On one silent night. from a gust of wind came an earthquake.
Wind Shear, Gust,and Yaw-Induced Dynamic Stallon Wind ...
Transcript of Wind Shear, Gust,and Yaw-Induced Dynamic Stallon Wind ...
Wind Shear, Gust, and Yaw-Induced Dynamic
Stall on Wind-Turbine Blades
by
Benen Piers laBastide
A thesis submitted to the
Department of Mechanical & Materials Engineering
in conformity with the requirements for
the degree of Master of Applied Science
Queen’s University
Kingston, Ontario, Canada
May 2016
Copyright c© Benen Piers laBastide, 2016
Abstract
This study examined the effect of a spanwise angle of attack gradient on the growth
and stability of a dynamic stall vortex in a rotating system. It was found that a
spanwise angle of attack gradient induces a corresponding spanwise vorticity gradient,
which, in combination with spanwise flow, results in a redistribution of circulation
along the blade. Specifically, when modelling the angle of attack gradient experi-
enced by a wind turbine at the 30% span position during a gust event, the spanwise
vorticity gradient was aligned such that circulation was transported from areas of
high circulation to areas of low circulation, increasing the local dynamic stall vortex
growth rate, which corresponds to an increase in the lift coefficient, and a decrease
in the local vortex stability at this point. Reversing the relative alignment of the
spanwise vorticity gradient and spanwise flow results in circulation transport from
areas of low circulation generation to areas of high circulation generation, acting
to reduce local circulation and stabilise the vortex. This circulation redistribution
behaviour describes a mechanism by which the fluctuating loads on a wind turbine
are magnified, which is detrimental to turbine lifetime and performance. Therefore,
an understanding of this phenomenon has the potential to facilitate optimised wind
turbine design.
i
Acknowledgments
I would like to acknowledge the funding provided by Ontario Graduate Scholarships,
the Queen Elizabeth II scholarship, and NSERC, which financially supported this
study. Thank you to my supervisor, Dr. David Rival, for giving me this opportunity,
and providing guidance throughout the process. I would like to express my gratitude
for the support I received from Jaime Wong, who was instrumental in the completion
of this thesis. Finally, I would like to thank John Fernando, Giuseppe Rosi, and the
entire OTTER lab for the advice given, and knowledge shared over the last two years.
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Nomenclature
A area
AR blade aspect ratio
c chord
d shear layer thickness
f frequency
H hub height
k reduced frequency
m′(t) vorticity containing mass
r, z, θ turbine coordinates
r1, r2 bounds of experimental span
R turbine radius
t time
T period
U∞ freestream velocity
∆U axial velocity change
Ueff effective velocity
u(ξ, t) shear layer velocity
ur, uz, uθ vector components of velocity
x, y, z global coordinate system
α angle of attack
αang angular acceleration
αcen centripetal acceleration
αCor Coriolis acceleration
Γ circulation
γ2 vortex centre parameter
λ tip speed ratio
λr local speed ratio
ω vorticity
Ω angular velocity
ζ blade twist
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Contents
Abstract i
Acknowledgments ii
Nomenclature iii
Contents iv
List of Figures vi
Chapter 1: Introduction 1
1.1 Challenges in Wind Turbine Modelling and Design . . . . . . . . . . 11.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 Wind Turbine Frame of Reference . . . . . . . . . . . . . . . . 21.2.2 Structure of the Atmospheric Boundary Layer . . . . . . . . . 41.2.3 The Effect of Gusts on Angle of Attack . . . . . . . . . . . . . 101.2.4 Wind Turbine Operation in Transient Conditions . . . . . . . 131.2.5 Two-Dimensional Dynamic Stall . . . . . . . . . . . . . . . . . 141.2.6 Three-Dimensional Dynamic Stall . . . . . . . . . . . . . . . . 19
1.3 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Chapter 2: Methodology 25
2.1 Strategy of investigation . . . . . . . . . . . . . . . . . . . . . . . . . 252.2 Test Case Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2.1 Wind Turbine Reference . . . . . . . . . . . . . . . . . . . . . 262.2.2 Experimental Motions . . . . . . . . . . . . . . . . . . . . . . 28
2.3 Physical Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.3.1 Towing Tank and Traverse System . . . . . . . . . . . . . . . 302.3.2 Actuation Mechanism . . . . . . . . . . . . . . . . . . . . . . 312.3.3 Blade Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4 Particle Tracking Velocimetry . . . . . . . . . . . . . . . . . . . . . . 332.5 Treatment of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
iv
Chapter 3: Results and Discussion 37
3.1 Vortex Growth Flow Visualization . . . . . . . . . . . . . . . . . . . . 383.2 Integral Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.1 Spanwise Flow . . . . . . . . . . . . . . . . . . . . . . . . . . 403.2.2 Spanwise Vorticity Gradient . . . . . . . . . . . . . . . . . . . 423.2.3 Circulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.2.4 Circulation Profile . . . . . . . . . . . . . . . . . . . . . . . . 47
Chapter 4: Conclusions and Outlook 48
4.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.1.1 Relationship Between Spanwise Angle of Attack and Vorticity
Gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.1.2 Vorticity Transport and Circulation Redistribution . . . . . . 50
4.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
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List of Figures
1.1 A schematic of the wind turbine polar coordinate system where: z is
the rotational axis of the turbine, r is the radial axis that falls along
the span of the blade, and θ is the azimuthal coordinate of the plane of
rotation. The turbine rotates at an angular velocity of Ω around the
z axis, experiences a free stream velocity U∞ along the axial direction,
has a tip radius R, and has a hub height H above the ground. The
inboard point r1 and outboard point r2 bound the span of the blade
that will be modelled in the current study. Each spanwise position has
a chord length c and experiences an angle of attack α. . . . . . . . . . 4
1.2 An example wind shear profile due to vertical wind shear present in the
atmospheric boundary layer is shown relative to a wind turbine. The
blade experiences a change in axial velocity as a function of azimuthal
angle. The period of the change in the local blade velocity is equal to
the period of the turbine rotation, shown graphically on the right. . . 6
vi
1.3 Turbine yaw at an angle β, from the axis of the turbine on the horizon-
tal plane, results in the turbine blade experiencing a change in effective
velocity as a function of azimuthal position. Lower effective freestream
velocities will be experienced by the blade as it moves away from the
oncoming flow direction, depicted here as the top of rotation (A) than
when it moves in to the oncoming flow direction, depicted here as the
bottom of rotation (B). The period of the velocity change is equal to
the period of the turbine rotation. . . . . . . . . . . . . . . . . . . . . 7
1.4 Wind velocity power spectral density function collected at Brookhaven
National Laboratory, showing peaks for time frames on the order of
four days, semi-daily, and a few seconds. The high frequency fluctu-
ations, which the turbine can not adequately react to, are of interest
for this study and are encompassed by the dotted box. Adapted from
DeMarrais (1959). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5 Velocity triangles demonstrating the effective velocity and angle of at-
tack change experienced by two arbitrary spanwise positions during a
gust event. The inboard location r1 < r2 experiences a greater change
in effective angle of attack. . . . . . . . . . . . . . . . . . . . . . . . . 11
1.6 Spanwise angle of attack magnitude and gradient change experienced
by a turbine blade during a gust. The region investigated in this study
is highlighted in grey with corresponding boundaries r1 and r2 indicated. 12
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1.7 Stages of dynamic stall: (t = t0−) static stall angle is exceeded, flow
reversal takes place in boundary layer for airfoil profiles; (t = t0+)
separation occurs at the leading edge of the airfoil creating the dynamic
stall vortex; (t = t1) the dynamic stall vortex grows and convects over
the suction side of the profile; (t = t2) vortex reaches trailing edge and
the airfoil enters a fully separated regime similar to classical stall. . . 16
1.8 The integration of vorticity within a shear-layer segment of length l
and thickness d.From Wong and Rival (2015) . . . . . . . . . . . . . . 18
1.9 A section of a rotating turbine blade experiencing a gust event has
a spanwise variation in angle of attack in the presence of radial flow,
resulting in vorticity convection (ur∂ωr/∂r) towards the blade tip. . . 23
1.10 Predicted shift in the wind turbine blade circulation profile due to
spanwise transport of vorticity. The spanwise transport is a result of
a combination of the spanwise vorticity gradient and spanwise flow,
causing circulation to be transported from areas of high circulation
generation to areas of low circulation generation. ∆r represents the
expected increase in circulation for a spanwise location experiencing a
negative vorticity gradient. . . . . . . . . . . . . . . . . . . . . . . . . 24
2.1 Modeling wind turbine blade response in a gust event results in an angle
of attack magnitude and spanwise angle of attack gradient change as
a function of convective time for the test case motions. The grey areas
represent the two measurement domains during which the dynamic
stall vortex was observed in the experiments described in following
sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
viii
2.2 All test cases were conducted in a 15m long 1m × 1m cross section
towing tank. The model (II) was actuated using a robotic pitch flap
mechanism (I), which was towed from right to left along the upper
traverse. A 4 camera setup (III) was used to capture the motion of the
seeding particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3 The model blade was mounted to the computer-controlled pitch-flap
mechanism as shown. The blade is towed at a constant free-stream
velocity and is actuated in both pitch φ and flap ψ. The 14×14×1 cm3
4D-PTV measurement volume described below is highlighted in green. 31
2.4 The blade motion intersects two adjacent measurement fields of view
taken over consecutive runs. An example flow field is shown, with the
profile indicated for scale . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1 The dynamic stall vortex grows in size over the measurement period
as visualized for the rotational turbine case (right column) and the
reference case (left column) at three convective times t∗ = 0.25, 0.75,
and 0.9, coloured by magnitude of spanwise vorticity (ωr). At t∗ = 0.25
the dynamic stall vortex initiates for both the turbine rotational (B)
and reference (A) case. The rotational turbine case exhibits a larger
size at all convective times. The vortex remains attached to the profile
over the entire measurement domain. . . . . . . . . . . . . . . . . . . 39
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3.2 The spatially-averaged spanwise flow within the dynamic stall vortex
was similar between the turbine and flapping cases. In both rotational
cases the flow increases as a function of convective time and was on
the order of the rotational velocity (Ωr), in close agreement with Max-
worthy (2007). The reference case exhibited negligible spanwise flow.
The error bars denote the standard deviation of the 10 runs. . . . . . 42
3.3 The spatially averaged spanwise vorticity gradient for both the turbine
and flapping case increases in magnitude as a function of the convective
time, due to the constantly increasing spanwise angle of attack gradient
through the test motion. The absolute value of the vorticity gradient
is shown here to facilitate a comparison between cases. The spanwise
flow in the turbine case is negative. The error bars denote the standard
deviation of the 10 runs. . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4 The growth rate of circulation in the turbine case was found to be
greater than that of the reference case. In contrast, the growth rate
of circulation in the flapping case was lower than that of the reference
case. The difference in circulation growth is a result of the relative
alignment of spanwise flow and the spanwise vorticity gradient between
the cases. The error bars denote the standard deviation of the 10 runs. 46
x
4.1 Postulated global spanwise redistribution of circulation based on rela-
tive circulation observed in the turbine and flapping cases. In positive
spanwise vorticity gradients, the circulation of the dynamic stall vortex
was found to decrease, whereas, in negative spanwise vorticity gradi-
ents, the circulation of the dynamic stall vortex was found to increase.
the net effect of this is the transport of circulation in the outboard
direction, which is aligned with the direction of spanwise flow . . . . 52
xi
1
Chapter 1
Introduction
1.1 Challenges in Wind Turbine Modelling and Design
Modelling wind turbine performance, and subsequently determining design specifica-
tions for turbine blades, is most often performed using blade element models, such as
those described by Glauert (1935). A limitation inherent in these models, as discussed
by Burton et al. (2001), is that they assume little to no interaction between the blade
elements, such that each element is treated as an independent two-dimensional airfoil
section. In reality, a turbine blade is a three-dimensional system with fluid and mo-
mentum transported along its span. This momentum transport is often modelled by
correction factors, such as those of Ronsten (1992), and Du and Selig (1998), which
use an empirical correction to account for this three-dimensional behaviour in steady
operation. However, due to the empirical, as opposed to predictive, nature of these
methods, such correction factors can not account for the highly unsteady detached
flows one expects in gusty conditions, such as the formation of a dynamic stall vortex.
This results in large errors from these models when predicting aerodynamic loading
on turbine blades, as discussed by Tangler and Kocurek (2005). Additionally, both
1.2. BACKGROUND 2
Tangler (2004) and Wachter et al. (2011) find that such unsteady detached flows
are responsible for the fatigue cycles with the highest peak-to-peak loading for both
blade and rotor shaft bending, reducing turbine lifetime. Therefore, an understanding
of the flow physics which dictate these forces would be beneficial in designing more
reliable wind turbines.
1.2 Background
In order to provide a greater understanding of the flow over wind turbine blades in un-
steady environments, the current thesis attempts to isolate and describe the physical
mechanism that dictates the spanwise redistribution of circulation along the blade.
Therefore, in order to introduce the above problem, the first chapter will describe: 1.
the reference frame of the wind turbine system and an outline of the nomenclature
used in this study; 2. the transient behaviour observed in the atmospheric boundary
layer, giving rise to dynamic flow over the turbine blades; 3. previous work modelling
dynamic stall vortex evolution, emphasising rotating systems; and 4. the specific
three-dimensional considerations observed in wind turbines, as opposed to other ro-
tating systems. Based on this established context, the problem formulation will be
developed at the end of the chapter.
1.2.1 Wind Turbine Frame of Reference
To facilitate the examination of the effect of transient conditions on turbine operation,
a turbine frame of reference is defined in polar coordinates. This frame of reference is
shown graphically in Figure 1.1, where z is the rotational axis of the turbine, r is the
radial axis that falls along the span of the blade, and θ is the azimuthal coordinate of
1.2. BACKGROUND 3
the plane of rotation. The turbine blades of length R rotate at an angular velocity of
Ω about a hub of height H , for a given free stream velocity U∞. The tip speed ratio
λ = ΩRU∞
describes blade tip velocity relative to the axial flow velocity. A twist angle ζ
is built into large scale wind turbine blades to account for the spanwise distribution
in angle of attack in steady operation under a free stream velocity U∞ of the form:
ζ(r) = arctan(U∞/Ωr). (1.1)
The inboard point r1, and outboard point r2, bound the span of the blade that will be
modelled in the following sections. Each spanwise position has a chord length c, and
experiences an angle of attack α, which is a function of the local blade velocity Ωr,
the free stream velocity U∞, and the twist angle of the blade ζ . To conform with wind
turbine literature, α is used to symbolise the effective angle of attack experienced by
the profile. In airfoil theory this value is often denoted as αeff . The operational tip
Reynolds number of a large scale wind turbine is on the order of Re = 107, which
equates to a Mach number of Ma ≈ 0.25.
1.2. BACKGROUND 4
R
ΩU∞
H
r1
r2
c
U∞
Ωr
α
θz
r
rz
θ
Figure 1.1: A schematic of the wind turbine polar coordinate system where: z isthe rotational axis of the turbine, r is the radial axis that falls alongthe span of the blade, and θ is the azimuthal coordinate of the plane ofrotation. The turbine rotates at an angular velocity of Ω around the zaxis, experiences a free stream velocity U∞ along the axial direction, hasa tip radius R, and has a hub height H above the ground. The inboardpoint r1 and outboard point r2 bound the span of the blade that will bemodelled in the current study. Each spanwise position has a chord lengthc and experiences an angle of attack α.
1.2.2 Structure of the Atmospheric Boundary Layer
As described by Blocken et al. (2007), wind turbines operate within the lower log-
layer of the atmospheric boundary layer (ABL). Because this region of the boundary
layer is fully turbulent, the velocity experienced by the turbine will vary in both time
1.2. BACKGROUND 5
and space. In this analysis, the unsteadiness present in the ABL will be decomposed
into three components: mean wind shear in the vertical direction, turbine yaw, and
wind gusts. As described by Burton et al. (2001), the relative impact that these
components have on the flow experienced by the turbine is dependent on the thermal
regime of the ABL, which is classified into three categories: stable, unstable, and
neutral. The cause of these conditions and their effect on turbine operation will be
discussed below.
Vertical Wind Shear
Wind shear is the local spatial variation in the wind velocity. In wind turbine op-
eration, the dominant component of wind shear is due to the mean boundary layer
profile, and thus we will focus on the vertical direction. Subsequently, the oncoming
flow velocity experienced by the turbine is a function of height, U∞(h), the profile
of which is shown in relation to a turbine in Figure 1.2. Due to the rotation of the
turbine in operation, a blade section will experience a change in vertical position as
a function of azimuthal angle. As the freestream velocity is a function of height, and
the vertical location of a blade element is a function of azimuthal angle, the local
velocity of the blade section becomes a function of the azimuthal angle, with a period
equal to the period of rotation for the turbine.
High levels of vertical wind shear occur predominately in stable ABL conditions,
where rising air is expanded and cooled adiabatically such that it becomes colder
than its surroundings and vertical motion is suppressed. As a result, large scale
convection cells are inhibited and turbulence is dominated by frictional interaction
with the ground, leading to high levels of vertical wind shear. Stable conditions
1.2. BACKGROUND 6
generally occur in cool night conditions when surface heating is minimal.
Figure 1.2: An example wind shear profile due to vertical wind shear present in theatmospheric boundary layer is shown relative to a wind turbine. Theblade experiences a change in axial velocity as a function of azimuthalangle. The period of the change in the local blade velocity is equal to theperiod of the turbine rotation, shown graphically on the right.
Turbine Yaw
Turbine yaw occurs when the oncoming flow direction deviates in angle from the axis
of the turbine, as shown in Figure 1.3. Under these conditions, the turbine blade
experiences a lower velocity during the half-cycle of rotation when it is travelling
away from the wind, where the component of freestream velocity projected onto the
rotor plane acts to detract from the local velocity experienced by the blade, depicted
in profile A in Figure 1.3. A higher velocity will be experienced during the half-
cycle of rotation when the blade is travelling into the wind, where the component of
freestream velocity projected onto the rotor plane acts to augment the local velocity
experienced by the blade, depicted in profile B in Figure 1.3. Similar to wind shear,
turbine yaw introduces a periodic fluctuation in the velocity experienced by a blade,
1.2. BACKGROUND 7
with a period equal to that of the wind turbine rotation, as outlined by Bechly et al.
(2002).
Yaw occurs predominately under unstable ABL conditions, where air heated at
the earth’s surface rises and cools adiabatically such that it does not reach thermal
equilibrium with its surroundings, and therefore continues to rise. Under these con-
ditions large convection cells are generated, resulting in a thick boundary layer with
large-scale vortices that influence the flow direction experienced by the turbine.
U∞
Bottom of Rotation (B)
Top of Rotation (A)
β
Ω
ΩrΩr
Ueff
U∞
Ωr
Ueff
U∞
x
zy
Figure 1.3: Turbine yaw at an angle β, from the axis of the turbine on the horizon-tal plane, results in the turbine blade experiencing a change in effectivevelocity as a function of azimuthal position. Lower effective freestreamvelocities will be experienced by the blade as it moves away from the on-coming flow direction, depicted here as the top of rotation (A) than whenit moves in to the oncoming flow direction, depicted here as the bottomof rotation (B). The period of the velocity change is equal to the periodof the turbine rotation.
1.2. BACKGROUND 8
Wind Gusts
Wind gusts are most pronounced in a neutral ABL, where air cools adiabatically as it
rises such that it remains in thermal equilibrium with its surroundings. This condition
generally occurs in cases of strong winds, where turbulent structures generated by
interaction with the ground results in a highly mixed boundary layer. As described
by De Visscher (2014), these turbulent structures, such as vortices, act to temporally
vary the velocity observed at a point in space. In turbulence theory, it is customary
to break this point velocity into the average speed u and the wind speed fluctuation
u′ following:
u = u+ u′, (1.2)
referred to as the Reynolds decomposition. Wind turbines are designed primarily
based on the average velocity u, however, it is the change in velocity u′ that causes
the dynamic stall conditions responsible for the high peak-to-peak loading cycles, and
is therefore of interest in the current study.
As the turbulent structures in the atmospheric boundary layer consist of many
varying length scales, gusts occur over a broad range of frequencies. A typical distri-
bution of energy is given in figure 1.4 as a function of frequency, based on data col-
lected at Brookhaven National Laboratory by DeMarrais (1959). Three pronounced
peaks are present: Low frequency fluctuations on the order weeks make up the first
peak, representing synoptic-scale weather and climate; the second peak is comprised
of diurnal fluctuations following the growth and contraction of the mixing layer with
day and night; and lastly, of particular interest to the current study, the third peak
indicates fluctuations that occur on the order of seconds, representing individual tur-
bulent structures within the flow. Wind turbines have the ability to adapt to the
1.2. BACKGROUND 9
low and medium fluctuations through mechanisms such as yaw and pitch control.
However, as shown by Muljadi (2001), the turbine is not able to adequately react
to the high frequency fluctuations on the order of seconds. The turbulent structures
incident on wind turbines can be considered in terms of their length scale relative to
the chord of the turbine blade. Turbulent structures with a length scale much smaller
than the chord of the blade average out over the profile, and therefore have little
effect on the blade loading, see Sytsma and Ukeiley (2010). Alternately, structures
with length scales much larger than the chord act to change the mean wind speed,
and therefore act as quasi steady loading. As a result, following Wong et al. (2013),
it is structures with a length scale on the order of the blade chord that have a large
impact on turbine loading, and will therefore be considered in this study. As a result
of these high frequency fluctuations, rapid changes in effective angle of attack act-
ing on the blade are introduced, resulting in the formation of dynamic stall vortices.
The growth and separation of the dynamic stall vortex is of principle interest to the
current work and will be described in the following section.
1.2. BACKGROUND 10
Figure 1.4: Wind velocity power spectral density function collected at BrookhavenNational Laboratory, showing peaks for time frames on the order of fourdays, semi-daily, and a few seconds. The high frequency fluctuations,which the turbine can not adequately react to, are of interest for thisstudy and are encompassed by the dotted box. Adapted from DeMarrais(1959).
1.2.3 The Effect of Gusts on Angle of Attack
As a result of the transient conditions described above, the turbine will experience
rapid changes in angle of attack, which greatly influence the aerodynamic forces
experienced by the blade. Under steady operating conditions, the turbine blade is
designed to maintain a constant circulation profile over the span of the blade as
described by Hansen et al. (2011). However, in gust conditions, the change in angle
of attack across the blade is highly non-uniform, following the relationship:
∆α(r) = arctan (U∞ +∆U/Ωr)− α0, (1.3)
1.2. BACKGROUND 11
where ∆α(r) is the change in angle of attack as a function of radius r, ∆U is the change
in the free stream velocity, and α0 is the initial angle of attack. This relationship
is shown in Figure 1.5 for two spanwise positions r1 and r2 under a change in axial
velocity ∆U . At the inboard spanwsie position r1 the change in axial velocity ∆U has
a larger impact on the effective velocity experienced by the blade-section as the change
in free-stream velocity ∆U is large in comparison to the velocity due to rotation Ωr1.
Subsequently, inboard spanwise position r1 experiences a greater change in angle of
attack then spanwise position r2. In turn, spanwise position r2 experiences a smaller
change in the magnitude of the angle of attack.
Ωr1 Ωr2
U∞U∞
ΔUΔU
Δα2Δα1
r1 r2 > r1
Figure 1.5: Velocity triangles demonstrating the effective velocity and angle of attackchange experienced by two arbitrary spanwise positions during a gustevent. The inboard location r1 < r2 experiences a greater change ineffective angle of attack.
When the angle of attack is calculated at all spanwise positions for a rotating bade
experiencing a gust event, it is found that a spanwise gradient in angle of attack is
generated, as shown in Figure 1.6. Both the magnitude change and spanwise gradient
of angle of attack are largest in the near-root region, and decrease as a function of
radius towards the tip of the blade.
1.2. BACKGROUND 12
0 0.2 0.4 0.6 0.8 1
r/R
0 0.2 0.4 0.6 0.8 1
r/R
r2
r1 ∆α
d
dr∆α
Figure 1.6: Spanwise angle of attack magnitude and gradient change experienced bya turbine blade during a gust. The region investigated in this study ishighlighted in grey with corresponding boundaries r1 and r2 indicated.
Local Speed Ratio
To generalize the development of the angle of attack gradient across rotating systems,
we can define a dimensionless quantity called the local speed ratio (LSR):
λr =Ωr
U∞
, (1.4)
where λr is the local speed ratio, Ω is the rotational velocity, r is the local spanwise
location, and U∞ is the free stream velocity. The local speed ratio λr is useful as it
describes the relative sensitivity to a change in free-stream velocity along the span
of a blade. The local-speed ratio is equal to the tip-speed ratio at the blade tip.
Utilizing this parameter, a change in angle of attack magnitude ∆α during an axial
change in velocity can be given as a function of the corresponding local speed ratios:
∆α = arctan
(
λr0 − λr1λr0λr1 + 1
)
, (1.5)
1.2. BACKGROUND 13
where λr0 is the initial LSR and λr1 is the LSR at a later time within the gust.
In conjunction with the change in angle of attack magnitude given in Equation 1.5,
the change in the spanwise gradient of angle of attack along the blade can also be
expressed in terms of the local speed ratio:
d∆α
dr=c
r
(
λr1λ2r0 + 1
−λr0
λ2r0 + 1
)
, (1.6)
where d∆αdr
is the spanwise gradient in angle of attack. These relationships will be
employed to define the gust profile used in this study.
1.2.4 Wind Turbine Operation in Transient Conditions
As introduced previously, the angle of attack gradient generated on a turbine blade
during a gust results in large errors when predicting aerodynamic performance using
two-dimensional models. For example, Wood (1991) observed that three-dimensional
effects lead to stall delay in which, increased lift coefficients are observed past the
static stall angle. This result was attributed to a reduction in the adverse pressure
gradient on the upper surface of the blade from solidity effects, where solidity is the
ratio of the blade chord to swept area, which result in delayed boundary layer separa-
tion. Schreck and Robinson (2002) also found that rotating conditions dramatically
amplified lift forces acting on a turbine blade using data from a full scale horizontal
axis turbine in delayed stall conditions. For an NREL S809 airfoil, Tangler (2004)
found that in a rotating frame lift coefficients increase by over a factor of two at
radial positions located near the one-third span position of the blade when compared
to a purely translating case at the same angle of attack. Tangler (2004) also observed
that outboard positions of the turbine blade experience two-dimensional static stall,
1.2. BACKGROUND 14
characterised by two-dimensional separated flow, while at the inboard locations flow
is three dimensional, and remains attached.
The mechanism that causes this increase in lift coefficients is poorly understood,
and is an active area of research over a wide range of Reynolds numbers; for example,
see Carr and Chandrasekhara (1996), and Tangler (2004). Computational techniques
such as zonal methods described by Ekaterinaris et al. (1994) can be used to predict
aerodynamic forces on the turbine blade in transient conditions; however, these meth-
ods have high computational cost, which limits their use in design studies that must
explore a large parameter space. Furthermore, a range of empirical models by groups
such as Snel et al. (1993), Corrigan (1994), Chaviaropoulos and Hansen (2000), and
Raj (2000) have been developed to account for three-dimensional rotational effects on
two-dimensional airfoil data. However, these models are not only inconsistent with
each other, but disagree with experimental findings such as those of Breton and Coton
(2008). Therefore, the following sections outline the phenomenological understanding
of the dynamic stall vortex with which we can describe the difference between two-
and three-dimensional cases.
1.2.5 Two-Dimensional Dynamic Stall
Rapid changes in effective incidence, such as those from gusts, wind shear and turbine
yaw, cause stall behaviour that is fundamentally different than typical static stall,
outlined by Leishman (2006). In static stall, as described by Cebeci et al. (2005),
the onset of flow separation can begin near either the leading or trailing edges of the
profile. In the leading edge case, a separation bubble is formed that bursts once a
critical incidence angle is exceeded. Alternatively, in the trailing edge case, separation
1.2. BACKGROUND 15
initiates at the trailing edge and subsequently migrates towards the leading edge of
the profile. The evolution of static stall is strongly dependant on the Reynolds number
of the flow. In comparison, dynamic stall has been shown by McCroskey (1982) to be
Reynolds number independent, and can be broken into four main phases as shown in
Figure 1.7. Initially, as the effective angle of attack of the profile increases past the
static stall angle flow reversal is observed in the boundary layer of an airfoil, denoted
as stage A in Figure 1.7. Subsequently, flow separation occurs at the leading edge, as
opposed to the trailing edge as observed in static stall case, initiating the formation
of stall vortex denoted as stage B in Figure 1.7. The stall vortex grows in size until
it detaches and convects downstream passing over the chord, denoted as stage C in
Figure 1.7. This detachment process is described in greater detail below. Finally,
after the vortex reaches the trailing edge, the airfoil progresses into full separation,
which is correlated with a sudden loss of lift and a large increase in the drag force,
subsequently exhibiting behaviour similar to quasi-steady stall denoted as stage D in
Figure 1.7.
1.2. BACKGROUND 16
Figure 1.7: Stages of dynamic stall: (t = t0−) static stall angle is exceeded, flow rever-sal takes place in boundary layer for airfoile profiles; (t = t0+) separationoccurs at the leading edge of the airfoil creating the dynamic stall vortex;(t = t1) the dynamic stall vortex grows and convects over the suction sideof the profile; (t = t2) vortex reaches trailing edge and the airfoil enters afully separated regime similar to classical stall.
The lift produced by the dynamic stall vortex can be modelled using the methodof von Karman and Sears (1938) who developed a relationship based on the rate ofmomentum change:
L = −ρd
dt
∑
Γixi, (1.7)
where L is the rate of momentum change, Γi is a closed region of vorticity, andxi is the line of action of the respective vorticity regions. This method provides astraightforward means of calculating lift on a blade profile if the vortex circulationstrength and relative location is known. In a general sense, this equation shows thatif location is held constant, an increase in circulation within the dynamic stall vortexcorresponds to an increase in lift on the blade profile.
Kaden (1931) describes the vortex growth in terms of the transport of vorticity
from a wing-tip shear layer into the vortex core. Building upon this, Sattari et al.
(2012) developed and validated a model to describe vortex growth in a start up vortex
1.2. BACKGROUND 17
generated from a two dimensional shear layer. Subsequently, this model was adapted
by Wong and Rival (2015) to describe dynamic stall on plate, finding that in an
incompressible fluid the mass flux into the vortex is described by conservation of
mass:
m′(t) = ρ
∫ t0
0
∫ d
0
u(ξ, t) dξdt, (1.8)
where m′(t) is the vorticity-containing mass per unit span, u(ξ, t) is the velocity
profile of the shear layer and ξ is location within the shear-layer thickness d. For
incompressible conditions m′(t) is proportional to the vortex area. Approximating
the vortex area as a semi-circle attached to the suction side of the profile, as shown
in Figure 1.8, results in a radius R(t) of:
R(t) =
√
2
π
m′(t)
ρ. (1.9)
The circulation can then be calculated using the line integral of the velocity around
the vortex core:
Γ(t) =
∮
~u · d~l = πu(d, t)R(t), (1.10)
where u(d, t) is the velocity around the vortex, which is assumed to be zero at the
wall. In order to find the circulation the profile of the outer velocity u(d, t) is required.
This velocity is the summation of three velocities:
u(d, t) ∝ U∞
(
1 +R2(t)
(R(t) + d)2
)
sin (α) +Γ(t)
2πr+ ~ue sin (α), (1.11)
1.2. BACKGROUND 18
where the terms on the right hand side are, in order: the velocity due to acceleration
around a cylinder, the velocity induced by the vortex, and the chord normal compo-
nent of the effective velocity. From this result it can be seen that the outer velocity,
and subsequently the circulating flux into the vortex is a function of the angle of
attack of the profile, with larger angles of attack resulting in a higher vortex feeding
rate.
αeff
u(d,t)
d
0
uξl
Integration path
ueff
Figure 1.8: The integration of vorticity within a shear-layer segment of length l andthickness d. Taken from Wong and Rival (2015)
At some point after this growth stage, the delayed stall vortex will detach for
all two-dimensional cases. Rival et al. (2014) found that a dynamic stall vortex
remains attached to the suction side of a profile up until the stagnation streamline
bounding the leading-edge vortex reaches the trailing edge, which once breached
indicates the detachment of the vortex itself. Therefore, detachment occurs when the
vortex diameter approaches a size on the order of the chord of the profile. Thus, in
summary, after initiation, the dynamic stall vortex is fed from circulation generated in
the leading edge shear layer up until it reaches a critical size and detaches. Therefore,
large effective angles of attack result in fast growing vortices that quickly become
unstable and detach from the profile.
1.2. BACKGROUND 19
1.2.6 Three-Dimensional Dynamic Stall
Under the rotating conditions found in wind turbine operation, the process of dynamic
stall becomes more complex, with three-dimensional effects becoming prevalent. Due
to the spanwise angle of attack gradients outlined above, the initiation of stall and
vortex evolution becomes a function of the spanwise position on the blade. Inboard
locations, as described previously, experience higher effective angle of attack changes
during a gust event, causing dynamic stall to initiate earlier, as described by Shipley
et al. (1995). Following stall initiation, higher effective angles of attack correspond
to a higher rate of circulation generation, which corresponds to a higher rate of
circulation growth within the dynamic stall vortex. Subsequently, neglecting spanwise
interactions, the dynamic stall vortex at inboard locations would be expected to reach
the limiting one-chord length-scale and detach sooner than outboard positions. This
effect is reversed for other classes of rotating airfoils, such as in flapping wing flight
where outboard positions experience a greater angle of attack change, corresponding
to decreased stability at these points. However, as observed in both rotating and
flapping systems by Ellington et al. (1996), Birch and Dickinson (2001), Bomphrey
et al. (2005), Lentink and Dickinson (2009b), and Harbig et al. (2013), a persistent
dynamic stall vortex is often generated on rotating and flapping profiles, which lasts
for much larger time-scales in such three-dimensional cases than the two-dimensional
case. Lentink and Dickinson (2009a) proposed that rotational accelerations act to
stabilise the vortex, and identified three critical rotational accelerations: the angular
acceleration (aang), centripetal acceleration (acen), and Coriolis acceleration (aCor):
aang =ˆΩ× r, (1.12)
1.2. BACKGROUND 20
acen = Ω× (Ω× r), (1.13)
aCor = 2Ω× ˆuloc, (1.14)
where uloc is the local velocity in the rotating frame. Note than in quasi-steady rota-
tion cases the angular acceleration goes to zero as Ω = 0. The centripetal acceleration
acen induces a pressure gradient that drives spanwise flow. The local velocity uloc con-
tains both the velocity component from the free stream velocity and the velocity of
the fluid induced by the flapping motion of the wing. In steady wind turbine oper-
ation, the freestream velocity lies along the axis of rotation, and therefore does not
contribute to the Coriolis acceleration, which becomes exclusively a function of the
flow induced by the blade rotation:
aCor = 2Ω× uloc = 2Ω× (Ω× r). (1.15)
Lentink et al. (2009) considered the impact of these accelerations in terms of a lin-
ear momentum balance described by the Navier-Stokes equation, and found that the
Coriolis effect acts to mediate LEV stability. The current work uses an angular mo-
mentum balance, described by the vorticity transport equation, to examine a similar
situation. Within this framework, the Coriolis effect is manifested as an induced
spanwise flow, as described by Maxworthy (2007). Ellington et al. (1996) found span-
wise flow on the order of flap velocity in a conical dynamic stall vortex increasing
in size towards the blade tip in a flapping motion. This spanwise flow contributes
to the redistribution of vorticity along the span of the blade following the vorticity
transport equation:
1.2. BACKGROUND 21
Dω
Dt= (ω · ∇)~u+ ν∇2~ω, (1.16)
where the terms from left to right describe the change in vorticity of the fluid due to
unsteadiness and convection, vortex tilting and stretching, and the viscous diffusion of
vorticity, respectively. For a gust event acting on a rotating blade, viscous diffusion
can be neglected under the assumption that the timescales of diffusion are much
larger than the timescales of vortex growth itself, following from Rival et al. (2014).
Therefore, the spanwise component of the vorticity transport equation in the rotating
frame takes the form:
∂ωr
∂t+ ur
∂ωr
∂r+uθr
∂ωr
∂θ+ uz
∂ωr
∂z= ωr
∂ur∂r
+ωθ
r
∂ur∂θ
+ ωz
∂ur∂z
+ 2Ω∂ur∂z
, (1.17)
where the terms from left to right are the constituent terms of the vector equation
above representing the rate of change of vorticity due to unsteadiness, the convection
of vorticity in the r−, θ−, and z− directions, vortex tilting and vortex stretching,
and Coriolis effects, respectively. A schematic of the hypothesised vorticity balance
is shown in Figure 1.9, where circulation generated in the shear layer is balanced by
spanwise vorticity convection. Following Wong and Rival (2015), it is assumed that
the vortex is aligned approximately parallel with the span of the blade, and that
therefore ωr is the dominant component of vorticity present in the flow. Following
Wojcik and Buchholz (2014) and Wong and Rival (2015), the rate of spanwise cir-
culation redistribution is the integral of the vorticity-transport equation across the
vortex-core area:
1.2. BACKGROUND 22
∂Γ
∂t= −
∫
ur∂ωr
∂rdA, (1.18)
where the vortex tilting term vanishes as it occurs out of the plane of integration and
therefore does not have a large effect when computing circulation, and the stretching
terms vanishes, as stretching acts to increase centre line vorticity but does not trans-
port vorticity along the blade span. Additionally, for a vortex tube attached near
the leading edge of the blade profile, gradients in the spanwise direction will be much
larger than the gradients in the axial direction, resulting in the Coriolis term having
an negligible direct impact on spanwise vorticity transport. Using mean values across
the vortex area, 1.18 reduces to:
∂Γ
∂t= −ur
∂ωr
∂rA, (1.19)
where Γ is the circulation of the vortex and dA is a differential area within the vortex.
The only term that remains is the spanwise convection of vorticity (ur∂ωr
∂r). Therefore,
as constituent elements of vorticity convection, spanwise flow and spanwise vorticity
gradients drive the spanwise redistribution of circulation.
1.2. BACKGROUND 23
ωr
ur
ur(∂ωr/∂r)
Γ1
Γ2
U∞ueff2
ΔU
Ωr1
ueff1
ΔUgust ueff1
gust ueff2
U∞
Ωr2
rz
θ
Figure 1.9: A section of a rotating turbine blade experiencing a gust event has a span-wise variation in angle of attack in the presence of radial flow, resultingin vorticity convection (ur∂ωr/∂r) towards the blade tip.
Based on the sign of the vorticity convection term, blade locations with negative
spanwise vorticity gradient will experience an increase in local circulation due to
vorticity transport, whereas, blade locations with a positive vorticity gradient will
experience a decrease in local circulation due to vorticity transport. When this effect is
considered over the span of the blade in combination with the angle of attack gradient
developed on a turbine blade during a gust event, we find that the circulation profile
is shifted in the outboard direction relative to that predicted using two dimensional
models as shown in Figure 1.10. This outboard shift in circulation on a rotating
system is consistent with that found by Lentink et al. (2009), who considered the
rotational accelerations in a linear momentum context.
1.3. PROBLEM FORMULATION 24
ΔΓ(r)
Γ distribution without spanwise interaction
Γ distribution with spanwise interaction
r1 r2
Figure 1.10: Predicted shift in the wind turbine blade circulation profile due to span-wise transport of vorticity. The spanwise transport is a result of a com-bination of the spanwise vorticity gradient and spanwise flow, causingcirculation to be transported from areas of high circulation generation toareas of low circulation generation. ∆r represents the expected increasein circulation for a spanwise location experiencing a negative vorticitygradient.
1.3 Problem Formulation
As examined above, in transient flow conditions wind turbines develop a gradient
in angle of attack along the blade span, from which a spanwise vorticity gradient is
formed. It is postulated that, in combination with the spanwise flow induced by ro-
tational accelerations, this spanwise vorticity gradient acts to redistribute circulation
along the span of the blade. This redistribution would result in a greater magnitude
of local circulation at the 30% span of a turbine blade, increasing the lift experienced
at this location while reducing the stability of the local dynamic stall vortex.
25
Chapter 2
Methodology
2.1 Strategy of investigation
In chapter 1, a hypothesis was developed that states in gust conditions, the 30% span
of a turbine blade will experience a magnification in transient lift forces as a result of
circulation redistribution driven by the combination of spanwise flow and a spanwise
vorticity gradient. In order to test this hypothesis, the spanwise angle of attack
gradient and spanwise flow found on a wind turbine during a gust were recreated
in a laboratory environment using a model blade mounted to a robotic pitch-flap
actuator that was moved through a towing tank on a traverse system. Given this
reproduction at lab scales, the flow field developed on the suction side of the profile
was observed using optical measurement techniques. By using the observed flow field
to quantify the spanwise vorticity gradient, spanwise flow, and resulting change in
local circulation relative to a two-dimensional reference case, the effect of the spanwise
angle of attack gradient on dynamic stall vortex size and stability, which corresponds
the the magnitude and frequency of transient lift forces, can be determined. The
details of this process are outlined below.
2.2. TEST CASE KINEMATICS 26
2.2 Test Case Kinematics
The kinematics of the pitching-flapping motion were determined by replicating the
angle of attack and spanwise gradient of angle of attack experienced by a large scale
wind turbine. The specific reference turbine is outlined below, after which, the ex-
perimental motions will be discussed.
2.2.1 Wind Turbine Reference
The turbine chosen as a reference was the well documented 5MW NREL reference tur-
bine outlined by Jonkman et al. (2009). The operational parameters of the reference
turbine are as follows:
• Tip speed ratio (quasi-steady) of λ = 7
• Rated wind velocity of U∞ = 11m/s
• Rated angular velocity of Ω = 1.2rad/s
• Rotor diameter of R = 126m
• Chord at 30% span of c = 4.3m
• Local aspect ratio at 30% span of AR = 4
A sinusoidal change in free-stream velocity was used to model the change in axial
velocity experienced by the turbine during a gust event, similar to the work of Wong
et al. (2013). The velocity change in terms of the local speed ratio was of the form:
λrt = λr0 + (λr0 − λr1)sin(2U∞k
c), (2.1)
2.2. TEST CASE KINEMATICS 27
where λrt is the local speed ratio at a chosen point within the gust, and λr0 and λr1
are the initial and final local speed ratios, respectively, and k is the reduced frequency
of the gust, which measures the unsteadiness of the system. The reduced frequency
is related to the frequency through the relationship:
k =πfc
U∞
, (2.2)
where U∞ is the initial free stream velocity, f is the physical frequency of the gust,
and c is the local chord length. A reduced frequency of k = 0.35 was used for all
test cases as it represents the gust conditions experienced by a wind turbine. All test
cases were realized using a constant chord NACA0012 airfoil, and the initial angle of
attack was set at α = 10.
Based on the the reference turbine definitions and the sinusoidal gust profile out-
lined above, the angle of attack history was determined across the whole span of a
turbine blade. This spanwise resolution was required in order to determine the time-
history of the spanwise angle of attack gradient. The peak change in the angle of
attack occurs around the r ≈ 0.1R span location, which corresponds to the transition
point between a cylindrical cross section and an airfoil profile for the reference tur-
bine blade outlined by Jonkman et al. (2009). Using the angle of attack gradient as a
function of radius and time, parameters where chosen under which three-dimensional
stall has been observed on wind turbine blades by Tangler (2004). As a result, the
parameter space was based around the 30% span position of the blade in order to
maximize spanwise interactions while minimizing hub effects, which have been shown
by Burton et al. (2001) to be negligible at this radius. The resultant magnitude and
2.2. TEST CASE KINEMATICS 28
spanwise gradients in angle of attack experienced over the gust for the 30% span posi-
tion is shown in Figure 2.1. These parameters will be realised using the test motions
described in the following section.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
10
15
20
View 1 View 2
t∗
∆α
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.05
0.1
0.15
0.2
∂α
∂r
∆α∂α
∂r
Figure 2.1: Modeling wind turbine blade response in a gust event results in an angleof attack magnitude and spanwise angle of attack gradient change as afunction of convective time for the test case motions. The grey areasrepresent the two measurement domains during which the dynamic stallvortex was observed in the experiments described in following sections.
2.2.2 Experimental Motions
The angle of attack magnitude and spanwise gradient change found on the reference
turbine during a gust was used to inform the selection of the experimental motions. As
a result, three test cases were developed. The first test case, hereonin referred to as the
turbine case, was set up to exactly mimic the temporal angle of attack change, change
in the spanwise gradient of angle of attack, and spanwise flow direction experienced
at the 30% span of the reference 5MW turbine. This case was developed in order to
2.3. PHYSICAL SETUP 29
visualize and quantify the effect of spanwise redistribution of circulation on a wind
turbine blade.
The second test case, hereonin referred to as the flapping case, was set up such
that the temporal angle of attack change, and change in the spanwise gradient of angle
of attack, was equal in magnitude but opposite in orientation to the reference turbine
while maintaining the same spanwise flow direction. The orientation of the spanwise
vorticity gradient relative to the spanwise flow direction in this case is the same as
that found in flapping systems such as birds and insects. This case was developed in
order to inform discussion on the global behaviour of the spanwise circulation profile
The third test case, hereonin referred to as the reference case, was set up to be a
quasi two-dimensional case with no spanwise gradient in angle of attack, while having
a magnitude change in angle of attack equal to the other test cases. This case was
developed as a baseline so that the integral properties observed in the two other cases
would have a comparison to a case with no spanwise interaction. These test cases
were realised using the physical apparatus described below.
2.3 Physical Setup
All tests in the current study were conducted in the OTTER lab towing tank located
at Queen’s University. A computer-controlled pitching and flapping mechanism was
used to manipulate a NACA0012 blade within the towing tank to recreate the desired
motions. The details of these facilities are outlined below.
2.3. PHYSICAL SETUP 30
2.3.1 Towing Tank and Traverse System
All tests were conducted in the 1m × 1m cross section, optical towing tank. The
tank is 15m long and uses water as the working fluid. The side and bottom walls of
the tank are glass to allow for five-sided optical access. A traverse system, running
the length of the towing tank, on which the actuator system was mounted, is fixed
above the tank. The entirety of the tank and traverse system is shown in Figure 2.2.
An in-house LabView program was used to control the traverse, which was set to
maintain a constant velocity of U∞ = 0.33m/s, which was maintained for ten chord
lengths prior to the beginning of the motion. The pitch and flap actuator mechanism
described below was mounted underneath this traverse system.
Model Towing Direction
U∞
I
II
III
Figure 2.2: All test cases were conducted in a 15m long 1m × 1m cross section towingtank. The model (II) was actuated using a robotic pitch flap mechanism(I), which was towed from right to left along the upper traverse. A 4camera setup (III) was used to capture the motion of the seeding particles.
2.3. PHYSICAL SETUP 31
2.3.2 Actuation Mechanism
The test cases outlined above were realised using a computer-controlled pitching and
flapping mechanism. The set-up of the actuator system is shown in Figure 2.3. The
pitch-flap mechanism consisted of two linear actuators, which controlled the pitching
and flapping axes independently, attached to moment arms rotating around z and
θ axes. The actuators had a displacement of 20cm, which resulted in a range of
motion of ±25 in flap and ±45 in pitch. The actuator system was designed to
accept an arbitrary timeseries of blade pitch and flap angles, within the maximum
actuator velocity and displacement range. The pitching and flapping mechanism was
subsequently synchronized to the traverse described in Section 2.3.1.
Figure 2.3: The model blade was mounted to the computer-controlled pitch-flapmechanism as shown. The blade is towed at a constant free-stream ve-locity and is actuated in both pitch φ and flap ψ. The 14×14×1 cm3
4D-PTV measurement volume described below is highlighted in green.
In order to achieve the spanwise gradient in angle of attack found on a wind
turbine blade, the model wing was actuated in flap through an angle of 26 over
the period of motion. An actuation of 24 in pitch was required in the turbine case
2.3. PHYSICAL SETUP 32
in order to match the angle of attack history found on a wind turbine blade while
inducing the correctly oriented spanwise flow. The flapping case required a smaller
actuation in pitch of 8 as the effective incidences from pitch and flap were additive,
as opposed to subtractive, as in the turbine case.
2.3.3 Blade Geometry
Mounted to the pitching flapping mechanism was a NACA0012 profile blade. The
blade had a span of 1m, spanning the towing tank vertically from the upper to the
lower surfaces of the tank. The blade had a chord of c=30cm. The 30cm chord of
the model is one order of magnitude smaller than that of a wind turbine blade. In
combination with the towing velocity, the blade size chosen resulted in a Reynolds
number based on chord of Rec = 105. This Reynolds number is large enough to
provide an analogue for the effects of dynamic stall on a wind turbine blade, as
Eastman et al. (1939) has shown that pre-stall lift curve for a NACA0012 profile
remain generally constant above a Reynolds number of Rec = 5×104, and McCroskey
(1982) has shown that dynamic stall is Reynolds number independent. The blade was
pitched about the one-third chord location, as this was the thickest part of the airfoil
profile, and thus facilitated the attachment of the sting. Roughness elements in the
form of zig-zag strips were applied to the 20% chord location in order to trip the
boundary layer in an otherwise transitional flow, mimicking large scale wind turbine
operation. This tripping mechanism ensured that the boundary layer was initially
attached prior to the onset of the gust motion, and influenced the counter-clockwise
circulatory flow present near the surface of the profile in dynamic stall conditions.
2.4. PARTICLE TRACKING VELOCIMETRY 33
2.4 Particle Tracking Velocimetry
Four-dimensional particle tracking velocimetry (4D-PTV), as described by Schanz
et al. (2016), was used to capture the flow field on the suction side of the blade.
A 14cm × 14cm × 1cm measurement volume was oriented with its major axis lying
parallel to the tank bottom and was located at the midspan location of the test model.
In order to observe the vortex evolution over a longer time period, two adjacent fields
of view were employed in order to provide approximately one convective time of data,
as shown in Figure 2.4. The measurement volume was illuminated using a Photonics
Industries DM40 Nd:YLF pulsed laser operating at 1500Hz. Conditioning optics
where used to expand the laser beam into a 1cm thick sheet and direct the laser in
the desired orientation. Four Photron SA4 high-speed cameras with a resolution of
1024 x 1024 pixels were mounted under the tank, observing the measurement volume
through the tank bottom. The laser acted as the frequency source to synchronise the
cameras at the desired frequency of 1500Hz. A three dimensional calibration target
was used to align the cameras.
The tank was seeded with 55µm particles that, through Mie scattering, resulted
in a particle size on the order of 6 pixels being observed by the camera. The quantity
of seeded particles resulted in a seeding density of 0.04 particles per pixel. Initial
processing of the particle images was conducted using DaVis and proprietary software
developed at the German Aerospace Centre by Schanz et al. (2016). Using this
software an average of 4000 tracks were obtained for each the 1500 recorded frames.
The Lagrangian velocities and accelerations were determined by differentiation of the
particle tracks in time.
2.5. TREATMENT OF DATA 34
U∞
View 1
View 2
Figure 2.4: The blade motion intersects two adjacent measurement fields of viewtaken over consecutive runs. An example flow field is shown, with theprofile indicated for scale
2.5 Treatment of Data
Flow visualizations and integral properties were obtained using the particle positions
and velocities output from the 4D-PTV software. The vorticity field in the measure-
ment volume was determined by using a second order central differencing method to
compute the curl of the velocity vectors, which were interpolated on an Eulerian grid
with grid spacing on the order of the inter-particle distance. Subsequently the clock-
wise vorticity above a thresholding value was plotted for each timestep and coloured
based on the vorticity magnitude. The centre of the dynamic stall vortex was iden-
tified and tracked over the entire convective time using the γ2 criterion outlined by
Graftieaux et al. (2001):
γ2 =1
N
∑
S
sin (θM), (2.3)
2.5. TREATMENT OF DATA 35
where N is the number of points inside area S, and θM represents the angle between the
radius vector, which is the vector between the interrogation point and point M, and
the velocity vector, which is the velocity vector of point M. γ2 is a dimensionless scalar
whose value approaches a magnitude of one if a point is surrounded by concentric
circular streamlines centred upon that point, and whose sign varies between clockwise
and counter-clockwise motion. Ten runs were conducted for each case. Integral
properties were computed and phase averaged across the ten runs in order to improve
the signal to noise ratio. A single value for spanwise flow was computed at each time-
step by taking the mean value of those particles within the vortex core, as defined by
a vorticity threshold:
ur =1
p
p∑
i=1
uri, (2.4)
where ur is the computed spanwise flow, uri is the spanwise velocity of particle i,
and p is the number of particles within the defined vortex area. The spanwsie flow
was then normalised by the effective velocity ueff experienced at the blade section. A
single value for spanwise vorticity gradient was computed at each time-step by taking
the mean value of the spanwise vorticity gradient interpolated onto an Eulerian grid
within the vortex core, as defined by a vorticity threshold:
∂ωr
∂r=
1
p
∑
i=1
[∂ωr
∂r
]
i, (2.5)
where ∂ωr
∂ris the computed spanwise vorticity gradient,
[
∂ωr
∂r
]
iis the spanwise vorticity
gradient at point i, and p is the number of points i within the defined vortex area.
The spanwise vorticity gradient was then normalised by the square of the chord over
2.5. TREATMENT OF DATA 36
the effective velocity of the blade c2
ueff
. Circulation was calculated by using trapezoidal
rule integration of the spanwise vorticity field for each plane of of Eulerian data, and
the mean value was taken.
A Savitzky-Golay filter was applied to all data sets to increase the signal to noise
ratio without greatly distorting the signal, as described by Sophocles (1996). The
moving polynomial fit filter works by fitting low order polynomials to successive
subsets of the data using the linear least squares method. A length of 50 frames,
corresponding to a convective time of t∗ = 1
30, was used for the data smoothing. All
integral values in the results section are presented in terms of convective time:
t∗ =U∞t
c, (2.6)
Which was observed for periods of t∗=0.18 to 0.52 and 0.6 to 0.88 in the experiment.
37
Chapter 3
Results and Discussion
In this chapter, vortex behaviour in a rotating frame will be examined through a
comparison of the two-dimensional reference case and the two three-dimensional ro-
tating cases that were detailed in Chapter 2. For all cases, a dynamic stall vortex
was observed over the duration of the measured convective times. Fields of view 1
and 2 captured the dynamic stall vortex for convective times ranging from t∗ =0.18
to 0.52, and 0.6 to 0.88, respectively. For all test cases the vortex remained attached
for the entire observed period. However, the vortex in the turbine case was found
to be both physically larger and have a higher circulation than the reference case
vortex for all convective times, whereas the flapping case had a physically smaller
and lower circulation dynamic stall vortex. The effect of an angle of attack gradient
on the growth and stability of the dynamic stall vortex was explored through flow
visualizations and three main integral parameters, consisting of the spanwise flow,
the spanwise vorticity gradient, and the circulation.
3.1. VORTEX GROWTH FLOW VISUALIZATION 38
3.1 Vortex Growth Flow Visualization
The physical size of the dynamic stall vortex in the rotational turbine case is larger
than the two-dimensional reference case over the period of the observed motion, as
shown with spanwise vorticity projected on a single plane in Figure 3.1. The left
column is the reference case and the right column is the turbine rotational case. Near
the start of the motion (t∗ = 0.25) the dynamic stall vortex is in the early stages of
formation near the leading edge of the blade as shown in Frame A and B of Figure 3.1,
respectively. Subsequently, the dynamic stall vortex grows as the motion progresses
for both the two-dimensional reference case, and the rotational turbine case, driven
by circulation generated in the leading edge shear layer shown stretching from the
leading edge to the dynamic stall vortex in Frames C-F of Figure 3.1. The dynamic
stall vortex has a larger diameter at each time-step for the turbine rotational case,
indicating a less stable dynamic stall vortex case as outlined in chapter 1. In order to
test the vorticity transport hypotheses developed in Chapter 1, an integral property
analysis will be conducted in the following section.
3.1. VORTEX GROWTH FLOW VISUALIZATION 39
0
0.25
0.5
0.25
0.75
y/c
0.2 0.40x/c
0
0.25
0.5
0.25
0.75
y/c
0.2 0.40x/c
0
0.25
0.5
0.25
0.75
y/c
0.2 0.40x/c
0
0.25
0.5
0.25
0.75
y/c
0.2 0.40x/c
0
0.25
0.5
0.25
0.75
y/c
0.2 0.40x/c
0
0.25
0.5
0.25
0.75
y/c
0.2 0.40x/c
(A) (B)
(C) (D)
(F)(E)
Figure 3.1: The dynamic stall vortex grows in size over the measurement period asvisualized for the rotational turbine case (right column) and the refer-ence case (left column) at three convective times t∗ = 0.25, 0.75, and0.9, coloured by magnitude of spanwise vorticity (ωr). At t∗ = 0.25 thedynamic stall vortex initiates for both the turbine rotational (B) and ref-erence (A) case. The rotational turbine case exhibits a larger size at allconvective times. The vortex remains attached to the profile over theentire measurement domain.
3.2. INTEGRAL PROPERTIES 40
3.2 Integral Properties
Integral properties of the dynamic stall vortex were quantified in order to compare
the vortex evolution in each of the three cases. In this way, the precise mechanism
by which the three cases are distinguished can be elucidated. Specifically, spanwise
flow, spanwise vorticity gradients, and the resultant modification in circulation are
discussed below. All integral values plotted below were computed using the ensemble
average of 10 independent runs for each test case. The standard deviation between
the runs was calculated and denoted on Figures 3.2 - 3.4 as vertical bars plotted for
every 20th frame.
3.2.1 Spanwise Flow
Under dynamic stall conditions, the fluid in the separated region, primarily the dy-
namic stall vortex, is trapped on the suction side of the wing, resulting in the mean
chordwise velocity being small relative to the free-stream in the reference frame of
the blade, as described by Burton et al. (2001). As a result, the dominant velocity of
the entrained fluid is the rotational velocity of the blade, accelerating the fluid in the
spanwise direction via a pressure gradient generated from rotational accelerations.
This acceleration generates spanwise flow velocities on the order of the local blade
speed Ωr in rotation, which agrees with the results of Ellington et al. (1996). The
specifics of the spanwise flow observed in each case is discussed below.
Rotational Turbine Case
The spanwise flow ur observed in the turbine rotational case increased with convec-
tive time for the entire measurement period, as shown in Figure 3.2. The effective
3.2. INTEGRAL PROPERTIES 41
velocity was used to normalize the spanwise flow in order to account for the rotational
contribution to the effective velocity experienced in the turbine case. The spanwise
velocity increased with convective time for the measurement period relative to the ef-
fective velocity as a result of the rotational velocity constituting a larger proportion of
the overall velocity across the motion. The observed spanwise flow velocity was near
unity with the local rotational velocity, Ωr, at the measured spanwise position, which
is consistent with the model of Maxworthy (2007) based on centripetal acceleration
and the results observed by Wachter et al. (2011). The direction of spanwise flow is
in the direction of decreasing angle of attack for the turbine rotational case, which
mirrors that of a wind turbine experiencing a gust event. In comparison, the spanwise
flow found in the reference case was consistent with a small positive bias indicating
nearly two-dimensional flow, with the offset potentially being cased by asymmetric
boundary conditions.
Rotational Flapping Case
Similar to the turbine rotational case, the flapping case exhibited increasing spanwise
flow ur within the dynamic stall vortex over the the entire measurement period as
shown in Figure 3.2. The spanwise flow was in the same direction as the turbine
rotational case, moving from inboard to outboard span locations, due to the pressure
gradient induced by rotational accelerations. However, this was in the direction of
increasing angle of attack, opposite to that of the turbine rotating case. The spanwise
velocity fell within the standard deviation of the turbine case, which indicates that the
spanwise flow is not coupled of the angle of attack gradient and is instead a function
of the rotational velocity Ω of the blade.
3.2. INTEGRAL PROPERTIES 42
t∗
ur/U
eff
View 1 View 2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.2
0.4
0.6
0.8
1
Turbine Case
Flapping case
2D Reference Case
Figure 3.2: The spatially-averaged spanwise flow within the dynamic stall vortex wassimilar between the turbine and flapping cases. In both rotational casesthe flow increases as a function of convective time and was on the order ofthe rotational velocity (Ωr), in close agreement with Maxworthy (2007).The reference case exhibited negligible spanwise flow. The error barsdenote the standard deviation of the 10 runs plotted every 20 frames.
3.2.2 Spanwise Vorticity Gradient
For both rotational cases, a spanwise vorticity gradient was observed over the mea-
surement period. This gradient was generated due to the proportionality between
angle of attack and circulation generation, as discussed in Chapter 1. The specific
behaviour of the spanwise flow for each case is discussed below.
Rotational Turbine Case
For the turbine case, the spanwise vorticity gradient within the dynamic stall vortex
was negative, decreasing towards the tip, becoming increasingly negative as a function
3.2. INTEGRAL PROPERTIES 43
of the convective time, as shown in Figure 3.3. This is likely due to the angle of
attack gradient along the span of the blade generated during a gust event, which
results in an increased circulation generation at inboard spanwise locations. Similar
to the spanwise flow, the spanwise vorticity gradient in the two-dimensional case had
a small positive bias over the measured period.
Flapping Rotational Case
Due to the difference in the angle of attack gradient between the turbine and flapping
cases, the spanwise vorticity gradient developed on the flapping case was positive,
with vorticity increasing towards the tip. This positive gradient in spanwise vorticity
was observed over the entire period of the measurement, and increased as a function
of convective time, as shown in Figure 3.3. The magnitude of the spanwise vorticity
gradient fell within one standard deviation between the two rotational cases. For both
cases the spanwise gradients in vorticity and angle of attack were aligned, which agrees
with the predicted proportionality between angle of attack and vorticity generation
presented in Chapter 1.
3.2. INTEGRAL PROPERTIES 44
t∗
∣ ∣ ∣
∂ω
r
∂r
c2
Uef
f
∣ ∣ ∣
View 1 View 2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
10
15
Turbine Case
Flapping case
2D Reference Case
Figure 3.3: The spatially averaged spanwise vorticity gradient for the both the turbineand flapping case increases in magnitude as a function of the convectivetime, due to the constantly increasing spanwise angle of attack gradientthrough the test motion. The absolute value of the vorticity gradient isshown here to facilitate a comparison between cases. The spanwise flow inthe turbine case is negative. The error bars denote the standard deviationof the 10 runs plotted every 20 frames.
3.2.3 Circulation
The circulation of the dynamic stall vortex within the measurement volume is a
function of the circulation generated in the leading edge shear layer and the circulation
transported from adjacent spanwise positions. The reference case was designed with
an identical angle of attack history to the rotational cases such that the contribution
from transported circulation could be isolated. Transport of circulation is expected
to follow Equation 1.18 , which can be inferred from the relationship between the
three cases.
3.2. INTEGRAL PROPERTIES 45
Turbine Case
In the turbine rotational case, the circulation observed within the measurement vol-
ume was greater than that observed for the reference case over the entire measured
period of convective time as shown in Figure 3.4. This indicates that vorticity trans-
port due to the combination of spanwise flow and a spanwise vorticity gradient is
acting to redistribute circulation from areas of high circulation generation on the
blade to areas of low circulation generation. The relative orientation of the spanwise
flow and spanwise vorticity gradient dictates the direction of this effect. The higher
levels of circulation growth indicate that locally, the dynamic stall vortex is less stable
in the turbine rotational case, and will reach the critical size described by Rival et al.
(2014) sooner than the reference case.
3.2. INTEGRAL PROPERTIES 46
t∗
Γ/U
effc
View 1 View 2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Turbine Case
Flapping case
2D Reference Case
Figure 3.4: The growth rate of circulation in the turbine case was found to be greaterthan that of the reference case. In contrast, The growth rate of circulationin flapping case was lower than that of the reverence case. The differencein circulation growth is a result of the relative alignment of spanwise flowand the spanwise vorticity gradient between the cases. The error barsdenote the standard deviation of the 10 runs plotted every 20 frames.
Flapping Rotational Case
The observed circulation of the flapping case was lower than the two-dimensional
reference case over the entire measurement period, as shown in Figure 3.4. The
decrease in circulation is a function of the relative alignment between the spanwise
flow and spanwise vorticity gradient generated on the blade. The vorticity gradient
in the flapping case was parallel with the spanwise flow, which based on equation 1.18
resulted in circulation being transported from areas of low generation to areas of high
generation.
3.2. INTEGRAL PROPERTIES 47
3.2.4 Circulation Profile
Based on the results from the turbine and flapping cases, it can be observed that
in the case of spanwise flow from the root to the tip, a spanwise location with a
negative spanwise vorticity gradient, as in the rotational case, experiences an increase
in the magnitude of circulation. This is in contrast to a spanwise location with
a positive spanwise vorticity gradient, as in the flapping case, which experiences a
decrease in the magnitude of circulation. The cumulative effect of this circulation
redistribution can be speculated to be a a bulk shift in the outboard direction for
the global blade spanwise circulation profile. The redistributed circulation profile fits
with the increased lift at the 30% span observed by Tangler (2004) and Shipley et al.
(1995).
48
Chapter 4
Conclusions and Outlook
4.1 Conclusions
In this study, the effect of an angle of attack gradient on dynamic stall vortex growth
and stability in a rotating system has been investigated. Three cases were considered:
1. The turbine case was actuated such that the angle of attack magnitude and
spanwise gradient generated on the test model was equivalent to that found at
the 30% span of a wind turbine blade experiencing a transient gust event.
2. The flapping case was actuated such that the spanwise angle of attack gradient
was equal in magnitude, and opposite in direction, relative to the spanwise flow
velocity found at the 30% span of a wind turbine blade experiencing a transient
gust event.
3. The quasi two-dimensional reference case was actuated in pure pitch such that it
had an identical angle of attack history to the rotational cases over the observed
convective time.
4.1. CONCLUSIONS 49
The Reynolds number based on the free stream velocity Re = 105 and reduced fre-
quency k = 0.35 were held constant for all cases. Two major conclusions have been
drawn. First, it has been shown that inducing an angle of attack gradient along
the span of the blade results in a corresponding spanwise vorticity gradient. Second,
it has been shown that, in combination with a spanwise flow velocity induced from
rotational accelerations, the spanwise vorticity gradient results in a redistribution of
circulation along the span of the blade which has an impact on the dynamic loading
of turbines in gust condition.
4.1.1 Relationship Between Spanwise Angle of Attack and Vorticity Gra-
dients
The predicted proportionality between the angle of attack gradient and the vorticity
gradient based on increased vorticity generation in the leading edge shear layer was
observed in the turbine and flapping cases. In the turbine case, where the magnitude
of the angle of attack change was inversely proportional to radial distance, a negative
vorticity gradient was observed within the dynamic stall vortex. Whereas, in the
flapping case, the direction of the angle of attack gradient was reversed and a posi-
tive vorticity gradient was observed. No significant spanwise vorticity gradient was
observed in the reference case, demonstrating that during dynamic stall, vorticity is
generated at a higher rate at spanwise positions experiencing a larger angle of attack
resulting in a gradient along the span of the blade.
4.1. CONCLUSIONS 50
4.1.2 Vorticity Transport and Circulation Redistribution
Under rotation, spanwise flow is induced within the dynamic stall vortex due the
spanwise pressure gradient generated from rotational accelerations. The redistribu-
tion of circulation through vorticity transport observed was driven by a combination
of this spanwise flow and the spanwise vorticity gradient described above. The be-
haviour of this circulation transport is described by the spanwise convection term
ur∂ωr
∂rof the vorticity transport equation. The Coriolis term of the vorticity trans-
port equation does not effect the transport of angular momentum directly. Rather,
as described by Lentink et al. (2009), the Coriolis effect is manifested by inducing
a spanwise flow. The above presents an equivalent description of this phenomenon,
where the circulation-transporting effect of this spanwise flow is described through
the convection of angular momentum.
In the turbine case, the spanwise vorticity gradient was anti-parallel to the span-
wise flow, resulting in transport of vorticity from areas of high circulation generation,
to areas of low circulation generation, which is manifested as an increase in circulation
observed within the dynamic stall vortex compared to the reference case. Based on
the stability criteria developed by Rival et al. (2014), the increase in vortex growth
rate corresponds to a locally less stable vortex. Conversely, in the flapping rotational
case, the spanwise vorticity gradient was parallel with the spanwise flow, resulting in
transport of vorticity from areas of low circulation generation to areas of high cir-
culation generation. This effect is manifested as a decrease in circulation compared
to the reference case observed in the measurement volume, indicating increased lo-
cal stability. The decreased vortex stability and increased vortex circulation in the
4.2. OUTLOOK 51
turbine case describes a situation where transient aerodynamic loads increase in fre-
quency and magnitude at the 30% span location of a wind turbine in gust conditions.
These loads reduce the lifetime of the wind turbine. Therefore, mitigating the highly
transient loads through modifications in either spanwise flow or spanwise vorticity
gradient could potentially be an important area of design for increased turbine life.
4.2 Outlook
The current work examined the three-dimensional factors that influence the dynamic
stall vortex by modelling the conditions experienced on a specific section of the blade
span. Based on the resulting behaviour of the vortex under these conditions a general
argument for the modification of the spanwise circulation profile experienced by a
wind turbine blade in a gust event was put forward. Building on this argument,
consider the difference in circulation between the turbine and flapping cases. In
the turbine case, there is an increase in circulation due to the spanwise flow and
spanwise vorticity gradient being anti-parallel, which corresponds to the outboard
span positions of the turbine blade. In the flapping case, there is a decrease in
circulation due to the spanwise flow and spanwise vorticity gradient being parallel,
which corresponds to the inboard span positions of the turbine blade. Globally,
this results in the spanwise redistribution of circulation on a turbine blade shown
in Figure 4.1, which indicates that the direction of global circulation transport is
exclusively dependent on, and aligned with, the spanwise flow direction. In a wind
turbine context, this would result in higher torque loads and bending moments on
the blades being generated than those predicted using two-dimensional models, as
the higher lift forces associated with the increased circulation occur at greater radial
4.2. OUTLOOK 52
positions. A future study in this topic may consider conducting a complete mapping
of the circulation profile at each spanwise position of the blade. Using this mapping,
the exact functional impact of spanwise vorticity transport on the performance of
the blade could be quantified and compared to the circulation profile predicted using
current modelling techniques. Subsequently, flow control techniques, such as shaped
baffles, could be implemented in order to promote delayed stall vortex stability by
increasing spanwise circulation transport with a corresponding increase in spanwise
flow, or decrease peak load values by decreasing spanwise circulation transport with
a corresponding decrease in spanwise flow.
Figure 4.1: Postulated global spanwise redistribution of circulation based on relativecirculation observed in the turbine and flapping cases. In positive span-wise vorticity gradients, the circulation of the dynamic stall vortex wasfound to decrease, whereas, in negative spanwise vorticity gradients, thecirculation of the dynamic stall vortex was found to increase. the net ef-fect of this is the transport of circulation in the outboard direction, whichis aligned with the direction of spanwise flow.
Another potential area for further exploration would be to conduct three-dimensional
particle tracking velocimetry on a continuously rotating blade or complete turbine
model, which would facilitate the examination of the influence of tip and hub effects
4.2. OUTLOOK 53
on the evolution of the dynamic stall vortex. Using a complete turbine model would
also allow torque and power to be monitored over the gust event, allowing the re-
lationship between the spanwise dependent circulation profile on the blade and the
power output of the turbine to be directly observed.
BIBLIOGRAPHY 54
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