in 𝑐
',)
with Re, all of the curves have been shifted so that they pass through the origin in
figure 5.20. There is a noticeable increase in 𝑐
',)
with Re, and 𝑐
',)
for each Re, estimated with a
linear least squares fit and averaged over three tests, can be found in figure 5.21b. The averaged
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
c
l
α [
o
]
Re = 20k
Re = 30k
Re = 40k
Re = 50k
86
𝑐
',)
values match or exceed the thin airfoil theory result of 2π for all of the Re tested. Once again,
this change in airfoil can be attributed to changes in the effective airfoil shape at a given 𝛼 with
changes in Re.

Figure 5.20: 𝑐
'
𝛼 curves shifted to illustrate change in 𝑐
',)
with Re

a) b)
Figure 5.21: a) 𝛼
#$%
and b) 𝑐
',)
data for Re = [2, 3, 4, 5] × 10
4
at small α

-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
-0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60
c
l
α-α
L=0
[
o
]
Re = 20k
Re = 30k
Re = 40k
Re = 50k
87
5.2.2 Re = 5 × 10
4
– 9 × 10
4

Because of the limitations of the Dryden Wind Tunnel force balance, the AR = 3 wing, used
for PIV tests, was used to generate time-averaged force balance data when the Re was increased
above 4 × 10
4
. It was shown in section 5.1.3 that despite small changes in 𝑐
',)
, 𝛼
#$%
, and 𝛼
?Ba
,
and the elimination of the hysteresis loop, time-averaged force balance results generated with the
AR = 3 wing are qualitatively similar to those generated with the AR = 12.9 wing, justifying the
use of the smaller AR model.
Force balance tests were carried out for Re = [5, 6, 7, 8, 9] × 10
4
. The resulting lift and drag
data are plotted in figure 5.22, and the drag polar data are plotted in figure 5.23. There are several
clear patterns in the data. 𝛼
#$%
shifts left as Re increases, as was seen for Re = 2 × 10
4
– 5 × 10
4

in the previous section. 𝛼
?Ba
shifts left as Re increases, due to larger amplification rates in the
separated shear layer at higher Re (Boutilier & Yarusevych, 2012b), which will lead to earlier
shear layer roll-up and therefore earlier boundary layer reattachment. Lift and drag data for all Re
agree once the high lift state is reached. 𝑐
',)
remains relatively constant as Re changes: 0.084 <
𝑐
',)
< 0.089 for -5
o
< 𝛼 < 4
o
when a linear least squares fit is applied to the data. A prominent kink
in the lift curve between -2
o
< α < -1
o
is present for Re = 5 × 10
4
and 8 × 10
4
, but it is not clear
what the cause of this is, and the kink is in opposite directions for the two Re. A similar kink is
present in the lift curve of the AR = 12.9 wing at Re = 4 × 10
4
and 2 × 10
4
. The average 𝑐
g,nBP

decreases as Re increases, as is expected, because the separated region behind the airfoil should
shrink with increasing Re. 𝑐
g,nBP
shifts from approximately 𝛼 = -1
o
at Re = 5 × 10
4
to α = -2.5
o
at
Re = 6 × 10
4
, then remains at this 𝛼 as Re is increased further to 9 × 10
4
, however the uncertainty
for the drag measurements is large, making it difficult to draw any definite conclusions with regard
to 𝑐
g,nBP
. The jump to higher lift is accompanied by a jump to a lower drag value that clearly
occurs at lower 𝛼 as Re increases.
The jump to the high lift state becomes more gradual as Re is increased. An explanation
for this is suggested that has to do with the size of the hole in the bottom endplate. The larger wing
deflection at the higher Re, where forces on the model were larger, necessitated a larger hole in
the bottom endplate. Previous tests on the AR = 12.9 wing showed a similar, more gradual jump
to the high lift state when the size of the endplate hole was not minimized. A larger hole allows
88
more air to leak from the pressure to the suction surface of the wing, which can alter the flow near
the bottom endplate, possibly causing early boundary layer reattachment in this region. This means
the flow does not suddenly reattach at the same α along the entire span at larger Re. As the force
balance measures the integrated force over the entire model, this will make the jump to the high
lift/low drag state appear less sudden. Using a larger AR wing would reduce the relative effective
of this leakage, but the forces generated by a wing increase with AR, so a stiffer force balance that
allows for less deflection will need to be used for future tests at the higher Re. Despite this, figure
5.22 still appears to shows two distinct lift and drag states at all Re tested.

Figure 5.22: a) 𝑐
'
𝛼 and b) 𝑐
g
𝛼 curves for NACA 65(1)-412 as Re is increased from 5×10
4
to
9×10
4

89

Figure 5.23: 𝑐
'
𝑐
g
for NACA 65(1)-412 as Re is increased from 5×10
4
to 9×10
4

The data presented here have shown that, although the three-dimensional flows at the wing
tips most likely alter some characteristics of lift and drag curves for low AR wings, they do not
change the fact that there are two lift/drag states at Re = 2 × 10
4
– 9 × 10
4
. Switching between the
two lift states has been shown to occur naturally at some Re-dependent 𝛼
?Ba
(or range of 𝛼 for
low AR wings) for the entire Re range investigated, and it is believed that applying acoustic forcing
may be effective in reducing this 𝛼
?Ba
value. Although the force balance data are altered by the
three-dimensional flow near the wing tips, Boutilier & Yarusevych (2012c) and Mueller & Batill
(1980) have shown that the flow over the center portion of wings of AR = 2 and 1.6 respectively
is largely uniform when endplates are used. Therefore, this portion of the flow should behave as a
flow control model based on DNS predicts. This is supported by the fact that at Re = 2 × 10
4
and
at 𝛼 = 4
o
, the PIV flow fields from the mid-span location of the AR = 3 wing were shown to match
well with the two-dimensional DNS flow fields in section 5.1.2. All flow control sensors and
actuators should then be placed near the center span of the model. If acoustic forcing can switch
the flow over the center of the wing from the low lift state to the high lift state, it should create a
measurable improvement in the airfoil performance, thus proving the effectiveness of the control
system being tested. Therefore, if the current force balance is used, it is proposed that force balance
testing of future flow control systems is carried out at Re = 9 × 10
4
with an AR = 3 wing. A wing
90
with c = 10 cm and b = 30 cm would produce a maximum aerodynamic force of ~3.9 N. A second
option would be to use a new, stiffer force balance that can handle larger forces and can therefore
be used with a larger AR wing. If an AR = 13 is used (c = 10 cm, b = 130 cm), the maximum axial
and normal forces measured with the force balance will be approximately 17 N and 1.5 N
respectively.
91
6 Conclusions

The aim of this study was to gain a better understanding of the boundary layer behaviors
over airfoils at low Re and their impact on performance, and to compare experiments to
computations in an effort to determine whether agreement can be found, and if it can not, why. A
better understanding of boundary layer behavior will lead to the development of more effective
flow control methods, and knowing when experiments and computations can be expected to agree,
and why they sometimes do not, will eventually lead to more confident design decisions based on
computations. Therefore, the two main objectives of the work were to 1) experimentally
investigate the aerodynamic performance and boundary layer behavior of the NACA 0012 and
NACA 65(1)-412, at Re = 5 × 10
4
and Re = 2 × 10
4
- 9 × 10
4
respectively, in the low turbulence
Dryden Wind Tunnel and the USC water channel using force balance measurements, time-
averaged PIV, and dye-injection flow visualization, and 2) compare the experimental data for the
NACA 65(1)-412 with DNS that will be used to develop a closed loop flow control system to
improve the performance of airfoils at low Re.

6.1 NACA 0012

A Re of 5 × 10
4
was chosen for the NACA 0012 tests so that comparisons could be made
with existing DNS data in the literature. Time-averaged force measurements revealed several
regions of nearly constant slope in the lift curve, and lift values that exceed the inviscid thin airfoil
theory prediction at several 𝛼, whereas the drag curve had a shape similar to that of symmetric
airfoils at higher Re. Distinct regions in the lift curve were linked to boundary layer behaviors
using time-averaged PIV. Most notably, negative lift values found at small, positive 𝛼 were linked
to boundary layer separation locations over the top and bottom surface of the airfoil that lead to an
effective negative camber. It is believed that similar behavior will generally be found for other
thick, symmetric airfoils at low Re and 𝛼. An LSB was found at several 𝛼 where the lift exceeded
the thin airfoil theory prediction, demonstrating how an LSB can increase airfoil lift at low Re by
changing the effective airfoil shape. The lift and drag curves were compared with existing
experiments and computations in the literature, and very little agreement was found, as is common
92
at low Re. As the experimental measurements presented here were made using a low T wind tunnel,
sensitive force balance, and high AR model that are all well suited for low Re testing, they can
serve as a baseline that can be compared to future experimental and computational data sets.

6.2 NACA 65(1)-412

The NACA 65(1)-412 was tested at a Re of 2 × 10
4
so that comparisons could be made
with DNS. Time-averaged PIV was used to identify boundary layer behaviors that have a large
impact on the airfoil performance. Changes in the lift curve slope with 𝛼 were attributed to changes
in the effective airfoil shape, which consists of the actual airfoil as well as the slow, viscous,
recirculating region behind and/or above the airfoil, both of which affect the shape of the outer
streamlines around the airfoil. Dye-injection flow visualization tests showed that the separated
boundary layer remains laminar until the trailing edge at low 𝛼, and vortex roll-up moves upstream
at moderate 𝛼 until 𝛼
?Ba
, where roll-up reaches far enough upstream to allow for boundary layer
reattachment and LSB formation, resulting in a large and sudden increase in lift and decrease in
drag. Similar flow patterns were found in both PIV and flow visualization tests, but the 𝛼 at which
these patterns were seen was found to depend on at least model AR, experimental setup, and free-
stream disturbance environment. Analysis of dye-injection flow visualization images in the wake
led to the hypothesis that the movement of the shear layer roll-up location upstream of the trailing
edge leads to a change in the dominant instability mode responsible for wake vortex shedding.
Experimental and DNS lift and drag coefficients were shown to agree well when both sets
of data indicate that the airfoil is in the same flow state (i.e. low lift state due to boundary layer
separation without reattachment or high lift state due to boundary layer separation with
reattachment). Comparisons of experimental and DNS flow fields showed close qualitative and
quantitative agreement at 𝛼 = 4
o
, and a similar evolution of the LSB with increasing 𝛼 after 𝛼
?Ba
.
Based on these findings, it appears it would be appropriate to use DNS data during the development
of a closed loop flow control system.
Time-averaged force measurements were made for 2 × 10
4
< Re < 9 × 10
4
, and an increase
in Re was shown to decrease 𝛼
#$%
while increasing 𝑐
',)
near α = 0
o
for 2 × 10
4
< Re < 5 × 10
4
.
These changes in the lift curve with Re are believed to be due to changes in the boundary layer
separation location, and therefore the effective airfoil shape, with Re. Increasing Re to as high as
93
9 × 10
4
was shown to decrease 𝛼
?Ba
, but did not eliminate the existence of two lift and drag states
between 𝛼 = 0
o
and stall. The preservation of the qualitative behavior of the airfoil with increased
Re suggests that a flow control system developed using Re = 2 × 10
4
data may be effective, perhaps
with some minor modifications, in wind tunnel tests at higher free stream velocities, where
accurate surface pressure data can be collected and fed back into the controller.

6.3 Future Work

Now that comparisons with experiments have shown acceptable agreement and reasons for
discrepancies have been suggested, the high resolution DNS can be used with more confidence
along with future experiments to explore the boundary layer behavior in more detail. A better
understanding of the transition process for the boundary layer over airfoils will allow for the
development of more accurate models to predict transition. As the transition location can greatly
impact airfoil performance, this will lead to better performance predictions. The unsteady
properties of the LSB, such as the unstable frequencies in the separated boundary layer and their
spatial amplification rates, can be experimentally measured using hot-wire or pressure
measurements along the airfoil chord or estimated using linear stability theory and compared to
two- and three-dimensional DNS. It is important that the unstable frequencies from DNS (on which
the flow controller will be based) and experiment are similar, as these are the frequencies that will
be targeted by the control system. Modifications to test setup in experiments can be made in an
effort to determine with more certainty the exact factors that can affect 𝛼
?Ba
. Hot-wire
measurements can be made in the boundary layer and wake of the NACA 65(1)-412 at Re = 2 ×
10
4
in order to verify the wake vortex shedding frequency measurements in this work and further
investigate the interaction between the separated shear layer and shear layer vortices with the wake.
Force measurements along with experimental boundary layer measurements would allow for the
testing of different methods to approximate the effective airfoil shape, such as increasing airfoil
thickness by an amount equal to the displacement thickness, so that inviscid methods can be used
to predict airfoil performance at low Re. Finally, the high resolution DNS can be used to develop
a novel, closed loop flow control system, leveraging insights gained from the analysis of LCS
fields, that can then be tested in the Dryden Wind Tunnel.
94
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108
Appendix A: Blockage Effects in Dryden Wind Tunnel
The dimensions of all of the equipment in the wind tunnel during a PIV or force balance
test are given in tables B1 – B3. The approximate volume for the wings and the shroud (which has
an airfoil shape) are calculated as 0.7 × thickness × chord × span, as is suggested by Barlow et al.
(1999).

Table B1: Model dimensions
Wing Dimensions
NACA 0012 NACA 65(1)-412 (FB) NACA 65(1)-412 (PIV)
Chord [m] 0.075 0.055 0.075
Span [m] 0.480 0.710 0.225
Thickness [m] 0.009 0.007 0.009
Approx. Volume [m
3
] 2.3×10
-4
1.8×10
-4
1.8×10
-4

Max frontal Area [m
2
] 0.006 0.007 0.003

Table B2: Endplate dimensions
Endplate Dimensions
Length [m] 0.711
Width [m] 0.356
Thickness [m] 0.013
Volume [m
3
] (both) 0.007
Max Frontal Area [m
2
] (both) 0.009

Table B3: Shroud dimensions
Shroud Dimensions
Chord [m] 0.150
Span [m] 0.360
Thickness [m] 0.050
Approx. Volume [m
3
] 0.002
Max Frontal Area [m
2
] 0.018

The following calculation of blockage effects was adopted from Selig et al. (1995):

Solid body blockage: 𝜀
M}
=

¡/
= 0.004 (all models)
Where: K
1
= wind tunnel correction constant for solid blockage effects = 1 (thought to be
a conservative value)
V
m
= approximate volume of all objects inside tunnel (model, endplates, shroud)
A = area of the tunnel cross section = 1.56 m
2

109
Wake blockage: 𝜀
}
=

G¢
i£
𝑐
g
¤
= 0.002 (NACA 0012)
= 0.004 (NACA 65(1)-412 FB)
= 0.005 (NACA 65(1)-412, PIV)
Where: c = model chord
h
ts
= effective height of the test section ( 𝐴 = 1.25 m)
c
du
= maximum uncorrected drag coefficient (~0.16 for NACA 65(1)-412, ~0.08
for NACA 0012)

Buoyancy: According to Barlow et al. (1999), horizontal buoyancy is usually insignificant for
wings.

Streamline curvature:
∆¥
¦,£§
¥
¦
=𝜎 =
¨

H©

¢
i£
G
= 7 × 10
-4
(NACA 0012, NACA 65(1)-412 PIV),
= 4 × 10
-4
(NACA 65(1)-412 FB)
Where: Δc
l,sc
= change in lift coefficient due to streamline curvature
c
l
= lift coefficient
c = model chord
h
ts
= effective height of the test section ( 𝐴 = 1.25 m)

Total corrections:

¥
¦
¥
¦,¤
=
Tª
Tc«
£¬
c«
¬

= 0.986 (NACA 0012)
= 0.984 (NACA 65(1)-412 FB)
= 0.981 (NACA 65(1)-412 PIV)

¥

¥
,¤
=
T«
£¬
Tc«
£¬
c«
¬

= 0.982 (NACA 0012)
= 0.980 (NACA 65(1)-412 FB)
= 0.978 (NACA 65(1)-412 PIV)

Where: 𝐶
v
= corrected force coefficient
𝐶
v,|
= uncorrected coefficient.

Therefore, the maximum error due to blockage effects is always less than 2.5%. These
corrections were therefore not made to any of the data reported in this document.

110
Appendix B: Water Channel Equipment Drawings

Figure B1: Top endplate, positioned above wing. The endplate plug extended through the center
hole (see Figure B5).
111

Figure B2: Water channel wing. The hollow support rod (see Figure B6) fit into the spanwise
hole, and dye could be injected into the flow through the four leading edge holes. The endplate
plug (see Figure B5) fit over the top end of the wing.
112

Figure B3: 𝛼 - setting device, fixed bottom plate. The hollow support rod (see Figure B6) passed
through the center hole. The rotating top plate (see Figure B4) positioned on top of the fixed
bottom plate and attacked to the hollow support rod. Pins were inserted through the slots in the
rotating top plate and into a hole in the fixed bottom plate to set angle of attack.
113

Figure B4: 𝛼 - setting device, rotating top plate. 0.094 holes were replaced with slots in final
design. A set screw or pin was used to connect the rotating top plate to the hollow support rod
(see Figure B6). Angle of attack was set by inserting pins into through the slots and into the
holes in the fixed bottom plate (see Figure B3).
114

Figure B5: Endplate plug. A slot was machined into the bottom of the plug so that it slid over the
wing (0.5 inch) and fit snug. The top half of the plug extended into the hole in the top endplate
(see Figure B1). The plug was attached to the support rod with set screws.
115

Figure B6: Hollow support rod. The rod attached to the 𝛼 - setting device and the endplate plug
by tightening set screws onto the machined flats.

Abstract (if available)

Abstract In recent years, the reduction in the size and weight of electronics has allowed for the development of small scale, fixed wing flying devices that operate at Reynolds numbers (Re) below 5 × 10⁵. These vehicles, which include small scale UAVs and MAVs, are comparable in both size and speed to birds and model airplanes. At these “low” Re, smooth airfoil performance is generally poor (i.e. low lift, high drag) compared to that seen at the higher Re due to laminar boundary layer separation that often occurs, even at small angles of attack. There have been numerous experimental studies that have focused on the lift and drag generated by airfoils at low Re, but even carefully run tests on the same airfoil shape in different facilities have produced conflicting data sets. This will become an increasingly important issue as interest in low Re vehicles increases, and high quality airfoil performance data is needed. Experimental data is also needed to establish baseline agreements with computations, including three-dimensional direct numerical simulations (DNS) which have recently become available for airfoils at Re > 10⁴. The lack of agreement in low Re experimental data is primarily due to two factors: 1) the sensitivity of lift and drag to experimental conditions that are highly facility dependent, such as free stream turbulence level, surface finish, model mounting technique, and acoustic environment, and 2) the difficulties associated with measuring the small aerodynamic forces generated at low Re, especially drag, with acceptable uncertainties. The increased sensitivity to experimental conditions at low Re is due to the increased impact these conditions can have on the boundary layer over the airfoil. ❧ The boundary layer behaviors seen over airfoils at low Re have a significant impact on performance and can differ significantly from those seen at higher Re. Laminar boundary layer separation can lead to either a large, recirculating region behind the airfoil, or the formation of the location of boundary layer transition, and laminar separation bubble (LSB) that covers a significant portion of the airfoil surface. An LSB forms when laminar separation is quickly followed by a transition to a turbulent state, allowing for boundary layer reattachment to the surface in a time-averaged sense. The boundary layer separation location, the location of transition to turbulence, and whether or not the boundary layer reattaches to the surface after separation to form an LSB can change the effective shape of the airfoil, and cause the aerodynamic performance to differ significantly from the classical potential flow theory predictions in often unexpected ways. More high quality experimental data is needed to better understand the effects of these different boundary layer behaviors on airfoil performance. In addition, a better understanding of the transition process over airfoils at low Re will assist in the development of better models to predict the boundary layer behavior. ❧ In the current study, two airfoils shapes, one symmetric and one cambered, were investigated in order to gain a better understanding of airfoil behavior at low Re: the NACA 0012 (Re = 5 × 10⁴) and the NACA 65(1)-412 (2 × 10⁴ ≤ Re ≤ 9 × 10⁴). Well resolved lift and drag data were collected with a force balance, and explanations for behaviors that differ from those seen at high Re (e.g. changing lift slope before stall, negative lift at positive angles of attack, a sudden jump to a high lift/low drag state) were given based on time-averaged PIV flow fields. Dye-injection flow visualization images were then collected in a water channel for the NACA 65(1)-412 to investigate time-dependent boundary layer characteristics and wake vortex shedding frequencies. The insights gained from this study can help in the future design of low Re fliers and the development of flow control systems. The high quality lift and drag data can also be used as reference data for future low Re experimental or computational studies. ❧ Once the boundary layer behavior and its impact on performance is better understood, it can be manipulated to improve aerodynamic performance. Increasing performance is especially important at these low Re, where the maximum lift to drag ratios (L/D) for smooth airfoils (L/D) are known to be much lower than at Re > 10⁶. Previous studies have suggested that the flow is most sensitive to forcing near the boundary layer separation point, which can be approximated in unsteady flows by identifying the location at which an attracting Lagrangian coherent structure (LCS) approaches the airfoil surface. Therefore, a flow control technique that leverages insights from LCS fields is suggested. If a measurable signal signature of the separation location can be identified, this information can be fed back to a controller, so that the forcing location can be adjusted depending on the changing flow field to optimize performance (i.e. maximize L/D). Additional, perhaps unintuitive, forcing locations may be identified based on the locations of prominent LCS, as LCS are dynamically important structures that play a role in organizing the flow field, and a flow control technique that aims to manipulate the behavior of LCS to alter the flow field is currently under development by collaborators at the University of Minnesota. A closed loop flow control system would be able to respond to changes in the flow field in a way that the current open loop flow control techniques with fixed forcing locations cannot. ❧ Time-averaged force and flow field data for the NACA 65(1)-412 at Re = 2 × 10⁴ have been compared with direct numerical simulations provided by collaborators at San Diego State University, and the agreement has been found to be satisfactory. This clears the way for the development of reduced Navier-Stokes or data driven flow control models based on the high resolution computational data. The lift and drag curves for the NACA 65(1)-412 have been shown experimentally to remain qualitatively similar as Re is increased from 2 × 10⁴ to 9 × 10⁴, which suggests that flow control models developed using computations at Re = 2 × 10⁴ may be effective at a higher Re, where a model size/free stream velocity balance can be struck that allows for accurate time-resolved pressure measurements at the airfoil surface. A novel closed loop flow control system will be tested as part of a proposed continuation of this work.

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Asset Metadata

Creator Tank, Joseph David (author)

Core Title Aerodynamics at low Re: separation, reattachment, and control

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Aerospace Engineering

Publication Date 10/15/2018

Defense Date 08/24/2018

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag Aerodynamics,flow control,fluid mechanics,Lagrangian coherent structures,laminar separation bubble,LCS,low Reynolds number,OAI-PMH Harvest,particle image velocimetry,PIV

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Spedding, Geoffrey (committee chair), Bermejo-Moreno, Ivan (committee member), De Barros, Felipe (committee member), Luhar, Mitul (committee member), Uranga, Alejandra (committee member)

Creator Email joseph.tank18@gmail.com,jtank@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-89462

Unique identifier UC11675514

Identifier etd-TankJoseph-6824.pdf (filename),usctheses-c89-89462 (legacy record id)

Legacy Identifier etd-TankJoseph-6824.pdf

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Document Type Dissertation

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Rights Tank, Joseph David

Type texts

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