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.

ii

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

iii

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

v

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

vii

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

ix

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)


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


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.


2.3.1 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.


2.3.2 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


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)


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


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


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.


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


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.


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.


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.


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.


3.2.4 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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